Heat and mass transfer from the mantle: heat flow and He-isotope constraints

Terrestrial heat flow density, q, is inversely correlated with the age, t, of tectono-magmatic activity in the Earth's crust (Polyak and Smirnov, 1966; etc.). «Heat flow-age dependence» indicates unknown temporal heat sources in the interior considered a priori as the mantle-derived diapirs. The validity of this hypothesis is demonstrated by studying the helium isotope ratio, 3He/4He = R, in subsurface fluids. This study discovered the positive correlation between the regionally averaged (background) estimations of R- and q-values (Polyak et al., 1979a). Such a correlation manifests itself in both pan-regional scales (Norhtern Eurasia) and separate regions, e.g., Japan (Sano et al., 1982), Eger Graben (Polyak et al., 1985) Eastern China rifts (Du, 1992), Southern Italy (Italiano et al., 2000), and elsewhere. The R-q relation indicates a coupled heat and mass transfer from the mantle into the crust. From considerations of heat-mass budget this transfer can be provided by the flux consisting of silicate matter rather than He or other volatiles. This conclusion is confirmed by the correlation between 3He/ 4He and 87Sr/86Sr ratios in the products of the volcanic and hydrothermal activity in Italy (Polyak et al., 1979b; Parello et al., 2000) and other places. Migration of any substance through geotemperature field transports thermal energy accumulated within this substance, i.e. represents heat and mass transfer. Therefore, only the coupled analysis of both material and energy aspects of this transfer makes it possible to characterise the process adequately and to decipher an origin of terrestrial heat flow observed in upper parts of the earth crust. An attempt of such kind is made in this paper

Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

A non-linear conjugate gradient optimization scheme is used to obtain excitation energies within the Random Phase Approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size, N, is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular- orbital-free algorithm is found to be robust and computationally efficient providing a first step toward a large-scale, reduced complexity calculation of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent Density Functional theory.Comment: 9 pages, 7 figure

The Cinchona Primary Amine-Catalyzed Asymmetric Epoxidation and Hydroperoxidation of α,β-Unsaturated Carbonyl Compounds with Hydrogen Peroxide

Using cinchona alkaloid-derived primary amines as catalysts and aqueous hydrogen peroxide as the oxidant, we have developed highly enantioselective Weitz–Scheffer-type epoxidation and hydroperoxidation reactions of α,β-unsaturated carbonyl compounds (up to 99.5:0.5 er). In this article, we present our full studies on this family of reactions, employing acyclic enones, 5–15-membered cyclic enones, and α-branched enals as substrates. In addition to an expanded scope, synthetic applications of the products are presented. We also report detailed mechanistic investigations of the catalytic intermediates, structure–activity relationships of the cinchona amine catalyst, and rationalization of the absolute stereoselectivity by NMR spectroscopic studies and DFT calculations

Neurosteroid-Mediated Regulation of Brain Innate Immunity in HIV/Aids: DHEA-S Suppresses Neurovirulence

Neurosteroids are cholesterol-derived molecules synthesized within the brain, which exert trophic and protective actions. Infection by human and feline immunodeficiency viruses (HIV and FIV, respectively) causes neuroinflammation and neurodegeneration, leading to neurological deficits. Secretion of neuroinflammatory host and viral factors by glia and infiltrating leukocytes mediates the principal neuropathogenic mechanisms during, although the effect of neurosteroids on these processes is unknown. We investigated the interactions between neurosteroid mediated effects and lentivirus infection outcomes. Analyses of HIV-infected uninfected human brains disclosed a reduction in neurosteroid synthesis enzyme expression. Human neurons exposed to supernatants from HIV macrophages exhibited suppressed enzyme expression without reduced cellular viability. HIV human macrophages treated with sulfated dehydroepiandrosterone (DHEA-S) showed suppression of inflammatory gene (IL-1, IL-6, TNF-) expression. IV-infected IV) animals treated daily with 15mg/kg body weight. DHEA-S treatment reduced inflammatory gene transcripts (IL-1, TNF-, CD3, GFAP) in brain compared to vehicle-(-cyclodextrin)-treated FIV animals similar to levels found in vehicle treated FIV animals. DHEA-S treatment also increased CD4T-cell levels and prevented neurobehavioral deficits and neuronal loss among FIV animals, compared to vehicle-treated FIV animals. Reduced neuronal neuro-steroid synthesis was evident in lentivirus infections, but treatment with DHEA-S limited neuroinflammation and prevented neurobehavioral deficits. Neurosteroid-derived therapies could be effective in the treatment of virus- or inflammation-mediated neurodegeneration

The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization

Using normal coordinates in a Poincar\'e-Birkhoff-Witt basis for the Hopf algebra of renormalization in perturbative quantum field theory, we investigate the relation between the twisted antipode axiom in that formalism, the Birkhoff algebraic decomposition and the universal formula of Kontsevich for quantum deformation.Comment: 21 pages, 15 figure

Gradient methods for problems with inexact model of the objective

We consider optimization methods for convex minimization problems under inexact information on the objective function. We introduce inexact model of the objective, which as a particular cases includes inexact oracle [19] and relative smoothness condition [43]. We analyze gradient method which uses this inexact model and obtain convergence rates for convex and strongly convex problems. To show potential applications of our general framework we consider three particular problems. The first one is clustering by electorial model introduced in [49]. The second one is approximating optimal transport distance, for which we propose a Proximal Sinkhorn algorithm. The third one is devoted to approximating optimal transport barycenter and we propose a Proximal Iterative Bregman Projections algorithm. We also illustrate the practical performance of our algorithms by numerical experiments

Intratumor heterogeneity defines treatment-resistant HER2+ breast tumors.

Targeted therapy for patients with HER2-positive (HER2+) breast cancer has improved overall survival, but many patients still suffer relapse and death from the disease. Intratumor heterogeneity of both estrogen receptor (ER) and HER2 expression has been proposed to play a key role in treatment failure, but little work has been done to comprehensively study this heterogeneity at the single-cell level. In this study, we explored the clinical impact of intratumor heterogeneity of ER protein expression, HER2 protein expression, and HER2 gene copy number alterations. Using combined immunofluorescence and in situ hybridization on tissue sections followed by a validated computational approach, we analyzed more than 13 000 single tumor cells across 37 HER2+ breast tumors. The samples were taken both before and after neoadjuvant chemotherapy plus HER2-targeted treatment, enabling us to study tumor evolution as well. We found that intratumor heterogeneity for HER2 copy number varied substantially between patient samples. Highly heterogeneous tumors were associated with significantly shorter disease-free survival and fewer long-term survivors. Patients for which HER2 characteristics did not change during treatment had a significantly worse outcome. This work shows the impact of intratumor heterogeneity in molecular diagnostics for treatment selection in HER2+ breast cancer patients and the power of computational scoring methods to evaluate in situ molecular markers in tissue biopsies

Advances in low-memory subgradient optimization

One of the main goals in the development of non-smooth optimization is to cope with high dimensional problems by decomposition, duality or Lagrangian relaxation which greatly reduces the number of variables at the cost of worsening differentiability of objective or constraints. Small or medium dimensionality of resulting non-smooth problems allows to use bundle-type algorithms to achieve higher rates of convergence and obtain higher accuracy, which of course came at the cost of additional memory requirements, typically of the order of n2, where n is the number of variables of non-smooth problem. However with the rapid development of more and more sophisticated models in industry, economy, finance, et all such memory requirements are becoming too hard to satisfy. It raised the interest in subgradient-based low-memory algorithms and later developments in this area significantly improved over their early variants still preserving O(n) memory requirements. To review these developments this chapter is devoted to the black-box subgradient algorithms with the minimal requirements for the storage of auxiliary results, which are necessary to execute these algorithms. To provide historical perspective this survey starts with the original result of N.Z. Shor which opened this field with the application to the classical transportation problem. The theoretical complexity bounds for smooth and non-smooth convex and quasi-convex optimization problems are briefly exposed in what follows to introduce to the relevant fundamentals of non-smooth optimization. Special attention in this section is given to the adaptive step-size policy which aims to attain lowest complexity bounds. Unfortunately the non-differentiability of objective function in convex optimization essentially slows down the theoretical low bounds for the rate of convergence in subgradient optimization compared to the smooth case but there are different modern techniques that allow to solve non-smooth convex optimization problems faster then dictate lower complexity bounds. In this work the particular attention is given to Nesterov smoothing technique, Nesterov Universal approach, and Legendre (saddle point) representation approach. The new results on Universal Mirror Prox algorithms represent the original parts of the survey. To demonstrate application of non-smooth convex optimization algorithms for solution of huge-scale extremal problems we consider convex optimization problems with non-smooth functional constraints and propose two adaptive Mirror Descent methods. The first method is of primal-dual variety and proved to be optimal in terms of lower oracle bounds for the class of Lipschitz-continuous convex objective and constraints. The advantages of application of this method to sparse Truss Topology Design problem are discussed in certain details. The second method can be applied for solution of convex and quasi-convex optimization problems and is optimal in a sense of complexity bounds. The conclusion part of the survey contains the important references that characterize recent developments of non-smooth convex optimization

Topological entropy of a stiff ring polymer and its connection to DNA knots

We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through numerical simulations using some knot invariants, we show that the topological entropy of a stiff ring polymer with a fixed knot is described by a scaling formula as a function of the thickness and length of the circular chain. The result is consistent with the viewpoint that for stiff polymers such as DNAs, the length and diameter of the chains should play a central role in their statistical and dynamical properties. Furthermore, we show that the new formula extends a known theoretical formula for DNA knots.Comment: 14pages,11figure