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Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…
We introduce a real-parameter refinement of the classical integer hierarchies underlying Schmidt number, block-positivity, and $k$-positivity for maps between matrix algebras. Starting from a compact family of $\alpha$-admissible unit…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
Our companion work \cite{Stojnicl1BnBxasymldp} considers random under-determined linear systems with box-constrained sparse solutions and provides an asymptotic analysis of a couple of modified $\ell_1$ heuristics adjusted to handle such…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
We first consider the sequential detection of transient signals by generalizing the moving average chart to exponential family and study the false detection probability (FDP) and power of detection (POD) in the steady state. Then windowed…
Parity-time (PT) symmetric systems have two distinguished phases, e.g., one with real energy eigenvalues and the other with complex conjugate eigenvalues. To enter one phase from the other, it is believed that the system must pass through…
Quantum linear system solvers typically realize the inverse map as a polynomial transformation of the spectrum, so their practical cost hinges on implementing this transformation at a low polynomial degree. We introduce constrained optimal…
The Earth's subsurface is a cornerstone of modern society, providing essential energy resources like hydrocarbons, geothermal, and minerals while serving as the primary reservoir for $CO_2$ sequestration. However, full physics numerical…
A novel pinching antenna system (PASS) enabled wireless power transfer (WPT) framework is proposed, where energy harvesting receivers (EHRs) and information decoding receivers (IDRs) coexist. By activating pinching antennas (PAs) near both…
Analytical results are presented for the structure of networks that evolve via a preferential-attachment-random-deletion (PARD) model in the regime of overall network growth and in the regime of overall contraction. The phase transition…
We study parameterized and approximation algorithms for a variant of Set Cover, where the universe of elements to be covered consists of points in the plane and the sets with which the points should be covered are segments. We call this…
The tensor-structured parametric analysis (TPA) has been recently developed for simulating and analysing stochastic behaviours of gene regulatory networks [Liao et. al., 2015]. The method employs the Fokker-Planck approximation of the…
In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given…
We first show the existence and nature of convergence to a limiting set of roots for polynomials in a three-term recurrence of the form $p_{n+1}(z) = Q_k(z)p_{n}(z)+ \gamma p_{n-1}(z)$ as $n$ $\rightarrow$ $\infty$, where the coefficient…
Quantum tomography is a process of quantum state reconstruction using data from multiple measurements. An essential goal for a quantum tomography algorithm is to find measurements that will maximize the useful information about an unknown…
In the foreseeable future, toolchains for quantum computing should offer automatic means of transforming a high level problem formulation down to a hardware executable form. Thereby, it is crucial to find (multiple) transformation paths…
Many integrable stochastic particle systems in one space dimension (such as TASEP - totally asymmetric simple exclusion process - and its various deformations, with a notable exception of ASEP) remain integrable when we equip each particle…
Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for…
Modern deep learning for asset allocation typically separates forecasting from optimization. We argue this creates a fundamental mismatch where minimizing prediction errors fails to yield robust portfolios. We propose the Signature Informed…