• Resolving nanoscopic structuring and interfacial THz dynamics in setting cements

      Song, Fu V.; Yang, Bin; Di Tommaso, Devis; orcid: 0000-0002-4485-4468; Donnan, Robert S.; Chass, Gregory A.; orcid: 0000-0002-5265-6672; Yada, Rickey Y.; Farrar, David H.; Tian, Kun V.; orcid: 0000-0003-0102-0620 (Royal Society of Chemistry (RSC), 2022)
      The setting dynamics of commercial cements were tracked non-destructively by THz spectroscopy probing interfacial dynamics and neutron scattering resolving structural evolutions over 1–30 nm, with trends made comprehensible by computational models.
    • Binary self-dual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search scheme

      Dougherty, Steven; Korban, Adrian; Șahinkaya, Serap; Ustun, Deniz (American Institute of Mathematical Sciences (AIMS), 2022)
      <p style='text-indent:20px;'>We present a generator matrix of the form <inline-formula><tex-math id="M1">\begin{document}$ [ \sigma(v_1) \ | \ \sigma(v_2)] $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}$ v_1 \in RG $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ v_2\in RH $\end{document}</tex-math></inline-formula>, for finite groups <inline-formula><tex-math id="M4">\begin{document}$ G $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ H $\end{document}</tex-math></inline-formula> of order <inline-formula><tex-math id="M6">\begin{document}$ n $\end{document}</tex-math></inline-formula> for constructing self-dual codes and linear complementary dual codes over the finite Frobenius ring <inline-formula><tex-math id="M7">\begin{document}$ R $\end{document}</tex-math></inline-formula>. In general, many of the constructions to produce self-dual codes forces the code to be an ideal in a group ring which implies that the code has a rich automorphism group. Unlike the traditional cases, codes constructed from the generator matrix presented here are not ideals in a group ring, which enables us to find self-dual and linear complementary dual codes that are not found using more traditional techniques. In addition to that, by using this construction, we improve <inline-formula><tex-math id="M8">\begin{document}$ 10 $\end{document}</tex-math></inline-formula> of the previously known lower bounds on the largest minimum weights of binary linear complementary dual codes for some lengths and dimensions. We also obtain <inline-formula><tex-math id="M9">\begin{document}$ 82 $\end{document}</tex-math></inline-formula> new binary linear complementary dual codes, <inline-formula><tex-math id="M10">\begin{document}$ 50 $\end{document}</tex-math></inline-formula> of which are either optimal or near optimal of lengths <inline-formula><tex-math id="M11">\begin{document}$ 41 \leq n \leq 61 $\end{document}</tex-math></inline-formula> which are new to the literature.</p>
    • Numerical methods for Caputo-Hadamard fractional differential equations with graded and non-uniform meshes

      Green, Charles; Liu, Yanzhi; Yan, Yubin; University of Chester; Lvliang University
      We consider the predictor-corrector numerical methods for solving Caputo-Hadamard fractional differential equation with the graded meshes $\log t_{j} = \log a + \big ( \log \frac{t_{N}}{a} \big ) \big ( \frac{j}{N} \big )^{r}, \, j=0, 1, 2, \dots, N$ with $a \geq 1$ and $ r \geq 1$, where $\log a = \log t_{0} < \log t_{1} < \dots < \log t_{N}= \log T$ is a partition of $[\log t_{0}, \log T]$. We also consider the rectangular and trapezoidal methods for solving Caputo-Hadamard fractional differential equation with the non-uniform meshes $\log t_{j} = \log a + \big ( \log \frac{t_{N}}{a} \big ) \frac{j (j+1)}{N(N+1)}, \, j=0, 1, 2, \dots, N$. Under the weak smoothness assumptions of the Caputo-Hadamard fractional derivative, e.g., $\prescript{}{CH}D^\alpha_{a,t}y(t) \notin C^{1}[a, T]$ with $ \alpha \in (0, 2)$, the optimal convergence orders of the proposed numerical methods are obtained by choosing the suitable graded mesh ratio $r \geq 1$. The numerical examples are given to show that the numerical results are consistent with the theoretical findings.
    • Weak convergence of the L1 scheme for a stochastic subdiffusion problem driven by fractionally integrated additive noise

      Hu, Ye; Li, Changpin; Yan, Yubin; University of Chester; Lvliang University; Shanghai University
      The weak convergence of a fully discrete scheme for approximating a stochastic subdiffusion problem driven by fractionally integrated additive noise is studied. The Caputo fractional derivative is approximated by the L1 scheme and the Riemann-Liouville fractional integral is approximated with the first order convolution quadrature formula. The noise is discretized by using the Euler method and the spatial derivative is approximated with the linear finite element method. Based on the nonsmooth data error estimates of the corresponding deterministic problem, the weak convergence orders of the fully discrete schemes for approximating the stochastic subdiffusion problem driven by fractionally integrated additive noise are proved by using the Kolmogorov equation approach. Numerical experiments are given to show that the numerical results are consistent with the theoretical results.
    • A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression

      Hatzikirou, Haralampos; orcid: 0000-0002-1270-7885; email: haralampos.hatzikirou@ku.ac.ae; Kavallaris, Nikos I.; Leocata, Marta; orcid: 0000-0002-5261-3699; email: mleocata@luiss.it (MDPI, 2021-10-09)
      Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. Here, we are interested in stochastic differential equations for which the white noise is nonlinearly integrated into the corresponding evolution term, typically termed as random ordinary differential equations (RODEs). The classical averaging methods fail to treat such RODEs. Therefore, we introduce a novel averaging method appropriate to be applied to a specific class of RODEs. To exemplify the importance of our method, we apply it to an important biomedical problem, in particular, we implement the method to the assessment of intratumoral heterogeneity impact on tumor dynamics. Precisely, we model gliomas according to a well-known Go or Grow (GoG) model, and tumor heterogeneity is modeled as a stochastic process. It has been shown that the corresponding deterministic GoG model exhibits an emerging Allee effect (bistability). In contrast, we analytically and computationally show that the introduction of white noise, as a model of intratumoral heterogeneity, leads to monostable tumor growth. This monostability behavior is also derived even when spatial cell diffusion is taken into account.
    • Oscillatory and stability of a mixed type difference equation with variable coefficients

      Yan, Yubin; Pinelas, Sandra; Ramdani, Nedjem; Yenicerioglu, Ali Fuat; RUDN University; University of Saad Dahleb Blida; Kocaeli University; University of Chester (Inderscience, 2021-08-12)
      The goal of this paper is to study the oscillatory and stability of the mixed type difference equation with variable coefficients \[ \Delta x(n)=\sum_{i=1}^{\ell}p_{i}(n)x(\tau_{i}(n))+\sum_{j=1}^{m}q_{j}(n)x(\sigma_{i}(n)),\quad n\ge n_{0}, \] where $\tau_{i}(n)$ is the delay term and $\sigma_{j}(n)$ is the advance term and they are positive real sequences for $i=1,\cdots,l$ and $j=1,\cdots,m$, respectively, and $p_{i}(n)$ and $q_{j}(n)$ are real functions. This paper generalise some known results and the examples illustrate the results.
    • Spatial Discretization for Stochastic Semi-Linear Subdiffusion Equations Driven by Fractionally Integrated Multiplicative Space-Time White Noise

      Yan, Yubin; Hoult, James; Wang, Junmei; University of Chester; LuLiang University (MDPI, 2021-08-12)
      Spatial discretization of the stochastic semilinear subdiffusion driven by integrated multiplicative space-time white noise is considered. The spatial discretization scheme discussed in Gy\"ongy \cite{gyo_space} and Anton et al. \cite{antcohque} for stochastic quasi-linear parabolic partial differential equations driven by multiplicative space-time noise is extended to the stochastic subdiffusion. The nonlinear terms $f$ and $\sigma$ satisfy the global Lipschitz conditions and the linear growth conditions. The space derivative and the integrated multiplicative space-time white noise are discretized by using finite difference methods. Based on the approximations of the Green functions which are expressed with the Mittag-Leffler functions, the optimal spatial convergence rates of the proposed numerical method are proved uniformly in space under the suitable smoothness assumptions of the initial values.
    • Error estimates of a continuous Galerkin time stepping method for subdiffusion problem

      Yan, Yubin; Yan, Yuyuan; Liang, Zongqi; Egwu, Bernard; Jimei University; University of Chester (Springer, 2021-07-29)
      A continuous Galerkin time stepping method is introduced and analyzed for subdiffusion problem in an abstract setting. The approximate solution will be sought as a continuous piecewise linear function in time $t$ and the test space is based on the discontinuous piecewise constant functions. We prove that the proposed time stepping method has the convergence order $O(\tau^{1+ \alpha}), \, \alpha \in (0, 1)$ for general sectorial elliptic operators for nonsmooth data by using the Laplace transform method, where $\tau$ is the time step size. This convergence order is higher than the convergence orders of the popular convolution quadrature methods (e.g., Lubich's convolution methods) and L-type methods (e.g., L1 method), which have only $O(\tau)$ convergence for the nonsmooth data. Numerical examples are given to verify the robustness of the time discretization schemes with respect to data regularity.
    • A Comprehensive Review of the Composition, Nutritional Value, and Functional Properties of Camel Milk Fat

      Bakry, Ibrahim A; Yang, Lan; Farag, Mohamed A.; orcid: 0000-0001-5139-1863; email: mohamed.alifarag@aucegypt.edu; Korma, Sameh A; Khalifa, Ibrahim; orcid: 0000-0002-7648-2961; email: Ibrahiem.khalifa@fagr.bu.edu.eg; Cacciotti, Ilaria; orcid: 0000-0002-3478-6510; Ziedan, Noha I.; Jin, Jun; Jin, Qingzhe; Wei, Wei; et al. (MDPI, 2021-09-13)
      Recently, camel milk (CM) has been considered as a health-promoting icon due to its medicinal and nutritional benefits. CM fat globule membrane has numerous health-promoting properties, such as anti-adhesion and anti-bacterial properties, which are suitable for people who are allergic to cow’s milk. CM contains milk fat globules with a small size, which accounts for their rapid digestion. Moreover, it also comprises lower amounts of cholesterol and saturated fatty acids concurrent with higher levels of essential fatty acids than cow milk, with an improved lipid profile manifested by reducing cholesterol levels in the blood. In addition, it is rich in phospholipids, especially plasmalogens and sphingomyelin, suggesting that CM fat may meet the daily nutritional requirements of adults and infants. Thus, CM and its dairy products have become more attractive for consumers. In view of this, we performed a comprehensive review of CM fat’s composition and nutritional properties. The overall goal is to increase knowledge related to CM fat characteristics and modify its unfavorable perception. Future studies are expected to be directed toward a better understanding of CM fat, which appears to be promising in the design and formulation of new products with significant health-promoting benefits.
    • Layer Dynamics for the one dimensional $\eps$-dependent Cahn-Hilliard / Allen-Cahn Equation

      Antonopoulou, Dimitra; Karali, Georgia; Tzirakis, Konstantinos; University of Chester; University of Crete; IACM/FORTH (Springer, 2021-08-27)
      We study the dynamics of the one-dimensional ε-dependent Cahn-Hilliard / Allen-Cahn equation within a neighborhood of an equilibrium of N transition layers, that in general does not conserve mass. Two different settings are considered which differ in that, for the second, we impose a mass-conservation constraint in place of one of the zero-mass flux boundary conditions at x = 1. Motivated by the study of Carr and Pego on the layered metastable patterns of Allen-Cahn in [10], and by this of Bates and Xun in [5] for the Cahn-Hilliard equation, we implement an N-dimensional, and a mass-conservative N−1-dimensional manifold respectively; therein, a metastable state with N transition layers is approximated. We then determine, for both cases, the essential dynamics of the layers (ode systems with the equations of motion), expressed in terms of local coordinates relative to the manifold used. In particular, we estimate the spectrum of the linearized Cahn-Hilliard / Allen-Cahn operator, and specify wide families of ε-dependent weights δ(ε), µ(ε), acting at each part of the operator, for which the dynamics are stable and rest exponentially small in ε. Our analysis enlightens the role of mass conservation in the classification of the general mixed problem into two main categories where the solution has a profile close to Allen-Cahn, or, when the mass is conserved, close to the Cahn-Hilliard solution.
    • New Extremal Binary Self-dual Codes from block circulant matrices and block quadratic residue circulant matrices

      Gildea, Joe; Kaya, Abidin; Taylor, Rhian; Tylyshchak, Alexander; Yildiz, Bahattin; University of Chester; Sampoerna University; Uzhgorod National University; Northern Arizona University (Elsevier, 2021-08-20)
      In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2 and F2 + uF2. Using extensions, neighbours and sequences of neighbours, we construct many new self-dual codes. In particular, we construct one new self-dual code of length 66 and 51 new self-dual codes of length 68.
    • New Self-dual Codes from 2 x 2 block circulant matrices, Group Rings and Neighbours of Neighbours

      Gildea, Joe; Kaya, Abidin; Roberts, Adam; Taylor, Rhian; Tylyshchak, Alexander; University of Chester; Harmony Public Schools; Uzhgorod National University (American Institute of Mathematical Sciences, 2021-09-01)
      In this paper, we construct new self-dual codes from a construction that involves a unique combination; $2 \times 2$ block circulant matrices, group rings and a reverse circulant matrix. There are certain conditions, specified in this paper, where this new construction yields self-dual codes. The theory is supported by the construction of self-dual codes over the rings $\FF_2$, $\FF_2+u\FF_2$ and $\FF_4+u\FF_4$. Using extensions and neighbours of codes, we construct $32$ new self-dual codes of length $68$. We construct 48 new best known singly-even self-dual codes of length 96.
    • Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise

      Yan, Yubin; Kang, Wenyan; Egwu, Bernard; Pani, Amiya; University of Chester, Lvliang University, P. R. China, Indian Institute of Technology Bombay (Oxford Academic, 2021-05-21)
      A Galerkin finite element method is applied to approximate the solution of a semilinear stochastic space and time fractional subdiffusion problem with the Caputo fractional derivative of the order $ \alpha \in (0, 1)$, driven by fractionally integrated additive noise. After discussing the existence, uniqueness and regularity results, we approximate the noise with the piecewise constant function in time in order to obtain a regularized stochastic fractional subdiffusion problem. The regularized problem is then approximated by using the finite element method in spatial direction. The mean squared errors are proved based on the sharp estimates of the various Mittag-Leffler functions involved in the integrals. Numerical experiments are conducted to show that the numerical results are consistent with the theoretical findings.
    • New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction.

      Gildea, Joe; Korban, Adrian; Roberts, Adam; University of Chester (Elsevier, 2021-05-31)
      In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using $\lambda$-circulant matrices. The new construction was derived as a modification of the well-known four circulant construction of self-dual codes. Applying this technique together with the building-up construction, we construct singly-even binary self-dual codes of lengths 56, 58, 64, 80 and 92 that were not known in the literature before. Singly-even self-dual codes of length 80 with $\beta \in \{2,4,5,6,8\}$ in their weight enumerators are constructed for the first time in the literature.
    • Composite Matrices from Group Rings, Composite G-Codes and Constructions of Self-Dual Codes

      Dougherty, Steven; Gildea, Joe; Korban, Adrian; Kaya, Abidin; University of Scranton; University of Chester; Harmony School of Technology (Springer, 2021-05-19)
      In this work, we define composite matrices which are derived from group rings. We extend the idea of G-codes to composite G-codes. We show that these codes are ideals in a group ring, where the ring is a finite commutative Frobenius ring and G is an arbitrary finite group. We prove that the dual of a composite G-code is also a composite G-code. We also define quasi-composite G-codes. Additionally, we study generator matrices, which consist of the identity matrices and the composite matrices. Together with the generator matrices, the well known extension method, the neighbour method and its generalization, we find extremal binary self-dual codes of length 68 with new weight enumerators for the rare parameters $\gamma$ = 7; 8 and 9: In particular, we find 49 new such codes. Moreover, we show that the codes we find are inaccessible from other constructions.
    • High order algorithms for numerical solution of fractional differential equations

      Asl, Mohammad Shahbazi; Javidi, Mohammad; Yan, Yubin; University of Chester; University of Tabriz (SpringerOpen, 2021-02-17)
      In this paper, two novel high order numerical algorithms are proposed for solving fractional differential equations where the fractional derivative is considered in the Caputo sense. The total domain is discretized into a set of small subdomains and then the unknown functions are approximated using the piecewise Lagrange interpolation polynomial of degree three and degree four. The detailed error analysis is presented, and it is analytically proven that the proposed algorithms are of orders 4 and 5. The stability of the algorithms is rigorously established and the stability region is also achieved. Numerical examples are provided to check the theoretical results and illustrate the efficiency and applicability of the novel algorithms.
    • G-Codes, self-dual G-Codes and reversible G-Codes over the Ring Bj,k

      Dougherty, Steven; Gildea, Joe; Korban, Adrian; Sahinkaya, Serap; Tarsus University; University of Chester (Springer, 2021-05-03)
      In this work, we study a new family of rings, Bj,k, whose base field is the finite field Fpr . We study the structure of this family of rings and show that each member of the family is a commutative Frobenius ring. We define a Gray map for the new family of rings, study G-codes, self-dual G-codes, and reversible G-codes over this family. In particular, we show that the projection of a G-code over Bj,k to a code over Bl,m is also a G-code and the image under the Gray map of a self-dual G-code is also a self-dual G-code when the characteristic of the base field is 2. Moreover, we show that the image of a reversible G-code under the Gray map is also a reversible G2j+k-code. The Gray images of these codes are shown to have a rich automorphism group which arises from the algebraic structure of the rings and the groups. Finally, we show that quasi-G codes, which are the images of G-codes under the Gray map, are also Gs-codes for some s.
    • The multi-dimensional Stochastic Stefan Financial Model for a portfolio of assets

      Antonopoulou, Dimitra; Bitsaki, Marina; Karali, Georgia; University of Chester; University of Crete (American Institute of Mathematical Sciences (AIMS), 2021-04-01)
      The financial model proposed in this work involves the liquidation process of a portfolio of n assets through sell or (and) buy orders placed, in a logarithmic scale, at a (vectorial) price with volatility. We present the rigorous mathematical formulation of this model in a financial setting resulting to an n-dimensional outer parabolic Stefan problem with noise. The moving boundary encloses the areas of zero trading, the so-called solid phase. We will focus on a case of financial interest when one or more markets are considered. In particular, our aim is to estimate for a short time period the areas of zero trading, and their diameter which approximates the minimum of the n spreads of the portfolio assets for orders from the n limit order books of each asset respectively. In dimensions n = 3, and for zero volatility, this problem stands as a mean field model for Ostwald ripening, and has been proposed and analyzed by Niethammer in [25], and in [7] in a more general setting. There in, when the initial moving boundary consists of well separated spheres, a first order approximation system of odes had been rigorously derived for the dynamics of the interfaces and the asymptotic pro le of the solution. In our financial case, we propose a spherical moving boundaries approach where the zero trading area consists of a union of spherical domains centered at portfolios various prices, while each sphere may correspond to a different market; the relevant radii represent the half of the minimum spread. We apply It^o calculus and provide second order formal asymptotics for the stochastic version dynamics, written as a system of stochastic differential equations for the radii evolution in time. A second order approximation seems to disconnect the financial model from the large diffusion assumption for the trading density. Moreover, we solve the approximating systems numerically.
    • Numerical approximation of the Stochastic Cahn-Hilliard Equation near the Sharp Interface Limit

      Antonopoulou, Dimitra; Banas, Lubomir; Nurnberg, Robert; Prohl, Andreas; University of Chester; University of Bielefeld; Imperial College London; University of Tuebingen
      Abstract. We consider the stochastic Cahn-Hilliard equation with additive noise term that scales with the interfacial width parameter ε. We verify strong error estimates for a gradient flow structure-inheriting time-implicit discretization, where ε only enters polynomially; the proof is based on higher-moment estimates for iterates, and a (discrete) spectral estimate for its deterministic counterpart. For γ sufficiently large, convergence in probability of iterates towards the deterministic Hele-Shaw/Mullins-Sekerka problem in the sharp-interface limit ε → 0 is shown. These convergence results are partly generalized to a fully discrete finite element based discretization. We complement the theoretical results by computational studies to provide practical evidence concerning the effect of noise (depending on its ’strength’ γ) on the geometric evolution in the sharp-interface limit. For this purpose we compare the simulations with those from a fully discrete finite element numerical scheme for the (stochastic) Mullins-Sekerka problem. The computational results indicate that the limit for γ ≥ 1 is the deterministic problem, and for γ = 0 we obtain agreement with a (new) stochastic version of the Mullins-Sekerka problem.
    • Entropy-driven cell decision-making predicts "fluid-to-solid" transition in multicellular systems

      Kavallaris, Nikos; Barua, Arnab; Syga, Simon; Mascheroni, Pietro; Meyer-Hermann, Michael; Deutsch, Andreas; Hatzikirou, Haralampos; University of Chester; Helmholtz Centre for Infection Research; Technische Univesität Dresden; Technische Universität Braunschweig; Khalifa University (IOP Publishing, 2020-12-22)
      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.