bluuebunny/crossref_metadata_2025_split huggingface dataset:
Reflections on and Reminiscences of The Royal Air Force
Authors: Roberts Silyn 
Published: July 2016

The Royal Air Force came into being towards the end of the 1914–18 War. In the time and space available it is impossible to write anything approaching a full history of it from its inception to the present day. I shall, therefore, only attempt to mention those events which have impressed themselves on my mind as landmarks in the history of the Service.I shall also endeavour to outline briefly some of the achievements of some of our pilots between the Wars as they illustrate the development of aeroplane performance, followed by a few reminiscences and digressions in an attempt to illustrate the post-War trend.
A Discourse
Authors: Watson-Watt Robert 
Published: July 2016

The celebration of an individual human birthday is an almost completely one-sided recapitulation of pleasant experiences in earlier years, together with a warmly optimistic forecast for coming years. This is wholly right and proper, although even here an occasional muted warning is of genuine value.The celebration of a “technological birthday”, the review of the partial success, through one or more years of operation, of a man-sustained project, deserves notice of the same general type of review, promising further success, warning of potential difficulty, hoping for circumstances and facilities favourable to continued satisfaction, continuously qualified by mention of possible—indeed probable— change in the social climate, for good or ill.
Lipid structure does not modify incorporation of EPA and DHA into blood lipids in healthy adults: a randomised-controlled trial
Authors: West Annette L. , Burdge Graham C. , Calder Philip C. 
Published: July 2016

AbstractDietary supplementation is an effective means to improve EPA and DHA status. However, it is unclear whether lipid structure affects EPA+DHA bioavailability. We determined the effect of consuming different EPA and DHA lipid structures on their concentrations in blood during the postprandial period and during dietary supplementation compared with unmodified fish oil TAG (uTAG). In a postprandial cross-over study, healthy men (n9) consumed in random order test meals containing 1·1 g EPA+0·37 g DHA as either uTAG, re-esterified TAG, free fatty acids (FFA) or ethyl esters (EE). In a parallel design supplementation study, healthy men and women (n10/sex per supplement) consumed one supplement type for 12 weeks. Fatty acid composition was determined by GC. EPA incorporation over 6 h into TAG or phosphatidylcholine (PC) did not differ between lipid structures. EPA enrichment in NEFA was lower from EE than from uTAG (P=0·01). Plasma TAG, PC or NEFA DHA incorporation did not differ between lipid structures. Lipid structure did not affect TAG or NEFA EPA incorporation and PC or NEFA DHA incorporation following dietary supplementation. Plasma TAG peak DHA incorporation was greater (P=0·02) and time to peak shorter (P=0·02) from FFA than from uTAG in men. In both studies, the order of EPA and DHA incorporation was PC>TAG>NEFA. In conclusion, EPA and DHA lipid structure may not be an important consideration in dietary interventions.
Avoiding the Braess paradox in non-cooperative networks
Authors: Korilis Yannis A. , Lazar Aurel A. , Orda Ariel 
Published: July 2016

The exponential growth of computer networking demands massive upgrades in the capacity of existing networks. Traditional capacity design methodologies, developed with the single-class networking paradigm in mind, overlook the non-cooperative structure of modern networks. Consequently, such design approaches entail the danger of degraded performance when resources are added to a network, a phenomenon known as the Braess paradox.
The present paper proposes methods for adding resources efficiently to a non-cooperative network of general topology. It is shown that the paradox is avoided when resources are added across the network, rather than on a local scale, and when upgrades are focused on direct connections between the sources and destinations. The relevance of these results for modern networks is demonstrated.
A unified approach to the study of tail probabilities of compound distributions
Authors: Cai Jun , Garrido José 
Published: July 2016

We consider the tail probabilities of a class of compound distributions. First, the relations between reliability distribution classes and heavy-tailed distributions are discussed. These relations reveal that many previous results on estimating the tail probabilities are not applicable to heavy-tailed distributions.
Then, a generalized Wald's identity and identities for compound geometric distributions are presented in terms of renewal processes. Using these identities, lower and upper bounds for the tail probabilities are derived in a unified way for the class of compound distributions, both under the conditions of NBU and NWU tails, which include exponential tails, as well as under the condition of heavy-tailed distributions.
Finally, simplified bounds are derived by the technique of stochastic ordering. This method removes some unnecessary technical assumptions and corrects errors in the proof of some previous results.
Local risk minimization and numéraire
Authors: Biagini F. , Pratelli M. 
Published: July 2016

The ‘change of numéraire’ technique has been introduced by Geman, El Karoui and Rochet for pricing and hedging contingent claims in the case of complete markets. In this paper we study the ‘change of numéraire’ using the ‘locally risk-minimizing approach’, when the market is not complete. We prove that, if the stochastic process which represents the prices is continuous, the l.r.m. strategy is invariant by a change of numéraire (this result is false in the right-continuous case, as is shown by some counterexamples).
We also give an extension of Merton's formula to the case of stochastic volatility.
On the M/G/1 queue by additional inputs
Authors: Ott Teunis J. 
Published: July 2016

A single-server queueing system is studied, the input into which consists of the sum of two independent stochastic processes. One of these is an ‘M/G' type input process, the other a much more general process which need not be Markov. There are two types of busy period, depending on which arrival process started the busy period. Stochastic monotonicity results are derived and it is found that under a stationarity-like condition the probability of being in a busy period which started with an ‘M/G' arrival is independent of time and is the same it would be with the ‘M/G' process as only input process. Also, distributional results are obtained for the virtual waiting-time process, and these results are used to reduce the study of a single-server queueing system with as input the sum of independent ‘M/G' and ‘GI/G' input streams to the study of a related GI/G/1 queueing system.
The purpose of this paper is to pave the way for a study of an M/G/1 queueing system with periodic arrivals of additional work, and for optimal scheduling of maintenance processes in certain real-time computer systems.
The sojourn-time distribution in the M/G/1 queue by processor sharing
Authors: Ott Teunis J. 
Published: July 2016

This paper gives, in the form of Laplace–Stieltjes transforms and generating functions, the joint distribution of the sojourn time and the number of customers in the system at departure for customers in the general M/G/1 queue with processor sharing (M/G/1/PS).
Explicit formulas are given for a number of conditional and unconditional moments, including the variance of the sojourn time of an ‘arbitrary' customer.
Waitingtimes between record observations
Authors: Neuts Marcel F. 
Published: July 2016

If Δ
r
denotes the waitingtime between the (r − 1)st and the rth upper record in a sequence of independent, identically distributed random variables with a continuous distribution, then it is shown that Δ
r
satisfies the weak law of large numbers and a central limit theorem.
This theorem supplements those of Foster and Stuart and Rényi, who investigated the index Vr
of the rth upper record.
Qualitatively the theorems establish the intuitive fact that for higher records, the waitingtime between the last two records outweighs even the total waitingtime for previous records. This explains also why the asymptotic normality of logVr
is very inadequate for approximation purposes—Barton and Mallows.
A note on the inverse problem for reducible Markov chains
Authors: Pittenger A. O. 
Published: July 2016

Suppose a physical process is modelled by a Markov chain with transition probability on S
1 ∪ S
2, S
1 denoting the transient states and S
2 a set of absorbing states.
If v denotes the output distribution on S
2, the question arises as to what input distributions (of raw materials) on S
1 produce v. In this note we give an alternative to the formulation of Ray and Margo [2] and reduce the problem to one system of linear inequalities. An application to random walk is given and the equiprobability case examined in detail.
Some new results in the mathematical theory of phage-reproduction
Authors: Puri Prem S. 
Published: July 2016

Summary
In the theory of phage reproduction, the mathematical models considered thus far (see Gani [5]) assume that the bacterial burst occurs a fixed time after infection, after a fixed number of generations of phage multiplication, or when the number of mature bacteriophages has reached a fixed threshold. In the present paper, a more realistic assumption is considered: given that until time t the bacterial burst has not taken place, its occurence between tand t + Δt is a random event with probability f(· | t)Δt + o(Δt), where f is a non-negative and non-decreasing function of the number X(t) of vegetative phages and of Z(t), the number of mature bacteriophages at time t. More specifically it is assumed that f = b(t)X(t) + c(t)Z(t) with b(t), c(t) ≦ 0. Here X(t) denotes the survivors in a linear birth and death process and Z(t) the number of deaths until time t. The joint distribution of XT
and ZT
, the respective numbers of vegetative and mature bacteriophages at the burst time is considered. The distribution of ZT
is then fitted to some observed data of Delbrück [2].
Optimal strategies for discovering new species in continuous time
Authors: Alsmeyer Gerold , Irle Albrecht 
Published: July 2016

Consider a population of distinct species Sj
, j∈J, members of which are selected at different time points T
1
, T
2,· ··, one at each time. Assume linear costs per unit of time and that a reward is earned at each discovery epoch of a new species. We treat the problem of finding a selection rule which maximizes the expected payoff. As the times between successive selections are supposed to be continuous random variables, we are dealing with a continuous-time optimal stopping problem which is the natural generalization of the one Rasmussen and Starr (1979) have investigated; namely, the corresponding problem with fixed times between successive selections. However, in contrast to their discrete-time setting the derivation of an optimal strategy appears to be much harder in our model as generally we are no longer in the monotone case.
This note gives a general point process formulation for this problem, leading in particular to an equivalent stopping problem via stochastic intensities which is easier to handle. Then we present a formal derivation of the optimal stopping time under the stronger assumption of i.i.d. (X
1
, A
1) (X2, A2
), · ·· where Xn
gives the label (j for Sj
) of the species selected at Tn
and An
denotes the time between the nth and (n – 1)th selection, i.e. An
= Tn – Tn–

1. In the case where even Xn
and An
are independent and An
has an IFR (increasing failure rate) distribution, an explicit solution for the optimal strategy is derived as a simple consequence.
The exact and asymptotic formulas for the state probabilities in simple epidemics with m kinds of susceptibles
Authors: Lacayo H. , Langberg Naftali A. 
Published: July 2016

A population of susceptible individuals partitioned into m groups and exposed to a contagious disease is considered.
The progress of this simple epidemic is modeled by an m -dimensional stochastic process, whose components are the number of infective individuals in the respective groups at time t. Exact and approximate formulas for the joint and marginal state probabilities are obtained.
On the waiting time of a two-stage queueing system with blocking
Authors: Langaris Christos , Conolly Brian 
Published: July 2016

An analysis is given of the first-come-first-served waiting-time process in stages 1 and 2 of a two-stage service system with k and n parallel service channels in the first and second stages respectively, and m intermediate waiting places (k, n ≧ 1, m ≧ 0).
Although the method of analysis is straightforward the details are intricate and require careful study of the location of the zeros of a high-degree polynomial.
The analysis paves the way for an extensive study of the numerical effect on waiting time of blocking in commonly encountered systems of this nature. ‘Effective service time' in stage 1, defined so as to include blocked time, is considered separately.
Approximations for the GI/G/c queue
Authors: Van Hoorn M. H. , Seelen L. P. 
Published: July 2016

In this paper, we give good-quality approximations for multiserver queues with general service-time distributions. For the interarrival-time distribution we consider hyperexponential distributions and mixtures of Erlang distributions with the same scale parameters. We give an algorithm to compute various operating characteristics such as the delay probability and the mean queue length.The approximations are obtained by making assumptions regarding the residual service times of services in progress at service completion epochs, whereas the arrival process is modelled exactly. As the operating characteristics are far more sensitive to changes in the parameters of the arrival process, the latter is very important.The quality of the approximations is extensively tested by using the exact results of more than 2000 cases. In heavy traffic the average relative error is up to 1% and in moderate traffic about 4%.
Uniformization for semi-Markov decision processes under stationary policies
Authors: Beutler Frederick J. , Ross Keith W. 
Published: July 2016

Uniformization permits the replacement of a semi-Markov decision process (SMDP) by a Markov chain exhibiting the same average rewards for simple (non-randomized) policies. It is shown that various anomalies may occur, especially for stationary (randomized) policies; uniformization introduces virtual jumps with concomitant action changes not present in the original process. Since these lead to discrepancies in the average rewards for stationary processes, uniformization can be accepted as valid only for simple policies.
We generalize uniformization to yield consistent results for stationary policies also. These results are applied to constrained optimization of SMDP, in which stationary (randomized) policies appear naturally. The structure of optimal constrained SMDP policies can then be elucidated by studying the corresponding controlled Markov chains. Moreover, constrained SMDP optimal policy computations can be more easily implemented in discrete time, the generalized uniformization being employed to relate discrete- and continuous-time optimal constrained policies.
A versatile Markovian point process
Authors: Neuts Marcel F. 
Published: July 2016

We introduce a versatile class of point processes on the real line, which are closely related to finite-state Markov processes. Many relevant probability distributions, moment and correlation formulas are given in forms which are computationally tractable. Several point processes, such as renewal processes of phase type, Markov-modulated Poisson processes and certain semi-Markov point processes appear as particular cases. The treatment of a substantial number of existing probability models can be generalized in a systematic manner to arrival processes of the type discussed in this paper.
Several qualitative features of point processes, such as certain types of fluctuations, grouping, interruptions and the inhibition of arrivals by bunch inputs can be modelled in a way which remains computationally tractable.
The basic structures of Voronoi and generalized Voronoi polygons
Authors: Miles R. E. , Maillardet R. J. 
Published: July 2016

For each particle in an aggregate of point particles in the plane, the set of points having it as closest particle is a convex polygon, and the aggregate V of such Voronoi polygons tessellates the plane. The geometric and stochastic structure of a random Voronoi polygon relative to a homogeneous Poisson process is specified.
Similarly, those points of the plane possessing the same n nearest particles constitute a convex polygon cell in the generalized Voronoi tessellation 𝒱 (n = 2, 3, ·· ·). In fact, 𝒱 = 𝒱1, but to ease exposition n always takes the values 2, 3, ···. A key geometrical lemma elucidates the geometric structure of members of 𝒱
n
, showing it to be simpler in one important respect than that of members of 𝒱; in that, for each such N-gon of given ‘type', there is a uniquely determined set of N generating particles. The corresponding jacobian is given, and used to derive the basic ergodic structure of 𝒱
n
relative to a homogeneous Poisson process.
Unlike 𝒱 no 𝒱
n
contains any triangles. As n →∞, the vertices of the quadrangles of 𝒱
n
tend to circularity, so that the sums of their opposite interior angles tend to π.
The scale of perfection
Authors: Kendall David G. 
Published: July 2016

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?
Inference for general Ising models
Authors: Pickard David K. 
Published: July 2016

In previous papers (1976), (1977a), (1979) limit theorems were obtained for the classical Ising model, and these provided the basis for asymptotic inference. The present paper extends these results to more general Ising models.
In two and more dimensions, likelihood inference for the thermodynamic parameters (i.e. the interaction energies) is effectively impossible. The problem is that the error in locating critical and/or confidence regions is as large as their diameters. To remedy this requires more accurate characterizations of the partition functions, but these seem unlikely to be forthcoming. Besag's coding estimators for these parameters are inverse hyperbolic tangents of the roots of simultaneous polynomial equations and hence avoid such location errors. However, little is yet known about their sampling characteristics. Finally, likelihood inference for lattice averages (an alternative parametrization) is straightforward from the limit theorems.
Stochastic population processes in the theory of radiative transfer
Authors: Brockwell P. J. 
Published: July 2016

Summary
Starting from a characterization of radiative transfer in terms of a collision rate λ and a single-collision transition probability Ψ, we study the distribution of the generalized state ζ(t) of a radiation particle at time t conditional on a specified initial state at time t
= 0. The generalized state is a vector consisting of the state ω(t) at time t and the states ω
1, ω
2, …, ω

n
of the particle immediately after the collisions it experiences in the time interval (0, t]. The variable ζ(t) takes values in a population space and can be studied conveniently with the aid of a certain generating functional G. The first-collision integral equation and the backward integro-differential equation for G are derived. Simultaneous consideration of the first-collision and last-collision equations lead to a generalized reciprocity principle for G. First-passage problems are also considered. Finally a number of illustrative examples are given.
A note on Belyaev's limiting distribution of the intervals between losses in an n-server system
Authors: Tambouratzis D. G. 
Published: July 2016

Summary
The aim of the present note is to give an alternative simpler proof to a result of Belyaev [1], namely that in a loss system of n servers with recurrent input and negative exponential service times the intervals between losses, suitably scaled to have constant mean, tend to a negative exponential distribution as n tends to infinity.
On the waiting time distribution in a generalized GI/G/1 queueing system
Authors: Loris-Teghem Jacqueline 
Published: July 2016

The model considered in this paper describes a queueing system in which the station is dismantled at the end of a busy period and re-established on arrival of a new customer, in such a way that the closing-down process consists of N
1 phases of random duration and that a customer 𝒞
n
who arrives while the station is being closed down must wait a random time
idn
(i = 1, ···, N
1) if the ith phase is going on at the arrival instant. (For each fixed index i, the random variables
idn
are identically distributed.) A customer 𝒞
n
arriving when the closing-down of the station is already accomplished has to wait a random time (N
1 + 1)
dn
corresponding to the set up time of the station. Besides, a customer 𝒞
n
who arrives when the station is busy has to wait an additional random time 0
dn. We thus have (N
1 + 2) types of “delay” (additional waiting time). Similarly, we consider (N
2 + 2) types of service time and (N
3 + 2) probabilities of joining the queue. This may be formulated as a model with (N + 2) types of triplets (delay, service time, probability of joining the queue). We consider the general case where the random variables defining the model all have an arbitrary distribution.
The process {wn
}, where wn
denotes the waiting time of customer 𝒞
n
if he joins the queue at all, is not necessarily Markovian, so that we first study (by algebraic considerations) the transient behaviour of a Markovian process {vn
} related to {wn
}, and then derive the distribution of the variables wn.
A note on the first emptiness time of an infinite reservoir with inputs forming a Markov chain
Authors: Lehoczky J. P. 
Published: July 2016

Summary
The first emptiness time of an infinite reservoir with unit release and discrete input forming a stationary. Markov chain is investigated. The exact distribution of the first emptiness time is derived without the use of moment generating functions. The first and second moments of this distribution are given explicity. The close relationship between the process with stationary independent input and Markov chain input is emphasized.
The first moment of the area beneath the sample path up to first emptiness is computed. This area is often used as a measure of total delay in traffic flow theory.
Some results on Markovian replacement processes
Authors: Mandl Petr 
Published: July 2016

Summary
A replacement of type (jk) in a Markov process with rewards means an instantaneous shift of the trajectory from state j into state k. A formula is obtained for the characteristic function of the total reward from the process under an arbitrary non-anticipative replacement policy. From the formula results are deduced concerning Markov policies, optimal policies and policies minimizing the variance of the reward.