A second moment turbulence closure model of the type used before for flows with density stratification, frame rotation and streamline curvature is augmented to describe MHD flows with small magnetic Reynolds number. I...
While sexual reproduction is a general feature of animals, fissiparity and budding are relatively uncommon modes of asexual reproduction by which a fragment from a parent becomes an independent organism. Unlike unitar...
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While sexual reproduction is a general feature of animals, fissiparity and budding are relatively uncommon modes of asexual reproduction by which a fragment from a parent becomes an independent organism. Unlike unitary development, tumor cells can be included in the detached fragment destined to become offspring. Although fragmentation facilitates the vertical transmission of parental tumor cells to nascent progeny, this process requires significantly fewer cell replications than development from a zygote. The former is a risk factor for cancer, while the latter reduces oncogenic mutations during replication, indicating that two opposite effects of carcinogenesis are involved in fragmentation. If fragmentation can significantly reduce the number of cell replications for the development and a small portion of parental cancer is transmitted to the offspring during fragmentation, consecutive fragmentation across generations can gradually diminish the cancer risk of offspring, which I term fragmentational purging. On the other hand, consecutive fragmentation may aggravate the cancer risk of the progeny, a process of fragmentational accumulation. The model results imply that fragmentational purging does not necessarily guarantee the evolution of fragmentation, nor does fragmentational accumulation ensure its exclusion. Other relevant factors including juvenile susceptibility of sexual reproduction and loss of genetic diversity stemming from asexual reproduction can influence the selective advantage of fragmentation. Furthermore, owing to the common features of stemness and self-renewal, the existence of pluripotent adult stem cells required for fragmentation could be coupled with elevated cancer risk. The model results across diverse parameters and the associated mathematical analyses highlight multifaceted evolutionary trajectories toward fragmentation. Further investigation of cancer-suppression strategies that fragmentational animals employ could provide insights into
This paper proposes a novel approach for solving nonlinear partial differential equations (PDEs) with a quantum computer, the trainable embedding quantum physics informed neural network (TE-QPINN). We combine quantum ...
This paper proposes a novel approach for solving nonlinear partial differential equations (PDEs) with a quantum computer, the trainable embedding quantum physics informed neural network (TE-QPINN). We combine quantum machine learning (QML) with physics informed neural networks (PINNs) in a hybrid approach. By leveraging the advantages of classical and quantum computers, we can create algorithms that have a potential to be run on noisy intermediate-scale quantum devices (NISQ). We use feedforward neural networks (FNN) as problem-agnostic embedding functions, giving the used quantum circuit greater expressibility than previously introduced embedding. This expressibility allows us to solve a wide range of problems without using a problem specific ansatz. Additionally, we introduce a hybrid backpropagation algorithm that allows efficient updates of the used weights and biases in the FNN embedding functions. In this paper we showcase the capabilities of TE-QPINNs of a wide range of problems, including the two-dimensional Poisson, Burgers and Navier-Stokes equations. In direct comparison with classical PINNs, this approach showed an ability to achieve superior results while using the same number of parameters, highlighting their potential for more efficient optimization in high-dimensional parameter spaces, which could be transformative for future applications.
The question of whether all species in a multispecies community governed by differential equations can persist for all time is one of the most important in theoretical ecology. Criteria for this property vary widely, ...
The question of whether all species in a multispecies community governed by differential equations can persist for all time is one of the most important in theoretical ecology. Criteria for this property vary widely, asymptotic stability and global asymptotic stability being 2 of the conditions most widely used. Neither of these criteria appears to reflect intuitive concepts of persistence in a satisfactory manner: the 1st because it is only a local condition, the 2nd because it rules out cyclic behavior. A more realistic criterion is that of permanent coexistence, which essentially requires that there should be a region separated from the boundary (corresponding to a zero value of the population of at least 1 sp.) which all orbits enter and remain within. A mathematical technique for establishing permanent coexistence is illustrated by an application to the long-standing problem of predator-mediated coexistence in a 2-prey 1-predator community.
Predator mediated coexistence of 2 competing species with general frequency dependent switching in the predator is examined. The stability criterion used is permanent coexistence. This is a global criterion which ensu...
Predator mediated coexistence of 2 competing species with general frequency dependent switching in the predator is examined. The stability criterion used is permanent coexistence. This is a global criterion which ensures that eventually the species end up in a region M of phase space separated from the boundary (corresponding to extinction of at least one of the species), but which places no restriction on the behavior in M, and so allows, for example, the existence of a stable limit cycle. The principal determinant of survival turns out to be the strength of the switching when 1 prey is rare, the form of the switching elsewhere being irrelevant. Strong switching is a powerful influence for coexistence. In contrast with the conclusion of previous investigations, the influence of switching is complex, and under some circumstances weak switching can actually destroy coexistence in a system which without switching leads to survival of all species.
An FFT method for solving the discrete Poisson equation on a rectangle using a regular hexagonal grid is described and the results obtained for a model Dirichlet problem are compared with those obtained on a rectangul...
An FFT method for solving the discrete Poisson equation on a rectangle using a regular hexagonal grid is described and the results obtained for a model Dirichlet problem are compared with those obtained on a rectangular grid. For a given grid size the results demonstrate that the hexagonal method is more accurate, but rather less efficient, than the usual 5-point method, whereas for comparable accuracy to be achieved by both methods, the hexagonal method was found to be approximately 20 to 30 times faster than the 5-point method for the model problem.
An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is prove...
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An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.
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