The document discusses mathematical models for analyzing the spread of infectious diseases and their application to problems related to bioterrorism defense and disease control. It describes models representing disease spread through social networks and thresholds for infection. Different vaccination strategies are analyzed and compared using these models on simple graphs. Discrete mathematics tools like threshold processes, independent sets, and conversion sets are introduced for modeling disease spread and determining optimal vaccination strategies.
Parallel Programming Approaches for an Agent-based Simulation of Concurrent P...Subhajit Sahu
Highlighted notes while preparing for project on Computational Epidemics:
Parallel Programming Approaches for an Agent-based Simulation of Concurrent Pandemic and Seasonal Influenza Outbreaks
Milton Soto-Ferraria
Peter Holvenstot
Diana Prietoa
Elise de Doncker
John Kapenga
2013 International Conference on Computational Science
Procedia Computer Science 18 ( 2013 ) 2187 – 2192
In this paper we propose parallelized versions of an agent-based simulation for concurrent pandemic and seasonal influenza outbreaks. The objective of the implementations is to significantly reduce the replication time and allow faster evaluation of mitigation strategies during an ongoing emergency. The simulation was initially parallelized using the g++ OpenMP library. We simulated the outbreak in a population of 1,000,000 individuals to evaluate algorithm performance and results. In addition to the OpenMP parallelization, a proposed CUDA implementation is also presented.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Parallel Programming Approaches for an Agent-based Simulation of Concurrent P...Subhajit Sahu
Highlighted notes while preparing for project on Computational Epidemics:
Parallel Programming Approaches for an Agent-based Simulation of Concurrent Pandemic and Seasonal Influenza Outbreaks
Milton Soto-Ferraria
Peter Holvenstot
Diana Prietoa
Elise de Doncker
John Kapenga
2013 International Conference on Computational Science
Procedia Computer Science 18 ( 2013 ) 2187 – 2192
In this paper we propose parallelized versions of an agent-based simulation for concurrent pandemic and seasonal influenza outbreaks. The objective of the implementations is to significantly reduce the replication time and allow faster evaluation of mitigation strategies during an ongoing emergency. The simulation was initially parallelized using the g++ OpenMP library. We simulated the outbreak in a population of 1,000,000 individuals to evaluate algorithm performance and results. In addition to the OpenMP parallelization, a proposed CUDA implementation is also presented.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
A COMPUTER VIRUS PROPAGATION MODEL USING DELAY DIFFERENTIAL EQUATIONS WITH PR...IJCNCJournal
The SIR model is used extensively in the field of epidemiology, in particular, for the analysis of communal
diseases. One problem with SIR and other existing models is that they are tailored to random or Erdos type networks since they do not consider the varying probabilities of infection or immunity per node. In this paper, we present the application and the simulation results of the pSEIRS model that takes into account the probabilities, and is thus suitable for more realistic scale free networks. In the pSEIRS model, the death rate and the excess death rate are constant for infective nodes. Latent and immune periods are assumed to be constant and the infection rate is assumed to be proportional to I (t) N(t) , where N (t) is the size of the total population and I(t) is the size of the infected population. A node recovers from an infection
temporarily with a probability p and dies from the infection with probability (1-p).
ICON experts give an in-depth overview of infectious disease modeling with a focus on assessment of interventions and its challenges.
The nature of communicable diseases results in unique epidemiological characteristics that must be accounted for when considering the epidemiological, clinical, and economic consequences of interventions that modify transmission. These interventions clearly include vaccines, but also drug treatments that may reduce the duration of infectiousness.
This webinar outlines the unique epidemiological characteristics of communicable diseases and demonstrates how correctly accounting for these in clinical and economic assessments of interventions can capture the full value of these interventions. Some of the challenges faced when performing these analyses are also addressed.
Key Topics Include:
- Understanding infectious disease modeling
- Why infectious disease modeling is needed
- Challenges associated with infectious disease modeling
I appreciate any answer. Thank you. For each of the following descri.pdfamiteksecurity
I appreciate any answer. Thank you. For each of the following description!) formulate a
mathematical model as a system of differential equations. In each case give a suitable
compartment diagram and define any parameters or symbols that you introduce that were not
mentioned as part of the question. Consider a model for the spread of a disease where lifelong
immunity is attained after catching the disease. The susceptibles are continuously vaccinated at a
per-capita rate mu against the disease. Develop differential equations for the number of
susceptibles S(t). the number of infectives I(t). the number vaccinated V(t) and the number
recovered. R(t). assuming all who recovered from the infection become immune for life. The
infectious disease Dengue fever is spread by infected mosquitoes that transmit the disease to
humans when they bite susceptible humans. Similarly, when a susceptible mosquito bites an
infected human the mosquito becomes infected Assume that humans cannot directly infect other
humans nor infected mosquitoes infect other mosquitoes. Let Sm(t) and Im(t) denote the number
of susceptible and infected mosquitoes respectively and let S h(t) and I h(t) denote the member of
susceptible and infected humans. Assume that there are no birth or deaths of humans over the
time-scale of interest but that there is a per-capita birth-rate of mosquitoes 6 and per-capita death
rate of mosquitoes of a. Also, assume that humans are infected for a period of gamma-1 and then
recover with immunity. Mosquitoes do not recover. (Note: typically gamma-1 is about. 2 weeks
for dengue fever).
Solution
The number of Vaccinated people (V(t)) is a simple one.
dV/dt = mu * S(t), where S(t) is the number of susceptable people.
A certain percentage of the people who need to be vaccinated are vaccinated every year, and this
will slow down as less people need to be vaccinated.
Susceptable people are decreasing over time, once you have been vaccinated, become sick, or
recover you are set for life.
S(t) = 1 - V(t) - R(t) - I(t)
The growth of the infective population depends on how infective the disease is, but it is also
dependant on how many people can be infected still. Let\'s say every infective person infects
beta percent of other vulnerable people, and they recover x days later.
dI/dt = [beta * I(t) * S(t)] - I(t-x)
The number of recovered people will follow the number of infective people but unlike infective
people they remain recovered
dR/dt = I(t-x)
All of these equations use a total population size of one, you are modelling the percentage of the
population that has fallen under these conditions. Eventually, the equations should reach these
final end conditions when t = infinity:
S(t) = 0, V(t) + R(t) = 1, and I(t) = 0.
Part two is just using these equations and applying them..
The COVID-19 pandemic is an urgent call for rethinking our collective social-ecological and socio-technical systems. In this free webinar, I speak about how the framework of Mindfulness Engineering can provide answer to some of the current challenges that the coronavirus have imposed on global systems
The Susceptible-Infectious Model of Disease Expansion Analyzed Under the Scop...cscpconf
This paper presents a model to approach the dynamics of infectious diseases expansion. Our
model aims to establish a link between traditional simulation of the Susceptible-Infectious (SI)
model of disease expansion based on ordinary differential equations (ODE), and a very simple
approach based on both connectivity between people and elementary binary rules that define
the result of these contacts. The SI deterministic compartmental model has been analysed and
successfully modelled by our method, in the case of 4-connected neighbourhood.
THE SUSCEPTIBLE-INFECTIOUS MODEL OF DISEASE EXPANSION ANALYZED UNDER THE SCOP...csandit
This paper presents a model to approach the dynamics of infectious diseases expansion. Our model aims to establish a link between traditional simulation of the Susceptible-Infectious (SI) model of disease expansion based on ordinary differential equations (ODE), and a very simple approach based on both connectivity between people and elementary binary rules that define the result of these contacts. The SI deterministic compartmental model has been analysed and successfully modelled by our method, in the case of 4-connected neighbourhood.
Presentazione per il sesto WebMeetup del Machine Learning / Data Science Meetup Roma: https://www.meetup.com/it-IT/Machine-Learning-Data-Science-Meetup/events/273089965/
Interval observer for uncertain time-varying SIR-SI model of vector-borne dis...FGV Brazil
The issue of state estimation is considered for an SIR-SI model describing a vector-borne disease such as dengue fever, with seasonal variations and uncertainties in the transmission rates. Assuming continuous measurement of the number of new infectives in the host population per unit time, a class of interval observers with estimate-dependent gain is constructed, and asymptotic error bounds are provided. The synthesis method is based on the search for a common linear Lyapunov function for monotone systems representing the evolution of the estimation errors.
Date: 2017
Authors:
Soledad Aronna, Maria
Bliman, Pierre-Alexandre
This presentation takes you through the basic components of an SIR model and the in the context of COVID-19. I shall also discuss incorporation of healthcare workers in the model
Dynamics and Control of Infectious Diseases (2007) - Alexander Glaser Wouter de Heij
See also:
- https://food4innovations.blog/2020/03/26/montecarlo-simulaties-tonen-aan-wat-de-onzekerheid-is-en-dat-we-minimaal-1600-maar-misschien-wel-2000-2500-ic-plaatsen-nodig-hebben/
A COMPUTER VIRUS PROPAGATION MODEL USING DELAY DIFFERENTIAL EQUATIONS WITH PR...IJCNCJournal
The SIR model is used extensively in the field of epidemiology, in particular, for the analysis of communal
diseases. One problem with SIR and other existing models is that they are tailored to random or Erdos type networks since they do not consider the varying probabilities of infection or immunity per node. In this paper, we present the application and the simulation results of the pSEIRS model that takes into account the probabilities, and is thus suitable for more realistic scale free networks. In the pSEIRS model, the death rate and the excess death rate are constant for infective nodes. Latent and immune periods are assumed to be constant and the infection rate is assumed to be proportional to I (t) N(t) , where N (t) is the size of the total population and I(t) is the size of the infected population. A node recovers from an infection
temporarily with a probability p and dies from the infection with probability (1-p).
ICON experts give an in-depth overview of infectious disease modeling with a focus on assessment of interventions and its challenges.
The nature of communicable diseases results in unique epidemiological characteristics that must be accounted for when considering the epidemiological, clinical, and economic consequences of interventions that modify transmission. These interventions clearly include vaccines, but also drug treatments that may reduce the duration of infectiousness.
This webinar outlines the unique epidemiological characteristics of communicable diseases and demonstrates how correctly accounting for these in clinical and economic assessments of interventions can capture the full value of these interventions. Some of the challenges faced when performing these analyses are also addressed.
Key Topics Include:
- Understanding infectious disease modeling
- Why infectious disease modeling is needed
- Challenges associated with infectious disease modeling
I appreciate any answer. Thank you. For each of the following descri.pdfamiteksecurity
I appreciate any answer. Thank you. For each of the following description!) formulate a
mathematical model as a system of differential equations. In each case give a suitable
compartment diagram and define any parameters or symbols that you introduce that were not
mentioned as part of the question. Consider a model for the spread of a disease where lifelong
immunity is attained after catching the disease. The susceptibles are continuously vaccinated at a
per-capita rate mu against the disease. Develop differential equations for the number of
susceptibles S(t). the number of infectives I(t). the number vaccinated V(t) and the number
recovered. R(t). assuming all who recovered from the infection become immune for life. The
infectious disease Dengue fever is spread by infected mosquitoes that transmit the disease to
humans when they bite susceptible humans. Similarly, when a susceptible mosquito bites an
infected human the mosquito becomes infected Assume that humans cannot directly infect other
humans nor infected mosquitoes infect other mosquitoes. Let Sm(t) and Im(t) denote the number
of susceptible and infected mosquitoes respectively and let S h(t) and I h(t) denote the member of
susceptible and infected humans. Assume that there are no birth or deaths of humans over the
time-scale of interest but that there is a per-capita birth-rate of mosquitoes 6 and per-capita death
rate of mosquitoes of a. Also, assume that humans are infected for a period of gamma-1 and then
recover with immunity. Mosquitoes do not recover. (Note: typically gamma-1 is about. 2 weeks
for dengue fever).
Solution
The number of Vaccinated people (V(t)) is a simple one.
dV/dt = mu * S(t), where S(t) is the number of susceptable people.
A certain percentage of the people who need to be vaccinated are vaccinated every year, and this
will slow down as less people need to be vaccinated.
Susceptable people are decreasing over time, once you have been vaccinated, become sick, or
recover you are set for life.
S(t) = 1 - V(t) - R(t) - I(t)
The growth of the infective population depends on how infective the disease is, but it is also
dependant on how many people can be infected still. Let\'s say every infective person infects
beta percent of other vulnerable people, and they recover x days later.
dI/dt = [beta * I(t) * S(t)] - I(t-x)
The number of recovered people will follow the number of infective people but unlike infective
people they remain recovered
dR/dt = I(t-x)
All of these equations use a total population size of one, you are modelling the percentage of the
population that has fallen under these conditions. Eventually, the equations should reach these
final end conditions when t = infinity:
S(t) = 0, V(t) + R(t) = 1, and I(t) = 0.
Part two is just using these equations and applying them..
The COVID-19 pandemic is an urgent call for rethinking our collective social-ecological and socio-technical systems. In this free webinar, I speak about how the framework of Mindfulness Engineering can provide answer to some of the current challenges that the coronavirus have imposed on global systems
The Susceptible-Infectious Model of Disease Expansion Analyzed Under the Scop...cscpconf
This paper presents a model to approach the dynamics of infectious diseases expansion. Our
model aims to establish a link between traditional simulation of the Susceptible-Infectious (SI)
model of disease expansion based on ordinary differential equations (ODE), and a very simple
approach based on both connectivity between people and elementary binary rules that define
the result of these contacts. The SI deterministic compartmental model has been analysed and
successfully modelled by our method, in the case of 4-connected neighbourhood.
THE SUSCEPTIBLE-INFECTIOUS MODEL OF DISEASE EXPANSION ANALYZED UNDER THE SCOP...csandit
This paper presents a model to approach the dynamics of infectious diseases expansion. Our model aims to establish a link between traditional simulation of the Susceptible-Infectious (SI) model of disease expansion based on ordinary differential equations (ODE), and a very simple approach based on both connectivity between people and elementary binary rules that define the result of these contacts. The SI deterministic compartmental model has been analysed and successfully modelled by our method, in the case of 4-connected neighbourhood.
Presentazione per il sesto WebMeetup del Machine Learning / Data Science Meetup Roma: https://www.meetup.com/it-IT/Machine-Learning-Data-Science-Meetup/events/273089965/
Interval observer for uncertain time-varying SIR-SI model of vector-borne dis...FGV Brazil
The issue of state estimation is considered for an SIR-SI model describing a vector-borne disease such as dengue fever, with seasonal variations and uncertainties in the transmission rates. Assuming continuous measurement of the number of new infectives in the host population per unit time, a class of interval observers with estimate-dependent gain is constructed, and asymptotic error bounds are provided. The synthesis method is based on the search for a common linear Lyapunov function for monotone systems representing the evolution of the estimation errors.
Date: 2017
Authors:
Soledad Aronna, Maria
Bliman, Pierre-Alexandre
This presentation takes you through the basic components of an SIR model and the in the context of COVID-19. I shall also discuss incorporation of healthcare workers in the model
Dynamics and Control of Infectious Diseases (2007) - Alexander Glaser Wouter de Heij
See also:
- https://food4innovations.blog/2020/03/26/montecarlo-simulaties-tonen-aan-wat-de-onzekerheid-is-en-dat-we-minimaal-1600-maar-misschien-wel-2000-2500-ic-plaatsen-nodig-hebben/
Similar to GraphDiseaseSpreadModels-Threshold&FirefighterCapeTown6-10-07 (20)
A tale of scale & speed: How the US Navy is enabling software delivery from l...sonjaschweigert1
Rapid and secure feature delivery is a goal across every application team and every branch of the DoD. The Navy’s DevSecOps platform, Party Barge, has achieved:
- Reduction in onboarding time from 5 weeks to 1 day
- Improved developer experience and productivity through actionable findings and reduction of false positives
- Maintenance of superior security standards and inherent policy enforcement with Authorization to Operate (ATO)
Development teams can ship efficiently and ensure applications are cyber ready for Navy Authorizing Officials (AOs). In this webinar, Sigma Defense and Anchore will give attendees a look behind the scenes and demo secure pipeline automation and security artifacts that speed up application ATO and time to production.
We will cover:
- How to remove silos in DevSecOps
- How to build efficient development pipeline roles and component templates
- How to deliver security artifacts that matter for ATO’s (SBOMs, vulnerability reports, and policy evidence)
- How to streamline operations with automated policy checks on container images
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
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!
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Climate Impact of Software Testing at Nordic Testing DaysKari Kakkonen
My slides at Nordic Testing Days 6.6.2024
Climate impact / sustainability of software testing discussed on the talk. ICT and testing must carry their part of global responsibility to help with the climat warming. We can minimize the carbon footprint but we can also have a carbon handprint, a positive impact on the climate. Quality characteristics can be added with sustainability, and then measured continuously. Test environments can be used less, and in smaller scale and on demand. Test techniques can be used in optimizing or minimizing number of tests. Test automation can be used to speed up testing.
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The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
zkStudyClub - Reef: Fast Succinct Non-Interactive Zero-Knowledge Regex ProofsAlex Pruden
This paper presents Reef, a system for generating publicly verifiable succinct non-interactive zero-knowledge proofs that a committed document matches or does not match a regular expression. We describe applications such as proving the strength of passwords, the provenance of email despite redactions, the validity of oblivious DNS queries, and the existence of mutations in DNA. Reef supports the Perl Compatible Regular Expression syntax, including wildcards, alternation, ranges, capture groups, Kleene star, negations, and lookarounds. Reef introduces a new type of automata, Skipping Alternating Finite Automata (SAFA), that skips irrelevant parts of a document when producing proofs without undermining soundness, and instantiates SAFA with a lookup argument. Our experimental evaluation confirms that Reef can generate proofs for documents with 32M characters; the proofs are small and cheap to verify (under a second).
Paper: https://eprint.iacr.org/2023/1886
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
3. Mathematical Models of Disease Spread Mathematical models of infectious diseases go back to Daniel Bernoulli’s mathematical analysis of smallpox in 1760.
4. Understanding infectious systems requires being able to reason about highly complex biological systems, with hundreds of demographic and epidemiological variables . Intuition alone is insufficient to fully understand the dynamics of such systems. smallpox
5. Experimentation or field trials are often prohibitively expensive or unethical and do not always lead to fundamental understanding. Therefore, mathematical modeling becomes an important experimental and analytical tool.
6. Mathematical models have become important tools in analyzing the spread and control of infectious diseases, especially when combined with powerful, modern computer methods for analyzing and/or simulating the models.
7. Great concern about the deliberate introduction of diseases by bioterrorists has led to new challenges for mathematical modelers. anthrax
8. Great concern about possibly devastating new diseases like avian influenza has also led to new challenges for mathematical modelers.
9.
10.
11.
12. The size and overwhelming complexity of modern epidemiological problems -- and in particular the defense against bioterrorism -- calls for new approaches and tools.
13.
14.
15.
16.
17.
18. The Model: Moving From State to State Social Network = Graph Vertices = People Edges = contact Let s i (t) give the state of vertex i at time t. Simplified Model: Two states: = susceptible, = infected (SI Model) Times are discrete: t = 0, 1, 2, … t=0
19. The Model: Moving From State to State More complex models: SI, SEI, SEIR, etc. S = susceptible, E = exposed, I = infected, R = recovered (or removed) measles SARS
20. Threshold Processes Irreversible k-Threshold Process : You change your state from to at time t+1 if at least k of your neighbors have state at time t. You never leave state . Disease interpretation? Infected if sufficiently many of your neighbors are infected. Special Case k = 1: Infected if any of your neighbors is infected.
28. Vaccination Strategies Mathematical models are very helpful in comparing alternative vaccination strategies. The problem is especially interesting if we think of protecting against deliberate infection by a bioterrorist.
29. Vaccination Strategies If you didn’t know whom a bioterrorist might infect, what people would you vaccinate to be sure that a disease doesn’t spread very much? (Vaccinated vertices stay at state regardless of the state of their neighbors.) Try odd cycles. Consider an irreversible 2-threshold process. Suppose your adversary has enough supply to infect two individuals. 5-cycle C 5
30. Vaccination Strategies One strategy: “Mass vaccination ” : Make everyone and immune in initial state. In 5-cycle C 5 , mass vaccination means vaccinate 5 vertices. This obviously works. In practice, vaccination is only effective with a certain probability, so results could be different. Can we do better than mass vaccination? What does better mean? If vaccine has no cost and is unlimited and has no side effects, of course we use mass vaccination.
31. Vaccination Strategies What if vaccine is in limited supply? Suppose we only have enough vaccine to vaccinate 2 vertices. two different vaccination strategies: Vaccination Strategy I Vaccination Strategy II V V V V
32. Vaccination Strategy I: Worst Case (Adversary Infects Two) Two Strategies for Adversary Adversary Strategy Ia Adversary Strategy Ib I I I I This assumes adversary doesn’t attack a vaccinated vertex. Problem is interesting if this could happen – or you encourage it to happen. V V V V
33. The “alternation” between your choice of a defensive strategy and your adversary’s choice of an offensive strategy suggests we consider the problem from the point of view of game theory. The Food and Drug Administration is studying the use of game-theoretic models in the defense against bioterrorism.
40. Vaccination Strategy II: Worst Case (Adversary Infects Two) Two Strategies for Adversary Adversary Strategy IIa Adversary Strategy IIb I I I I V V V V
47. Conclusions about Strategies I and II Vaccination Strategy II never leads to more than two infected individuals, while Vaccination Strategy I sometimes leads to three infected individuals (depending upon strategy used by adversary). Thus, Vaccination Strategy II is better. More on vaccination strategies later.
48. The Saturation Problem Attacker’s Problem : Given a graph, what subsets S of the vertices should we plant a disease with so that ultimately the maximum number of people will get it? Economic interpretation: What set of people do we place a new product with to guarantee “saturation” of the product in the population? Defender’s Problem : Given a graph, what subsets S of the vertices should we vaccinate to guarantee that as few people as possible will be infected?
49. k-Conversion Sets Attacker’s Problem: Can we guarantee that ultimately everyone is infected? Irreversible k-Conversion Set : Subset S of the vertices that can force an irreversible k-threshold process to the situation where every state s i (t) = ? Comment: If we can change back from to at least after awhile, we can also consider the Defender’s Problem: Can we guarantee that ultimately no one is infected, i.e., all s i (t) = ?
50. What is an irreversible 2-conversion set for the following graph? x 1 x 2 x 3 x 4 x 6 x 5
51. x 1 , x 3 is an irreversible 2-conversion set. t = 0 x 1 x 2 x 3 x 4 x 6 x 5
52. x 1 , x 3 is an irreversible 2-conversion set. t = 1 x 1 x 2 x 3 x 4 x 6 x 5
53. x 1 , x 3 is an irreversible 2-conversion set. t = 2 x 1 x 2 x 3 x 4 x 6 x 5
54. x 1 , x 3 is an irreversible 2-conversion set. t = 3 x 1 x 2 x 3 x 4 x 6 x 5
55.
56. Irreversible k-Conversion Sets in Regular Graphs G is r-regular if every vertex has degree r. Set of vertices is independent if there are no edges. Theorem (Dreyer 2000): Let G = (V,E) be a connected r-regular graph and D be a set of vertices. Then D is an irreversible r-conversion set iff V-D is an independent set. Note: same r
57. k-Conversion Sets in Regular Graphs Corollary (Dreyer 2000): The size of the smallest irreversible 2- conversion set in C n is ceiling[n/2].
58. k-Conversion Sets in Regular Graphs Corollary (Dreyer 2000): The size of the smallest irreversible 2- conversion set in C n is ceiling[n/2]. C 5 is 2-regular. The smallest irreversible 2-conversion set has three vertices: the red ones.
59. k-Conversion Sets in Regular Graphs Corollary (Dreyer 2000): The size of the smallest irreversible 2- conversion set in C n is ceiling[n/2]. Proof : C n is 2-regular. The largest independent set has size floor[n/2]. Thus, the smallest D so that V-D is independent has size ceiling[n/2].
61. k-Conversion Sets in Regular Graphs Another Example: This is 3- regular. Let k = 3. The largest independent set has 2 vertices. a e d c b f
62.
63. Irreversible k-Conversion Sets in Graphs of Maximum Degree r Theorem (Dreyer 2000): Let G = (V,E) be a connected graph with maximum degree r and S be the set of all vertices of degree < r. If D is a set of vertices, then D is an irreversible r-conversion set iff S D and V-D is an independent set.
64. How Hard is it to Find out if There is an Irreversible k-Conversion Set of Size at Most p? Problem IRREVERSIBLE k-CONVERSION SET : Given a positive integer p and a graph G, does G have an irreversible k-conversion set of size at most p? How hard is this problem?
65. Difficulty of Finding Irreversible Conversion Sets Problem IRREVERSIBLE k-CONVERSION SET : Given a positive integer p and a graph G, does G have an irreversible k-conversion set of size at most p? Theorem (Dreyer 2000): IRREVERSIBLE k-CONVERSION SET is NP-complete for fixed k > 2. (Whether or not it is NP-complete for k = 2 remains open.) Thus in technical CS terms, the problem is HARD.
68. Irreversible k-Conversion Sets in Trees The simplest case is when every internal vertex of the tree has degree > k. Leaf = vertex of degree 1; internal vertex = not a leaf. What is an irreversible 2-conversion set here?
69. Irreversible k-Conversion Sets in Trees The simplest case is when every internal vertex of the tree has degree > k. Leaf = vertex of degree 1; internal vertex = not a leaf. What is an irreversible 2-conversion set here? Do you know any vertices that have to be in such a set?
75. Irreversible k-Conversion Sets in Trees So k = 2 is easy. What about k > 2? Also easy. Proposition (Dreyer 2000): Let T be a tree and every internal vertex have degree > k, where k > 1. Then the smallest irreversible k-conversion set has size equal to the number of leaves of the tree.
76. Irreversible k-Conversion Sets in Trees What if not every internal vertex has degree > k? If there is an internal vertex of degree < k, it will have to be in any irreversible k-conversion set and will never change sign. So, to every neighbor, this vertex v acts like a leaf, and we can break T into deg(v) subtrees with v a leaf in each. If every internal vertex has degree k, one can obtain analogous results to those for the > k case by looking at maximal connected subsets of vertices of degree k.
77. Irreversible k-Conversion Sets in Trees What if not every internal vertex has degree > k? Question: Can you find an example where the set of leaves is not an irreversible k-conversion set?
78. Irreversible k-Conversion Sets in Trees What if not every internal vertex has degree > k? Question: Can you find an example where the set of leaves is not an irreversible k-conversion set? Yes: if a vertex has degree < k, even if it is not a leaf, it must be in every irreversible k-conversion set.
79. Irreversible k-Conversion Sets in Trees Dreyer presents an O(n) algorithm for finding the size of the smallest irreversible k-conversion set in a tree of n vertices. O(n) is considered very efficient.
80. Irreversible k-Conversion Sets in Special Graphs Studied for many special graphs. Let G(m,n) be the rectangular grid graph with m rows and n columns. G(3,4)
81. Toroidal Grids The toroidal grid T(m,n) is obtained from the rectangular grid G(m,n) by adding edges from the first vertex in each row to the last and from the first vertex in each column to the last. Toroidal grids are easier to deal with than rectangular grids because they form regular graphs: Every vertex has degree 4. Thus, we can make use of the results about regular graphs.
83. Irreversible4-Conversion Sets in Toroidal Grids Theorem (Dreyer 2000): In a toroidal grid T(m,n), the size of the smallest irreversible 4-conversion set is max{n(ceiling[m/2]), m(ceiling[n/2])} m or n odd mn/2 m, n even {
84. Part of the Proof : Recall that D is an irreversible 4-conversion set in a 4-regular graph iff V-D is independent. V-D independent means that every edge {u,v} in G has u or v in D. In particular, the ith row must contain at least ceiling[n/2] vertices in D and the ith column at least ceiling[m/2] vertices in D (alternating starting with the end vertex of the row or column). We must cover all rows and all columns, and so need at least max{n(ceiling[m/2]), m(ceiling[n/2])} vertices in an irreversible 4-conversion set.
85. Irreversible k-Conversion Sets for Rectangular Grids Let C k (G) be the size of the smallest irreversible k-conversion set in graph G. Theorem (Dreyer 2000): C 4 [G(m,n)] = 2m + 2n - 4 + floor[(m-2)(n-2)/2] Theorem (Flocchini, Lodi, Luccio, Pagli, and Santoro): C 2 [G(m,n)] = ceiling([m+n]/2)
86. Irreversible 3-Conversion Sets for Rectangular Grids For 3-conversion sets, the best we have are bounds: Theorem (Flocchini, Lodi, Luccio, Pagli, and Santoro): [(m-1)(n-1)+1]/3 C 3 [G(m,n)] [(m-1)(n-1)+1]/3 +[3m+2n-3]/4 + 5 Finding the exact value is an open problem.
87. Irreversible Conversion Sets for Rectangular Grids Exact values are known for the size of the smallest irreversible k-conversion set for some special classes of graphs and some values of k: 2xn grids, 3xn grids, trees, etc.
88. Bounds on the Size of the Smallest Conversion Sets In general, it is difficult to get exact values for the size of the smallest irreversible k-conversion set in a graph. So, what about bounds? Sample result: Theorem (Dreyer, 2000): If G is an r-regular graph with n vertices, then C k (G) (1 – r/2k)n for k r 2k.
89. Vaccination Strategies Stephen Hartke worked on a different problem: Defender: can vaccinate v people per time period . Attacker: can only infect people at the beginning. Irreversible k-threshold model. What vaccination strategy minimizes number of people infected? Sometimes called the firefighter problem : alternate fire spread and firefighter placement. Usual assumption: k = 1. (We will assume this.) Variation: The vaccinator and infector alternate turns, having v vaccinations per period and i doses of pathogen per period. What is a good strategy for the vaccinator? Chapter in Hartke’s Ph.D. thesis at Rutgers (2004)
90. A Survey of Some Results on the Firefighter Problem Thanks to Kah Loon Ng DIMACS For the following slides, slightly modified by me
104. Containing Fires in Infinite Grids L d …… d 3: Wang and Moeller (2002): If G is an r -regular graph, r – 1 firefighters per time step is always sufficient to contain any fire outbreak (at a single vertex) in G . ( r-regular : every vertex has r neighbors.) .….
105. Containing Fires in Infinite Grids L d d 3: In L d , every vertex has degree 2 d . Thus: 2 d -1 firefighters per time step are sufficient to contain any outbreak starting at a single vertex. Theorem (Hartke 2004): If d 3, 2 d – 2 firefighters per time step are not enough to contain an outbreak in L d. Thus, 2 d – 1 firefighters per time step is the minimum number required to contain an outbreak in L d and containment can be attained in 2 time steps.
114. Algorithmic and Complexity Matters FIREFIGHTER: Instance: A rooted graph (G,u) and an integer p 1. Question: Is MVS(G,u) p? That is, is there a finite sequence d 1 , d 2 , …, d t of vertices of G such that if the fire breaks out at u, then, 1. vertex d i is neither burning nor defended at time i 2. at time t, no undefended vertex is next to a burning vertex 3. at least p vertices are saved at the end of time t.
115. Algorithmic and Complexity Matters Theorem (MacGillivray and Wang, 2003): FIREFIGHTER is NP-complete. Thus, it is HARD in the sense of computer science.
117. Algorithmic and Complexity Matters Greedy algorithm : For each v in V(T), define weight (v) = number descendants of v + 1 Algorithm: At each time step, place firefighter at vertex that has not been saved such that weight ( v ) is maximized.
120. Algorithmic and Complexity Matters Theorem (Hartnell and Li, 2000): For any tree with one fire starting at the root and one firefighter to be deployed per time step, the greedy algorithm always saves more than ½ of the vertices that any algorithm saves.
121.
122. More Realistic Models Consider an irreversible process in which you stay in the infected state (state ) for d time periods after entering it and then go back to the uninfected state (state ). Consider an irreversible k-threshold process in which we vaccinate a person in state once k-1 neighbors are infected (in state ). Etc. – experiment with a variety of assumptions