Quantum phase transitions in fully connected spin models: an entanglement perspective

We consider a set of fully connected spins models that display first- or second-order transitions and for which we compute the ground-state entanglement in the thermodynamical limit. We analyze several entanglement measures (concurrence, R\'enyi entropy, and negativity), and show that, in general, discontinuous transitions lead to a jump of these quantities at the transition point. Interestingly, we also find examples where this is not the case.Comment: 9 pages, 7 figures, published versio

ODE parameter inference using adaptive gradient matching with Gaussian processes

Parameter inference in mechanistic models based on systems of coupled differential equa- tions is a topical yet computationally chal- lenging problem, due to the need to fol- low each parameter adaptation with a nu- merical integration of the differential equa- tions. Techniques based on gradient match- ing, which aim to minimize the discrepancy between the slope of a data interpolant and the derivatives predicted from the differen- tial equations, offer a computationally ap- pealing shortcut to the inference problem. The present paper discusses a method based on nonparametric Bayesian statistics with Gaussian processes due to Calderhead et al. (2008), and shows how inference in this model can be substantially improved by consistently inferring all parameters from the joint dis- tribution. We demonstrate the efficiency of our adaptive gradient matching technique on three benchmark systems, and perform a de- tailed comparison with the method in Calder- head et al. (2008) and the explicit ODE inte- gration approach, both in terms of parameter inference accuracy and in terms of computa- tional efficiency

Ballistic-to-diffusive transition in spin chains with broken integrability

We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundary-driven XXZ spin-chain. Studying the evolution of the spin current density $\mathcal J^s$ as a function of the system size $L$, we show that, accounting for boundary effects, the transition has a non-trivial universal behavior close to the XX limit. It is controlled by the scattering length $L^*\propto V^{-2}$, where $V$ is the strength of the integrability breaking term. In the XXZ model, the interplay of interactions controls the emergence of a transient "quasi-ballistic" regime at length scales much shorter than $L^*$. This parametrically large regime is characterized by a strong renormalization of the current which forbids a universal scaling, unlike the XX model. Our results are based on Matrix Product Operator numerical simulations and agree with perturbative analytical calculations.Comment: 13 pages, 9 figure

Measurement of kinematic and nuclear dependence of R = σ_L/σ_T in deep inelastic electron scattering

We report results on a precision measurement of the ratio R=σ_L/σ_T in deep inelastic electron-nucleon scattering in the kinematic range 0.2≤x≤0.5 and 1≤Q^2≤10 (GeV/c)^2. Our results show, for the first time, a clear falloff of R with increasing Q^2. Our R results are in agreement with QCD predictions only when corrections for target mass effects and some additional higher twist effects are included. At small x, the data on R favor structure functions with a large gluon contribution. We also report results on the differences R_A-R_D and the cross section ratio σ^A/σ^D between Fe and Au nuclei and the deuteron. Our results for R_A-R_D are consistent with zero for all x, Q^2 indicating that possible contributions to R from nuclear higher twist effects and spin-0 constituents in nuclei are not different from those in nucleons. The ratios σ^A/σ^D from all recent experiments, at all x, Q^2 values, are now in agreement

Parameter inference in mechanistic models of cellular regulation and signalling pathways using gradient matching

A challenging problem in systems biology is parameter inference in mechanistic models of signalling pathways. In the present article, we investigate an approach based on gradient matching and nonparametric Bayesian modelling with Gaussian processes. We evaluate the method on two biological systems, related to the regulation of PIF4/5 in Arabidopsis thaliana, and the JAK/STAT signal transduction pathway

Measurement of the Difference in R=σ_L/σ_T and of σ^A/σ^D in Deep-Inelastic e-D, e-Fe, and e-Au Scattering

We measured the differences in R=σ_L/σ_T and the cross-section ratio σA/σD in deep-inelastic electron scattering from D, Fe, and Au nuclei in the kinematic range 0.2≤x≤0.5 and 1≤Q^2≤5 (Gev/c)^2. Our results for R^A-R^D are consistent with zero for all x and Q^2, indicating that possible contributions to R from nuclear higher-twist effects and spin-0 constituents in nuclei are not different from those in nucleons. The European Muon Collaboration effect is reconfirmed, and the low-x data from all recent experiments, at all Q^2, are now in agreement

Social ski driver conditional autoregressive-based deep learning classifier for flight delay prediction

The importance of robust flight delay prediction has recently increased in the air transportation industry. This industry seeks alternative methods and technologies for more robust flight delay prediction because of its significance for all stakeholders. The most affected are airlines that suffer from monetary and passenger loyalty losses. Several studies have attempted to analysed and solve flight delay prediction problems using machine learning methods. This research proposes a novel alternative method, namely social ski driver conditional autoregressive-based (SSDCA-based) deep learning. Our proposed method combines the Social Ski Driver algorithm with Conditional Autoregressive Value at Risk by Regression Quantiles. We consider the most relevant instances from the training dataset, which are the delayed flights. We applied data transformation to stabilise the data variance using Yeo-Johnson. We then perform the training and testing of our data using deep recurrent neural network (DRNN) and SSDCA-based algorithms. The SSDCA-based optimisation algorithm helped us choose the right network architecture with better accuracy and less error than the existing literature. The results of our proposed SSDCA-based method and existing benchmark methods were compared. The efficiency and computational time of our proposed method are compared against the existing benchmark methods. The SSDCA-based DRNN provides a more accurate flight delay prediction with 0.9361 and 0.9252 accuracy rates on both dataset-1 and dataset-2, respectively. To show the reliability of our method, we compared it with other meta-heuristic approaches. The result is that the SSDCA-based DRNN outperformed all existing benchmark methods tested in our experiment

BootCMatch: A software package for bootstrap AMG based on graph weighted matching

This article has two main objectives: one is to describe some extensions of an adaptive Algebraic Multigrid (AMG) method of the form previously proposed by the first and third authors, and a second one is to present a new software framework, named BootCMatch, which implements all the components needed to build and apply the described adaptive AMG both as a stand-alone solver and as a preconditioner in a Krylov method. The adaptive AMG presented is meant to handle general symmetric and positive definite (SPD) sparse linear systems, without assuming any a priori information of the problem and its origin; the goal of adaptivity is to achieve a method with a prescribed convergence rate. The presented method exploits a general coarsening process based on aggregation of unknowns, obtained by a maximum weight matching in the adjacency graph of the system matrix. More specifically, a maximum product matching is employed to define an effective smoother subspace (complementary to the coarse space), a process referred to as compatible relaxation, at every level of the recursive two-level hierarchical AMG process. Results on a large variety of test cases and comparisons with related work demonstrate the reliability and efficiency of the method and of the software