arXiv subjects

Dipankar Maity

Publications and source records attributed to Dipankar Maity.

At least 19 recordsLinked to original sources

arXiv2026

On the internal homotopy theory of motivic categories

We develop a general $\infty$-categorical framework for internal Eilenberg-MacLane objects, internal homotopy groups, and an internal notion of covering spaces, and study their behavior under suitable localizations. Applying this to the ordinary motivic localization, we identify internal $n$-Eilenberg-MacLane objects with strongly $\mathbb{A}^1$-invariant sheaves of (abelian when $n\geq 2$) groups, yielding a formal obstruction to the motivic homotopy category being an $\infty$-topos. We prove that taking $\mathbb{A}^1$-localizations induces an equivalence between classical $\mathbb{A}^1$-coverings of a Nisnevich local space and the internal motivic coverings of its motivic localization, providing a streamlined proof of a generalized motivic Van Kampen theorem. Along the way, we establish a Nisnevich-local-to-global $\mathbb{A}^1$-connectivity criterion: a $k$-scheme is $\mathbb{A}^1$-connected if and only if it admits a Nisnevich cover by $\mathbb{A}^1$-connected schemes such that each pairwise intersection has a ($k$-)point. Finally, we show that over a general Qcqs base, passing to the birational motivic homotopy category recovers certain essential topos-theoretic properties absent in the ordinary $\mathbb{A}^1$-setting. In fact, for a scheme with finitely many generic points, we show that the birational motivic homotopy category is a Postnikov-complete $\infty$-topos of cohomological dimension $0$.

math.AG↗

arXiv2026

Schematic Functorialities of Birational Motivic Homotopy Categories

We promote the $n$-birational motivic homotopy category assignment $S\mapsto \mathcal{H}^n(S)$ to a $Pr^L$-valued presheaf on $Corr(\mathrm{Sch})_{uglt,sm}$. As a consequence, the birational motivic homotopy category $\mathcal{H}^{b\mathbb{A}^1}(X)$ of a scheme $X$ with finitely many generic points decomposes as the cartesian product of the birational motivic homotopy categories of those generic points; in particular, for a variety $V$, $\mathcal{H}^{b\mathbb{A}^1}(V) \simeq \mathcal{H}^{b\mathbb{A}^1}(k(V))$. This implies that birational equivalences of schemes in $Sm_X$ can be detected via the birational contractibility of their generic fibers. Finally, we show that stably birational morphisms and purely transcendental field extensions induce fully faithful embeddings of birational motivic homotopy categories.

math.AG↗

arXiv2026

Birational Algebraic Topology

Over a qcqs scheme $S$, we analyze the birational localization $L_{\mathrm{bir}}\mathcal{H}^{\mathbb{A}^1}(S)$ of the motivic $\infty$-category $\mathcal{H}^{\mathbb{A}^1}(S)$. We establish that the associated localization functor $L_{bir}$ commutes with the bar construction, thereby preserving connectivity over fields. When the field is perfect, we show that a sheaf of groups is birational exactly when it is strongly $\mathbb{A}^1$-invariant and has trivial $\mathbb{G}_m$-contraction. For connected motivic spaces over such fields, this yields a canonical equivalence between $L_{bir}$ and the $S^{2,1}$-nullification functor $L^{2,1}$. For a general field $k$, we identify $\pi_0^b(X)$ with $\pi_0^{b\mathbb{A}^1}(X)$ for proper $k$-schemes and show that $\mathbb{A}^1$-connectedness is equivalent to birational connectedness for (ind-)proper $k$-schemes. This also confirms that $\pi_0^{b\mathbb{A}^1}(-)$ and $\mathbb{H}_0^{\mathbb{A}^1}(-)$ are stable birational invariants of smooth proper $k$-schemes, satisfying the expected universal property for invariants valued in birational sheaves (of sets and abelian groups respectively). Finally, we show that etale birational equivalences to $S$ are precisely the dense open immersions into $S$.

math.AG↗

arXiv2026

Eigenspace-Based Clustering for Personalized System Identification

We study the problem of system identification in heterogeneous settings, where different systems may follow distinct underlying dynamics. Existing clustered system identification approaches often rely on iterative training-based cluster assignment, which can be sensitive to learning uncertainty and model initialization. In contrast, we propose a one-shot, training-free clustering method that identifies similar systems using the structure of their locally observed data. Specifically, each system estimates a local state covariance matrix, and cluster identities are inferred by measuring the alignment between the leading covariance eigenspaces of different systems. We provide a mathematical interpretation of the proposed similarity score and develop a finite-sample analysis that characterizes how covariance estimation error induces eigenspace perturbations in terms of the underlying system dynamics. We then derive a probability bound for pairwise false merges and a global clustering success guarantee. Numerical experiments demonstrate that the proposed eigenspace-based clustering method effectively identifies systems with shared dynamics, leading to lower personalized model-estimation error compared with training-based clustering and non-clustered baselines.

eess.SY↗

arXiv2026

Performance-Driven Environment Abstraction with Multi-Timescale Learning

We study performance-driven environment abstraction for decision-making in large Markov decision processes. Rather than preserving geometric or topological structure, we seek abstractions that directly optimize decision quality. We model abstraction as a controlled approximation obtained by aggregating the state space and enforcing a shared action distribution within each aggregated state. For a fixed partition, we establish a performance guarantee that separates value-function approximation error from the loss introduced by action sharing. Guided by this analysis, we develop a multi-timescale reinforcement learning framework that jointly adapts the policy and a tree-structured environment abstraction. The resulting algorithm refines and coarsens regions of the state space based on Q-value discrepancies, balancing performance against abstraction size and complexity. Empirical results demonstrate substantial state compression, improved sample efficiency, and faster replanning compared to actor-critic baselines.

cs.LG↗

arXiv2026

On Type Deception in Linear-Quadratic Differential Games

We consider two-player linear-quadratic differential games of incomplete information, in which one player has a private type initially unknown to the other. The typed player has incentive to conceal their type, while the uninformed player has the potential to infer it during play. Any ex-ante equilibrium in this setting will decompose into a deceptive, pooling phase, and a complete-information, revelatory phase. We demonstrate how to solve both phases via nested Riccati equations. Candidate equilibria are then found by maximizing the game value over a scalar revelation time, for which we provide a gradient in the case of time-homogeneous system matrices. We conclude by demonstrating our framework in a pursuit-evasion game with time-varying control advantages, finding interior optimal revelation times that confirm deception has quantifiable ex-ante value.

cs.GT↗

arXiv2026

Collaborative Navigation and Exploration with $\beta$-Sparse Gaussian Processes

Collaborative navigation of heterogeneous robots in unknown environments poses significant challenges due to sensing, communication, and computational limitations. In this work, a lead robot navigates toward a target while a mobile sensor robot (e.g., a drone) assists by transmitting information about its locally observed map under bandwidth constraints. We propose a framework that enables the sensor to jointly select its transmitted map points and navigation actions online, while also predicting unexplored regions of the environment. To this end, we present $\beta$-Sparse Gaussian Processes, a robust variational sparse Gaussian Process model for task-aware inducing point selection under cardinality constraints. Furthermore, we develop an action-selection strategy that balances task relevance with exploration. Simulations on Mars and Earth maps show that the framework can reduce path cost by 18% relative to no communication and decrease transmitted information by 76% compared to raw-data transmission baselines.

cs.RO↗

arXiv2026

Linear Reformulation of Event-Triggered LQG Control under Unreliable Communication

We consider event-triggered linear-quadratic Gaussian (LQG) control when sensor updates are transmitted over an i.i.d. packet-erasure channel. Although the optimal controller in a standard LQG setup is available in closed form, choosing when to transmit remains computationally and analytically difficult because packet drops randomize packet delivery and couple scheduling decisions with the estimation-error dynamics, making direct dynamic-programming solutions impractical. By certainty equivalence, the co-design problem becomes choosing a binary send/skip sequence that balances control performance and communication cost. We derive a closed-form expansion of the error covariance as precomputable Gramian terms scaled by a survival factor that depends only on the number of transmission attempts on each interval. This converts the problem into an unconstrained binary program that we linearize exactly via running attempt counters and a one-hot encoding, yielding a compact MILP well suited to receding-horizon implementation. On the linearized Boeing-747 benchmark, a model predictive control (MPC) scheduler lowers cost while attempting far fewer transmissions than a one-shot baseline across channel success rates.

eess.SY↗

arXiv2026

Enhancing Robustness of Federated Learning via Server Learning

This paper explores the use of server learning for enhancing the robustness of federated learning against malicious attacks even when clients' training data are not independent and identically distributed. We propose a heuristic algorithm that uses server learning and client update filtering in combination with geometric median aggregation. We demonstrate via experiments that this approach can achieve significant improvement in model accuracy even when the fraction of malicious clients is high, even more than $50\%$ in some cases, and the dataset utilized by the server is small and could be synthetic with its distribution not necessarily close to that of the clients' aggregated data.

cs.LG↗

arXiv2026

Optimal Hiding with Partial Information of the Seeker's Route

We consider a hide-and-seek game between a Hider and a Seeker over a finite set of locations. The Hider chooses one location to conceal a stationary treasure, while the Seeker visits the locations sequentially along a route. As the search progresses, the Hider observes a prefix of the Seeker's route. After observing this information, the Hider has the option to relocate the treasure at most once to another unvisited location by paying a switching cost. We study two seeker models. In the first, the Seeker is unaware of the fact that the Hider can relocate. In the second, the Seeker select its route while accounting for the possibility that the Hider observes its path and reallocates. For the restricted case, we define the value-of-information created by the reveal and derive upper bounds in terms of the switching cost using a worst-case evaluation over routes. We also show that seeker awareness reduces the game value, with the difference between the restricted and feedback models bounded by the entry-wise gap between the corresponding payoff matrices. Numerical examples show how this benefit decreases as the switching cost increases and as the reveal occurs later along the route.

eess.SY↗

arXiv2025

Where to Fly, What to Send: Communication-Aware Aerial Support for Ground Robots

In this work we consider a multi-robot team operating in an unknown environment where one aerial agent is tasked to map the environment and transmit (a portion of) the mapped environment to a group of ground agents that are trying to reach their goals. The entire operation takes place over a bandwidth-limited communication channel, which motivates the problem of determining what and how much information the assisting agent should transmit and when while simultaneously performing exploration/mapping. The proposed framework enables the assisting aerial agent to decide what information to transmit based on the Value-of-Information (VoI), how much to transmit using a Mixed-Integer Linear Programming (MILP), and how to acquire additional information through an utility score-based environment exploration strategy. We perform a communication-motion trade-off analysis between the total amount of map data communicated by the aerial agent and the navigation cost incurred by the ground agents.

cs.RO↗

arXiv2025

A Dual Approach for Hierarchical Information-Theoretic Tree Abstractions

In this paper, we consider establishing a formal connection between two distinct tree-abstraction problems inspired by the information-bottleneck (IB) method. Specifically, we consider the hard- and soft-constrained formulations that have recently appeared in the literature to determine the conditions for which the two approaches are equivalent. Our analysis leverages concepts from Lagrangian relaxation and duality theory to relate the dual function of the hard-constrained problem to the Q-function employed in Q-tree search and shows the connection between tree phase transitions and solutions to the dual problem obtained by exploiting the problem structure. An algorithm is proposed that employs knowledge of the tree phase transitions to find a setting of the dual variable that solves the dual problem. Furthermore, we present an alternative approach to select the dual variable that leverages the integer programming formulation of the hard-constrained problem and the strong duality of linear programming. To obtain a linear program, we establish that a relaxation of the integer programming formulation of the hard-constrained tree-search problem has the integrality property by showing that the program constraint matrix is totally unimodular. Empirical results that corroborate the theoretical developments are presented and discussed throughout.

cs.IT↗

arXiv2025

The Silence that Speaks: Neural Estimation via Communication Gaps

Accurate remote state estimation is a fundamental component of many autonomous and networked dynamical systems, where multiple decision-making agents interact and communicate over shared, bandwidth-constrained channels. These communication constraints introduce an additional layer of complexity, namely, the decision of when to communicate. This results in a fundamental trade-off between estimation accuracy and communication resource usage. Traditional extensions of classical estimation algorithms (e.g., the Kalman filter) treat the absence of communication as 'missing' information. However, silence itself can carry implicit information about the system's state, which, if properly interpreted, can enhance the estimation quality even in the absence of explicit communication. Leveraging this implicit structure, however, poses significant analytical challenges, even in relatively simple systems. In this paper, we propose CALM (Communication-Aware Learning and Monitoring), a novel learning-based framework that jointly addresses the dual challenges of communication scheduling and estimator design. Our approach entails learning not only when to communicate but also how to infer useful information from periods of communication silence. We perform comparative case studies on multiple benchmarks to demonstrate that CALM is able to decode the implicit coordination between the estimator and the scheduler to extract information from the instances of 'silence' and enhance the estimation accuracy.

eess.SY↗

arXiv2025

Target Defense against Sequentially Arriving Intruders: Algorithm for Agents with Dubins Dynamics

We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. Both the defender and the intruders have non-holonomic dynamics. The intruders' objective is to breach the target perimeter without being captured by the defender, while the defender's goal is to capture as many intruders as possible. After one intruder breaches or is captured, the next appears randomly on a fixed circle surrounding the target. Therefore, the defender's final position in one game becomes its starting position for the next. We divide an intruder-defender engagement into two phases, partial information and full information, depending on the information available to the players. We address the capturability of an intruder by the defender using the notions of Dubins path and guarding arc. We quantify the percentage of capture for both finite and infinite sequences of incoming intruders. Finally, the theoretical results are verified through numerical examples using Monte-Carlo-type random trials of experiments.

eess.SY↗

arXiv2025

Data to Certificate: Guaranteed Cost Control with Quantization-Aware System Identification

Cloud-assisted system identification and control have emerged as practical solutions for low-power, resource-constrained control systems such as micro-UAVs. In a typical cloud-assisted setting, state and input data are transmitted from local agents to a central computer over low-bandwidth wireless links, leading to quantization. This paper investigates the impact of state and input data quantization on a linear time invariant (LTI) system identification, derives a worst-case bound on the identification error, and develops a robust controller for guaranteed cost control. We establish a fundamental bound on the model error that depends only on the quantized data and quantization resolution, and develop a linear matrix inequality (LMI) based guaranteed cost robust controller under this error bound.

eess.SY↗

arXiv2025

Multi-Attacker Single-Defender Target Defense in Conical Environments

We consider a variant of the target defense problem in a planar conical environment where a single defender is tasked to capture a sequence of incoming attackers. The attackers' objective is to breach the target boundary without being captured by the defender. As soon as the current attacker breaches the target or gets captured by the defender, the next attacker appears at the boundary of the environment and moves radially toward the target with maximum speed. Therefore, the defender's final location at the end of the current game becomes its initial location for the next game. The attackers pick strategies that are advantageous for the current as well as for future engagements between the defender and the remaining attackers. The attackers have their own sensors with limited range, using which they can perfectly detect if the defender is within their sensing range. We derive equilibrium strategies for all the players to optimize the capture percentage using the notions of capture distribution. Finally, the theoretical results are verified through numerical examples using Monte Carlo type random trials of experiments.

eess.SY↗

arXiv2025

A Linear Programming Framework for Optimal Event-Triggered LQG Control

This letter explores intelligent scheduling of sensor-to-controller communication in networked control systems, particularly when data transmission incurs a cost. While the optimal controller in a standard linear quadratic Gaussian (LQG) setup can be computed analytically, determining the optimal times to transmit sensor data remains computationally and analytically challenging. We show that, through reformulation and the introduction of auxiliary binary variables, the scheduling problem can be cast as a computationally efficient mixed-integer linear program (MILP). This formulation not only simplifies the analysis but also reveals structural insights and provides clear decision criteria at each step. Embedding the approach within a model predictive control (MPC) framework enables dynamic adaptation, and we prove that the resulting scheduler performs at least as well as any deterministic strategy (e.g., periodic strategy). Simulation results further demonstrate that our method consistently outperforms traditional periodic scheduling.

eess.SY↗

arXiv2025

Target Defense Using a Turret and Mobile Defender Team

A scenario is considered wherein a stationary, turn constrained agent (Turret) and a mobile agent (Defender) cooperate to protect the former from an adversarial mobile agent (Attacker). The Attacker wishes to reach the Turret prior to getting captured by either the Defender or Turret, if possible. Meanwhile, the Defender and Turret seek to capture the Attacker as far from the Turret as possible. This scenario is formulated as a differential game and solved using a geometric approach. Necessary and sufficient conditions for the Turret-Defender team winning and the Attacker winning are given. In the case of the Turret-Defender team winning equilibrium strategies for the min max terminal distance of the Attacker to the Turret are given. Three cases arise corresponding to solo capture by the Defender, solo capture by the Turret, and capture simultaneously by both Turret and Defender.

eess.SY↗