Talk to the Kirksville Chapter of Sigma Xi that describes research on describing the vascular structure of networks of HUVEC cells. I also talk a little bit about Truman's mathematical biology program.
This paper proposes a new fuzzy similarity measure called Fuzzy Monotonic Inclusion (FMI) to measure similarity between images for image retrieval systems. The FMI approach segments images into regions, extracts features for each region, and maps the features into a fuzzy similarity model based on fuzzy inclusion. Experimental results on the Label Me image dataset show the FMI approach achieves higher precision than other methods like Unified Feature Matching and Fuzzy Histogram in identifying images by semantic class.
International Refereed Journal of Engineering and Science (IRJES)irjes
This document provides a survey of pattern recognition techniques using fuzzy clustering approaches for image segmentation. It discusses how fuzzy logic and soft computing techniques can be applied to edge detection and image segmentation problems. Specifically, it describes fuzzy clustering algorithms like fuzzy c-means clustering and hierarchical clustering that have been used for image segmentation. It also discusses other related topics like fuzzy logic in pattern recognition and image processing, and different methods for evaluating image segmentation techniques.
Comparative analysis and evaluation of image imprinting algorithmsAlexander Decker
This document compares and evaluates two different types of image inpainting algorithms: Marcelo Bertalmio's PDE-based algorithm and Zhaolin Lu et al's exemplar-based algorithm. Both algorithms are tested on images with variable occlusion sizes. The PDE-based algorithm is better at preserving linear structures for small regions but cannot reconnect structures or restore texture in large regions. The exemplar-based algorithm can find proper textures to fill large regions while preserving linear structures. Quantitative evaluation using PSNR shows that the exemplar-based algorithm achieves lower MSE values, especially for larger occlusion sizes. Therefore, the exemplar-based algorithm produces better results overall, particularly for filling in large missing regions of an image.
11.comparative analysis and evaluation of image imprinting algorithmsAlexander Decker
This document compares and evaluates two image inpainting algorithms: Marcelo Bertalmio's PDE-based algorithm and Zhaolin Lu et al's exemplar-based algorithm. Through experiments on images with different sized occluded regions, it finds that the PDE-based algorithm cannot reconnect structures or restore textures in large regions, while the exemplar-based algorithm can find patches to fill regions while preserving structures. Quantitative evaluation using PSNR shows the exemplar-based algorithm achieves lower MSE (error) for occlusion sizes from 10 to 40 pixels. The document provides examples comparing output of the two algorithms and discusses parameters needed for each.
The document proposes a novel Spatial Fuzzy C-Means (PET-SFCM) clustering algorithm to segment PET scan images of patients with neurodegenerative disorders like Alzheimer's disease. The algorithm incorporates spatial neighborhood information into the traditional Fuzzy C-Means algorithm. It was tested on real patient data sets and showed satisfactory results compared to conventional FCM and K-Means clustering algorithms. The PET-SFCM algorithm provides an effective way to segment PET images and analyze brain changes related to neurological conditions.
Object recognition is the challenging problem in the real world application. Object recognition can be achieved through the shape matching. Shape matching is preceded by i) detecting the edges of the objects from the images. ii) Finding the correspondence between the shapes. iii) Measuring the dissimilarity between the shapes using the correspondence. iv) Classifying the object into classes by using this dissimilarity measures. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts. The one to one correspondence is achieved through the cost based bipartite graph matching. The cost matrix is reduced through Hungarian algorithm. The dissimilarity between the two shapes is computed using Canberra distance. The nearest neighbor classifier is used to classify the objects with the matching error. The results are obtained using the MATLAB for MINIST hand written digits.
This document contains questions from a student about digital photogrammetry. It discusses various image matching techniques including intensity-based matching using cross-correlation and least squares matching, and feature-based matching using points, edges, and blobs. It also discusses relational matching and compares area-based and feature-based matching. Typical problems for image matching are described like lack of texture, straight features, repetitive patterns, and occlusions. Epipolar geometry and its advantages for image matching are explained, noting that it defines geometric constraints between images from different camera positions.
This paper proposes a new fuzzy similarity measure called Fuzzy Monotonic Inclusion (FMI) to measure similarity between images for image retrieval systems. The FMI approach segments images into regions, extracts features for each region, and maps the features into a fuzzy similarity model based on fuzzy inclusion. Experimental results on the Label Me image dataset show the FMI approach achieves higher precision than other methods like Unified Feature Matching and Fuzzy Histogram in identifying images by semantic class.
International Refereed Journal of Engineering and Science (IRJES)irjes
This document provides a survey of pattern recognition techniques using fuzzy clustering approaches for image segmentation. It discusses how fuzzy logic and soft computing techniques can be applied to edge detection and image segmentation problems. Specifically, it describes fuzzy clustering algorithms like fuzzy c-means clustering and hierarchical clustering that have been used for image segmentation. It also discusses other related topics like fuzzy logic in pattern recognition and image processing, and different methods for evaluating image segmentation techniques.
Comparative analysis and evaluation of image imprinting algorithmsAlexander Decker
This document compares and evaluates two different types of image inpainting algorithms: Marcelo Bertalmio's PDE-based algorithm and Zhaolin Lu et al's exemplar-based algorithm. Both algorithms are tested on images with variable occlusion sizes. The PDE-based algorithm is better at preserving linear structures for small regions but cannot reconnect structures or restore texture in large regions. The exemplar-based algorithm can find proper textures to fill large regions while preserving linear structures. Quantitative evaluation using PSNR shows that the exemplar-based algorithm achieves lower MSE values, especially for larger occlusion sizes. Therefore, the exemplar-based algorithm produces better results overall, particularly for filling in large missing regions of an image.
11.comparative analysis and evaluation of image imprinting algorithmsAlexander Decker
This document compares and evaluates two image inpainting algorithms: Marcelo Bertalmio's PDE-based algorithm and Zhaolin Lu et al's exemplar-based algorithm. Through experiments on images with different sized occluded regions, it finds that the PDE-based algorithm cannot reconnect structures or restore textures in large regions, while the exemplar-based algorithm can find patches to fill regions while preserving structures. Quantitative evaluation using PSNR shows the exemplar-based algorithm achieves lower MSE (error) for occlusion sizes from 10 to 40 pixels. The document provides examples comparing output of the two algorithms and discusses parameters needed for each.
The document proposes a novel Spatial Fuzzy C-Means (PET-SFCM) clustering algorithm to segment PET scan images of patients with neurodegenerative disorders like Alzheimer's disease. The algorithm incorporates spatial neighborhood information into the traditional Fuzzy C-Means algorithm. It was tested on real patient data sets and showed satisfactory results compared to conventional FCM and K-Means clustering algorithms. The PET-SFCM algorithm provides an effective way to segment PET images and analyze brain changes related to neurological conditions.
Object recognition is the challenging problem in the real world application. Object recognition can be achieved through the shape matching. Shape matching is preceded by i) detecting the edges of the objects from the images. ii) Finding the correspondence between the shapes. iii) Measuring the dissimilarity between the shapes using the correspondence. iv) Classifying the object into classes by using this dissimilarity measures. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts. The one to one correspondence is achieved through the cost based bipartite graph matching. The cost matrix is reduced through Hungarian algorithm. The dissimilarity between the two shapes is computed using Canberra distance. The nearest neighbor classifier is used to classify the objects with the matching error. The results are obtained using the MATLAB for MINIST hand written digits.
This document contains questions from a student about digital photogrammetry. It discusses various image matching techniques including intensity-based matching using cross-correlation and least squares matching, and feature-based matching using points, edges, and blobs. It also discusses relational matching and compares area-based and feature-based matching. Typical problems for image matching are described like lack of texture, straight features, repetitive patterns, and occlusions. Epipolar geometry and its advantages for image matching are explained, noting that it defines geometric constraints between images from different camera positions.
MODELING SOCIAL GAUSS-MARKOV MOBILITY FOR OPPORTUNISTIC NETWORK csandit
Mobility is attracting more and more interests due to its importance for data forwarding
mechanisms in many networks such as mobile opportunistic network. In everyday life mobile
nodes are often carried by human. Thus, mobile nodes’ mobility pattern is inevitable affected by
human social character. This paper presents a novel mobility model (HNGM) which combines
social character and Gauss-Markov process together. The performance analysis on this
mobility model is given and one famous and widely used mobility model (RWP) is chosen to
make comparison..
Medicinal Applications of Quantum ComputingbGeniusLLC
Here, I study to understand how computational and mathematical models are used to describe EEG readings of the brain in order to assess if these methods can be expanded into further research efforts to create better antidepressants.
EVOLUTIONARY CENTRALITY AND MAXIMAL CLIQUES IN MOBILE SOCIAL NETWORKSijcsit
This paper introduces an evolutionary approach to enhance the process of finding central nodes in mobile networks. This can provide essential information and important applications in mobile and social networks. This evolutionary approach considers the dynamics of the network and takes into consideration the central nodes from previous time slots. We also study the applicability of maximal cliques algorithms in mobile social networks and how it can be used to find the central nodes based on the discovered maximal cliques. The experimental results are promising and show a significant enhancement in finding the central nodes.
This document provides an overview of exponential random graph models (ERGMs) for statistically modeling social networks. It discusses the goals of using ERGMs, which are to understand structural features of networks, test hypotheses about network formation processes, and link macro network structures to micro behaviors. Example model terms that can be used in ERGMs are described, ranging from simple models with just edges to more complex models incorporating triangles, degree distributions, and homophily. The document outlines the challenges of estimating ERGM parameters using maximum likelihood due to the normalizing constant, and notes that simulation-based approximations are typically used.
This document provides an overview of exponential random graph models (ERGMs) for statistically modeling social networks. It discusses the goals of using ERGMs, which are to understand structural features of networks, test hypotheses about network formation processes, and link macro network structures to micro behaviors. Example model terms that can be used in ERGMs are described, ranging from simple models with just edges to more complex models incorporating triangles, degree distributions, and homophily. The document outlines the challenges of estimating ERGM parameters using maximum likelihood due to the normalizing constant, and notes that simulation-based approximations are typically used instead.
An experimental evaluation of similarity-based and embedding-based link predi...IJDKP
The task of inferring missing links or predicting future ones in a graph based on its current structure
is referred to as link prediction. Link prediction methods that are based on pairwise node similarity
are well-established approaches in the literature and show good prediction performance in many realworld graphs though they are heuristic. On the other hand, graph embedding approaches learn lowdimensional representation of nodes in graph and are capable of capturing inherent graph features,
and thus support the subsequent link prediction task in graph. This paper studies a selection of
methods from both categories on several benchmark (homogeneous) graphs with different properties
from various domains. Beyond the intra and inter category comparison of the performances of the
methods, our aim is also to uncover interesting connections between Graph Neural Network(GNN)-
based methods and heuristic ones as a means to alleviate the black-box well-known limitation.
ABSTRACT
This paper introduces an evolutionary approach to enhance the process of finding central nodes in mobile networks. This can provide essential information and important applications in mobile and social networks. This evolutionary approach considers the dynamics of the network and takes into consideration the central nodes from previous time slots. We also study the applicability of maximal cliques algorithms in mobile social networks and how it can be used to find the central nodes based on the discovered maximal cliques. The experimental results are promising and show a significant enhancement in finding the central nodes.
This document discusses applications of graph theory concepts like Delaunay triangulations, minimum spanning trees, and Steiner trees in mobile ad hoc networks (MANETs). It reviews prior research applying these concepts to problems like multicasting and routing in MANETs. The paper presents a network model of a MANET using a random geometric graph and simulations conducted in MATLAB. The simulations analyze minimum spanning trees constructed on Delaunay triangulations formed in the MANET to study issues related to MANET multicasting and routing.
This document discusses applications of graph theory concepts like Delaunay triangulations, minimum spanning trees, and Steiner trees in mobile ad hoc networks (MANETs). It reviews prior research applying these concepts to problems like multicasting and routing in MANETs. The paper presents a network model of a MANET using a random geometric graph and simulations analyzing minimum spanning trees constructed on Delaunay triangulations of the MANET. The simulations aim to study constructing multiple minimum spanning trees on the Delaunay triangulations.
The document summarizes a thesis presentation on graph clustering and community detection algorithms. It discusses:
1. The main contributions of the thesis, which include improving existing clustering algorithms and applying the new algorithms to synthetic and real-world networks.
2. An outline of the presentation covering introduction, literature review, proposed algorithms, experimentation on graphs, and applications.
3. Critical observations on existing clustering algorithms related to scalability, accuracy, and memory requirements.
4. The objectives of investigating improved clustering techniques to address issues in existing methods and apply the new algorithms to complex networks.
Higher-order spectral graph clustering with motifsAustin Benson
Higher-order spectral graph clustering uses motifs to find clusters in networks. It forms a weighted matrix based on a motif (e.g., triangles) and runs spectral clustering on that matrix. This captures clusters defined by the motif better than standard edge-based clustering. The technique has theoretical guarantees via a motif Cheeger inequality. Applications show it outperforms edge methods on food webs, gene networks, and transportation networks. Experiments on stochastic block models suggest the motif weighting improves cluster detection, potentially by making eigenvectors more localized to clusters. Open questions remain around eigenvalue distributions and convergence properties.
one of the areas of discrete mathematics is graph theory. From a pure mathematics viewpoint, graph theory studies the pairwise relationships between objects. Those objects are vertices. Graph theory is frequently applied to analysing relationships between objects. It is a natural extension of graph theory to apply that mathematical tool to the evaluation of forensic evidence. In fact the literature reveals several, limited, forensic applications of graph theory. The current paper describes a more broad based application of graph theory to the problem of evaluation relationships in forensic investigation. The process takes standard graph theory and identifies entities in the investigation as vertices with the connections between the various entities as edges. Those entities can be suspects, victims, computer system, or any entity relevant to the investigation. Regardless of the nature of the entity, all entities are represented as vertices, and the relationship between them is represented as edges connecting the vertices. This allows the mathematical modelling of the events in question and facilitates analysis of the data.
Conditional Matching Preclusion Number of Certain Graphsijcoa
The document discusses the conditional matching preclusion number of certain graphs. It is defined as the minimum number of edges whose deletion results in a graph with no isolated vertices and has neither a perfect matching nor almost perfect matching. The paper finds the conditional matching preclusion number for triangular ladder, Cn with parallel chords, Trampoline Graph, diamond Snake Graph and K- Polygonal Snake Graph.
A SURVEY ON SIMILARITY MEASURES IN TEXT MINING mlaij
The Volume of text resources have been increasing in digital libraries and internet. Organizing these text documents has become a practical need. For organizing great number of objects into small or minimum number of coherent groups automatically, Clustering technique is used. These documents are widely used for information retrieval and Natural Language processing tasks. Different Clustering algorithms require a metric for quantifying how dissimilar two given documents are. This difference is often measured by similarity measure such as Euclidean distance, Cosine similarity etc. The similarity measure process in text
mining can be used to identify the suitable clustering algorithm for a specific problem. This survey discusses the existing works on text similarity by partitioning them into three significant approaches; String-based, Knowledge based and Corpus-based similarities.
Collective dynamics of ‘small-world’ networksTokyo Tech
The document discusses small-world networks, which have short average path lengths like random graphs but high clustering like regular lattices. It presents a model (WS model) that randomly rewires edges in a ring lattice to interpolate between regular and random graphs. For large networks with few rewirings, the model produces small-world networks with short average path lengths but retained high clustering. Empirical analysis of actor collaborations, power grids, and neural networks finds they exhibit the small-world phenomenon.
Community detection aims to identify groups of nodes in a network that are more densely connected internally than to the rest of the network. It can reveal properties of networks without privacy risks. While similar to clustering, community detection methods consider graph properties directly due to challenges from network data. Two recent methods are discussed - one based on shortest path betweenness to iteratively remove inter-community edges, and another based on optimizing modularity, a measure of community structure quality. Modularity can be computed using the eigenvectors of the modularity matrix.
This document discusses predicting new friendships in social networks using temporal information. It describes research on predicting new links in social networks over time using supervised learning models trained on temporal features from past network interactions. The researchers used anonymized Facebook data over 28 months to train decision tree and neural network classifiers to predict new relationships, finding models using temporal information performed better than those without it.
An experimental evaluation of similarity-based and embedding-based link predi...IJDKP
The task of inferring missing links or predicting future ones in a graph based on its current structure
is referred to as link prediction. Link prediction methods that are based on pairwise node similarity
are well-established approaches in the literature and show good prediction performance in many realworld graphs though they are heuristic. On the other hand, graph embedding approaches learn lowdimensional representation of nodes in graph and are capable of capturing inherent graph features,
and thus support the subsequent link prediction task in graph. This paper studies a selection of
methods from both categories on several benchmark (homogeneous) graphs with different properties
from various domains. Beyond the intra and inter category comparison of the performances of the
methods, our aim is also to uncover interesting connections between Graph Neural Network(GNN)-
based methods and heuristic ones as a means to alleviate the black-box well-known limitation
Computational Acoustic Identification of Bat SpeciesJason Miller
in this talk, I describe a project I've been working on with undergraduates on and off for several years. We are attempting to solve an inverse problem where we identify a bat's species using only measurements made from a recording of its search-phase echolocation call.
Bats of the Channel Islands: Using Mathematics to Protect our Elusive Noctur...Jason Miller
Bats are a misunderstood species. This general audience talk aims to introduce an audience of Southern Californians to bats, their history, their habits, their benefits, and some threats to their well being. Of special interest are the bats of the Channel Islands National Park. Also discussed some mathematics on acoustic classification of bats.
Genericity, Transversality, and Relative Critical SetsJason Miller
The document summarizes a talk on genericity, transversality, and relative critical sets. It discusses:
1) Defining 1-dimensional ridges and the structure theorem stating that generically, the closure of 1-dimensional ridges is a discrete set of smooth curves with boundary points at certain critical points.
2) Defining genericity as a property holding for a residual set of functions.
3) Defining transversality and Thom's transversality theorem.
4) How the structure theorem is established by using structure mappings, collecting submanifolds of jet space, and applying Thom's theorem.
Bats and Stats: Summary of Effort to Identify Bats to SpeciesJason Miller
In this talk to undergraduates, I describe work previously done on the question of identifying bat species using information about their search phase echolocation calls. I then open the door to continuing this work with students on the Channel Islands.
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Mobility is attracting more and more interests due to its importance for data forwarding
mechanisms in many networks such as mobile opportunistic network. In everyday life mobile
nodes are often carried by human. Thus, mobile nodes’ mobility pattern is inevitable affected by
human social character. This paper presents a novel mobility model (HNGM) which combines
social character and Gauss-Markov process together. The performance analysis on this
mobility model is given and one famous and widely used mobility model (RWP) is chosen to
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This paper introduces an evolutionary approach to enhance the process of finding central nodes in mobile networks. This can provide essential information and important applications in mobile and social networks. This evolutionary approach considers the dynamics of the network and takes into consideration the central nodes from previous time slots. We also study the applicability of maximal cliques algorithms in mobile social networks and how it can be used to find the central nodes based on the discovered maximal cliques. The experimental results are promising and show a significant enhancement in finding the central nodes.
This document provides an overview of exponential random graph models (ERGMs) for statistically modeling social networks. It discusses the goals of using ERGMs, which are to understand structural features of networks, test hypotheses about network formation processes, and link macro network structures to micro behaviors. Example model terms that can be used in ERGMs are described, ranging from simple models with just edges to more complex models incorporating triangles, degree distributions, and homophily. The document outlines the challenges of estimating ERGM parameters using maximum likelihood due to the normalizing constant, and notes that simulation-based approximations are typically used.
This document provides an overview of exponential random graph models (ERGMs) for statistically modeling social networks. It discusses the goals of using ERGMs, which are to understand structural features of networks, test hypotheses about network formation processes, and link macro network structures to micro behaviors. Example model terms that can be used in ERGMs are described, ranging from simple models with just edges to more complex models incorporating triangles, degree distributions, and homophily. The document outlines the challenges of estimating ERGM parameters using maximum likelihood due to the normalizing constant, and notes that simulation-based approximations are typically used instead.
An experimental evaluation of similarity-based and embedding-based link predi...IJDKP
The task of inferring missing links or predicting future ones in a graph based on its current structure
is referred to as link prediction. Link prediction methods that are based on pairwise node similarity
are well-established approaches in the literature and show good prediction performance in many realworld graphs though they are heuristic. On the other hand, graph embedding approaches learn lowdimensional representation of nodes in graph and are capable of capturing inherent graph features,
and thus support the subsequent link prediction task in graph. This paper studies a selection of
methods from both categories on several benchmark (homogeneous) graphs with different properties
from various domains. Beyond the intra and inter category comparison of the performances of the
methods, our aim is also to uncover interesting connections between Graph Neural Network(GNN)-
based methods and heuristic ones as a means to alleviate the black-box well-known limitation.
ABSTRACT
This paper introduces an evolutionary approach to enhance the process of finding central nodes in mobile networks. This can provide essential information and important applications in mobile and social networks. This evolutionary approach considers the dynamics of the network and takes into consideration the central nodes from previous time slots. We also study the applicability of maximal cliques algorithms in mobile social networks and how it can be used to find the central nodes based on the discovered maximal cliques. The experimental results are promising and show a significant enhancement in finding the central nodes.
This document discusses applications of graph theory concepts like Delaunay triangulations, minimum spanning trees, and Steiner trees in mobile ad hoc networks (MANETs). It reviews prior research applying these concepts to problems like multicasting and routing in MANETs. The paper presents a network model of a MANET using a random geometric graph and simulations conducted in MATLAB. The simulations analyze minimum spanning trees constructed on Delaunay triangulations formed in the MANET to study issues related to MANET multicasting and routing.
This document discusses applications of graph theory concepts like Delaunay triangulations, minimum spanning trees, and Steiner trees in mobile ad hoc networks (MANETs). It reviews prior research applying these concepts to problems like multicasting and routing in MANETs. The paper presents a network model of a MANET using a random geometric graph and simulations analyzing minimum spanning trees constructed on Delaunay triangulations of the MANET. The simulations aim to study constructing multiple minimum spanning trees on the Delaunay triangulations.
The document summarizes a thesis presentation on graph clustering and community detection algorithms. It discusses:
1. The main contributions of the thesis, which include improving existing clustering algorithms and applying the new algorithms to synthetic and real-world networks.
2. An outline of the presentation covering introduction, literature review, proposed algorithms, experimentation on graphs, and applications.
3. Critical observations on existing clustering algorithms related to scalability, accuracy, and memory requirements.
4. The objectives of investigating improved clustering techniques to address issues in existing methods and apply the new algorithms to complex networks.
Higher-order spectral graph clustering with motifsAustin Benson
Higher-order spectral graph clustering uses motifs to find clusters in networks. It forms a weighted matrix based on a motif (e.g., triangles) and runs spectral clustering on that matrix. This captures clusters defined by the motif better than standard edge-based clustering. The technique has theoretical guarantees via a motif Cheeger inequality. Applications show it outperforms edge methods on food webs, gene networks, and transportation networks. Experiments on stochastic block models suggest the motif weighting improves cluster detection, potentially by making eigenvectors more localized to clusters. Open questions remain around eigenvalue distributions and convergence properties.
one of the areas of discrete mathematics is graph theory. From a pure mathematics viewpoint, graph theory studies the pairwise relationships between objects. Those objects are vertices. Graph theory is frequently applied to analysing relationships between objects. It is a natural extension of graph theory to apply that mathematical tool to the evaluation of forensic evidence. In fact the literature reveals several, limited, forensic applications of graph theory. The current paper describes a more broad based application of graph theory to the problem of evaluation relationships in forensic investigation. The process takes standard graph theory and identifies entities in the investigation as vertices with the connections between the various entities as edges. Those entities can be suspects, victims, computer system, or any entity relevant to the investigation. Regardless of the nature of the entity, all entities are represented as vertices, and the relationship between them is represented as edges connecting the vertices. This allows the mathematical modelling of the events in question and facilitates analysis of the data.
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The document discusses the conditional matching preclusion number of certain graphs. It is defined as the minimum number of edges whose deletion results in a graph with no isolated vertices and has neither a perfect matching nor almost perfect matching. The paper finds the conditional matching preclusion number for triangular ladder, Cn with parallel chords, Trampoline Graph, diamond Snake Graph and K- Polygonal Snake Graph.
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The Volume of text resources have been increasing in digital libraries and internet. Organizing these text documents has become a practical need. For organizing great number of objects into small or minimum number of coherent groups automatically, Clustering technique is used. These documents are widely used for information retrieval and Natural Language processing tasks. Different Clustering algorithms require a metric for quantifying how dissimilar two given documents are. This difference is often measured by similarity measure such as Euclidean distance, Cosine similarity etc. The similarity measure process in text
mining can be used to identify the suitable clustering algorithm for a specific problem. This survey discusses the existing works on text similarity by partitioning them into three significant approaches; String-based, Knowledge based and Corpus-based similarities.
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The document discusses small-world networks, which have short average path lengths like random graphs but high clustering like regular lattices. It presents a model (WS model) that randomly rewires edges in a ring lattice to interpolate between regular and random graphs. For large networks with few rewirings, the model produces small-world networks with short average path lengths but retained high clustering. Empirical analysis of actor collaborations, power grids, and neural networks finds they exhibit the small-world phenomenon.
Community detection aims to identify groups of nodes in a network that are more densely connected internally than to the rest of the network. It can reveal properties of networks without privacy risks. While similar to clustering, community detection methods consider graph properties directly due to challenges from network data. Two recent methods are discussed - one based on shortest path betweenness to iteratively remove inter-community edges, and another based on optimizing modularity, a measure of community structure quality. Modularity can be computed using the eigenvectors of the modularity matrix.
This document discusses predicting new friendships in social networks using temporal information. It describes research on predicting new links in social networks over time using supervised learning models trained on temporal features from past network interactions. The researchers used anonymized Facebook data over 28 months to train decision tree and neural network classifiers to predict new relationships, finding models using temporal information performed better than those without it.
An experimental evaluation of similarity-based and embedding-based link predi...IJDKP
The task of inferring missing links or predicting future ones in a graph based on its current structure
is referred to as link prediction. Link prediction methods that are based on pairwise node similarity
are well-established approaches in the literature and show good prediction performance in many realworld graphs though they are heuristic. On the other hand, graph embedding approaches learn lowdimensional representation of nodes in graph and are capable of capturing inherent graph features,
and thus support the subsequent link prediction task in graph. This paper studies a selection of
methods from both categories on several benchmark (homogeneous) graphs with different properties
from various domains. Beyond the intra and inter category comparison of the performances of the
methods, our aim is also to uncover interesting connections between Graph Neural Network(GNN)-
based methods and heuristic ones as a means to alleviate the black-box well-known limitation
Similar to Connectedness as a Measure of Robustness (18)
Computational Acoustic Identification of Bat SpeciesJason Miller
in this talk, I describe a project I've been working on with undergraduates on and off for several years. We are attempting to solve an inverse problem where we identify a bat's species using only measurements made from a recording of its search-phase echolocation call.
Bats of the Channel Islands: Using Mathematics to Protect our Elusive Noctur...Jason Miller
Bats are a misunderstood species. This general audience talk aims to introduce an audience of Southern Californians to bats, their history, their habits, their benefits, and some threats to their well being. Of special interest are the bats of the Channel Islands National Park. Also discussed some mathematics on acoustic classification of bats.
Genericity, Transversality, and Relative Critical SetsJason Miller
The document summarizes a talk on genericity, transversality, and relative critical sets. It discusses:
1) Defining 1-dimensional ridges and the structure theorem stating that generically, the closure of 1-dimensional ridges is a discrete set of smooth curves with boundary points at certain critical points.
2) Defining genericity as a property holding for a residual set of functions.
3) Defining transversality and Thom's transversality theorem.
4) How the structure theorem is established by using structure mappings, collecting submanifolds of jet space, and applying Thom's theorem.
Bats and Stats: Summary of Effort to Identify Bats to SpeciesJason Miller
In this talk to undergraduates, I describe work previously done on the question of identifying bat species using information about their search phase echolocation calls. I then open the door to continuing this work with students on the Channel Islands.
Preparing Undergraduates to Work at the Intersection of Biology and MathematicsJason Miller
Research, writing, presentation
AAC&U 2012
Summer
Residence Hall
Meals
Small Group Meetings + Mentors
Weekly Discussions/Workshops
Social Events
MathBio Seminar
A Research-based Model for Interdisciplinary Training of STEM Undergraduat…Jason Miller
Truman State University has developed a mechanism for effective training undergraduates to work at the intersection of the life and mathematical sciences, and it uses the pedagogy of undergraduate research. This 'machine' can be appropriated for other interdisciplinary pairings our groupings. Slides are for a talk given for the Missouri State University's Chemistry Seminar on 17 October 2012.
Undergraduate Research and Interdisciplinary TrainingJason Miller
A quick talk for the Trinity University's Fall 2012 HHMI conference on Truman's undergraduate mathematical biology program and how it's lead to broadening participation in STEM in different but powerful ways.
Highs and Lows of An Interdepartmental MathBio ProgramJason Miller
This talk describes the interdisciplinary undergraduate mathematical biology program at Truman State University, its history and development, and the minor degree it offers.
Conference on Transfer and Articulation 2012 PresentationJason Miller
This document proposes establishing pre-STEM pathways to increase success in four-year STEM degrees. It notes declining STEM enrollment in Missouri and increasing national rates. Existing programs like STEP increased STEM degrees but identified issues with STEM transfer pathways. The proposal suggests a pre-STEM pathway where students take STEM-focused courses at two-year schools with advising before transferring to complete their AA and bachelor's degrees.
Interdisciplinary Training in Mathematical Biology Through Team-based Undergr...Jason Miller
The document discusses the development of an interdisciplinary undergraduate program in mathematical biology at Truman State University. It describes how the program grew out of undergraduate research projects involving both mathematics and biology faculty mentoring students from different disciplines. The program now includes an interdisciplinary minor that requires hands-on research experience and competencies in areas like modeling, computation, and statistics. The speaker advocates for more programs training "convergent" scientists who can work across disciplinary boundaries.
Rising Above the Gathering Storm by Building Bridges for STEM Transfers from ...Jason Miller
Increasing the production of STEM degree holders requires efforts to broaden participation in STEM degree programs. Because more students choose to start their college careers at community colleges, we must understand the special challenges they face along the pathway to earning a baccalaureate degree in STEM. These slides communicate the results of am October 2009 workshop in Belknap Springs aimed at understanding these challenges and identifying best-practices in overcoming them. The workshops was sponsored by the National Science Foundation and is associated with the NSF DUE STEP program.
Computer Vision, Computation, and GeometryJason Miller
Jason Miller is an associate professor of mathematics who studies visual perception and computation using techniques from geometry and topology. He gave a talk outlining his work using medial axes and relative critical sets to analyze medical images and segment objects. This involves translating assumptions about images into mathematical models and comparing implications to real data. His subsequent work has applied these methods to projects in biology and medical imaging.
Since 2004, Truman State University has trained students to conduct interdisciplinary research in mathematical biology through a combination of research experiences with faculty collaborators, courses, and field trips. This program of experiences for undergraduates has been made possible by the National Science Foundation’s Interdisciplinary Training for Undergraduates in Biology and Mathematics (UBM) program. This talk will outline our courses and our research program (including a portfolio-based interdisciplinary minor in mathematical biology), what we have learned about assessing interdisciplinary learning, and the role field trips have played in the professional development of faculty and students.
The Undergraduate Research Machine at TrumanJason Miller
This is a short, 10 minute, presentation at a Council on Undergraduate Research (CUR) institute hosted by Truman. The presentation outlined the highlights of the Good Things we do to provide undergraduates with high quality learning experiences through research with faculty.
Training Undergraduates in Mathematical Biology using Research with FacultyJason Miller
Truman State University has Missouri's only undergraduate program in mathematical biology. We prepare undergraduate to work at the intersection of the life and mathematical sciences through coursework and through an innovative, team-based research program.
Relative Critical Sets: Structure and applicationsJason Miller
A talk at the 2009 Joint Mathematics Meeting in Washington, D.C., on relative critical sets and their properties. The talk ends with an open question whose answer will help extend our understanding of the local generic structure of relative critical sets.
Charting a Course Toward Interdisciplinary CollaborationsJason Miller
Prof. Jason Miller discusses forming interdisciplinary collaborations between different academic fields, specifically coming together to influence curriculum and help students understand connections between STEM fields. He details his experiences with successes, failures, and enjoyment working to bridge disciplines through undergraduate research projects at Truman State University, where he is an Associate Professor of Mathematics.
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-und-domino-lizenzkostenreduzierung-in-der-welt-von-dlau/
DLAU und die Lizenzen nach dem CCB- und CCX-Modell sind für viele in der HCL-Community seit letztem Jahr ein heißes Thema. Als Notes- oder Domino-Kunde haben Sie vielleicht mit unerwartet hohen Benutzerzahlen und Lizenzgebühren zu kämpfen. Sie fragen sich vielleicht, wie diese neue Art der Lizenzierung funktioniert und welchen Nutzen sie Ihnen bringt. Vor allem wollen Sie sicherlich Ihr Budget einhalten und Kosten sparen, wo immer möglich. Das verstehen wir und wir möchten Ihnen dabei helfen!
Wir erklären Ihnen, wie Sie häufige Konfigurationsprobleme lösen können, die dazu führen können, dass mehr Benutzer gezählt werden als nötig, und wie Sie überflüssige oder ungenutzte Konten identifizieren und entfernen können, um Geld zu sparen. Es gibt auch einige Ansätze, die zu unnötigen Ausgaben führen können, z. B. wenn ein Personendokument anstelle eines Mail-Ins für geteilte Mailboxen verwendet wird. Wir zeigen Ihnen solche Fälle und deren Lösungen. Und natürlich erklären wir Ihnen das neue Lizenzmodell.
Nehmen Sie an diesem Webinar teil, bei dem HCL-Ambassador Marc Thomas und Gastredner Franz Walder Ihnen diese neue Welt näherbringen. Es vermittelt Ihnen die Tools und das Know-how, um den Überblick zu bewahren. Sie werden in der Lage sein, Ihre Kosten durch eine optimierte Domino-Konfiguration zu reduzieren und auch in Zukunft gering zu halten.
Diese Themen werden behandelt
- Reduzierung der Lizenzkosten durch Auffinden und Beheben von Fehlkonfigurationen und überflüssigen Konten
- Wie funktionieren CCB- und CCX-Lizenzen wirklich?
- Verstehen des DLAU-Tools und wie man es am besten nutzt
- Tipps für häufige Problembereiche, wie z. B. Team-Postfächer, Funktions-/Testbenutzer usw.
- Praxisbeispiele und Best Practices zum sofortigen Umsetzen
AI 101: An Introduction to the Basics and Impact of Artificial IntelligenceIndexBug
Imagine a world where machines not only perform tasks but also learn, adapt, and make decisions. This is the promise of Artificial Intelligence (AI), a technology that's not just enhancing our lives but revolutionizing entire industries.
CAKE: Sharing Slices of Confidential Data on BlockchainClaudio Di Ciccio
Presented at the CAiSE 2024 Forum, Intelligent Information Systems, June 6th, Limassol, Cyprus.
Synopsis: Cooperative information systems typically involve various entities in a collaborative process within a distributed environment. Blockchain technology offers a mechanism for automating such processes, even when only partial trust exists among participants. The data stored on the blockchain is replicated across all nodes in the network, ensuring accessibility to all participants. While this aspect facilitates traceability, integrity, and persistence, it poses challenges for adopting public blockchains in enterprise settings due to confidentiality issues. In this paper, we present a software tool named Control Access via Key Encryption (CAKE), designed to ensure data confidentiality in scenarios involving public blockchains. After outlining its core components and functionalities, we showcase the application of CAKE in the context of a real-world cyber-security project within the logistics domain.
Paper: https://doi.org/10.1007/978-3-031-61000-4_16
Threats to mobile devices are more prevalent and increasing in scope and complexity. Users of mobile devices desire to take full advantage of the features
available on those devices, but many of the features provide convenience and capability but sacrifice security. This best practices guide outlines steps the users can take to better protect personal devices and information.
Removing Uninteresting Bytes in Software FuzzingAftab Hussain
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
Driving Business Innovation: Latest Generative AI Advancements & Success StorySafe Software
Are you ready to revolutionize how you handle data? Join us for a webinar where we’ll bring you up to speed with the latest advancements in Generative AI technology and discover how leveraging FME with tools from giants like Google Gemini, Amazon, and Microsoft OpenAI can supercharge your workflow efficiency.
During the hour, we’ll take you through:
Guest Speaker Segment with Hannah Barrington: Dive into the world of dynamic real estate marketing with Hannah, the Marketing Manager at Workspace Group. Hear firsthand how their team generates engaging descriptions for thousands of office units by integrating diverse data sources—from PDF floorplans to web pages—using FME transformers, like OpenAIVisionConnector and AnthropicVisionConnector. This use case will show you how GenAI can streamline content creation for marketing across the board.
Ollama Use Case: Learn how Scenario Specialist Dmitri Bagh has utilized Ollama within FME to input data, create custom models, and enhance security protocols. This segment will include demos to illustrate the full capabilities of FME in AI-driven processes.
Custom AI Models: Discover how to leverage FME to build personalized AI models using your data. Whether it’s populating a model with local data for added security or integrating public AI tools, find out how FME facilitates a versatile and secure approach to AI.
We’ll wrap up with a live Q&A session where you can engage with our experts on your specific use cases, and learn more about optimizing your data workflows with AI.
This webinar is ideal for professionals seeking to harness the power of AI within their data management systems while ensuring high levels of customization and security. Whether you're a novice or an expert, gain actionable insights and strategies to elevate your data processes. Join us to see how FME and AI can revolutionize how you work with data!
UiPath Test Automation using UiPath Test Suite series, part 6DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 6. In this session, we will cover Test Automation with generative AI and Open AI.
UiPath Test Automation with generative AI and Open AI webinar offers an in-depth exploration of leveraging cutting-edge technologies for test automation within the UiPath platform. Attendees will delve into the integration of generative AI, a test automation solution, with Open AI advanced natural language processing capabilities.
Throughout the session, participants will discover how this synergy empowers testers to automate repetitive tasks, enhance testing accuracy, and expedite the software testing life cycle. Topics covered include the seamless integration process, practical use cases, and the benefits of harnessing AI-driven automation for UiPath testing initiatives. By attending this webinar, testers, and automation professionals can gain valuable insights into harnessing the power of AI to optimize their test automation workflows within the UiPath ecosystem, ultimately driving efficiency and quality in software development processes.
What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
4. Exploration of real-world use cases illustrating the benefits of AI-driven test automation for UiPath
Topics covered:
What is generative AI
Test Automation with generative AI and Open AI.
UiPath integration with generative AI
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Full-RAG: A modern architecture for hyper-personalizationZilliz
Mike Del Balso, CEO & Co-Founder at Tecton, presents "Full RAG," a novel approach to AI recommendation systems, aiming to push beyond the limitations of traditional models through a deep integration of contextual insights and real-time data, leveraging the Retrieval-Augmented Generation architecture. This talk will outline Full RAG's potential to significantly enhance personalization, address engineering challenges such as data management and model training, and introduce data enrichment with reranking as a key solution. Attendees will gain crucial insights into the importance of hyperpersonalization in AI, the capabilities of Full RAG for advanced personalization, and strategies for managing complex data integrations for deploying cutting-edge AI solutions.
Essentials of Automations: The Art of Triggers and Actions in FMESafe Software
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
Unlocking Productivity: Leveraging the Potential of Copilot in Microsoft 365, a presentation by Christoforos Vlachos, Senior Solutions Manager – Modern Workplace, Uni Systems
Programming Foundation Models with DSPy - Meetup SlidesZilliz
Prompting language models is hard, while programming language models is easy. In this talk, I will discuss the state-of-the-art framework DSPy for programming foundation models with its powerful optimizers and runtime constraint system.
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdfMalak Abu Hammad
Discover how MongoDB Atlas and vector search technology can revolutionize your application's search capabilities. This comprehensive presentation covers:
* What is Vector Search?
* Importance and benefits of vector search
* Practical use cases across various industries
* Step-by-step implementation guide
* Live demos with code snippets
* Enhancing LLM capabilities with vector search
* Best practices and optimization strategies
Perfect for developers, AI enthusiasts, and tech leaders. Learn how to leverage MongoDB Atlas to deliver highly relevant, context-aware search results, transforming your data retrieval process. Stay ahead in tech innovation and maximize the potential of your applications.
#MongoDB #VectorSearch #AI #SemanticSearch #TechInnovation #DataScience #LLM #MachineLearning #SearchTechnology
Have you ever been confused by the myriad of choices offered by AWS for hosting a website or an API?
Lambda, Elastic Beanstalk, Lightsail, Amplify, S3 (and more!) can each host websites + APIs. But which one should we choose?
Which one is cheapest? Which one is fastest? Which one will scale to meet our needs?
Join me in this session as we dive into each AWS hosting service to determine which one is best for your scenario and explain why!
Your One-Stop Shop for Python Success: Top 10 US Python Development Providersakankshawande
Simplify your search for a reliable Python development partner! This list presents the top 10 trusted US providers offering comprehensive Python development services, ensuring your project's success from conception to completion.
HCL Notes and Domino License Cost Reduction in the World of DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-and-domino-license-cost-reduction-in-the-world-of-dlau/
The introduction of DLAU and the CCB & CCX licensing model caused quite a stir in the HCL community. As a Notes and Domino customer, you may have faced challenges with unexpected user counts and license costs. You probably have questions on how this new licensing approach works and how to benefit from it. Most importantly, you likely have budget constraints and want to save money where possible. Don’t worry, we can help with all of this!
We’ll show you how to fix common misconfigurations that cause higher-than-expected user counts, and how to identify accounts which you can deactivate to save money. There are also frequent patterns that can cause unnecessary cost, like using a person document instead of a mail-in for shared mailboxes. We’ll provide examples and solutions for those as well. And naturally we’ll explain the new licensing model.
Join HCL Ambassador Marc Thomas in this webinar with a special guest appearance from Franz Walder. It will give you the tools and know-how to stay on top of what is going on with Domino licensing. You will be able lower your cost through an optimized configuration and keep it low going forward.
These topics will be covered
- Reducing license cost by finding and fixing misconfigurations and superfluous accounts
- How do CCB and CCX licenses really work?
- Understanding the DLAU tool and how to best utilize it
- Tips for common problem areas, like team mailboxes, functional/test users, etc
- Practical examples and best practices to implement right away
Building Production Ready Search Pipelines with Spark and MilvusZilliz
Spark is the widely used ETL tool for processing, indexing and ingesting data to serving stack for search. Milvus is the production-ready open-source vector database. In this talk we will show how to use Spark to process unstructured data to extract vector representations, and push the vectors to Milvus vector database for search serving.
1. Introduction Graph Theory Cells Community
Connectedness As A Measure of Robustness
Dr. Jason Miller
Department of Mathematics
Truman State University
November 17, 2006
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
2. Introduction Graph Theory Cells Community
About the Talk
Introduction
1
Graph Theory
2
Vascular Networks
3
Research Communities
4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
3. Introduction Graph Theory Cells Community
What is Graph Theory?
Fundamental Objects
An abstract graph is made up of
nodes, and
edges that connect nodes.
Example
This is the complete graph on 5
nodes. Its nodes are most thoroughly
interconnected.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
4. Introduction Graph Theory Cells Community
What is Graph Theory?
Fundamental Objects
An abstract graph is made up of
nodes, and
edges that connect nodes.
Example
This is the complete graph on 5
nodes. Its nodes are most thoroughly
interconnected.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
5. Introduction Graph Theory Cells Community
What is Graph Theory?
Fundamental Objects
An abstract graph is made up of
nodes, and
edges that connect nodes.
Example
This is the complete graph on 5
nodes. Its nodes are most thoroughly
interconnected.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
6. Introduction Graph Theory Cells Community
What is Graph Theory?
Fundamental Objects
An abstract graph is made up of
nodes, and
edges that connect nodes.
Example
This is the complete graph on 5
nodes. Its nodes are most thoroughly
interconnected.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
7. Introduction Graph Theory Cells Community
Applications of Graph Theory
Applications
Graphs is used to illuminate questions in ecology, epidemiology,
sociology, business, and computer science.
Example (The Internet)
Consider the graph where nodes represent servers on the Internet
and edge represent neworking that connects the computers.
Analysis of such a graph can illuminate network traffic problems.
Example (Transportation Flow)
Consider the graph where edges represent a roadways and nodes
represent intersections. Analysis of such a graph can illuminate
how vehicular flow relates to road configuration.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
8. Introduction Graph Theory Cells Community
Applications of Graph Theory
Applications
Graphs is used to illuminate questions in ecology, epidemiology,
sociology, business, and computer science.
Example (The Internet)
Consider the graph where nodes represent servers on the Internet
and edge represent neworking that connects the computers.
Analysis of such a graph can illuminate network traffic problems.
Example (Transportation Flow)
Consider the graph where edges represent a roadways and nodes
represent intersections. Analysis of such a graph can illuminate
how vehicular flow relates to road configuration.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
9. Introduction Graph Theory Cells Community
Applications of Graph Theory
Applications
Graphs is used to illuminate questions in ecology, epidemiology,
sociology, business, and computer science.
Example (The Internet)
Consider the graph where nodes represent servers on the Internet
and edge represent neworking that connects the computers.
Analysis of such a graph can illuminate network traffic problems.
Example (Transportation Flow)
Consider the graph where edges represent a roadways and nodes
represent intersections. Analysis of such a graph can illuminate
how vehicular flow relates to road configuration.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
10. Introduction Graph Theory Cells Community
Applications of Graph Theory
Applications
Graphs is used to illuminate questions in ecology, epidemiology,
sociology, business, and computer science.
Example (The Internet)
Consider the graph where nodes represent servers on the Internet
and edge represent neworking that connects the computers.
Analysis of such a graph can illuminate network traffic problems.
Example (Transportation Flow)
Consider the graph where edges represent a roadways and nodes
represent intersections. Analysis of such a graph can illuminate
how vehicular flow relates to road configuration.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
11. Introduction Graph Theory Cells Community
Applications of Graph Theory
Applications
Graphs is used to illuminate questions in ecology, epidemiology,
sociology, business, and computer science.
Example (The Internet)
Consider the graph where nodes represent servers on the Internet
and edge represent neworking that connects the computers.
Analysis of such a graph can illuminate network traffic problems.
Example (Transportation Flow)
Consider the graph where edges represent a roadways and nodes
represent intersections. Analysis of such a graph can illuminate
how vehicular flow relates to road configuration.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
12. Introduction Graph Theory Cells Community
Theorems on Connectedness
Connectedness
My Interest
Graph connectedness is a measure of
1 robustness.
Example (Complete Graph, 5 Nodes)
2 5 Complete graphs are robust against
losing nodes.
Lose node #5, and the remaining
nodes and edges still form a single
network.
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
13. Introduction Graph Theory Cells Community
Theorems on Connectedness
Connectedness
My Interest
Graph connectedness is a measure of
1 robustness.
Example (Complete Graph, 5 Nodes)
2 5 Complete graphs are robust against
losing nodes.
Lose node #5, and the remaining
nodes and edges still form a single
network.
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
14. Introduction Graph Theory Cells Community
Theorems on Connectedness
Connectedness
My Interest
Graph connectedness is a measure of
1 robustness.
Example (Complete Graph, 5 Nodes)
2 5 Complete graphs are robust against
losing nodes.
Lose node #5, and the remaining
nodes and edges still form a single
network.
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
15. Introduction Graph Theory Cells Community
Theorems on Connectedness
Connectedness
My Interest
Graph connectedness is a measure of
1 robustness.
Example (Complete Graph, 5 Nodes)
2 5 Complete graphs are robust against
losing nodes.
Lose node #5, and the remaining
nodes and edges still form a single
network.
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
16. Introduction Graph Theory Cells Community
Theorems on Connectedness
Connectedness
My Interest
Graph connectedness is a measure of
1 robustness.
Example
2 5 This graph is not robust against
losing nodes.
Lose node #5, and the remaining
nodes and edges form two separate
networks.
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
17. Introduction Graph Theory Cells Community
Theorems on Connectedness
Connectedness
My Interest
Graph connectedness is a measure of
1 robustness.
Example
2 5 This graph is not robust against
losing nodes.
Lose node #5, and the remaining
nodes and edges form two separate
networks.
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
18. Introduction Graph Theory Cells Community
Theorems on Connectedness
A network structure can be encoded into a matrix using node
adjacency.
Definition (Adjacency Matrix)
The ijth entry of the n × n adjacency matrix A of a graph G is
1 if i = j and the i th and jth nodes are
Aij = connected with an edge
0 otherwise
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
19. Introduction Graph Theory Cells Community
Theorems on Connectedness
Example (Adjacency Matrix of the Complete graph)
1
0 1 1 1 1
1 0 1 1 1
2 5
A= 1 1 0 1 1
1 1 1 0 1
1 1 1 1 0
(Note: i → column, j → row)
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
20. Introduction Graph Theory Cells Community
Theorems on Connectedness
Example (Adjacency Matrix of the Complete graph)
1
0 1 1 1 1
1 0 1 1 1
2 5
A= 1 1 0 1 1
1 1 1 0 1
1 1 1 1 0
(Note: i → column, j → row)
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
21. Introduction Graph Theory Cells Community
Theorems on Connectedness
Example (Adjacency Matrix of the Complete graph)
1
0 1 1 1 1
1 0 1 1 1
2 5
A= 1 1 0 1 1
1 1 1 0 1
1 1 1 1 0
(Note: i → column, j → row)
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
22. Introduction Graph Theory Cells Community
Theorems on Connectedness
Example (Adjacency Matrix of the Complete graph)
1
0 1 1 1 1
1 0 1 1 1
2 5
A= 1 1 0 1 1
1 1 1 0 1
1 1 1 1 0
(Note: i → column, j → row)
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
23. Introduction Graph Theory Cells Community
Theorems on Connectedness
Example (Adjacency Matrix of the Complete graph)
1
0 1 1 1 1
1 0 1 1 1
2 5
A= 1 1 0 1 1
1 1 1 0 1
1 1 1 1 0
(Note: i → column, j → row)
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
24. Introduction Graph Theory Cells Community
Theorems on Connectedness
Example (Adjacency Matrix)
1
0 1 0 0 1
1 0 0 0 1
2 5
A= 0 0 0 1 0
0 0 1 0 1
1 1 0 1 0
(Note: i → column, j → row)
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
25. Introduction Graph Theory Cells Community
Theorems on Connectedness
Example (Adjacency Matrix)
1
0 1 0 0 1
1 0 0 0 1
2 5
A= 0 0 0 1 0
0 0 1 0 1
1 1 0 1 0
(Note: i → column, j → row)
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
26. Introduction Graph Theory Cells Community
Theorems on Connectedness
Example (Adjacency Matrix)
1
0 1 0 0 1
1 0 0 0 1
2 5
A= 0 0 0 1 0
0 0 1 0 1
1 1 0 1 0
(Note: i → column, j → row)
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
27. Introduction Graph Theory Cells Community
Theorems on Connectedness
Example (Adjacency Matrix)
1
0 1 0 0 1
1 0 0 0 1
2 5
A= 0 0 0 1 0
0 0 1 0 1
1 1 0 1 0
(Note: i → column, j → row)
3 4
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
28. Introduction Graph Theory Cells Community
Theorems on Connectedness
Adjacency
From the matrix, we can deduce much about the structure of the
graph G . For example,
the number of edges that meet at each node (degree)
whether the graph is a single connected object (connectivity)
Spectral Graph Theory
An adjacency matrix for a graph can be tweaked slightly into
another matrix call a Laplacian matrix whose eigenvalues and
eigenvectors give structural information about the graph. We hope
to exploit this information to describe the robustness of vascular
networks.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
29. Introduction Graph Theory Cells Community
Theorems on Connectedness
Adjacency
From the matrix, we can deduce much about the structure of the
graph G . For example,
the number of edges that meet at each node (degree)
whether the graph is a single connected object (connectivity)
Spectral Graph Theory
An adjacency matrix for a graph can be tweaked slightly into
another matrix call a Laplacian matrix whose eigenvalues and
eigenvectors give structural information about the graph. We hope
to exploit this information to describe the robustness of vascular
networks.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
30. Introduction Graph Theory Cells Community
Theorems on Connectedness
Adjacency
From the matrix, we can deduce much about the structure of the
graph G . For example,
the number of edges that meet at each node (degree)
whether the graph is a single connected object (connectivity)
Spectral Graph Theory
An adjacency matrix for a graph can be tweaked slightly into
another matrix call a Laplacian matrix whose eigenvalues and
eigenvectors give structural information about the graph. We hope
to exploit this information to describe the robustness of vascular
networks.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
31. Introduction Graph Theory Cells Community
Theorems on Connectedness
Adjacency
From the matrix, we can deduce much about the structure of the
graph G . For example,
the number of edges that meet at each node (degree)
whether the graph is a single connected object (connectivity)
Spectral Graph Theory
An adjacency matrix for a graph can be tweaked slightly into
another matrix call a Laplacian matrix whose eigenvalues and
eigenvectors give structural information about the graph. We hope
to exploit this information to describe the robustness of vascular
networks.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
32. Introduction Graph Theory Cells Community
Theorems on Connectedness
Adjacency
From the matrix, we can deduce much about the structure of the
graph G . For example,
the number of edges that meet at each node (degree)
whether the graph is a single connected object (connectivity)
Spectral Graph Theory
An adjacency matrix for a graph can be tweaked slightly into
another matrix call a Laplacian matrix whose eigenvalues and
eigenvectors give structural information about the graph. We hope
to exploit this information to describe the robustness of vascular
networks.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
33. Introduction Graph Theory Cells Community
Vascular Networks
Background: Vasculogenesis
A tumor, an abnormal growth of tissue, is bad for you.
Cancerous tumors are really bad for you.
For cancerous tissue to grow, it need nutrients.
Growth of tumorous tissue that acquire nutrients through
diffusion is limited; dead inside.
Some tumors can “arrange for” the formation of blood vessels
near to or inside the tumor. (Some attract host vessel, others
create their own vasculature.)
Big Question
What are some of the mechanisms at work that allow this? How
can they be inhibited?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
34. Introduction Graph Theory Cells Community
Vascular Networks
Background: Vasculogenesis
A tumor, an abnormal growth of tissue, is bad for you.
Cancerous tumors are really bad for you.
For cancerous tissue to grow, it need nutrients.
Growth of tumorous tissue that acquire nutrients through
diffusion is limited; dead inside.
Some tumors can “arrange for” the formation of blood vessels
near to or inside the tumor. (Some attract host vessel, others
create their own vasculature.)
Big Question
What are some of the mechanisms at work that allow this? How
can they be inhibited?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
35. Introduction Graph Theory Cells Community
Vascular Networks
Background: Vasculogenesis
A tumor, an abnormal growth of tissue, is bad for you.
Cancerous tumors are really bad for you.
For cancerous tissue to grow, it need nutrients.
Growth of tumorous tissue that acquire nutrients through
diffusion is limited; dead inside.
Some tumors can “arrange for” the formation of blood vessels
near to or inside the tumor. (Some attract host vessel, others
create their own vasculature.)
Big Question
What are some of the mechanisms at work that allow this? How
can they be inhibited?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
36. Introduction Graph Theory Cells Community
Vascular Networks
Background: Vasculogenesis
A tumor, an abnormal growth of tissue, is bad for you.
Cancerous tumors are really bad for you.
For cancerous tissue to grow, it need nutrients.
Growth of tumorous tissue that acquire nutrients through
diffusion is limited; dead inside.
Some tumors can “arrange for” the formation of blood vessels
near to or inside the tumor. (Some attract host vessel, others
create their own vasculature.)
Big Question
What are some of the mechanisms at work that allow this? How
can they be inhibited?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
37. Introduction Graph Theory Cells Community
Vascular Networks
Background: Vasculogenesis
A tumor, an abnormal growth of tissue, is bad for you.
Cancerous tumors are really bad for you.
For cancerous tissue to grow, it need nutrients.
Growth of tumorous tissue that acquire nutrients through
diffusion is limited; dead inside.
Some tumors can “arrange for” the formation of blood vessels
near to or inside the tumor. (Some attract host vessel, others
create their own vasculature.)
Big Question
What are some of the mechanisms at work that allow this? How
can they be inhibited?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
38. Introduction Graph Theory Cells Community
Vascular Networks
Background: Vasculogenesis
A tumor, an abnormal growth of tissue, is bad for you.
Cancerous tumors are really bad for you.
For cancerous tissue to grow, it need nutrients.
Growth of tumorous tissue that acquire nutrients through
diffusion is limited; dead inside.
Some tumors can “arrange for” the formation of blood vessels
near to or inside the tumor. (Some attract host vessel, others
create their own vasculature.)
Big Question
What are some of the mechanisms at work that allow this? How
can they be inhibited?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
39. Introduction Graph Theory Cells Community
Vascular Networks
Background: Angiogenesis
Vessel formation can be good, too.
Example
Wounds heal.
Example
Blood flow reroutes when vessels are blocked (e.g., stroke).
Big Question
What are some of the mechanisms at work that allow this? How
can they be promoted?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
40. Introduction Graph Theory Cells Community
Vascular Networks
Background: Angiogenesis
Vessel formation can be good, too.
Example
Wounds heal.
Example
Blood flow reroutes when vessels are blocked (e.g., stroke).
Big Question
What are some of the mechanisms at work that allow this? How
can they be promoted?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
41. Introduction Graph Theory Cells Community
Vascular Networks
Background: Angiogenesis
Vessel formation can be good, too.
Example
Wounds heal.
Example
Blood flow reroutes when vessels are blocked (e.g., stroke).
Big Question
What are some of the mechanisms at work that allow this? How
can they be promoted?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
42. Introduction Graph Theory Cells Community
Vascular Networks
Background: Angiogenesis
Vessel formation can be good, too.
Example
Wounds heal.
Example
Blood flow reroutes when vessels are blocked (e.g., stroke).
Big Question
What are some of the mechanisms at work that allow this? How
can they be promoted?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
43. Introduction Graph Theory Cells Community
Vascular Networks
Research Project
Question
How can we effectively measure the effects of promoting or
inhibiting vasculogenic or angiogenic processes?
This is a question posed to a group of faculty and
undergraduates in 2004 by Robert Baer.
Example (Model system)
Human umbilical vein endothelial cells (HUVEC) self organize into
networks of vessels.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
44. Introduction Graph Theory Cells Community
Vascular Networks
Research Project
Question
How can we effectively measure the effects of promoting or
inhibiting vasculogenic or angiogenic processes?
This is a question posed to a group of faculty and
undergraduates in 2004 by Robert Baer.
Example (Model system)
Human umbilical vein endothelial cells (HUVEC) self organize into
networks of vessels.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
45. Introduction Graph Theory Cells Community
Vascular Networks
Research Project
Question
How can we effectively measure the effects of promoting or
inhibiting vasculogenic or angiogenic processes?
This is a question posed to a group of faculty and
undergraduates in 2004 by Robert Baer.
Example (Model system)
Human umbilical vein endothelial cells (HUVEC) self organize into
networks of vessels.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
46. Introduction Graph Theory Cells Community
Vascular Networks
Mathematical Biology Initiative, summer 2004
An NSF training grant in mathematical biology allowed this group
to take an image analytic approach to this question.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
47. Introduction Graph Theory Cells Community
Vascular Networks
Product: Vascular Network Toolkit
number of junctions
network length
network area
number of meshes
size of meshes
Computer Aided Analysis
How can we get a computer to make these measurements
effectively with a minimum of human direction?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
48. Introduction Graph Theory Cells Community
Vascular Networks
Product: Vascular Network Toolkit
number of junctions
network length
network area
number of meshes
size of meshes
Computer Aided Analysis
How can we get a computer to make these measurements
effectively with a minimum of human direction?
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
49. Introduction Graph Theory Cells Community
Vascular Networks
Product: Vascular Network Toolkit
raw image
segmented vasculature
(view 1)
medial axis
meshes
segmented vasculature
(view 2)
medial information,
nodes
medial graph
newtwork
representation
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
50. Introduction Graph Theory Cells Community
Vascular Networks
Product: Vascular Network Toolkit
raw image
segmented vasculature
(view 1)
medial axis
meshes
segmented vasculature
(view 2)
medial information,
nodes
medial graph
newtwork
representation
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
51. Introduction Graph Theory Cells Community
Vascular Networks
Product: Vascular Network Toolkit
raw image
segmented vasculature
(view 1)
medial axis
meshes
segmented vasculature
(view 2)
medial information,
nodes
medial graph
newtwork
representation
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
52. Introduction Graph Theory Cells Community
Vascular Networks
Product: Vascular Network Toolkit
raw image
segmented vasculature
(view 1)
medial axis
meshes
segmented vasculature
(view 2)
medial information,
nodes
medial graph
newtwork
representation
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
53. Introduction Graph Theory Cells Community
Vascular Networks
Product: Vascular Network Toolkit
raw image
segmented vasculature
(view 1)
medial axis
meshes
segmented vasculature
(view 2)
medial information,
nodes
medial graph
newtwork
representation
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
54. Introduction Graph Theory Cells Community
Vascular Networks
Product: Vascular Network Toolkit
raw image
segmented vasculature
(view 1)
medial axis
meshes
segmented vasculature
(view 2)
medial information,
nodes
medial graph
newtwork
representation
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
55. Introduction Graph Theory Cells Community
Vascular Networks
Product: Vascular Network Toolkit
raw image
segmented vasculature
(view 1)
medial axis
meshes
segmented vasculature
(view 2)
medial information,
nodes
medial graph
newtwork
representation
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
56. Introduction Graph Theory Cells Community
Vascular Networks
Product: Vascular Network Toolkit
raw image
segmented vasculature
(view 1)
medial axis
meshes
segmented vasculature
(view 2)
medial information,
nodes
medial graph
newtwork
representation
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
57. Introduction Graph Theory Cells Community
Research Groups
Mathematical Biology Initiative, summer 2004
At the same time in 2004, another research group was supported
by the same NSF training grant - statistical habitat suitability
model for Lesquerella filiformis (the MO Bladder-pod).
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
58. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
This small NSF supported pilot program quickly evolved into
something bigger.
Biweekly Mathematical Biology Seminar, — a life science
fashion show
Connected more research active biology faculty with more
talented mathematics faculty
Supported the evolution of faculty scholarship in math and
biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
59. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
This small NSF supported pilot program quickly evolved into
something bigger.
Biweekly Mathematical Biology Seminar, — a life science
fashion show
Connected more research active biology faculty with more
talented mathematics faculty
Supported the evolution of faculty scholarship in math and
biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
60. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
This small NSF supported pilot program quickly evolved into
something bigger.
Biweekly Mathematical Biology Seminar, — a life science
fashion show
Connected more research active biology faculty with more
talented mathematics faculty
Supported the evolution of faculty scholarship in math and
biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
61. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
This small NSF supported pilot program quickly evolved into
something bigger.
Biweekly Mathematical Biology Seminar, — a life science
fashion show
Connected more research active biology faculty with more
talented mathematics faculty
Supported the evolution of faculty scholarship in math and
biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
62. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
This small NSF supported pilot program quickly evolved into
something bigger.
Biweekly Mathematical Biology Seminar, — a life science
fashion show
Connected more research active biology faculty with more
talented mathematics faculty
Supported the evolution of faculty scholarship in math and
biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
63. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
The next NSF grant (2004) formalized this:
cross disciplinary teams working in 12 month intervals with
intensive summer term
academic year seminar
field trips
peer reviewed product – presentations (poster & oral) at
national and international conferences
sending students to interdisciplinary graduate program
courses and a future minor in mathematical biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
64. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
The next NSF grant (2004) formalized this:
cross disciplinary teams working in 12 month intervals with
intensive summer term
academic year seminar
field trips
peer reviewed product – presentations (poster & oral) at
national and international conferences
sending students to interdisciplinary graduate program
courses and a future minor in mathematical biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
65. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
The next NSF grant (2004) formalized this:
cross disciplinary teams working in 12 month intervals with
intensive summer term
academic year seminar
field trips
peer reviewed product – presentations (poster & oral) at
national and international conferences
sending students to interdisciplinary graduate program
courses and a future minor in mathematical biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
66. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
The next NSF grant (2004) formalized this:
cross disciplinary teams working in 12 month intervals with
intensive summer term
academic year seminar
field trips
peer reviewed product – presentations (poster & oral) at
national and international conferences
sending students to interdisciplinary graduate program
courses and a future minor in mathematical biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
67. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
The next NSF grant (2004) formalized this:
cross disciplinary teams working in 12 month intervals with
intensive summer term
academic year seminar
field trips
peer reviewed product – presentations (poster & oral) at
national and international conferences
sending students to interdisciplinary graduate program
courses and a future minor in mathematical biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
68. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
The next NSF grant (2004) formalized this:
cross disciplinary teams working in 12 month intervals with
intensive summer term
academic year seminar
field trips
peer reviewed product – presentations (poster & oral) at
national and international conferences
sending students to interdisciplinary graduate program
courses and a future minor in mathematical biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
69. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
The next NSF grant (2004) formalized this:
cross disciplinary teams working in 12 month intervals with
intensive summer term
academic year seminar
field trips
peer reviewed product – presentations (poster & oral) at
national and international conferences
sending students to interdisciplinary graduate program
courses and a future minor in mathematical biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
70. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
The next NSF grant (2004) formalized this:
cross disciplinary teams working in 12 month intervals with
intensive summer term
academic year seminar
field trips
peer reviewed product – presentations (poster & oral) at
national and international conferences
sending students to interdisciplinary graduate program
courses and a future minor in mathematical biology
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
71. Introduction Graph Theory Cells Community
Community
Research-focused Learning Communities in Mathematical
Biology
The next NSF grant (2004) formalized this:
cross disciplinary teams working in 12 month intervals with
intensive summer term
academic year seminar
field trips
peer reviewed product – presentations (poster & oral) at
national and international conferences
sending students to interdisciplinary graduate program
courses and a future minor in mathematical biology
Currently, over 9 biology faculty, 10 math & cs faculty, and 3 other
faculty are actively involved in this community.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
72. Introduction Graph Theory Cells Community
Community
Inter-STEM Research community
At the same time, a proposal went into the NSF to use
undergraduate research as a way to
expand the STEM talent pool through high-quality
undergraduate research experiences
bring together research faculty in all STEM areas into a single
summer community
foster faculty scholarship
Community
Together, the Next STEP and MathBio programs have
dramatically increased the connections between faculty and
students of different disciplines.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
73. Introduction Graph Theory Cells Community
Community
Inter-STEM Research community
At the same time, a proposal went into the NSF to use
undergraduate research as a way to
expand the STEM talent pool through high-quality
undergraduate research experiences
bring together research faculty in all STEM areas into a single
summer community
foster faculty scholarship
Community
Together, the Next STEP and MathBio programs have
dramatically increased the connections between faculty and
students of different disciplines.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
74. Introduction Graph Theory Cells Community
Community
Inter-STEM Research community
At the same time, a proposal went into the NSF to use
undergraduate research as a way to
expand the STEM talent pool through high-quality
undergraduate research experiences
bring together research faculty in all STEM areas into a single
summer community
foster faculty scholarship
Community
Together, the Next STEP and MathBio programs have
dramatically increased the connections between faculty and
students of different disciplines.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
75. Introduction Graph Theory Cells Community
Community
Inter-STEM Research community
At the same time, a proposal went into the NSF to use
undergraduate research as a way to
expand the STEM talent pool through high-quality
undergraduate research experiences
bring together research faculty in all STEM areas into a single
summer community
foster faculty scholarship
Community
Together, the Next STEP and MathBio programs have
dramatically increased the connections between faculty and
students of different disciplines.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
76. Introduction Graph Theory Cells Community
Community
Inter-STEM Research community
At the same time, a proposal went into the NSF to use
undergraduate research as a way to
expand the STEM talent pool through high-quality
undergraduate research experiences
bring together research faculty in all STEM areas into a single
summer community
foster faculty scholarship
This is Truman’s “The Next STEP” program.
Community
Together, the Next STEP and MathBio programs have
dramatically increased the connections between faculty and
students of different disciplines.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
77. Introduction Graph Theory Cells Community
Community
Inter-STEM Research community
At the same time, a proposal went into the NSF to use
undergraduate research as a way to
expand the STEM talent pool through high-quality
undergraduate research experiences
bring together research faculty in all STEM areas into a single
summer community
foster faculty scholarship
This is Truman’s “The Next STEP” program.
Community
Together, the Next STEP and MathBio programs have
dramatically increased the connections between faculty and
students of different disciplines.
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
78. Introduction Graph Theory Cells Community
Community
Challenges
Sustainability
Conversion of student collaborations to peer reviewed work
Supporting continued faculty scholarship and research
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
79. Introduction Graph Theory Cells Community
Community
Challenges
Sustainability
Conversion of student collaborations to peer reviewed work
Supporting continued faculty scholarship and research
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
80. Introduction Graph Theory Cells Community
Community
Challenges
Sustainability
Conversion of student collaborations to peer reviewed work
Supporting continued faculty scholarship and research
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
81. Introduction Graph Theory Cells Community
Community
Acknowledgements
Truman administrative leaders who support this work and are
helping us look for solutions to the challenges
Truman STEM colleagues who have embraced this effort, and
joyfully made connections with others outside their disciplines
Rob Baer and Jim Rhoades
the hundreds of students whose raw talent and enthusiasm for
learning make all this work a joy
Jennifer Thompson, our Program Coodinator
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
82. Introduction Graph Theory Cells Community
Community
Acknowledgements
Truman administrative leaders who support this work and are
helping us look for solutions to the challenges
Truman STEM colleagues who have embraced this effort, and
joyfully made connections with others outside their disciplines
Rob Baer and Jim Rhoades
the hundreds of students whose raw talent and enthusiasm for
learning make all this work a joy
Jennifer Thompson, our Program Coodinator
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
83. Introduction Graph Theory Cells Community
Community
Acknowledgements
Truman administrative leaders who support this work and are
helping us look for solutions to the challenges
Truman STEM colleagues who have embraced this effort, and
joyfully made connections with others outside their disciplines
Rob Baer and Jim Rhoades
the hundreds of students whose raw talent and enthusiasm for
learning make all this work a joy
Jennifer Thompson, our Program Coodinator
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
84. Introduction Graph Theory Cells Community
Community
Acknowledgements
Truman administrative leaders who support this work and are
helping us look for solutions to the challenges
Truman STEM colleagues who have embraced this effort, and
joyfully made connections with others outside their disciplines
Rob Baer and Jim Rhoades
the hundreds of students whose raw talent and enthusiasm for
learning make all this work a joy
Jennifer Thompson, our Program Coodinator
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness
85. Introduction Graph Theory Cells Community
Community
Acknowledgements
Truman administrative leaders who support this work and are
helping us look for solutions to the challenges
Truman STEM colleagues who have embraced this effort, and
joyfully made connections with others outside their disciplines
Rob Baer and Jim Rhoades
the hundreds of students whose raw talent and enthusiasm for
learning make all this work a joy
Jennifer Thompson, our Program Coodinator
J. Miller Department of Mathematics Truman State University
Connectedness As A Measure of Robustness