Fisher Information for Inverse Problems and Trace Class Operators

This paper provides a mathematical framework for Fisher information analysis for inverse problems based on Gaussian noise on infinite-dimensional Hilbert space. The covariance operator for the Gaussian noise is assumed to be trace class, and the Jacobian of the forward operator Hilbert-Schmidt. We show that the appropriate space for defining the Fisher information is given by the Cameron-Martin space. This is mainly because the range space of the covariance operator always is strictly smaller than the Hilbert space. For the Fisher information to be well-defined, it is furthermore required that the range space of the Jacobian is contained in the Cameron-Martin space. In order for this condition to hold and for the Fisher information to be trace class, a sufficient condition is formulated based on the singular values of the Jacobian as well as of the eigenvalues of the covariance operator, together with some regularity assumptions regarding their relative rate of convergence. An explicit example is given regarding an electromagnetic inverse source problem with "external" spherically isotropic noise, as well as "internal" additive uncorrelated noise.Comment: Submitted to Journal of Mathematical Physic

Correlator Bank Detection of GW chirps. False-Alarm Probability, Template Density and Thresholds: Behind and Beyond the Minimal-Match Issue

The general problem of computing the false-alarm rate vs. detection-threshold relationship for a bank of correlators is addressed, in the context of maximum-likelihood detection of gravitational waves, with specific reference to chirps from coalescing binary systems. Accurate (lower-bound) approximants for the cumulative distribution of the whole-bank supremum are deduced from a class of Bonferroni-type inequalities. The asymptotic properties of the cumulative distribution are obtained, in the limit where the number of correlators goes to infinity. The validity of numerical simulations made on small-size banks is extended to banks of any size, via a gaussian-correlation inequality. The result is used to estimate the optimum template density, yielding the best tradeoff between computational cost and detection efficiency, in terms of undetected potentially observable sources at a prescribed false-alarm level, for the simplest case of Newtonian chirps.Comment: submitted to Phys. Rev.

C-terminus of transcription factor TnrA from Bacillus subtilis controls DNA-binding domain activity but is not required for dimerization

The transcription factor TnrA, which belongs to the MerR transcription regulators, in Bacillus subtilis controls genes of nitrogen metabolism during nitrogen limiting conditions. As all the DNA-binding proteins, it is active as a dimer in cells, but the dimerization site is still unknown. The multiple alignment of TnrA homologs from other Bacilli allowed to identify the putative dimerization sites. Using the C-terminal truncated TnrA proteins it is established, that, in contrast to other MerR-proteins, the TnrA C-terminus does not participate in dimerization. Surface plasmon resonance has revealed that C-terminus truncations of TnrA do not inactivate its DNA-binding activity. Contrary, increased the affinity towards DNA, confirming that C-terminus controls the DNA-binding activity in a full-length TnrA. © 2013 Pleiades Publishing, Ltd

Generalized compactness in linear spaces and its applications

The class of subsets of locally convex spaces called $\mu$-compact sets is considered. This class contains all compact sets as well as several noncompact sets widely used in applications. It is shown that many results well known for compact sets can be generalized to $\mu$-compact sets. Several examples are considered. The main result of the paper is a generalization to $\mu$-compact convex sets of the Vesterstrom-O'Brien theorem showing equivalence of the particular properties of a compact convex set (s.t. openness of the mixture map, openness of the barycenter map and of its restriction to maximal measures, continuity of a convex hull of any continuous function, continuity of a convex hull of any concave continuous function). It is shown that the Vesterstrom-O'Brien theorem does not hold for pointwise $\mu$-compact convex sets defined by the slight relaxing of the $\mu$-compactness condition. Applications of the obtained results to quantum information theory are considered.Comment: 27 pages, the minor corrections have been mad

Bosonization method for second super quantization

A bosonic-fermionic correspondence allows an analytic definition of functional super derivative, in particular, and a bosonic functional calculus, in general, on Bargmann- Gelfand triples for the second super quantization. A Feynman integral for the super transformation matrix elements in terms of bosonic anti-normal Berezin symbols is rigorously constructed.Comment: In memoriam of F. A. Berezin, accepted in Journal of Nonlinear Mathematical Physics, 15 page

Supersymmetry and LHC

The motivation for introduction of supersymmetry in high energy physics as well as a possibility for supersymmetry discovery at LHC (Large Hadronic Collider) are discussed. The main notions of the Minimal Supersymmetric Standard Model (MSSM) are introduced. Different regions of parameter space are analyzed and their phenomenological properties are compared. Discovery potential of LHC for the planned luminosity is shown for different channels. The properties of SUSY Higgs bosons are studied and perspectives of their observation at LHC are briefly outlined.Comment: Lectures given at the 9th Moscow International School of Physics (XXXIV ITEP Winter School of Physics

Thio derivatives of 2(5H)-furanone as inhibitors against Bacillus subtilis biofilms

© 2015 Park-media, Ltd. Gram-positive bacteria cause a wide spectrum of infectious diseases, including nosocomial infections. While in the biofilm, bacteria exhibit increased resistance to antibiotics and the human immune system, causing difficulties in treatment. Thus, the development of biofilm formation inhibitors is a great challenge in pharmacology. The gram-positive bacterium Bacillus subtilis is widely used as a model organism for studying biofilm formation. Here, we report on the effect of new synthesized 2(5H)-furanones on the biofilm formation by B.subtilis cells. Among 57 compounds tested, sulfur-containing derivatives of 2(5H)-furanone (F12, F15, and F94) repressed biofilm formation at a concentration of 10 μg/ml. Derivatives F12 and F94 were found to inhibit the biosynthesis of GFP from the promoter of the eps operon encoding genes of the biofilm exopolysaccharide synthesis (EPS). Using the differential fluorescence staining of alive/dead cells, we demonstrated an increased bacterial sensitivity to antibiotics (kanamycin and chloramphenicol) in the presence of F12, F15, and F94, with F12 being the most efficient one. The derivative F15 was capable of disrupting an already formed biofilm and thereby increasing the efficiency of antibiotics

Analysis of the archetypal functional equation in the non-critical case

We study the archetypal functional equation of the form $y(x)=\iint_{R^2} y(a(x-b))\,\mu(da,db)$ ($x\in R$), where $\mu$ is a probability measure on $R^2$; equivalently, $y(x)=E\{y(\alpha (x-\beta))\}$, where $E$ is expectation with respect to the distribution $\mu$ of random coefficients $(\alpha,\beta)$. Existence of non-trivial (i.e. non-constant) bounded continuous solutions is governed by the value $K:=\iint_{R^2}\ln |a| \mu(da,db) =E \{\ln |\alpha|\}$; namely, under mild technical conditions no such solutions exist whenever $K0$ (and $\alpha>0$) then there is a non-trivial solution constructed as the distribution function of a certain random series representing a self-similar measure associated with $(\alpha,\beta)$. Further results are obtained in the supercritical case $K>0$, including existence, uniqueness and a maximum principle. The case with $P(\alpha0$ is drastically different from that with $\alpha>0$; in particular, we prove that a bounded solution $y(\cdot)$ possessing limits at $\pm\infty$ must be constant. The proofs employ martingale techniques applied to the martingale $y(X_n)$, where $(X_n)$ is an associated Markov chain with jumps of the form $x\rightsquigarrow\alpha (x-\beta)$

Myectomy versus alcohol septal ablation in patients with hypertrophic obstructive cardiomyopathy

OBJECTIVES: There is very little evidence comparing the safety and efficacy of alcohol septal ablation versus septal myectomy for a septal reduction in patients with hypertrophic obstructive cardiomyopathy. This study aimed to compare the immediate and long-term outcomes of these procedures. METHODS: Following propensity score matching, we retrospectively analysed outcomes in 105 patients who underwent myectomy and 105 who underwent septal ablation between 2011 and 2017 at 2 reference centres. RESULTS: The mean age was 51.9 ± 14.3 and 52.2 ± 14.3 years in the myectomy and ablation groups, respectively (P = 0.855), and postoperative left ventricular outflow tract gradients were 13 (10-19) mmHg vs 16 (12-26) mmHg; P = 0.025. The 1-year prevalence of the New York Heart Association class III-IV was higher in the ablation group (none vs 6.4%; P = 0.041). The 5-year overall survival rate [96.8% (86.3-99.3) after myectomy and 93.5% (85.9-97.1) after ablation; P = 0.103] and cumulative incidence of sudden cardiac death [0% and 1.9% (0.5-7.5), respectively P = 0.797] did not differ between the groups. The cumulative reoperation rate within 5 years was lower after myectomy than after ablation [2.0% (0.5-7.6) vs 14.6% (8.6-24.1); P = 0.003]. Ablation was associated with a higher reoperation risk (subdistributional hazard ratio = 5.9; 95% confidence interval 1.3-26.3, P = 0.020). At follow-up, left ventricular outflow tract gradient [16 (11-20) vs 23 (15-59) mmHg; P < 0.001] and prevalence of 2+ mitral regurgitation (1.1% vs 10.6%; P = 0.016) were lower after myectomy than after ablation. CONCLUSIONS: Both procedures improved functional capacity; however, myectomy better-resolved classes III-IV of heart failure. Septal ablation was associated with higher reoperation rates. Myectomy demonstrated benefits in gradient relief and mitral regurgitation elimination. The results suggest that decreasing rates of myectomy procedures need to be investigated and reconsidered. © The Author(s) 2020. Published by Oxford University Press on behalf of the European Association for Cardio-Thoracic Surgery. All rights reserved

The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

We consider an "elastic" version of the statistical mechanical monomer-dimer problem on the n-dimensional integer lattice. Our setting includes the classical "rigid" formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for "Manhattan" EDM systems where the dimer potential is a weighted l1-distance and the auxiliary GRF is a Markov random field of Pickard type which behaves in space like autoregressive processes do in time. For one-dimensional Manhattan EDM systems, we compute the MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a compact transfer operator on a Hilbert space which is related to the annihilation and creation operators of the quantum harmonic oscillator and also recast it as the eigenvalue problem for a pantograph functional-differential equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue of DCDS-