Research
Research
Research
Research
9,033+ open-access research outputs.
We give a self-contained, modern exposition of \'Edouard Goursat's 1887 theorem on pseudo-elliptic integrals -- those integrals of the form $\int F(t)\,\d t/\sqrt{R(t)}$ with $R$ a cubic or quartic po…
We develop a geometric and information-theoretic framework for encoder-decoder learning built on the Information Bottleneck (IB) principle. Recasting IB as a rate-distortion problem with Kullback-Leib…
Software stacks embedded on microcontroller-based hardware typically provide rudimentary APIs programmed in C/C++, basic connectivity and, sometimes, a firmware update mechanism. Such coarse mechanism…
Computing edge-connected components in directed and undirected graphs is a fundamental and well-studied problem in graph algorithms. In a very recent breakthrough, Korhonen [STOC 2025] showed that for…
Category-based coordination mechanisms allocate resources by mapping a declared service category to a fixed resource profile, without observing individual demand types. We establish three results for …
The Gram matrix is a classical object formed from the pairwise inner products of a collection of vectors, with fundamental roles in functional analysis, statistics, combinatorics, and coding theory. I…
Distributional learning provides a framework for studying the learnability of structured languages from positive data. In this paper, we extend this framework to graph languages generated by fixed-int…
Algorithms with predictions is a growing area that aims to leverage machine-learned predictions to design faster beyond-worst-case algorithms. In this paper, we use this framework to design a learned …
Goppa codes form an important class of alternant codes with wide applications in algebraic coding theory and code-based cryptography. Determining the true minimum distance of a Goppa code is a difficu…
Job-scheduling games have traditionally assumed fixed processing times. However, in many realistic environments, ranging from cyber-security response to high-frequency trading, a task's duration depen…
Injecting artificial noise (AN) along the tangent space of a curved constellation makes each transmitted symbol induce a Gaussian observation with a symbol-dependent rank-one covariance, so the matche…
Barrett reduction is the nonlinear core of every practical NTT-based post-quantum cryptography implementation. Existing composition frameworks (ISW, t-SNI, PINI, DOM) address Boolean masking over GF(2…
Large language model (LLM) agents increasingly operate as sequential software systems, but their reliability is often summarized by scalar benchmark metrics. Metrics such as pass$@k$, pass$^k$, and th…
Trusted Execution Environments (TEEs) on low-power microcontrollers (e.g., ARM TrustZone-M) enable isolation of Secure and Non-Secure software but still require both worlds to share resources, includi…
A heap is a dynamic data structure that stores a set of labeled values under the following operations: pop returns the minimum value of the heap, Push($x_i$) pushes a new value $x_i$ onto the heap, an…
The Fr\'echet distance is a popular distance measure between trajectories or curves in space, or between walks in graphs. We study computing the Fr\'echet distance between walks in the $d$-dimensional…
A compressed self-index stores a string in compressed form while supporting locate queries without decompression. For highly repetitive strings (arising in web crawls, versioned documents, and genomic…
We prove that any algorithm for detecting cycles in an $m \times n$ grid graph, where cells are colored and adjacency is defined by matching colors, must read all $mn$ cells in the worst case for all …
When writing programs involving matrices or tensors in general, it is desirable to rule out the inconsistency of tensor shapes (i.e., the generalization of matrix sizes) before actual computation. For…
In Transformer models, non-GEMM (non-General Matrix Multiplication) operations -- especially Softmax and Layer Normalization (LayerNorm) -- often dominate hardware cost due to their nonlinear nature. …
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