Related papers: Algorithmic pure states for the negative spherical…

We report large effects of Parisi replica permutation symmetry breaking (RPSB) on elementary excitations of fermionic systems with frustrated magnetic interactions. The electronic density of states is obtained exactly in the zero…

In the study of disordered models like spin glasses the key object of interest is the rugged energy hypersurface defined in configuration space. The statistical mechanics calculation of the Gibbs-Boltzmann Partition Function gives the…

In scalar-vector-tensor (SVT) theories with parity invariance, we perform a gauge-ready formulation of cosmological perturbations on the flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) background by taking into account a matter perfect…

We consider the problem of recovering a complex vector $\mathbf{x}\in \mathbb{C}^n$ from $m$ quadratic measurements $\{\langle A_i\mathbf{x}, \mathbf{x}\rangle\}_{i=1}^m$. This problem, known as quadratic feasibility, encompasses the well…

In binary classification, kernel-free linear or quadratic support vector machines are proposed to avoid dealing with difficulties such as finding appropriate kernel functions or tuning their hyper-parameters. Furthermore, Universum data…

Let $X$ be a symmetric, isotropic random vector in $\mathbb{R}^m$ and let $X_1...,X_n$ be independent copies of $X$. We show that under mild assumptions on $\|X\|_2$ (a suitable thin-shell bound) and on the tail-decay of the marginals…

We study the distribution of the eigenvalue condition numbers $\kappa_i=\sqrt{ (\mathbf{l}_i^* \mathbf{l}_i)(\mathbf{r}_i^* \mathbf{r}_i)}$ associated with real eigenvalues $\lambda_i$ of partially asymmetric $N\times N$ random matrices…

In this thesis we address a series of new problems in non-hermitian optical scattering with increasing degrees of complexity. We develop the theory of reflectionless scattering modes, introducing a novel and broad class of impedance-matched…

The coherent superposition of non-orthogonal fermionic Gaussian states has been shown to be an efficient approximation to the ground states of quantum impurity problems [Bravyi and Gosset,Comm. Math. Phys.,356 451 (2017)]. We present a…

Based on \cite{H}, it is well known that the rescaled two point correlation functions \[ \sqrt{N} \langle \sigma_i ; \sigma_j\rangle = \sqrt{N} \big( \langle \sigma_i \sigma_j\rangle -\langle \sigma_i\rangle \langle \sigma_j\rangle\big) \]…

Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously…

I examine spectral properties of a dissipative chaotic quantum map with the help of a recently discovered semiclassical trace formula. I show that in the presence of a small amount of dissipation the traces of any finite power of the…

Within QRPA we achieve partial restoration of the isospin symmetry and hence fulfillment of the requirement that the $2\nu\beta\beta$ Fermi matrix element $M^{2\nu}_F$ vanishes, as it should, unlike in the previous version of the method.…

Optimizing a high-dimensional non-convex function is, in general, computationally hard and many problems of this type are hard to solve even approximately. Complexity theory characterizes the optimal approximation ratios achievable in…

Optical traps and lattices provide a new opportunity to study strongly correlated high spin systems with cold atoms. In this article, we review the recent progress on the hidden symmetry properties in the simplest high spin fermionic…

We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the…

We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…

This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator $T$ on a Hilbert space with an orthogonal basis, we define the isomorphic structure $\Sigma(T)$ as the family of all subsets…

Let $Z_1,\ldots,Z_n$ be i.i.d. isotropic random vectors in $\mathbb{R}^p$, and $T \subset \mathbb{R}^p$ be a compact set. A classical line of empirical process theory characterizes the size of the suprema of the quadratic process…

Self Consistent Quasiparticle Random Phase Approximation (SCQRPA) is considered in application to the Fermi transitions within the O(5) model. It is demonstrated that SCQRPA improves on renormalized QRPA (RQRPA), a method that has recently…