Strong memoryless times and rare events in Markov renewal point processes

Let W be the number of points in (0,t] of a stationary finite-state Markov renewal point process. We derive a bound for the total variation distance between the distribution of W and a compound Poisson distribution. For any nonnegative random variable \zeta, we construct a ``strong memoryless time'' \hat \zeta such that \zeta-t is exponentially distributed conditional on {\hat \zeta\leq t, \zeta>t}, for each t. This is used to embed the Markov renewal point process into another such process whose state space contains a frequently observed state which represents loss of memory in the original process. We then write W as the accumulated reward of an embedded renewal reward process, and use a compound Poisson approximation error bound for this quantity by Erhardsson. For a renewal process, the bound depends in a simple way on the first two moments of the interrenewal time distribution, and on two constants obtained from the Radon-Nikodym derivative of the interrenewal time distribution with respect to an exponential distribution. For a Poisson process, the bound is 0.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000005

Conditions for convergence of random coefficient AR(1) processes and perpetuities in higher dimensions

A $d$-dimensional RCA(1) process is a generalization of the $d$-dimensional AR(1) process, such that the coefficients $\{M_t;t=1,2,\ldots\}$ are i.i.d. random matrices. In the case $d=1$, under a nondegeneracy condition, Goldie and Maller gave necessary and sufficient conditions for the convergence in distribution of an RCA(1) process, and for the almost sure convergence of a closely related sum of random variables called a perpetuity. We here prove that under the condition $\Vert {\prod_{t=1}^nM_t}\Vert \stackrel{\mathrm{a.s.}}{\longrightarrow}0$ as $n\to\infty$, most of the results of Goldie and Maller can be extended to the case $d>1$. If this condition does not hold, some of their results cannot be extended.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ513 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

A set-valued framework for birth-and-growth process

We propose a set-valued framework for the well-posedness of birth-and-growth process. Our birth-and-growth model is rigorously defined as a suitable combination, involving Minkowski sum and Aumann integral, of two very general set-valued processes representing nucleation and growth respectively. The simplicity of the used geometrical approach leads us to avoid problems arising by an analytical definition of the front growth such as boundary regularities. In this framework, growth is generally anisotropic and, according to a mesoscale point of view, it is not local, i.e. for a fixed time instant, growth is the same at each space point

Helicobacter suis infection alters glycosylation and decreases the pathogen growth inhibiting effect and binding avidity of gastric mucins

Helicobacter suis is the most prevalent non-Helicobacter pylori Helicobacter species in the human stomach and is associated with chronic gastritis, peptic ulcer disease, and gastric mucosa-associated lymphoid tissue (MALT) lymphoma. H. suis colonizes the gastric mucosa of 60-95% of pigs at slaughter age, and is associated with chronic gastritis, decreased weight gain, and ulcers. Here, we show that experimental H. suis infection changes the mucin composition and glycosylation, decreasing the amount of H. suis-binding glycan structures in the pig gastric mucus niche. Similarly, the H. suis-binding ability of mucins from H. pylori-infected humans is lower than that of noninfected individuals. Furthermore, the H. suis growth-inhibiting effect of mucins from both noninfected humans and pigs is replaced by a growth-enhancing effect by mucins from infected individuals/pigs. Thus, Helicobacter spp. infections impair the mucus barrier by decreasing the H. suis-binding ability of the mucins and by decreasing the antiprolific activity that mucins can have on H. suis. Inhibition of these mucus-based defenses creates a more stable and inhabitable niche for H. suis. This is likely of importance for long-term colonization and outcome of infection, and reversing these impairments may have therapeutic benefits

Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source

We present two novel approaches for the computation of the exact distribution of a pattern in a long sequence. Both approaches take into account the sparse structure of the problem and are two-part algorithms. The first approach relies on a partial recursion after a fast computation of the second largest eigenvalue of the transition matrix of a Markov chain embedding. The second approach uses fast Taylor expansions of an exact bivariate rational reconstruction of the distribution. We illustrate the interest of both approaches on a simple toy-example and two biological applications: the transcription factors of the Human Chromosome 5 and the PROSITE signatures of functional motifs in proteins. On these example our methods demonstrate their complementarity and their hability to extend the domain of feasibility for exact computations in pattern problems to a new level

Statistical aspects of birth--and--growth stochastic processes

The paper considers a particular family of set--valued stochastic processes modeling birth--and--growth processes. The proposed setting allows us to investigate the nucleation and the growth processes. A decomposition theorem is established to characterize the nucleation and the growth. As a consequence, different consistent set--valued estimators are studied for growth process. Moreover, the nucleation process is studied via the hitting function, and a consistent estimator of the nucleation hitting function is derived.Comment: simpler notations typo

Exact distribution of a pattern in a set of random sequences generated by a Markov source: applications to biological data

<p>Abstract</p> <p>Background</p> <p>In bioinformatics it is common to search for a pattern of interest in a potentially large set of rather short sequences (upstream gene regions, proteins, exons, etc.). Although many methodological approaches allow practitioners to compute the distribution of a pattern count in a random sequence generated by a Markov source, no specific developments have taken into account the counting of occurrences in a set of independent sequences. We aim to address this problem by deriving efficient approaches and algorithms to perform these computations both for low and high complexity patterns in the framework of homogeneous or heterogeneous Markov models.</p> <p>Results</p> <p>The latest advances in the field allowed us to use a technique of optimal Markov chain embedding based on deterministic finite automata to introduce three innovative algorithms. Algorithm 1 is the only one able to deal with heterogeneous models. It also permits to avoid any product of convolution of the pattern distribution in individual sequences. When working with homogeneous models, Algorithm 2 yields a dramatic reduction in the complexity by taking advantage of previous computations to obtain moment generating functions efficiently. In the particular case of low or moderate complexity patterns, Algorithm 3 exploits power computation and binary decomposition to further reduce the time complexity to a logarithmic scale. All these algorithms and their relative interest in comparison with existing ones were then tested and discussed on a toy-example and three biological data sets: structural patterns in protein loop structures, PROSITE signatures in a bacterial proteome, and transcription factors in upstream gene regions. On these data sets, we also compared our exact approaches to the tempting approximation that consists in concatenating the sequences in the data set into a single sequence.</p> <p>Conclusions</p> <p>Our algorithms prove to be effective and able to handle real data sets with multiple sequences, as well as biological patterns of interest, even when the latter display a high complexity (PROSITE signatures for example). In addition, these exact algorithms allow us to avoid the edge effect observed under the single sequence approximation, which leads to erroneous results, especially when the marginal distribution of the model displays a slow convergence toward the stationary distribution. We end up with a discussion on our method and on its potential improvements.</p

Bullying : How does the educationalist combat bullying?

Detta arbete handlar om mobbning. Syftet är att ta reda på vad pedagogen ska göra då den upptäckt mobbning. Jag har valt att avgränsa till mobbning mellan barn/elever. Även om fokus riktar sig mot pedagogen tas även målsman och elever upp, eftersom de är viktiga parter i detta sammanhang. Mobbning finns i alla åldrar och försämrar skolprestationer. Vad och hur vuxna talar påverkar barn och elevers beteenden. Grupparbeten, gruppaktiviteter och lekgrupper kan pedagogen använda sig av för att skapa bra sammanhållning och gemenskap i klassen eller gruppen. Val av metod i detta arbete är fyra intervjuer. Två med lärare i årskurs 1-3, en förskolepedagog och en gruppintervju på tre pedagoger som arbetar inom förskolan. Resultatet blev bland annat att lärarna arbetar olika beroende på om det är verbal-, fysisk- eller tyst mobbning, medan förskolepedagogerna får den vardagliga kontakten med föräldrar. Arbetet utvärderas av skribenten i metoddiskussionen