Global existence in a two-dimensional chemotaxis-consumption model with weakly singular sensitivity

In this paper we study a two-dimensional chemotaxis-consumption system with singular sensitivity and endowed with Neumann boundary conditions. Sufficient conditions on the data of the problem are given so that the globability of classical solutions is shown, thus excluding any finite-time blow-up scenario.     

Global well-posedness for the Euler-Boussinesq system with axisymmetric data

In this paper we prove the global well-posedness for the three-dimensional Euler-Boussinesq system with axisymmetric initial data without swirl. This system couples the Euler equation with a transport-diffusion equation governing the temperature.     

Methodology for determining the acceptability of system designs in uncertain environments

In practice, managers often wish to ascertain that a particular engineering design of a production system meets their requirements. The future environment of this design is likely to differ from the environment assumed during the design. Therefore it is crucial to find out which variations in that environment may make this design unacceptable (unfeasible). This article proposes a methodology for estimating which uncertain environmental parameters are important (so managers can become pro-active) and which combinations of parameter values (scenarios) make the design unacceptable. The proposed methodology combines simulation, bootstrapping, design of experiments, and linear regression metamodeling. This methodology is illustrated through a simulated manufacturing system, including fourteen uncertain parameters of the input distributions for the various arrival and service times. These parameters are investigated through the simulation of sixteen scenarios, selected through a two-level fractional–factorial statistical design. The resulting simulation Input/Output (I/O) data are analyzed through a first-order polynomial metamodel and bootstrapping. A second experiment with other scenarios gives some outputs that turn out to be unacceptable. In general, polynomials fitted to the simulation’s I/O data can estimate the border line (frontier) between acceptable and unacceptable environments.     

Integrated data envelopment analysis: Global vs. local optimum

Chiou et al. (2010) (A joint measurement of efficiency and effectiveness for non-storable commodities: integrated data envelopment analysis approaches. European Journal of Operational Research 201, 477–489) propose an integrated data envelopment analysis model in measuring decision making units (DMUs) that have a two-stage internal network structure with multiple inputs, outputs, and consumptions. They claim that any optimal solutions determined by their DEA model are a global optimum, not a local optimum. We show that such a conclusion is a false statement due to their misuse of Hessian matrix in examining the concavity of the objective function, and their DEA model is actually a non-convex optimization problem. As a result, their DEA model is unusable in practice due to a lack of efficient algorithm for this particular non-convex DEA model. We further show that Chiou et al.’s (2010) model is a special case of a well-known two-stage network DEA model, and it can be transformed into a parametric linear program for which an approximate global optimal solution can be obtained by solving a sequence of linear programs in combination with a simple search algorithm.     

A methodology for sensitivity analysis of models fitted to data using statistical methods

A simple methodology is presented for sensitivity analysis ofmodels that have been fitted to data by statistical methods.Such analysis is a decision support tool that can focus theeffort of a modeller who wishes to further refine a model and/orto collect more data. A formula is given for the calculationof the proportional reduction in the variance of the model ‘output’that would be achievable with perfect knowledge of a subsetof the model parameters. This is a measure of the importanceof the set of parameters, and is shown to be asymptoticallyequal to the squared correlation between the model output andits best predictor based on the omitted parameters. The methodology is illustrated with three examples of OR problems,an age-based equipment replacement model, an ARIMA forecastingmodel and a cancer screening model. The sampling error of thecalculated percentage of variance reduction is studied theoretically,and a simulation study is then used to exemplify the accuracyof the method as a function of sample size.     

Equilibrium and sensitivity analysis of a spatio-temporal host-vector epidemic model

Insect-borne diseases are diseases carried by insects affecting humans, animals or plants. They have the potential to generate massive outbreaks such as the Zika epidemic in 2015–2016 mostly distributed in the Americas, the Pacific and Southeast Asia, and the multi-foci outbreak caused by the bacterium Xylella fastidiosa in Europe in the 2010s. In this article, we propose and analyze the behavior of a spatially-explicit compartmental model adapted to pathosystems with fixed hosts and mobile vectors disseminating the disease. The behavior of this model based on a system of partial differential equations is complementarily characterized via a theoretical study of its equilibrium states and a numerical study of its transient phase using global sensitivity analysis. The results are discussed in terms of implications concerning the surveillance and control of the disease over a medium-to-long temporal horizon.     

A feasible implementation procedure for interval analysis method from measurement data

An uncertain quantification and propagation procedure via interval analysis is proposed to deal with the uncertain structural problems in the case of the small sample measurement data in this study. By virtue of the construction of a membership function, a finite number of sample data on uncertain structural parameters are processed, and the effective interval estimation on uncertain parameters can be obtained. Moreover, uncertainty propagation based on interval analysis is performed to obtain the structural responses interval according to the quantified results of the uncertain structural parameters. The proposed method can decrease the demanding on the sample number of measurement data in comparison with the classical probabilistic method. For instance, the former only need several to tens of sample data, whereas the latter usually need several tens to several hundreds of them. The numerical examples illustrate the feasibility and validity of the proposed method for non-probabilistic quantification of limited uncertain information as well as propagation analysis.     

Notes on ‘Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis’

In our previous work published in this journal, we showed how the Hit-And-Run (HAR) procedure enables efficient sampling of criteria weights from a space formed by restricting a simplex with arbitrary linear inequality constraints. In this short communication, we note that the method for generating a basis of the sampling space can be generalized to also handle arbitrary linear equality constraints. This enables the application of HAR to sampling spaces that do not coincide with the simplex, thereby allowing the combined use of imprecise and precise preference statements. In addition, it has come to our attention that one of the methods we proposed for generating a starting point for the Markov chain was flawed. To correct this, we provide an alternative method that is guaranteed to produce a starting point that lies within the interior of the sampling space.     

Estimating freeway traffic measures from mobile phone location data

The worldwide propagation of mobile phone and the rapid development of location technologies have provided the chance to monitor freeway traffic conditions without requiring extra infrastructure investment. Over the past decade, a number of research studies and operational tests have attempted to investigate the methods to estimate traffic measures using information from mobile phone. However, most of these works ignored the fact that each vehicle has more than one phone due to the rapid popularity of mobile phone. This paper considered the circumstance of multi-phones and proposed a relatively simplistic clustering technique to identify whether phones travel in the same vehicle. By using this technique, mobile phone data can be used to determine not only speed, but also vehicle counts by type, and therefore density. A complex simulation covering different traffic condition and location accuracy of mobile phone has been developed to evaluate the proposed approach. Simulation results indicate that location accuracy of mobile phone is a crucial factor to estimate accurate traffic measures in case of a given location frequency and the number of continuous location data. In addition, traffic demand and clustering method have a certain effect on the accuracy of traffic measures.     

On Global Hypoellipticity

We consider a first order linear partial differential operator of principal type on a closed connected orientable two-dimensional manifold sending sections of one complex line bundle to sections of another. We prove that the assumption of global hypoellipticity of the operator implies a relation between the degrees of the line bundles and the Euler characteristic of the manifold.     

Global well-posedness for the 2-D nonhomogeneous incompressible MHD equations with large initial data

In this paper, we consider the 2-D nonhomogeneous incompressible magnetohydrodynamic equations with variable viscosity and variable conductivity. We obtain the global existence of solutions for this system with initial data in the scaling invariant Besov spaces and without size restriction for the initial velocity and magnetic field.     

A sensitivity analysis algorithm for hierarchical decision models

In this paper, a comprehensive algorithm is developed to analyze the sensitivity of hierarchical decision models (HDM), including the analytic hierarchy process and its variants, to single and multiple changes in the local contribution matrices at any level of the decision hierarchy. The algorithm is applicable to all HDM that use an additive function to derive the overall contribution vector. It is independent of pairwise comparison scales, judgment quantification techniques and group opinion combining methods. The allowable range/region of perturbations, contribution tolerance, operating point sensitivity coefficient, total sensitivity coefficient and the most critical decision element at a certain level are identified in the HDM SA algorithm. An example is given to demonstrate the application of the algorithm and show that HDM SA can reveal information more significant and useful than simply knowing the rank order of the decision alternatives.     

Global well-posedness and asymptotic stabilization for chemotaxis system with signal-dependent sensitivity

A fully parabolic chemotaxis system

$u_t=\mathrm{\Delta }u?\mathrm{?}?(u\chi (v)\mathrm{?}v),v_t=\mathrm{\Delta }v?v+u,$

in a smooth bounded domain $\mathrm{\Omega }?{\mathbb{R}}^N$, $N\ge 2$ with homogeneous Neumann boundary conditions is considered, where the non-negative chemotactic sensitivity function χ satisfies $\chi (v)\le \mu {(a+v)}^{?k}$, for some $a\ge 0$ and $k\ge 1$. It is shown that a novel type of weight function can be applied to a weighted energy estimate for $k>1$. Consequently, the range of μ for the global existence and uniform boundedness of classical solutions established by Mizukami and Yokota [23] is enlarged. Moreover, under a convexity assumption on Ω, an asymptotic Lyapunov functional is obtained and used to establish the asymptotic stability of spatially homogeneous equilibrium solutions for $k\ge 1$ under a smallness assumption on μ. In particular, when $\chi (v)=\mu /v$ and $N<8$, it is shown that the spatially homogeneous steady state is a global attractor whenever $\mu \le 1/2$.     

Global existence and asymptotic dynamics in a 3D fractional chemotaxis system with singular sensitivity

In this paper, we investigate the global existence and asymptotic dynamics of solutions to a fractional singular chemotaxis system in three dimensional whole space. We deal with the new difficulties arising from fractional diffusion by using Riesz transform and Kato-Ponce’s commutator estimates appropriately, and establish the local existence of solution. Then with the help of combining the local existence and the a priori estimates, the global existence and uniqueness of solution with small initial data is derived. Moreover, we obtain the asymptotic decay rates of solution by the method of energy estimates.     

Some proximity and sensitivity results in quadratic integer programming

We show that for any optimal solution for a given separable quadratic integer programming problem there exist an optimal solution for its continuous relaxation such that wheren is the number of variables and(A) is the largest absolute subdeterminant of the integer constraint matrixA. Also for any feasible solutionz, which is not optimal for the separable quadratic integer programming problem, there exists a feasible solution having greater objective function value and with . We further prove, under some additional assumptions, that the distance between a pair of optimal solutions to an integer quadratic programming problem with right hand side vectorsb andb, respectively, depends linearly on b–b₁. Finally the validity of all the results for nonseparable mixed-integer quadratic programs is established. The proximity results obtained in this paper are extensions of some of the results described in Cook et al. (1986) for linear integer programming.This research was partially supported by Natural Sciences and Engineering Research Council of Canada Grant 5-83998.     

Exact bounds for the sensitivity analysis of structures with uncertain-but-bounded parameters

Based on interval mathematical theory, the interval analysis method for the sensitivity analysis of the structure is advanced in this paper. The interval analysis method deals with the upper and lower bounds on eigenvalues of structures with uncertain-but-bounded (or interval) parameters. The stiffness matrix and the mass matrix of the structure, whose elements have the initial errors, are unknown except for the fact that they belong to given bounded matrix sets. The set of possible matrices can be described by the interval matrix. In terms of structural parameters, the stiffness matrix and the mass matrix take the non-negative decomposition. By means of interval extension, the generalized interval eigenvalue problem of structures with uncertain-but-bounded parameters can be divided into two generalized eigenvalue problems of a pair of real symmetric matrix pair by the real analysis method. Unlike normal sensitivity analysis method, the interval analysis method obtains informations on the response of structures with structural parameters (or design variables) changing and without any partial differential operation. Low computational effort and wide application rang are the characteristic of the proposed method. Two illustrative numerical examples illustrate the efficiency of the interval analysis.     

Positive vector measures with given marginals

Suppose E is an ordered locally convex space, X ₁ and X ₂ Hausdorff completely regular spaces and Q a uniformly bounded, convex and closed subset of M _t ⁺ (X ₁ × X ₂, E). For i = 1, 2, let μ _i   M _t ⁺ (X _i , E). Then, under some topological and order conditions on E, necessary and sufficient conditions are established for the existence of an element in Q, having marginals μ ₁ and μ ₂.     

Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data

We consider the defocusing, -critical Hartree equation for the radial data in all dimensions (n5). We show the global well-posedness and scattering results in the energy space. The new ingredient in this paper is that we first take advantage of the term in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity.