Local Central Limit Theorem for Determinantal Point Processes

We prove a local central limit theorem (LCLT) for the number of points $N(J)$ in a region $J$ in $\mathbb R^d$ specified by a determinantal point process with an Hermitian kernel. The only assumption is that the variance of $N(J)$ tends to infinity as $|J| \to \infty$. This extends a previous result giving a weaker central limit theorem (CLT) for these systems. Our result relies on the fact that the Lee-Yang zeros of the generating function for $\{E(k;J)\}$ --- the probabilities of there being exactly $k$ points in $J$ --- all lie on the negative real $z$-axis. In particular, the result applies to the scaled bulk eigenvalue distribution for the Gaussian Unitary Ensemble (GUE) and that of the Ginibre ensemble. For the GUE we can also treat the properly scaled edge eigenvalue distribution. Using identities between gap probabilities, the LCLT can be extended to bulk eigenvalues of the Gaussian Symplectic Ensemble (GSE). A LCLT is also established for the probability density function of the $k$-th largest eigenvalue at the soft edge, and of the spacing between $k$-th neigbors in the bulk.Comment: 12 pages; claims relating to LCLT for Pfaffian point processes of version 1 withdrawn in version 2 and replaced by determinantal point processes; improved presentation version

Triviality of ϕ44\phi^4_4 theory: small volume expansion and new data

We study a renormalized coupling g and mass m in four dimensional phi^4 theory on tori with finite size z=mL. Precise numerical values close to the continuum limit are reported for z=1,2,4, based on Monte Carlo simulations performed in the equivalent all-order strong coupling reformulation. Ordinary renormalized perturbation theory is found to work marginally at z=2 and and to fail at z=1. By exactly integrating over the constant field mode we set up a renormalized expansion in z and compute three nontrivial orders. These results reasonably agree with the numerical data at small z. In the new expansion, the universal continuum limit exists as expected from multiplicative renormalizability. The triviality scenario is corroborated with significant precision.Comment: 27 pages, 7 figures, 4 table

Thermodynamic anomalies in open quantum systems: Strong coupling effects in the isotropic XY model

The exactly solvable model of a one dimensional isotropic XY spin chain is employed to study the thermodynamics of open systems. For this purpose the chain is subdivided into two parts, one part is considered as the system while the rest as the environment or bath. The equilibrium properties of the system display several anomalous aspects such as negative entropies, negative specific heat, negative susceptibilities in dependence of temperature and coupling strength between system and bath. The statistical mechanics of this system is studied in terms of a reduced density matrix. At zero temperature and for a certain parameter values we observe a change of the ground state, a situation akin to a quantum phase transition.Comment: 12 pages, 8 figures. Published in the special issue of Chemical Physics "Stochastic processes in Physics and Chemistry" (in honor of Peter H\"anggi

Brownian motion from molecular dynamics

Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force which enter the generalized Langevin equation of the Brownian particle are determined and their dependence on mass and diameter are investigated for two different fluid densities. Deviations of the fluctuating force distribution from a Gaussian form are observed for small particle diameters. For heavy particles the deviations of the fluctuating force from the total force acting on the Brownian particle decrease linearly with the mass ratio m/M where m denotes the mass of a fluid particle

Frequency dependent specific heat of viscous silica

We apply the Mori-Zwanzig projection operator formalism to obtain an expression for the frequency dependent specific heat c(z) of a liquid. By using an exact transformation formula due to Lebowitz et al., we derive a relation between c(z) and K(t), the autocorrelation function of temperature fluctuations in the microcanonical ensemble. This connection thus allows to determine c(z) from computer simulations in equilibrium, i.e. without an external perturbation. By considering the generalization of K(t) to finite wave-vectors, we derive an expression to determine the thermal conductivity \lambda from such simulations. We present the results of extensive computer simulations in which we use the derived relations to determine c(z) over eight decades in frequency, as well as \lambda. The system investigated is a simple but realistic model for amorphous silica. We find that at high frequencies the real part of c(z) has the value of an ideal gas. c'(\omega) increases quickly at those frequencies which correspond to the vibrational excitations of the system. At low temperatures c'(\omega) shows a second step. The frequency at which this step is observed is comparable to the one at which the \alpha-relaxation peak is observed in the intermediate scattering function. Also the temperature dependence of the location of this second step is the same as the one of the $\alpha-$peak, thus showing that these quantities are intimately connected to each other. From c'(\omega) we estimate the temperature dependence of the vibrational and configurational part of the specific heat. We find that the static value of c(z) as well as \lambda are in good agreement with experimental data.Comment: 27 pages of Latex, 8 figure

Interaction of Rep and DnaB on DNA

Genome duplication requires not only unwinding of the template but also the displacement of proteins bound to the template, a function performed by replicative helicases located at the fork. However, accessory helicases are also needed since the replicative helicase stalls occasionally at nucleoprotein complexes. In Escherichia coli, the primary and accessory helicases DnaB and Rep translocate along the lagging and leading strand templates, respectively, interact physically and also display cooperativity in the unwinding of model forked DNA substrates. We demonstrate here that this cooperativity is displayed only by Rep and not by other tested helicases. ssDNA must be exposed on the leading strand template to elicit this cooperativity, indicating that forks blocked at protein–DNA complexes contain ssDNA ahead of the leading strand polymerase. However, stable Rep–DnaB complexes can form on linear as well as branched DNA, indicating that Rep has the capacity to interact with ssDNA on either the leading or the lagging strand template at forks. Inhibition of Rep binding to the lagging strand template by competition with SSB might therefore be critical in targeting accessory helicases to the leading strand template, indicating an important role for replisome architecture in promoting accessory helicase function at blocked replisomes

Coupling of transcription and replication machineries in λ DNA replication initiation: evidence for direct interaction of Escherichia coli RNA polymerase and the λO protein

Transcription proceeding downstream of the λ phage replication origin was previously shown to support initial steps of the λ primosome assembly in vitro and to regulate frequency and directionality of λ DNA replication in vivo. In this report, the data are presented indicating that the RNA polymerase β subunit makes a direct contact with the λO protein, a replication initiator of λ phage. These results suggest that the role of RNA polymerase during the initiation of λ phage DNA replication may be more complex than solely influencing DNA topology. Results demonstrated in this study also show that gyrase supercoiling activity stimulates the formation of a complex between λO and RNA polymerase, suggesting that the introduction of negative supercoils by DNA gyrase, besides lowering the energy required for DNA strand separation, may play an additional role in modeling protein–protein interactions at early steps of DNA replication initiation

Tumor Necrosis Factor Receptor SF10A (TNFRSF10A) SNPs Correlate With Corticosteroid Response in Duchenne Muscular Dystrophy

Background Duchenne muscular dystrophy (DMD) is a rare and severe X-linked muscular dystrophy in which the standard of care with variable outcome, also due to different drug response, is chronic off-label treatment with corticosteroids (CS). In order to search for SNP biomarkers for corticosteroid responsiveness, we genotyped variants across 205 DMD-related genes in patients with differential response to steroid treatment. Methods and Findings We enrolled a total of 228 DMD patients with identified dystrophin mutations, 78 of these patients have been under corticosteroid treatment for at least 5 years. DMD patients were defined as high responders (HR) if they had maintained the ability to walk after 15 years of age and low responders (LR) for those who had lost ambulation before the age of 10 despite corticosteroid therapy. Based on interactome mapping, we prioritized 205 genes and sequenced them in 21 DMD patients (discovery cohort or DiC = 21). We identified 43 SNPs that discriminate between HR and LR. Discriminant Analysis of Principal Components (DAPC) prioritized 2 response-associated SNPs in theTNFRSF10Agene. Validation of this genotype was done in two additional larger cohorts composed of 46 DMD patients on corticosteroid therapy (validation cohorts or VaC1), and 150 non ambulant DMD patients and never treated with corticosteroids (VaC2). SNP analysis in all validation cohorts (N= 207) showed that the CT haplotype is significantly associated with HR DMDs confirming the discovery results. Conclusion We have shown that TNFRSF10A CT haplotype correlates with corticosteroid response in DMD patients and propose it as an exploratory CS response biomarker