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We propose a general alternating minimization algorithm for nonconvex optimization problems with separable structure and nonconvex coupling between blocks of variables. To fix our ideas, we apply the methodology to the problem of blind…

In this paper, we present an innovative method for constructing proper priors for the skewness (shape) parameter in the skew-symmetric family of distributions. The proposed method is based on assigning a prior distribution on the…

Denoising Diffusion Probabilistic models have emerged as simple yet very powerful generative models. Unlike other generative models, diffusion models do not suffer from mode collapse or require a discriminator to generate high-quality…

A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…

Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution.…

For the model of communication through a discrete memoryless channel using i.i.d. random block codes, where the channel is changing slowly from block to block, we propose a stochastic algorithm for adaptation of the generating distribution…

In this two-part work, we propose an algorithmic framework for solving non-convex problems whose objective function is the sum of a number of smooth component functions plus a convex (possibly non-smooth) or/and smooth (possibly non-convex)…

We propose the continuous-variable quantum key distribution protocol based on the Gaussian modulation of a single quadrature of the coherent states of light, which is aimed to provide simplified implementation compared to the symmetrically…

Single-mode or mode multiplexed free-space atmospheric optical channels draw increasingly more attention in the last decade. The scope of their possible applications spans from the compatibility with the telecom WDM technology, fiber…

We consider the asymptotic key rates achieved in the simplest quantum key distribution protocols, namely the BB84 and the six-state protocols, when non-uniform noise is present in the system. We first observe that higher qubit error rates…

We study constrained stochastic programs where the decision vector at each time slot cannot be chosen freely but is tied to the realization of an underlying random state vector. The goal is to minimize a general objective function subject…

We show that one may take advantages in both robusty and key rate of asymmetric channel noise.

This paper deals with the critical issue of approximating the pre-exponential factor in semiclassical molecular dynamics. The pre-exponential factor is important because it accounts for the quantum contribution to the semiclassical…

This paper presents centralized and distributed Alternating Direction Method of Multipliers (ADMM) frameworks for solving large-scale nonconvex optimization problems with binary decision variables subject to spanning tree or rooted…

A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move…

We propose a new quantum key distribution scheme that uses the blind polarization basis. In our scheme the sender and the receiver share key information by exchanging qubits with arbitrary polarization angles without basis reconciliation.…

This work considers communication networks where individual links can be described as MIMO channels. Unlike orthogonal modulation methods (such as the singular-value decomposition), we allow interference between sub-channels, which can be…

Distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive Hermitian matrices. The inverse Fourier transform of the distribution is shown to be a Fredholm determinant of a…

Mutually unbiased bases have been extensively studied in the literature and are simple and effective in quantum key distribution protocols, but they are not optimal. Here equiangular spherical codes are introduced as a more efficient and…

A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion…