We give algorithms for approximation by low-rank positive semidefinite (PSD) matrices. For symmetric input matrix A ∈ Rn×n, target rank k, and error parameter ε > 0, one algorithm finds with constant probability a PSD matrix Ỹ of rank k such that ‖A− Ỹ ‖2F ≤ (1+ε)‖A−Ak,+‖ 2 F , where Ak,+ denotes the best rank-k PSD approximation to A, and the norm is Frobenius. The algorithm takes time O(nnz(A...

Hepatitis B virus (HBV) pregenomic RNA contains a hairpin structure (ε) located in the preCore region, essential for viral replication. ε stability is enhanced by the presence of preCore variants and ε is recognized by the HBV polymerase (Pol). Mutations in the retrotranscriptase domain (YMDD) of Pol are associated with treatment resistance. The aim of this study was to analyze the preCore regi...

We focus on the minimal time control problem for single-input control-affine systems ẋ = X(x) + u1Y1(x) in IR with fixed initial and final time conditions x(0) = x̂0, x(t f ) = x̂1, and where the scalar control u1 satisfies the constraint |u1(·)| 6 1. For these systems a concept of conjugate time tc has been defined in e.g. [3, 30, 33] in the bang-bang case. Besides, theoretical and practical iss...

The widespread use of biogas and biomass fuels in facility agro-industrial parks has led to a significant increase their carbon emissions. A day-ahead optimal scheduling model for an integrated energy system (IES) is proposed, that considers the coupling power gas (P2G) reduce emissions during operation industrial park. proposed incorporates two evaluation indices economy by IES park, formulate...

Until recently, it was not known whether it was possible to sort stably (i.e., keeping equal elements in their initial order) an array of n elements using only O(n) data moves and O(1) extra space. In [13] an algorithm was given to perform this task in O(n2) comparisons in the worst case. Here, we develop a new algorithm for the problem that performs only O(n1+ε) comparisons (0 < ε ≤ 1 is any f...

1. INTRODUCTION In order to describe linear viscoelastic properties of polymers one is interested in the relaxation time spectrum h, as it supplies information about the material properties. Moreover given h it is easy to convert one material function into another one. Additionally many microscopic theories are based on h and provide predictions about its character. Unfortunately the relaxation...

We investigate the problem of estimating a random variable Y ∈ Y under a privacy constraint dictated by another correlated random variable X ∈ X , where estimation efficiency and privacy are assessed in terms of two different loss functions. In the discrete case, we use the Hamming loss function and express the corresponding utility-privacy tradeoff in terms of the privacy-constrained guessing ...

The material properties of greatest importance in microwave processing of a dielectric are the complex relative permittivity ε = ε′ jε′′, and the loss tangent, tan δ = ε′′/ ε′. The real part of the permittivity, ε′, sometimes called the dielectric constant, mostly determines how much of the incident energy is reflected at the air-sample interface, and how much enters the sample. This paper show...

In this paper, we propose an uniformly convergent adaptive finite element method with hybrid basis (AFEM-HB) for the discretization of singularly perturbed nonlinear eigenvalue problems under constraints with applications in Bose-Einstein condensation (BEC) and quantum chemistry. We begin with the time-independent Gross-Pitaevskii equation and show how to reformulate it into a singularly pertur...