arXiv subjects

Madhav V. Marathe

Publications and source records attributed to Madhav V. Marathe.

At least 19 recordsLinked to original sources

arXiv2026

Boundary Degree as a Node-level Feature for Epidemic Scenario Identification in Agent-based Cascade Simulations

Characterizing the scenario underlying an epidemic from its disease cascade is an important task in simulation analytics. We propose boundary degree, the count of an infected node's contacts in the underlying contact network that were not infected, as a per-node cascade feature for this task. Through systematic ablation on realistic social contact networks of Tennessee and Virginia, we show that boundary degree alone improves scenario identification accuracy by 19%. Edge features, whose importance was observed empirically by prior work, consistently improve accuracy across all settings; we provide theoretical grounding for this observation. These effects are complementary. We prove that certain epidemic scenarios are indistinguishable without boundary or edge information. Prior feature engineering approaches included aggregate boundary statistics, but these were not among the top-ranked feature groups; the per-node representation we propose reveals their importance clearly. Our results suggest that contact tracing applications should track contacts with non-infected individuals, not only transmissions.

cs.SI↗

arXiv2026

A High-Resolution, US-scale Digital Similar of Interacting Livestock, Wild Birds, and Human Ecosystems with Applications to Multi-host Epidemic Spread

One Health issues, such as the spread of highly pathogenic avian influenza~(HPAI), present significant challenges at the human-animal-environmental interface. Recent H5N1 outbreaks underscore the need for comprehensive modeling efforts that capture the complex interactions between various entities in these interconnected ecosystems. To support such efforts, we develop a methodology to construct a synthetic spatiotemporal gridded dataset of livestock production and processing, human population, and wild birds for the contiguous United States, called a \emph{digital similar}. This representation is a result of fusing diverse datasets using statistical and optimization techniques, followed by extensive verification and validation. The livestock component includes farm-level representations of four major livestock types -- cattle, poultry, swine, and sheep -- including further categorization into subtypes such as dairy cows, beef cows, chickens, turkeys, ducks, etc. Weekly abundance data for wild bird species identified in the transmission of avian influenza are included. Gridded distributions of the human population, along with demographic and occupational features, capture the placement of agricultural workers and the general population. We demonstrate how the digital similar can be applied to evaluate spillover risk to dairy cows and poultry from wild bird population, then validate these results using historical H5N1 incidences. The resulting subtype-specific spatiotemporal risk maps identify hotspots of high risk from H5N1 infected wild bird population to dairy cattle and poultry operations, thus guiding surveillance efforts.

cs.CE↗

arXiv2025

IGraSS: Learning to Identify Infrastructure Networks from Satellite Imagery by Iterative Graph-constrained Semantic Segmentation

Accurate canal network mapping is essential for water management, including irrigation planning and infrastructure maintenance. State-of-the-art semantic segmentation models for infrastructure mapping, such as roads, rely on large, well-annotated remote sensing datasets. However, incomplete or inadequate ground truth can hinder these learning approaches. Many infrastructure networks have graph-level properties such as reachability to a source (like canals) or connectivity (roads) that can be leveraged to improve these existing ground truth. This paper develops a novel iterative framework IGraSS, combining a semantic segmentation module-incorporating RGB and additional modalities (NDWI, DEM)-with a graph-based ground-truth refinement module. The segmentation module processes satellite imagery patches, while the refinement module operates on the entire data viewing the infrastructure network as a graph. Experiments show that IGraSS reduces unreachable canal segments from around 18% to 3%, and training with refined ground truth significantly improves canal identification. IGraSS serves as a robust framework for both refining noisy ground truth and mapping canal networks from remote sensing imagery. We also demonstrate the effectiveness and generalizability of IGraSS using road networks as an example, applying a different graph-theoretic constraint to complete road networks.

cs.CV↗

arXiv2025

On Some Fundamental Problems for Multi-Agent Systems Over Multilayer Networks

Many researchers have considered multi-agent systems over single-layer networks as models for studying diffusion phenomena. Since real-world networks involve connections between agents with different semantics (e.g., family member, friend, colleague), the study of multi-agent systems over multilayer networks has assumed importance. Our focus is on one class of multi-agent system models over multilayer networks, namely multilayer synchronous dynamical systems (MSyDSs). We study several fundamental problems for this model. We establish properties of the phase spaces of MSyDSs and bring out interesting differences between single-layer and multilayer dynamical systems. We show that, in general, the problem of determining whether two given MSyDSs are inequivalent is NP-complete. This hardness result holds even when the only difference between the two systems is the local function at just one node in one layer. We also present efficient algorithms for the equivalence problem for restricted versions of MSyDSs (e.g., systems where each local function is a bounded-threshold function, systems where the number of layers is fixed and each local function is symmetric). In addition, we investigate the expressive power of MSyDSs based on the number of layers. In particular, we examine conditions under which a system with k >= 2 layers has an equivalent system with k-1 or fewer layers.

cs.MA↗

arXiv2025

Pandemics In Silico: Scaling an Agent-Based Simulation on Realistic Social Contact Networks

Preventing the spread of infectious diseases requires implementing interventions at various levels of government and evaluating the potential impact and efficacy of those preemptive measures. Agent-based modeling can be used for detailed studies of epidemic diffusion and possible interventions. Modeling of epidemic diffusion in large social contact networks requires the use of parallel algorithms and resources. In this work, we present Loimos, a scalable parallel framework for simulating epidemic diffusion. Loimos uses a hybrid of time-stepping and discrete-event simulation to model disease spread, and is implemented on top of an asynchronous, many-task runtime. We demonstrate that Loimos is to able to achieve significant speedups while scaling to large core counts. In particular, Loimos is able to simulate 200 days of a COVID-19 outbreak on a digital twin of California in about 42 seconds, for an average of 4.6 billion traversed edges per second (TEPS), using 4096 cores on Perlmutter at NERSC.

cs.DC↗

arXiv2024

Efficient PAC Learnability of Dynamical Systems Over Multilayer Networks

Networked dynamical systems are widely used as formal models of real-world cascading phenomena, such as the spread of diseases and information. Prior research has addressed the problem of learning the behavior of an unknown dynamical system when the underlying network has a single layer. In this work, we study the learnability of dynamical systems over multilayer networks, which are more realistic and challenging. First, we present an efficient PAC learning algorithm with provable guarantees to show that the learner only requires a small number of training examples to infer an unknown system. We further provide a tight analysis of the Natarajan dimension which measures the model complexity. Asymptotically, our bound on the Nararajan dimension is tight for almost all multilayer graphs. The techniques and insights from our work provide the theoretical foundations for future investigations of learning problems for multilayer dynamical systems.

cs.LG↗

arXiv2024

Assigning Agents to Increase Network-Based Neighborhood Diversity

Motivated by real-world applications such as the allocation of public housing, we examine the problem of assigning a group of agents to vertices (e.g., spatial locations) of a network so that the diversity level is maximized. Specifically, agents are of two types (characterized by features), and we measure diversity by the number of agents who have at least one neighbor of a different type. This problem is known to be NP-hard, and we focus on developing approximation algorithms with provable performance guarantees. We first present a local-improvement algorithm for general graphs that provides an approximation factor of 1/2. For the special case where the sizes of agent subgroups are similar, we present a randomized approach based on semidefinite programming that yields an approximation factor better than 1/2. Further, we show that the problem can be solved efficiently when the underlying graph is treewidth-bounded and obtain a polynomial time approximation scheme (PTAS) for the problem on planar graphs. Lastly, we conduct experiments to evaluate the per-performance of the proposed algorithms on synthetic and real-world networks.

cs.DS↗

arXiv2024

Networked Anti-Coordination Games Meet Graphical Dynamical Systems: Equilibria and Convergence

Evolutionary anti-coordination games on networks capture real-world strategic situations such as traffic routing and market competition. In such games, agents maximize their utility by choosing actions that differ from their neighbors' actions. Two important problems concerning evolutionary games are the existence of a pure Nash equilibrium (NE) and the convergence time of the dynamics. In this work, we study these two problems for anti-coordination games under sequential and synchronous update schemes. For each update scheme, we examine two decision modes based on whether an agent considers its own previous action (self essential ) or not (self non-essential ) in choosing its next action. Using a relationship between games and dynamical systems, we show that for both update schemes, finding an NE can be done efficiently under the self non-essential mode but is computationally intractable under the self essential mode. To cope with this hardness, we identify special cases for which an NE can be obtained efficiently. For convergence time, we show that the best-response dynamics converges in a polynomial number of steps in the synchronous scheme for both modes; for the sequential scheme, the convergence time is polynomial only under the self non-essential mode. Through experiments, we empirically examine the convergence time and the equilibria for both synthetic and real-world networks.

cs.GT↗

arXiv2024

Finding Nontrivial Minimum Fixed Points in Discrete Dynamical Systems

Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the dissemination of undesirable contagions (such as rumors and misinformation), convergence to fixed points with a small number of affected nodes is a desirable goal. Motivated by such considerations, we formulate a novel optimization problem of finding a nontrivial fixed point of the system with the minimum number of affected nodes. We establish that, unless P = NP, there is no polynomial time algorithm for approximating a solution to this problem to within the factor n^1-εfor any constant epsilon > 0. To cope with this computational intractability, we identify several special cases for which the problem can be solved efficiently. Further, we introduce an integer linear program to address the problem for networks of reasonable sizes. For solving the problem on larger networks, we propose a general heuristic framework along with greedy selection methods. Extensive experimental results on real-world networks demonstrate the effectiveness of the proposed heuristics.

cs.SI↗

arXiv2024

Learning the Topology and Behavior of Discrete Dynamical Systems

Discrete dynamical systems are commonly used to model the spread of contagions on real-world networks. Under the PAC framework, existing research has studied the problem of learning the behavior of a system, assuming that the underlying network is known. In this work, we focus on a more challenging setting: to learn both the behavior and the underlying topology of a black-box system. We show that, in general, this learning problem is computationally intractable. On the positive side, we present efficient learning methods under the PAC model when the underlying graph of the dynamical system belongs to some classes. Further, we examine a relaxed setting where the topology of an unknown system is partially observed. For this case, we develop an efficient PAC learner to infer the system and establish the sample complexity. Lastly, we present a formal analysis of the expressive power of the hypothesis class of dynamical systems where both the topology and behavior are unknown, using the well-known formalism of the Natarajan dimension. Our results provide a theoretical foundation for learning both the behavior and topology of discrete dynamical systems.

cs.LG↗

arXiv2019

Symmetry Properties of Nested Canalyzing Functions

Many researchers have studied symmetry properties of various Boolean functions. A class of Boolean functions, called nested canalyzing functions (NCFs), has been used to model certain biological phenomena. We identify some interesting relationships between NCFs, symmetric Boolean functions and a generalization of symmetric Boolean functions, which we call $r$-symmetric functions (where $r$ is the symmetry level). Using a normalized representation for NCFs, we develop a characterization of when two variables of an NCF are symmetric. Using this characterization, we show that the symmetry level of an NCF $f$ can be easily computed given a standard representation of $f$. We also present an algorithm for testing whether a given $r$-symmetric function is an NCF. Further, we show that for any NCF $f$ with $n$ variables, the notion of strong asymmetry considered in the literature is equivalent to the property that $f$ is $n$-symmetric. We use this result to derive a closed form expression for the number of $n$-variable Boolean functions that are NCFs and strongly asymmetric. We also identify all the Boolean functions that are NCFs and symmetric.

cs.DM↗

arXiv2017

Guided Deep List: Automating the Generation of Epidemiological Line Lists from Open Sources

Real-time monitoring and responses to emerging public health threats rely on the availability of timely surveillance data. During the early stages of an epidemic, the ready availability of line lists with detailed tabular information about laboratory-confirmed cases can assist epidemiologists in making reliable inferences and forecasts. Such inferences are crucial to understand the epidemiology of a specific disease early enough to stop or control the outbreak. However, construction of such line lists requires considerable human supervision and therefore, difficult to generate in real-time. In this paper, we motivate Guided Deep List, the first tool for building automated line lists (in near real-time) from open source reports of emerging disease outbreaks. Specifically, we focus on deriving epidemiological characteristics of an emerging disease and the affected population from reports of illness. Guided Deep List uses distributed vector representations (ala word2vec) to discover a set of indicators for each line list feature. This discovery of indicators is followed by the use of dependency parsing based techniques for final extraction in tabular form. We evaluate the performance of Guided Deep List against a human annotated line list provided by HealthMap corresponding to MERS outbreaks in Saudi Arabia. We demonstrate that Guided Deep List extracts line list features with increased accuracy compared to a baseline method. We further show how these automatically extracted line list features can be used for making epidemiological inferences, such as inferring demographics and symptoms-to-hospitalization period of affected individuals.

cs.CL↗

arXiv2014

The Potential Impact of Increased Hospital Capacity to Contain and Control Ebola in Liberia

West Africa is currently experiencing a severe outbreak of Ebola virus disease (EVD). As part of the international effort to address this outbreak, the United States has committed to building specialized Ebola treatment facilities with 1700 beds. However, the effectiveness of this increase in the available healthcare facilities to treat Ebola is unclear, especially in light of the rapidly increasing number of cases. Adapting a previously validated mathematical model of Ebola in West Africa, we examine the potential impact of an increase in hospital capacity to mitigate the impact of Ebola under several scenarios, ranging from the planned scenario of 1700 beds in 10 weeks to a considerably more aggressive approach of twice the number of beds in 5 weeks. We find that even for the most aggressive scenarios, while increasing the availability of healthcare reduces the number of Ebola cases and slows the outbreak, it is not sufficient to stop the epidemic within the next three months. We find that only a combination of increased hospital beds and a dramatic decrease in the rate of transmission within the community can bring the epidemic under control within the near future.

q-bio.PE↗

arXiv2008

Adversarial Scheduling in Evolutionary Game Dynamics

Consider a system in which players at nodes of an underlying graph G repeatedly play Prisoner's Dilemma against their neighbors. The players adapt their strategies based on the past behavior of their opponents by applying the so-called win-stay lose-shift strategy. This dynamics has been studied in (Kittock 94), (Dyer et al. 2002), (Mossel and Roch, 2006). With random scheduling, starting from any initial configuration with high probability the system reaches the unique fixed point in which all players cooperate. This paper investigates the validity of this result under various classes of adversarial schedulers. Our results can be sumarized as follows: 1. An adversarial scheduler that can select both participants to the game can preclude the system from reaching the unique fixed point on most graph topologies. 2. A nonadaptive scheduler that is only allowed to choose one of the participants is no more powerful than a random scheduler. With this restriction even an adaptive scheduler is not significantly more powerful than the random scheduler, provided it is "reasonably fair". The results exemplify the adversarial scheduling approach we propose as a foundational basis for the generative approach to social science (Epstein 2007).

cs.DM↗

arXiv2008

Adversarial Scheduling Analysis of Game Theoretic Models of Norm Diffusion

In (Istrate, Marathe, Ravi SODA 2001) we advocated the investigation of robustness of results in the theory of learning in games under adversarial scheduling models. We provide evidence that such an analysis is feasible and can lead to nontrivial results by investigating, in an adversarial scheduling setting, Peyton Young's model of diffusion of norms. In particular, our main result incorporates into Peyton Young's model.

cs.GT↗

arXiv1998

Bicriteria Network Design Problems

We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same %(note that the cost functions continue to be different) we present a ``black box'' parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a cluster-based approach to devise a approximation algorithms --- the solutions output violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. We show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.

cs.CC↗

arXiv1998

Approximation Algorithms for PSPACE-Hard Hierarchically and Periodically Specified Problems

We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in \cite{Le89} or are specified by 1-dimensional finite narrow periodic specifications as in \cite{Wa93}. We show that, for most of the problems $Π$ considered when specified using {\bf k-level-restricted} hierarchical specifications or $k$-narrow periodic specifications the following holds: \item Let $ρ$ be any performance guarantee of a polynomial time approximation algorithm for $Π$, when instances are specified using standard specifications. Then $\forall ε> 0$, $ Π$ has a polynomial time approximation algorithm with performance guarantee $(1 + ε) ρ$. \item $Π$ has a polynomial time approximation scheme when restricted to planar instances. \end{romannum} These are the first polynomial time approximation schemes for PSPACE-hard hierarchically or periodically specified problems. Since several of the problems considered are PSPACE-hard, our results provide the first examples of natural PSPACE-hard optimization problems that have polynomial time approximation schemes. This answers an open question in Condon et. al. \cite{CF+93}.

cs.CC↗

arXiv1998

The Complexity of Planar Counting Problems

We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat, Minimum Vertex Cover, Minimum Dominating Set, Minimum Feedback Vertex Set, X3C, Partition Into Triangles, and Clique Cover.} \end{romannum} We also prove the {\sf NP}-completeness of the {\sc Ambiguous Satisfiability} problems \cite{Sa80} and the {\sf D$^P$}-completeness (with respect to random polynomial reducibility) of the unique satisfiability problems \cite{VV85} associated with several of the above problems, when restricted to planar instances. Previously, very few {\sf #P}-hardness results, no {\sf NP}-hardness results, and no {\sf D$^P$}-completeness results were known for counting problems, ambiguous satisfiability problems and unique satisfiability problems, respectively, when restricted to planar instances. Assuming {\sf P $\neq $ NP}, one corollary of the above results is There are no $ε$-approximation algorithms for the problems of maximizing or minimizing a linear objective function subject to a planar system of linear inequality constraints over the integers.

cs.CC↗