1645542 results (page 4 of 65822)
-
A Least-Squares Weak Galerkin Method for the Biharmonic Cauchy Problem
We develop a least-squares weak Galerkin (LS-WG) finite element method for the Cauchy problem of the biharmonic equation. The proposed approach reformulates the fourth-order equation as a coupled system of two second-order equations, which are discretized using discrete weak Laplacian operators on weak finite element spaces. The resulting least-squares formulation yields a symmetric positive defin…
-
A General Set-Based Framework for Cognitive State Estimation: Theory and Application to Conditionally Automated Driving
We present a set-based framework for estimating human cognitive states in human-automation interaction (HAI) contexts. Unlike probabilistic approaches dominant in the HAI literature, our framework treats process and measurement uncertainties as unknown but bounded, avoiding the need for large structured datasets or distributional assumptions on noise. We demonstrate the framework in the context of…
-
The Push-Forward Transform for Continuous and Robust Comparison of Dynamic Shapes
We introduce a mathematical framework for shape comparison based on mapping functions from the shape domain to a common reference domain. This Push-Forward Transform enables invariant and robust comparison of shapes, preserving intrinsic geometric information. Quantitatively comparing shapes and their temporal evolution is a fundamental challenge in image analysis. Meaningful shape comparison requ…
-
Real-rootedness of Kazhdan--Lusztig and $Z$-polynomials of thagomizer matroids and graphic matroids of $K_{2,n}$
Let $T_n=K_{1,1,n}$, and let $P_n(x)$ denote the Kazhdan--Lusztig polynomial of its graphic matroid. We prove that, whenever $n\ge2$ and $0\leλ\le n/2$, the polynomial $P_n(x)+λx$ has exactly $\lfloor n/2\rfloor$ zeros, all of which are negative and simple. In particular, the Kazhdan--Lusztig polynomials of the graphic matroids of $T_n$ and $K_{2,n}$ are real-rooted. We also prove that, for $n\ge2…
-
Ramsey multiplicity for ordered graphs
Let \(\cG_1,\ldots,\cG_k\) be fixed vertex-ordered graphs, each containing at least one edge. The ordered Ramsey number \(\oR(\cG_1,\ldots,\cG_k)\) is the least integer \(N\) such that every \(k\)-edge-coloring of the ordered complete graph \(\cK_N\) contains an order-preserving copy of \(\cG_i\) in color \(i\) for some \(i\in[k]\). For positive weights \(\blambda=(λ_1,\ldots,λ_k)\), let \(\oM_{\b…
-
Quantum resetting with memory
We introduce a quantum stochastic resetting protocol with uniform memory, in which each resetting event returns the system to a state visited at a time chosen uniformly from its entire history. The resulting dynamics is nonunitary, non-Markovian and a direct quantum generalization of the classical preferential relocation model. Working in the energy eigenbasis, we derive the exact evolution of eve…
-
Dynamic Traffic Allocation for Revenue Maximization on Creator Economy Platform
Creator economy platforms face a strategic dilemma: allocating traffic to established stars for immediate ad revenue versus nurturing emerging creators to build a follower base for future monetization. We develop a continuous-time dynamic optimization model to characterize the optimal traffic allocation policy for a platform managing heterogeneous creators with dual revenue streams (advertising an…
-
Spectral Properties of Power Graphs of Metacyclic Groups
For a group $Ω$, the associated power graph $P(Ω)$ is defined as the graph whose vertices are the elements of $Ω$, with two distinct vertices $u,v\in Ω$ being adjacent if either $u=v^m$ or $v=u^n$ for some $m,n \in \mathbb{N}$. In this paper, we completely characterise the structure of the power graph associated with the class of metacyclic groups. Building on this structural description, we deriv…
-
Counting cliques in graphs with small independence number
We prove that for all fixed $k\geq 4$, any $N$ vertex graph with no independent set of size $n$ and $N\geq Ω(n^{k-1}/\log^{k-2}n)$ contains at least $$ Ω\bigg(\binom Nk \Big(\frac{\log n}{n}\Big)^{\binom k2}/\log n\bigg) $$ cliques of order $k$, and for $k\geq 5$ this is best possible conditional on the known upper bounds for $r(k,n)$. This is also true and tight for $k=2$ by Turán's Theorem and f…
-
Effects of realistic pulse shapes in two-dimensional spectroscopy
Two-dimensional (2D) spectroscopy is a powerful pump-pump-probe technique for revealing couplings between quantum states and disentangling the different contributions to the optical response of a system. We present an efficient method for 2D spectroscopy simulations in the Markovian limit for the environment, capable of handling arbitrary pulse shapes and reproducing time-ordering and overlapping …
-
On Erdős--Ko--Rado and Hilton--Milner Theorems for Direct Products
Let $X=X_1\mathbin{\dot\cup}\cdots\mathbin{\dot\cup}X_p$ and $\mathcal{H}(\boldsymbol k)=\{F\subseteq X:|F\cap X_i|=k_i\text{ for every }i\}$. We study $t$-intersecting families in one such layer and in finite unions of layers under the ordinary condition $|A\cap B|\ge t$. A generating-set method reduces every shifted extremal non-star system to at most $pt$ supporting points. This gives coordinat…
-
Hidden Symmetry of Kerr-deSitter from Manifest Symmetry of Painlevé VI
We show that the recently discovered ``mass symmetries" of the radial Teukolsky equation for Kerr-deSitter black holes can be understood from a corresponding symmetry of the Painlevé VI equation via the classical theory of ``isomonodromic deformations". It is known that a subset of the mass symmetries transforms the Teukolsky equation to a wave equation on a ``dual" Lorentzian spacetime. We find t…
-
Discrete-Time Adaptive Control in High Dimensions: Near Dimension-Free Performance via Mirror Descent
Motivated by the use of modern high-capacity models in real-time control problems, this paper studies the adaptive control of high-dimensional discrete-time nonlinear systems with an unknown matrix-valued parameter. We focus on regimes where the number of unknown parameter entries is large, but the parameter matrix possesses exploitable structure, such as entrywise sparsity, group sparsity, low ra…
-
A Frequency-Domain approach to detect nonstationarity in dependent data
Distinguishing long memory behaviour from nonstationarity can be very difficult as in both cases the sample autocovariance function decays very slowly. Available stationarity tests either do not include long memory or fare poorly in terms of empirical size, especially near the boundary between long memory and nonstationarity. We propose a testing procedure based on evaluating periodograms at diffe…
-
Phase-Drift Limits and Adaptive Quadrature Readout in Programmable Photonic Processors
Phase fluctuations between optical inputs limit programmable photonic processors because their output powers depend on coherent interference. We study the phase-drift penalty that arises when sine and cosine quadratures are measured sequentially rather than simultaneously. The analysis is motivated by measurements from an eight-mode programmable photonic processor, including 35 free-running record…
-
An Accessible Solution for Deformable Image Registration Compared with Learning-Based Approaches
Deformable image registration (DIR) is a core problem in medical image analysis; but, unlike labeling decision problems such as classification and segmentation, registration is a problem class that involves stringent physical constraints. Although deep learning methods have made faster registration possible, the resulting models are often difficult to interpret compared to hand-crafted methods wit…
-
Quantum computer-based simulation of Stark many-body localization in a 1D Fermi-Hubbard model
Many-body localization (MBL) is a dynamical phenomenon that describes the non-ergodicity of isolated quantum many-body systems. In contrast to thermalization, this phenomenon leads to a long-lived memory of initial states of local systems and slow growth of entanglement. In this work, we study Stark MBL in a 12-qubit correlated fermionic system described by the one-dimensional Fermi-Hubbard model …
-
Efficiency and Cost Alignment in Batched LLM Serving via Resource-Fair Scheduling
This paper studies a resource-allocation inefficiency in batched large language model (LLM) serving: heterogeneous requests that share a decode batch impose max-driven computational costs on one another. Because the wall-clock cost of a batch step is largely governed by the largest active KV-cache footprint, a short request co-batched with a long request can experience latency and GPU-resource con…
-
Linear Lower Bounds for the Modular Chromatic Index
Let $k\geq2$ be an integer. A $1\bmod k$ edge-coloring of a graph $G$ is an edge-coloring in which every nonzero degree in each color class is congruent to $1$ modulo $k$. Let $χ'_k(G)$ denote the minimum number of colors required, and let $χ'_k$ be the supremum of $χ'_k(G)$ over all finite simple graphs $G$. Botler, Colucci, and Kohayakawa conjectured that there exists an absolute constant $C$ su…
-
Multiple Zeta Values
These lecture notes are based on three courses given at Nagoya University. Their purpose is to give a beginner-friendly introduction to multiple zeta values and several of their variants, such as finite and symmetric multiple zeta values, q-analogues of multiple zeta values, and multiple Eisenstein series. These notes will be updated in the future.
-
On the Impact of Gas-Line Absorption in Long-Haul C+L-Band Hollow-Core Fibre Transmission
We numerically investigate gas-line absorption in hollow-core fibre C+L-band transmission. Results show limited C-band but severe L-band performance degradation. Ideal suppression enables a 1.5$\times$ higher L-band throughput, reaching 59.1 Tb/s over 1000 km, while reducing repeater number by up to 3.3$\times$.
-
Discontinuous Galerkin Semidiscretization of the Information Geometric Regularized Compressible Euler Equations
Shock stabilization in compressible Euler flows remains a central challenge for high-order numerical methods. Existing shock-capturing approaches, including limiters, artificial viscosity, and reconstruction-based methods, involve tradeoffs between robustness, accuracy, preservation of fine-scale flow features, and computational complexity. In this work, we develop a discontinuous Galerkin (DG) di…
-
Solving the Dissipation Inequality not as a constitutive restriction
A solution procedure is formulated and solved for treating the nonlinear Dissipation Inequality as a constraint equation within continuum mechanics, and allowing for incomplete knowledge of constitutive behavior. The scheme is demonstrated in the context of the rate-dependent, elastoplastic response of a bar, resulting in a nonlinear problem of constrained optimization. Both closed form and comput…
-
The narrow escape problem in arbitrary dimension
The narrow escape problem is a prototypical example for studying entropic metastability, motivated by the analysis of biological and chemical systems. The problem concerns the determination of the exit time and position of a Brownian particle trapped in a domain with a reflecting boundary pierced by narrow holes. Our goal is to investigate this problem in a general domain in any dimension (greater…
-
Self-supervised DXA representations encode multi-system disease risk, biological aging and heritability
Whole-body dual-energy X-ray absorptiometry (DXA) scans are routinely acquired to measure bone density and regional body composition, leaving their spatial structure largely unused. Here, we show that self-supervised learning (SSL) can convert raw DXA images into representations of systemic health. We introduce LeDXA, a vision model based on a joint-embedding predictive architecture (JEPA) that le…