1. The document discusses path compression, a technique used in disjoint set data structures that improves the running time of find operations from logarithmic to almost constant.
2. It explains how path compression works by redirecting parent pointers during find operations so that future finds take direct paths to the root.
3. The document also discusses some applications of set theory in mathematics like defining mathematical structures and relations, and serving as a foundation for other areas of math. Transferring files between computers on a network using disjoint sets is provided as an example algorithm.
In this paper, we deals about exact double domination in graphs. In a graph a vertex is said to dominate itself and all its neighbours. A double dominating set is exact if every vertex of G is dominated exactly twice. If a double dominating set exist then all such sets have the same size and bounds on this size. We established a necessary and sufficient condition of exact double dominating set in a connected cubic graph with application.
In this paper, we deals about exact double domination in graphs. In a graph a vertex is said to dominate itself and all its neighbours. A double dominating set is exact if every vertex of G is dominated exactly twice. If a double dominating set exist then all such sets have the same size and bounds on this size. We established a necessary and sufficient condition of exact double dominating set in a connected cubic graph with application.
A NEW PARALLEL ALGORITHM FOR COMPUTING MINIMUM SPANNING TREEijscmc
Computing the minimum spanning tree of the graph is one of the fundamental computational problems. In
this paper, we present a new parallel algorithm for computing the minimum spanning tree of an undirected
weighted graph with n vertices and m edges. This algorithm uses the cluster techniques to reduce the
number of processors by fraction 1/f (n) and the parallel work by the fraction O ( 1 lo g ( f ( n )) ),where f (n) is an
arbitrary function. In the case f (n) =1, the algorithm runs in logarithmic-time and use super linear work on
EREWPRAM model. In general, the proposed algorithm is the simplest one.
Minimality and Equicontinuity of a Sequence of Maps in Iterative Wayinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
The class of affine array access, where each array index is expressed as affine expressions of loop indexes and symbolic constants.
1.Affine Accesses
2.Affine and Nonaffine Accesses in Practice
3.Exercises for Section 11.4
Discovering Novel Information with sentence Level clustering From Multi-docu...irjes
Specific objective to discover some novel information from a set of documents initially retrieved in response to some query. Clustering sentences level text, effective use and update is still an open research issue, especially in domain of text mining. Since most existing system uses pattern belong to a single cluster. But here we can use patterns belongs to all cluster with different degree of membership. Since sentences of those documents we would expect at least one of the clusters to be closely related to the concepts described by the query term. This paper presents a Novel Fuzzy Clustering Algorithm that operates on relational input data (i.e. data in the form of square matrix of pair wise similarities between data objects).
word2vec, node2vec, graph2vec, X2vec: Towards a Theory of Vector Embeddings o...Subhajit Sahu
Below are the important points I note from the 2020 paper by Martin Grohe:
- 1-WL distinguishes almost all graphs, in a probabilistic sense
- Classical WL is two dimensional Weisfeiler-Leman
- DeepWL is an unlimited version of WL graph that runs in polynomial time.
- Knowledge graphs are essentially graphs with vertex/edge attributes
ABSTRACT:
Vector representations of graphs and relational structures, whether handcrafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures. A wide range of methods for generating such embeddings have been studied in the machine learning and knowledge representation literature. However, vector embeddings have received relatively little attention from a theoretical point of view.
Starting with a survey of embedding techniques that have been used in practice, in this paper we propose two theoretical approaches that we see as central for understanding the foundations of vector embeddings. We draw connections between the various approaches and suggest directions for future research.
A NEW PARALLEL ALGORITHM FOR COMPUTING MINIMUM SPANNING TREEijscmc
Computing the minimum spanning tree of the graph is one of the fundamental computational problems. In
this paper, we present a new parallel algorithm for computing the minimum spanning tree of an undirected
weighted graph with n vertices and m edges. This algorithm uses the cluster techniques to reduce the
number of processors by fraction 1/f (n) and the parallel work by the fraction O ( 1 lo g ( f ( n )) ),where f (n) is an
arbitrary function. In the case f (n) =1, the algorithm runs in logarithmic-time and use super linear work on
EREWPRAM model. In general, the proposed algorithm is the simplest one.
Minimality and Equicontinuity of a Sequence of Maps in Iterative Wayinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
The class of affine array access, where each array index is expressed as affine expressions of loop indexes and symbolic constants.
1.Affine Accesses
2.Affine and Nonaffine Accesses in Practice
3.Exercises for Section 11.4
Discovering Novel Information with sentence Level clustering From Multi-docu...irjes
Specific objective to discover some novel information from a set of documents initially retrieved in response to some query. Clustering sentences level text, effective use and update is still an open research issue, especially in domain of text mining. Since most existing system uses pattern belong to a single cluster. But here we can use patterns belongs to all cluster with different degree of membership. Since sentences of those documents we would expect at least one of the clusters to be closely related to the concepts described by the query term. This paper presents a Novel Fuzzy Clustering Algorithm that operates on relational input data (i.e. data in the form of square matrix of pair wise similarities between data objects).
word2vec, node2vec, graph2vec, X2vec: Towards a Theory of Vector Embeddings o...Subhajit Sahu
Below are the important points I note from the 2020 paper by Martin Grohe:
- 1-WL distinguishes almost all graphs, in a probabilistic sense
- Classical WL is two dimensional Weisfeiler-Leman
- DeepWL is an unlimited version of WL graph that runs in polynomial time.
- Knowledge graphs are essentially graphs with vertex/edge attributes
ABSTRACT:
Vector representations of graphs and relational structures, whether handcrafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures. A wide range of methods for generating such embeddings have been studied in the machine learning and knowledge representation literature. However, vector embeddings have received relatively little attention from a theoretical point of view.
Starting with a survey of embedding techniques that have been used in practice, in this paper we propose two theoretical approaches that we see as central for understanding the foundations of vector embeddings. We draw connections between the various approaches and suggest directions for future research.
Neural Model-Applying Network (Neuman): A New Basis for Computational Cognitionaciijournal
NeuMAN represents a new model for computational cognition synthesizing important results across AI, psychology, and neuroscience. NeuMAN is based on three important ideas: (1) neural mechanisms perform all requirements for intelligence without symbolic reasoning on finite sets, thus avoiding exponential matching algorithms; (2) the network reinforces hierarchical abstraction and composition for sensing and acting; and (3) the network uses learned sequences within contextual frames to make predictions, minimize reactions to expected events, and increase responsiveness to high-value information. These systems exhibit both automatic and deliberate processes. NeuMAN accords with a wide variety of findings in neural and cognitive science and will supersede symbolic reasoning as a foundation for AI and as a model of human intelligence. It will likely become the principal mechanism for engineering intelligent systems.
NEURAL MODEL-APPLYING NETWORK (NEUMAN): A NEW BASIS FOR COMPUTATIONAL COGNITIONaciijournal
NeuMAN represents a new model for computational cognition synthesizing important results across AI,
psychology, and neuroscience. NeuMAN is based on three important ideas: (1) neural mechanisms perform
all requirements for intelligence without symbolic reasoning on finite sets, thus avoiding exponential
matching algorithms; (2) the network reinforces hierarchical abstraction and composition for sensing and
acting; and (3) the network uses learned sequences within contextual frames to make predictions, minimize
reactions to expected events, and increase responsiveness to high-value information. These systems exhibit
both automatic and deliberate processes. NeuMAN accords with a wide variety of findings in neural and
cognitive science and will supersede symbolic reasoning as a foundation for AI and as a model of human
intelligence. It will likely become the principal mechanism for engineering intelligent systems.
Accelerating materials property predictions using machine learningGhanshyam Pilania
The materials discovery process can be significantly expedited and simplified if we can learn effectively from available knowledge and data. In the present contribution, we show that efficient and accurate prediction of a diverse set of properties of material systems is possible by employing machine (or statistical) learning
methods trained on quantum mechanical computations in combination with the notions of chemical similarity. Using a family of one-dimensional chain systems, we present a general formalism that allows us to discover decision rules that establish a mapping between easily accessible attributes of a system and its properties. It is shown that fingerprints based on either chemo-structural (compositional and configurational information) or the electronic charge density distribution can be used to make ultra-fast, yet accurate, property predictions. Harnessing such learning paradigms extends recent efforts to systematically explore and mine vast chemical spaces, and can significantly accelerate the discovery of new application-specific materials.
Mathematical Model of Affinity Predictive Model for Multi-Class Predictioninventionjournals
The notion of affinity which is one of the predictive models can bedefined as the distance or closeness between two objects.Unlike the fuzzy Set and Rough Set, the affinity can deal with third objects and deals with time dimension. In addition, it could deal with entities or abstract side by side with real objects. However, the existing model of affinity is developed for binary classification or prediction. In this paper, Affinity Predictive Modelhas been proposed in order to provide a multi-classprediction. This developed method can be used in many applications when multi-classpredictions are needed.
The dynamics of networks enables the function of a variety of systems we rely on every day, from gene regulation and metabolism in the cell to the distribution of electric power and communication of information. Understanding, steering and predicting the function of interacting nonlinear dynamical systems, in particular if they are externally driven out of equilibrium, relies on obtaining and evaluating suitable models, posing at least two major challenges. First, how can we extract key structural system features of networks if only time series data provide information about the dynamics of (some) units? Second, how can we characterize nonlinear responses of nonlinear multi-dimensional systems externally driven by fluctuations, and consequently, predict tipping points at which normal operational states may be lost? Here we report recent progress on nonlinear response theory extended to predict tipping points and on model-free inference of network structural features from observed dynamics.
Hierarchical topics in texts generated by a streamkevig
We observe a stream of text messages, generated by Twitter or by a text file
and present a tool which constructs a dynamic list of topics. Each tweet generates edges of
a graph where the nodes are the tags and edges link the author of the tweet with the tags
present in the tweet. We consider the large clusters of the graph and approximate the stream
of edges with a Reservoir sampling. We study the giant components of the Reservoir and each
large component represents a topic. The nodes of high degree and their edges provide the
first layer of a topic, and the iteration over the nodes provide a hierarchical decomposition.
For a standard text, we use a Weighted Reservoir sampling where the weight is the similarity
between words given by Word2vec. We consider dynamic overlapping windows and provide
the topicalization on each window. We compare this approach with the Word2content and LDA techniques in the case of a standard text, viewed as a stream.
Hierarchical topics in texts generated by a streamkevig
We observe a stream of text messages, generated by Twitter or by a text file
and present a tool which constructs a dynamic list of topics. Each tweet generates edges of
a graph where the nodes are the tags and edges link the author of the tweet with the tags
present in the tweet. We consider the large clusters of the graph and approximate the stream
of edges with a Reservoir sampling. We study the giant components of the Reservoir and each
large component represents a topic. The nodes of high degree and their edges provide the
first layer of a topic, and the iteration over the nodes provide a hierarchical decomposition.
For a standard text, we use a Weighted Reservoir sampling where the weight is the similarity
between words given by Word2vec. We consider dynamic overlapping windows and provide
the topicalization on each window. We compare this approach with the Word2content and
LDA techniques in the case of a standard text, viewed as a stream.
Applied Mathematics and Sciences: An International Journal (MathSJ)mathsjournal
The main goal of this research is to give the complete conception about numerical integration including
Newton-Cotes formulas and aimed at comparing the rate of performance or the rate of accuracy of
Trapezoidal, Simpson’s 1/3, and Simpson’s 3/8. To verify the accuracy, we compare each rules
demonstrating the smallest error values among them. The software package MATLAB R2013a is applied to
determine the best method, as well as the results, are compared. It includes graphical comparisons
mentioning these methods graphically. After all, it is then emphasized that the among methods considered,
Simpson’s 1/3 is more effective and accurate when the condition of the subdivision is only even for solving
a definite integral.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
2. Data structure
1.Path Compression:
Using unthreaded tress, Find takes logarithmic time
and everything else is constant;
Threaded trees, Union takes logarithmic amortized
time and everything else is constant.
A third method allows us to get both of these
operations to have almost constant running time.
We start with the original unthreaded tree
representation, where every object points to a parent.
3. The key observation is that in any Find operation,
once we determine the leader of an object x, we can
speed up future Finds by redirecting x ’ s parent
pointer directly to that leader.
The effect of path compression after find(7) on the
above worst-case tree .
Worst –case tree for N=8
1
2
5
3
4
6
7
8
4. ROUTINE FOR DISJOINT SET FIND WITH PATH
COMPRESSION:
Set Type Find(Element type X , Disjoint S)
{
If(S[X]<=0)
return x:
else
return S[X]=Find(S[X],S)
}
Path compression is a trivial change to the basic find
algorithm. The only change to the find routine is that S[X]
is made equal to the value returned by find , thus after the
root of the set is found recursively , X is made to point
directly to it.
5. •s It has been proven that when path compression is
done , a sequence of M operations required at most
O(M log N) time.
• path compression is perfectly compatible with union
by size. It executes a sequence of M operations in line
time.
•Path compression is not entirely compatible with
union-by size. It executes a sequence of M operations
in line time.
•Path compression is not entirely compatible with
union-by-height , because path compression can
change the heights of the trees.
6. APPLICATION OF SET
Many mathematical concepts can be defined
precisely using only set theoretic concepts. For
example, mathematical structures as diverse
as graphs, manifolds, rings, and vector spaces
can all be defined as sets satisfying various
(axiomatic) properties.
Equivalence and order relations are ubiquitous
in mathematics, and the theory of
mathematical relations can be described in set
theory.
7. Set theory is also a promising foundational system
for much of mathematics. Since the publication of
the first volume of Principia Mathematical,
It has been claimed that most or even all
mathematical theorems can be derived using an
aptly designed set of axioms for set theory,
augmented with many definitions, using first
or second order logic.
For example, properties of the natural and real
numbers can be derived within set theory, as each
number system can be identified with a set
of equivalence classes under a suitable equivalence
relation whose field is some infinite set.
8. Set theory as a foundation for mathematical
analysis, topology, abstract algebra, and discrete
mathematics is likewise uncontroversial;
mathematicians accept that (in principle)
theorems in these areas can be derived from the
relevant definitions and the axioms of set theory.
Few full derivations of complex mathematical
theorems from set theory have been formally
verified, however, because such formal derivations
are often much longer than the natural language
proofs mathematicians commonly present. c
9. One verification project, Met math, includes
human-written, computer‐verified derivations of
more than 12,000 theorems starting from ZFC set
theory, first order logic and propositional logic.
An algorithms to transfer file from any computer
on the network to any other In on-line uses set
concept. The following steps are performed to do
this task,
Initially put every computer in its own test.
10. our invariant is that two computers
can transfer files is an only is they are
in the same set.
the ability to transfer files forms an
equivalence relation.
then connections are read one at a
time say(u , v) and it is tested to see
whether u and v are in the same set
or in different sets.
11. if they are in the same set, nothing is done else
merge there sets.
At the end of the algorithm, the graph is
connected is and only if there is exactly one set.
If there are M connections and N computers, the
space requirements is O(N). Using union-by-size
and path compression , worst-case running time
of O(M &(M,N)) is obtained.
10 10 55 10 10
5
W RE