Regular Subgraphs in Graphs and Rooted Graphs and Definability in Monadic Second - Order Logic

We investigate the definability in monadic ∑₁¹ and monadic Π₁¹ of the problems REG_k, of whether there is a regular subgraph of degree k in some given graph, and XREG_k, of whether, for a given rooted graph, there is a regular subgraph of degree k in which the root has degree k, and their restrictions to graphs in which every vertex has degree at most k, namely REG_k^k and XREG_k^k, respectively, for k ≥ 2 (all our graphs are undirected). Our motivation partly stems from the fact (which we prove here) that REG_k^k and XREG_k^k are logspace equivalent to CONN and REACH, respectively, for k ≥ 3, where CONN is the problem of whether a given graph is connected and REACH is the problem of whether a given graph has a path joining two given vertices. We use monadic first - order reductions, monadic ∑₁¹ games and a recent technique due to Fagin, Stockmeyer and Vardi to almost completely classify whether these problems are definable in monadic ∑₁¹ and monadic Π₁¹, and we compare the definability of these problems (in monadic ∑₁¹ and monadic Π₁¹ with their computational complexity (which varies from solvable using logspace to NP - complete).     

Spin-glass energy landscape

We consider a nearest-neighbor-interaction ±J Ising spin glass in a square lattice. Inspired by natural evolution, we design a dynamic rule that includesselection, randomness, andmultibranch exploration. Following this rule, we succeed in walking along the space of states between local energy maxima and minima alternately. During the walk, we store various information about the spin states corresponding to these minima and maxima for later statistical analysis. In particular, we plot a histogram displaying how many times each minimum (or maximum) energy is visited as a function of the corresponding density value. Through finite-size scaling analysis, we conclude that a nonvanishing fraction of bonds remains unsatisfied (satisfied) at these energy minimum (maximum) states in the thermodynamic limit. This fraction measures the degree of unavoidable frustration of the system. Also in this limit, the width of these histograms vanishes, meaning that almost all metastable states occur at the same energy density value, with no dispersion.     

Thermorheological analysis of PVC blends

The effect of temperature on dynamic viscoelastic measurements of miscible poly (vinyl chloride) (PVC)/ethylene‐vinyl acetate–carbon monoxide terpolymer (EVA‐CO) and immiscible PVC/high‐density polyethylene (HDPE) and PVC/chlorinated polyethylene (CPE) molten blends is discussed. PVC plasticized with di(2 ethyl hexyl) phthalate (PVC/DOP) and CaCO₃ filled HDPE (HDPE/CaCO₃) are also considered for comparison purposes. Thermorheological complexity is analyzed using two time–temperature superposition methods: double logarithmic plots of storage modulus, G′, vs. loss modulus, G″, and loss tangent, tan δ, vs. complex modulus, G*, plots. Both methods reveal that miscible PVC/EVA‐CO and PVC/DOP systems are thermorheologically complex, which is explained by the capacity of PVC to form microdomains or crystallites during mixing and following cooling of the blends. For immiscible PVC/HDPE and PVC/CPE blends the results of log G′ vs. log G″ show temperature independence. However, when tan δ vs. log G* plots are used, the immiscible blends are shown to be thermorheologically complex, indicating that the morphology observed by microscopy and constitued by a PVC phase dispersed in a HDPE or CPE matrix, is reflected by this rheological technique. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 469–477, 2000     

Study of a Monod–Haldene type food chain chemostat with pulsed substrate

In this paper, we introduce and study a model of a Monod–Haldene type food chain chemostat with pulsed substrate. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey, and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period-doubling and period-halfing.     

Bulk and shear rheology of silica/polystyrene nanocomposite: Reinforcement and dynamics

Bulk and shear rheological studies were performed on a 10 wt % silica nanoparticle‐filled polystyrene nanocomposite. The limiting moduli in glassy and rubbery states are higher for the nanocomposite than for the neat polymer; the increase is consistent with hydrodynamic reinforcement and is slightly higher than the lower bound of the rule of mixtures prediction. All evidence indicates that the presence of nanoparticles does not significantly change the polymer dynamics associated with glass transition, except to increase the T_g by 3 K. Comparison of the bulk and shear retardation spectra suggests that the underlying mechanisms for both responses are similar at short times and that the long‐time chain modes available to the shear are not available to the bulk, consistent with Plazek's earlier findings. In addition, T ? T_g and TV^γ scaling, along with the findings of thermorheological complexity, are discussed. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 621–632     

On estimating model complexity and prediction errors in multivariate calibration: generalized resampling by random sample weighting (RSW)

The present paper focuses on determining the number of PLS components by using resampling methods such as cross validation (CV), Monte Carlo cross validation (MCCV), bootstrapping (BS), etc. To resample the training data, random non‐negative weights are assigned to the original training samples and a sample‐weighted PLS model is developed without increasing the computational burden much. Random weighting is a generalization of the traditional resampling methods and is expected to have a lower risk of getting an insufficient training set. For prediction, only the training samples with random weights less than a threshold value are selected to ensure that the prediction samples have less influence on training. For complicated data, because the optimal number of PLS components is often not unique or readily distinguished and there might exist an optimal region of model complexity, the distribution of prediction errors can be more useful than a single value of root mean squared error of prediction (RMSEP). Therefore, the distribution of prediction errors are estimated by repeated random sample weighting and used to determine model complexity. RSW is compared with its traditional counterparts like CV, MCCV, BS and a recently proposed randomization test method to demonstrate its usefulness. Copyright © 2010 John Wiley & Sons, Ltd.     

Spatiotemporal and statistical symmetries

The notion of symmetries, either statistical or deterministic, can be useful for the characterization of complex systems and their bifurcations. In this paper, we investigate the connection between the (microscopic) spatiotemporal symmetries of a space-time functionu(x, t), on the one hand, and the (macroscopic) symmetries of statistical quantities such as the spatial (resp. temporal) two-point correlations and the spatial (resp. temporal) average, on the other hand. We show, how, under certain conditions, these symmetries are related to the symmetries of the orbits described byu(x, t) in the characteristic (phase) spaces. We also determine the largest group of spatiotemporal symmetries (in the sense introduced in our earlier work) satisfied by a given space-time functionu(x, t) and indicate how to extract the subgroups of point symmetries, namely those directly implemented on the space and time variables. Conversely, we determine all the functions invariant by a given space-time symmetry group. Finally, we illustrate all the previous points with specific examples.     

计算的量子飞跃

利用量子力学的迭加和纠缠等特性进行的量子计算是计算技术的巨大飞跃。它能够比经典计算远为有效地解决一些问题。例如最为著名的Ｓｈｏｒ的算法原则上能够以多项式的时间因子化大的合数,从而使得经典计算机难以计算的这一问题得以解决。文章介绍了至今所发现的主要量子算法的基本原理和步骤,并且概述了量子计算的优越性、现状和发展前景,同时讨论了量子计算在物理学上的应用和意义。