Research
Research
Research
Research
15,928+ open-access research outputs.
This work investigates minimal parametric networks in hyperspaces of closed subsets of metric spaces endowed with the Hausdorff distance. It is shown that the problems of finding such networks are non…
We develop the ODE/IM correspondence for the higher-order Mathieu equation arising from the quantum Seiberg-Witten curve of the pure $SU(r+1)$ ${\cal N}=2$ supersymmetric Yang-Mills theory. From the s…
A foundational assumption in CNN interpretability -- that deep encoders suppress background pixels while classifiers merely select from a cleaned feature pool (the Spatial Funnel Hypothesis) -- remain…
Many well-known theorems establish sufficient criteria for linearizability of a vector field in terms of the eigenvalues of its linear approximation. By attaching weights to coordinates so that some d…
The maximum likelihood estimator in nonlinear panel data models with interactive fixed effects is biased. Several bias correction methods, such as analytical and jackknife approaches, have been propos…
We present a Spatially Embedded Evolutionary Algorithm where robot individuals exist in a physically simulated 2D environment, must navigate to encounter potential mates, and compete for survival unde…
Motivated by sensing modalities in modern autonomous systems that involve hardware-constrained spatial sampling over large arrays with limited coherence time, we develop a novel framework for rapid su…
We consider the problems of computing the optimal rank-$1$ Hankel and Toeplitz-structured approximation of arbitrary matrices under $L_2$ and $L_1$-norm error. Such problems arise naturally in enginee…
We prove that if a small Hankel operator on the product Hardy space belongs to some Schatten class $S^p$, $p < \infty$, then it has a symbol in product BMO. In other words, the conclusion of Nehari's …
As Rust gains traction for developing safer systems software, a reality check for the microcontroller hardware segment becomes necessary. How ready is the Rust ecosystem for this segment? Can Rust com…
One of the most important applications of topological recursion concerns spectral curves for which the functions $(x,y)$ defining the spectral curve are allowed to have logarithmic singularities. This…
The Strongly Connected Steiner Subgraph (SCSS) problem is a well-studied network design problem that asks for a minimum subgraph that strongly connects a given set of terminals. In this paper, we pres…
In this paper, we investigate the role of spectral networks in quantum Liouville theory, with particular emphasis on spectral networks of Fenchel-Nielsen-type. In the first part, we construct q-parall…
In the previous paper, the author showed that for a smooth family $X \to \mathbb{X} \to B$ of a homotopy $K3$ surface, the obstruction for the tangent bundle along the fibers $T_B \mathbb{X}$ to have …
While the optimal sample complexity of binary classification in terms of the VC dimension is well-established, determining the optimal sample complexity of multiclass classification has remained open.…
We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smoot…
We show that in critical loop models, torus 1-point functions can be expressed in terms of sphere 4-point functions at a different central charge. Unlike in the Moore--Seiberg formalism, crossing symm…
This paper proposes a new randomized design of digital nets in which the generating matrices are chosen to be random Hankel matrices. Compared with previous randomized designs of digital nets, this ap…
We study a renormalization-group (RG) improved Schwarzschild-like black hole (BH) whose lapse interpolates between a classical Schwarzschild exterior and a quantum-smoothed interior governed by a cuto…
Vehicle diagnostics has become essential for detecting in-vehicle errors and ensuring safety. While the Unified Diagnostic Services (UDS) protocol is widely adopted for diagnostic operations, it relie…
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