A Stochastic SEIRS Epidemic Model with Infection Forces and Intervention Strategies

The spread of epidemics has been extensively investigated using susceptible-exposed infectious-recovered-susceptible (SEIRS) models. In this work, we propose a SEIRS pandemic model with infection forces and intervention strategies. The proposed model is characterized by a stochastic differential equation (SDE) framework with arbitrary parameter settings. Based on a Markov semigroup hypothesis, we demonstrate the effect of the proliferation number R 0 S on the SDE solution. On the one hand, when R 0 S < 1 , the SDE has an illness-free solution set under gentle additional conditions. This implies that the epidemic can be eliminated with a likelihood of 1. On the other hand, when R 0 S > 1 , the SDE has an endemic stationary circulation under mild additional conditions. This prompts the stochastic regeneration of the epidemic. Also, we show that arbitrary fluctuations can reduce the infection outbreak. Hence, valuable procedures can be created to manage and control epidemics.

A Relativistic Toda Lattice Hierarchy, Discrete Generalized (m,2N−m)-Fold Darboux Transformation and Diverse Exact Solutions

This paper investigates a relativistic Toda lattice system with an arbitrary parameter that is a very remarkable generalization of the usual Toda lattice system, which may describe the motions of particles in lattices. Firstly, we study some integrable properties for this system such as Hamiltonian structures, Liouville integrability and conservation laws. Secondly, we construct a discrete generalized (m,2N−m)-fold Darboux transformation based on its known Lax pair. Thirdly, we obtain some exact solutions including soliton, rational and semi-rational solutions with arbitrary controllable parameters and hybrid solutions by using the resulting Darboux transformation. Finally, in order to understand the properties of such solutions, we investigate the limit states of the diverse exact solutions by using graphic and asymptotic analysis. In particular, we discuss the asymptotic states of rational solutions and exponential-and-rational hybrid solutions graphically for the first time, which might be useful for understanding the motions of particles in lattices. Numerical simulations are used to discuss the dynamics of some soliton solutions. The results and properties provided in this paper may enrich the understanding of nonlinear lattice dynamics.

Problems using ordinal traits with continuous measures of functional diversity

Continuous indices of functional diversity are popular in studies examining community structure and ecosystem function across a wide range of subfields from paleontology to range management. These indices were designed to replace the use of more arbitrary, discrete functional groups or guilds; however, the effect of typical methodological decisions on these new continuous measures has not been fully investigated. To test the effect of using ordinal traits in functional diversity analysis, I first calculated relative functional diversity index values in real plant communities with real continuous trait data and Euclidean distances. I then compared these original values to "treatment" functional diversity index values obtained by discretizing the trait data and using Gower's distance. Agreement between original and treatment values was highly unpredictable and often abysmal. Small methodological choices, such as whether to treat a functional trait as continuous (mm) or ordinal ("small", "medium", "large"), could completely change a perceived functional diversity relationship along an environmental gradient. Some parameter combinations returned results that were no better than random noise. Because simple methodological choices can have such a large impact on continuous functional diversity indices, it is ambiguous whether analyses using ordinal traits are actually measuring an underlying functional diversity relationship between communities or just reflecting the arbitrary parameter choices of researchers.

A parameter-free statistical test for neuronal responsiveness

Neurophysiological studies depend on a reliable quantification of whether and when a neuron responds to stimulation. Simple methods to determine responsiveness require arbitrary parameter choices, such as binning size, while more advanced model-based methods require fitting and hyperparameter tuning. These parameter choices can change the results, which invites bad statistical practice and reduces the replicability. New recording techniques that yield increasingly large numbers of cells would benefit from a test for cell-inclusion that requires no manual curation. Here, we present the parameter-free ZETA-test, which outperforms t-tests, ANOVAs, and renewal-process-based methods by including more cells at a similar false-positive rate. We show that our procedure works across brain regions and recording techniques, including calcium imaging and Neuropixels data. Furthermore, in illustration of the method, we show in mouse visual cortex that 1) visuomotor-mismatch and spatial location are encoded by different neuronal subpopulations; and 2) optogenetic stimulation of VIP cells leads to early inhibition and subsequent disinhibition.

The Axial Anomaly in Lorentz Violating Theories: Towards the Electromagnetic Response of Weakly Tilted Weyl Semimetals

Using the path integral formulation in Euclidean space, we extended the calculation of the abelian chiral anomalies in the case of Lorentz violating theories by considering a new fermionic correction term provided by the standard model extension, which arises in the continuous Hamiltonian of a weakly tilted Weyl semimetal, and whose cones have opposite tilting. We found that this anomaly is insensitive to the tilting parameter, retaining its well-known covariant form. This independence on the Lorentz violating parameters is consistent with other findings reported in the literature. The initially imposed gauge invariant regularization was consistently recovered at the end of the calculation by the appearance of highly non-trivial combinations of the covariant derivatives, which ultimately managed to give only terms containing the electromagnetic tensor. We emphasize that the value of the anomaly with an arbitrary parameter is not automatically related to the effective action describing the electromagnetic response of such materials.

Development of the monitoring system for user's actions in the informational system

Currently, there are a large number of mechanisms for protecting computer systems, one of the directions is the creation of systems that respond to possible threats to the information security of the enterprise. Since according to statistics, a large number of information-related crimes are committed by employees of enterprises, monitoring of user actions in the information environment is a particularly important and relevant issue. The main advantages of such monitoring systems are the ability to represent arbitrary parameter values in the form of analytics of specified values, the ability to take into account a large number of development scenarios, the ability to use this system when making decisions, when describing schemes for analyzing information flows, and also to track a large number of computer parameters. In order to respond to information security incidents in a timely manner, it is important to develop a system that also takes into account the interrelationship of user actions. The authors of this paper hypothesized that the user's actions in a computer system are interrelated with each other, that is, if a user performs suspicious actions in a separate monitored parameter, then with a greater degree of confidence, we can say that this user will perform suspicious actions in another monitored parameter. Correlation analysis is necessary for possible reduction of the number of iterations during the program operation, which in the future allows to speed up the analysis of user actions in the information environment. In order to study the statistical relationship of the parameters, the authors found a mathematical measure of correlation - the correlation coefficient (Pearson correlation coefficient) for the studied parameters. Based on the analysis, fuzzy rules were formulated, on the basis of which a system for monitoring user actions in the information environment is built. In this development, a term such as reference user behavior is introduced. Any deviation from this "standard" is considered as a suspicious action and requires a timely response to a possible incident.

Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination

The widely cited Haken–Kelso–Bunz (HKB) model of motor coordination is used in an enormous range of applications. In this paper, we show analytically that the weakly damped, weakly coupled HKB model of two oscillators depends on only two dimensionless parameters; the ratio of the linear damping coefficient and the linear coupling coefficient and the ratio of the combined nonlinear damping coefficients and the combined nonlinear coupling coefficients. We illustrate our results with a mechanical analogue. We use our analytic results to predict behaviours in arbitrary parameter regimes and show how this led us to explain and extend recent numerical continuation results of the full HKB model. The key finding is that the HKB model contains a significant amount of behaviour in biologically relevant parameter regimes not yet observed in experiments or numerical simulations. This observation has implications for the development of virtual partner interaction and the human dynamic clamp, and potentially for the HKB model itself.

Travelling wave solutions to the proximate equations for LWSW

By feat of Maple 17 and a subsidiary ordinary differential equation, a new extension algebraic method is chosen to construct the travelling wave solutions to the proximate equation set involving an arbitrary parameter for long waves over shallow-water. Multiple triangle periodic solutions and new Jacobi elliptic function solutions are obtained. This procedure is applicable to other nonlinear partial differential equations as well.