Now showing items 38-57 of 194

• #### Data aggregation in wireless sensor networks with minimum delay and minimum use of energy: A comparative study

The 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.
• #### Data-driven selection and parameter estimation for DNA methylation mathematical models

Epigenetics 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 method

This 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 meshes

We 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 cell-cytotoxic T lymphocyte interaction

Dendritic 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 antigen-presenting DC. However, the success of DC-based immunotherapeutic treatment of human cancer, for example, is still limited because the details of the regulation and kinetics of the DC-CTL 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 DC-induced CTL responses. The model integrates a predator-prey-type interaction of DC and CTL with the non-linear compartmental dynamics of T cells. We found that T cell receptor avidity, the half-life of DC, and the rate of CTL-mediated DC-elimination are the major control parameters for optimal DC-induced 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 DC-based immunotherapy.

• #### The diffusion-driven instability and complexity for a single-handed discrete Fisher equation

For 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 diffusion-driven instability/Turing instability for a single-handed discrete Fisher equation with the Neumann boundary conditions may occur and a series of 2-periodic patterns have been observed. Motivated by these pattern formations, the existence of 2-periodic 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 equations

In 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 $q-1, q \geq 1$, 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 application

We 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 problems

This 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 Caputo-type conditions are given away from the origin.
• #### DOMestic Energy Systems and Technologies InCubator (DOMESTIC) and indoor air quality of the built environment

Oral 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 Self-Dual Codes from Group Rings over Frobenius Rings

In this work, we describe a double bordered construction of self-dual 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 self-dual codes of lengths 64, 68 and 80; the new codes and their corresponding weight enumerators are listed in several tables
• #### A Dufort-Frankel Difference Scheme for Two-Dimensional Sine-Gordon Equation

A standard Crank-Nicolson finite-difference scheme and a Dufort-Frankel finite-difference scheme are introduced to solve two-dimensional damped and undamped sine-Gordon equations. The stability and convergence of the numerical methods are considered. To avoid solving the nonlinear system, the predictor-corrector 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 Gierer-Meinhardt system on an evolving domain

The main purpose of the current paper is to contribute towards the comprehension of the dynamics of the shadow system of a singular Gierer-Meinhardt 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 Gierer-Meinhardt model is reduced to a single though non-local equation whose dynamics is thoroughly investigated throughout the manuscript. The main focus is on the derivation of blow-up results for this non-local equation, which can be interpreted as instability patterns of the shadow system. In particular, a diffusion-driven instability (DDI), or Turing instability, in the neighbourhood of a constant stationary solution, which then is destabilised via diffusion-driven blow-up, is observed. The latter indicates the formation of some unstable patterns, whilst some stability results of global-in-time solutions towards non-constant 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.
• #### Edge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes

For the case of approximation of convection–diffusion equations using piecewise affine continuous finite elements a new edge-based 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.
• #### Entropy-driven cell decision-making predicts "fluid-to-solid" transition in multicellular systems

Cellular 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 spatio-temporal 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 epithelial-mesenchymal 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 LEUP-driven migration/resting and migration/proliferation plasticity on the corresponding multicellular spatiotemporal dynamics with a stochastic cell-based mathematical model for the spatio-temporal dynamics of the cell phenotypes. In the case of the go or rest plasticity, a corresponding mean-field 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 LEUP-driven cell decisions.
• #### Error estimates of high-order numerical methods for solving time fractional partial differential equations

Error estimates of some high-order numerical methods for solving time fractional partial differential equations are studied in this paper. We first provide the detailed error estimate of a high-order numerical method proposed recently by Li et al. \cite{liwudin} for solving time fractional partial differential equation. We prove that this method has the convergence order $O(\tau^{3- \alpha})$ for all $\alpha \in (0, 1)$ when the first and second derivatives of the solution are vanish at $t=0$, where $\tau$ is the time step size and $\alpha$ is the fractional order in the Caputo sense. We then introduce a new time discretization method for solving time fractional partial differential equations, which has no requirements for the initial values as imposed in Li et al. \cite{liwudin}. We show that this new method also has the convergence order $O(\tau^{3- \alpha})$ for all $\alpha \in (0, 1)$. The proofs of the error estimates are based on the energy method developed recently by Lv and Xu \cite{lvxu}. We also consider the space discretization by using the finite element method. Error estimates with convergence order $O(\tau^{3- \alpha} + h^2)$ are proved in the fully discrete case, where $h$ is the space step size. Numerical examples in both one- and two-dimensional cases are given to show that the numerical results are consistent with the theoretical results.
• #### Error estimates of a high order numerical method for solving linear fractional differential equations

In this paper, we first introduce an alternative proof of the error estimates of the numerical methods for solving linear fractional differential equations proposed in Diethelm [6] where a first-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and the convergence order of the proposed numerical method is O(∆t 2−α ), 0 < α < 1, where α is the order of the fractional derivative and ∆t is the step size. We then use the similar idea to prove the error estimates of a high order numerical method for solving linear fractional differential equations proposed in Yan et al. [37], where a second-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and we show that the convergence order of the numerical method is O(∆t 3−α ), 0 < α < 1. The numerical examples are given to show that the numerical results are consistent with the theoretical results.
• #### Existence and regularity of solution for a Stochastic CahnHilliard / Allen-Cahn equation with unbounded noise diffusion

The Cahn-Hilliard/Allen-Cahn equation with noise is a simpliﬁed mean ﬁeld model of stochastic microscopic dynamics associated with adsorption and desorption-spin ﬂip mechanisms in the context of surface processes. For such an equation we consider a multiplicative space-time white noise with diﬀusion coeﬃcient of linear growth. Applying technics from semigroup theory, we prove local existence and uniqueness in dimensions d = 1,2,3. Moreover, when the diﬀusion coeﬃcient satisﬁes a sub-linear growth condition of order α bounded by 1 3, which is the inverse of the polynomial order of the nonlinearity used, we prove for d = 1 global existence of solution. Path regularity of stochastic solution, depending on that of the initial condition, is obtained a.s. up to the explosion time. The path regularity is identical to that proved for the stochastic Cahn-Hilliard equation in the case of bounded noise diﬀusion. Our results are also valid for the stochastic Cahn-Hilliard equation with unbounded noise diﬀusion, for which previous results were established only in the framework of a bounded diﬀusion coeﬃcient. As expected from the theory of parabolic operators in the sense of Petrovsk˘ıı, the bi-Laplacian operator seems to be dominant in the combined model.
• #### Existence of time periodic solutions for a class of non-resonant discrete wave equations

In this paper, a class of discrete wave equations with Dirichlet boundary conditions are obtained by using the center-difference method. For any positive integers m and T, when the existence of time mT-periodic solutions is considered, a strongly indefinite discrete system needs to be established. By using a variant generalized weak linking theorem, a non-resonant superlinear (or superquadratic) result is obtained and the Ambrosetti-Rabinowitz condition is improved. Such a method cannot be used for the corresponding continuous wave equations or the continuous Hamiltonian systems; however, it is valid for some general discrete Hamiltonian systems.