Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel K that can be seen, in a discrete setting, as a matrix storing the similarity between points. The main exact algorithm to sample DPPs uses the spectral decomposition of K, a computation that becomes costly when dealing with a high number of points. Here we present an alternative exact algorithm to sample in discrete spaces that avoids the eigenvalues and the eigenvectors computation. The method used here is innovative, and numerical experiments show competitive results with respect to the initial algorithm.

In the first part of this paper we study approximations of trajectories of piecewise deterministic processes (PDPs) when the flow is not given explicitly by the thinning method. We also establish a strong error estimate for PDPs as well as a weak error expansion for piecewise deterministic Markov processes (PDMPs). These estimates are the building blocks of the multilevel Monte Carlo (MLMC) method, which we study in the second part. The coupling required by the MLMC is based on the thinning procedure. In the third part we apply these results to a two-dimensional Morris–Lecar model with stochastic ion channels. In the range of our simulations the MLMC estimator outperforms classical Monte Carlo.

We construct entropy increasing monotone factors in the context of a Bernoulli shift over the free group of rank at least two.

When a range of weed densities is needed for competition experiments, one method of reducing existing populations is to remove all weeds in strips of specified length down the crop row. This technique also can be used to create different sizes of weed dusters. Two methods of sampling weed densities after such thinning were compared: unrestricted sampling (under which quadrats are placed randomly within the row) and restricted sampling (under which quadrats are randomly placed within a row under the restriction that they coincide with the beginning of an infested strip). The bias of estimators of weed density under each of these two approaches was derived and bias-corrected estimators of weed density from the two methods were compared on the basis of their variance. The variance under restricted sampling is less than or equal to the variance under unrestricted sampling so that, by a minimum variance criterion, restricted sampling using a bias correction is the better technique.

In this paper we focus on a class of linear Hawkes processes with general immigrants. These are counting processes with shot-noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept of the age pyramid which evolves according to immigration and births. The virtue of this approach that combines an intensity process definition and a branching representation is that the population age pyramid keeps track of all past events. This is used to compute new distribution properties for a class of Hawkes processes with general immigrants which generalize the popular exponential fertility function. The pathwise construction of the Hawkes process and its underlying population is also given.

Thinning a large concentric ring array by an evolutionary algorithm needs to handle a large amount of variables. The computational time to find out the optimum elements set increases with the increase of array size. Moreover, thinning significantly reduces the directivity of the array. In this paper, the authors propose a pattern synthesis method to reduce the peak sidelobe level (peak SLL) while keeping first null beamwidth (FNBW) of the array fixed by thinning the outermost rings of the array based on Gravitational Search Algorithm (GSA). Two different cases have been studied. In the first case only the outermost ring of the array is thinned and in the second case the two outermost rings are thinned. The FNBW of the optimized array is kept equal to or less than that of a fully populated, uniformly excited and 0.5 λ spaced concentric ring array of same number of elements and rings. The directivity of the optimized array for the above two cases are compared with an array optimized by thinning all the rings, while keeping the design criteria same as the above two cases. The optimized array by thinning the outermost rings gives higher directivity over the optimized array by thinning all the rings. Time required for computing the optimum elements state for the above two cases using GSA are shown lesser compared to the optimized array by thinning all the rings using the same algorithm. The peak SLL and the FNBW of the optimized array for the above two cases are also compared with the optimized array by thinning all the rings.

Nature inspired optimization algorithms, namely artificial bee colony (ABC) optimization and firefly algorithm (FA), have been applied to synthesize beam patterns of a hexagonal planar array of isotropic elements. Two different cases, comprising two different beam patterns of a pencil beam and a square footprint pattern over a bounded region with lower peak sidelobe levels are presented. The pencil beam is generated by thinning the uniformly excited array and the square footprint pattern is generated by imposing optimum amplitudes, phases, and their corresponding states (“on”/“off”) to the array elements. The optimum values of the parameters for both the cases are computed using ABC and FA individually, and the superiority of FA over ABC for the proposed problem in terms of computing solutions for both the cases is established.

We describe a novel method for in situ measurement of the local thickness of a freely suspended solid-state membrane after thinning with a focused helium ion beam. The technique utilizes a custom stage for the helium ion microscope that allows the secondary electron detector used for normal imaging to collect information from ions transmitted through the sample. We find that relative brightness in the transmission image scales directly with the membrane thickness as determined by atomic force microscopy measurements.

Introduction. The aim of ourresearch was to optimize the number of young mango (Mangiferaindica L. cv. ‘Arumanis’) fruits that could be maintainedper panicle and to improve the criteria for the selection of fruitto be maintained in loco to allow a high yieldto be achieved. Materials and methods. The factors investigatedwere the number of young fruits maintained per panicle (either 2,4 or 6), while the criteria of young fruits to be maintained were:the number of biggest fruit, fruits attached at the base of thepanicle, and fruits distributed evenly from the base to the topof the panicle. Results. Our study shows that maintainingsix young fruits per panicle gave the highest weight of harvestedmango fruits per plant (33 kg) and the lowest weight per fruit (466 g).Maintaining the biggest mango fruit on the panicle resulted in thehighest weight per fruit (496 g). Conclusion. Increasingthe number of young fruits maintained per panicle from 2 to 6 linearlyincreased the weight of fruits per plant, although it decreasedthe weight per fruit linearly.

In a repulsive point process, points act as if they are repelling one another, leading to underdispersed configurations when compared to a standard Poisson point process. Such models are useful when competition for resources exists, as in the locations of towns and trees. Bertil Matérn introduced three models for repulsive point processes, referred to as types I, II, and III. Matérn used types I and II, and regarded type III as intractable. In this paper an algorithm is developed that allows for arbitrarily accurate approximation of the likelihood for data modeled by the Matérn type-III process. This method relies on a perfect simulation method that is shown to be fast in practice, generating samples in time that grows nearly linearly in the intensity parameter of the model, while the running times for more naive methods grow exponentially.

Our objective is to construct a perfect simulation algorithm for unmarked and marked Hawkes processes. The usual straightforward simulation algorithm suffers from edge effects, whereas our perfect simulation algorithm does not. By viewing Hawkes processes as Poisson cluster processes and using their branching and conditional independence structures, useful approximations of the distribution function for the length of a cluster are derived. This is used to construct upper and lower processes for the perfect simulation algorithm. A tail-lightness condition turns out to be of importance for the applicability of the perfect simulation algorithm. Examples of applications and empirical results are presented.

Introduction. The chemical fruit thinning of apple trees carried out after flowering is a current practice used to improve fruit size and quality, to ensure the return of flowering and to reduce the biennial bearing. Our work studied the effectiveness of two particular chemical thinners (Accel and carbaryl) applied to three apple tree cultivars, and their effects on the fruit yield and quality. Materials and methods. Two identical experiments were undertaken on mature apple trees in 1995 and 1996. They made it possible to test spraying after flowering of Accel and carbaryl at three different concentrations and applied to the three `Empire', `Jan-A-Red' and `Braeburn' apple tree cultivars. The effect of the chemical substances was evaluated with parameters of fruit set, fruit quality and yield. Results and discussion. For the three apple tree cultivars studied, the spraying of Accel and carbaryl made it possible to reduce the fruit set and to improve the apple yield, pH and soluble solids concentrations. However, the treatments did not affect the fruit seed number, the fruit length and diameter, or the [fruit length / fruit diameter] ratio. Conclusion. With the concentrations used, Accel and carbaryl were effective for thinning the three apple tree cultivars tested. These chemical thinners increased yield and improved certain parameters of the apple quality.

Introduction. Plusieurs facteurs peuvent contribuer à l'obtention des niveaux excessifs de nouaison chez le pommier. Cette nouaison excessive aboutit généralement à l'obtention de fruits de petit calibre et de qualité médiocre et peut accentuer le phénomène d'alternance. Les travaux présentés ont permis de tester différents traitements d'éclaircissage chimique adaptés aux conditions marocaines. Matériel et méthodes. Deux produits chimiques ont été testés à deux concentrations différentes chacun : l'acide naphtalène acétique (ANA) à (1,0 et 1,5) g$\cdot$100 L-1 et le N-méthyl carbamate de napthyl-1 (carbaryl) à (80 et 100) g$\cdot$100 L-1, sur deux variétés de pommier couramment cultivées au Maroc : `Golden Smoothee' et `Ozark Gold'. Les traitements témoins ont été constitués par des pommiers éclaircis manuellement ou non éclaircis. Les produits ont été appliqués sur des fruits au stade de (10 à 12) mm de diamètre, soit 17 j après pleine floraison. Résultats. Les résultats d'éclaircissage ont varié avec la variété, le produit utilisé et sa concentration. Cette variation s'est manifestée sur l'évolution de la chute des fruits, la proportion de corymbes portant moins de quatre fruits, le rendement et le calibre du fruit. L'éclaircissage a été plus satisfaisant pour `Ozark Gold' que pour `Golden Smoothee' et pour le carbaryl que pour l'ANA. Conclusion. Le carbaryl à 100 g$\cdot$100 L-1 a donné de très bons résultats, notamment sur `Ozark Gold'. Il a permis d'obtenir des taux de chute de fruits, des proportions de corymbes à peu de fruits et de fruits de calibre supérieur, ainsi qu'un rendement quantitatif équivalents à ceux obtenus sur les plants témoins éclaircis manuellement.

This is a follow-up of a previous paper by the author, where claims reserving in non-life insurance is treated in the framework of a marked Poisson claims process. A key result on decomposition of the process is generalized, and a number of related results are added. Their usefulness is demonstrated by examples and, in particular, the connection to the analogous discrete time model is clarified. The problem of predicting the outstanding part of reported but not settled claims is revisited and, by way of example, solved in a model where the partial payments are governed by a Dirichlet process. The process of reported claims is examined, and its dual relationship to the process of occurred claims is pointed out.

We consider a class of stationary infinite-order moving average processes with margins in the class of infinitely divisible exponential dispersion models. The processes are constructed by means of the thinning operation of Joe (1996), generalizing the binomial thinning used by McKenzie (1986, 1988) and Al-Osh and Alzaid (1987) for integer-valued time series. As a special case we obtain a class of autoregressive moving average processes that are different from the ARMA models proposed by Joe (1996). The range of possible marginal distributions for the new models is extensive and includes all infinitely divisible distributions with finite moment generating functions, hereunder many known discrete, continuous and mixed distributions.

One result that is of both theoretical and practical importance regarding point processes is the method of thinning. The basic idea of this method is that under some conditions, there exists an embedded Poisson process in any point process such that all its arrival points form a sub-sequence of the Poisson process. We extend this result by showing that on the embedded Poisson process of a uni- or multi-variable marked point process in which interarrival time distributions may depend on the marks, one can define a Markov chain with a discrete state that characterizes the stage of the interarrival times. This implies that one can construct embedded Markov chains with countable state spaces for the state processes of many practical systems that can be modeled by such point processes.

Discrete minification processes are introduced and it is proved that the discrete first-order autoregression of McKenzie (1986) and the discrete minification process are mutually time-reversible if and only if they have common marginal geometric distribution, corresponding to a result for continuous processes given by Chernick et al. (1988). It is also proved that a discrete minification process is time-reversible if and only if it has marginal Bernoulli distribution.

It is shown that the gamma distribution with shape parameter α can be obtained through a p-thinning for every 0 < p < 1, when 0 < α ≦ 1. In the case α > 1, the gamma distribution cannot be obtained through thinning. The class of renewal processes with gamma-distributed times between events is considered. It is shown that an ordinary gamma renewal process is a Cox process if and only if 0 < α ≦ 1. Necessary and sufficient conditions for delayed gamma renewal processes to be Cox are also given. Finally, a short description of the gamma renewal process as a Cox process is given.

Some simple models are described which may be used for the modelling or generation of sequences of dependent discrete random variates with negative binomial and geometric univariate marginal distributions. The models are developed as analogues of well-known continuous variate models for gamma and negative exponential variates. The analogy arises naturally from a consideration of self-decomposability for discrete random variables. An alternative derivation is also given wherein both the continuous and the discrete variate processes arise simultaneously as measures on a process of overlapping intervals. The former is the process of interval lengths and the latter is a process of counts on these intervals.