From Goal Programming for Continuous Multi-Criteria Optimization to the Target Decision Rule for Mixed Uncertain Problems

Goal programming (GP) is applied to the discrete and continuous version of multi-criteria optimization. Recently, some essential analogies between multi-criteria decision making under certainty (M-DMC) and scenario-based one-criterion decision making under uncertainty (1-DMU) have been revealed in the literature. The aforementioned similarities allow the adjustment of GP to an entirely new domain. The aim of the paper is to create a new decision rule for mixed uncertain problems on the basis of the GP methodology. The procedure can be used by pessimists, optimists and moderate decision makers. It is designed for one-shot decisions. One of the significant advantages of the novel approach is related to the possibility to analyze neutral criteria, which are not directly taken into account in existing classical procedures developed for 1-DMU.

Reverse integral Hardy inequality on metric measure spaces

In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, we give necessary and sufficient conditions for the weighted reverse Hardy inequality to be true. The main tool in our proof is a continuous version of the reverse Minkowski inequality. In addition, we present some consequences of the obtained reverse Hardy inequality on the homogeneous groups, hyperbolic spaces and Cartan-Hadamard manifolds.

Weak Convergence Rates for Spatial Spectral Galerkin Approximations of Semilinear Stochastic Wave Equations with Multiplicative Noise

Stochastic wave equations appear in several models for evolutionary processes subject to random forces, such as the motion of a strand of DNA in a liquid or heat flow around a ring. Semilinear stochastic wave equations can typically not be solved explicitly, but the literature contains a number of results which show that numerical approximation processes converge with suitable rates of convergence to solutions of such equations. In the case of approximation results for strong convergence rates, semilinear stochastic wave equations with both additive or multiplicative noise have been considered in the literature. In contrast, the existing approximation results for weak convergence rates assume that the diffusion coefficient of the considered semilinear stochastic wave equation is constant, that is, it is assumed that the considered wave equation is driven by additive noise, and no approximation results for multiplicative noise are known. The purpose of this work is to close this gap and to establish essentially sharp weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise. In particular, our weak convergence result establishes as a special case essentially sharp weak convergence rates for the continuous version of the hyperbolic Anderson model. Our method of proof makes use of the Kolmogorov equation and the Hölder-inequality for Schatten norms.

Optimization of the dynamic transition in the continuous coloring problem

Random constraint satisfaction problems (CSPs) can exhibit a phase where the number of constraints per variable α makes the system solvable in theory on the one hand, but also makes the search for a solution hard, meaning that common algorithms such as Monte Carlo (MC) method fail to find a solution. The onset of this hardness is deeply linked to the appearance of a dynamical phase transition where the phase space of the problem breaks into an exponential number of clusters. The exact position of this dynamical phase transition is not universal with respect to the details of the Hamiltonian one chooses to represent a given problem. In this paper, we develop some theoretical tools in order to find a systematic way to build a Hamiltonian that maximizes the dynamic α d threshold. To illustrate our techniques, we will concentrate on the problem of continuous coloring, where one tries to set an angle x i ∈ [0; 2π] on each node of a network in such a way that no adjacent nodes are closer than some threshold angle θ, that is cos(x i − x j )⩽ cos θ. This problem can be both seen as a continuous version of the discrete graph coloring problem or as a one-dimensional version of the Mari–Krzakala–Kurchan model. The relevance of this model stems from the fact that continuous CSPs on sparse random graphs remain largely unexplored in statistical physics. We show that for sufficiently small angle θ this model presents a random first order transition and compute the dynamical, condensation and Kesten–Stigum transitions; we also compare the analytical predictions with MC simulations for values of θ = 2π/q, q ∈ N . Choosing such values of q allows us to easily compare our results with the renowned problem of discrete coloring.

The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications

Continuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continuous version is called the exponentiated Burr–Hatke (EBuH) distribution. We also propose a new discrete analog, namely the discrete exponentiated Burr–Hatke (DEBuH) distribution. The probability density and the hazard rate functions exhibit decreasing or upside-down shapes, whereas the reversed hazard rate function. Some statistical and reliability properties of the EBuH distribution are calculated. The EBuH parameters are estimated using some classical estimation techniques. The simulation results are conducted to explore the behavior of the proposed estimators for small and large samples. The applicability of the EBuH and DEBuH models is studied using two real-life data sets. Moreover, the maximum likelihood approach is adopted to estimate the parameters of the EBuH distribution under constant-stress accelerated life-tests (CSALTs). Furthermore, a real data set is analyzed to validate our results under the CSALT model.

A Clinical Update on the Prognostic Effect of microRNA Biomarkers for Survival Outcome in Nasopharyngeal Carcinoma: A Systematic Review and Meta-Analysis

Background: Nasopharyngeal carcinoma (NPC), a relatively uncommon malignancy in the Western world, is highly prevalent in Southeast Asia where the treatment outcomes are poor. Despite recent improvements in diagnosis and treatment locoregional control, distant metastasis and chemoresistance continue to be a significant cause of mortality. Identification of a reliable and comprehensive prognostic biomarker is highly desirable. The potential relevance of microRNAs (miRNAs) as prognostic markers in NPC is assessed in this systematic review and meta-analysis. Methods: A systematic review was performed using the PubMed and Science Direct databases. The search was limited to search results between 2018 and 2020 with the keywords and search strings developed as per the Preferred Reporting Items for Systematic Review and Meta-analysis (PRISMA) guidelines. The recovered articles were carefully screened based on the selection criteria. In the meta-analysis study, high and low expression levels of miRNAs were measured using the hazard ratio (HR) and 95 percent confidence interval (CI) for patients’ survival outcomes. Egger’s bias indicator test and funnel plot symmetry were used to assess the risk of bias. Results: Amongst the 25 studies, 13 fulfilled the conditions of inclusion in this meta-analysis. The researchers further delved into the 21 miRNA expression levels from 3015 NPC patients to ascertain a link between miRNA’s predictive role and survival outcomes. The majority of the articles retrieved during this study were from China, with two studies from Canada and Malaysia. The overall pooled effect size estimation (HR) for dysregulated miRNAs was 1.590 (95% CI: 1.253–2.017), displaying that miRNA marker expression increased the risk of mortality in NPC patients by 59%. Conclusions: This meta-analysis is novel and looks at the prognostic significance of miRNAs as biomarkers in NPC patients using a continuous version pooled meta-analysis. Although our findings are ambiguous, they do show that greater miRNA expression in NPC may be associated with a lower overall survival rate. To acquire clear conclusions, more prospective studies with large cohorts are required to determine the clinical utility of miRNAs as prognostic biomarkers.

Using Continuous Directed Evolution to Improve Enzymes for Plant Applications

Continuous directed evolution of enzymes and other proteins in microbial hosts is capable of outperforming classical directed evolution by executing hypermutation and selection concurrently in vivo, at scale, with minimal manual input. Provided that a target enzyme’s activity can be coupled to growth of the host cells, the activity can be improved simply by selecting for growth. Like all directed evolution, the continuous version requires no prior mechanistic knowledge of the target. Continuous directed evolution is thus a powerful new way to modify plant or non-plant enzymes for use in plant metabolic research and engineering. Here, we first describe the basic features of the Saccharomyces cerevisiae OrthoRep system for continuous directed evolution and compare it briefly with other systems. We then give a step-by-step account of three ways in which OrthoRep can be deployed to evolve primary metabolic enzymes, using a THI4 thiazole synthase as an example and illustrating the mutational outcomes obtained. We close by outlining applications of OrthoRep that serve growing demands (i) to change the characteristics of plant enzymes destined for return to plants, and (ii) to adapt (‘plantize’) enzymes from prokaryotes – especially exotic prokaryotes – to function well in mild, plant-like conditions.One-sentence summaryContinuous directed evolution using the yeast OrthoRep system is a powerful new way to improve enzymes for use in plant engineering as illustrated by ‘plantizing’ a bacterial thiamin synthesis enzyme..

Understanding the Effect of Categorization of a Continuous Predictor with Application to Neuro Oncology

Many Neuro-Oncology studies commonly assess the association between a prognostic factor (predictor) and disease or outcome, such as the association between age and glioma. Predictors can be continuous (e.g., age) or categorical (e.g., race/ethnicity). Effects of categorical predictors are frequently easier to visualize and interpret than effects of continuous variables. This makes it an attractive, and seemingly justifiable, option to subdivide the continuous predictors into categories (e.g., age< 50 years vs. age ≥50 years). However, this approach results in loss of information (and power) compared to the continuous version. This review outlines the use cases for continuous and categorized predictors and provides tips and pitfalls for interpretation of these approaches.

A New 4D Hyperchaotic System and Its Analog and Digital Implementation

This work presents a new four-dimensional autonomous hyperchaotic system based on Méndez-Arellano-Cruz-Martínez (MACM) 3D chaotic system. Analytical and numerical studies of the dynamic properties are conducted for the new hyperchaotic system (NHS) in its continuous version (CV), where the Lyapunov exponents are calculated. The CV of the NHS is simulated and implemented using operational amplifiers (OAs), whereas the Discretized Version (DV) is simulated and implemented in real-time. Besides, a novel study of the algorithm performance of the proposed DV of NHS is conducted with the digital-electronic implementation of the floating-point versus Q1.15 fixed-point format by using the Digital Signal Processor (DSP) engine of a 16-bit dsPIC microcontroller and two external dual digital to analog converters (DACs) in an embedded system (ES).

Optimal Placement and Sizing of D-STATCOM in Radial and Meshed Distribution Networks Using a Discrete-Continuous Version of the Genetic Algorithm

In this paper, we propose a new discrete-continuous codification of the Chu–Beasley genetic algorithm to address the optimal placement and sizing problem of the distribution static compensators (D-STATCOM) in electrical distribution grids. The discrete part of the codification determines the nodes where D-STATCOM will be installed. The continuous part of the codification regulates their sizes. The objective function considered in this study is the minimization of the annual operative costs regarding energy losses and installation investments in D-STATCOM. This objective function is subject to the classical power balance constraints and devices’ capabilities. The proposed discrete-continuous version of the genetic algorithm solves the mixed-integer non-linear programming model that the classical power balance generates. Numerical validations in the 33 test feeder with radial and meshed configurations show that the proposed approach effectively minimizes the annual operating costs of the grid. In addition, the GAMS software compares the results of the proposed optimization method, which allows demonstrating its efficiency and robustness.