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The focus of this paper is to develop a new partial differential equation model for the pattern formation of the human pathogen Staphylococcus aureus, starting from a newly developed model of selected gene regulation mechanisms. In our model, we do not only account for the bacteria densities and nutrient concentrations, but also for the quorum sensing and biofilm components, since they enable bacteria to coordinate their behavior and provide the environment in which the colony grows. To this end, we model the relevant gene regulation systems using ordinary differential equations and therefrom derive our evolution equations for quorum sensing and biofilm environment by time-scale arguments. Furthermore, we compare and validate our model and the corresponding simulation results with biological real data observations of Staphylococcus aureus mutant colony growth in the laboratory. We show that we are able to adequately display the qualitative biological features of pattern formation in selected mutants, using the parameter changes indicated by the gene regulation mechanisms. [ABSTRACT FROM AUTHOR]

The paper deals with monocular image-based sense and avoid assuming constant aircraft velocities and straight flight paths. From very limited two dimensional image information it finally characterizes the whole three dimensional collision situation by estimating the time to closest point of approach, the horizontal relative distance and its direction and the vertical relative distance also. The distances are relative to the intruder aircraft horizontal and vertical sizes. The overall estimated relative distance is the closest between the two aircraft in three dimension. So finally, every important information can be extracted to be used in a collision decision. The applicability of the developed method is presented in software-in-the-loop simulation test runs. Several intruder size and speed values are considered together with trajectories covering the whole three dimensional space. The horizontal intruder flight directions relative to the own aircraft cover 360∘ and the intruder can come from below ar above also. Detailed evaluation and discussion of the results is also included. Finally, the missed detection rate results to be superior (below 3% in every test scenario) though the false alarm rate results a bit high between 7-14%. [ABSTRACT FROM AUTHOR]

In this paper, structure-preserving model reduction methods for second-order systems are investigated. By introducing an appropriate parameter, the second-order system is represented by a strictly dissipative realization and the H2 norm of the strictly dissipative system is discussed. Then, based on the Krylov subspace techniques, two model reduction methods are proposed to reduce the order of the strictly dissipative system. Further, the reduced second-order systems are obtained. Moreover, according to the factorization of the error system, the H2 error bounds are represented by the Kronecker product and the vectorization operator. Finally, two numerical examples illustrate the efficiency of our methods. [ABSTRACT FROM AUTHOR]

Understanding the relation between large-scale and small-scale functionality is an acute problem in large systems. This paper presents possible structures that capture those relations. Here “structure” means a functor on a category, in this case the category of “combinatorial systems” that model manufacturing systems and supply networks. The details of the dynamics of these systems are frequently the domain of specialists and are ill understood outside such areas. Clustering activities in subsystems introduces covers as scales of analysis. This allows the development of sheaves of schedules and their properties which are analyzed by an adaptation of Čech cohomology. These are applied in supply networks to characterize the fragmentation of these networks and to characterize the conditions for local changes in schedules to extend to the whole system. The intent of this paper is to see sheaves and their cohomology as analytical probes that can enhance our understanding of large-scale systems. [ABSTRACT FROM AUTHOR]

In this paper, a new reliable algorithm called the multistage homotopy analysis method (MHAM) based on an adaptation of the standard homotopy analysis method (HAM) is presented to solve a time-fractional enzyme kinetics. This enzyme–substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The new algorithm is only a simple modification of the HAM, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding systems. Numerical comparisons between the MHAM and the classical fourth-order Runge–Kutta method in the case of integer-order derivatives reveal that the new technique is a promising tool for nonlinear systems of integer and fractional order. [ABSTRACT FROM AUTHOR]

Our aim in this work is to synthesize optimal feeding strategies that maximize, over a time period, the biogas production in a continuously filled bioreactor controlled by its dilution rate. Such an anaerobic process is described by a four-dimensional dynamical system. Instead of modeling the optimization of the biogas production as a Lagrange-type optimal control problem, we propose a slightly different optimal control approach in this paper: We study the minimal time control problem to reach a target point, which is chosen in such a way that it maximizes the biogas production at steady state. Thanks to the Pontryagin maximum principle and the geometric control theory, we provide an optimal feedback control for the minimal time control problem, when the initial conditions are taken within the invariant and attractive manifold of the system. The optimal synthesis exhibits turnpike and anti-turnpike singular arcs and a cut locus. [ABSTRACT FROM AUTHOR]

Nonlocal interactions, which have attracted attention in various fields, result from the integration of microscopic information such as a transition possibility, molecular events, and signaling networks of living creatures. Nonlocal interactions are useful to reproduce various patterns corresponding to such detailed microscopic information. However, the approach is inconvenient for observing the specific mechanisms behind the target phenomena because of the compression of the information. Therefore, we previously proposed a method capable of approximating any nonlocal interactions by a reaction-diffusion system with auxiliary factors (Ninomiya et al., J Math Biol 75:1203-1233, 2017). In this paper, we provide an explicit method for determining the parameters of the reaction-diffusion system for the given kernel shape by using Jacobi polynomials under appropriate assumptions. We additionally introduce a numerical method to specify the parameters of the reaction-diffusion system with the general diffusion coefficients by the Tikhonov regularization. [ABSTRACT FROM AUTHOR]

This paper proposes a differential equation model of the human vision system. Our model has a hierarchical structure in the known retinal cell neural network, and hence, enable to explain what aspects of behaviors of the vision system is affected by which parameters. As the result, our model possesses the following two characteristics: First, it enable the derivation of an integral equation model with a Mexican-hat shape kernel as a necessary result of mechanisms (reduction of the retinal image resolution and a self-control mechanism formed by non-local interaction), in contrast to previous models that assumed various types of Mexican-hat shapes a priori. Second, it can explain two mutually contradicting phenomena called lightness contrast and assimilation. Moreover, our model explains the reason why lightness optical illusions do or do not occur via the magnitude of a control parameter. [ABSTRACT FROM AUTHOR]

Recent years have seen the introduction of non-local interactions in various fields. A typical example of a non-local interaction is where the convolution kernel incorporates short-range activation and long-range inhibition. This paper presents the relationship between non-local interactions and reaction-diffusion systems in the following sense: (a) the relationship between the instability induced by non-local interaction and diffusion-driven instability; (b) the realization of non-local interactions by reaction-diffusion systems. More precisely, it is shown that the non-local interaction of a Mexican-hat kernel destabilizes the stable homogeneous state and that this instability is related to diffusion-driven instability. Furthermore, a reaction-diffusion system that approximates the non-local interaction system with any even convolution kernel is shown to exist. [ABSTRACT FROM AUTHOR]

Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange-Dirac mechanical systems provide a broad category of mathematical models that are closed under interconnection, and in this paper, we develop a framework for the interconnection of discrete Lagrange-Dirac mechanical systems, with a view toward constructing geometric structure-preserving discretizations of interconnected systems. This work builds on previous work on the interconnection of continuous Lagrange-Dirac systems (Jacobs and Yoshimura in J Geom Mech 6(1):67-98, 2014) and discrete Dirac variational integrators (Leok and Ohsawa in Found Comput Math 11(5), 529-562, 2011). We test our results by simulating some of the continuous examples given in Jacobs and Yoshimura (2014). [ABSTRACT FROM AUTHOR]

Probabilistic finite state automata (PFSA) have found their applications in diverse systems. This paper presents the construction of an inner-product space structure on a class of PFSA over the real field via an algebraic approach. The vector space is constructed in a stationary setting, which eliminates the need for an initial state in the specification of PFSA. This algebraic model formulation avoids any reference to the related notion of probability measures induced by a PFSA. A formal language-theoretic and symbolic modeling approach is adopted. Specifically, semantic models are constructed in the symbolic domain in an algebraic setting. Applicability of the theoretical formulation has been demonstrated on experimental data for robot motion recognition in a laboratory environment. [ABSTRACT FROM AUTHOR]

An important research area in life sciences is devoted to modeling, prediction, and dynamics of gene-expression patterns. As clearly understood in these days, this enterprise cannot become satisfactory without acknowledging the role of the environment. To a representation of past, present, and most likely future states, we also encounter measurement errors and uncertainties. This paper surveys and improves recent advances in understanding the foundations and interdisciplinary implications of the newly introduced gene–environment networks, and it integrates the important theme of carbon dioxide emission reduction into the networks and dynamics. We also introduce some operational and managerial issues of practical working and decision making, expressed in terms of sliding windows, quadrants ( modules) of parametric effects, and navigating ( controlling) between such effects and directing them. Given data from DNA microarray experiments and environmental records, we extract nonlinear ordinary differential equations that contain parameters that have to be determined. For this, we employ modern (Chebychevian) approximation and (generalized semi-infinite) optimization. After this is provided, time- discretized dynamical systems are studied. A combinatorial algorithm with polyhedra sequences allows to detect the region of parametric stability. Finally, we analyze the topological landscape of gene–environment networks with its structural (in)stability. By embedding as a module and investigating CO2 emission control and figuring out game theoretical aspects, we conclude. This pioneering work is theoretically elaborated, practically devoted to health care, medicine, education, living conditions, and environmental protection, and it invites the readers to future research. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel eigenface-based face recognition approach. First we describe a continuous model for facial feature extraction, involving the covariance operator associated with gradient of the 2-D image function. Then we provide a discretized version of this model. Face identification and verification procedures, using a supervised classification technique, are also proposed. [ABSTRACT FROM AUTHOR]

This paper describes a new algorithm for policy evaluation for Markov decision processes (MDP) that possess a quasi birth-death structure. The proposed algorithm is based on matrix analytic methods which use probabilistic concepts associated with restricting the underlying Markov process to certain state subsets. A telecommunications application example shows that the method offers significant computational reduction compared to a standard MDP policy evaluation approach. [ABSTRACT FROM AUTHOR]

Depending on a field study for one of the largest iron and paints warehouses in Egypt, this paper presents a new multi-item periodic review inventory model considering the refunding quantity cost. Through this field study, we found that the inventory level is monitored periodically at equal time intervals. Returning a part of the goods that were previously ordered is permitted. Also, a shortage is permissible to occur despite having orders, and it is a combination of the backorder and lost sales. This model has been applied in both crisp and fuzzy environments since the fuzzy case is more suitable for real-life than crisp. The Lagrange multiplier technique is used for solving the restricted mathematical model. Here, the demand is a random variable that follows the normal distribution with zero lead-time. Finally, the model is followed by a real application to clarify the model and prove its efficiency. [ABSTRACT FROM AUTHOR]

In living organisms, cascades of covalent modification cycles are one of the major intracellular signaling mechanisms, allowing to transduce physical or chemical stimuli of the external world into variations of activated biochemical species within the cell. In this paper, we develop a novel method to study the stimulus-response of signaling cascades and overall the concept of pathway activation profile which is, for a given stimulus, the sequence of activated proteins at each tier of the cascade. Our approach is based on a correspondence that we establish between the stationary states of a cascade and pieces of orbits of a 2D discrete dynamical system. The study of its possible phase portraits in function of the biochemical parameters, and in particular of the contraction/expansion properties around the fixed points of this discrete map, as well as their bifurcations, yields a classification of the cascade tiers into three main types, whose biological impact within a signaling network is examined. In particular, our approach enables to discuss quantitatively the notion of cascade amplification/attenuation from this new perspective. The method allows also to study the interplay between forward and 'retroactive' signaling, i.e., the upstream influence of an inhibiting drug bound to the last tier of the cascade. [ABSTRACT FROM AUTHOR]

In this paper we present a generalization of the classical bitangential Nevanlinna-Pick theory in which one bounds not the norm of the interpolating functions but their structured singular value This work was motivated by some problems arising in robust control of systems with structured uncertainty. This approach is based on the commutant lifting theory of Sz.-Nagy and Foias (1968) and extends previous work of Bercovici, Foias and Tannenbaum (1990) on structured matrix Nevanlinna-Pick interpolation. [ABSTRACT FROM AUTHOR]

The paper deals with terrestrial locomotion systems. Worms and snakes are living paragons for the development of biological inspired crawling robots. We set up certain models of worm- and snake-like locomotion systems and present purely analytical investigations in this paper. We try to follow an analytical framework, i.e., analyzing kinematics at first. Later on, we switch to dynamics and control of these models, to get hints for a technical development. The systems are modeled as chains of mass points. The mass points are interconnected via massless links with time-varying link-length. In contrast to the literature, the snake systems exhibit passive joints, but active links and rotatable skids. The combination of shape variation (via active links) together with the ground contact (via ideal spikes guaranteeing a one-sided velocity restriction) results in a global movement of the systems — undulatory locomotion. In dynamics, these link functions should be adjusted via, e.g., a force actuator between each mass point. Because it is impossible to determine a-priori these force outputs generating a desired gait, we apply an adaptive controller which adjusts these force outputs on-line on its own and λ -tracks a certain gait to achieve a movement of the whole system. [ABSTRACT FROM AUTHOR]

In this paper, we consider global stability for an anthrax model with distributed delay. The model incorporates vaccination and carcass disposal. The basic reproduction number of the anthrax model is derived, which completely determine the stability of equilibria. By using the direct Lyapunov method and constructing appropriate Lyapunov functional, the global stability for the anthrax epidemic model with distributed delay is investigated. It is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than one, and the unique endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than one. In addition, numerical simulation results are presented to demonstrate the analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, we present a fractional model of interacting phytoplankton species in which one species produces chemical which is stimulatory in nature to the other species. We study existence, uniqueness, permanence, persistence and stability of the solution. We introduce a new method to prove permanence and persistence, which may be applicable to several ecological models of fractional order. At the end we propose a discritization method and perform some numerical simulations to validate our analytical findings. [ABSTRACT FROM AUTHOR]

The building industry is becoming very important in sustainable development. The recently developed policies in European Union directives on energy and their transposition to Spanish regulations make the Energy Performance Certification process for buildings mandatory. Two software tools have been developed in Spain to carry out this process: Lider and Calener. These software tools have been used in this paper to simulate energy performance in new semidetached houses after taking into account the thermal envelope of the building and facilities. This has been done in different climatic zones in Spain and for all the possible energy ratings. Based on the energy rating and construction cost variables, it has been possible to obtain mathematical models that explain the behaviour of global costs of buildings based on energy ratings and climatic zones. Depreciation costs, maintenance costs, energy consumption and CO2emissions during the service life of a house have also been modelled. [ABSTRACT FROM AUTHOR]

This paper studies some problems related to the stability and the spectral radius of a finite set of matrices. A seasonal epidemic model is given to illustrate the use of the obtained results. In this example, the relationship between the obtained results and the stability of a discrete time periodic linear system is obtained. [ABSTRACT FROM PUBLISHER]

This paper proposes an identification method for estimating the parameters of a stable second-order system based on the impulse response experiment. From the impulse response experiment, the measured data are collected for implementing parameter estimation. By defining and minimizing a cost function, a Newton iterative algorithm is derived for estimating the parameters of the system. The multi-point identification method is used to show the effectiveness of the proposed Newton iterative algorithm. The results show that the estimated model by the proposed Newton iterative estimation method has higher accuracy. Based on the estimated model, a design method of the proportional derivative controller is presented according to the system dynamical performance. The simulation test shows that the proposed controller design method can meet the desired dynamic specifications. [ABSTRACT FROM AUTHOR]

Bregman iterative algorithms have been extensively used forand total variation regularization problems, allowing to obtain simple, fast and effective algorithms. In this paper, three already-available algorithms for geosounding inversion are modified by including them in a Bregman iterative procedure. The resulting algorithms are easy to implement and do not require any optimization package. Modelling results are presented for synthetic and field data, observing better convergence properties than the original versions, avoiding the need of any continuation descent procedure. [ABSTRACT FROM AUTHOR]

Human habitat connectivity, movement rates, and spatial heterogeneity have tremendous impact on malaria transmission. In this paper, a deterministic system of differential equations for malaria transmission incorporating human movements and the development of drug resistance malaria in an $$n$$ patch system is presented. The disease-free equilibrium of the model is globally asymptotically stable when the associated reproduction number is less than unity. For a two patch case, the boundary equilibria (drug sensitive-only and drug resistance-only boundary equilibria) when there is no movement between the patches are shown to be locally asymptotically stable when they exist; the co-existence equilibrium is locally asymptotically stable whenever the reproduction number for the drug sensitive malaria is greater than the reproduction number for the resistance malaria. Furthermore, numerical simulations of the connected two patch model (when there is movement between the patches) suggest that co-existence or competitive exclusion of the two strains can occur when the respective reproduction numbers of the two strains exceed unity. With slow movement (or low migration) between the patches, the drug sensitive strain dominates the drug resistance strain. However, with fast movement (or high migration) between the patches, the drug resistance strain dominates the drug sensitive strain. [ABSTRACT FROM AUTHOR]

Vendor–retailer collaboration has an important role in supply chain management. Although vendor–retailer collaboration results in better supply chain profit, collaboration is difficult to realize. This is because most vendors and retailers try to optimize their own profit. This paper applies the Stackelberg game with stochastic demand for the vendor–retailer system. The vendor as a leader determines the product price, and the retailer decides order quantity and frequency of price markdown. This study develops example and sensitivity analyses to illustrate the theory. Results show that the price markdown option has a better total supply chain profit than without a price markdown policy, and the vendor receives more benefit. For different demand variances, the retailer profit is more sensitive than the vendor profit. [ABSTRACT FROM AUTHOR]