Random unitary matrices associated to a graph

We analyze composed quantum systems consisting of $k$ subsystems, each described by states in the $n$-dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual subsystems and edges denoting a generic interaction, modeled by random unitary matrices of order $n^2$. The global evolution operator is represented by a unitary matrix of size $N=n^k$. We investigate statistical properties of such matrices and show that they display spectral properties characteristic to Haar random unitary matrices provided the corresponding graph is connected. Thus basing on random unitary matrices of a small size $n^2$ one can construct a fair approximation of large random unitary matrices of size $n^{k}$. Graph--structured random unitary matrices investigated here allow one to define the corresponding structured ensembles of random pure states.Comment: 13 pages, 10 figures, 1 tabl

Model of communities isolation at hierarchical modular networks

The model of community isolation was extended to the case when individuals are randomly placed at nodes of hierarchical modular networks. It was shown that the average number of blocked nodes (individuals) increases in time as a power function, with the exponent depending on network parameters. The distribution of time when the first isolated cluster appears is unimodal, non-gaussian. The developed analytical approach is in a good agreement with the simulation data

Quest for Compounds at the Verge of Charge Transfer Instabilities: The Case of Silver(II) Chloride †

Electron-transfer processes constitute one important limiting factor governing stability of solids. One classical case is that of CuI2, which has never been prepared at ambient pressure conditions due to feasibility of charge transfer between metal and nonmetal (CuI2 → CuI + ½ I2). Sometimes, redox instabilities involve two metal centers, e.g., AgO is not an oxide of divalent silver but rather silver(I) dioxoargentate(III), Ag(I)[Ag(III)O2]. Here, we look at the particularly interesting case of a hypothetical AgCl2 where both types of redox instabilities operate simultaneously. Since standard redox potential of the Ag(II)/Ag(I) redox pair reaches some 2 V versus Normal Hydrogen Electrode (NHE), it might be expected that Ag(II) would oxidize Cl− anion with great ease (standard redox potential of the ½ Cl2/Cl− pair is + 1.36 V versus Normal Hydrogen Electrode). However, ionic Ag(II)Cl2 benefits from long-distance electrostatic stabilization to a much larger degree than Ag(I)Cl + ½ Cl2, which affects relative stability. Moreover, Ag(II) may disproportionate in its chloride, just like it does in an oxide; this is what AuCl2 does, its formula corresponding in fact to Au(I)[Au(III)Cl4]. Formation of polychloride substructure, as for organic derivatives of Cl3− anion, is yet another possibility. All that creates a very complicated potential energy surface with a few chemically distinct minima i.e., diverse polymorphic forms present. Here, results of our theoretical study for AgCl2 will be presented including outcome of evolutionary algorithm structure prediction method, and the chemical identity of the most stable form will be uncovered together with its presumed magnetic properties. Contrary to previous rough estimates suggesting substantial instability of AgCl2, we find that AgCl2 is only slightly metastable (by 52 meV per formula unit) with respect to the known AgCl and ½ Cl2, stable with respect to elements, and simultaneously dynamically (i.e., phonon) stable. Thus, our results point out to conceivable existence of AgCl2 which should be targeted via non-equilibrium approaches

Prevalence of Vitamin D Deficiency in Patients Treated for Juvenile Idiopathic Arthritis and Potential Role of Methotrexate: A Preliminary Study

Background: Vitamin D deficiency is reported in rheumatological diseases in adults. The aim was to evaluate the prevalence of vitamin D deficiency in children with juvenile idiopathic arthritis (JIA) and to investigate potential correlations between vitamin D status and clinical factors, laboratory traits, and medical treatment, including methotrexate (MTX) and glucocorticoids (GCs). Methods: In 189 patients aged 3–17.7 years, with JIA in the stable stage of the disease, anthropometry, clinical status, serum 25-hydroxyvitamin D [25(OH)D], calcium (Ca), phosphate (PO4), total alkaline phosphatase (ALP), erythrocyte sedimentation rate (ESR), and C-reactive protein (CRP) were assessed. Results: Median 25(OH)D level was 15.00 ng/mL, interquartile range (IQR) 12.00 ng/mL. Vitamin D deficiency was found in 67.2% and was independent of sex, disease manifestation, and CRP, ESR, ALP, or PO4 levels. Higher doses of MTX corresponded with lower 25(OH)D levels using both univariate and multivariate models (p < 0.05). No such trend was found for GCs treatment. Serum Ca was lower in patients treated with GCs (p = 0.004), MTX (p = 0.03), and combined GCs/MTX (p = 0.034). Conclusions: JIA patients are vitamin D depleted independently of disease activity or inflammatory markers. MTX therapy may be an iatrogenic factor leading to inadequate 25(OH)D levels. Vitamin D supplementation should be considered in all children with JIA, particularly those receiving long-term MTX therapy