bluuebunny/crossref_metadata_2025 huggingface dataset:
Nosocomial Pneumonia After Acute Stroke
Authors: Hilker Ruediger , Poetter Carsten , Findeisen Nahide , Sobesky Jan , Jacobs Andreas , Neveling Michael , Heiss Wolf-Dieter
Published: April 2003

Background and Purpose—

Pneumonia has been estimated to occur in about one third of patients after acute stroke. Only limited data are available on stroke-associated pneumonia (SAP) in specialized neurological intensive care units (NICUs).

Methods—

We enrolled 124 patients with acute stroke who were treated at our university hospital NICU in a prospective observational study. Incidence rates and risk factors of SAP and long-term clinical outcome were determined.

Results—

SAP incidence was 21% with a spectrum of pathogens, which is comparable to previously published data on general ICU patients. Mechanical ventilation, multiple location, and vertebrobasilar stroke, as well as dysphagia and abnormal chest x-ray findings, were identified as risk factors for the disease. SAP patients showed higher mortality rates than nondiseased subjects (acute, 26.9% versus 8.2%; long-term, 35.3% versus 14.3%) and a significantly poorer long-term clinical outcome (Barthel Index, 50.5±42.4 versus 81.5±27.8; Rankin Scale, 3.5±1.7 versus 2.2±1.6).

Conclusions—

Our data underline the considerable epidemiological and prognostic impact of SAP for the treatment of acute stroke patients in a specialized NICU setting. They demonstrate that the occurrence of SAP deteriorates clinical outcome in these patients. Our results allow us to identify high-risk stroke patients at time of NICU admission in whom the use of preventive treatment strategies is most promising.
Constraint-Induced Movement Therapy and Rehabilitation Exercises Lessen Motor Deficits and Volume of Brain Injury After Striatal Hemorrhagic Stroke in Rats
Authors: DeBow Suzanne B. , Davies Melissa L.A. , Clarke Heather L. , Colbourne Frederick
Published: April 2003

Background and Purpose—

Constraint-induced movement therapy (CIMT) promotes motor recovery after occlusive stroke in humans, but its efficacy after intracerebral hemorrhage (ICH) has not been investigated clinically or in the laboratory. In this study we tested whether CIMT and a rehabilitation exercise program would lessen motor deficits after ICH in rats.

Methods—

Rats were subjected to striatal ICH (via infusion of collagenase) or sham stroke. Seven days later, treatment began with CIMT (8 h/d of ipsilateral forelimb restraint), rehabilitation exercises (eg, reaching, walking; 1 h/d), or both for 7 days. Some rats were not treated. Motor deficits were assessed up to the 60-day survival time, after which the volume of tissue lost was determined.

Results—

Untreated ICH rats made more limb slips traversing a horizontal ladder and showed an asymmetry toward less use of the contralateral paw in the cylinder test of limb use asymmetry (day 28). These rats were also significantly less successful in the Montoya staircase test (days 55 to 59) of skilled reaching. Neither therapy alone provided much benefit. However, the combination of daily exercises and CIMT substantially and persistently improved recovery. Unexpectedly, this group had a statistically smaller volume of tissue lost than untreated ICH rats.

Conclusions—

The combination of focused rehabilitation exercises and CIMT effectively promotes functional recovery after ICH, while either therapy alone is less effective. This therapy may work in part by reducing the volume of tissue lost, likely through reducing atrophy while promoting remodeling.
Opening of Mitochondrial ATP-Sensitive Potassium Channels Is a Trigger of 3-Nitropropionic Acid–Induced Tolerance to Transient Focal Cerebral Ischemia in Rats
Authors: Horiguchi Takashi , Kis Bela , Rajapakse Nishadi , Shimizu Katsuyoshi , Busija David W.
Published: April 2003

Background and Purpose—

The role of mitochondrial ATP-sensitive potassium channels (mitoK
ATP
) in ischemic tolerance has been well documented in heart, but little work has been done in brain. To investigate the involvement of mitoK
ATP
activation in chemical preconditioning in brain, we examined the effect of 5-hydroxydecanoate (5-HD), a selective mitoK
ATP
blocker, on neurotoxin 3-nitropropionic acid (3-NPA)–induced ischemic tolerance to transient focal cerebral ischemia in rats.

Methods—

Male Wistar rats were administrated 3-NPA (20 mg/kg IP; n=16) or vehicle (saline; n=16) 3 days before temporary occlusion (120 minutes) of the middle cerebral artery; 5-HD (40 mg/kg IP; n=16) was injected 20 minutes before 3-NPA administration. Infarct volumes were measured 4 days after reperfusion. To directly investigate whether chemical preconditioning activates mitoK
ATP
, we tested the effect of prior incubation with 1 mmol/L 5-HD on 300 μmol/L 3-NPA–induced alterations of mitochondrial membrane potential (ΔΨ
m
) in cultured neurons and astrocytes using the fluorescent dye tetramethylrhodamine ethyl ester.

Results—

Treatment with 3-NPA exhibited a 16% reduction (
P
<0.05) and 23% reduction in infarct volume (
P
<0.01) for total brain and cortex, respectively. Pretreatment with 5-HD completely abolished the neuroprotective effect of chemical preconditioning. In cultured cells, 3-NPA resulted in mitochondrial depolarization. This change of ΔΨ
m
was completely blocked by 5-HD pretreatment.

Conclusions—

These results strongly suggest that opening of mitoK
ATP
plays a key role as the trigger in the development of 3-NPA–induced ischemic tolerance in brain.
Increased Expression of Neuronal Apolipoprotein E in Human Brain With Cerebral Infarction
Authors: Aoki Kazuko , Uchihara Toshiki , Sanjo Nobuo , Nakamura Ayako , Ikeda Kenji , Tsuchiya Kuniaki , Wakayama Yoshihiro
Published: April 2003

Background and Purpose—

Cellular origin of apolipoprotein E (ApoE) in the human brain and its roles in physiological and pathological conditions remain to be clarified.

Methods—

Immunolocalization of ApoE was investigated in a series of autopsied human brains with or without infarction. ApoE expression was also estimated on immunoblot on protein extracts from autopsied brains and a cultured neuroblastoma cell line of human origin (GOTO) subjected to an oxidative stress induced by exposure to hydrogen peroxide (0.2 mmol/L).

Results—

In addition to astrocytes and microglia, neurons and degenerated axons in and around the ischemic foci contained ApoE-like immunoreactivity, which was more intense in recent ischemic foci. Immunoblot demonstrated an increase in expression of ApoE in brain extracts from ischemic lesion, and this increase was also pronounced in the cultured neuroblastoma cell line after the stress.

Conclusions—

Accumulation of ApoE in neurons in and around ischemic foci of the human brain is related to an increase in ApoE synthesis in neurons, as seen in cultured neuronal cells after oxidative stress. Intrinsic regenerative activity of neuron in reaction to external insults may be related to this increase in ApoE of neuronal origin.
Bedside Monitoring of Circulating Blood Volume After Subarachnoid Hemorrhage
Authors: Kasuya Hidetoshi , Onda Hideaki , Yoneyama Taku , Sasaki Toshiyuki , Hori Tomokatsu
Published: April 2003

Background and Purpose—

Maintenance of an adequate intravascular volume is important in the management of patients with subarachnoid hemorrhage (SAH). The purpose of this study was to investigate the circulating blood volume (CBV) after SAH with the use of indocyanine green pulse spectrophotometry.

Methods—

CBV and plasma hormones related to stress and fluid regulation were measured 4 times: day 2 to 3, day 4 to 5, day 7 to 8, and day 14 in 50 consecutive patients with SAH surgically treated within 48 hours.

Results—

The mean value of CBV was 64 mL/kg on day 2 to 3, which gradually increased to 69 mL/kg on day 4 to 5, 71 mL/kg on day 7 to 8, and 70 mL/kg on day 14 (
P
=0.005) (control, 72 mL/kg). The clinical grades and plasma corticotropin levels were higher in patients with <60 mL/kg of CBV on day 2 to 3 (
P
<0.05 for both). There were no significant differences in other physiological and laboratory parameters such as time for surgery, estimated blood loss, levels of plasma noradrenaline, brain natriuretic peptide, serum sodium, and hematocrit. When CBV was decreased >10% of the former level, there were decreases in hematocrit (
P
<0.05), serum sodium (
P
<0.01), and serum albumin (
P
<0.05) and an increase in urinary sodium (
P
<0.05).

Conclusions—

A significant reduction of CBV, especially in patients with poor clinical grades, was noted after SAH and early surgery, which could not be detected by routine examinations. Anemia, central salt wasting, and hypoalbuminemia may be related to a decrease in CBV from the former level. Indocyanine green pulse spectrophotometry may be a powerful tool for the management of patients with SAH.
Clinical Relevance of Atrial Fibrillation/Flutter, Stroke, Pacemaker Implant, and Heart Failure in Emery-Dreifuss Muscular Dystrophy
Authors: Boriani Giuseppe , Gallina Margherita , Merlini Luciano , Bonne Gisèle , Toniolo Daniela , Amati Silvia , Biffi Mauro , Martignani Cristian , Frabetti Lorenzo , Bonvicini Marco , Rapezzi Claudio , Branzi Angelo
Published: April 2003

Background and Purpose—

Emery-Dreifuss muscular dystrophy (EDMD) is a rare inherited disorder associated with cardiac involvement. We investigated the spectrum and relevance of the cardiac manifestations of EDMD, focusing on bradyarrhythmias and tachyarrhythmias (including atrial fibrillation/flutter), embolic stroke, and heart failure.

Methods and Results—

Eighteen patients (age 42.8±19.6 years) with genetically confirmed X-linked (n=10, including 3 carriers) or autosomal dominant (n=8) EDMD were followed for a period ranging from 1 to 30 years in a research center for neuromuscular diseases and in a university cardiological department. Pacemakers were required by 10 of 18 (56%) patients for bradyarrhythmia, and related complications occurred in 3 of 10 (30%) cases. Atrial fibrillation/flutter developed in 11 of 18 (61%) patients, with atrial standstill subsequently occurring in 5 of 11 (45%) cases and embolic stroke (most often disabling) in 4 of 11 (36%). Heart failure requiring transplantation occurred in 1 of 18 (6%) patients, and asymptomatic left ventricular dysfunction in a further 3 (17%). No relationship was evident between neuromuscular impairment and cardiac involvement.

Conclusions—

Both X-linked and autosomal dominant EDMD patients risk not only bradyarrhythmia (requiring pacemaker implant) but also atrial fibrillation/flutter, which often anticipates atrial standstill and can cause disabling embolic stroke at a relatively young age. Antithromboembolic prophylaxis has to be recommended in EDMD patients with atrial fibrillation/flutter or atrial standstill. With careful monitoring, survival after pacemaker implant may be long. Heart failure, which seems to occur only in a minority of patients, may be severe.
Epidemiological Impact in the United States of a Tissue-Based Definition of Transient Ischemic Attack
Authors: Ovbiagele Bruce , Kidwell Chelsea S. , Saver Jeffrey L.
Published: April 2003

Background and Purpose—

The traditional definition of transient ischemic attack (TIA), based on an arbitrary time criterion of symptom resolution within 24 hours, is problematic because a large number of patients with traditionally defined TIAs have a relevant cerebral infarction on brain imaging. The objective of this study was to characterize the epidemiological impact of adopting a tissue-based definition of TIA.

Methods—

Estimates of the annual US incidence of traditionally defined transient ischemic attacks were abstracted from the literature. Models were then constructed for determining the frequency of brain injury in traditionally defined TIAs, derived from recent human studies of MR diffusion-weighted imaging (DWI) in transient cerebral ischemia.

Results—

Traditionally defined US TIA annual incidence rates ranged from 37 to 107 per 100 000 per year. Across 5 series, the raw frequency of DWI positivity in traditionally defined TIAs was 44%. Adjusting for an overrepresentation of longer-duration TIAs in MR series yielded an expected frequency of diffusion MRI positivity of 33% in unselected, traditionally defined TIAs. Applying this model to the US population in the year 2000 showed that adopting a tissue-based definition of TIA would decrease the annual number of events classified as TIAs from 179 840 to 120 493 and increase events classified as strokes from 821 181 to 880 520.

Conclusions—

Adopting a tissue-based definition of transient ischemic attack would reduce estimates of the annual incidence of TIA by 33% (sensitivity analysis range, 19% to 44%) and increase estimates of the annual incidence of stroke in the United States by 7% (range, 4% to 10%).
Platelet Function Under Aspirin, Clopidogrel, and Both After Ischemic Stroke
Authors: Grau Armin J. , Reiners Sven , Lichy Christoph , Buggle Florian , Ruf Andreas
Published: April 2003

Background and Purpose—

Combined antiplatelet agents may offer additive protection over single drugs after stroke. We investigated whether platelet activation is reduced under combined aspirin and clopidogrel compared with each drug alone.

Methods—

In a case-crossover study, 31 patients with previous atherothrombotic or lacunar stroke who were treated with aspirin (100 to 300 mg/d) received clopidogrel (75 mg/d) and both aspirin and clopidogrel for 4 weeks. Platelet function in whole blood was studied after each treatment period and in healthy control subjects to assess activation-dependent antigens CD62p and CD63 by flow cytometry and collagen/epinephrine (CEPI-CT) and collagen/ADP (CADP-CT) closure times with the platelet function analyzer PFA-100, which investigates platelet-related function under shear stress.

Results—

CD62p expression and CD63 expression were not different under the 3 treatment regimens. CD63 but not CD62p expression was lower in control subjects than in stroke patients regardless of the antiplatelet treatment (
P
<0.05). CEPI-CT was prolonged under aspirin and aspirin plus clopidogrel compared with clopidogrel monotherapy (
P
<0.0001). CADP-CT was longer under combination therapy than under aspirin (
P
=0.0009) or clopidogrel (
P
=0.0074) or in control subjects (
P
=0.0010), mainly because of strong prolongation in a patient subgroup (28%).

Conclusions—

CD63 expression reflecting the release of platelet lysosomes is consistently increased after stroke and incompletely suppressed by treatment with aspirin, clopidogrel, or both. The strong prolongation of CADP-CT under combined aspirin and clopidogrel in a patient subgroup may indicate a lower risk of thrombosis but also a higher risk of hemorrhage. The predictive value of platelet activation parameters requires investigation in prospective studies.
Weighted renewal functions: a hierarchical approach
Authors: Omey Edward , Teugels Jef L.
Published: April 2003

We extend classical renewal theorems to the weighted case. A hierarchical chain of successive sharpenings of asymptotic statements on the weighted renewal functions is obtained by imposing stronger conditions on the weighting coefficients.
Asymptotics of locally-interacting Markov chains with global signals
Authors: Horst Ulrich
Published: April 2003

We study the long-run behaviour of interactive Markov chains on infinite product spaces. The behaviour at a single site is influenced by the local situation in some neighbourhood and by a random signal about the average situation throughout the whole system. The asymptotic behaviour of such Markov chains is analyzed on the microscopic level and on the macroscopic level of empirical fields. We give sufficient conditions for convergence on the macroscopic level. Combining a convergence result from the theory of random systems with complete connections with a perturbation of the Dobrushin-Vasserstein contraction technique, we show that macroscopic convergence implies that the underlying microscopic process has local asymptotic loss of memory.
Density approximation and exact simulation of random variables that are solutions of fixed-point equations
Authors: Devroye Luc , Neininger Ralph
Published: April 2003

An algorithm is developed for exact simulation from distributions that are defined as fixed points of maps between spaces of probability measures. The fixed points of the class of maps under consideration include examples of limit distributions of random variables studied in the probabilistic analysis of algorithms. Approximating sequences for the densities of the fixed points with explicit error bounds are constructed. The sampling algorithm relies on a modified rejection method.
Invariant distributions for shapes in sequences of randomly-divided rectangles
Authors: Chen Francis K. C. , Cowan Richard
Published: April 2003

Interest has been shown in Markovian sequences of geometric shapes. Mostly the equations for invariant probability measures over shape space are extremely complicated and multidimensional. This paper deals with rectangles which have a simple one-dimensional shape descriptor. We explore the invariant distributions of shape under a variety of randomised rules for splitting the rectangle into two sub-rectangles, with numerous methods for selecting the next shape in sequence. Many explicit results emerge. These help to fill a vacant niche in shape theory, whilst contributing at the same time, new distributions on [0,1] and interesting examples of Markov processes or, in the language of another discipline, of stochastic dynamical systems.
First contact distributions for spatial patterns: regularity and estimation
Authors: Hansen Martin B. , Baddeley Adrian J. , Gill Richard D.
Published: April 2003

For applications in spatial statistics, an important property of a random set X in ℝk is its first contact distribution. This is the distribution of the distance from a fixed point 0 to the nearest point of X, where distance is measured using scalar dilations of a fixed test set B. We show that, if B is convex and contains a neighbourhood of 0, the first contact distribution function FB is absolutely continuous. We give two explicit representations of FB, and additional regularity conditions under which FB is continuously differentiable. A Kaplan-Meier estimator of FB is introduced and its basic properties examined.
The convex hull of samples from self-similar distributions
Authors: Hueter Irene
Published: April 2003

Let X1, X2,… be i.i.d. random points in ℝ2 with distribution ν, and let Nn denote the number of points spanning the convex hull of X1, X2,…,Xn. We obtain lim infn→∞E(Nn)n-1/3 ≥ γ1 and E(Nn) ≤ γ2n1/3(logn)2/3 for some positive constants γ1, γ2 and sufficiently large n under the assumption that ν is a certain self-similar measure on the unit disk. Our main tool consists in a geometric application of the renewal theorem. Exactly the same approach can be adopted to prove the analogous result in ℝd.
Estimating the reduced moments of a random measure
Authors: Kiêu Kiên , Mora Marianne
Published: April 2003

We consider a random measure for which distribution is invariant under the action of a standard transformation group. The reduced moments are defined by applying classical theorems on invariant measure decomposition. We present a general method for constructing unbiased estimators of reduced moments. Several asymptotic results are established under an extension of the Brillinger mixing condition. Examples related to stochastic geometry are given.
A Duality for Poisson Flats
Authors: Schneider Rolf
Published: April 2003

In keeping with the intersection density of a stationary Poisson process of r-flats in Euclidean d-space, where r ≥ d/2, we introduce a notion of closeness, called proximity, for such processes if r < d/2. It is shown that the two notions are connected by a duality: the proximity of a stationary Poisson r-flat process is, up to a constant factor, the intersection density of a certain unique stationary Poisson (d − r)-flat process.
Perfect simulation of some point processes for the impatient user
Authors: Thönnes Elke
Published: April 2003

Recently Propp and Wilson [14] have proposed an algorithm, calledcoupling from the past(CFTP), which allows not only an approximate but perfect (i.e. exact) simulation of the stationary distribution of certain finite state space Markov chains. Perfect sampling using CFTP has been successfully extended to the context of point processes by, amongst other authors, Häggströmet al. [5]. In [5] Gibbs sampling is applied to a bivariate point process, the penetrable spheres mixture model [19]. However, in general the running time of CFTP in terms of number of transitions is not independent of the state sampled. Thus an impatient user who aborts long runs may introduce a subtle bias, the user impatience bias. Fill [3] introduced an exact sampling algorithm for finite state space Markov chains which, in contrast to CFTP, is unbiased for user impatience. Fill's algorithm is a form of rejection sampling and similarly to CFTP requires sufficient monotonicity properties of the transition kernel used. We show how Fill's version of rejection sampling can be extended to an infinite state space context to produce an exact sample of the penetrable spheres mixture process and related models. Following [5] we use Gibbs sampling and make use of the partial order of the mixture model state space. Thus we construct an algorithm which protects against bias caused by user impatience and which delivers samples not only of the mixture model but also of the attractive area-interaction and the continuum random-cluster process.
Reduced subcritical Galton-Watson processes in a random environment
Authors: Fleischmann Klaus , Vatutin Vladimir A.
Published: April 2003

We study the structure of genealogical trees of reduced subcritical Galton-Watson processes in a random environment assuming that all (randomly varying in time) offspring generating functions are fractional linear. We show that this structure may differ significantly from that of the ‘classical’ reduced subcritical Galton-Watson processes. In particular, it may look like a complex ‘hybrid’ of classical reduced super and subcritical processes. Some relations with random walks in a random environment are discussed.
Markov Chain Monte Carlo simulation of the distribution of some perpetuities
Authors: Paulsen Jostein , Hove Arne
Published: April 2003

We study the present valueZ∞= ∫0∞e-Xt-dYtwhere (X,Y) is an integrable Lévy process. This random variable appears in various applications, and several examples are known where the distribution ofZ∞is calculated explicitly. Here sufficient conditions forZ∞to exist are given, and the possibility of finding the distribution ofZ∞by Markov chain Monte Carlo simulation is investigated in detail. Then the same ideas are applied to the present valueZ-∞= ∫0∞exp{-∫0tRsds}dYtwhereYis an integrable Lévy process andRis an ergodic strong Markov process. Numerical examples are given in both cases to show the efficiency of the Monte Carlo methods.
On the supremum distribution of integrated stationary Gaussian processes with negative linear drift
Authors: Choe Jinwoo , Shroff Ness B.
Published: April 2003

In this paper we study the supremum distribution of a class of Gaussian processes having stationary increments and negative drift using key results fromExtreme Value Theory. We focus on deriving an asymptotic upper bound to the tail of the supremum distribution of such processes. Our bound is valid for both discrete- and continuous-time processes. We discuss the importance of the bound, its applicability to queueing problems, and show numerical examples to illustrate its performance.
Central limit theorem for wave-functionals of Gaussian processes
Authors: Piterbarg Vladimir , Rychlik Igor
Published: April 2003

In this paper a central limit theorem is proved for wave-functionals defined as the sums of wave amplitudes observed in sample paths of stationary continuously differentiable Gaussian processes. Examples illustrating this theory are given.
Smallest-fit selection of random sizes under a sum constraint: weak convergence and moment comparisons
Authors: Boshuizen Frans A. , Kertz Robert P.
Published: April 2003

In this paper, in work strongly related with that of Coffman et al. [5], Bruss and Robertson [2], and Rhee and Talagrand [15], we focus our interest on an asymptotic distributional comparison between numbers of ‘smallest’ i.i.d. random variables selected by either on-line or off-line policies. Let X1,X2,… be a sequence of i.i.d. random variables with distribution function F(x), and let X1,n,…,Xn,n be the sequence of order statistics of X1,…,Xn. For a sequence (cn)n≥1 of positive constants, the smallest fit off-line counting random variable is defined by Ne(cn) := max {j ≤ n : X1,n + … + Xj,n ≤ cn}. The asymptotic joint distributional comparison is given between the off-line count Ne(cn) and on-line counts Nnτ for ‘good’ sequential (on-line) policies τ satisfying the sum constraint ∑j≥1XτjI(τj≤n) ≤ cn. Specifically, for such policies τ, under appropriate conditions on the distribution function F(x) and the constants (cn)n≥1, we find sequences of positive constants (Bn)n≥1, (Δn)n≥1 and (Δ'n)n≥1 such that

for some non-degenerate random variables W and W'. The major tools used in the paper are convergence of point processes to Poisson random measure and continuous mapping theorems, strong approximation results of the normalized empirical process by Brownian bridges, and some renewal theory.
Stably coalescent stochastic froths
Authors: Clark J. M. C. , Katsouros V.
Published: April 2003

A model of a stochastic froth is introduced in which the rate of random coalescence of a pair of bubbles depends on an inverse power law of their sizes. The main question of interest is whether froths with a large number of bubbles can grow in a stable fashion; that is, whether under some time-varying change of scale the distributions of rescaled bubble sizes become approximately stationary. It is shown by way of a law of large numbers for the froths that the question can be re-interpreted in terms of a measure flow solving a nonlinear Boltzmann equation that represents an idealized deterministic froth. Froths turn out to be stable in the sense that there are scalings in which the rescaled measure flow is tight and, for a particular case, stable in the stronger sense that the rescaled flow converges to an equilibrium measure. Precise estimates are also given for the degree of tightness of the rescaled measure flows.
The asymptotic final size distribution of multitype chain-binomial epidemic processes
Authors: Andersson Mikael
Published: April 2003

A multitype chain-binomial epidemic process is defined for a closed finite population by sampling a simple multidimensional counting process at certain points. The final size of the epidemic is then characterized, given the counting process, as the smallest root of a non-linear system of equations. By letting the population grow, this characterization is used, in combination with a branching process approximation and a weak convergence result for the counting process, to derive the asymptotic distribution of the final size. This is done for processes with an irreducible contact structure both when the initial infection increases at the same rate as the population and when it stays fixed.
Asymptotics of palm-stationary buffer content distributions in fluid flow queues
Authors: Rolski Tomasz , Schlegel Sabine , Schmidt Volker
Published: April 2003

We study a fluid flow queueing system with m independent sources alternating between periods of silence and activity; m ≥ 2. The distribution function of the activity periods of one source, is supposed to be intermediate regular varying. We show that the distribution of the net increment of the buffer during an aggregate activity period (i.e. when at least one source is active) is asymptotically tail-equivalent to the distribution of the net input during a single activity period with intermediate regular varying distribution function. In this way, we arrive at an asymptotic representation of the Palm-stationary tail-function of the buffer content at the beginning of aggregate activity periods. Our approach is probabilistic and extends recent results of Boxma (1996; 1997) who considered the special case of regular variation.
Large deviations, moderate deviations, and queues with long-range dependent input
Authors: Chang Cheng-Shang , Yao David D. , Zajic Tim
Published: April 2003

Long-range dependence has been recently asserted to be an important characteristic in modeling telecommunications traffic. Inspired by the integral relationship between the fractional Brownian motion and the standard Brownian motion, we model a process with long-range dependence, Y, as a fractional integral of Riemann-Liouville type applied to a more standard process X—one that does not have long-range dependence. When X takes the form of a sample path process with bounded stationary increments, we provide a criterion for X to satisfy a moderate deviations principle (MDP). Based on the MDP of X, we then establish the MDP for Y. Furthermore, we characterize, in terms of the MDP, the transient behavior of queues when fed with the long-range dependent input process Y. In particular, we identify the most likely path that leads to a large queue, and demonstrate that unlike the case where the input has short-range dependence, the path here is nonlinear.
On connected component Markov point processes
Authors: Chin Y. C. , Baddeley A. J.
Published: April 2003

We note some interesting properties of the class of point processes which are Markov with respect to the ‘connected component’ relation. Results in the literature imply that this class is closed under random translation and independent cluster generation with almost surely non-empty clusters. We further prove that it is closed under superposition. A wide range of examples is also given.
Central limit theorem for a class of random measures associated with germ-grain models
Authors: Heinrich Lothar , Molchanov Ilya S.
Published: April 2003

The germ-grain model is defined as the union of independent identically distributed compact random sets (grains) shifted by points (germs) of a point process. The paper introduces a family of stationary random measures in ℝdgenerated by germ-grain models and defined by the sum of contributions of non-overlapping parts of the individual grains. The main result of the paper is the central limit theorem for these random measures, which holds for rather general independently marked germ-grain models, including those with non-Poisson distribution of germs and non-convex grains. It is shown that this construction of random measures includes those random measures obtained by positively extended intrinsic volumes. In the Poisson case it is possible to prove a central limit theorem under weaker assumptions by using approximations bym-dependent random fields. Applications to statistics of the Boolean model are also discussed. They include a standard way to derive limit theorems for estimators of the model parameters.
Quermass-interaction processes: conditions for stability
Authors: Kendall W. S. , van Lieshout M. N. M. , Baddeley A. J.
Published: April 2003

We consider a class of random point and germ-grain processes, obtained using a rather natural weighting procedure. Given a Poisson point process, on each point one places agrain, a (possibly random) compact convex set. Let Ξ be the union of all grains. One can now construct new processes whose density is derived from an exponential of a linear combination of quermass functionals of Ξ. If only the area functional is used, then the area-interaction point process is recovered. New point processes arise if we include the perimeter length functional, or the Euler functional (number of components minus number of holes). The main question addressed by the paper is that of when the resulting point process is well-defined: geometric arguments are used to establish conditions for the point process to be stable in the sense of Ruelle.
Random p-content of a p-parallelotope in Euclidean n-space
Authors: Mathai A. M.
Published: April 2003

Techniques currently available in the literature in dealing with problems in geometric probabilities seem to rely heavily on results from differential and integral geometry. This paper provides a radical departure in this respect. By using purely algebraic procedures and making use of some properties of Jacobians of matrix transformations and functions of matrix argument, the distributional aspects of the random p-content of a p-parallelotope in Euclidean n-space are studied. The common assumptions of independence and rotational invariance of the random points are relaxed and the exact distributions and arbitrary moments, not just integer moments, are derived in this article. General real matrix-variate families of distributions, whose special cases include the mulivariate Gaussian, a multivariate type-1 beta, a multivariate type-2 beta and spherically symmetric distributions, are considered.
Stopping sets: Gamma-type results and hitting properties
Authors: Zuyev Sergei
Published: April 2003

Recently in the paper by Møller and Zuyev (1996), the following Gamma-type result was established. Givennpoints of a homogeneous Poisson process defining a random figure, its volume is Γ(n,λ) distributed, where λ is the intensity of the process. In this paper we give an alternative description of the class of random sets for which the Gamma-type results hold. We show that it corresponds to the class ofstopping setswith respect to the natural filtration of the point process with certain scaling properties. The proof uses the martingale technique for directed processes, in particular, an analogue of Doob's optional sampling theorem proved in Kurtz (1980). As well as being compact, this approach provides a new insight into the nature of geometrical objects constructed with respect to a Poisson point process. We show, in particular, that in this framework the probability that a point is covered by a stopping set does not depend on whether it is a point of the process or not.
One-dimensional Kohonen maps are super-stable with exponential rate
Authors: Burton Robert M. , Plaehn David C.
Published: April 2003

Kohonen self-organizing interval maps are considered. In this model a linear graph is embedded randomly into the unit interval. At each time a point is chosen randomly according to a fixed distribution. The nearest vertex and some of its nearby neighbors are moved closer to the point. These models have been proposed as models of learning in the audio-cortex. The models possess not only the structure of a Markov chain, but also the added structure of a random dynamical system. This structure is used to show that for a large class of these models, in a strong way, the initial conditions are unimportant and only the dynamics govern the future. A contractive condition is proven in spite of the fact that the maps are not continuous. This, in turn, shows that the Markov chain is uniformly ergodic.
Asymptotic results for multiplexing subexponential on-off processes
Authors: Jelenković Predrag R. , Lazar Aurel A.
Published: April 2003

Consider an aggregate arrival process AN obtained by multiplexing N on-off processes with exponential off periods of rate λ and subexponential on periods τon. As N goes to infinity, with λN → Λ, AN approaches an M/G/∞ type process. Both for finite and infinite N, we obtain the asymptotic characterization of the arrival process activity period.

Using these results we investigate a fluid queue with the limiting M/G/∞ arrival process At∞ and capacity c. When on periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable QtP observed at the beginning of the arrival process activity periods

where ρ = 𝔼At∞ < c; r (c ≤ r) is the rate at which the fluid is arriving during an on period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions regarding on periods than regular variation.

In addition, we analyse a queueing system in which one on-off process, whose on period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential processes with aggregate expected rate 𝔼et. This system is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value 𝔼et.
Tail probabilities for non-standard risk and queueing processes with subexponential jumps
Authors: Asmussen Søren , Schmidli Hanspeter , Schmidt Volker
Published: April 2003

A well-known result on the distribution tail of the maximum of a random walk with heavy-tailed increments is extended to more general stochastic processes. Results are given in different settings, involving, for example, stationary increments and regeneration. Several examples and counterexamples illustrate that the conditions of the theorems can easily be verified in practice and are in part necessary. The examples include superimposed renewal processes, Markovian arrival processes, semi-Markov input and Cox processes with piecewise constant intensities.
Asymptotics of poisson approximation to random discrete distributions: an analytic approach
Authors: Hwang Hsien-Kuei
Published: April 2003

A general analytic scheme for Poisson approximation to discrete distributions is studied in which the asymptotic behaviours of the generalized total variation, Fortet-Mourier (or Wasserstein), Kolmogorov and Matusita (or Hellinger) distances are explicitly characterized. Applications of this result include many number-theoretic functions and combinatorial structures. Our approach differs from most of the existing ones in the literature and is easily amended for other discrete approximations; arithmetic and combinatorial examples for Bessel approximation are also presented. A unified approach is developed for deriving uniform estimates for probability generating functions of the number of components in general decomposable combinatorial structures, with or without analytic continuation outside their circles of convergence.
Stochastic orders in preservation properties by Bernstein-type operators
Authors: Adell Jose A. , Perez-Palomares Ana
Published: April 2003

In this paper, we are concerned with preservation properties of first and second order by an operator L representable in terms of a stochastic process Z with non-decreasing right-continuous paths. We introduce the derived operator D of L and the derived process V of Z in order to characterize the preservation of absolute continuity and convexity. To obtain different characterizations of the preservation of convexity, we introduce two kinds of duality, the first referring to the process Z and the second to the derived process V. We illustrate the preceding results by considering some examples of interest both in probability and in approximation theory - namely, mixtures, centred subordinators, Bernstein polynomials and beta operators. In most of them, we find bidensities to describe the duality between the derived processes. A unified approach based on stochastic orders is given.
The maximum of a function of a Markov chain and application to linkage analysis
Authors: Tu I-Ping , Siegmund David
Published: April 2003

One method of linkage analysis in humans is based on identity-by-descent of pairs of relatives who share a phenotype of interest (for example, a particular disease). We replace the convenient assumption of continuous specification of regions of identity by descent by the more realistic, although still artificially simple, assumption of data from a discrete set of equally spaced infinitely polymorphic markers. We generalize the continuous time Markov chain analysis of Feingold (1993b) and compare the accuracy of the new approximation with that of the simpler Gaussian approximation of Feingold, Brown and Siegmund (1993) under a variety of assumptions about the composition of the pedigrees to be studied. We also suggest a perturbation of the Gaussian approximation as a compromise to achieve reasonable accuracy with minimal computational effort.
Abel-Gontcharoff pseudopolynomials and the exact final outcome of SIR epidemic models (III)
Authors: Lefèvre Claude , Picard Philippe
Published: April 2003

The paper is concerned with the final state and severity of a number of SIR epidemic models in finite populations. Two different classes of models are considered, namely the classical SIR Markovian models and the collective models introduced recently by the authors. First, by applying a simple martingale argument, it is shown that in both cases, there exists a common algebraic structure underlying the exact law of the final state and severity. Then, a unified approach to these statistics is developed by exploiting the theory of Abel-Gontcharoff pseudopolynomials (presented in a preceding paper).
Reaching goals by a deadline: digital options and continuous-time active portfolio management
Authors: Browne Sid
Published: April 2003

We study a variety of optimal investment problems for objectives related to attaining goals by a fixed terminal time. We start by finding the policy that maximizes the probability of reaching a given wealth level by a given fixed terminal time, for the case where an investor can allocate his wealth at any time between n + 1 investment opportunities: n risky stocks, as well as a risk-free asset that has a positive return. This generalizes results recently obtained by Kulldorff and Heath for the case of a single investment opportunity. We then use this to solve related problems for cases where the investor has an external source of income, and where the investor is interested solely in beating the return of a given stochastic benchmark, as is sometimes the case in institutional money management. One of the benchmarks we consider for this last problem is that of the return of the optimal growth policy, for which the resulting controlled process is a supermartingale. Nevertheless, we still find an optimal strategy. For the general case, we provide a thorough analysis of the optimal strategy, and obtain new insights into the behavior of the optimal policy. For one special case, namely that of a single stock with constant coefficients, the optimal policy is independent of the underlying drift. We explain this by exhibiting a correspondence between the probability maximizing results and the pricing and hedging of a particular derivative security, known as a digital or binary option. In fact, we show that for this case, the optimal policy to maximize the probability of reaching a given value of wealth by a predetermined time is equivalent to simply buying a European digital option with a particular strike price and payoff. A similar result holds for the general case, but with the stock replaced by a particular (index) portfolio, namely the optimal growth or log-optimal portfolio.
The size of the connected components of excursion sets of χ2, t and F fields
Authors: Cao J.
Published: April 2003

The distribution of the size of one connected component and the largest connected component of the excursion set is derived for stationary χ2, t and F fields, in the limit of high or low thresholds. This extends previous results for stationary Gaussian fields (Nosko 1969, Adler 1981) and for χ2 fields in one and two dimensions (Aronowich and Adler 1986, 1988). An application of this is to detect regional changes in positron emission tomography (PET) images of blood flow in human brain, using the size of the largest connected component of the excursion set as a test statistic.
On the size of a random sphere of influence graph
Authors: Chalker T. K. , Godbole A. P. , Hitczenko P. , Radcliff J. , Ruehr O. G.
Published: April 2003

We approach sphere of influence graphs (SIGs) from a probabilistic perspective. Ordinary SIGs were first introduced by Toussaint as a type of proximity graph for use in pattern recognition, computer vision and other low-level vision tasks. A random sphere of influence graph (RSIG) is constructed as follows. Consider n points uniformly and independently distributed within the unit square in d dimensions. Around each point,
Xi, draw an open ball (‘sphere of influence’) with radius equal to the distance to Xi's nearest neighbour. Finally, draw an edge between two points if their spheres of influence intersect. Asymptotically exact values for the expected number of edges in a RSIG are determined for all values of d; previously, just upper and lower bounds were known for this quantity. A modification of the Azuma-Hoeffding exponential inequality is employed to exhibit the sharp concentration of the number of edges around its expected value.
The volume fraction of a Poisson germ model with maximally non-overlapping spherical grains
Authors: Daley D. J. , Stoyan H. , Stoyan D.
Published: April 2003

This paper considers a germ-grain model for a random system of non-overlapping spheres in ℝd for d = 1, 2 and 3. The centres of the spheres (i.e. the ‘germs’ for the ‘grains’) form a stationary Poisson process; the spheres result from a uniform growth process which starts at the same instant in all points in the radial direction and stops for any sphere when it touches any other sphere. Upper and lower bounds are derived for the volume fraction of space occupied by the spheres; simulation yields the values 0.632, 0.349 and 0.186 for d = 1, 2 and 3. The simulations also provide an estimate of the tail of the distribution function of the volume of a randomly chosen sphere; these tails are compared with those of two exponential distributions, of which one is a lower bound and is an asymptote at the origin, and the other has the same mean as the simulated distribution. An upper bound on the tail of the distribution is also an asymptote at the origin but has a heavier tail than either of these exponential distributions. More detailed information for the one-dimensional case has been found by Daley, Mallows and Shepp; relevant information is summarized, including the volume fraction 1 - e-1 = 0.63212 and the tail of the grain volume distribution e-yexp(e-y - 1), which is closer to the simulated tails for d = 2 and 3 than the exponential bounds.
Isotropic correlation functions ond-dimensional balls
Authors: Gneiting Tilmann
Published: April 2003

A popular procedure in spatial data analysis is to fit a line segment of the formc(x) = 1 - α ||x||, ||x|| < 1, to observed correlations at (appropriately scaled) spatial lagxind-dimensional space. We show that such an approach is permissible if and only if

the upper bound depending on the spatial dimensiond. The proof relies on Matheron's turning bands operator and an extension theorem for positive definite functions due to Rudin. Side results and examples include a general discussion of isotropic correlation functions defined ond-dimensional balls.
Asymptotics for geometric location problems over random samples
Authors: McGivney K. , Yukich J. E.
Published: April 2003

Consider the basic location problem in which k locations from among n given points X1,…,Xn are to be chosen so as to minimize the sum M(k; X1,…,Xn) of the distances of each point to the nearest location. It is assumed that no location can serve more than a fixed finite number D of points. When the Xi, i ≥ 1, are i.i.d. random variables with values in [0,1]d and when k = ⌈n/(D+1)⌉ we show that

where α := α(D,d) is a positive constant, f is the density of the absolutely continuous part of the law of X1, and c.c. denotes complete convergence.