A functional traits approach was adopted to examine patterns of fish diversity in relation to environmental and spatial variables and for comparison with findings from earlier analyses of fish taxonomic diversity in a nearly pristine river in the Llanos region of Colombia. Fishes were surveyed during the low-water period at 34 sites along the longitudinal fluvial gradient of the Bita River, a clearwater tributary of the Orinoco River. We compiled a matrix of 37 traits associated with locomotion, feeding, and defense for 132 species to compute functional β diversity metrics among four reaches along the entire longitudinal fluvial gradient and also within reaches. Functional redundancy (trait under-dispersion) was found to be common throughout the fluvial gradient. Functional β diversity was high at both spatial scales, with widespread evidence of functional nestedness and functional turnover, especially in upper reaches. In the Bita River, environmental filtering and stochastic processes, such as random dispersal, appear to be the dominant mechanisms influencing fish functional diversity. Inferences derived from analysis of functional versus taxonomic diversity are largely congruent, although analysis of functional β diversity found more evidence of nestedness than turnover at both spatial scales. Both lines of evidence stress the importance of habitat heterogeneity and aquatic habitat connectivity for conservation of high species diversity in this system.

The general theory developed by Ben Yaacov for metric structures provides Fraïssé limits which are approximately ultrahomogeneous. We show here that this result can be strengthened in the case of relational metric structures. We give an extra condition that guarantees exact ultrahomogenous limits. The condition is quite general. We apply it to stochastic processes, the class of diversities, and its subclass of $L_1$ diversities.

We investigate the concept of orbital free entropy from the viewpoint of the matrix liberation process. We will show that many basic questions around the definition of orbital free entropy are reduced to the question of full large deviation principle for the matrix liberation process. We will also obtain a large deviation upper bound for a certain family of random matrices that is essential to define the orbital free entropy. The resulting rate function is made up into a new approach to free mutual information.

The Quicksort process R (Rösler (2018)) can be characterized as the unique endogenous solution of the inhomogeneous stochastic fixed point equation R=D(UR1(1∧t∕U)+𝟭{U<t}(1-U)R2((t-U)∕(1-U))+C(U,t))t on the space 𝒟 of càdlàg functions, such that R(1) has the Quicksort distribution. In this paper we characterize all 𝒟-valued solutions of that equation. Every solution can be represented as the convolution of a solution of the inhomogeneous equation and a general solution of the homogeneous equation (Rüschendorf (2006)). The general solutions of the homogeneous equation are the distributions of Cauchy processes Y with constant drift. Any distribution of R+Y for independent R and Y is a solution of the inhomogeneous equation. Every solution of the inhomogeneous equation is of the form R+Y, where R and Y are independent. The endogenous solutions for the inhomogeneous equation are the shifted Quicksort process distributions. In comparison, the Quicksort distribution is the endogenous solution of the Quicksort fixed point equation unique up to a constant (Rösler (1991)). The general solution can be represented as the convolution of the shifted Quicksort distribution and some symmetric Cauchy distribution (Fill and Janson (2000)), possibly degenerate.

We construct a response adaptive design, described in terms of a two-color urn model, targeting fixed asymptotic allocations. We prove asymptotic results for the process of colors generated by the urn and for the process of its compositions. An application of the proposed urn model is presented in an estimation problem context.

One of the central results in Einstein’s theory of Brownian motion is that the mean square displacement of a randomly moving Brownian particle scales linearly with time. Over the past few decades sophisticated experiments and data collection in numerous biological, physical and financial systems have revealed anomalous sub-diffusion in which the mean square displacement grows slower than linearly with time. A major theoretical challenge has been to derive the appropriate evolution equation for the probability density function of sub-diffusion taking into account further complications from force fields and reactions. Here we present a derivation of the generalised master equation for an ensemble of particles undergoing reactions whilst being subject to an external force field. From this general equation we show reductions to a range of well known special cases, including the fractional reaction diffusion equation and the fractional Fokker-Planck equation.

The ‘coupon collection problem’ refers to a class of occupancy problems in which j identical items are distributed, independently and at random, to n cells, with no restrictions on multiple occupancy. Identifying the cells as coupons, a coupon is ‘collected’ if the cell is occupied by one or more of the distributed items; thus, some coupons may never be collected, whereas others may be collected once or twice or more. We call the number of coupons collected exactly r times coupons of type r. The coupon collection model we consider is general, in that a random number of purchases occurs at each stage of collecting a large number of coupons; the sample sizes at each stage are independent and identically distributed according to a sampling distribution. The joint behavior of the various types is an intricate problem. In fact, there is a variety of joint central limit theorems (and other limit laws) that arise according to the interrelation between the mean, variance, and range of the sampling distribution, and of course the phase (how far we are in the collection processes). According to an appropriate combination of the mean of the sampling distribution and the number of available coupons, the phase is sublinear, linear, or superlinear. In the sublinear phase, the normalization that produces a Gaussian limit law for uncollected coupons can be used to obtain a multivariate central limit law for at most two other types — depending on the rates of growth of the mean and variance of the sampling distribution, we may have a joint central limit theorem between types 0 and 1, or between types 0, 1, and 2. In the linear phase we have a multivariate central limit theorem among the types 0, 1,…, k for any fixed k.

We use the recently proposed Nested Stochastic Simulation Algorithm (Nested SSA) to simulate the cell cycle model for budding yeast. The results show that Nested SSA is able to significantly reduce the computational cost while capturing the essential dynamical features of the system.

One shows that the linearized Navier-Stokes equation in ${\mathcal{O}}{\subset} R^d,\;d \ge 2$ , around an unstable equilibriumsolution is exponentially stabilizable in probability by aninternal noise controller $V(t,\xi)=\displaystyle\sum\limits_{i=1}^{N} V_i(t)\psi_i(\xi)\dot\beta_i(t)$ , $\xi\in{\mathcal{O}}$ , where $\{\beta_i\}^N_{i=1}$ areindependent Brownian motions in a probability space and $\{\psi_i\}^N_{i=1}$ is a system of functions on ${\mathcal{O}}$ withsupport in an arbitrary open subset ${\mathcal{O}}_0\subset {\mathcal{O}}$ . Thestochastic control input $\{V_i\}^N_{i=1}$ is found in feedbackform. One constructs also a tangential boundary noise controllerwhich exponentially stabilizes in probability the equilibriumsolution.

Face à la nécessité d'accroître les performances de mobilité tout terrain de ses véhicules et à sa volonté d'y intégrer désormais des équipements "low cost" provenant du secteur civil, la Société Nexter s'est dotée de démarches de conception sécurisantes, permettant de faire face à ce type de compromis antinomique.Basée sur la capacité d'évaluer rapidement les valeurs des contraintes extrêmes produites sur les structures embarquées, dès le début du cycle de développement du produit, l'originalité de la démarche de conception proposée réside dans le fait qu'elle permet de synthétiser un grand nombre de processus d'excitation stochastique, décrits par le profil d'emploi opérationnel des clients, prendre en compte le caractère aléatoire des excitations concernées, en supposant de surcroît une indépendance statistique des situations stochastiques retenues, et de revenir à un chargement dynamique unique, reproduisant fidèlement les valeurs des contraintes extrêmes des processus concernés, avec un risque de dépassement maîtrisé puisque spécifié.Éprouvée dans le cadre du développement du VBCI (Véhicule Blindé de Combat d'Infanterie), cette démarche de conception dynamique a notamment mis en évidence le caractère peu sécurisant des démarches de conception forfaitaire à caractère statique déployées dans le passé.

The ‘square root formula’ in the Internet transmission control protocol (TCP) states that if the probability p of packet loss becomes small and there is independence between packets, then the stationary distribution of the congestion window W is such that the distribution of W√p is almost independent of p and is completely characterizable. This paper gives an elementary proof of the convergence of the stationary distributions for a much wider class of processes that includes classical TCP as well as T. Kelly's ‘scalable TCP’. This paper also gives stochastic dominance results that translate to a rate of convergence.

We consider the class of real-valued stochastic processes indexed on a compact subset of R or R2 with almost surely absolutely continuous sample paths. We obtain an implicit formula for the distributions of their maxima. The main result is the derivation of numerical bounds that turn out to be very accurate, in the Gaussian case, for levels that are not large. We also present the first explicit upper bound for the distribution tail of the maximum in the two-dimensional Gaussian framework. Numerical comparisons are performed with known tools such as the Rice upper bound and expansions based on the Euler characteristic. We deal numerically with the determination of the persistence exponent.

Objectives: The cost-effectiveness of alternating pressure-relieving devices, mattress replacements, and mattress overlays compared with a standard hospital (high-specification foam mattress) for the prevention and treatment of pressure ulcers in hospital patients in the United Kingdom was investigated.

Methods: A decision-analytic model was constructed to evaluate different strategies to prevent or treat pressure ulcers. Three scenarios were evaluated: the prevention of pressure ulcers, the treatment of superficial ulcers, and the treatment of severe ulcers. Epidemiological and effectiveness data were obtained from the clinical literature. Expert opinion using a rating scale technique was used to obtain quality of life data. Costs of the devices were obtained from manufacturers, whereas costs of treatment were obtained from the literature. Uncertainty was explored through probabilistic sensitivity analysis.

Results: Using £30,000/QALY (quality-adjusted life year) as the decision-maker's cut off point (the current UK standard), in scenario 1 (prevention), the cost-effective strategy was the mattress overlay at 1, 4, and 12 weeks. In scenarios 2 and 3, the cost-effective strategy was the mattress replacement at 1, 4, and 12 weeks. Standard care was a dominated intervention in all scenarios for values of the decision-maker's ceiling ratio ranging from £5,000 to £100,000/QALY. However, the probabilistic sensitivity analysis results reflected the high uncertainty surrounding the choice of devices.

Conclusions: Current information suggests that alternating pressure mattress overlays may be cost-effective for the prevention of pressure ulcers, whereas alternating pressure mattress replacements appears to be cost-effective for the treatment of superficial and severe pressure ulcers.

Probability theory, and its dynamic aspect stochastic process theory, is both a venerable subject, in that its roots go back to the mid-seventeenth century, and a young one, in that its modern formulation happened comparatively recently - well within living memory. The year 2003 marked the seventieth anniversary of Kolmogorov's Grundbegriffe der Wahrscheinlichkeitsrechnung, usually regarded as having inaugurated modern (measure-theoretic) probability theory. It also marked the fiftieth anniversary of Doob's Stochastic Processes. The profound and continuing influence of this classic work prompts the present piece.

We are developing a decision support tool to help clinicians and policy makers estimate the impact of various coronary heart disease (CHD) treatments on disease outcomes for populations. We have created seven modules that correspond to states commonly encountered with CHD, that is, congestive heart failure, tachyarrhythmia, stable angina pectoris, acute coronary syndrome, bradycardia, postmyocardial infarction, and postcoronary artery bypass grafting, and a healthy individual module. Within each module, we created event-decision- intervention-outcome flow pathways to simulate risk of a clinical event and the expected outcome as the result of a particular intervention. We will combine disease state probability estimates based on the experience of the Olmsted County, Minnesota, population and estimates of intervention efficacy based on clinical trial data to estimate the impact of interventions on a population. We plan to make this tool available to the public through the internet.“This project was made possible through a Cooperative Agreement between the Center for Disease Control and Prevention (CDC) and the Association of Teachers of Preventive Medicine (ATPM), award # TS-0892; its contents are the responsibility of the authors and do not necessarily reflect the official views of the CDC or ATPM. Supported in part by an unrestricted research grant from McNeil Consumer Healthcare.”

In this paper, the instantaneous availability of a system maintained under periodic inspection is investigated using random walk models. Two cases are considered. In the first model, the system is repaired or modified and it is assumed to be as good as new upon periodic inspection and maintenance. In the second model, the system is not modified after the inspection if the system is still working, and the condition of the system is assumed to be the same as that before the inspection. For both models the failures only can be found through the inspection. Perfect repair or replacement of a failed system is assumed to be carried out, but the time it takes can be constant or of a random length. The relationship between this problem and the random walk model in a two-dimensional plane is described. Several new results are also shown.

An index lying between 0 and 1 is presented to describe the degree of liberation (or separation) of one component of a particulate material. It is shown how the index is related to the covariance function of the material, the distribution of shapes and sizes of the particles and to the interaction between fracture surfaces and the structure of the material. The variation of the index with the extent of crushing is investigated, together with the problem of stereological estimation. The index is evaluated for some particular probability models.

A device is repaired at failure. With probability p, it is returned to the ‘good-as-new' state (perfect repair), with probability 1 – p, it is returned to the functioning state, but it is only as good as a device of age equal to its age at failure (imperfect repair). Repair takes negligible time. We obtain the distribution Fp of the interval between successive good-as-new states in terms of the underlying life distribution F. We show that if F is in any of the life distribution classes IFR, DFR, IFRA, DFRA, NBU, NWU, DMRL, or IMRL, then Fp is in the same class. Finally, we obtain a number of monotonicity properties for various parameters and random variables of the stochastic process. The results obtained are of interest in the context of stochastic processes in general, as well as being useful in the particular imperfect repair model studied.