Algorithmic differentiation and the calculation of forces by quantum Monte Carlo

We describe an efficient algorithm to compute forces in quantum Monte Carlo using adjoint algorithmic differentiation. This allows us to apply the space warp coordinate transformation in differential form, and compute all the 3M force components of a system with M atoms with a computational effort comparable with the one to obtain the total energy. Few examples illustrating the method for an electronic system containing several water molecules are presented. With the present technique, the calculation of finite-temperature thermodynamic properties of materials with quantum Monte Carlo will be feasible in the near future.Comment: 32 pages, 4 figure, to appear in The Journal of Chemical Physic

Routh reduction and Cartan mechanics

In the present work a Cartan mechanics version for Routh reduction is considered, as an intermediate step toward Routh reduction in field theory. Motivation for this generalization comes from an scheme for integrable systems [12], used for understanding the occurrence of Toda field theories in so called Hamiltonian reduction of WZNW field theories [11]. As a way to accomplish with this intermediate aim, this article also contains a formulation of the Lagrangian Adler-Kostant-Symes systems discussed in [12] in terms of Routh reduction.Comment: 46 pages, comments are welcome. Version 2 contains an additional section concerning reduced equations of motion in quasicoordinate

Unified formalism for Palatini gravity

This paper is devoted to the construction of a unified formalism for Palatini and unimodular gravity. The idea is to employ a relationship between unified formalism for a Griffiths variational problem and its classical Lepage-equivalent variational problem. The main geometrical tools involved in these constructions are canonical forms living on the first jet of the frame bundle for the spacetime manifold. These forms play an essential role in providing a global version of the Palatini Lagrangian and expressing the metricity condition in an invariant form. With them, we were able to find the associated equations of motion in invariant terms and, by using previous results from the literature, to prove their involutivity. As a bonus, we showed how this construction can be used to provide a unified formalism for the so-called unimodular gravity by employing a reduction of the structure group of the frame bundle to the special linear group.Fil: Capriotti, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentin

A Closed-Form Approximation of Likelihood Functions for Discretely Sampled Diffusions: the Exponent Expansion

In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a series expansion of the deviation of its logarithm from that of a Gaussian distribution. Through this procedure, dubbed {\em exponent expansion}, the transition probability is obtained as a power series in $\Delta t$. This becomes asymptotically exact if an increasing number of terms is included, and provides remarkably accurate results even when truncated to the first few (say 3) terms. The coefficients of such expansion can be determined straightforwardly through a recursion, and involve simple one-dimensional integrals. We present several examples of financial interest, and we compare our results with the state-of-the-art approximation of discretely sampled diffusions [A\"it-Sahalia, {\it Journal of Finance} {\bf 54}, 1361 (1999)]. We find that the exponent expansion provides a similar accuracy in most of the cases, but a better behavior in the low-volatility regime. Furthermore the implementation of the present approach turns out to be simpler. Within the functional integration framework the exponent expansion allows one to obtain remarkably good approximations of the pricing kernels of financial derivatives. This is illustrated with the application to simple path-dependent interest rate derivatives. Finally we discuss how these results can also be used to increase the efficiency of numerical (both deterministic and stochastic) approaches to derivative pricing.Comment: 28 pages, 7 figure

Finite-size spin-wave theory of a collinear antiferromagnet

The ground-state and low-energy properties of the two-dimensional $J_1{-}J_2$ Heisenberg model in the collinear phase are investigated using finite-size spin-wave theory [Q. F. Zhong and S. Sorella, {\em Europhys. Lett.} {\bf 21}, 629 (1993)], and Lanczos exact diagonalizations. For spin one-half -- where the effects of quantization are the strongest -- the spin-wave expansion turns out to be quantitatively accurate for $J_2/J_1\gtrsim 0.8$. In this regime, both the magnetic structure factor and the spin susceptibility are very close to the spin-wave predictions. The spin-wave estimate of the order parameter in the collinear phase, $m^\dagger\simeq 0.3$, is in remarkable agreement with recent neutron scattering measurements on ${\rm Li_2VOSiO_4}$.Comment: 10 pages, 3 figure

Ising transition in the two-dimensional quantum J1−J2J_1-J_2 Heisenberg model

We study the thermodynamics of the spin-$S$ two-dimensional quantum Heisenberg antiferromagnet on the square lattice with nearest ($J_1$) and next-nearest ($J_2$) neighbor couplings in its collinear phase ($J_2/J_1>0.5$), using the pure-quantum self-consistent harmonic approximation. Our results show the persistence of a finite-temperature Ising phase transition for every value of the spin, provided that the ratio $J_2/J_1$ is greater than a critical value corresponding to the onset of collinear long-range order at zero temperature. We also calculate the spin- and temperature-dependence of the collinear susceptibility and correlation length, and we discuss our results in light of the experiments on Li$_2$VOSiO$_4$ and related compounds.Comment: 4 page, 4 figure

The evaluation of protein folding rate constant is improved by predicting the folding kinetic order with a SVM-based method

Protein folding is a problem of large interest since it concerns the mechanism by which the genetic information is translated into proteins with well defined three-dimensional (3D) structures and functions. Recently theoretical models have been developed to predict the protein folding rate considering the relationships of the process with tolopological parameters derived from the native (atomic-solved) protein structures. Previous works classified proteins in two different groups exhibiting either a single-exponential or a multi-exponential folding kinetics. It is well known that these two classes of proteins are related to different protein structural features. The increasing number of available experimental kinetic data allows the application to the problem of a machine learning approach, in order to predict the kinetic order of the folding process starting from the experimental data so far collected. This information can be used to improve the prediction of the folding rate. In this work first we describe a support vector machine-based method (SVM-KO) to predict for a given protein the kinetic order of the folding process. Using this method we can classify correctly 78% of the folding mechanisms over a set of 63 experimental data. Secondly we focus on the prediction of the logarithm of the folding rate. This value can be obtained as a linear regression task with a SVM-based method. In this paper we show that linear correlation of the predicted with experimental data can improve when the regression task is computed over two different sets, instead of one, each of them composed by the proteins with a correctly predicted two state or multistate kinetic order.Comment: The paper will be published on WSEAS Transaction on Biology and Biomedicin

PhD-SNPg: a webserver and lightweight tool for scoring single nucleotide variants

One of the major challenges in human genetics is to identify functional effects of coding and non-coding single nucleotide variants (SNVs). In the past, several methods have been developed to identify disease-related single amino acid changes but only few tools are able to score the impact of non-coding variants. Among the most popular algorithms, CADD and FATHMM predict the effect of SNVs in non-coding regions combining sequence conservation with several functional features derived from the ENCODE project data. Thus, to run CADD or FATHMM locally, the installation process requires to download a large set of pre-calculated information. To facilitate the process of variant annotation we develop PhD-SNPg, a new easy-to-install and lightweight machine learning method that depends only on sequence-based features. Despite this, PhD-SNPg performs similarly or better than more complex methods. This makes PhD-SNPg ideal for quick SNV interpretation, and as benchmark for tool development