arXiv subjects

M. Caselle

Publications and source records attributed to M. Caselle.

At least 37 records · Page 2Linked to original sources

arXiv2007

Effective string theory description of the interface free energy

We compare the predictions of the Nambu-Goto effective string model with a set of high precision Monte Carlo results for interfaces with periodic boundary conditions in the 3D Ising model. We compute the free energy in the covariant gauge exactly, up to the inclusion of the Liouville mode. The perturbative expansion of this result agrees both with the result evaluated several years ago by Dietz and Filk in the physical gauge and with a recent calculation with the Polchinski-Strominger action. We also derive the effective string spectrum which, because of the different boundary conditions, is very different from the well known one of Arvis. Taking into proper account the effective string corrections and exploiting some technical improvements in the simulations we obtain precise estimate of the amplitude ratios T_c/\sqrt{sigma}, m_{0++}/\sqrtσ and sigma xi_{2nd}^2. We also discuss the behaviour of the effective string free energy in the dimensional reduction limit (i.e., near the deconfinement transition of the dual 3d gauge Ising model) and its relationship with the 2d Ising model interfaces

hep-lat↗

arXiv2007

DrosOCB: a high resolution map of conserved non coding sequences in Drosophila

Comparative genomics methods are widely used to aid the functional annotation of non coding DNA regions. However, aligning non coding sequences requires new algorithms and strategies, in order to take into account extensive rearrangements and turnover during evolution. Here we present a novel large scale alignment strategy which aims at drawing a precise map of conserved non coding regions between genomes, even when these regions have undergone small scale rearrangments events and a certain degree of sequence variability. We applied our alignment approach to obtain a genome-wide catalogue of conserved non coding blocks (CNBs) between Drosophila melanogaster and 11 other Drosophila species. Interestingly, we observe numerous small scale rearrangement events, such as local inversions, duplications and translocations, which are not observable in the whole genome alignments currently available. The high rate of observed low scale reshuffling show that this database of CNBs can constitute the starting point for several investigations, related to the evolution of regulatory DNA in Drosophila and the in silico identification of unannotated functional elements.

q-bio.GN↗

arXiv2007

On the ratio of string tensions in the 3D Z_4 lattice gauge theory

It was recently pointed out that simple scaling properties of Polyakov correlation functions of gauge systems in the confining phase suggest that the ratios of k-string tensions in the low temperature region is constant up to terms of order T^3. Here we argue that, at least in a three-dimensional Z_4 gauge model, the above ratios are constant in the whole confining phase. This result is obtained by combining numerical experiments with known exact results on the mass spectrum of an integrable two-dimensional spin model describing the infrared behaviour of the gauge system near the deconfining transition.

hep-lat↗

arXiv2007

Universal behaviour of interfaces in 2d and dimensional reduction of Nambu-Goto strings

We propose a simple effective model for the description of interfaces in 2d statistical models, based on the first-order treatment of an action corresponding to the length of the interface. The universal prediction of this model for the interface free energy agrees with the result of an exact calculation in the case of the 2d Ising model. This model appears as a dimensional reduction of the Nambu-Goto stringy description of interfaces in 3d, i.e., of the capillary wave model.

hep-th↗

arXiv2007

Universal power law behaviors in genomic sequences and evolutionary models

We study the length distribution of a particular class of DNA sequences known as 5'UTR exons. These exons belong to the messanger RNA of protein coding genes, but they are not coding (they are located upstream of the coding portion of the mRNA) and are thus less constrained from an evolutionary point of view. We show that both in mouse and in human these exons show a very clean power law decay in their length distribution and suggest a simple evolutionary model which may explain this finding. We conjecture that this power law behaviour could indeed be a general feature of higher eukaryotes.

q-bio.GN↗

arXiv2006

Correlated fragile site expression allows the identification of candidate fragile genes involved in immunity and associated with carcinogenesis

Common fragile sites (cfs) are specific regions in the human genome that are particularly prone to genomic instability under conditions of replicative stress. Several investigations support the view that common fragile sites play a role in carcinogenesis. We discuss a genome-wide approach based on graph theory and Gene Ontology vocabulary for the functional characterization of common fragile sites and for the identification of genes that contribute to tumour cell biology. CFS were assembled in a network based on a simple measure of correlation among common fragile site patterns of expression. By applying robust measurements to capture in quantitative terms the non triviality of the network, we identified several topological features clearly indicating departure from the Erdos-Renyi random graph model. The most important outcome was the presence of an unexpected large connected component far below the percolation threshold. Most of the best characterized common fragile sites belonged to this connected component. By filtering this connected component with Gene Ontology, statistically significant shared functional features were detected. Common fragile sites were found to be enriched for genes associated to the immune response and to mechanisms involved in tumour progression such as extracellular space remodeling and angiogenesis. Our results support the hypothesis that fragile sites serve a function; we propose that fragility is linked to a coordinated regulation of fragile genes expression.

q-bio.GN↗

arXiv2006

Study of the flux tube thickness in 3d LGT's by means of 2d spin models

We study the flux tube thickness in the confining phase of the (2+1)d SU(2) Lattice Gauge Theory near the deconfining phase transition. Following the Svetitsky-Yaffe conjecture, we map the problem to the study of the correlation function in the two-dimensional spin model with Z_2 global symmetry, (i.e. the 2d Ising model) in the high-temperature phase. Using the form factor approach we obtain an explicit expression for this function and from it we infer the behaviour of the flux density of the original (2+1)d LGT. Remarkably enough the result we obtain for the flux tube thickness agrees (a part from an overall normalization) with the effective string prediction for the same quantity.

hep-th↗

arXiv2006

The partition function of interfaces from the Nambu-Goto effective string theory

We consider the Nambu-Goto bosonic string model as a description of the physics of interfaces. By using the standard covariant quantization of the bosonic string, we derive an exact expression for the partition function in dependence of the geometry of the interface. Our expression, obtained by operatorial methods, resums the loop expansion of the NG model in the "physical gauge" computed perturbatively by functional integral methods in the literature. Recently, very accurate Monte Carlo data for the interface free energy in the 3d Ising model became avaliable. Our proposed expression compares very well to the data for values of the area sufficiently large in terms of the inverse string tension. This pattern is expected on theoretical grounds and agrees with previous analyses of other observables in the Ising model.

hep-th↗

arXiv2006

Symmetric space description of carbon nanotubes

Using an innovative technique arising from the theory of symmetric spaces, we obtain an approximate analytic solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation in the insulating regime of a metallic carbon nanotube with symplectic symmetry and an odd number of conducting channels. This symmetry class is characterized by the presence of a perfectly conducting channel in the limit of infinite length of the nanotube. The derivation of the DMPK equation for this system has recently been performed by Takane, who also obtained the average conductance both analytically and numerically. Using the Jacobian corresponding to the transformation to radial coordinates and the parameterization of the transfer matrix given by Takane, we identify the ensemble of transfer matrices as the symmetric space of negative curvature SO^*(4m+2)/[SU(2m+1)xU(1)] belonging to the DIII-odd Cartan class. We rederive the leading-order correction to the conductance of the perfectly conducting channel and its variance Var(log(delta g)). Our results are in complete agreement with Takane's. In addition, our approach based on the mapping to a symmetric space enables us to obtain new universal quantities: a universal group theoretical expression for the ratio Var(log(delta g)/ and as a byproduct, a novel expression for the localization length for the most general case of a symmetric space with BC_m root system, in which all three types of roots are present.

cond-mat.mes-hall↗

arXiv2005

Potts correlators and the static three-quark potential

We discuss the two- and three-point correlators in the two-dimensional three-state Potts model in the high-temperature phase of the model. By using the form factor approach and perturbed conformal field theory methods we are able to describe both the large distance and the short distance behaviours of the correlators. We compare our predictions with a set of high precision Monte-Carlo simulations (performed on the triangular lattice realization of the model) finding a complete agreement in both regimes. In particular we use the two-point correlators to fix the various non-universal constants involved in the comparison (whose determination is one of the results of our analysis) and then use these constants to compare numerical results and theoretical predictions for the three-point correlator with no free parameter. Our results can be used to shed some light on the behaviour of the three-quark correlator in the confining phase of the (2+1)-dimensional SU(3) lattice gauge theory which is related by dimensional reduction to the three-spin correlator in the high-temperature phase of the three-state Potts model. The picture which emerges is that of a smooth crossover between a Δtype law at short distances and a Y type law at large distances.

hep-th↗

arXiv2005

QCD string from D0 branes

We report the results of a set of high precision simulations performed in the 3d gauge Ising model. We evaluated the interquark potential and the first few energy levels and compared them with the predictions obtained with the effective Nambu-Goto string and with the free bosonic string. The data are precise enough to unambiguously distinguish between the free string predictions and those obtained using the N-G effective string. At large distances we find a remarkable agreement between Monte Carlo data and N-G predictions for the first excited energy level, while the free string picture is definitely excluded. As the interquark distance is decreased (and/or the finite temperature becomes higher) the Monte Carlo results show larger and larger deviations both from the N-G and from the free string predictions. In order to better understand this behaviour we re-derived the effective Nambu-Goto theory result for the Polyakov loop correlator using a covariant quantization. We chose as boundary conditions those of an open string attached to two D0-branes at spatial distance $R$, in a target space with compact euclidean time. Obviously our treatment is fully consistent only in $d=26$. The extension to generic $d$ requires taking into account the Liouville mode of Polyakov's formulation. The analogy with the standard light cone calculation suggests that the contribution due to the Liouville field can be neglected for large $R$. At shorter scales, the Liouville mode cannot be neglected and its contribution to the interquark potential might be the source of the discrepancies with respect to the effective N-G results that we observe in our Monte Carlo simulations.

hep-lat↗

arXiv2005

Polyakov loop correlators from D0-brane interactions in bosonic string theory

In this paper we re-derive the effective Nambu-Goto theory result for the Polyakov loop correlator, starting from the free bosonic string and using a covariant quantization. The boundary conditions are those of an open string attached to two D0-branes at spatial distance R, in a target space with compact euclidean time. The one-loop free energy contains topologically distinct sectors corresponding to multiple covers of the cylinder in target space bordered by the Polyakov loops. The sector that winds once reproduces exactly the Nambu-Goto partition function. In our approach, the world-sheet duality between the open and closed channel is most evident and allows for an explicit interpretation of the free energy in terms of tree level exchange of closed strings between boundary states. Our treatment is fully consistent only in d=26; extension to generic d may be justified for large R, and is supported by Montecarlo data. At shorter scales, consistency and Montecarlo data seem to suggest the necessity of taking into account the Liouville mode of Polyakov's formulation.

hep-th↗

arXiv2004

Amplitude ratios for the mass spectrum of the 2d Ising model in the high-T, H \neq 0 phase

We study the behaviour of the 2d Ising model in the symmetric high temperature phase in presence of a small magnetic perturbation. We successfully compare the quantum field theory predictions for the shift in the mass spectrum of the theory with a set of high precision transfer matrix results. Our results rule out a prediction for the same quantity obtained some years ago with strong coupling methods.

hep-lat↗

arXiv2004

Static quark potential and effective string corrections in the (2+1)-d SU(2) Yang-Mills theory

We report on a very accurate measurement of the static quark potential in SU(2) Yang-Mills theory in (2+1) dimensions in order to study the corrections to the linear behaviour. We perform numerical simulations at zero and finite temperature comparing our results with the corrections given by the effective string picture in these two regimes. We also check for universal features discussing our results together with those recently published for the (2+1)-d Z(2) and SU(3) pure gauge theories.

hep-lat↗

arXiv2004

Short distance behaviour of the effective string

We study the Polyakov loop correlator in the (2+1) dimensional Z_2 gauge model. An algorithm that we have presented recently, allows us to reach high precision results for a large range of distances and temperatures, giving us the opportunity to test predictions of the effective Nambu-Goto string model. Here we focus on the regime of low temperatures and small distances. In contrast to the high temperature, large distance regime, we find that our numerical results are not well described by the two loop-prediction of the Nambu-Goto model. In addition we compare our data with those for the SU(2) and SU(3) gauge models in (2+1) dimensions obtained by other authors. We generalize the result of Lüscher and Weisz for a boundary term in the interquark potential to the finite temperature case.

hep-lat↗

arXiv2004

Random matrix theory and symmetric spaces

In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important results can be obtained from this identification. In particular the Cartan classification of triplets of symmetric spaces with positive, zero and negative curvature gives rise to a new classification of random matrix ensembles. The review is organized into two main parts. In Part I the theory of symmetric spaces is reviewed with particular emphasis on the ideas relevant for appreciating the correspondence with random matrix theories. In Part II we discuss various applications of symmetric spaces to random matrix theories and in particular the new classification of disordered systems derived from the classification of symmetric spaces. We also review how the mapping from integrable Calogero--Sutherland models to symmetric spaces can be used in the theory of random matrices, with particular consequences for quantum transport problems. We conclude indicating some interesting new directions of research based on these identifications.

cond-mat↗

arXiv2003

A new class of short distance universal amplitude ratios

We propose a new class of universal amplitude ratios which involve the first terms of the short distance expansion of the correlators of a statistical model in the vicinity of a critical point. We will describe the critical system with a conformal field theory (UV fixed point) perturbed by an appropriate relevant operator. In two dimensions the exact knowledge of the UV fixed point allows for accurate predictions of the ratios and in many nontrivial integrable perturbations they can even be evaluated exactly. In three dimensional O(N) scalar systems feasible extensions of some existing results should allow to obtain perturbative expansions for the ratios. By construction these universal ratios are a perfect tool to explore the short distance properties of the underlying quantum field theory even in regimes where the correlation length and one point functions are not accessible in experiments or simulations.

hep-th↗

arXiv2003

String effects in SU(2) lattice gauge theory

We discuss the effective string picture for the confining regime of lattice gauge theories at zero and finite temperature. We present results of extensive Monte Carlo simulations - performed with the Luscher and Weisz algorithm - for SU(2) Yang-Mills theory in 2+1 dimensions. We also address the issue of "string universality" by comparing our results with those obtained in other lattice gauge theories.

hep-lat↗