Related papers: Limited bisimulations for nondeterministic fuzzy t…
Clustering is essential in data analysis and machine learning, but traditional algorithms like $k$-means and Gaussian Mixture Models (GMM) often fail with nonconvex clusters. To address the challenge, we introduce the Flexible Bivariate…
Bisimulation is a concept that captures behavioural equivalence of states in a variety of types of transition systems. It has been widely studied in a discrete-time setting where the notion of a step is fundamental. In our setting we are…
In this paper we introduce and study fused lasso nearly-isotonic signal approximation, which is a combination of fused lasso and generalized nearly-isotonic regression. We show how these three estimators relate to each other, derive…
Stochastic optimization of engineering systems is often infeasible due to repeated evaluations of a computationally expensive, high-fidelity simulation. Bi-fidelity methods mitigate this challenge by leveraging a cheaper, approximate model…
Hybrid $k$-Clustering is a model of clustering that generalizes two of the most widely studied clustering objectives: $k$-Center and $k$-Median. In this model, given a set of $n$ points $P$, the goal is to find $k$ centers such that the sum…
Few-shot learning is an important research field of machine learning in which a classifier must be trained in such a way that it can adapt to new classes which are not included in the training set. However, only small amounts of examples of…
A local and distributive algorithm is proposed to find an optimal trial wave-function minimizing the Hamiltonian expectation in a quantum system. To this end, the quantum state of the system is connected to the Gibbs state of a classical…
Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…
We propose a homotopy continuation method called FLUX for approximating complicated probability density functions. It is based on progressive processing for smoothly morphing a given density into the desired one. Distributed ordinary…
Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization…
We introduce new method of optimization for finding free parameters of affine iterated function systems (IFS), which are used for fractal approximation. We provide the comparison of effectiveness of fractal and quadratic types of…
This paper introduces factored conditional filters, new filtering algorithms for simultaneously tracking states and estimating parameters in high-dimensional state spaces. The conditional nature of the algorithms is used to estimate…
Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a…
We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that…
A finite form of de Finetti's representation theorem is established using elementary information-theoretic tools: The distribution of the first $k$ random variables in an exchangeable binary vector of length $n\geq k$ is close to a mixture…
Recent progress in the design and optimization of neural-network quantum states (NQSs) has made them an effective method to investigate ground-state properties of quantum many-body systems. In contrast to the standard approach of training a…
The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the…
Understanding quantum phase transitions in physical systems is fundamental to characterize their behavior at low temperatures. Achieving this requires both accessing good approximations to the ground state and identifying order parameters…
Given a Probabilistic Finite Automata (PFA), a set of states S, and an error threshold e > 0, our algorithm approximates the infimum probability (quantifying over all infinite words) that the automata reaches S. Our result contrasts with…
We consider deterministic and {\em randomized} quantum algorithms simulating $e^{-iHt}$ by a product of unitary operators $e^{-iA_jt_j}$, $j=1,...,N$, where $A_j\in\{H_1,...,H_m\}$, $H=\sum_{i=1}^m H_i$ and $t_j > 0$ for every $j$.…