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Active galactic nuclei (AGN) are key drivers of galaxy evolution, yet many remain undetected in ultraviolet and optical surveys due to heavy dust obscuration. In these systems, absorbed emission is re-radiated at infrared (IR) wavelengths,…
Simulation-based testing is widely used to validate Cyber-Physical Systems (CPSs), yet modern CPS simulators frequently exhibit non-deterministic (flaky) behavior, making failures difficult to reproduce and debug. Although delta debugging…
This paper addresses statistical inference for stochastic partial differential equations. We study the stochastic Allen-Cahn equation driven by space-time white noise and analyze its mild solution. Our main focus is the asymptotic behavior…
We study the simultaneous approximation of constant-degree polynomials over convex sets. For any family of $m$ degree-$d$ polynomials and any convex set ${H} \subseteq \mathbb{R}_{\ge0}^n$, we construct an $\epsilon$-Cover of the joint…
Synchronization often emerges spontaneously among interacting people, yielding practical benefits for tasks such as sports, physical rehabilitation, and collaborative manufacturing, and fostering a sense of unity and trust. Although visual…
We study the combinatorial Yamabe flow on infinitely triangulated surfaces with piecewise hyperbolic metrics. Under the assumptions of uniformly bounded vertex degree and $\epsilon$-uniformly nondegenerate initial metric, we first establish…
Proximity effects in layered heterostructures are usually represented by static parameters fitted to first-principles bands, which discards the energy dependence of the virtual hybridization, the momentum transfer, and the spatial…
Semidefinite relaxations of binary optimization problems often fail Slater's condition. Full facial reduction restores strict feasibility but may require auxiliary problems as costly as the original relaxation. We analyze partial facial…
Antichiral states propagate in the same direction on opposite boundaries, defying the conventional constraint that boundary modes must cancel net chirality. Previously found antichiral states have been limited to first-order topological…
Full-field reconstruction of air pollution is essential for evaluating pollution exposure and supporting public health decision-making. However, the complex interactions among pollutants, hard-to-predict weather patterns, and limited…
We prove that the resonances for a generic smooth expanding map are simple and that zero is a regular value for the associated resonant states. Moreover, the real-valued resonant states are Morse functions. Using Nash-Moser theory, we also…
The probability-flow ordinary differential equation (PF-ODE) associated with a diffusion process is widely used in score-based generative modeling as a deterministic sampler that reproduces the marginal distributions of the diffusion. While…
We study the quantum mechanics of a charged particle confined to the surface of a cube enclosing a magnetic monopole. The magnetic field is chosen to have a constant magnitude on each face and to point along the outward normal, preserving…
Characterizing when the symbolic and ordinary powers of an ideal coincide is a central problem in commutative algebra, and ideals satisfying this property are called Simis ideals. In this article, we investigate the Simis property of…
In this work, we introduce $t$-colorable $k$-plane drawings, that is, drawings of graphs with a $t$-edge-coloring where every edge is crossed by at most $k$ edges of each color. We give tight upper bounds on the edge- and crossing density…
Cognitive distortion amplifies negative emotions and contributes to mental health disorders. Cognitive Behavioral Therapy (CBT) is an effective way to address cognitive distortions, but its large-scale application is limited by the shortage…
We propose Rashomon Alignment (RA), a new measure to assess functional similarity between two models. Existing functional similarity measures are distributional, quantifying differences between outputs of models applied to real-world data.…
Multimodal behavioral analysis offers a scalable approach to assessing depression, anxiety, and stress, yet generic fusion models often ignore the psychometric structure of questionnaire labels. In DASS-21, risk labels are derived from…
Controlling heat flow in small quantum systems is a central goal of quantum thermodynamics and nanoscale transport. A key challenge is to achieve strong thermal rectification without suppressing the transmitted heat current, a tradeoff that…
This note discusses zero-sum games with open-ended innovation, whereby each player may introduce new strategies. The innovation process is modelled as a draw of new strategies form a distribution. It is argued that, under generic…