Interactions between Viral Regulatory Proteins Ensure an MOI-Independent Probability of Lysogeny during Infection by Bacteriophage P1

Phage P1 has been shown potentially to play an important role in disseminating antibiotic resistance among bacteria during lysogenization, as evidenced by the prevalence of P1 phage-like elements in animal and human pathogens. In contrast to phage λ, a cell fate decision-making paradigm, P1 lysogenization was shown to be independent of MOI.

Some Studies in Hemirings by the Falling Fuzzy k -Ideals

In this article, we establish the idea of falling fuzzy k -ideals in hemirings through the falling shadow theory and fuzzy sets. We shall express the relations between fuzzy k -ideals and falling fuzzy k -ideals in hemirings. In particular, we shall establish different characterizations of k -hemiregular hemirings in the perfect positive correlation and independent probability space by means of falling fuzzy k -ideals.

Likely striping in stochastic nematic elastomers

For monodomain nematic elastomers, we construct generalised elastic–nematic constitutive models combining purely elastic and neoclassical-type strain energy densities. Inspired by recent developments in stochastic elasticity, we extend these models to stochastic–elastic–nematic forms, where the model parameters are defined by spatially independent probability density functions at a continuum level. To investigate the behaviour of these systems and demonstrate the effects of the probabilistic parameters, we focus on the classical problem of shear striping in a stretched nematic elastomer for which the solution is given explicitly. We find that, unlike the neoclassical case, where the inhomogeneous deformation occurs within a universal interval that is independent of the elastic modulus, for the elastic–nematic models, the critical interval depends on the material parameters. For the stochastic extension, the bounds of this interval are probabilistic, and the homogeneous and inhomogeneous states compete, in the sense that both have a a given probability to occur. We refer to the inhomogeneous pattern within this interval as ‘likely striping’.

Stochastic Online Learning with Probabilistic Graph Feedback

We consider a problem of stochastic online learning with general probabilistic graph feedback, where each directed edge in the feedback graph has probability pij. Two cases are covered. (a) The one-step case, where after playing arm i the learner observes a sample reward feedback of arm j with independent probability pij. (b) The cascade case where after playing arm i the learner observes feedback of all arms j in a probabilistic cascade starting from i – for each (i,j) with probability pij, if arm i is played or observed, then a reward sample of arm j would be observed with independent probability pij. Previous works mainly focus on deterministic graphs which corresponds to one-step case with pij ∈ {0,1}, an adversarial sequence of graphs with certain topology guarantees, or a specific type of random graphs. We analyze the asymptotic lower bounds and design algorithms in both cases. The regret upper bounds of the algorithms match the lower bounds with high probability.

On the Empirical Validity of Cumulative Prospect Theory: Experimental Evidence of Rank‐Independent Probability Weighting

Cumulative Prospect Theory (CPT), the leading behavioral account of decisionmaking under uncertainty, avoids the dominance violations implicit in Prospect Theory (PT) by assuming that the probability weight applied to a given outcome depends on its ranking. We devise a simple and direct nonparametric method for measuring the change in relative probability weights resulting from a change in payoff ranks. We find no evidence that these weights are even modestly sensitive to ranks. Conventional calibrations of CPT preferences imply that the percentage change in probability weights should be an order of magnitude larger than we observe. It follows either that probability weighting is not rank‐dependent, or that the weighting function is nearly linear. Nonparametric measurement of the change in relative probability weights resulting from changes in probabilities rules out the second possibility. Additional tests nevertheless indicate that the dominance patterns predicted by PT do not arise. We reconcile these findings by positing a form of complexity aversion that generalizes the well‐known certainty effect.

Uncertainty quantification of elastic material responses: testing, stochastic calibration and Bayesian model selection

Motivated by the need to quantify uncertainties in the mechanical behaviour of solid materials, we perform simple uniaxial tensile tests on a manufactured rubber-like material that provide critical information regarding the variability in the constitutive responses between different specimens. Based on the experimental data, we construct stochastic homogeneous hyperelastic models where the parameters are described by spatially independent probability density functions at a macroscopic level. As more than one parametrised model is capable of capturing the observed material behaviour, we apply Baye theorem to select the model that is most likely to reproduce the data. Our analysis is fully tractable mathematically and builds directly on knowledge from deterministic finite elasticity. The proposed stochastic calibration and Bayesian model selection are generally applicable to more complex tests and materials.

Topological supersymmetry breaking: The definition and stochastic generalization of chaos and the limit of applicability of statistics

The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found supersymmetric theory of stochastics (STS), all stochastic differential equations (SDEs) possess topological or de Rahm supersymmetry and stochastic chaos is the phenomenon of its spontaneous breakdown. Even though the STS is free of approximations and thus is technically solid, it is still missing a firm interpretational basis in order to be physically sound. Here, we make a few important steps toward the construction of the interpretational foundation for the STS. In particular, we discuss that one way to understand why the ground states of chaotic SDEs are conditional (not total) probability distributions, is that some of the variables have infinite memory of initial conditions and thus are not “thermalized”, i.e., cannot be described by the initial-conditions-independent probability distributions. As a result, the definitive assumption of physical statistics that the ground state is a steady-state total probability distribution is not valid for chaotic SDEs.

A Behaviorally Informed Survey-Powered Market Agent

We introduce a new method for converting individual probability estimates (obtained through surveys) into market orders for use in a Continuous Double Auction prediction market. Our Survey-Powered Market Agent (SPMA) algorithm is based on actual forecaster behavior, and offers notable advantages over existing market agent algorithms such as Zero Intelligence Plus (ZIP) agents: SPMAs only require probability estimates (and not bid direction nor quantity), are more behaviorally realistic, and work well when probabilities change over time. We validate SPMA using prediction market data and probability estimates elicited through surveys from a large set of forecasters on 88 individual forecasting problems over the course of a year. SPMA outperforms simple averages of the same probability forecasts and is competitive with sophisticated opinion poll aggregation methods and prediction markets. We use a rich set of market and poll data to empirically test the assumptions behind SPMA’s operation. In addition to aggregation efficiency, SPMA provides a framework for studying how forecasters convert probability estimates into trading orders, and offers a foundation for building hybrid markets which mix market traders and individuals producing independent probability estimates.

Minimum-Gap Evaluation Model for Multi-Constraint in One Dimension

The gap between components in an assembly refers to the performance of the assembly. While variation of the gap is associated with tolerancing specifications of components, it is an important issue to investigate the limits of the gap between corresponding components. In this work, we treat the minimum gap gmin, the dominant dimension for a multiconstraint assembly in one dimension, as an index related to the performance of the assembly. We then propose a calculation method for finding the minimum gap, when fitting conditions of linear dimensions are linearly independent. If the fitting conditions are not linear independent, we will find an independent probability distribution function which is defined to conform to all the other fitting conditions. Finally, an evaluation model for multi-constraint in one dimension, similar to the idea of Taguchi loss function, is proposed with an illustration. The assembled state of an assembly with multiconstraint in one dimension thus can be evaluated based on the model and calculation method proposed in this paper. By comparing the minimum gap, the assembly with least clearance is then identified.

Comparisons of Continuous and Discrete Methods for Combining Probability Values Associated with Matched-Pairs t-Test Data

Fisher's well-known continuous method for combining independent probability values from continuous distributions is compared with an exact discrete analog of Fisher's continuous method for combining independent probability values from discrete distributions using matched-pairs t-test data. Fisher's continuous method is shown to be inadequate for combining probability values from many discrete distributions, given the continuity assumption when discrete distributions are considered. Although Fisher's continuous method does not detect a well-documented effect among distributions, the exact discrete analog method clearly detects the effect.