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Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this…
Previous work on soft-gluon resummation for direct photon production is extended to include additional subleading logarithmic terms through O(alpha alpha_s^3) and some representative comparisons are made to experimental results from the…
Weakly distance-regular digraphs are a natural directed version of distance-regular graphs. In [8], the third author and Suzuki proposed a question when an orientation of a distance-regular graph defines a weakly distance-regular digraph.…
We give the first truly subquadratic time algorithm, with $O^*(n^{2-1/18})$ running time, for computing the diameter of an $n$-vertex unit-disk graph, resolving a central open problem in the literature. Our result is obtained as an instance…
Strong product is an efficient way to construct a larger digraph through some specific small digraphs. The large digraph constructed by the strong product method contains the factor digraphs as its subgraphs, and can retain some good…
Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse and complex molecular and biomolecular datasets due to the limited…
Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced…
Diameter, radius and eccentricities are fundamental graph parameters, which are extensively studied in various computational settings. Typically, computing approximate answers can be much more efficient compared with computing exact…
Discrete diffusion models offer a promising alternative to autoregressive generation through parallel decoding, but they suffer from a sampling wall: once categorical sampling occurs, rich distributional information collapses into one-hot…
A partition $(C_1,C_2,...,C_q)$ of $G = (V,E)$ into clusters of strong (respectively, weak) diameter $d$, such that the supergraph obtained by contracting each $C_i$ is $\ell$-colorable is called a strong (resp., weak) $(d,…
Network decomposition is a central tool in distributed graph algorithms. We present two improvements on the state of the art for network decomposition, which thus lead to improvements in the (deterministic and randomized) complexity of…
Differential calculus on discrete spaces is studied in the manner of non-commutative geometry by representing the differential calculus by an operator algebra on a suitable Krein space. The discrete analogue of a (pseudo-)Riemannian metric…
We initiate the study of differentially private data-compression schemes motivated by the insecurity of the popular "Compress-Then-Encrypt" framework. Data compression is a useful tool which exploits redundancy in data to reduce…
All parallel algorithms for directed reachability and shortest paths crucially rely on efficient shortcut constructions. These constructions find directed paths and shortcut them by adding edges, with the goal to reduce the diameter of the…
It is shown that every tree of size $n$ over a fixed set of $\sigma$ different ranked symbols can be decomposed (in linear time as well as in logspace) into $O\big(\frac{n}{\log_\sigma n}\big) = O\big(\frac{n \log \sigma}{\log n}\big)$ many…
Data-parallel SGD is the de facto algorithm for distributed optimization, especially for large scale machine learning. Despite its merits, communication bottleneck is one of its persistent issues. Most compression schemes to alleviate this…
We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…
Understanding the dimension dependency of computational complexity in high-dimensional sampling problem is a fundamental problem, both from a practical and theoretical perspective. Compared with samplers with unbiased stationary…
Optical diagnostic diagrams are powerful tools to separate different ionizing sources in galaxies. However, the model-constraining power of the most widely-used diagrams is very limited and challenging to visualize. In addition, there have…
A regularity lemma for polynomials provides a decomposition in terms of a bounded number of approximately independent polynomials. Such regularity lemmas play an important role in numerous results, yet suffer from the familiar shortcoming…