Research
Research
Research
Research
195+ open-access research outputs.
Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testi…
While first-order stationary points (FOSPs) are the traditional targets of non-convex optimization, they often correspond to undesirable strict saddle points. To circumvent this, attention has shifted…
Self-generated skills for web agents are often unstable and can even hurt performance relative to direct acting. We argue that the key bottleneck is not only skill generation quality, but the fact tha…
We study curvature-driven edge reweighting for community recovery in the balanced two-block stochastic block model. Given a graph G with initial weights equal to the adjacency matrix, we iteratively u…
In continuous aperture arrays (CAPAs), careful consideration of the underlying physics is essential, among which electromagnetic (EM) mutual coupling plays a critical role in beamforming performance. …
Increasingly artificial intelligence (AI) has been cast in "god-like" roles (to name a few: film industry - Matrix, The Creator, Mission Impossible, Foundation, Dune etc.; literature - Children of Tim…
We investigate the following longstanding open questions raised by Kraj\'i\v{c}ek and Pudl\'ak (J. Symb. L. 1989), Sadowski (FCT 1997), K\"obler and Messner (CCC 1998) and Messner (PhD 2000). Q1: Do…
In sparse LU factorization, nonzero elements after symbolic factorization tend to distribute in diagonal and right-bottom region of sparse matrices. However, regular 2D blocking on this non-uniform di…
This paper presents a novel algorithm for constructing a sum-of-squares (SOS) decomposition for positive semi-definite polynomials with rational coefficients. Unlike previous methods that typically yi…
The configuration model is a cornerstone of statistical assessment of network structure. While the Chung-Lu model is among the most widely used configuration models, it systematically oversamples edge…
This article introduces HYLU, a hybrid parallel LU factorization-based general-purpose solver designed for efficiently solving sparse linear systems (Ax=b) on multi-core shared-memory architectures. T…
Efficiently solving large-scale linear systems is a critical challenge in electromagnetic simulations, particularly when using the Crank-Nicolson Finite-Difference Time-Domain (CN-FDTD) method. Existi…
The assortative behavior of a network is the tendency of similar (or dissimilar) nodes to connect to each other. This tendency can have an influence on various properties of the network, such as its r…
Due to their numerous applications, in particular in Mechanism Design, Prophet Inequalities have experienced a surge of interest. They describe competitive ratios for basic stopping time problems wher…
In this work, we prove upper and lower bounds over fields of positive characteristics for several fragments of the Ideal Proof System (IPS), an algebraic proof system introduced by Grochow and Pitassi…
Augmenting the input of algorithms with predictions is an algorithm design paradigm that suggests leveraging a (possibly erroneous) prediction to improve worst-case performance guarantees when the pre…
Given a directed graph $G$ with $n$ vertices and $m$ edges, a parameter $k$ and two disjoint subsets $S,T \subseteq V(G)$, we show that the number of all-subsets important separators, which is the num…
The online stochastic matching problem was introduced by [FMMM09], together with the $(1-\frac1e)$-competitive Suggested Matching algorithm. In the most general edge-weighted setting, this ratio has n…
Let $A$ and $B$ be two number sequences of length $n$ and $m$, respectively, where $m\le n$. Given a positive number $\delta$, a common almost increasing sequence $s_1\ldots s_k$ is a common subsequen…
We consider the (offline) vertex-weighted Online Matching problem under Known Identical and Independent Distributions (KIID) with integral arrival rates. We propose a meta-algorithm, denoted as $\math…
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