Constructive effects of diversity in a multi-neuron model of the homeostatic regulation of the sleep–wake cycle

As an instance of diversity-induced resonance and of the constructive role of heterogeneity in complex systems, here we study a generalized version of a physiologically-motivated sleep–wake cycle model taking into account the role of orexin [Patriarca et al. (2012) [16]; Postnova et al. (2009) [9]]. With respect to the versions of the model studied previously, here we consider systems containing both a set of orexin neurons — responsible for the production of orexin — and a set of glutaminergic neurons — representing mental activity or sleep depending on their firing or silent state, respectively — within some basic network topologies. The neurons of one or both types are diversified and it is shown how the interplay between the heterogeneous constituent units produces as an emergent effect the recovering or improving of the sleep-wake cycle. At a general level, the results obtained suggest that also systems with a dynamics driven by a homeostatic mechanism, with a time scale much longer than that of the constituent excitable units, may present diversity-induced resonance.     

Nonlinear features in protein circuitry

The noise involved in protein circuit can result in fluctuations in protein concentrations. Then we have explored the effect of such noise on the feedback loop between p53 and its repressor Mdm2, the negative feedback dynamics and oscillatory activities are presented. Recent experimental results show that under certain conditions, the activity of the average protein level of p53 behaves with dampened oscillation in response to DNA damage, and it has non-decaying oscillatory behavior in individual cells, and we show that the dampening is induced by intrinsic noise, namely the uncertainty associated with chemical kinetics in dealing with when and in what order reactions take place in the p53 system. Furthermore, the experimental results are reproduced in this paper.     

Extinction and stability of an impulsive system with pure delays

In this paper, we consider an impulsive competitive system with infinite delays and investigate the extinction and stability of the system. For the corresponding impulsive logistic model, our stability conditions are weaker than those of Yang et al. (2011).     

Global attractivity of equilibrium in Gierer–Meinhardt system with activator production saturation and gene expression time delays

In this work we investigate a diffusive Gierer–Meinhardt system with gene expression time delays in the production of activators and inhibitors, and also a saturation in the activator production, which was proposed by Seirin Lee et al. (2010) [10]. We rigorously consider the basic kinetic dynamics of the Gierer–Meinhardt system with saturation. By using an upper and lower solution method, we show that when the saturation effect is strong, the unique constant steady state solution is globally attractive despite the time delays. This result limits the parameter space for which spatiotemporal pattern formation is possible.     

A new discrete dynamical system of signed integer partitions

In Brylawski (1973) Brylawski described the covering property for the domination order on non-negative integer partitions by means of two rules. Recently, in Bisi et al. (in press), Cattaneo et al. (2014), Cattaneo et al. (2015) the two classical Brylawski covering rules have been generalized in order to obtain a new lattice structure in the more general signed integer partition context. Moreover, in Cattaneo et al. (2014), Cattaneo et al. (2015), the covering rules of the above signed partition lattice have been interpreted as evolution rules of a discrete dynamical model of a two-dimensional p–n semiconductor junction in which each positive number represents a distribution of holes (positive charges) located in a suitable strip at the left semiconductor of the junction and each negative number a distribution of electrons (negative charges) in a corresponding strip at the right semiconductor of the junction. In this paper we introduce and study a new sub-model of the above dynamical model, which is constructed by using a single vertical evolution rule. This evolution rule describes the natural annihilation of a hole–electron pair at the boundary region of the two semiconductors. We prove several mathematical properties of such new discrete dynamical model and we provide a discussion of its physical properties.     

Fast performance assessment of IEEE 802.11-based wireless networks

In this paper, we introduce a brand new analytical perspective for analyzing and evaluating the IEEE 802.11-based networks. We identify a tightly-coupled relationship between the number of contending nodes and their contention window sizes in the networks. Based on the relationship, we propose a downsizing model for reducing the computational complexity and for improving the simulation performance in the evaluation of the IEEE 802.11-based networks. We first formally prove that the proposed model preserves the operational characteristics of the original networks in their downsized networks through well-known analytical frameworks, such as the models proposed by Bianchi (2000) [7], Calí et al. (2000) [2], and Hu et al. (2006) [8]. We then demonstrate that the proposed model speeds up the simulation by maximally two orders of magnitude. Even though the simulation shows some difference between the results from an original network and those in its corresponding downsized networks in a wide range of network sizes and traffic patterns, the difference is acceptable since it has minimal values of 1% in most cases and maximum values of 10% in a very few cases. We also present the effectiveness of both the downsizing model and the downsizing-model-based simulation in comparison with other performance models and simulation techniques. As the size and complexity of wireless networks are increasing nowadays, we vision that the new proposed model will be of great advantage in conducting fast and accurate packet-level wireless simulations, as well as being a helpful tool for performing the numerically tractable theoretical studies for extensive performance evaluations, such as determining the network-wide throughput or end-to-end delays.     

Asymptotic behavior of the reaction–diffusion model of plankton allelopathy with nonlocal delays

In this paper, we consider a reaction–diffusion model of plankton allelopathy with nonlocal delays. Using an iterative technique, the global stability of the positive steady state and the semi-trivial steady states of the system is investigated under some weaker conditions than those assumed in Tian et al. [C.R. Tian, L. Zhang and Z. Ling, The stability of a diffusion model of plankton allelopathy with atio-temporal delays, Nonlinear Anal. RWA 10 (2009) 2036–2046]. We also show that toxic substances and nonlocal delays are harmless for the stability of the positive steady state. Finally, some examples are presented to verify our main results.     

Testing the no-treatment effect based on a possibly misspecified accelerated failure time model

The accelerated failure time model is a useful alternative to the Cox proportional hazard model. We investigate whether or not a misspecified accelerated failure time model provides a valid test of the no-treatment effect in randomized clinical trials. We show that the minimum dispersion statistic based on rank regression by Wei et al. (1990) must be modified in order to conduct valid tests under misspecification, whereas the resampling-based methods by Jin et al. (2003) are valid without any modification. Numerical studies are conducted to examine the small sample behavior of the modified minimum dispersion statistic and the resampling-based method. Finally, an illustration is given with a dataset from a clinical trial.     

Analysis of a delayed and diffusive oncolytic M1 virotherapy model with immune response

Oncolytic virotherapy (OVT) is a promising therapeutic approach that uses replication-competent viruses to target and kill tumor cells. Alphavirus M1 is a selective oncolytic virus which showed high efficacy against tumor cells. Wang et al. (2016) studied an ordinary differential equation (ODE) model to verify the potent efficacy of M1 virus. Our purpose is to extend their model to include the effect of time delays and anti-tumor immune response. Also, we assume that all elements of the extended model undergo diffusion in a bounded domain. We study the existence, non-negativity and boundedness of solutions in order to verify the well-posedness of the model. We calculate all possible equilibrium points and determine the threshold conditions required for their existence and stability. These points reflect three different fates for OVT: partial success, complete success, or complete failure. We prove the global asymptotic stability of all equilibrium points by constructing suitable Lyapunov functionals, and verify the corresponding instability conditions. We conduct some numerical simulations to confirm the analytical results and show the crucial role of time delays and immune response in the success of OVT.     

Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model

Infection with HIV-1, degrading the human immune system and recent advances of drug therapy to arrest HIV-1 infection, has generated considerable research interest in the area. Bonhoeffer et al. (1997) [1], introduced a population model representing long term dynamics of HIV infection in response to available drug therapies. We consider a similar type of approximate model incorporating time delay in the process of infection on the healthy T cells which, in turn, implies inclusion of a similar delay in the process of viral replication. The model is studied both analytically and numerically. We also include a similar delay in the killing rate of infected CD4⁺ T cells by Cytotoxic T-Lymphocyte (CTL) and in the stimulation of CTL and analyse two resulting models numerically.The models with no time delay present have two equilibria: one where there is no infection and a non-trivial equilibrium where the infection can persist. If there is no time delay then the non-trivial equilibrium is locally asymptotically stable. Both our analytical results (for the first model) and our numerical results (for all three models) indicate that introduction of a time delay can destabilize the non-trivial equilibrium. The numerical results indicate that such destabilization occurs at realistic time delays and that there is a threshold time delay beneath which the equilibrium with infection present is locally asymptotically stable and above which this equilibrium is unstable and exhibits oscillatory solutions of increasing amplitude.     

A new model transformation method and its application to extending a class of stability criteria of neutral type systems

This paper proposes a generalized equivalent model transformation method, which can include methods proposed by Fridman et al. and Bellen et al., for the stability analysis of a class of neutral type systems. By using the proposed model transformation method, a class of existing stability criteria derived by the Lyapunov functional approach can be extended to less conservative ones in terms of nonlinear matrix inequalities. Furthermore, procedures to solve these nonlinear matrix inequalities are also proposed. Illustrative examples are presented to demonstrate the effectiveness of the proposed model transformation method.     

The wavelet transform method applied to a coupled chaotic system with asymmetric coupling schemes

The wavelet transform method originated by Wei et al. (2002) [19] is an effective tool for enhancing the transverse stability of the synchronous manifold of a coupled chaotic system. Much of the theoretical study on this matter is centered on networks that are symmetrically coupled. However, in real applications, the coupling topology of a network is often asymmetric; see Belykh et al. (2006)  [23], [24], Chavez et al. (2005)  [25], Hwang et al. (2005)  [26], Juang et al. (2007)  [17], and Wu (2003)  [13]. In this work, a certain type of asymmetric sparse connection topology for networks of coupled chaotic systems is presented. Moreover, our work here represents the first step in understanding how to actually control the stability of global synchronization from dynamical chaos for asymmetrically connected networks of coupled chaotic systems via the wavelet transform method. In particular, we obtain the following results. First, it is shown that the lower bound for achieving synchrony of the coupled chaotic system with the wavelet transform method is independent of the number of nodes. Second, we demonstrate that the wavelet transform method as applied to networks of coupled chaotic systems is even more effective and controllable for asymmetric coupling schemes as compared to the symmetric cases.     

Optimal admission control for two station tandem queues with loss

We consider a two-station tandem queue with a buffer size of one at the first station and a finite buffer size at the second station. Silva et al. (2013) gave a criterion determining the optimal admission control policy for this model. In this paper, we improve the results of Silva et al. (2013) and also solve the problem conjectured by Silva et al. (2013).     

Global optimization of multilevel electricity market models including network design and graph partitioning

We consider the combination of a network design and graph partitioning model in a multilevel framework for determining the optimal network expansion and the optimal zonal configuration of zonal pricing electricity markets, which is an extension of the model discussed in Grimm et al. (2019) that does not include a network design problem. The two classical discrete optimization problems of network design and graph partitioning together with nonlinearities due to economic modeling yield extremely challenging mixed-integer nonlinear multilevel models for which we develop two problem-tailored solution techniques. The first approach relies on an equivalent bilevel formulation and a standard KKT transformation thereof including novel primal-dual bound tightening techniques, whereas the second is a tailored generalized Benders decomposition. For the latter, we strengthen the Benders cuts of Grimm et al. (2019) by using the structure of the newly introduced network design subproblem. We prove for both methods that they yield global optimal solutions. Afterward, we compare the approaches in a numerical study and show that the tailored Benders approach clearly outperforms the standard KKT transformation. Finally, we present a case study that illustrates the economic effects that are captured in our model.     

Bifurcation analysis in a model of cytotoxic T-lymphocyte response to viral infections

In this paper, we study the dynamics of a mathematical model on primary and secondary cytotoxic T-lymphocyte (CTL) response to viral infections by Wodarz et al. This model has three equilibria and their stability criteria are discussed. The system transitions from one equilibrium to the next as the basic reproductive number, R₀, increases. When R₀ increases even further, we analytically show that periodic solutions may arise from the third equilibrium via Hopf bifurcation. Numerical simulations of the model agree with the theoretical results and these dynamics occur within biologically realistic parameter range. The normal form theory is also applied to find the amplitude, phase and stability information on the limit cycles. Biological implications of the results are discussed.     

The asymptotic behavior of an inertial alternating proximal algorithm for monotone inclusions

The aim of this paper is to investigate the asymptotic behavior of an inertial alternating algorithm based on the composition of resolvents of monotone operators. The proposed algorithm is a generalization of those proposed in Attouch et al. (2007) [3] and Bauschke et al. (2005) [1]. As a special case, we also recover the classical alternating minimization algorithm (Acker, 1980) [2], which itself is a natural extension of the alternating projection algorithm of von Neumann (1950) [4]. An application to equilibrium problems is also proposed.     

On the visibility in well-behaved random sets in Euclidean space

In Calka et al. (2009), the decay of the probability of reaching distance at least r in some direction from a given point without hitting any ball, in the Poisson Boolean model of continuum percolation, was studied. The methods used in Calka et al. (2009) include coverage techniques, and the most precise results were obtained in dimension 2. In this note, we strengthen some of the results obtained in Calka et al. (2009) to dimension 3 and higher and at the same time extend them to more general random sets.     

Dynamics and steady-state analysis of a consumer-resource model

This paper is concerned with the dynamics of a consumer-resource reaction diffusion model in the heterogeneous environment, proposed by Zhang et al. (2017). We use the comparison principle to improve the ultimate bounds step by step, and show that the unique steady state is globally asymptotically stable if the resources are fully limited uniformly in space and consumer population abundance is homogeneous in space.