Multi-point distribution of discrete time periodic TASEP

We study the one-dimensional discrete time totally asymmetric simple exclusion process with parallel update rules on a spatially periodic domain. A multi-point space-time joint distribution formula is obtained for general initial conditions. The formula involves contour integrals of Fredholm determinants with kernels acting on certain discrete spaces. For a class of initial conditions satisfying certain technical assumptions, we are able to derive large-time, large-period limit of the joint distribution, under the relaxation time scale $$t=O(L^{3/2})$$ t = O ( L 3 / 2 ) when the height fluctuations are critically affected by the finite geometry. The assumptions are verified for the step and flat initial conditions. As a corollary we obtain the multi-point distribution of discrete time TASEP on the whole integer lattice $${\mathbb {Z}}$$ Z by taking the period L large enough so that the finite-time distribution is not affected by the boundary. The large time limit for the multi-time distribution of discrete time TASEP on $${\mathbb {Z}}$$ Z is then obtained for the step initial condition.

Uniform probability distribution over all density matrices

Let $$\mathscr {H}$$ H be a finite-dimensional complex Hilbert space and $$\mathscr {D}$$ D the set of density matrices on $$\mathscr {H}$$ H , i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure u on $$\mathscr {D}$$ D that can be regarded as the uniform distribution over $$\mathscr {D}$$ D . We propose a measure on $$\mathscr {D}$$ D , argue that it can be so regarded, discuss its properties, and compute the joint distribution of the eigenvalues of a random density matrix distributed according to this measure.

From Intricacy to Conciseness: A Progressive Transfer Strategy for EEG-Based Cross-Subject Emotion Recognition

Emotion plays a significant role in human daily activities, and it can be effectively recognized from EEG signals. However, individual variability limits the generalization of emotion classifiers across subjects. Domain adaptation (DA) is a reliable method to solve the issue. Due to the nonstationarity of EEG, the inferior-quality source domain data bring negative transfer in DA procedures. To solve this problem, an auto-augmentation joint distribution adaptation (AA-JDA) method and a burden-lightened and source-preferred JDA (BLSP-JDA) approach are proposed in this paper. The methods are based on a novel transfer idea, learning the specific knowledge of the target domain from the samples that are appropriate for transfer, which reduces the difficulty of transfer between two domains. On multiple emotion databases, our model shows state-of-the-art performance.

High-Dimensional Radial Symmetry of Copula Functions: Multiplier Bootstrap vs. Randomization

We use a recently proposed fast test of copula radial symmetry based on multiplier bootstrap and obtain an equivalent randomization test. The literature shows the statistical superiority of the randomization approach in the bivariate case. We extend the comparison of statistical performance focusing on the high-dimensional regime in a simulation study. We document radial asymmetry in the joint distribution of the percentage changes of sectorial industrial production indices of the European Union.

An Introduction to Factored Regression Models with Blimp

In this paper, we provide an introduction to the factored regression framework. This modeling framework applies the rules of probability to break up or “factor” a complex joint distribution into a product of conditional regression models. Using this framework, we can easily specify the complex multivariate models that missing data modeling requires. The article provides a brief conceptual overview of factored regression and describes the functional notation used to conceptualize the models. Furthermore, we present a conceptual overview of how the models are estimated and imputations are obtained. Finally, we discuss how users can use the free software package, Blimp, to estimate the models in the context of a mediation example.

Effect Mechanism of Connection Joints in Fabricated Station Structures

The seismic response of a fabricated subway station is a complex structural connection problem that depends on the mechanical properties of the joints. In order to obtain the optimal joint distribution of a fabricated station structure under earthquake action, three finite element models of a single ring structure of fabricated subway stations assembled with seven, five, and four prefabricated components were proposed. Seismic wave characteristics, peak acceleration, and coupled horizontal and vertical seismic components were considered to study the seismic response of the fabricated subway station structure with different forms of the joint distribution. The dynamic time history method was used to analyze the seismic response in three aspects: structure plastic strain, interlayer relative deformation, and internal force. The damage indexes and residual strength indexes of the joints were offered based on the concrete damage index to evaluate the joints’ damage degree. The results showed that the joints of the vault or bottom plate had little influence on the seismic response of the fabricated station structure. The sidewall joints had the obvious seismic response and the most severe damage under horizontal ground motion or coupled ground motion, which were the weak joints of the fabricated station structure. The existence of vertical ground motion aggravated the damage degree of sidewall joints, making the damage occurrence time of sidewall joints earlier and the damage end time extended. On the premise of meeting the mechanical load and site requirements, an assembly scheme with fewer prefabricated components can be selected.

The population genetics of collateral resistance and sensitivity

Resistance mutations against one drug can elicit collateral sensitivity against other drugs. Multi-drug treatments exploiting such trade-offs can help slow down the evolution of resistance. However, if mutations with diverse collateral effects are available, a treated population may evolve either collateral sensitivity or collateral resistance. How to design treatments robust to such uncertainty is unclear. We show that many resistance mutations in Escherichia coli against various antibiotics indeed have diverse collateral effects. We propose to characterize such diversity with a joint distribution of fitness effects (JDFE) and develop a theory for describing and predicting collateral evolution based on simple statistics of the JDFE. We show how to robustly rank drug pairs to minimize the risk of collateral resistance and how to estimate JDFEs. In addition to practical applications, these results have implications for our understanding of evolution in variable environments.

Inhomogeneous asymmetric exclusion processes between two reservoirs: large deviations for the local empirical observables in the mean-field approximation

For a given inhomogeneous exclusion processes on N sites between two reservoirs, the trajectories probabilities allow to identify the relevant local empirical observables and to obtain the corresponding rate function at level 2.5. In order to close the hierarchy of the empirical dynamics that appear in the stationarity constraints, we consider the simplest approximation, namely the mean-field approximation for the empirical density of two consecutive sites, in direct correspondence with the previously studied mean-field approximation for the steady state. For a given inhomogeneous totally asymmetric model, this mean-field approximation yields the large deviations for the joint distribution of the empirical density profile and of the empirical current around the mean-field steady state; the further explicit contraction over the current allows to obtain the large deviations of the empirical density profile alone. For a given inhomogeneous asymmetric model, the local empirical observables also involve the empirical activities of the links and of the reservoirs; the further explicit contraction over these activities yields the large deviations for the joint distribution of the empirical density profile and of the empirical current. The consequences for the large deviations properties of time-additive space-local observables are also discussed in both cases.