Research
Research
Research
Research
10,718+ 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…
We prove the Jordan curve theorem by generalizing the sweepline algorithm for trapezoidal decomposition of a polygon. Our proof uses Zorn's lemma (or, equivalently the axiom of choice). Though several…
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 …
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…
Standard text-to-speech (TTS) evaluation measures intelligibility (WER, CER) and overall naturalness (MOS, UTMOS) but does not quantify accent. A synthesiser may score well on all four yet sound non-n…
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…
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