A general methodology for population analysis

This paper considers the cycle maximum in birth–death processes as a stepping stone to characterisation of the asymptotic behaviour of the maximum number of customers in single queues and open Kelly–Whittle networks of queues. For positive recurrent birth–death processes we show that the sequence of sample maxima is stochastically compact. For transient birth–death processes we show that the sequence of sample maxima conditioned on the maximum being finite is stochastically compact.We show that the Markov chain recording the total number of customers in a Kelly–Whittle network is a birth–death process with birth and death rates determined by the normalising constants in a suitably defined sequence of closed networks. Explicit or asymptotic expressions for these normalising constants allow asymptotic evaluation of the birth and death rates, which, in turn, allows characterisation of the cycle maximum in a single busy cycle, and convergence of the sequence of sample maxima for Kelly–Whittle networks of queues.

Using a part of a general methodology for population analysis, developed recently in Lazov and Lazov [1], and relying on the fundamental concepts of system information i and system entropy $$S=E\left( i \right) $$S=Ei, this paper promotes a methodology for information and capacity analysis of broadband wireless access (BWA) systems. A BWA system consists of a base station (BS) and a group of M users in its coverage area, with N simultaneously active users, $$0\le N\le M$$0≤N≤M, working in point-to-multipoint mode. As in [1], we model this system as family of birth-death processes (BDPs), with size $$M+1$$M+1, in equilibrium, indexed by the system utilization parameter $$\rho $$ź, ratio of its primary birth and death rates, $$\rho =\lambda /\mu $$ź=ź/μ. We evaluate the BWA system information and entropy, and full system capacity, and then, assuming the same Gaussian distribution for the arrival traffic at BS from any user, system capacity (as a function of the system information) and its mean value, and mean normalized square deviation of the system capacity from its linear part. We compare the information of empty $$\left( {N=0} \right) $$N=0 and full $$\left( {N=M} \right) $$N=M system with system entropy, and further, system mean capacity with full system capacity, as functions of parameter $$\rho $$ź. The developed methodology is illustrated on families of BDPs with truncated geometrical, truncated Poisson and Binomial distributions as their equilibrium ones, which model the information linear, Erlang loss and Binomial BWA systems, respectively.

We discuss connections between birth and death processes and orthogonal polynomials. We survey certain spectral properties of orthogonal polynomials and spectra of birth and death processes. Birth and death processes with linear birth and death rates are studied in some detail. We also mention some results concerning birth and death processes whose transition rates are rational functions.

A parking lot can accommodate a maximum number of vehicles, which determines its size. We model this parking lot as a family of Birth-Death Processes (BDPs) in equilibrium, with finite size, indexed by the parking lot utilization. Relying on the concepts of information and entropy (i.e., mean information) of a parking lot, we promote a methodology for revenue analysis of parking lots. Thereto, by definition, the park entropy is uncertainty, associated with the park. We evaluate the full park revenue (as a function of the full park information). Then, assuming the same Gaussian distribution for the revenue attained from any vehicle, the park revenue, its mean value and mean normalized square deviation of the park revenue from its linear part are also assessed. The last quantity is compared with park entropy, and park mean revenue with full park revenue, as functions of the park utilization, in order for an optimal trade-off between these measures to be established. Thus, when making decisions about the park utilization and size (as two key drivers of the parking business), park operators and planners who focus on the uncertainty become more proficient at their job than those who focus on revenue consequences only. The developed methodology is illustrated on the public parking lots, modeled as a family of BDPs with truncated Poisson distribution as its equilibrium one.

This paper is concerned with two problems in connection with exponential ergodicity for birth-death processes on a semi-infinite lattice of integers. The first is to determine from the birth and death rates whether exponential ergodicity prevails. We give some necessary and some sufficient conditions which suffice to settle the question for most processes encountered in practice. In particular, a complete solution is obtained for processes where, from some finite statenonwards, the birth and death rates are rational functions ofn. The second, more difficult, problem is to evaluate the decay parameter of an exponentially ergodic birth-death process. Our contribution to the solution of this problem consists of a number of upper and lower bounds.

The adhesion and friction force properties between a tenfold $\mathrm{Al}\text{\penalty1000-\hskip0pt}\mathrm{Ni}\text{\penalty1000-\hskip0pt}\mathrm{Co}$ decagonal quasicrystal and a titanium nitride (TiN)-coated tip were investigated using an atomic force microscope in ultrahigh vacuum. To suppress the strong chemical adhesion found in the clean quasicrystal surfaces, the sample was exposed to ethylene that formed a protective passivating layer. We show that the deformation mechanism of the tip-substrate junction changes from elastic to inelastic at a threshold pressure of $3.8\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}4.0\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Images of the indentation marks left above the threshold pressure indicate the absence of new steps, and indicate that surface damage is not accompanied by formation of slippage planes or dislocations, as found in plastically deforming crystalline materials. This is consistent with the lack of translational periodicity of quasicrystals. The work of adhesion in the inelastic regime is five times larger than in the elastic one, plausibly as a result of the displacement of the passivating layer. In the elastic regime, the friction dependence on load is accurately described by the Derjaguin-M\uller-Toporov (DMT) model, consistent with the high hardness of both the TiN tip and the quasicrystal sample. Above the threshold pressure, the friction versus load curve deviates from the DMT model, indicating that chemical bond formation and rupture contribute to the energy dissipation.

Benefits realisation management (BRM) aims to facilitate the process of identifying, measuring and tracking desired benefits derived from a project. Improvement methodology frameworks often describe BRM as integral to identifying...

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

When cancers or bacterial infections establish, small populations of cells have to free themselves from homoeostatic regulations that prevent their expansion. Trait evolution allows these populations to evade this regulation, escape stochastic extinction and climb up the fitness landscape. In this study, we analyse this complex process and investigate the fate of a cell population that underlies the basic processes of birth, death and mutation. We find that the shape of the fitness landscape dictates a circular adaptation trajectory in the trait space spanned by birth and death rates. We show that successful adaptation is less likely for parental populations with higher turnover (higher birth and death rates). Including density- or trait-affecting treatment we find that these treatment types change the adaptation dynamics in agreement with a geometrical analysis of fitness gradients. Treatment strategies that simultaneously target birth and death rates are most effective, but also increase evolvability. By mapping physiological adaptation pathways and molecular drug mechanisms to traits and treatments with clear eco-evolutionary consequences, we can achieve a much better understanding of the adaptation dynamics and the eco-evolutionary mechanisms at play in the dynamics of cancer and bacterial infections.

We study finite size corrections to the semiclassical string solutions of the Schrödinger spacetime. We compute the leading order exponential corrections to the infinite size dispersion relation of the single spin giant magnon and of the single spin single spike solutions. The solutions live in a S3 subspace of the five-sphere and extent in the Schrödinger part of the metric. In the limit of zero deformation the finite size dispersion relations flow to the undeformed AdS5 × S5 counterparts and in the infinite size limit the correction term vanishes and the known infinite size dispersion relations are obtained.

Grazing incidence fast atom diffraction (GIFAD) at surfaces has made rapid progress and has established itself as a surface analysis tool where effective energy E⊥ of the motion towards the surface is in the same range as that in thermal energy atom scattering (TEAS). To better compare the properties of both techniques, we use the diffraction patterns of helium and neon atoms impinging on a LiF (001) surface as a model system. E-Scan, θ-scan, and φ-scan are presented where the primary beam energy E is varied between a few hundred eV up to five keV, the angle of incidence θi between 0.2 and 2° and the azimuthal angle φi around 360°. The resulting diffraction charts are analyzed in terms of high and low values of effective energy E⊥. The former provides high resolution at the positions of the surface atoms and the attached repulsive interaction potentials while the second is sensitive to the attractive forces towards the surface. The recent progress of inelastic diffraction is briefly presented.

The birth-death process is widely used in phylogenetics to model speciation and extinction. Recent studies have shown that the inferred rates are sensitive to assumptions about the sampling probability of lineages. Here, we examine the effect of the method used to sample lineages. Whereas previous studies have assumed random sampling (RS), we consider two extreme cases of biased sampling: "diversified sampling" (DS), where tips are selected to maximize diversity and "cluster sampling (CS)," where sample diversity is minimized. DS appears to be standard practice, for example, in analyses of higher taxa, whereas CS may occur under special circumstances, for example, in studies of geographically defined floras or faunas. Using both simulations and analyses of empirical data, we show that inferred rates may be heavily biased if the sampling strategy is not modeled correctly. In particular, when a diversified sample is treated as if it were a random or complete sample, the extinction rate is severely underestimated, often close to 0. Such dramatic errors may lead to serious consequences, for example, if estimated rates are used in assessing the vulnerability of threatened species to extinction. Using Bayesian model testing across 18 empirical data sets, we show that DS is commonly a better fit to the data than complete, random, or cluster sampling (CS). Inappropriate modeling of the sampling method may at least partly explain anomalous results that have previously been attributed to variation over time in birth and death rates.

We consider birth-death processes taking values in but allow the death rate in state 0 to be positive, so that escape from is possible. Two such processes with transition functions are said to be similar if, for all there are constants c ij such that for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants c ij and ν such that for all t ≥ 0.

Assuming that both birth and death rates are density and time dependent, a diffusion approximation of the generalized birth and death process has been considered in this paper to obtain a suitable stochastic population model describing the population size and its moments. A simple method of estimating the parameters of the model Is discussed. The predictions of the expected size of the population, and the variance are made and compared with the corresponding census figures as well as with another deterministic projection series made for the corresponding period.

A simulation study on how the resource competition and anti-predator cooperation impact the motile-phytoplankton groups’ formation under predation stress