Related papers: Relations between multi-resolution analysis and qu…
Let $R=\Bbbk[x_1,\..., x_n]$ and $M=R^s/I$ a multigraded squarefree module. We discuss the construction of cochain complexes associated to $M$ and we show how to interpret homological invariants of $M$ in terms of topological computations.…
We develop an approach for building quantum models based on the exponentially growing orthonormal basis of Hartley kernel functions. First, we design a differentiable Hartley feature map parametrized by real-valued argument that enables…
High-quality, multi-modal benchmarks are crucial for advancing scientific reasoning in large models yet their manual creation is costly and unscalable. To address this bottleneck, we explore the potential for transforming Text-Only QA Pairs…
Quantum mechanics owes much of its extraordinary success to a Hilbertian program of mathematical formalization. Yet, the formalism remains poorly aligned with the practical limitations of computations in finite dimensions and under finite…
Advancements in the implementation of quantum hardware have enabled the acquisition of data that are intractable for emulation with classical computers. The integration of classical machine learning (ML) algorithms with these data holds…
This paper is concerned with the relationships between two concepts, vanishing of cohomology groups and the structure of free resolutions. In particular, we study the connection between vanishing theorems for the local cohomology of…
Quantum computation based on quantum cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in…
Motivated by single-particle cryo-electron microscopy, multi-reference alignment (MRA) models the task of recovering an unknown signal from multiple noisy observations corrupted by random rotations. The standard approach,…
Multiparameter quantum metrology is essential for a wide range of practical applications. However, simultaneously achieving the ultimate precision for all parameters, as prescribed by the quantum Cram\'er-Rao bound (QCRB), remains a…
We review the perturbative approach to multiparticle production in hard collision processes. It is investigated to what extent parton level analytical calculations at low momentum cut-off can reproduce experimental data on the hadronic…
Let K be a field, let R=K[x_1,..., x_m] be a polynomial ring with the standard Z^m-grading (multigrading), let L be a Noetherian multigraded R-module, and let F: E --> G be a finite free multigraded presentation of L over R. Given a choice…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
The linear subspaces of a multiresolution analysis (MRA) and the linear subspaces of the wavelet analysis induced by the MRA, together with the set inclusion relation, form a very special lattice of subspaces which herein is called a…
The multiple-quantum NMR spectroscopy has an extensive application in determination of the bio-macro-molecular structures and in the investigation of the properties of a variety of physical materials. In quantum computation the…
We classify the two-way independence quasi-independence models (or independence models with structural zeros) that have rational maximum likelihood estimators, or MLEs. We give a necessary and sufficient condition on the bipartite graph…
For a Hecke operator $R$, one defines the matrix bialgebra $\E_R$, which is considered as the function algebra on the quantum space of endomorphisms of the quantum space associated to $R$. One generalizes this notion, defining the function…
Many approaches to three-dimensional constrained macromolecular chains at thermal equilibrium, at about room temperatures, are based upon constrained Classical Hamiltonian Dynamics (cCHDa). Quantum-mechanical approaches (QMa) have also been…
We address the relation between quantum metrological resolution and coherence. We examine this dependence in two manners: we develop a quantum Wiener-Kintchine theorem for a suitable model of quantum ruler, and we compute the Fisher…
In this note we are dealing with a particular class of quadratic algebras -- the so-called quantum matrix algebras. The well-known examples are the algebras of quantized functions on classical Lie groups (the RTT algebras). We consider the…
Machine learning (ML) has become an attractive tool in information processing, however few ML algorithms have been successfully applied in the quantum domain. We show here how classical reinforcement learning (RL) could be used as a tool…