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Concerning periodic solutions to nonlinear discrete Volterra equations with finite memoryIn this paper we discuss the existence of periodic solutions of discrete (and discretized) nonlinear Volterra equations with finite memory. The literature contains a number of results on periodic solutions of non linear Volterra integral equations with finite memory, of a type that arises in biomathematics. The “summation” equations studied here can arise as discrete models in their own right but are (as we demonstrate) of a type that arise from the discretization of such integral equations. Our main results are in two parts: (i) results for discrete equations and (ii) consequences for quadrature methods applied to integral equations. The first set of results are obtained using a variety of fixed point theorems. The second set of results address the preservation of properties of integral equations on discretizing them. An expository style is adopted and examples are given to illustrate the discussion.

Constructing SelfDual Codes from Group Rings and Reverse Circulant MatricesIn this work, we describe a construction for selfdual codes in which we employ group rings and reverse circulant matrices. By applying the construction directly over different alphabets, and by employing the well known extension and neighbor methods we were able to obtain extremal binary selfdual codes of different lengths of which some have parameters that were not known in the literature before. In particular, we constructed three new codes of length 64, twentytwo new codes of length 68, twelve new codes of length 80 and four new codes of length 92.

Constructions for SelfDual Codes Induced from Group RingsIn this work, we establish a strong connection between group rings and selfdual codes. We prove that a group ring element corresponds to a selfdual code if and only if it is a unitary unit. We also show that the doublecirculant and fourcirculant constructions come from cyclic and dihedral groups, respectively. Using groups of order 8 and 16 we find many new construction methods, in addition to the wellknown methods, for selfdual codes. We establish the relevance of these new constructions by finding many extremal binary selfdual codes using them, which we list in several tables. In particular, we construct 10 new extremal binary selfdual codes of length 68.

CrankNicolson finite element discretizations for a twodimenional linear Schroedingertype equation posed in noncylindrical domainMotivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography, we consider an initialand boundaryvalue problem for a general Schr¨odingertype equation posed on a two spacedimensional noncylindrical domain with mixed boundary conditions. The problem is transformed into an equivalent one posed on a rectangular domain, and we approximate its solution by a Crank–Nicolson finite element method. For the proposed numerical method, we derive an optimal order error estimate in the L2 norm, and to support the error analysis we prove a global elliptic regularity theorem for complex elliptic boundary value problems with mixed boundary conditions. Results from numerical experiments are presented which verify the optimal order of convergence of the method.

Data aggregation in wireless sensor networks with minimum delay and minimum use of energy: A comparative studyThe prime objective of deploying large scale wireless sensor networks is to collect information from to control systems associated with these networks. Wireless sensor networks are widely used in application domains such as security and inspection, environmental monitoring, warfare, and other situations especially where immediate responses are required such as disasters and medical emergency. Whenever there is a growth there are challenges and to cope with these challenges strategies and solutions must be developed. This paper discusses the recently addressed issues of data aggregation through presenting a comparative study of different research work done on minimizing delay in different structures of wireless sensor networks. Finally we introduce our proposed method to minimize both delay and power consumption using a tree based clustering scheme with partial data aggregation.

Datadriven selection and parameter estimation for DNA methylation mathematical modelsEpigenetics is coming to the fore as a key process which underpins health. In particular emerging experimental evidence has associated alterations to DNA methylation status with healthspan and aging. Mammalian DNA methylation status is maintained by an intricate array of biochemical and molecular processes. It can be argued changes to these fundamental cellular processes ultimately drive the formation of aberrant DNA methylation patterns, which are a hallmark of diseases, such as cancer, Alzheimer's disease and cardiovascular disease. In recent years mathematical models have been used as e ective tools to help advance our understanding of the dynamics which underpin DNA methylation. In this paper we present linear and nonlinear models which encapsulate the dynamics of the molecular mechanisms which de ne DNA methylation. Applying a recently developed Bayesian algorithm for parameter estimation and model selection, we are able to estimate distributions of parameters which include nominal parameter values. Using limited noisy observations, the method also identifed which methylation model the observations originated from, signaling that our method has practical applications in identifying what models best match the biological data for DNA methylation.

Detailed error analysis for a fractional Adams methodThis preprint discusses a method for a numerical solution of a nonlinear fractional differential equation, which can be seen as a generalisation of the Adams–Bashforth–Moulton scheme.

Detailed error analysis for a fractional adams method with graded meshesWe consider a fractional Adams method for solving the nonlinear fractional differential equation $\, ^{C}_{0}D^{\alpha}_{t} y(t) = f(t, y(t)), \, \alpha >0$, equipped with the initial conditions $y^{(k)} (0) = y_{0}^{(k)}, k=0, 1, \dots, \lceil \alpha \rceil 1$. Here $\alpha$ may be an arbitrary positive number and $ \lceil \alpha \rceil$ denotes the smallest integer no less than $\alpha$ and the differential operator is the Caputo derivative. Under the assumption $\, ^{C}_{0}D^{\alpha}_{t} y \in C^{2}[0, T]$, Diethelm et al. \cite[Theorem 3.2]{dieforfre} introduced a fractional Adams method with the uniform meshes $t_{n}= T (n/N), n=0, 1, 2, \dots, N$ and proved that this method has the optimal convergence order uniformly in $t_{n}$, that is $O(N^{2})$ if $\alpha > 1$ and $O(N^{1\alpha})$ if $\alpha \leq 1$. They also showed that if $\, ^{C}_{0}D^{\alpha}_{t} y(t) \notin C^{2}[0, T]$, the optimal convergence order of this method cannot be obtained with the uniform meshes. However, it is well known that for $y \in C^{m} [0, T]$ for some $m \in \mathbb{N}$ and $ 0 < \alpha 1$, we show that the optimal convergence order of this method can be recovered uniformly in $t_{n}$ even if $\, ^{C}_{0}D^{\alpha}_{t} y$ behaves as $t^{\sigma}, 0< \sigma <1$. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

Determining control parameters for dendritic cellcytotoxic T lymphocyte interactionDendritic cells (DC) are potent immunostimulatory cells facilitating antigen transport to lymphoid tissues and providing efficient stimulation of T cells. A series of experimental studies in mice demonstrated that cytotoxic T lymphocytes (CTL) can be efficiently induced by adoptive transfer of antigenpresenting DC. However, the success of DCbased immunotherapeutic treatment of human cancer, for example, is still limited because the details of the regulation and kinetics of the DCCTL interaction are not yet completely understood. Using a combination of experimental mouse studies, mathematical modeling, and nonlinear parameter estimation, we analyzed the population dynamics of DCinduced CTL responses. The model integrates a predatorpreytype interaction of DC and CTL with the nonlinear compartmental dynamics of T cells. We found that T cell receptor avidity, the halflife of DC, and the rate of CTLmediated DCelimination are the major control parameters for optimal DCinduced CTL responses. For induction of high avidity CTL, the number of adoptively transferred DC was of minor importance once a minimal threshold of approximately 200 cells per spleen had been reached. Taken together, our study indicates that the availability of high avidity T cells in the recipient in combination with the optimal application regimen is of prime importance for successful DCbased immunotherapy.

Developing A Highperformance Liquid Chromatography Method for Simultaneous Determination of Loratadine and its Metabolite Desloratadine in Human Plasma.Allergic diseases are considered among the major burdons of public health with increased prevalence globally. Histamine H1receptor antagonists are the foremost commonly used drugs in the treatment of allergic disorders. Our target drug is one of this class, loratadine and its biometabolite desloratadine which is also a non sedating H1 receptor antagonist with antihistaminic action of 2.5 to 4 times greater than loratadine. To develop and validate a novel isocratic reversedphase high performance liquid chromatography (RPHPLC) method for rapid and simultaneous separation and determination of loratadine and its metabolite, desloratadine in human plasma. The drug extraction method from plasma was based on protein precipitation technique. The separation was carried out on a Thermo Scientific BDS Hypersil C18 column (5µm, 250 x 4.60 mm) using a mobile phase of MeOH : 0.025M KH2PO4 adjusted to pH 3.50 using orthophosphoric acid (85 : 15, v/v) at ambient temperature. The flow rate was maintained at 1 mL/min and maximum absorption was measured using PDA detector at 248 nm. The retention times of loratadine and desloratadine in plasma samples were recorded to be 4.10 and 5.08 minutes respectively, indicating a short analysis time. Limits of detection were found to be 1.80 and 1.97 ng/mL for loratadine and desloratadine, respectively, showing a high degree of method sensitivity. The method was then validated according to FDA guidelines for the determination of the two analytes in human plasma. The results obtained indicate that the proposed method is rapid, sensitive in the nanogram range, accurate, selective, robust and reproducible compared to other reported methods. [Abstract copyright: Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.net.]

The diffusiondriven instability and complexity for a singlehanded discrete Fisher equationFor a reaction diffusion system, it is well known that the diffusion coefficient of the inhibitor must be bigger than that of the activator when the Turing instability is considered. However, the diffusiondriven instability/Turing instability for a singlehanded discrete Fisher equation with the Neumann boundary conditions may occur and a series of 2periodic patterns have been observed. Motivated by these pattern formations, the existence of 2periodic solutions is established. Naturally, the periodic double and the chaos phenomenon should be considered. To this end, a simplest two elements system will be further discussed, the flip bifurcation theorem will be obtained by computing the center manifold, and the bifurcation diagrams will be simulated by using the shooting method. It proves that the Turing instability and the complexity of dynamical behaviors can be completely driven by the diffusion term. Additionally, those effective methods of numerical simulations are valid for experiments of other patterns, thus, are also beneficial for some application scientists.

Discontinuous Galerkin time stepping method for solving linear space fractional partial differential equationsIn this paper, we consider the discontinuous Galerkin time stepping method for solving the linear space fractional partial differential equations. The space fractional derivatives are defined by using Riesz fractional derivative. The space variable is discretized by means of a Galerkin finite element method and the time variable is discretized by the discontinuous Galerkin method. The approximate solution will be sought as a piecewise polynomial function in $t$ of degree at most $q1, q \geq 1$, which is not necessarily continuous at the nodes of the defining partition. The error estimates in the fully discrete case are obtained and the numerical examples are given.

A discrete mutualism model: analysis and exploration of a financial applicationWe perform a stability analysis on a discrete analogue of a known, continuous model of mutualism. We illustrate how the introduction of delays affects the asymptotic stability of the system’s positive nontrivial equilibrium point. In the second part of the paper we explore the insights that the model can provide when it is used in relation to interacting financial markets. We also note the limitations of such an approach.

Distributed order equations as boundary value problemsThis preprint discusses the existence and uniqueness of solutions and proposes a numerical method for their approximation in the case where the initial conditions are not known and, instead, some Caputotype conditions are given away from the origin.

DOMestic Energy Systems and Technologies InCubator (DOMESTIC) and indoor air quality of the built environmentOral presentation at RMetS Students and Early Career Scientists Conference 2020 on research project DOMESTIC (DOMestic Energy Systems and Technologies InCubator), which aims to build a facility for the demonstration of domestic technologies and design methodologies (i.e. air quality, energy efficiency).

Double Bordered Constructions of SelfDual Codes from Group Rings over Frobenius RingsIn this work, we describe a double bordered construction of selfdual codes from group rings. We show that this construction is effective for groups of order 2p where p is odd, over the rings F2 + uF2 and F4 + uF4. We demonstrate the importance of this new construction by finding many new binary selfdual codes of lengths 64, 68 and 80; the new codes and their corresponding weight enumerators are listed in several tables

A DufortFrankel Difference Scheme for TwoDimensional SineGordon EquationA standard CrankNicolson finitedifference scheme and a DufortFrankel finitedifference scheme are introduced to solve twodimensional damped and undamped sineGordon equations. The stability and convergence of the numerical methods are considered. To avoid solving the nonlinear system, the predictorcorrector techniques are applied in the numerical methods. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

Dynamics of shadow system of a singular GiererMeinhardt system on an evolving domainThe main purpose of the current paper is to contribute towards the comprehension of the dynamics of the shadow system of a singular GiererMeinhardt model on an isotropically evolving domain. In the case where the inhibitor's response to the activator's growth is rather weak, then the shadow system of the GiererMeinhardt model is reduced to a single though nonlocal equation whose dynamics is thoroughly investigated throughout the manuscript. The main focus is on the derivation of blowup results for this nonlocal equation, which can be interpreted as instability patterns of the shadow system. In particular, a diffusiondriven instability (DDI), or Turing instability, in the neighbourhood of a constant stationary solution, which then is destabilised via diffusiondriven blowup, is observed. The latter indicates the formation of some unstable patterns, whilst some stability results of globalintime solutions towards nonconstant steady states guarantee the occurrence of some stable patterns. Most of the theoretical results are verified numerically, whilst the numerical approach is also used to exhibit the dynamics of the shadow system when analytical methods fail.

Edgebased nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic fluxcorrection schemesFor the case of approximation of convection–diffusion equations using piecewise affine continuous finite elements a new edgebased nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

Entropydriven cell decisionmaking predicts "fluidtosolid" transition in multicellular systemsCellular decision making allows cells to assume functionally different phenotypes in response to microenvironmental cues, with or without genetic change. It is an open question, how individual cell decisions influence the dynamics at the tissue level. Here, we study spatiotemporal pattern formation in a population of cells exhibiting phenotypic plasticity, which is a paradigm of cell decision making. We focus on the migration/resting and the migration/proliferation plasticity which underly the epithelialmesenchymal transition (EMT) and the go or grow dichotomy. We assume that cells change their phenotype in order to minimize their microenvironmental entropy following the LEUP (Least microEnvironmental Uncertainty Principle) hypothesis. In turn, we study the impact of the LEUPdriven migration/resting and migration/proliferation plasticity on the corresponding multicellular spatiotemporal dynamics with a stochastic cellbased mathematical model for the spatiotemporal dynamics of the cell phenotypes. In the case of the go or rest plasticity, a corresponding meanfield approximation allows to identify a bistable switching mechanism between a diffusive (fluid) and an epithelial (solid) tissue phase which depends on the sensitivity of the phenotypes to the environment. For the go or grow plasticity, we show the possibility of Turing pattern formation for the "solid" tissue phase and its relation with the parameters of the LEUPdriven cell decisions.