Related papers: Upper bounds for Grothendieck constants, quantum c…

Since their discovery in 1927, the Heisenberg Inequalities have become an icon of quantum mechanics. Often inappropriately referred to as the Uncertainty Principle, these inequalities relating the standard deviations of the position and…

We study the complexity of optimizing highly smooth convex functions. For a positive integer $p$, we want to find an $\epsilon$-approximate minimum of a convex function $f$, given oracle access to the function and its first $p$ derivatives,…

This paper addresses the problem of finding the closest generalized essential matrix from a given $6\times 6$ matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not…

All the available results on the approximation of the k-spacings process to Gaussian processes have only used one approach, that is the Shorack and Pyke's one. Here, it is shown that this approach cannot yield a rate better than $% \left(…

This paper provides a discrete Poincar\'e inequality in $n$ space dimensions on a simplex $K$ with explicit constants. This inequality bounds the norm of the piecewise derivative of functions with integral mean zero on $K$ and all integrals…

We present two algorithms for constructing orthonormal bases of rational function vectors with respect to a discrete inner product, and discuss how to use them for a rational approximation problem. Building on the pencil-based formulation…

Kronecker-factored Approximate Curvature (K-FAC) method is a high efficiency second order optimizer for the deep learning. Its training time is less than SGD(or other first-order method) with same accuracy in many large-scale problems. The…

We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be…

For a Markovian open quantum system it is possible, by continuously monitoring the environment, to know the stochastically evolving pure state of the system without altering the master equation. In general, even for a system with a finite…

We extend the so-called "single ring theorem"[1], also known as the Haagerup-Larsen theorem[2], by showing that in the limit when the size of the matrix goes to infinity a particular correlator between left and right eigenvectors of the…

We describe the new version (v2.38j) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have…

Kramers-Kronig (KK) relations are usually invoked for causal response functions, but their precise status for non-Markovian quantum memory kernels is less explicit. We separate three Laplace-domain objects: the Nakajima-Zwanzig memory…

We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method provides rigorous…

The Hilbert-space Gaussian Process (HGP) approach offers a hyperparameter-independent basis function approximation for speeding up Gaussian Process (GP) inference by projecting the GP onto M basis functions. These properties result in a…

We establish ring isomorphisms between quantum Grothendieck rings of certain remarkable monoidal categories of finite-dimensional representations of quantum affine algebras of types $A_{2n-1}^{(1)}$ and $B_n^{(1)}$. Our proof relies in part…

This survey paper deals with upper and lower bounds on the number of $k$-matchings in regular graphs on $N$ vertices. For the upper bounds we recall the upper matching conjecture which is known to hold for perfect matchings. For the lower…

We derive explicit distance bounds for Stratonovich iterated integrals along two Gaussian processes (also known as signatures of Gaussian rough paths) based on the regularity assumption of their covariance functions. Similar estimates have…

Jensen's inequality is ubiquitous in measure and probability theory, statistics, machine learning, information theory and many other areas of mathematics and data science. It states that, for any convex function $f\colon K \to \mathbb{R}$…

Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such…

Quantum $k$-minimum finding is a fundamental subroutine with numerous applications in combinatorial problems and machine learning. Previous approaches typically assume oracle access to exact function values, making it challenging to…