PBP4: A New Perspective on Staphylococcus aureus β-Lactam Resistance.

β-lactam antibiotics are excellent drugs for treatment of staphylococcal infections, due to their superior efficacy and safety compared to other drugs. Effectiveness of β-lactams is severely compromised due to resistance, which is widespread among clinical strains of Staphylococcus aureus. β-lactams inhibit bacterial cells by binding to penicillin binding proteins (PBPs), which perform the penultimate steps of bacterial cell wall synthesis. Among PBPs of S. aureus, PBP2a has received the most attention for the past several decades due to its preeminent role in conferring both high-level and broad-spectrum resistance to the entire class of β-lactam drugs. Studies on PBP2a have thus unraveled incredible details of its mechanism of action. We have recently identified that an uncanonical, low molecular weight PBP of S. aureus, PBP4, can also provide high-level and broad-spectrum resistance to the entire class of β-lactam drugs at a level similar to that of PBP2a. The role of PBP4 has typically been considered not so important for β-lactam resistance of S. aureus, and as a result its mode of action remains largely unknown. In this article, we review our current knowledge of PBP4 mediating β-lactam resistance in S. aureus

The Stochastic Reach-Avoid Problem and Set Characterization for Diffusions

In this article we approach a class of stochastic reachability problems with state constraints from an optimal control perspective. Preceding approaches to solving these reachability problems are either confined to the deterministic setting or address almost-sure stochastic requirements. In contrast, we propose a methodology to tackle problems with less stringent requirements than almost sure. To this end, we first establish a connection between two distinct stochastic reach-avoid problems and three classes of stochastic optimal control problems involving discontinuous payoff functions. Subsequently, we focus on solutions of one of the classes of stochastic optimal control problems---the exit-time problem, which solves both the two reach-avoid problems mentioned above. We then derive a weak version of a dynamic programming principle (DPP) for the corresponding value function; in this direction our contribution compared to the existing literature is to develop techniques that admit discontinuous payoff functions. Moreover, based on our DPP, we provide an alternative characterization of the value function as a solution of a partial differential equation in the sense of discontinuous viscosity solutions, along with boundary conditions both in Dirichlet and viscosity senses. Theoretical justifications are also discussed to pave the way for deployment of off-the-shelf PDE solvers for numerical computations. Finally, we validate the performance of the proposed framework on the stochastic Zermelo navigation problem

Computer aided synthesis: a game theoretic approach

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

The Einstein-Cartan-Elko system

The present paper analyses the Einstein-Cartan theory of gravitation with Elko spinors as sources of curvature and torsion. After minimally coupling the Elko spinors to torsion, the spin angular momentum tensor is derived and its structure is discussed. It shows a much richer structure than the Dirac analogue and hence it is demonstrated that spin one half particles do not necessarily yield only an axial vector torsion component. Moreover, it is argued that the presence of Elko spinors partially solves the problem of minimally coupling Maxwell fields to Einstein-Cartan theory.Comment: 12 pages, no figure

Gravitational Slingshot of Young Massive Stars in Orion

The Orion Nebula Cluster (ONC) is the nearest region of massive star formation and thus a crucial testing ground for theoretical models. Of particular interest amongst the ONC's ~1000 members are: \theta^1 Ori C, the most massive binary in the cluster with stars of masses 38 and 9 MSun (Kraus et al. 2009); the Becklin-Neugebauer (BN) object, a 30 km/s runaway star of ~8 MSun (Tan 2004); and the Kleinmann-Low (KL) nebula protostar, a highly-obscured, ~15 MSun object still accreting gas while also driving a powerful, apparently "explosive" outflow (Allen & Burton 1993). The unusual behavior of BN and KL is much debated: How did BN acquire its high velocity? How is this related to massive star formation in the KL nebula? Here we report the results of a systematic survey using ~ 10^7 numerical experiments of gravitational interactions of the \theta^1C and BN stars. We show that dynamical ejection of BN from this triple system at its observed velocity leaves behind a binary with total energy and eccentricity matching those observed for \theta^1C. Five other observed properties of \theta^C are also consistent with it having ejected BN and altogether we estimate there is only a <~ 10^{-5} probability that \theta^1C has these properties by chance. We conclude that BN was dynamically ejected from the \theta^1C system about 4,500 years ago. BN has then plowed through the KL massive-star-forming core within the last 1,000 years causing its recently-enhanced accretion and outflow activity.Comment: 16 pages, 9 figures, 1 table, accepted to Ap

Collapsing Perfect Fluid in Higher Dimensional Spherical Spacetimes

The general metric for N-dimensional spherically symmetric and conformally flat spacetimes is given, and all the homogeneous and isotropic solutions for a perfect fluid with the equation of state $p = \alpha \rho$ are found. These solutions are then used to model the gravitational collapse of a compact ball. It is found that when the collapse has continuous self-similarity, the formation of black holes always starts with zero mass, and when the collapse has no such a symmetry, the formation of black holes always starts with a mass gap.Comment: Class. Quantum Grav. 17 (2000) 2589-259

Sex differences in DNA methylation and expression in zebrafish brain: a test of an extended ‘male sex drive’ hypothesis

The sex drive hypothesis predicts that stronger selection on male traits has resulted in masculinization of the genome. Here we test whether such masculinizing effects can be detected at the level of the transcriptome and methylome in the adult zebrafish brain. Although methylation is globally similar, we identified 914 specific differentially methylated CpGs (DMCs) between males and females (435 were hypermethylated and 479 were hypomethylated in males compared to females). These DMCs were prevalent in gene body, intergenic regions and CpG island shores. We also discovered 15 distinct CpG clusters with striking sex-specific DNA methylation differences. In contrast, at transcriptome level, more female-biased genes than male-biased genes were expressed, giving little support for the male sex drive hypothesis. Our study provides genome-wide methylome and transcriptome assessment and sheds light on sex-specific epigenetic patterns and in zebrafish for the first time

Chemotaxis When Bacteria Remember: Drift versus Diffusion

{\sl Escherichia coli} ({\sl E. coli}) bacteria govern their trajectories by switching between running and tumbling modes as a function of the nutrient concentration they experienced in the past. At short time one observes a drift of the bacterial population, while at long time one observes accumulation in high-nutrient regions. Recent work has viewed chemotaxis as a compromise between drift toward favorable regions and accumulation in favorable regions. A number of earlier studies assume that a bacterium resets its memory at tumbles -- a fact not borne out by experiment -- and make use of approximate coarse-grained descriptions. Here, we revisit the problem of chemotaxis without resorting to any memory resets. We find that when bacteria respond to the environment in a non-adaptive manner, chemotaxis is generally dominated by diffusion, whereas when bacteria respond in an adaptive manner, chemotaxis is dominated by a bias in the motion. In the adaptive case, favorable drift occurs together with favorable accumulation. We derive our results from detailed simulations and a variety of analytical arguments. In particular, we introduce a new coarse-grained description of chemotaxis as biased diffusion, and we discuss the way it departs from older coarse-grained descriptions.Comment: Revised version, journal reference adde

Functional limit theorems for random regular graphs

Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as n grows to infinity, either when d is kept fixed or grows slowly with n. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein's method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn-Szemer\'edi argument for estimating the second largest eigenvalue for all values of d and n.Comment: Added Remark 27. 39 pages. To appear in Probability Theory and Related Field