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Massive conscious neighborhood-based crow search algorithm for the pseudo-coloring problem: Advances in Swarm Intelligence
No full textThe pseudo-coloring problem (PsCP) is a combinatorial optimization challenge that involves assigning colors to elements in a way that meets specific criteria, often related to minimizing conflicts or maximizing some form of utility. A variety of metaheuristic algorithms have been developed to solve PsCP efficiently. However, these algorithms sometimes struggle with the quality of solutions, impacting their ability to achieve optimal or near-optimal results reliably. To overcome these issues, this study introduces an adapted conscious neighborhood-based crow search algorithm (CCSA) and a massive variant of CCSA specifically tailored for PsCP. The performance of CCSA and MCCSA are evaluated on real and synthetic images and compared with state-of-the-art optimizers. The results showed that the adapted CCSA and MCCSA outperformed offering an effective strategy for image pseudo-colorization
Convergence of cluster coagulation dynamics
Get PDFWe study hydrodynamic limits of the cluster coagulation model; a coagulation model introduced by Norris [, 209(2):407-435 (2000)]. In this process, pairs of particles in a measure space , merge to form a single new particle according to a transition kernel , in such a manner that a quantity, one may regard as the total mass of the system, is conserved. This model is general enough to incorporate various inhomogeneities in the evolution of clusters, for example, their shape, or their location in space. We derive sufficient criteria for trajectories associated with this process to concentrate among solutions of a generalisation of the , and, in some special cases, by means of a uniqueness result for solutions of this equation, prove a weak law of large numbers. This multi-type Flory equation is associated with associated with the process, which may encode different information to conservation of mass (for example, conservation of centre of mass in spatial models). We also apply criteria for gelation in this process to derive sufficient criteria for this equation to exhibit gelling solutions. When this occurs, this multi-type Flory equation encodes, via the associated conserved property, the interaction between the gel and the finite size sol particles
An agent-based modelling framework for tumour growth incorporating mechanical and evolutionary aspects of cell dynamics
Get PDFWe develop an agent-based modelling framework for tumour growth that in-corporates both mechanical and evolutionary aspects of the spatio-temporal dynamics of cancer cells. In this framework, cells are regarded as viscoelastic spheres that interact with other neighbouring cells through mechanical forces. The phenotypic state of each cell is described by the level of expression of an hypoxia-inducible factor that regulates the cellular response to available oxygen. The rules that govern proliferation and death of cells in different phenotypic states are then defined by integrating mechanical constraints and evolutionary principles. Computational simulations of the model are carried out under a variety of scenarios corresponding to different intra-tumoural distributions of oxygen. The results obtained, which indicate excellent agreement between simulation outputs and the results of formal analysis of phenotypic selection, recapitulate the emergence of stable phenotypic heterogeneity among cancer cells driven by inhomogeneities in the intra-tumoural distribution of oxygen. This article is intended to present a proof of concept for the ideas underlying the proposed modelling framework, with the aim to apply the related modelling methods to elucidate specific aspects of cancer progression in the future
Polynomial Volterra Processes
No full textWe study the class of continuous polynomial Volterra processes, which we define as solutions to stochas- tic Volterra equations driven by a continuous semimartingale with affine drift and quadratic diffusion matrix in the state of the Volterra process. To demonstrate the versatility of possible state spaces within our framework, we construct polynomial Volterra processes on the unit ball. This construction is based on a stochastic invariance principle for stochastic Volterra equations with possibly singular kernels. Similarly to classical polynomial processes, polynomial Volterra processes allow for tractable expressions of the mo- ments in terms of the unique solution to a system of deterministic integral equations, which reduce to a system of ODEs in the classical case. By applying this observation to the moments of the finite-dimensional distributions we derive a uniqueness result for polynomial Volterra processes. Moreover, we prove that the moments are polynomials with respect to the initial condition, another crucial property shared by classical polynomial processes. The corresponding coefficients can be interpreted as a deterministic dual process and solve integral equations dual to those verified by the moments themselves. Additionally, we obtain a representation of the moments in terms of a pure jump process with killing, which corresponds to another non-deterministic dual process
Modelling the age distribution of longevity leaders
Get PDFHuman longevity leaders with remarkably long lifespan play a crucial role in the advancement of longevity research. In this paper, we propose a stochastic model to describe the evolution of the age of the oldest person in the world by a Markov process, in which we assume that the births of the individuals follow a Poisson process with increasing intensity, lifespans of individuals are independent and can be characterized by a gamma-Gompertz distribution with time-dependent parameters. We utilize a dataset of the world's oldest person title holders since 1955, and we compute the maximum likelihood estimate for the parameters iteratively by numerical integration. Based on our preliminary estimates, the model provides a good fit to the data and shows that the age of the oldest person alive increases over time in the future. The estimated parameters enable us to describe the distribution of the age of the record holder process at a future time point
A Λ-Fleming-Viot Type Model with Intrinsically Varying Population Size
No full textWe propose an extension of the classical Λ-Fleming-Viot model to intrinsically varying population sizes. During events, instead of replacing a proportion of the population, a random mass dies and a, possibly different, random mass of new individuals is added. The model can also incorporate a (deterministic) drift term, representing infinitesimally small, but frequent events. We investigate elementary properties of the model, analyse its relation to the Λ-Fleming-Viot model and describe a duality relationship. Through the lookdown framework, we provide a forward-in-time analysis of fixation and coming down from infinity. A visual introduction to this paper can be found at youtube.com/watch?v=v59motZWQcY
The deal.II library, Version 9.6
No full textThis paper provides an overview of the new features of the finite element library deal.II, version 9.6
Numerical Simulation of High-Frequency Induction Welding in Longitudinal Welded Tubes
No full textIn the present paper the high-frequency induction welding process is studied numerically. The mathematical model comprises a harmonic vector potential formulation of the Maxwell equations and a quasi-static, convection dominated heat equation coupled through the Joule heat term and nonlinear constitutive relations. Its main novelties are a new analytic approach which permits to compute a spatially varying feed velocity depending on the angle of the Vee-opening and additional spring-back effects. Moreover, a numerical stabilization approach for the finite element discretization allows to consider realistic weld-line speeds and thus a fairly comprehensive three-dimensional simulation of the tube welding process
High-Probability Convergence for Composite and Distributed Stochastic Minimization and Variational Inequalities with Heavy-Tailed Noise
No full textHigh-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to derive good high-probability guarantees when the noise is heavy-tailed. However, if implemented naïvely, clipping can spoil the convergence of the popular methods for composite and distributed optimization (Prox-SGD/Parallel SGD) even in the absence of any noise. Due to this reason, many works on high-probability analysis consider only unconstrained non-distributed problems, and the existing results for composite/distributed problems do not include some important special cases (like strongly convex problems) and are not optimal. To address this issue, we propose new stochastic methods for composite and distributed optimization based on the clipping of stochastic gradient differences and prove tight high-probability convergence results (including nearly optimal ones) for the new methods. Using similar ideas, we also develop new methods for composite and distributed variational inequalities and analyze the high-probability convergence of these methods
Dynamical simulations of single-mode lasing in large-area all-semiconductor PCSELs
Get PDFWe perform modeling and dynamic simulations of all-semiconductor photonic crystal surface- emitting lasers (PCSELs). A two-dimensional photonic crystal consists of a GaAs layer with InGaP features, repeating periodically in both lateral directions. In our dynamic simulations, we demon- strate for the first time that photonic crystals with large isosceles triangular features, having a base angle close to 71.5°, enable suppression of higher-order modes and achieve single-mode, high-quality lasing in large-area all-semiconductor PCSELs under moderate and even high pump levels