相关论文: Positive Alexander Duality for Pursuit and Evasion

While many games were designed for steganography and robust watermarking, few focused on reversible watermarking. We present a two-encoder game related to the rate-distortion optimization of content-adaptive reversible watermarking. In the…

Exploration is a prerequisite for learning useful behaviors in sparse-reward, long-horizon tasks, particularly within 3D environments. Curiosity-driven reinforcement learning addresses this via intrinsic rewards derived from the mismatch…

Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…

One of the advantages of working with Alexander-Spanier-\v{C}ech type cohomology theory is the continuity property: For inverse systems of sufficiently well-behaved spaces, the result of taking the cohomology of their limit is a direct…

In this work I clarify VAT evasion incentives through a game theoretical approach. Traditionally, evasion has been linked to the decreasing risk aversion in higher revenues (Allingham and Sandmo (1972), Cowell (1985) (1990)). I claim tax…

This technical note compares two coding (quantization) schemes for random projections in the context of sub-linear time approximate near neighbor search. The first scheme is based on uniform quantization while the second scheme utilizes a…

This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of…

We investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first…

We consider the connections among algebraic cycles, abelian varieties, and stable rationality of smooth projective varieties in positive characteristic. Recently Voisin constructed two new obstructions to stable rationality for rationally…

When learning to play an imperfect information game, it is often easier to first start with the basic mechanics of the game rules. For example, one can play several example rounds with private cards revealed to all players to better…

In a previous paper we have suggested a number of ideas to attack circuit size complexity with cohomology. As a simple example, we take circuits that can only compute the AND of two inputs, which essentially reduces to SET COVER. We show a…

Code search is vital in the maintenance and extension of software systems. Past works have used separate language models for the natural language and programming language artifacts on models with multiple encoders and different loss…

We develop a homological duality framework based on a contravariant functor $D=\operatorname{Hom}_E(-,R)$ with dualizing object $R$. A morphism is called ethic when it satisfies the canonical double-dual compatibility $D^2(f)\eta=\eta f$.…

In this work we introduce and study a pursuit-evasion game in which the search is performed by heterogeneous entities. We incorporate heterogeneity into the classical edge search problem by considering edge-labeled graphs: once a search…

Continual learning systems operating in fixed-dimensional spaces face a fundamental geometric barrier: the flat manifold problem. When experience is represented as a linear trajectory in Euclidean space, the geodesic distance between…

The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled…

In this work we present a hierarchical framework for solving discrete stochastic pursuit-evasion games (PEGs) in large grid worlds. With a partition of the grid world into superstates (e.g., "rooms"), the proposed approach creates a…

The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…

We prove the vanishing of bounded cohomology with separable dual coefficients for many groups of interest in geometry, dynamics, and algebra. These include compactly supported structure-preserving diffeomorphism groups of certain manifolds;…

Many application areas collect unstructured trajectory data. In subtrajectory clustering, one is interested to find patterns in this data using a hybrid combination of segmentation and clustering. We analyze two variants of this problem…