相关论文: Generating series and matrix models for meandric s…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
This paper introduces a new probabilistic framework for supervised learning in neural systems. It is designed to model complex, uncertain systems whose random outputs are strongly non-Gaussian given deterministic inputs. The architecture…
We present the results of a quantitative study of the phase behavior of a model polymer chain with side spheres using two independent computer simulation techniques. We find that the mere addition of side spheres results in key…
Despite fundamental interests in learning quantum circuits, the existence of a computationally efficient algorithm for learning shallow quantum circuits remains an open question. Because shallow quantum circuits can generate distributions…
Closed meanders are planar configurations of one or several disjoint closed Jordan curves intersecting a given line or curve transversely. They arise as shooting curves of parabolic PDEs in one space dimension, as trajectories of Cartesian…
The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \int d{\bf H} [P({\bf H})] \ln [P({\bf H})], with suitable constraints. Here we construct and analyze…
In this work we present an algorithm to construct sparse-paving matroids over finite set $S$. From this algorithm we derive some useful bounds on the cardinality of the set of circuits of any Sparse-Paving matroids which allow us to prove…
Methods of parabolic geometries have been recently used to construct a class of elliptic complexes on quaternionic manifolds, the Salamon's complex being the simplest case. The purpose of this paper is to describe an algorithm how to…
We discuss a model for studying the statistical properties of the impedance ($Z$) and scattering ($S$) matrices of open electromagnetic cavities with several transmission lines or waveguides connected to the cavity. In this paper, we mainly…
The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all…
A polynomial matrix description(PMD) of a rational matrix $G(\lambda)$ is a matrix polynomial of the form $$ \mathbf{P}(\lambda) := \left[\begin{array}{c|c} A(\lambda) & B(\lambda) \\ \hline -C(\lambda) & D(\lambda)\end{array}\right] \text{…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
Determinantal varieties -- the sets of bounded-rank matrices or tensors -- have attracted growing interest in low-rank optimization. The tangent cone to low-rank sets is widely studied and underpins a range of geometric methods. The…
We suggest a new random model for links based on meander diagrams and graphs. We then prove that trivial links appear with vanishing probability in this model, no link $L$ is obtained with probability 1, and there is a lower bound for the…
We study the formation of short-depth designs beyond the unitary group. We provide a range of results on several groups of broad interest in quantum information science: the Clifford group, the orthogonal group, the unitary symplectic…
Additive manufacturing is advantageous for producing lightweight components while addressing complex design requirements. This capability has been bolstered by the introduction of unit lattice cells and the gradation of those cells. In…
Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization…
We propose a new Markov chain Monte Carlo method in which trial configurations are generated by evolving a state, sampled from a prior distribution, using a Markov transition matrix. We present two prototypical algorithms and derive their…
This paper deals with a simple and straightforward procedure for automatic generation of finite-element or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes…
This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…