On two reversible cellular automata with two particle species

We introduce a pair of time-reversible models defined on the discrete space-time lattice with 3 states per site, specifically, a vacancy and a particle of two flavours (species). The local update rules reproduce the rule 54 reversible cellular automaton when only a single species of particles is present, and satisfy the requirements of flavour exchange (C), space-reversal (P), and time-reversal (T) symmetries. We find closed-form expressions for three local conserved charges and provide an explicit matrix product form of the grand canonical Gibbs states, which are identical for both models. For one of the models this family of Gibbs states seems to be a complete characterisation of equilibrium (i.e. space and time translation invariant) states, while for the other model we empirically find a sequence of local conserved charges, one for each support size larger than 2, hinting to its algebraic integrability. Finally, we numerically investigate the behaviour of spatio-temporal correlation functions of charge densities, and test the hydrodynamic prediction for the model with exactly three local charges. Surprisingly, the numerically observed 'sound velocity' does not match the hydrodynamic value. The deviations are either significant, or they decay extremely slowly with the simulation time, which leaves us with an open question for the mechanism of such a glassy behaviour in a deterministic locally interacting system.

Direct Collocation with Reproducing Kernel Approximation for Two-Phase Coupling System in a Porous Enclosure

The direct strong-form collocation method with reproducing kernel approximation is introduced to efficiently and effectively solve the natural convection problem within a parallelogrammic enclosure. As the convection behavior in the fluid-saturated porous media involves phase coupling, the resulting system is highly nonlinear in nature. To this end, the local approximation is adopted in conjunction with Newton–Raphson method. Nevertheless, to unveil the performance of the method in the nonlinear analysis, only single thermal natural convection is of major concern herein. A unit square is designated as the model problem to investigate the parameters in the system related to the convergence; several benchmark problems are used to verify the accuracy of the approximation, in which the stability of the method is demonstrated by considering various initial conditions, disturbance of discretization, inclination, aspect ratio, and reproducing kernel support size. It is shown that a larger support size can be flexible in approximating highly irregular discretized problems. The derivation of explicit operators with two-phase variables in solving the nonlinear system using the direct collocation is carried out in detail.

Improving Mean Annual Precipitation Prediction Incorporating Elevation and Taking into Account Support Size

Accounting for secondary exhaustive variables (such as elevation) in modelling the spatial distribution of precipitation can improve their estimate accuracy. However, elevation and precipitation data are associated with different support sizes and it is necessary to define methods to combine such different spatial data. The paper was aimed to compare block ordinary cokriging and block kriging with an external drift in estimating the annual precipitation using elevation as covariate. Block ordinary kriging was used as reference of a univariate geostatistical approach. In addition, the different support sizes associated with precipitation and elevation data were also taken into account. The study area was the Calabria region (southern Italy), which has a spatially variable Mediterranean climate because of its high orographic variability. Block kriging with elevation as external drift, compared to block ordinary kriging and block ordinary cokriging, was the most accurate approach for modelling the spatial distribution of annual mean precipitation. The three measures of accuracy (MAE, mean absolute error; RMSEP, root-mean-squared error of prediction; MRE, mean relative error) have the lowest values (MAE = 112.80 mm; RMSEP = 144.89 mm, and MRE = 0.11), whereas the goodness of prediction (G) has the highest value (75.67). The results clearly indicated that the use of an exhaustive secondary variable always improves the precipitation estimate, but in the case of areas with elevations below 120 m, block cokriging makes better use of secondary information in precipitation estimation than block kriging with external drift. At higher elevations, the opposite is always true: block kriging with external drift performs better than block cokriging. This approach takes into account the support size associated with precipitation and elevation data. Accounting for elevation allowed to obtain more detailed maps than using block ordinary kriging. However, block kriging with external drift produced a map with more local details than that of block ordinary cokriging because of the local re-evaluation of the linear regression of precipitation on block estimates.

Growth kinetic control over MgFe2O4 to tune Fe occupancy and metal–support interactions for optimum catalytic performance

For the first time, the growth behavior with size-dependent Fe occupancies at different sites of MgFe2O4 was examined. Hybrid catalysts of Pt/MgFe2O4 with a support size of 20.6 nm exhibited an optimal performance of CO oxidation.

Optimal variable support size for mesh-free approaches using genetic algorithm

The main difficulty of the meshless methods is related to the support of shape functions. These methods become stable when sufficiently large support is used. Rather larger support size leads to higher calculation costs and greatly degraded quality. The continuous adjustment of the support size to approximate the shape functions during the simulation can avoid this problem, but the choice of the support size relative to the local density is not a trivial problem. In the present work, we deal with finding a reasonable size of influence domain by using a genetic algorithm coupled with high order mesh-free algorithms which the optimal value depends on the accuracy and stability of the results. The proposed strategy provides guarantees about the growth of approximation errors, monitor the level of error, and adapt the evaluation strategy to reach the required level of accuracy. This allows the adaptation of the proposed algorithm with problem complexity. This new strategy in meshless approaches are tested on some examples of structural analysis.

Inferring Sparse Preference Lists from Partial Information

Probability distributions over rankings are crucial for the modeling and design of a wide range of practical systems. In this work, we pursue a nonparametric approach that seeks to learn a distribution over rankings (aka the ranking model) that is consistent with the observed data and has the sparsest possible support (i.e., the smallest number of rankings with nonzero probability mass). We focus on first-order marginal data, which comprise information on the probability that item i is ranked at position j, for all possible item and position pairs. The observed data may be noisy. Finding the sparsest approximation requires brute force search in the worst case. To address this issue, we restrict our search to, what we dub, the signature family, and show that the sparsest model within the signature family can be found computationally efficiently compared with the brute force approach. We then establish that the signature family provides good approximations to popular ranking model classes, such as the multinomial logit and the exponential family classes, with support size that is small relative to the dimension of the observed data. We test our methods on two data sets: the ranked election data set from the American Psychological Association and the preference ordering data on 10 different sushi varieties.

Signaling Mechanism of Transcriptional Bursting: A Technical Resolution-Independent Study

Gene transcription has been uncovered to occur in sporadic bursts. However, due to technical difficulties in differentiating individual transcription initiation events, it remains debated as to whether the burst size, frequency, or both are subject to modulation by transcriptional activators. Here, to bypass technical constraints, we addressed this issue by introducing two independent theoretical methods including analytical research based on the classic two-model and information entropy research based on the architecture of transcription apparatus. Both methods connect the signaling mechanism of transcriptional bursting to the characteristics of transcriptional uncertainty (i.e., the differences in transcriptional levels of the same genes that are equally activated). By comparing the theoretical predictions with abundant experimental data collected from published papers, the results exclusively support frequency modulation. To further validate this conclusion, we showed that the data that appeared to support size modulation essentially supported frequency modulation taking into account the existence of burst clusters. This work provides a unified scheme that reconciles the debate on burst signaling.

INSPECTRE: Privately Estimating the Unseen

We develop differentially private methods for estimating various distributional properties. Given a sample from a discrete distribution p, some functional f, and accuracy and privacy parameters alpha and epsilon, the goal is to estimate f(p) up to accuracy alpha, while maintaining epsilon-differential privacy of the sample. We prove almost-tight bounds on the sample size required for this problem for several functionals of interest, including support size, support coverage, and entropy. We show that the cost of privacy is negligible in a variety of settings, both theoretically and experimentally. Our methods are based on a sensitivity analysis of several state-of-the-art methods for estimating these properties with sublinear sample complexities