On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

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Sobolev mappings: Lipschitz density is not an isometric invariant of the target

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A type of perturbation of the harmonic oscillator

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A Novel Pulse-Chase SILAC Strategy Measures Changes in Protein Decay and Synthesis Rates Induced by Perturbation of Proteostasis with an Hsp90 Inhibitor.

Standard proteomics methods allow the relative quantitation of levels of thousands of proteins in two or more samples. While such methods are invaluable for defining the variations in protein concentrations which follow the perturbation of a biological system, they do not offer information on the mechanisms underlying such changes. Expanding on previous work [1], we developed a pulse-chase (pc) variant of SILAC (stable isotope labeling by amino acids in cell culture). pcSILAC can quantitate in one experiment and for two conditions the relative levels of proteins newly synthesized in a given time as well as the relative levels of remaining preexisting proteins. We validated the method studying the drug-mediated inhibition of the Hsp90 molecular chaperone, which is known to lead to increased synthesis of stress response proteins as well as the increased decay of Hsp90 "clients". We showed that pcSILAC can give information on changes in global cellular proteostasis induced by treatment with the inhibitor, which are normally not captured by standard relative quantitation techniques. Furthermore, we have developed a mathematical model and computational framework that uses pcSILAC data to determine degradation constants kd and synthesis rates Vs for proteins in both control and drug-treated cells. The results show that Hsp90 inhibition induced a generalized slowdown of protein synthesis and an increase in protein decay. Treatment with the inhibitor also resulted in widespread protein-specific changes in relative synthesis rates, together with variations in protein decay rates. The latter were more restricted to individual proteins or protein families than the variations in synthesis. Our results establish pcSILAC as a viable workflow for the mechanistic dissection of changes in the proteome which follow perturbations. Data are available via ProteomeXchange with identifier PXD000538.

El mètode APT (Auto Adjusting Perturbation Theory) de diagonalització de matrius

Es presenta un nou algorisme per a la diagonalització de matrius amb diagonal dominant. Es mostra la seva eficàcia en el tractament de matrius no simètriques, amb elements definits sobre el cos complex i, fins i tot, de grans dimensions. Es posa de manifest la senzillesa del mètode així com la facilitat d'implementació en forma de codi de programació. Es comentenels seus avantatges i característiques limitants, així com algunes de les millores que es poden implementar. Finalment, es mostren alguns exemples numèrics

Compositional hypotheses of subcompositional stability and specific perturbation change and their testing

In standard multivariate statistical analysis common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. To motivate the statistical developments of this paper we present two challenging compositional problems from food production processes.Against this background the relevance of perturbations and subcompositions can beclearly seen. Moreover we can identify a number of hypotheses of interest involvingthe specification of particular perturbations or differences between perturbations and also hypotheses of subcompositional stability. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate analysis. We then develop appropriate estimation and testing procedures for a complete lattice of relevant compositional hypotheses

Perturbation expansions of multilocus fixation probabilities for frequency-dependent selection with applications to the Hill-Robertson effect and to the joint evolution of helping and punishment.

Natural populations are of finite size and organisms carry multilocus genotypes. There are, nevertheless, few results on multilocus models when both random genetic drift and natural selection affect the evolutionary dynamics. In this paper we describe a formalism to calculate systematic perturbation expansions of moments of allelic states around neutrality in populations of constant size. This allows us to evaluate multilocus fixation probabilities (long-term limits of the moments) under arbitrary strength of selection and gene action. We show that such fixation probabilities can be expressed in terms of selection coefficients weighted by mean first passages times of ancestral gene lineages within a single ancestor. These passage times extend the coalescence times that weight selection coefficients in one-locus perturbation formulas for fixation probabilities. We then apply these results to investigate the Hill-Robertson effect and the coevolution of helping and punishment. Finally, we discuss limitations and strengths of the perturbation approach. In particular, it provides accurate approximations for fixation probabilities for weak selection regimes only (Ns < or = 1), but it provides generally good prediction for the direction of selection under frequency-dependent selection.

Second-order Møller-Plesset perturbation theory without basis set superposition error : II : open-shell systems

The basis set superposition error-free second-order MØller-Plesset perturbation theory of intermolecular interactions was studied. The difficulties of the counterpoise (CP) correction in open-shell systems were also discussed. The calculations were performed by a program which was used for testing the new variants of the theory. It was shown that the CP correction for the diabatic surfaces should be preferred to the adiabatic ones

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

Initial convergence of the perturbation series expansion for vibrational nonlinear optical (NLO) properties was analyzed. The zero-point vibrational average (ZPVA) was obtained through first-order in mechanical plus electrical anharmonicity. Results indicated that higher-order terms in electrical and mechanical anharmonicity can make substantial contributions to the pure vibrational polarizibility of typical NLO molecules

Solving heterogeneous-agent models by projection and perturbation

The paper proposes a numerical solution method for general equilibrium models with a continuum of heterogeneous agents, which combines elements of projection and of perturbation methods. The basic idea is to solve first for the stationary solutionof the model, without aggregate shocks but with fully specified idiosyncratic shocks. Afterwards one computes a first-order perturbation of the solution in the aggregate shocks. This approach allows to include a high-dimensional representation of the cross-sectional distribution in the state vector. The method is applied to a model of household saving with uninsurable income risk and liquidity constraints. The model includes not only productivity shocks, but also shocks to redistributive taxation, which cause substantial short-run variation in the cross-sectional distribution of wealth. If those shocks are operative, it is shown that a solution method based on very few statistics of the distribution is not suitable, while the proposed method can solve the model with high accuracy, at least for the case of small aggregate shocks. Techniques are discussed to reduce the dimension of the state space such that higher order perturbations are feasible.Matlab programs to solve the model can be downloaded.

Perturbation theory and locality in the Field-Antifield formalism

The BatalinVilkovisky formalism is studied in the framework of perturbation theory by analyzing the antibracket BecchiRouetStoraTyutin (BRST) cohomology of the proper solution S0. It is concluded that the recursive equations for the complete proper solution S can be solved at any order of perturbation theory. If certain conditions on the classical action and on the gauge generators are imposed the solution can be taken local.

Perturbation theory for classical thermodynamic Green's functions

A systematic time-dependent perturbation scheme for classical canonical systems is developed based on a Wick's theorem for thermal averages of time-ordered products. The occurrence of the derivatives with respect to the canonical variables noted by Martin, Siggia, and Rose implies that two types of Green's functions have to be considered, the propagator and the response function. The diagrams resulting from Wick's theorem are "double graphs" analogous to those introduced by Dyson and also by Kawasaki, in which the response-function lines form a "tree structure" completed by propagator lines. The implication of a fluctuation-dissipation theorem on the self-energies is analyzed and compared with recent results by Deker and Haake.

Rapid Perturbation in Viremia Levels Drives Increases in Functional Avidity of HIV-specific CD8 T Cells.

The factors determining the functional avidity and its relationship with the broad heterogeneity of antiviral T cell responses remain partially understood. We investigated HIV-specific CD8 T cell responses in 85 patients with primary HIV infection (PHI) or chronic (progressive and non-progressive) infection. The functional avidity of HIV-specific CD8 T cells was not different between patients with progressive and non-progressive chronic infection. However, it was significantly lower in PHI patients at the time of diagnosis of acute infection and after control of virus replication following one year of successful antiretroviral therapy. High-avidity HIV-specific CD8 T cells expressed lower levels of CD27 and CD28 and were enriched in cells with an exhausted phenotype, i.e. co-expressing PD-1/2B4/CD160. Of note, a significant increase in the functional avidity of HIV-specific CD8 T cells occurred in early-treated PHI patients experiencing a virus rebound after spontaneous treatment interruption. This increase in functional avidity was associated with the accumulation of PD-1/2B4/CD160 positive cells, loss of polyfunctionality and increased TCR renewal. The increased TCR renewal may provide the mechanistic basis for the generation of high-avidity HIV-specific CD8 T cells. These results provide insights on the relationships between functional avidity, viremia, T-cell exhaustion and TCR renewal of antiviral CD8 T cell responses.