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Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework…
Quantum detector tomography (QDT) is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we utilize regularization to improve the QDT accuracy whenever the probe states are…
In this paper, we propose and prove the theorem regarding the stability of attributes in a decision system. Based on the theorem, we propose the LRA framework for accelerating rough set algorithms. It is a general-purpose framework which…
This paper studies Set Shaping Theory (SST) in a database-index setting under a revised interpretation: SST is not treated as a competing hashing method, but as a structural pre processing layer that can be applied before an existing…
In modern data analytics, analysts frequently face the challenge of searching for desirable entities by evaluating, for each entity, a collection of its feature relations to derive key analytical properties. This search is challenging…
We introduce some classical complexity-theoretic techniques to Parameterized Complexity. First, we study relativization for the machine models that were used by Chen, Flum, and Grohe (2005) to characterize a number of parameterized…
How can we use a quantum computer to detect the entanglement structure of a quantum state? Bouland et al. (2024) recently provided an algorithm that, given multiple input copies of the state, finds the "hidden cuts"-partitions into fully…
Many of the most consequential dynamics in human cognition occur \emph{before} events become explicit: before decisions are finalized, emotions are labeled, or meanings stabilize into narrative form. These pre-event states are characterized…
We show that the strongly symmetric spectral convex compact sets are precisely the normalized state spaces of finite-dimensional simple Euclidean Jordan algebras and the simplices. Spectrality is the property that every state has a convex…
Based on our \bl{\textbf{Random Duality Theory (RDT)}}, in a sequence of our recent papers \cite{Stojnicclupint19,Stojnicclupcmpl19,Stojnicclupplt19}, we introduced a powerful algorithmic mechanism (called \bl{\textbf{CLuP}}) that can be…
A central challenge in precision cosmology with galaxy surveys is to extract non-Gaussian information from large-scale structure while controlling systematic uncertainties such as tracer bias. Conventional clustering statistics, such as the…
We analyzed the performance of a biologically inspired algorithm called the Corrected Projections Algorithm (CPA) when a sparseness constraint is required to unambiguously reconstruct an observed signal using atoms from an overcomplete…
\texttt{rCOSA} is a software package interfaced to the R language. It implements statistical techniques for clustering objects on subsets of attributes in multivariate data. The main output of COSA is a dissimilarity matrix that one can…
We study the minimum spanning tree (MST) problem in the massively parallel computation (MPC) model. Our focus is particularly on the *strictly sublinear* regime of MPC where the space per machine is $O(n^\delta)$. Here $n$ is the number of…
Uniquely represented data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of $n$ keys from a totally ordered universe in this context. We introduce a two-layer data…
Robust Principal Component Analysis (RPCA) aims to recover a low-rank structure from noisy, partially observed data that is also corrupted by sparse, potentially large-magnitude outliers. Traditional RPCA models rely on convex relaxations,…
The regular spanners (characterised by vset-automata) are closed under the algebraic operations of union, join and projection, and have desirable algorithmic properties. The core spanners (introduced by Fagin, Kimelfeld, Reiss, and…
Coherent systems are representative of many practical applications, ranging from infrastructure networks to supply chains. Probabilistic evaluation of such systems remains challenging, however, because existing decomposition-based methods…
We study $\ell^1$ regularized least squares optimization problem in a separable Hilbert space. We show that the iterative soft-thresholding algorithm (ISTA) converges linearly, without making any assumption on the linear operator into play…
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: Does TAUT have (p-)optimal proof systems?…