Magnetic Fourier Integral Operators

In some previous papers we have defined and studied a 'magnetic' pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is present. In this paper we extend the standard Fourier Integral Operators Theory to the case with a magnetic field, proving composition theorems, continuity theorems in 'magnetic' Sobolev spaces and Egorov type theorems. The main application is the representation of the evolution group generated by a 1-st order 'magnetic' pseudodifferential operator (in particular the relativistic Schr\"{o}dinger operator with magnetic field) as such a 'magnetic' Fourier Integral Operator. As a consequence of this representation we obtain some estimations for the distribution kernel of this evolution group and a result on the propagation of singularities

Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $P$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $P$ by an approximation $\hat{P}$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel $\hat{P}$ is to the chain given by $P$. We apply these results to several examples from spatial statistics and network analysis.Comment: This version: results extended to non-uniformly ergodic Markov chain

Geometric Path Integrals. A Language for Multiscale Biology and Systems Robustness

In this paper we suggest that, under suitable conditions, supervised learning can provide the basis to formulate at the microscopic level quantitative questions on the phenotype structure of multicellular organisms. The problem of explaining the robustness of the phenotype structure is rephrased as a real geometrical problem on a fixed domain. We further suggest a generalization of path integrals that reduces the problem of deciding whether a given molecular network can generate specific phenotypes to a numerical property of a robustness function with complex output, for which we give heuristic justification. Finally, we use our formalism to interpret a pointedly quantitative developmental biology problem on the allowed number of pairs of legs in centipedes

Unstable particles as open quantum systems

We present the probability preserving description of the decaying particle within the framework of quantum mechanics of open systems taking into account the superselection rule prohibiting the superposition of the particle and vacuum. In our approach the evolution of the system is given by a family of completely positive trace preserving maps forming one-parameter dynamical semigroup. We give the Kraus representation for the general evolution of such systems which allows one to write the evolution for systems with two or more particles. Moreover, we show that the decay of the particle can be regarded as a Markov process by finding explicitly the master equation in the Lindblad form. We also show that there are remarkable restrictions on the possible strength of decoherence.Comment: 11 pp, 2 figs (published version

Conformations of Proteins in Equilibrium

We introduce a simple theoretical approach for an equilibrium study of proteins with known native state structures. We test our approach with results on well-studied globular proteins, Chymotrypsin Inhibitor (2ci2), Barnase and the alpha spectrin SH3 domain and present evidence for a hierarchical onset of order on lowering the temperature with significant organization at the local level even at high temperatures. A further application to the folding process of HIV-1 protease shows that the model can be reliably used to identify key folding sites that are responsible for the development of drug resistance .Comment: 6 pages, 3 eps figure

Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo

EVpedia: a community web portal for extracellular vesicles research

MOTIVATION: Extracellular vesicles (EVs) are spherical bilayered proteolipids, harboring various bioactive molecules. Due to the complexity of the vesicular nomenclatures and components, online searches for EV-related publications and vesicular components are currently challenging. RESULTS: We present an improved version of EVpedia, a public database for EVs research. This community web portal contains a database of publications and vesicular components, identification of orthologous vesicular components, bioinformatic tools and a personalized function. EVpedia includes 6879 publications, 172 080 vesicular components from 263 high-throughput datasets, and has been accessed more than 65 000 times from more than 750 cities. In addition, about 350 members from 73 international research groups have participated in developing EVpedia. This free web-based database might serve as a useful resource to stimulate the emerging field of EV research. Availability and implementation: The web site was implemented in PHP, Java, MySQL and Apache, and is freely available at http://evpedia.info. CONTACT: [email protected]

Cardiac Biomarkers and Risk of Atrial Fibrillation in Chronic Kidney Disease: The CRIC Study.

Background We tested associations of cardiac biomarkers of myocardial stretch, injury, inflammation, and fibrosis with the risk of incident atrial fibrillation (AF) in a prospective study of chronic kidney disease patients. Methods and Results The study sample was 3053 participants with chronic kidney disease in the multicenter CRIC (Chronic Renal Insufficiency Cohort) study who were not identified as having AF at baseline. Cardiac biomarkers, measured at baseline, were NT-proBNP (N-terminal pro-B-type natriuretic peptide), high-sensitivity troponin T, galectin-3, growth differentiation factor-15, and soluble ST-2. Incident AF ("AF event") was defined as a hospitalization for AF. During a median follow-up of 8 years, 279 (9%) participants developed a new AF event. In adjusted models, higher baseline log-transformed NT-proBNP (N-terminal pro-B-type natriuretic peptide) was associated with incident AF (adjusted hazard ratio [HR] per SD higher concentration: 2.11; 95% CI, 1.75, 2.55), as was log-high-sensitivity troponin T (HR 1.42; 95% CI, 1.20, 1.68). These associations showed a dose-response relationship in categorical analyses. Although log-soluble ST-2 was associated with AF risk in continuous models (HR per SD higher concentration 1.35; 95% CI, 1.16, 1.58), this association was not consistent in categorical analyses. Log-galectin-3 (HR 1.05; 95% CI, 0.91, 1.22) and log-growth differentiation factor-15 (HR 1.16; 95% CI, 0.96, 1.40) were not significantly associated with incident AF. Conclusions We found strong associations between higher NT-proBNP (N-terminal pro-B-type natriuretic peptide) and high-sensitivity troponin T concentrations, and the risk of incident AF in a large cohort of participants with chronic kidney disease. Increased atrial myocardial stretch and myocardial cell injury may be implicated in the high burden of AF in patients with chronic kidney disease

Protein structures and optimal folding emerging from a geometrical variational principle

Novel numerical techniques, validated by an analysis of barnase and chymotrypsin inhibitor, are used to elucidate the paramount role played by the geometry of the protein backbone in steering the folding to the correct native state. It is found that, irrespective of the sequence, the native state of a protein has exceedingly large number of conformations with a given amount of structural overlap compared to other compact artificial backbones; moreover the conformational entropies of unrelated proteins of the same length are nearly equal at any given stage of folding. These results are suggestive of an extremality principle underlying protein evolution, which, in turn, is shown to be associated with the emergence of secondary structures.Comment: Revtex, 5 pages, 5 postscript figure