bluuebunny/crossref_metadata_2025 huggingface dataset:
Systemic Inflammatory Response Syndrome in Nosocomial Bloodstream Infections with Pseudomonas aeruginosa and Enterococcus Species: Comparison of Elderly and Nonelderly Patients
Authors: Marra Alexandre R. , Bar Katharine , Bearman Gonzalo M. L. , Wenzel Richard P. , Edmond Michael B.
Published: April 2006

OBJECTIVES: To determine whether the systemic inflammatory response syndrome (SIRS), clinical course, and outcome of monomicrobial nosocomial bloodstream infection (BSI) due to Pseudomonas aeruginosa or Enterococcus spp. is different in elderly patients than in younger patients.

DESIGN: Historical cohort study.

SETTING: An 820‐bed tertiary care facility.

PARTICIPANTS: One hundred twenty‐seven adults with P. aeruginosa or enterococcal BSI.

MEASUREMENTS: SIRS scores were determined 2 days before the first positive blood culture through 14 days afterwards. Elderly patients (≥65, n=37) were compared with nonelderly patients (<65, n=90). Variables significant for predicting mortality in univariate analysis were entered into a logistic regression model.

RESULTS: No difference in SIRS was detected between the two groups. No significant difference was noted in the incidence of organ failure, 7‐day mortality, or overall mortality between the two groups. Univariate analysis revealed that Acute Physiology And Chronic Health Evaluation (APACHE) II score of 15 or greater at BSI onset; adjusted APACHE II score (points for age excluded) of 15 or greater at BSI onset; and respiratory, cardiovascular, renal, hematological, and hepatic failure were predictors of mortality. Age, sex, use of empirical antimicrobial therapy, and infection with imipenem‐resistant P. aeruginosa or vancomycin‐resistant enterococci did not predict mortality. Multivariate analysis revealed that hematological failure (odds ratio (OR)=8.1, 95% confidence interval (CI)=2.78–23.47), cardiovascular failure (OR=4.7, 95% CI=1.69–13.10), and adjusted APACHE II ≥ 15 at BSI onset (OR=3.1, 95% CI=1.12–8.81) independently predicted death.

CONCLUSION: Elderly patients did not differ from nonelderly patients with respect to severity of illness before or at the time of BSI. Elderly patients with pseudomonal or enterococcal BSIs did not have a greater mortality than nonelderly patients.
Gastric carcinosarcoma with neuroendocrine differentiation as the carcinoma component and leiomyosarcomatous and myofibroblastic differentiation as the sarcomatous component
Authors: KURODA N. , OONISHI K. , IWAMURA S. , OHARA M. , HIROUCHI T. , MIZUMO K. , MIYAZAKI E. , ENZAN H.
Published: April 2006

Gastric carcinosarcoma with neuroendocrine differentiation is a very rare neoplasm. In this article we present such a case. The gastroendoscopic examination of a 59‐year‐old Japanese man disclosed gastric cancer during follow‐up after operation for rectal cancer. Subsequently, total gastrectomy was carried out because of gastric cancer. A large tumor measuring 9.2×8.4 cm was observed in the posterior wall of the upper portion of the stomach. The tumor was composed of carcinoma and sarcomatous cells, and the histological transition of both components was observed. Immunohistochemically, carcinoma and sarcomatous cells were positive for cytokeratin CAM5.2. The carcinoma contained adenocarcinoma and malignant cells with neuroendocrine differentiation. The sarcomatous component showed leiomyosarcomatous and myofibroblastic differentiation. The present tumor is the fifth case of gastric carcinosarcoma with neuroendocrine differentiation and the first case of gastric carcinosarcoma with myofibroblastic differentiation. Pathologists should bear in mind that gastric carcinosarcoma may show various types of differentiation.
Clathrin is Important for Normal Actin Dynamics and Progression of Sla2p‐Containing Patches During Endocytosis in Yeast
Authors: Newpher Thomas M. , Lemmon Sandra K.
Published: April 2006

Clathrin is a major vesicle coat protein involved in receptor‐mediated endocytosis. In yeast and higher eukaryotes, clathrin is recruited to the plasma membrane during the early stage of endocytosis along with clathrin‐associated adaptors. As coated pits undergo maturation, a burst of actin polymerization accompanies and helps drive vesicle internalization. Here, we investigate the dynamics of clathrin relative to the early endocytic patch protein Sla2p. We find that clathrin is recruited to the cortex prior to Sla2p. In the absence of clathrin, normal numbers of Sla2p patches form, but many do not internalize or are dramatically delayed in completion of endocytosis. Patches that do internalize receive Sla1p late, which is followed by Abp1, which appears near the end of Sla2p lifetime. In addition, clathrin mutants develop actin comet tails, suggesting an important function in actin patch organization/dynamics. Similar to its mammalian counterparts, the light chain (LC) subunit of yeast clathrin interacts directly with the coiled‐coil domain of Sla2p. A mutant of Sla2p that no longer interacts with LC (sla2Δ376‐573) results in delayed progression of endocytic patches and aberrant actin dynamics. These data demonstrate an important role for clathrin in organization and progression of early endocytic patches to the late stages of endocytosis.
RISK ASSESSMENT IN TEXTILE AND WOOD, PROCESSING INDUSTRY
Authors: REINHOLD KARIN , TINT PIIA , KIIVET GUNNAR
Published: April 2006

The working conditions in textile and wood processing industries have been investigated using a simple risk assessment method and questionnaires worked out for the purpose. A simple/flexible risk assessment method (beginning with a two-stage model that could be enlarged into a six-stage model) is worked out by the authors (Tint & Kiivet) and the implementation possibilities are presented. It is necessary to increase interest from the side of employers for using the method and analyzing the work environment with the aim of improvement implementations. The main complaints in textile industry are high temperature in the workroom, bad ventilation, intense work and the dependence of workers' work results from the others. The main risk factors in wood processing industry are hazardous tools and equipment, also heavy physical load, noise, wood dust and odors of chemicals originating from polishes.
IMPACT OF SOFTWARE FAILURES ON THE RELIABILITY OF A MAN-COMPUTER SYSTEM
Authors: ZAMOJSKI WOJCIECH , CABAN DARIUSZ
Published: April 2006

Software failures and human errors are the most common reasons of inoparability of computer systems. Computers are increasingly reliable, but the level of transcient faults, caused by errors hidden in the programs, remains the same. For this reason software is becoming the key factor in the synthesis of highly reliable systems. Software errors do not result from operation, they either exist from the start or are inserted when patching or upgrading it. Some errors result from incorrect human interaction or unexpected environmental changes. Assessment of software impact requires functional-reliability approach to reliability analysis: the software fault occurs when it causes incorrect operation and not when it is introduced to the system. It is proposed to use software reliability models in system analysis, to predict the intensity of software faults. The software recovery after a failure is realized by restarts of various extend (microrestarts, minirestarts and macrorestarts). The impact of software failures and restarts on system availability is assessed.
Efficient Human Interferon-α Gene Transfer to Neuroendocrine Tumor Cells with Long-Term and Stable Expression
Authors: Liu Minghui , Kilarski Witold W. , Gerwins Pär , Öberg Kjell , Zhou Yinghua
Published: April 2006

Interferon (IFN)-α has been used in the treatment of neuroendocrine (NE) tumors; however, the feasibility of IFN-α gene therapy has not been evaluated in NE tumor cells. In this study, human IFN-α2 (hIFN-α2) gene has been transferred into a NE tumor cell line BON. hIFN-α2-expressing BON cells were subcutaneously inoculated in nude mice. The results demonstrated that hIFN-α2 exerted significant antiproliferative effects on NE tumor cell lines (BON and LCC18) and other tumor cell lines (CA46 and SW480) as well as porcine aorta cell line. Furthermore, hIFN-α2 demonstrated its antineovascular activity in mice tumor and a direct antiangiogenic effect in chicken chorioallantoic membrane assay. hIFN-α2-expressing BON cells had a stable and long-term expression. Mice implanted with hIFN-α2-expressing BON cells showed a lower incidence, a delayed development and a significantly longer doubling time of the tumor compared to both wild-type (WT) and vector group. In addition, IFN-α significantly inhibited cell adhesion of WT BON cells. hIFN-α2-expressing BON tumors had a high level of hIFN-α2 protein. Finally, mice implanted with a mixture of WT and hIFN-α2-expressing BON cells (1:1) presented a delayed tumor development and had an even lower incidence of tumors than those implanted with hIFN-α2-expressing BON cells only. The doubling time of tumor was also longest in the mixture group. Our data suggest that hIFN-α2 gene therapy might be possible to be used as a new treatment for NE tumor patients. Further studies on the regulation of hIFN-α expression are needed, especially in combination with other cytokines, which could lead to a better understanding and improvements of hIFN-α gene therapy.
Multiresolution Analysis of Radiative Transfer through Inhomogeneous Media. Part I: Theoretical Development
Authors: Ferlay Nicolas , Isaka Harumi
Published: April 2006

This paper derives a multiresolution formulation of the radiative transfer equation for inhomogeneous media. The multiresolution equation is separated into two sets of equations that help in its physical interpretation. The first set represents radiative transfer at some approximation scale, the second at smaller scales. These equations describe explicitly how the local-scale couplings, which occur between the fluctuations of optical properties and radiation fields at different scales, contribute to the radiation field at a prescribed scale and at a given location by introducing additional internal sourcelike functions. These functions are expressed by terms involving connection coefficients of the chosen multiresolution system and also scaling and wavelet coefficients of the inhomogeneous optical properties. This new formulation can provide new insights into the local-scale coupling governing radiative transfer in inhomogeneous media.
Finescale Spiral Band Features within a Numerical Simulation of Hurricane Opal (1995)
Authors: Romine Glen S. , Wilhelmson Robert B.
Published: April 2006

One of the most recognizable features associated with a well-organized tropical system are spiral rainbands. These quasi-stationary rainbands often extend hundreds of kilometers from the storm center and have been well described in the literature. Observational studies have since identified additional banding structures, including outward-propagating small-scale spiral bands. These rainbands may have considerable implications for “core type” tornadoes, local wind maxima associated with downburst damage swaths, as well as a role in overall hurricane dynamics. As such, here a numerical simulation of Hurricane Opal (1995) is examined with unprecedented resolution necessary to capture these small-scale spiral bands. Opal was an intense landfalling hurricane that demonstrated small-scale spiral banding features analogous to those observational studies. The scale and characteristics of the simulated bands are consistent with observed small-scale spiral banding of intense hurricanes. A varietal of Kelvin–Helmholtz instability combined with boundary layer shear is offered as the most plausible dynamical mechanism for the generation and maintenance of these propagating bands outward of the eyewall region.
A Dynamical Core with Double Fourier Series: Comparison with the Spherical Harmonics Method
Authors: Cheong Hyeong-Bin
Published: April 2006

A dynamical core of a general circulation model with the spectral method using double Fourier series (DFS) as basis functions is presented. The model uses the hydrostatic balance approximation and sigma coordinate system in the vertical direction and includes no topography. The model atmosphere is divided into 25 layers with equal sigma depths. Prognostic equations for the vorticity, divergence, temperature, and logarithmic surface pressure are solved by the DFS spectral-transform method with the Fourier filtering at middle and high latitudes. A semi-implicit time-stepping procedure, which deals with the eigendecomposition and inversion of the 3D Helmholtz equation associated with the gravity wave terms, is incorporated for the gravity wave–related terms. The DFS model is tested in terms of the solution of the 3D Helmholtz equation, balanced initial state, developing baroclinic waves, and short- and long-term Held–Suarez–Williamson simulations for T42, T62, T84, and T106 resolutions. It is found that the DFS model is stable and accurate and produces almost the same results as the spherical harmonics method (SHM). The normalized difference (i.e., L2 norm error) measured from the results of highest-resolution SHM-T106 showed a desirable convergence of the DFS solution with the resolution. The convergence property, however, varies with the test case and prognostic variables. The total mass (or global integrated surface pressure) is conserved to a good approximation in the long-term simulations. Computing on the high-performance computer NEC SX-5 (parallel-vector architecture) indicated that DFS is more efficient than the SHM and the efficiency increases with the resolution, for example, by factors of 2.09 and 7.68 for T212 and T1022, respectively.
Endodermal Cyst of the Oculomotor Nerve: Case Report
Authors: Okunaga Tomohiro , Tsutsumi Keisuke , Hayashi Tomayoshi , Nagata Izumi
Published: April 2006

OBJECTIVE:

Endodermal cysts are commonly found in the anterior spinal cord. Reports of intracranial cases are uncommon. We report a case of endodermal cyst located on the left oculomotor nerve.

CLINICAL PRESENTATION:

A 16-year-old female experienced diplopia followed by headache. Neurological examinations revealed left oculomotor nerve palsy. Magnetic resonance imaging scans showed a well-defined multilocular cystic mass in the proximity of the left oculomotor nerve at its exit from the midbrain.

INTERVENTION:

This patient underwent biopsy and drainage of the cyst. At surgery, the cyst seemed to be intrinsic to the oculomotor nerve and could not be totally resected. Pathological examination confirmed the diagnosis of endodermal cyst.

CONCLUSION:

Intracranial endodermal cysts are rare, particularly when associated with the cranial nerves. To our knowledge, this is the second case of endodermal cyst located on the oculomotor nerve. A detailed discussion and review of these case reports are presented.
Superficial Femoral Vein Invasion by a Benign Neurofibroma in a Non-neurofibromatosis Patient: Case Report
Authors: Châtillon Claude-Edouard , Guiot Marie-Christine , Corriveau Marc-Michel , Jacques Line
Published: April 2006

OBJECTIVE AND IMPORTANCE:

Neurofibromas are benign neural sheath tumors arising from intraneural supporting cells. Such tumors are characteristic of neurofibromatosis Type I (von Recklinghausen disease) but also occur sporadically. Vascular involvement by neurofibromata is rare, but has been described in the past in the context of neurofibromatosis. There is, to our knowledge, no description of vascular involvement by a neurofibroma in a non-neurofibromatosis patient.

CLINICAL PRESENTATION:

A 40-year-old woman presented with a 4 year history of a right thigh mass associated with diffuse lower extremity pain. She had no other clinical manifestations of neurofibromatosis and no known family member with neurofibromatosis Type I. Magnetic resonance imaging scans revealed a well-defined solid mass in the anteromedial aspect of the right thigh closely associated with the superficial femoral vein.

INTERVENTION:

The vessel segment and encapsulated mass were resected “en bloc” after proximal and distal ligation of the vein. The pathological appearance of the mass was consistent with a benign neurofibroma that had infiltrated all layers of the vessel.

CONCLUSION:

Vessel invasion by a benign sporadic neurofibroma is a rare occurrence with potentially severe implications for the patient. It suggests that surgical removal of asymptomatic benign-appearing lesions of that type should be considered if they are adjacent to important anatomical structures.
Hagiographie et essai religieux chez Amadou Hampt B
Authors: Benito Marina Lpez
Published: April 2006

The religious essay of Hampt B opposes archaism and modernity, rationality and spirituality, tolerance and dogma. His literary topoi, his formulas, are part of the Jewish, Christian, and Muslim monotheistic tradition. This article studies three aspects of his work: first, the way knowledge
is transmitted from master to disciple; second, the discourse linked to very old generic models such as exegetic commentary or the dissertation; and finally the characteristics of the knowledge transmitted: revelation through numerology; the sacred nature of memory, of the word, and of numbers;
the ways, both mystic and ascetic, of attaining knowledge.
Weak convergence of the average of flag processes
Authors: Iglehart Donald L. , Kennedy Douglas P.
Published: April 2006

Let be a sequence of non-negative random variables and the associated point process defined by
A generalized bivariate exponential distribution
Authors: Marshall Albert W. , Olkin Ingram
Published: April 2006

In a previous paper (Marshall and Olkin (1966)) the authors have derived a multivariate exponential distribution from points of view designed to indicate the applicability of the distribution. Two of these derivations are based on “shock models” and one is based on the requirement that residual life is independent of age.

The practical importance of the univariate exponential distribution is partially due to the fact that it governs waiting times in a Poisson process. In this paper, the distribution of joint waiting times in a bivariate Poisson process is investigated. There are several ways to define “joint waiting time”. Some of these lead to the bivariate exponential distribution previously obtained by the authors, but others lead to a generalization of it. This generalized bivariate exponential distribution is also derived from shock models. The moment generating function and other properties of the distribution are investigated.
Multivariate normal integrals for highly correlated samples from a wiener process
Authors: McFadden J. A. , Lewis James L.
Published: April 2006

If X1, …, Xn obey a multivariate normal distribution with zero means, then the probability that Xi > a for all i = 1, …, n is often called a multivariate normal integral. Such integrals have been considered by various investigators, particularly when a = 0. (For a bibliography, see Gupta.)
A recursion theorem on solving differential-difference equations and applications to some stochastic processes
Authors: Severo Norman C.
Published: April 2006

A recursive procedure leading to the solution of triangular systems of differential-difference equations is presented. It is shown that the equations for special families of multi-dimensional pure birth processes and pure death processes can be represented as such a system. The theory is used to resolve a difficult problem of stochastic cross-infection among groups. Additional applications to problems in epidemic theory are discussed.
A Combinatorial method for a class of matrix games
Authors: Restrepo Rodrigo A.
Published: April 2006

The optimal strategies of any finite matrix game can be characterized by means of the Snow-Shapley Theorem [1]. However, in order to use this theorem to compute the optimal strategies, it may be necessary to invert a large number of matrices, most of which are not related to the solutions of the game. The present paper will show that when the columns of the pay-off matrix satisfy some special relations, it is possible to enumerate a much smaller class of matrices from which the optimal strategies may be obtained. Furthermore, the maximizing strategies that are determined by these matrices can be written down by inspection as soon as the matrices are specified.
The Galton-Watson process with mean one
Authors: Seneta E.
Published: April 2006

Let Zn be the number of individuals in the n-th generation of a simple (discrete, one-type) Galton-Watson process, descended from a single ancestor. Write and assume, as usual, that 0 < F(0) < 1. It is well known that the p.g.f. of Zn is Fn(s), the n-th functional iterate of F(s), and that if the process is construed as a Markov chain on the states 0, 1, 2,…, then its n-step transition probabilities are given by
Sequential decisions in the control of a space-ship (finite fuel)
Authors: Bather John , Chernoff Herman
Published: April 2006

This paper is a sequel to [1] and considers a more realistic formulation of the same question: that of finding an optimal policy for controlling the path of a space-ship as it moves towards its target. The difference here is that we no longer suppose there is an infinite quantity of fuel, always available at a fixed price, for modifying the current direction of motion. This complicates the problem of reducing the final miss distance, by introducing an extra variable. As before, we shall be particularly concerned to find a control procedure which always minimizes the mean square terminal miss. From the theoretical point of view we are also interested to see whether the techniques used to approximate the optimal policy can be extended, and how far we shall be forced to adopt a new approach. Results are derived which provide bounds on the form of the optimal policy. The derivation depends on a comparison technique whose validity is intuitively obvious, but which is still only a conjecture. However, further confirmation is obtained in the quadratic case from asymptotic expansions giving the form of the solution both when the space-ship is far away from its target and during its final approach.
Sufficient Conditions for a First Passage Time Process to be that of Brownian Motion
Authors: Wasan M.T.
Published: April 2006

In this paper we assign a set of conditions to a strong Markov process and arrive at a differential equation analogous to the Kolmogorov equation. However, in this case the duration variable is the net distance travelled and the state variable is a time, a situation precisely opposite to that of Brownian motion. Solving this differential equation under certain boundary conditions produces the density function of the first passage times of Brownian motion with positive drift (see [1]), with the aid of which we define a new stochastic process.
Optimal stopping of constrained Brownian motion
Authors: Föllmer Hans
Published: April 2006

We discuss the potential theory of optimal stopping for a standard process and an unbounded reward function. This is applied to Brownian motion constrained to a N(m, σ2) distribution at time 1. Boyce [2] has discovered, via computer, various interesting features of this example. We provide direct proofs for some of them, in particular for the qualitative jump of the optimal strategy as the variance σ2 passes the critical value 1.
Some limit theorems for Markov branching processes
Authors: Leslie J. R.
Published: April 2006

Analogues of the central limit theorem and iterated logarithm law have recently been obtained for the Galton-Watson process; similar results are established in this paper for the temporally homogeneous Markov branching process and for the associated increasing process consisting of the number of splits in the original process up to time t.
The equivalence of some overlapping and non-overlapping generation models for the study of genetic drift
Authors: Cannings C.
Published: April 2006

The paper discusses models for genetic drift in haploid models; non-overlapping models following Wright, and overlapping models following Moran. It is shown that these models, and their extensions by Chia and Watterson, can all be restated as non-overlapping models. This equivalence between the two sets of models greatly facilitates the specification of latent roots and vectors.
An expansion for the distribution function of a random sum
Authors: Marsh L. M.
Published: April 2006

The Edgeworth expansion gives an indication of the rate of convergence of the distribution function of the sum of a fixed number of random variables to the normal distribution. A similar expansion is given here for the distribution function of the sum of a random number N of random variables, when the probability generating function of N takes a special form.
On a class of parabolic differential equations driven with stochastic point processes
Authors: Gopalsamy K. , Bharucha-Reid A. T.
Published: April 2006

This paper is concerned with the solution of an initial and boundary value problem for a parabolic differential equation driven by a stochastic point process.
A note on the age-dependent branching process with immigration
Authors: Kaplan Norman
Published: April 2006

Let {Z(t)}t0 be an age-dependent branching process with immigration. For a general class of functions Φ(x), a necessary and sufficient condition is given for when E{Φ (Z(t))} <∞. This result is a direct generalization of a theorem proven for the branching process without immigration.
A finite dam with variable release rate
Authors: Yeo G. F.
Published: April 2006

This note considers a finite dam fed by independently and identically distributed (i.i.d.) inputs, being either (i) of at least size β (> 0) or (ii) negative exponentially distributed, occurring in a Poisson process. The instantaneous release rate may be a function r(·) of the content; additional and numerical results are given for the special case where r(x) = µxα (0 ≦ α<∞, 0 < µ <∞) is proportional to the αth power of the content. The basic method used in [7] for the special case r(x) = µx for obtaining the distribution of the number of steps and of the time to first overflowing is shown to carry over almost completely in case (i), but only partially so in case (ii).
A note on the supercritical generalized age-dependent branching process
Authors: Kaplan Norman
Published: April 2006

A sufficient condition is given for a supercritical generalized age-dependent branching process, properly normalized, to converge to zero. This condition is the strongest one possible, for if it does not hold, then it is known that the normalized process does indeed converge to a legitimate random variable.
Basic analysis of a head-of-the-line priority queue with renewal type input
Authors: Schassberger R.
Published: April 2006

A single server is fed by a renewal stream of individual customers. These are of type k with probability πk, k = 1, …, N, and are all served individually. Upon completion of a service the server proceeds immediately with a customer of the lowest type (= highest priority) present, if any. Service times for type k are drawn from a general distribution function Bk(t) concentrated on (0, ∞).

We lay the foundations for a broad analysis of the model.
A Gaussian Markovian process on a square lattice
Authors: Moran P. A. P.
Published: April 2006

A definition of the Markovian property is given for a lattice process and a Gaussian Markovian lattice process is constructed on a torus lattice. From this a Gaussian Markovian process is constructed for a lattice in the plane and its properties are studied.
Weak convergence of probability measures and random functions in the function space D[0,∞)
Authors: Lindvall Torgny
Published: April 2006

This paper extends the theory of weak convergence of probability measures and random functions in the function space D[0,1] to the case D [0,∞), elaborating ideas of C. Stone and W. Whitt. 7)[0,∞) is a suitable space for the analysis of many processes appearing in applied probability.
The cost of a carrier-borne epidemic
Authors: Jerwood D.
Published: April 2006

In this paper, the cost of the carrier-borne epidemic is considered. The definition of duration, as used by Weiss (1965) and subsequent authors, is generalised and the probability distribution for the number of located carriers is obtained. One component of cost, namely the area generated by the trajectory of carriers, is examined and its probability density function derived. The expected area generated is then shown to be proportional to the expected number of carriers located during the epidemic, a result which has an analogue in the general stochastic epidemic.
A limit theorem for a class of supercritical branching processes
Authors: Doney R. A.
Published: April 2006

In the Bellman-Harris (B-H) age-dependent branching process, the birth of a child can occur only at the time of its parent's death. A general class of branching process in which births can occur throughout the lifetime of a parent has been introduced by Crump and Mode. This class shares with the B-H process the property that the generation sizes {ξn} form a Galton-Watson process, and so may be classified into subcritical, critical or supercritical according to the value of m = E{ξ1}. Crump and Mode showed that, as regards extinction probability, asymptotic behaviour, and for the supercritical case, convergence in mean square of Z(t)/E[Z(t)], as t → ∞, where Z(t) is the population size at time t given one ancestor at t = 0, properties of the B-H process can be extended to this general class. In this paper conditions are found for the convergence in distribution of Z(t)/E{Z(t)} in the supercritical case to a non-degenerate limit distribution. In contrast to the B-H process, these conditions are not the same as those for ξn/mn to have a non-degenerate limit. An integral equation is established for the generating function of Z(t), which is more complicated than the corresponding one for the B-H process and involves the conditional probability generating functional of N(x), x 0, ≧ the number of children born to an individual in the age interval [0, x].
An extension of Erlang's formulas which distinguishes individual servers
Authors: Chaiken Jan M. , Ignall Edward
Published: April 2006

For a particular kind of finite-server loss system in which the number and identity of servers depends on the type of the arriving call and on the state of the system, the limits of the state probabilities (as t → ∞) are found for an arbitrary service-time distribution.
The stationary distribution of an interesting Markov chain
Authors: Hendricks W. J.
Published: April 2006

In a single-shelf library of N books we suppose that books are returned by placing them at one end of the shelf. The probability of selecting each book is assumed to be known, and only one book is removed at a time. The N! arrangements of the books are considered as states of an ergodic Markov chain for which we find the stationary distribution.
Recognizing the maximum of a random sequence based on relative rank with backward solicitation
Authors: Yang Mark C. K.
Published: April 2006

The classical secretary problem is generalized to admit stochastically successful procurement of previous interviewees, but each has a certain probability of refusing the offer. A general formula for solving this problem is obtained. Two special cases: constant probability of refusing and geometric probability of refusing are discussed in detail. The optimal stopping rules in these two cases turn out to be simple.
A characterization of the geometric distribution
Authors: Dallas A. C.
Published: April 2006

The geometric distribution is characterized. The lack of memory property is replaced by the constancy of the conditional variance. Then the characterization is obtained.
Convergence properties of age distributions
Authors: Keenay G. A. , Morgan R. W. , Ray K. H.
Published: April 2006

The literature on supply models for manpower planning in a hierarchy shows that an important consideration is the size of the discrepancy between the age distribution of the population and the stationary age distribution which would be reached if present policies were continued indefinitely. We establish the convergence properties of age distribution in various cases and show under what circumstances a convergent age distribution exists. In the convergent case we examine both the speed of convergence and the form of the stationary age distribution.
Asymptotic growth of a class of size-and-age-dependent birth processes
Authors: Waugh W. A. O'N.
Published: April 2006

A class of binary fission stochastic population models is described, in which the fission probabilities may depend on the age of an individual and the total population size. Age-dependent binary branching processes with Erlangian lifelength distributions are a special case. An asymptotic expression for the growth of the population size is developed, which generalizes known theorems about the asymptotic exponential growth of a branching process.
The distribution on the shortest distance between random cuts on opposite strands of DNA
Authors: Litwin Samuel
Published: April 2006

Experiments involving random enzymatic or radioactive multiple cutting of single strands in double stranded DNA will occasionally cut it at pairs of positions on opposite strands that are within about 12 base pairs. In this case the DNA may unravel and come apart. The distribution of closest opposing breaks as a function of λ, the incidence of breaks per unit length, is obtained and graphs of the probability of critical distances as functions ofλare plotted. It is shown that for very largeλthe distance between closest opposite breaks is approximately exponential with parameter ½λ2.
Carrier-borne epidemics in a community consisting of different groups
Authors: Becker Niels
Published: April 2006

A model for the spread of a carrier-borne disease is considered which allows for individual variability. The solutions are used to study the effect of relaxing the assumption of ‘homogeneous mixing’. It is shown that the mean size of an epidemic outbreak is a minimum when the individuals are homogeneous.
The spectral density of a Markov process
Authors: Craven B. D.
Published: April 2006

For a Markov process in discrete time, having finite covariances, both the transient behaviour and the correlation structure may be summed up in a single generating function, here called the key function. If the process is stationary, and the key function possesses a suitable analytic extension, then the process possesses a continuous spectral density, which can be calculated from the key function. A converse result, and some results for the non-stationary process, are also obtained. The calculation is discussed in more detail for the waiting-time process in the GI/G/1 queue.
Non-linear matrix integral equations of Volterra type in queueing theory
Authors: Purdue Peter
Published: April 2006

The use of a branching process argument in complex queueing situations often leads to a discussion of a non-linear matrix integral equation of Volterra type. By the use of a fixed point theorem we show these equations have a unique solution.
The asymptotic frequencies of the types in a multitype age-dependent branching process allowing immigration
Authors: Radcliffe J.
Published: April 2006

The mean square and almost sure convergence of W(t) = e–αtZ(t) is proved for a super-critical multitype age-dependent branching process allowing immigration at the epochs of a renewal process. It is shown that the Malthusian parameter, asymptotic frequencies of types and stationary age distributions are the same for the processes with and without immigration.
Some problems of stochastic resource allocation
Authors: Gittins J. C.
Published: April 2006

Suppose that a number of jobs are to be carried out by a single processing unit orserver. The server can process any number of jobs at the same time but the time taken to finish all the jobs is the same no matter what scheduling policy is used, provided the server is never left idle. It is, however, possible to minimise the total delays to individual jobs by adopting a suitable policy. Optimal policies are derived here for the situation when the processing times are random variables. If the completion rates (analogous to hazard rates) for every job are increasing it is optimal to process the jobs in sequence. If they are decreasing the optimal policy involves simultaneous processing. These results are applied to a more general resource allocation problem arising in industrial chemical research.
Most stringent bounds on the probability of the union and intersection of m events for systems partially specified by s1, s2, …sk, 2 ≦ k < m
Authors: Kwerel Seymour M.
Published: April 2006

For dependent probability systems of m events partially specified by the quantities Sv, the sum of the probabilities of each of the combinations of v events, v = 1, 2, …, 2 ≦ k < m; this paper develops the most stringent upper and lower bounds on P1, the probability of the union of the m events; and on P[m], the probability of the simultaneous occurrence of the m events.
The rate and variance functions arising from the interaction of two stationary point processes
Authors: Lawrance A. J.
Published: April 2006

The paper gives the mean-time and variance-time functions of responses arising from a general type of interaction between two stationary point processes which are independent of each other. The mean-time function is obtained exactly and explicitly, thereby much improving on earlier work. A Laplace-transformed version of the variance-time function is derived under the general assumptions, and new results for the asymptotic slope and intercept are obtained when one of the point processes is renewal. Attention is drawn to the difficulties of dealing with non-renewal and non-regenerative point processes.
On the optimality of stationary replacement strategies
Authors: Bergman Bo
Published: April 2006

In this paper it is shown that for a large class of replacement problems the class of stationary replacement strategies is complete, i.e. in order to minimize the average long run cost per unit time it suffices to consider replacement rules which are equal for each new unit irrespectively of what has been observed from earlier units. The main result is based on a version of the law of large numbers for martingale differences proved in the appendix.
The moments of coverage of a linear set
Authors: Greenberg Irwin
Published: April 2006

A number of points are chosen at random along a line segment and used as the left end-points of lengths of fixed size. Finite sum expressions are derived for the moments of the portion of the line segment covered by one or more of the lengths. The derivation utilizes a relationship between the coverage and the busy time in an M/D/∞ queue.
Autoregressive processes with infinite variance
Authors: Hannan E. J. , Kanter Marek
Published: April 2006

The least squares estimators βi(N), j = 1, …, p, from N data points, of the autoregressive constants for a stationary autoregressive model are considered when the disturbances have a distribution attracted to a stable law of index α < 2. It is shown that N1/δ(βi(N) – β) converges almost surely to zero for any δ > α. Some comments are made on alternative definitions of the βi(N).
Remarks on the relation between fractional moments and fractional derivatives of characteristic functions
Authors: Laue G.
Published: April 2006

We consider fractional derivatives of characteristic functions. We use these fractional derivatives for the formulation of new conditions for the existence of non-integer moments. We also compare the known conditions for the existence of moments of arbitrary random variables with our new conditions. As a consequence many conditions can be written in a unified terminology.
Matched pairs in independent Poisson processes
Authors: Oakes David
Published: April 2006

Given two independent Poisson processes 𝒜 and ℬ with rates respectively α and β (α < β) we match each point of 𝒜 with the closest point of ℬ that has not already been matched. The points of 𝒜 are taken in random order. It is shown that the point process of unmatched points of ℬ is a renewal process with the same interval distribution as the busy period of an M/M/1 queue. The distribution and moments of the distance between a typical point of 𝒜 and the corresponding matched point of ℬ are obtained. Variants of the matching process in which the assigned point of ℬ must lie to the right of the point of 𝒜, and in which the matching distance must be less than a fixed tolerance are studied. The use of matched samples to control for bias in observational studies is discussed.
Characterizations of distributions through some identities
Authors: Prakasa Rao B. L. S.
Published: April 2006

Some characterizations of continuous and discrete exponential families of distributions are given. These characterizations are used to obtain some limit theorems.
Search for a moving target under minimax estimation
Authors: Corwin Thomas L.
Published: April 2006

A target is assumed to choose its starting position in a search at an unknown position in a finite search space. No prior probability distribution for the target's initial location is assumed. During the search the target is assumed to move from position to position in the search space according to a Markov process. A search is defined to be the observation of a sequence of random variables. Representations for the minimax estimator for target location at any stage of the search, the least favorable prior distribution for the target, and the value of the estimation game are presented. An example is computed in which Bayes estimators are compared with minimax estimators for target location.
On a general branching process
Authors: Daly Fergus
Published: April 2006

A branching process is described which contains some better-known simple branching processes as special cases. Variables examined are the rate of development, the number of individuals currently alive, and the duration of the process. The apparent dynamics of collapsing supercritical realisations are isolated.
Moments of the exit-time distribution for carboxyhemoglobin due to cigarette smoking
Authors: Marcus Allan H. , Czajkowski Stanley
Published: April 2006

Linear and non-linear secondary Poisson process models are developed for the level of carboxyhemoglobin in cigarette smoking. The moments of the time of first exit above a critical threshold are expanded as power series in the initial state of the process. Recurrence relations for the coefficients in the moment series are solved numerically. An explicit formula involving Poisson probability functions is obtained for the mean exit time of shot noise.
The asymptotic behaviour of a divergent linear birth and death process
Authors: Haigh John
Published: April 2006

A recent paper in Advances in Applied Probability (Siegel (1976)) considered the duration of the time Tmn for a linear birth and death process to grow from a (large) initial size m to a larger size n. The main aim was to show that, when the birth rate exceeds the death rate, Tmn is close to its mean value, log n/m, with high probability. This paper establishes this result using much simpler techniques.
Non-uniform breakage-mechanism branching processes and degradation of long-chain polymers
Authors: Olson William H.
Published: April 2006

We consider the problem of number and weight distributions for breakage-mechanism branching processes whose break distributions are general. We derive a recursive relation between the expected empirical distribution after (n + 1) breaks and after n breaks, making use of length-biased sampling. Using this relation and the strong law of large numbers, we derive integro-differential equations for the asymptotic expected empirical distribution and its associated weight distribution. The mean of the asymptotic number distribution is derived using the integro-differential equation. We then provide approximate solutions to these equations and the moments of these approximations. Finally we apply these results to the case where the break distribution is a symmetric beta distribution.
Asymptotic properties of non-discrete duels
Authors: Kimeldorf George , Lang John Patrick
Published: April 2006

For fixed accuracy functions, let Gnm be a non-discrete duel in which the amounts of ammunition available to the two players are n and m, respectively. Let vnm be the value of Gnm and let the support of the optimal pure strategies for the players be (anm, 1). The asymptotic relationships among the quantities n, m, vnm and anm are investigated.
The correlated random walk
Authors: Renshaw Eric , Henderson Robin
Published: April 2006

A one-dimensional random walk is studied in which, at each stage, the probabilities of continuing in the same direction or of changing direction are p and 1 – p, respectively. Exact expressions are derived for the n-step transition probabilities, and various limiting distributions are investigated.
On a class of non-Markov decision processes
Authors: Glazebrook K. D.
Published: April 2006

The optimal strategy for a class of non-Markov decision processes is characterised and has the property that changes of action may occur between successive transitions of the process. Results are given which enable the optimal strategy to be computed iteratively.
An identification problem in almost and asymptotically almost periodically correlated processes
Authors: Isokawa Y.
Published: April 2006

Consider a unknown realizable time-invariant linear filter driven by a point process. We are interested in the identification of this system, observing only the output random process. If the process is almost periodically correlated but not periodically correlated, we can identify the filter, using the second-order non-stationary spectrum of the process. We do not require the assumption that the filter is minimum phase.
The scale of perfection
Authors: Kendall David G.
Published: April 2006

A survey is given of the attitude to and use of the concepts of deficient, perfect, and abundant number from the time of Nicomachus of Gerasa to that of David Anakht and Alcuin of York. Alcuin's ‘Letter to Dafnin', the source of an anecdote frequently mentioned in mathematical texts, is included as an appendix.

The statistics of deficient, perfect, and abundant numbers over the range 1–50000 are studied and presented graphically in several novel ways and compared with the work of Davenport and others on the distribution-law for the values of z = σ (n)/(2n).

Some queries are raised concerning observations which ancient writers might have been expected to make; for example, did they notice that about one half of all the even numbers are abundant?
On generalized functions
Authors: Rennie B. C.
Published: April 2006

There are described in the literature many spaces of what are variously described as generalized functions, distributions, or improper functions. This article introduces another. The new space is like that of M. J. Lighthill in containing the Fourier transform of every element and in having a particularly simple theory of trigonometric and Fourier series; also it is constructed in a somewhat similar way. The new space breaks away from the tradition of every element being, for some n, the nth derivative of an ordinary function, and, for example, the exponential function and its Fourier transform are in the space.
Beyond the heuristic approach to Kolmogorov-Smirnov theorems
Authors: Pollard David
Published: April 2006

The theory of weak convergence has developed into an extensive and useful, but technical, subject. One of its most important applications is in the study of empirical distribution functions: the explication of the asymptotic behavior of the Kolmogorov goodness-of-fit statistic is one of its greatest successes. In this article a simple method for understanding this aspect of the subject is sketched. The starting point is Doob's heuristic approach to the Kolmogorov-Smirnov theorems, and the rigorous justification of that approach offered by Donsker. The ideas can be carried over to other applications of weak convergence theory.
Some notes on the total service time in certain loss systems
Authors: Parthasarathy P. R. , Sharafali M.
Published: April 2006

In this paper we discuss the total service rendered by all the servers in certain loss systems.