A bounded degree SOS hierarchy for polynomial optimization

We consider a new hierarchy of semidefinite relaxations for the general polynomial optimization problem $(P):\:f^{\ast}=\min \{\,f(x):x\in K\,\}$ on a compact basic semi-algebraic set $K\subset\R^n$. This hierarchy combines some advantages of the standard LP-relaxations associated with Krivine's positivity certificate and some advantages of the standard SOS-hierarchy. In particular it has the following attractive features: (a) In contrast to the standard SOS-hierarchy, for each relaxation in the hierarchy, the size of the matrix associated with the semidefinite constraint is the same and fixed in advance by the user. (b) In contrast to the LP-hierarchy, finite convergence occurs at the first step of the hierarchy for an important class of convex problems. Finally (c) some important techniques related to the use of point evaluations for declaring a polynomial to be zero and to the use of rank-one matrices make an efficient implementation possible. Preliminary results on a sample of non convex problems are encouraging

A New Class of Theta Function Identities in Two Variables

Copyright © 2010 Nova Science PublishersWe describe a new class of identities, which hold for certain general theta series, in two completely independent variables. We provide explicit examples of these identities involving the Dedekind eta function, Jacobi theta functions, and various theta functions of Ramanujan

Binding of Basic Dyes by the Algae, Chara aspera

Non-living biomass of the algae Chara aspera is capable of binding two basic dyes, methylene blue and basic blue 3, from aqueous solution. Factors such as dye concentration, contact time, sorbent dosage and pH of solution were studied. Maximum sorption capacities of the algae for methylene blue and basic blue 3 are 139.4 and 17.8 mg/g, respectively, as determined from the Langmuir isothenns

Role of Interleukin 17 in arthritis chronicity through survival of synoviocytes via regulation of synoviolin expression

Background: The use of TNF inhibitors has been a major progress in the treatment of chronic inflammation. However, not all patients respond. In addition, response will be often lost when treatment is stopped. These clinical aspects indicate that other cytokines might be involved and we focus here on the role of IL-17. In addition, the chronic nature of joint inflammation may contribute to reduced response and enhanced chronicity. Therefore we studied the capacity of IL-17 to regulate synoviolin, an E3 ubiquitin ligase implicated in synovial hyperplasia in human rheumatoid arthritis (RA) FLS and in chronic reactivated streptococcal cell wall (SCW)-induced arthritis.<p></p> Methodology/Principal Findings: Chronic reactivated SCW-induced arthritis was examined in IL-17R deficient and wild-type mice. Synoviolin expression was analysed by real-time RT-PCR, Western Blot or immunostaining in RA FLS and tissue, and p53 assessed by Western Blot. Apoptosis was detected by annexin V/propidium iodide staining, SS DNA apoptosis ELISA kit or TUNEL staining and proliferation by PCNA staining. IL-17 receptor A (IL-17RA), IL-17 receptor C (IL-17-RC) or synoviolin inhibition were achieved by small interfering RNA (siRNA) or neutralizing antibodies. IL-17 induced sustained synoviolin expression in RA FLS. Sodium nitroprusside (SNP)-induced RA FLS apoptosis was associated with reduced synoviolin expression and was rescued by IL-17 treatment with a corresponding increase in synoviolin expression. IL-17RC or IL-17RA RNA interference increased SNP-induced apoptosis, and decreased IL-17-induced synoviolin. IL-17 rescued RA FLS from apoptosis induced by synoviolin knockdown. IL-17 and TNF had additive effects on synoviolin expression and protection against apoptosis induced by synoviolin knowndown. In IL-17R deficient mice, a decrease in arthritis severity was characterized by increased synovial apoptosis, reduced proliferation and a marked reduction in synoviolin expression. A distinct absence of synoviolin expressing germinal centres in IL-17R deficient mice contrasted with synoviolin positive B cells and Th17 cells in synovial germinal centre-like structures.<p></p> Conclusion/Significance: IL-17 induction of synoviolin may contribute at least in part to RA chronicity by prolonging the survival of RA FLS and immune cells in germinal centre reactions. These results extend the role of IL-17 to synovial hyperplasia.<p></p&gt

Stable periodic waves in coupled Kuramoto-Sivashinsky - Korteweg-de Vries equations

Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky - Korteweg-de Vries (KS-KdV) equation, which is linearly coupled to an extra linear dissipative equation. The model describes, e.g., a two-layer liquid film flowing down an inclined plane. It has been recently shown that the system supports stable solitary pulses. We demonstrate that a perturbation analysis, based on the balance equation for the field momentum, predicts the existence of stable cnoidal waves (CnWs) in the same system. It is found that the mean value U of the wave field u in the main subsystem, but not the mean value of the extra field, affects the stability of the periodic waves. Three different areas can be distinguished inside the stability region in the parameter plane (L,U), where L is the wave's period. In these areas, stable are, respectively, CnWs with positive velocity, constant solutions, and CnWs with negative velocity. Multistability, i.e., the coexistence of several attractors, including the waves with several maxima per period, appears at large value of L. The analytical predictions are completely confirmed by direct simulations. Stable waves are also found numerically in the limit of vanishing dispersion, when the KS-KdV equation goes over into the KS one.Comment: a latex text file and 16 eps files with figures. Journal of the Physical Society of Japan, in pres

Stabilized Kuramoto-Sivashinsky system

A model consisting of a mixed Kuramoto - Sivashinsky - KdV equation, linearly coupled to an extra linear dissipative equation, is proposed. The model applies to the description of surface waves on multilayered liquid films. The extra equation makes its possible to stabilize the zero solution in the model, opening way to the existence of stable solitary pulses (SPs). Treating the dissipation and instability-generating gain in the model as small perturbations, we demonstrate that balance between them selects two steady-state solitons from their continuous family existing in the absence of the dissipation and gain. The may be stable, provided that the zero solution is stable. The prediction is completely confirmed by direct simulations. If the integration domain is not very large, some pulses are stable even when the zero background is unstable. Stable bound states of two and three pulses are found too. The work was supported, in a part, by a joint grant from the Israeli Minsitry of Science and Technology and Japan Society for Promotion of Science.Comment: A text file in the latex format and 20 eps files with figures. Physical Review E, in pres

Shell model description of Ge isotopes

A shell model study of the low energy region of the spectra in Ge isotopes for $38\leq N\leq 50$ is presented, analyzing the excitation energies, quadrupole moments, $B(E2)$ values and occupation numbers. The theoretical results have been compared with the available experimental data. The shell model calculations have been performed employing three different effective interactions and valence spaces.We have used two effective shell model interactions, JUN45 and jj44b, for the valence space $f_{5/2} \, p \,g_{9/2}$ without truncation. To include the proton subshell $f_{7/2}$ in valence space we have employed the $fpg$ effective interaction due to Sorlin {\it et al.}, with $^{48}$Ca as a core and a truncation in the number of excited particles.Comment: 10 pages, 10 figures, Proc. of the XXXV Nuclear Physics Symposium, January 3-6 2012, Cocoyoc, Morelos, Mexico. IOP Journal of Physics: Conference Series (in press

A quantitative framework for characterizing the evolutionary history of mammalian gene expression

The evolutionary history of a gene helps predict its function and relationship to phenotypic traits. Although sequence conservation is commonly used to decipher gene function and assess medical relevance, methods for functional inference from comparative expression data are lacking. Here, we use RNA-seq across seven tissues from 17 mammalian species to show that expression evolution across mammals is accurately modeled by the Ornstein–Uhlenbeck process, a commonly proposed model of continuous trait evolution. We apply this model to identify expression pathways under neutral, stabilizing, and directional selection. We further demonstrate novel applications of this model to quantify the extent of stabilizing selection on a gene’s expression, parameterize the distribution of each gene’s optimal expression level, and detect deleterious expression levels in expression data from individual patients. Our work provides a statistical framework for interpreting expression data across species and in disease