Background and Aim: The global pandemic of COVID-19 has posed an enormous threat to the economy and people's lives across various countries. Patients with COVID-19 most commonly present with respiratory symptoms. However, gastrointestinal (GI) symptoms can also occur. We aimed to study the relationship between GI symptoms and disease prognosis in patients with COVID-19. Methods: In a single-center and retrospective cohort study, the outcomes in COVID-19 patients with or without GI symptoms were compared. The propensity score is a conditional probability of having a particular exposure (COVID-19 patients with GI symptoms vs. without GI symptoms) given a set of baseline measured covariates. Survival was estimated using the Kaplan-Meier method, and any differences in survival were evaluated with a stratified log-rank-test. To explore the GI symptoms associated with ARDS, non-invasive ventilator treatment, tracheal intubation, tracheotomy, and CRRT, univariable and multivariable COX regression models were used. Results: Among 1,113 eligible patients, 359 patients with GI symptoms and 718 without GI symptoms had similar propensity scores and were included in the analyses. Patients with GI symptoms, as compared with those without GI symptoms, were associated with a similar risk of death, but with higher risks of ARDS, non-invasive mechanical ventilation in COVID-19 patients, respectively. Conclusions: The presence of GI symptoms was associated with a high risk of ARDS, non-invasive mechanical ventilation and tracheal intubation in patients with COVID-19 but not mortality.

In this paper, the dynamics of elementary cellular automata rule 42 is investigated in the bi-infinite symbolic sequence space. Rule 42, a member of Wolfram's class II which was said to be simply as periodic before, actually defines a chaotic global attractor; that is, rule 42 is topologically mixing on its global attractor and possesses the positive topological entropy. Therefore, rule 42 is chaotic in the sense of both Li-Yorke and Devaney. Meanwhile, the characteristic function and the basin tree diagram of rule 42 are explored for some finite length of binary strings, which reveal its Bernoulli characteristics. The method presented in this work is also applicable to studying the dynamics of other rules, especially the 112 Bernoulli-shift rules of the elementary cellular automata.

In this paper, we study consensus problems in a family of tree networks and investigate first and second order consensus denoted as network coherence characterized by Laplacian spectrum. According to the tree structures, we obtain the recursive relationships of Laplacian matrix and its Laplacian eigenvalues at two successive generations. We then obtain the analytical expressions for the sum of the reciprocals and the square reciprocals of all nonzero Laplacian eigenvalues. Finally, we calculate first and second order network coherence and see that the scalings of first and second order coherence with network size N are lnN and N, which are smaller than some studied tree graphs, such as Peano basin fractal, T-graph, and generalized Vicsek fractal.

As a paradigm for nonlinear spatial-temporal processing, cellular nonlinear networks (CNN) are biologically inspired systems where computation emerges from a collection of simple locally coupled nonlinear cells. Our investigation is an exploration of an important and difficult aspect of implementing arbitrary Boolean functions by using CNN. A typical class of basic key Boolean functions is the class of linearly separable ones. In this paper, we focus on establishing a complete set of mathematical theories for the linearly separable Boolean functions (LSBF) that are identical to a class of uncoupled CNN. First, we obtain an essential relationship between the template and the offset levels as well as the basis of the binary input vector set in the uncoupled CNN. More precisely, we construct a neat binary input-output truth table and some interesting properties of the offset levels of the uncoupled CNN, and develop a practical design formula for the class of CNN template. Especially, we found a criterion for LSBF, which depends only on symbolic relations between a Boolean function's outputs. Furthermore, we develop a method for representing any linearly nonseparable Boolean function into a logic operation of a sequence of linearly separable ones for a small number of inputs.Index Terms-Binary input-output truth table, cellular nonlinear network (CNN), linearly nonseparable Boolean function, linearly separable Boolean function (LSBF), template design.

In this paper we present a single-soliton two-component cellular automata (CA) model of waves as mobile self-localizations, also known as: particles, waves, or gliders; and its version with memory. The model is based on coding sets of strings where each chain represents a unique mobile self-localization. We will discuss briefly the original soliton models in CA proposed with filter automata, followed by solutions in elementary CA (ECA) domain with the famous universal ECA Rule 110, and reporting a number of new solitonic collisions in ECA Rule 54. A mobile self-localization in this study is equivalent a single soliton because the collisions of these mobile self-localizations studied in this paper satisfies the property of solitonic collisions. We also present a specific ECA with memory (ECAM), the ECAM Rule φR9maj:4, that displays single-soliton solutions from any initial codification (including random initial conditions) for a kind of mobile self-localization because such automaton is able to adjust any initial condition to soliton structures.