Research
Research
Research
Research
1,293+ open-access research outputs.
Let $\mathcal{OP}_n$ be the monoid of all orientation-preserving full transformations on $X_n=\{1,\dots, n\}$ with the natural order. For $\alpha \in \mathcal{OP}_n$, let $F(\alpha)=\{y\in X_n: y\alph…
We develop an analytical framework for Boolean Promise Constraint Satisfaction Problems (PCSPs) that studies polymorphisms through the notion of influence from Fourier analysis of Boolean functions. E…
We study existence and uniqueness for one-dimensional generalized stochastic differential equations with singular coefficients, including distributional drift and degenerate, possibly discontinuous, d…
For a simple graph $G$ with $n$ vertices, let $A_G$ denote the adjacency matrix of $G$, and let $\lambda_1(G) \geq \lambda_2(G) \geq \dots \geq \lambda_n(G)$ be its eigenvalues. For an integer $p \geq…
The response of Ni-Cr alloys to exposure to molten chloride and fluoride salts is typically characterized by Cr dealloying with the formation of a Cr-depleted bi-continuous porous subsurface layer. Th…
The present work is a continuation of our earlier investigation with the primary objective to systematically calculate the $E2$ matrix elements using the microscopic approach of the triaxial projected…
Since the breakthrough superpolynomial multilinear formula lower bounds of Raz (Theory of Computing 2006), proving such lower bounds against multilinear algebraic branching programs (mABPs) has been a…
Black hole thermodynamics in Lorentz-violating gravity is subtle because different excitations propagate at different speeds and hence identify different causal horizons. We revisit Einstein--AEther g…
The $k$-means problem is a classic objective for modeling clustering in a metric space. Given a set of points in a metric space, the goal is to find $k$ representative points so as to minimize the sum…
The Pareto sum of two-dimensional point sets $P$ and $Q$ in $\mathbb{R}^2$ is defined as the skyline of the points in their Minkowski sum. The problem of efficiently computing the Pareto sum arises fr…
Individual head-related transfer functions (HRTFs) are essential for accurate spatial audio binaural rendering but remain difficult to obtain due to measurement complexity. This study investigates whe…
We prove an asymptotic formula for the second moment of the first derivative of quadratic twists of modular $L$-functions with three leading order main terms. It improves the previous result of Kumar …
A three-component plasma model composed of ions, cool electrons, and hot electrons is adopted to investigate the existence of large amplitude electron-acoustic solitons not only for the model for whic…
Locally decodable codes (LDCs) are error correction codes that allow recovery of any single message symbol by probing only a small number of positions from the (possibly corrupted) codeword. Relaxed l…
We say a set of points $C\subset \mathbb{R}^n$ is canonically Ramsey if there is some set of points $S\subset \mathbb{R}^{n'}$ such that any colouring of $S$, with any number of colours, admits either…
The Spearman footrule is a voting rule that takes as input voter preferences expressed as rankings. It outputs a ranking that minimizes the sum of the absolute differences between the position of each…
In this work, we derive an exact vacuum solution to the Einstein field equations that depends on three constant parameters: the throat radius $r_0$, a parameter $q$, which is closely associated with t…
This paper investigates the semi-streaming complexity of \textit{$k$-partial coloring}, a generalization of proper graph coloring. For $k \geq 1$, a $k$-partial coloring requires that each vertex $v$ …
Let $\mathcal R_{n}$ be the set of all rational functions of the type $r(z) = f(z)/w(z)$, where $f(z)$ is a polynomial of degree at most $n$ and $w(z) = \prod_{j=1}^{n}(z-\beta_j)$, $|\beta_j|>1$ for …
A key tenet of general relativity is the dynamical nature of space-time, ideally represented as an initial value problem. Here we explore the variational formulation of classical Einstein-Hilbert grav…
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