Related papers: Constructing exact symmetric informationally compl…
We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a…
We use molecular dynamics simulations to test integral equation theory predictions for the structure of fluids of spherical particles with eight different piecewise-constant pair interaction forms comprising a hard core and a combination of…
We investigate the role of symmetric quantum cloning machines (QCMs) in quantifying the mutual incompatibility of quantum observables. Specifically, we identify a cloning-based incompatibility measure whereby the incompatibility of a set of…
High precision atomic data is indispensable for experiments involving studies of fundamental interactions, astrophysics, atomic clocks, plasma science, and others. We develop new parallel atomic structure codes and explore the difficulties…
Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum…
In the quest to unlock the maximum potential of quantum sensors, it is of paramount importance to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. However, it is still not known…
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…
Semi-algebraic proof systems such as sum-of-squares (SoS) have attracted a lot of attention recently due to their relation to approximation algorithms: constant degree semi-algebraic proofs lead to conjecturally optimal polynomial-time…
We propose orthogonal inductive matrix completion (OMIC), an interpretable approach to matrix completion based on a sum of multiple orthonormal side information terms, together with nuclear-norm regularization. The approach allows us to…
Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…
This paper studies the completeness of conjunctive queries over a partially complete database and the approximation of incomplete queries. Given a query and a set of completeness rules (a special kind of tuple generating dependencies) that…
Analog computing using bosonic computational states is a leading approach to surpassing the computational speed and energy limitations of von Neumann architectures. But the challenges of manufacturing large-scale photonic integrated…
The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the…
With the increasing adoption of vision-language models (VLMs) in critical decision-making systems such as healthcare or autonomous driving, the calibration of their uncertainty estimates becomes paramount. Yet, this dimension has been…
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these…
We provide a partial solution to the problem of constructing mutually unbiased bases (MUBs) and symmetric informationally complete POVMs (SIC-POVMs) in non-prime-power dimensions. An algebraic description of a SIC-POVM in dimension six is…
Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated…
Motivated by Wilmshurst's conjecture, we investigate the zeros of harmonic polynomials. We utilize a certified counting approach which is a combination of two methods from numerical algebraic geometry: numerical polynomial homotopy…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…
Many combinatorial problems can be formulated as a polynomial optimization problem that can be solved by state-of-the-art methods in real algebraic geometry. In this paper we explain many important methods from real algebraic geometry, we…