Directed Dominating Set Problem Studied by Cavity Method: Warning Propagation and Population Dynamics

The minimal dominating set for a digraph (directed graph) is a prototypical hard combinatorial optimization problem. In a previous paper, we studied this problem using the cavity method. Although we found a solution for a given graph that gives very good estimate of the minimal dominating size, we further developed the one step replica symmetry breaking theory to determine the ground state energy of the undirected minimal dominating set problem. The solution space for the undirected minimal dominating set problem exhibits both condensation transition and cluster transition on regular random graphs. We also developed the zero temperature survey propagation algorithm on undirected Erdös-Rényi graphs to find the ground state energy. In this paper we continue to develope the one step replica symmetry breaking theory to find the ground state energy for the directed minimal dominating set problem. We find the following. (i) The warning propagation equation can not converge when the connectivity is greater than the core percolation threshold value of 3.704. Positive edges have two types warning, but the negative edges have one. (ii) We determine the ground state energy and the transition point of the Erdös-Rényi random graph. (iii) The survey propagation decimation algorithm has good results comparable with the belief propagation decimation algorithm.     

The Cavity Method for the Rigidity Transition

In order to motivate an analogy between the rigidity theory and combinatorial optimization, we have used the cavity method to study the floppy to rigid transition in a 2-dimensional (2D) random graph as well as in a 3D small world chain. Our analytic results are in excellent agreement with numerical studies using the pebble game algorithm. We also illustrate that a transfer matrix method is equivalent to the cavity method at the replica symmetric level     

Comparison of Finite Volume Canonical and Grand Canonical Gibbs Measures: The Continuous Case

We consider a continuous gas with finite range positive pair potential and we assume that the cluster expansion convergence condition holds. We prove a sharp bound on the difference between the finite volume grand canonical and canonical expectation of local observable. The bound is given in terms of the support of the observable, of its grand canonical variance and of the volume on which the system is confined.     

Total neutron scattering: The key to the local and medium range structure of complex materials

Structural characterization is mainly based on the measurement of Bragg intensities and yields the average structure of crystalline materials. The total scattering pattern, however, contains structural information over all length scales, and it can be used to obtain a complete structural picture of complex materials. Suddenly one has access to a new parameter, the real-space range of the refinement and structures can be analysed as a function of length scale straightforwardly.      

二阶非线性耦合动力学系统守恒量的扩展Prelle-Singer求法与对称性研究

将扩展Prelle-Singer法(扩展P-S法)用于求x=Ф1(x,y),y=Ф2(x,y)类型的二阶非线性耦合动力学系统的守恒量,得到了积分乘子满足的微分方程与守恒量的一般形式,并讨论所得守恒量的Noether对称性与Lie对称性.最后用扩展P-S法求得了四次非谐振子系统的两个守恒量,并讨论了系统的对称性.     

Work and Thermal Fluctuations in Crystal Indentation under Deterministic and Stochastic Thermostats: The Role of System–Bath Coupling

The Jarzynski equality (JE) was originally derived under the deterministic Hamiltonian formalism, and later, it was demonstrated that stochastic Langevin dynamics also lead to the JE. However, the JE has been verified mainly in small, low-dimensional systems described by Langevin dynamics. Although the two theoretical derivations apparently lead to the same expression, we illustrate that they describe fundamentally different experimental conditions. While the Hamiltonian framework assumes that the thermal bath producing the initial canonical equilibrium switches off for the duration of the work process, the Langevin bath effectively acts on the system. Moreover, the former considers an environment with which the system may interact, whereas the latter does not. In this study, we investigate the effect of the bath on the measurable quantity of the JE through molecular dynamics simulations of crystal nanoindentation employing deterministic and stochastic thermostats. Our analysis shows that the distributions of the kinetic energy and the mechanical work produced during the indentation processes are affected by the interaction between the system and the thermostat baths. As a result, the type of thermostatting has also a clear effect on the left-hand side of the JE, which enables the estimation of the free-energy difference characterizing the process.     

Pseudospin and spin symmetries in 1+1 dimensions: The case of the Coulomb potential

The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar Coulomb potential plus a mixing of vector and scalar Coulomb potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. We show the relation between spin and pseudospin symmetries by means of charge-conjugation and γ⁵${\gamma }^5$ chiral transformations. The cases of pure pseudoscalar and mixed vector–scalar potentials, already analyzed in previous works, are obtained as particular cases. The results presented can be extended to 3+1 dimensions.     

Spatial Prediction of Current and Future Flood Susceptibility: Examining the Implications of Changing Climates on Flood Susceptibility Using Machine Learning Models

The main aim of this study was to predict current and future flood susceptibility under three climate change scenarios of RCP2.6 (i.e., optimistic), RCP4.5 (i.e., business as usual), and RCP8.5 (i.e., pessimistic) employing four machine learning models, including Gradient Boosting Machine (GBM), Random Forest (RF), Multilayer Perceptron Neural Network (MLP-NN), and Naïve Bayes (NB). The study was conducted for two watersheds in Canada, namely Lower Nicola River, BC and Loup, QC. Three statistical metrics were used to validate the models: Receiver Operating Characteristic Curve, Figure of Merit, and F1-score. Findings indicated that the RF model had the highest accuracy in providing the flood susceptibility maps (FSMs). Moreover, the provided FSMs indicated that flooding is more likely to occur in the Lower Nicola River watershed than the Loup watershed. Following the RCP4.5 scenario, the area percentages of the flood susceptibility classes in the Loup watershed in 2050 and 2080 have changed by the following percentages from the year 2020 and 2050, respectively: Very Low = −1.68%, Low = −5.82%, Moderate = +6.19%, High = +0.71%, and Very High = +0.6% and Very Low = −1.61%, Low = +2.98%, Moderate = −3.49%, High = +1.29%, and Very High = +0.83%. Likewise, in the Lower Nicola River watershed, the changes between the years 2020 and 2050 and between the years 2050 and 2080 were: Very Low = −0.38%, Low = −0.81%, Moderate = −0.95%, High = +1.72%, and Very High = +0.42% and Very Low = −1.31%, Low = −1.35%, Moderate = −1.81%, High = +2.37%, and Very High = +2.1%, respectively. The impact of climate changes on future flood-prone places revealed that the regions designated as highly and very highly susceptible to flooding, grow in the forecasts for both watersheds. The main contribution of this study lies in the novel insights it provides concerning the flood susceptibility of watersheds in British Columbia and Quebec over time and under various climate change scenarios.     

Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures

We give a condition on a Gibbs measure for an attractive Markov specification, which assures extremality and the global Markov property. As an example of application we consider the class of attractive Markov specifications defined on a compact configuration space over a two-dimensional lattice by the interaction Hamiltonians (assumed to have a finite set of periodic ground configurations) satisfying Peierl's condition. We prove that each extremal Gibbs measure for such a specification, at sufficiently low temperature, has the global Markov property.On leave of absence from the Institute of Theoretical Physics, University of Wrocaw, Poland.     

The Static Modes: An alternative approach for the treatment of macro- and bio-molecular induced-fit flexibility

We present a new competitive method for the atomic scale treatment of macromolecular flexibility called Static Mode method. This method is based on the “induced-fit” concept, i.e. it maps the intrinsic deformations of a macromolecule subject to diverse external excitations. The algorithm makes it possible to obtain a set of deformations, each one corresponding to a specific interaction on a specific molecular site, in terms of force constants contained in the energy model. In this frame, the docking problem can be expressed in terms of interaction sites between the two molecules, the molecular deformations being extracted from the pre-calculated Static Modes of each molecule. Some preliminary basic examples aimed at illustrating potential applications where macro- or bio-molecular flexibility is of key importance are given: flexibility inducing conformational changes in the case of furanose ring and flexibility for the characterization, including allostery, of poly(N-isopropylacrylamide)(P-NIPAM) active sites. We also discuss how this procedure allows “induced-fit” flexible molecular docking, beyond state-of-the-art semi-rigid methods.     

Slowly rocking symmetric, spatially periodic Hamiltonians: The role of escape and the emergence of giant transient directed transport

The nonintegrable Hamiltonian dynamics of particles placed in a symmetric, spatially periodic potential and subjected to a periodically varying field is explored. Such systems can exhibit a rich diversity of unusual transport features. In particular, depending on the setting of the initial phase of the drive, the possibility of a giant transient directed transport in a symmetric, space-periodic potential when driven with an adiabatically varying field arises. Here, we study the escape scenario and corresponding mean escape times of particles from a trapping region with the subsequent generation of a transient directed flow of an ensemble of particles. It is shown that for adiabatically slow inclination modulations the unidirectional flow proceeds over giant distances. The direction of escape and, hence, of the flow is entirely governed whether the periodic force, modulating the inclination of the potential, starts out initially positive or negative. In the phase space, this transient directed flow is associated with a long-lasting motion taking place within ballistic channels contained in the non-uniform chaotic layer. We demonstrate that for adiabatic modulations all escaping particles move ballistically into the same direction, leading to a giant directed current.