arXiv subjects

Ankur Mani

Publications and source records attributed to Ankur Mani.

12 recordsLinked to original sources

arXiv2026

Storage and Transport Capacity Design for a Self-Reliable Two-Node Stochastic Resource System

We study a two-node stochastic resource system operating over a finite horizon. Each node experiences uncertain supply and demand and is equipped with finite storage. The objective is to ensure that resource levels remain within prescribed limits with high probability. To this end, we formulate a chance-constrained capacity-design problem in which resources can be exchanged through a capacity-limited transport link. We characterize the minimum storage required at each node, derive the optimal transport policy, and quantify the trade-off between storage and transport capacities. Our results show the existence of a critical transport-capacity threshold that enables full risk pooling between the nodes. Moreover, this threshold decreases with the operating horizon, implying that full-pooling performance can be achieved with progressively smaller transport capacity over longer horizons.

eess.SY↗

arXiv2026

Context-Gated Associative Retrieval: From Theory to Transformers

Hopfield networks and their generalizations have established deep connections among biological associative memories, statistical physics, and transformers. Yet most models treat retrieval as a fixed query-to-memory mapping, ignoring the role of external context in recall. In this work, we propose a two-stage associative memory architecture, wherein a context-gate subcircuit reshapes the retrieval energy landscape before and during recall. We show theoretically that context gating increases inter-memory separation while inducing sparsity, translating into exponential improvements in retrieval. Crucially, we prove that the system admits a unique self-consistent fixed point, revealing that the resulting retrieval state is driven by both a direct contextual bias and a second-order retrieval-gate feedback loop. We then bridge this theory to transformers; specifically, we evaluate a first-order approximation on Llama-3, confirming that in-context learning acts as context-gated retrieval. Native dynamics mirror our theory: context localizes a memory subspace, enabling the zero-shot query to cleanly discriminate. Ultimately, this framework provides a mechanistic link between associative memory theory and LLM phenomenology.

cond-mat.dis-nn↗

arXiv2024

Guaranteeing Service in Connected Microgrids: Storage Planning and Optimal Power Sharing Policy

The integration of renewable energy sources (RES) into power distribution grids poses challenges to system reliability due to the inherent uncertainty in their power production. To address this issue, battery energy sources (BESs) are being increasingly used as a promising solution to counter the uncertainty associated with RES power production. During the overall system planning stage, the optimal capacity of the BES has to be decided. In the operational phase, policies on when to charge the BESs and when to use them to support loads must be determined so that the BES remains within its operating range, avoiding depletion of charge on one hand and remaining within acceptable margins of maximum charge on the other. In this paper, a stochastic control framework is used to determine battery capacity, for microgrids, which ensures that during the operational phase, BESs' operating range is respected with pre-specified high probability. We provide an explicit analytical expression of the required BESs energy capacity for a single microgrid with RES as the main power source. Leveraging insights from the single microgrid case, the article focuses on the design and planning of BESs for the two-microgrid scenario. In this setting, microgrids are allowed to share power while respecting the capacity constraints imposed by the power lines. We characterize the optimal power transfer policy between the microgrids and the optimal BES capacity for multiple microgrids. This provides the BES savings arising from connecting the microgrids.

eess.SY↗

arXiv2023

Transactive Framework for Dynamic Energy Storage Allocation for Critical Load Management

Increased penetration of Distributed Energy Resources (DER) and Renewable Energy Systems (RES) transforming the conventional distribution grid into a transactive framework supervised by a distribution system operator (DSO). Although the emerging transactive energy management techniques improve the grid reliability, the inherent uncertainty of RES poses a challenge in meeting the power demand of the critical infrastructure in the microgrid unless sufficient battery energy storage is maintained. However, maintaining expensive battery storage increases the operating cost of the DSO. In this article, we propose a cost-effective dynamic resource allocation strategy to optimize the battery reserve requirement while ensuring the critical demand is met with a provable guarantee. Our proposed scheme enables the DSO to optimize the RES and battery reserve allocation to eliminate the risk of over or underproduction. We present numerical simulations under three different scenarios of multiple microgrids with uncertain renewable generation. The simulation results demonstrate the efficacy of the proposed transactive stochastic control algorithm.

eess.SY↗

arXiv2023

Provably High-Quality Solutions for the Liquid Medical Oxygen Allocation Problem

Oxygen is an essential life-saving medicine used in several indications at all levels of healthcare. During the COVID-19 pandemic, the demand for liquid medical oxygen (LMO) has increased significantly due to the occurrence of lung infections in many patients. However, many countries and regions are not prepared for the emergence of this phenomenon, and the limited supply of LMO has resulted in unsatisfied usage needs in many regions. In this paper, we formulated a linear programming model with the objective to minimize the unsatisfied demand given the constraints of supply and transportation capacity. The decision variables are how much LMO should be transferred from a place to another at each time interval using a specific number of vehicles. Multiple storage points are added into the network to allow for more flexible allocation strategies. The proposed model is implemented in India with real-world LMO supply and demand data as a case study. Compared to the manually designed allocation strategy, the proposed model successfully reduces the unsatisfied demand.

eess.SY↗

arXiv2023

Learning Optimal Features via Partial Invariance

Learning models that are robust to distribution shifts is a key concern in the context of their real-life applicability. Invariant Risk Minimization (IRM) is a popular framework that aims to learn robust models from multiple environments. The success of IRM requires an important assumption: the underlying causal mechanisms/features remain invariant across environments. When not satisfied, we show that IRM can over-constrain the predictor and to remedy this, we propose a relaxation via $\textit{partial invariance}$. In this work, we theoretically highlight the sub-optimality of IRM and then demonstrate how learning from a partition of training domains can help improve invariant models. Several experiments, conducted both in linear settings as well as with deep neural networks on tasks over both language and image data, allow us to verify our conclusions.

cs.LG↗

arXiv2021

Balancing Fairness and Robustness via Partial Invariance

The Invariant Risk Minimization (IRM) framework aims to learn invariant features from a set of environments for solving the out-of-distribution (OOD) generalization problem. The underlying assumption is that the causal components of the data generating distributions remain constant across the environments or alternately, the data "overlaps" across environments to find meaningful invariant features. Consequently, when the "overlap" assumption does not hold, the set of truly invariant features may not be sufficient for optimal prediction performance. Such cases arise naturally in networked settings and hierarchical data-generating models, wherein the IRM performance becomes suboptimal. To mitigate this failure case, we argue for a partial invariance framework. The key idea is to introduce flexibility into the IRM framework by partitioning the environments based on hierarchical differences, while enforcing invariance locally within the partitions. We motivate this framework in classification settings with causal distribution shifts across environments. Our results show the capability of the partial invariant risk minimization to alleviate the trade-off between fairness and risk in certain settings.

cs.LG↗

arXiv2020

University Operations During a Pandemic: A Flexible Decision Analysis Toolkit

Modeling infection spread during pandemics is not new, with models using past data to tune simulation parameters for predictions. These help understand the healthcare burden posed by a pandemic and respond accordingly. However, the problem of how college/university campuses should function during a pandemic is new for the following reasons:(i) social contact in colleges are structured and can be engineered for chosen objectives, (ii) the last pandemic to cause such societal disruption was over 100 years ago, when higher education was not a critical part of society, (ii) not much was known about causes of pandemics, and hence effective ways of safe operations were not known, and (iii) today with distance learning, remote operation of an academic institution is possible. Our approach is unique in presenting a flexible simulation system, containing a suite of model libraries, one for each major component. The system integrates agent based modeling (ABM) and stochastic network approach, and models the interactions among individual entities, e.g., students, instructors, classrooms, residences, etc. in great detail. For each decision to be made, the system can be used to predict the impact of various choices, and thus enable the administrator to make informed decisions. While current approaches are good for infection modeling, they lack accuracy in social contact modeling. Our ABM approach, combined with ideas from Network Science, presents a novel approach to contact modeling. A detailed case study of the University of Minnesota's Sunrise Plan is presented. For each decisions made, its impact was assessed, and results used to get a measure of confidence. We believe this flexible tool can be a valuable asset for various kinds of organizations to assess their infection risks in pandemic-time operations, including middle and high schools, factories, warehouses, and small/medium sized businesses.

eess.SY↗

arXiv2020

On Mitigating the Uncertainty in Renewable Generation in Distribution Microgrids

In this article, we focus on the problem of mitigating the risk of not being able to meet the power demand, due to the inherent uncertainty of renewable energy generation sources in microgrids. We consider three different demand scenarios, namely meeting short-time horizon power demand, a sustained energy demand and a scenario where the power demand at a prescribed future time has to be met with almost sure guarantee with power generation being stochastic and following dynamics governed by geometric Brownian motion. For each of these scenarios we provide solutions to meet the electrical demand. We present results of numerical experiments to demonstrate the applicability of our schemes.

eess.SY↗

arXiv2020

Quantization Games on Social Networks and Language Evolution

We consider a strategic network quantizer design setting where agents must balance fidelity in representing their local source distributions against their ability to successfully communicate with other connected agents. We study the problem as a network game and show existence of Nash equilibrium quantizers. For any agent, under Nash equilibrium, the word representing a given partition region is the conditional expectation of the mixture of local and social source probability distributions within the region. Since having knowledge of the original source of information in the network may not be realistic, we show that under certain conditions, the agents need not know the source origin and yet still settle on a Nash equilibrium using only the observed sources. Further, the network may converge to equilibrium through a distributed version of the Lloyd-Max algorithm. In contrast to traditional results in the evolution of language, we find several vocabularies may coexist in the Nash equilibrium, with each individual having exactly one of these vocabularies. The overlap between vocabularies is high for individuals that communicate frequently and have similar local sources. Finally, we argue that error in translation along a chain of communication does not grow if and only if the chain consists of agents with shared vocabulary. Numerical results are given.

cs.IT↗

arXiv2010

Generalized Stable Matching in Bipartite Networks

In this paper we study the generalized version of weighted matching in bipartite networks. Consider a weighted matching in a bipartite network in which the nodes derive value from the split of the matching edge assigned to them if they are matched. The value a node derives from the split depends both on the split as well as the partner the node is matched to. We assume that the value of a split to the node is continuous and strictly increasing in the part of the split assigned to the node. A stable weighted matching is a matching and splits on the edges in the matching such that no two adjacent nodes in the network can split the edge between them so that both of them can derive a higher value than in the matching. We extend the weighted matching problem to this general case and study the existence of a stable weighted matching. We also present an algorithm that converges to a stable weighted matching. The algorithm generalizes the Hungarian algorithm for bipartite matching. Faster algorithms can be made when there is more structure on the value functions.

math.OC↗

arXiv2010

Existence of Stable Exclusive Bilateral Exchanges in Networks

In this paper we show that when individuals in a bipartite network exclusively choose partners and exchange valued goods with their partners, then there exists a set of exchanges that are pair-wise stable. Pair-wise stability implies that no individual breaks her partnership and no two neighbors in the network can form a new partnership while breaking other partnerships if any so that at least one of them improves her payoff and the other one does at least as good. We consider a general class of continuous, strictly convex and strongly monotone preferences over bundles of goods for individuals. Thus, this work extends the general equilibrium framework from markets to networks with exclusive exchanges. We present the complete existence proof using the existence of a generalized stable matching in \cite{Generalized-Stable-Matching}. The existence proof can be extended to problems in social games as in \cite{Matching-Equilibrium} and \cite{Social-Games}.

cs.GT↗