Invariance principle for biased bootstrap random walks

Our main goal is to study a class of processes whose increments are generated via a cellular automata rule. Given the increments of a simple biased random walk, a new sequence of (dependent) Bernoulli random variables is produced. It is built, from the original sequence, according to a cellular automata rule. Equipped with these two sequences, we construct two more according to the same cellular automata rule. The construction is repeated a fixed number of times yielding an infinite array ($\{?K,\dots ,K\}\times \mathbb{N}$) of (dependent) Bernoulli random variables. Taking partial sums of these sequences, we obtain a $(2K+1)$-dimensional process whose increments belong to the state space ${\{?1,1\}}^{2K+1}$.The aim of the paper is to study the long term behaviour of this process. In particular, we establish transience/recurrence properties and prove an invariance principle. The limiting behaviour of these processes depends strongly on the direction of the iteration, and exhibits few surprising features. This work is motivated by an earlier investigation (see Collevecchio et al. (2015)), in which the starting sequence is symmetric, and by the related work Ferrari et al. (2000).     

The sum-of-squares hierarchy on the sphere and applications in quantum information theory

Mathematical Programming - We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of sum-of-squares relaxations. Exploiting the polynomial kernel...     

Semidefinite Approximations of the Matrix Logarithm

Foundations of Computational Mathematics - The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator...     

Amorphous metal-aluminophosphate catalysts for aldol condensation of n-heptanal and benzaldehyde to jasminaldehyde

Amorphous aluminophosphate (AlP) and metal‐aluminophosphates (MAlPs, where M=2.5 mol%Cu, Zn, Cr, Fe, Ce, or Zr) were prepared by coprecipitation method. Their surface properties and catalytic activity ...     

Localization for Random Unitary Operators

We consider unitary analogs of one-dimensional Anderson models on defined by the product U _ω=D _ω S where S is a deterministic unitary and D _ω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of U _ω is pure point almost surely for all values of the parameter of S. We provide similar results for unitary operators defined on together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunsky coefficients of constant modulus and correlated random phases Mathematics Subject Classification. 82B44, 42C05, 81Q05     

Connection and inversion coefficients for basic hypergeometric polynomials

In this paper, we give a closed-form expression of the inversion and the connection coefficients for general basic hypergeometric polynomial sets using some known inverse relations. We derive expansion formulas corresponding to all the families within the q-Askey scheme and we connect some d-orthogonal basic hypergeometric polynomials.     

Influence of various diet regimens on deterioration of hepatic function and hematological parameters following carbon tetrachloride: a potential protective role of natural honey

The objective was to assess the effects of commercial regular diet as control, total food restriction with honey, commercial regular diet with dextrose, or total food restriction with dextrose, on blood variables after carbon tetrachloride (CCl4) administration. Sprague Dawley albino rats were divided into four groups, 10 rats each; Group 1 rats were on commercial regular diet, Group 2 rats were on commercial regular diet with 50% dextrose, Group 3 rats were on total food restriction with 50% dextrose, and Group 4 rats were on total food restriction with 50% honey. Rats in all the groups were i.m. administered CCL4 (2.4 mL kg b. wt.-1). Blood tests including ALT, AST, serum albumin, serum protein, BUN, blood glucose (BG), hemoglobin (Hb), and white blood cell (WBC) were performed before CCl4 administration and repeated after 48 and 96 h of post-injection. In Group 1, CCl4 caused significant elevation in AST and ALT, and decrease in BS, WBC, and BUN; lower elevation in AST and ALT at 48 h and decreased AST and ALT at 96 h were obtained when dextrose was added to commercial regular diet (Group 2). Using dextrose alone (Group 3), though there was significant elevation of AST and ALT and decrease in BUN and WBC as compared to baseline values, significant decrease in ALT, AST, and BUN as compared to control was obtained. During absolute honey feeding (Group 4), elevation in AST and ALT obtained, following CCl4 administration was significantly less than the values obtained in all other groups; with lower elevation in AST and ALT as compared to baseline values. Honey increased serum albumin, serum protein, BG, and caused lower reduction in Hb. Conclusively, exclusive honey feeding (50% concentration) significantly modifies and ameliorates biochemical and hematological changes obtained after CCl4 injection.     

Reactions with cyclic amidines II. The behaviour of cyclic amidines toward ethoxycarbonyl and aroyl isothiocyanates

The behaviour of the aminopyrazole derivatives 1a-c, 2-amino-4-phenylthiazole (2) and 2-amino-5-phenyl-1,3,4-thiadiazole (3) toward the action of ethoxycarbonyl and benzoyl iso-thiocyanate is reported. The data clearly demonstrates the dependence of the nature of the products obtained from the reaction of isothiocyanates with cyclic amidines on the nature of the substituents on the heterocyclic ring.     

Thymus algeriensis and Artemisia herba-alba Essential Oils: Chemical Analysis,Antioxidant Potential and In Vivo Anti-Inflammatory,Analgesic Activities,and Acute Toxicity

The study of bioactive molecules of natural origin is a focus of current research. Thymus algeriensis and Artemisia herba-alba are two medicinal plants widely used by the Moroccan population in the traditional treatment of several pathologies linked to inflammation. This study aimed to evaluate the single and combined antioxidant, anti-inflammatory and analgesic effects of the essential oils extracted from these two medicinal plants, and also their potential toxicity. Essential oils were extracted using hydro-distillation in a Clevenger-type apparatus. The antioxidant activity was evaluated by two methods: the scavenging of the free radical DPPH, and the reduction in iron. Anti-inflammatory activity was evaluated by evaluating the edema development induced by carrageenan injecting, while the analgesic power was evaluated according to the number of abdominal contortions induced by the intraperitoneal injection of acetic acid (0.7%). The acute oral toxicity was performed to assess the potential toxicity of the studied EOs, followed by an analysis of the blood biochemical parameters. The results of the two antioxidant tests indicated that our extract mixture exhibits good iron reduction capacity and very interesting DPPH free radical scavenging power, with an IC₅₀ of around 4.38 ± 0.98 μg/mL higher than that of the benchmark antioxidant, BHT. The anti-inflammatory test demonstrated that the mixture administered orally at a dose of 150 mg/kg has a better activity, exceeding that of 1% Diclofenac, with a percentage of maximum inhibition of the edema of 89.99 ± 4.08. The number of cramps in the mice treated with the mixture at a dose of 150 mg/kg is significantly lower (29.80 ± 1.92) than those of the group treated with Tramadol (42.00 ± 2.70), respectively. The toxicity results show no signs of toxicity with an LD₅₀ greater than 150 mg/Kg. These interesting results show that the two plants’ EOs had an important anti-inflammatory, analgesic, and antioxidant activity, and also a powerful synergistic effect, which encourages further in-depth investigations on their pharmacological proprieties.