A new look at the simple epidemic process

1979 ◽  
Vol 16 (01) ◽  
pp. 198-202 ◽  
Author(s):  
L. Billard ◽  
H. Lacayo ◽  
N. A. Langberg
Keyword(s):  
Waiting Times ◽  
Classical Model ◽  
Epidemic Models ◽  
Underlying Structure ◽  
Epidemic Process ◽  
Insight Into ◽  
New Look

Classical epidemic models have invariably proved to be mathematically intractable. By considering the distribution of the number of infectives in a simple epidemic process as a convolution of exponential waiting times, the solution to the classical model is obtained easily giving more insight into the underlying structure. The idea can be extended to other simple epidemic models.

A new look at the simple epidemic process

1979 ◽  
Vol 16 (1) ◽  
pp. 198-202 ◽  
Author(s):  
L. Billard ◽  
H. Lacayo ◽  
N. A. Langberg
Keyword(s):  
Waiting Times ◽  
Classical Model ◽  
Epidemic Models ◽  
Underlying Structure ◽  
Epidemic Process ◽  
Insight Into ◽  
New Look

Classical epidemic models have invariably proved to be mathematically intractable. By considering the distribution of the number of infectives in a simple epidemic process as a convolution of exponential waiting times, the solution to the classical model is obtained easily giving more insight into the underlying structure. The idea can be extended to other simple epidemic models.

On a tandem queueing model with identical service times at both counters, I

1979 ◽  
Vol 11 (3) ◽  
pp. 616-643 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Waiting Times ◽  
Sufficient Conditions ◽  
Complete Analysis ◽  
Single Server ◽  
Stationary Distributions ◽  
In Series ◽  
Queues In Series ◽  
Service Times ◽  
Necessary And Sufficient ◽  
Insight Into

This paper considers a queueing system consisting of two single-server queues in series, in which the service times of an arbitrary customer at both queues are identical. Customers arrive at the first queue according to a Poisson process.Of this model, which is of importance in modern network design, a rather complete analysis will be given. The results include necessary and sufficient conditions for stationarity of the tandem system, expressions for the joint stationary distributions of the actual waiting times at both queues and of the virtual waiting times at both queues, and explicit expressions (i.e., not in transform form) for the stationary distributions of the sojourn times and of the actual and virtual waiting times at the second queue.In Part II (pp. 644–659) these results will be used to obtain asymptotic and numerical results, which will provide more insight into the general phenomenon of tandem queueing with correlated service times at the consecutive queues.

scholarly journals Exploring genetic programming systems with MAP-Elites

2018 ◽  
Author(s):  
Emily Dolson ◽  
Alexander Lalejini ◽  
Charles Ofria
Keyword(s):  
Neural Networks ◽  
Genetic Programming ◽  
Pareto Front ◽  
Underlying Structure ◽  
Phenotypic Traits ◽  
Computation Technique ◽  
Phenotype Space ◽  
Programming Systems ◽  
Insight Into ◽  
Connection Cost

MAP-Elites is an evolutionary computation technique that has proven valuable for exploring and illuminating the genotype-phenotype space of a computational problem. In MAP-Elites, a population is structured based on phenotypic traits of prospective solutions; each cell represents a distinct combination of traits and maintains only the most fit organism found with those traits. The resulting map of trait combinations allows the user to develop a better understanding of how each trait relates to fitness and how traits interact. While MAP-Elites has not been demonstrated to be competitive for identifying the optimal Pareto front, the insights it provides do allow users to better understand the underlying problem. In particular, MAP-Elites has provided insight into the underlying structure of problem representations, such as the value of connection cost or modularity to evolving neural networks. Here, we extend the use of MAP-Elites to examine genetic programming representations, using aspects of program architecture as traits to explore. We demonstrate that MAP-Elites can generate programs with a much wider range of architectures than other evolutionary algorithms do (even those that are highly successful at maintaining diversity), which is not surprising as this is the purpose of MAP-Elites. Ultimately, we propose that MAP-Elites is a useful tool for understanding why genetic programming representations succeed or fail and we suggest that it should be used to choose selection techniques and tune parameters.

scholarly journals Probing the promiscuity of ent-kaurene oxidases via combinatorial biosynthesis

2016 ◽  
Vol 113 (9) ◽  
pp. 2526-2531 ◽  
Author(s):  
Sibongile Mafu ◽  
Meirong Jia ◽  
Jiachen Zi ◽  
Dana Morrone ◽  
Yisheng Wu ◽  
...  
Keyword(s):  
Natural Products ◽  
Metabolic Engineering ◽  
Substrate Specificity ◽  
Plant Hormone ◽  
Structural Similarity ◽  
Combinatorial Biosynthesis ◽  
Underlying Structure ◽  
Engineering System ◽  
Insight Into

The substrate specificity of enzymes from natural products’ metabolism is a topic of considerable interest, with potential biotechnological use implicit in the discovery of promiscuous enzymes. However, such studies are often limited by the availability of substrates and authentic standards for identification of the resulting products. Here, a modular metabolic engineering system is used in a combinatorial biosynthetic approach toward alleviating this restriction. In particular, for studies of the multiply reactive cytochrome P450, ent-kaurene oxidase (KO), which is involved in production of the diterpenoid plant hormone gibberellin. Many, but not all, plants make a variety of related diterpenes, whose structural similarity to ent-kaurene makes them potential substrates for KO. Use of combinatorial biosynthesis enabled analysis of more than 20 such potential substrates, as well as structural characterization of 12 resulting unknown products, providing some insight into the underlying structure–function relationships. These results highlight the utility of this approach for investigating the substrate specificity of enzymes from complex natural products’ biosynthesis.

scholarly journals POT METHODS: A NEW INSIGHT INTO THE ESTIMATION OF EXTREME VALUE DISTRIBUTIONS – APPLICATION TO EXTREME WAVE HEIGHTS

2012 ◽  
Vol 1 (33) ◽  
pp. 21
Author(s):  
Franck Mazas ◽  
Luc Hamm ◽  
Philippe Garat
Keyword(s):  
Extreme Values ◽  
Classical Model ◽  
Asymptotic Properties ◽  
Simulated Data ◽  
Location Parameter ◽  
Poisson Model ◽  
Parameter Setting ◽  
Extreme Wave ◽  
Wave Heights ◽  
Insight Into

Within the framework of the GPD-Poisson model for determining extreme values of environmental variables, we examine the sensitivity of this methodology to the lowest and to the largest data of the sample. We show the need for a clear distinction between the threshold selecting the data to be fitted with a location parameter setting the origin of the distribution and that the introduction of this latter parameter yields stable results, consistent with the physics. We also show that the likelihood maximum of the classical model is reached at an open upper bound of the parameter space with non-null derivatives: hence, the asymptotic properties of MLE are not proven and one should be quite cautious when using it. Applications are presented with real and simulated data.

CARTOGRAPHIC MODELS OF PEST DIFFUSION PROCESSES IN NETWORK CYBERSPACE

2021 ◽  
pp. 281-286
Author(s):  
Александр Григорьевич Остапенко ◽  
Алексей Леонидович Сердечный ◽  
Александр Алексеевич Остапенко ◽  
Сергей Сергеевич Куликов
Keyword(s):  
Diffusion Processes ◽  
Epidemic Models ◽  
Dynamic Information ◽  
Weighted Networks ◽  
Epidemic Process ◽  
Proposed Model ◽  
Malicious Codes ◽  
Network Mapping ◽  
Analytical Expressions ◽  
Graph Map

Рассматривается весьма актуальная проблема моделирования процесса диффузии вредоносных кодов и деструктивных контентов в киберпространстве, которое в современных условиях носит все более выраженный сетевой характер. В отличии от ранее широко используемых аналоговых и даже развивающих их дискретных эпидемических моделей, в настоящей работе учитываются статический (накопленную информацию) и динамический (информационный трафик) ресурсы узлов и ветвей сети. Наряду с этим принимается во внимание дозировка вредоноса, внедряемого в сеть для нарушения её работоспособности. Все это позволяет осуществить сетевое картографирование эпидемического процесса, порождаемого в результате диффузии вредоносной инъекции. Предлагаемая модель открывает новую страницу в описании информационных эпидемий (и не только) во взвешенных сетях, где предлагаемая авторами формализация масштабирует изображаемые размеры узлов и ветвей модели в соответствии со значениями ресурсов или потенциалов её элементов. Фактически получается граф (карта) исследуемого сетевого ландшафта, в котором циркулирует информация. В случае внедрения вредоноса компоненты карты окрашиваются с учетом дозировки его присутствия в них, где топологической основой выступают “звезды” сети. Для этого авторами предлагаются соответствующие аналитические выражения. The article deals with a very relevant problem of modeling the process of diffusion of malicious codes and destructive content in cyberspace, which in modern conditions has an increasingly pronounced network character. In contrast to the previously widely used analog and even developing discrete epidemic models, this paper takes into account the static (accumulated information) and dynamic (information traffic) resources of nodes and branches of the network. Along with this, the dosage of the malware introduced into the network to disrupt its performance is taken into account. All this makes it possible to carry out network mapping of the epidemic process generated as a result of the diffusion of malicious injection. The proposed model opens a new page in the description of information epidemics (and not only) in weighted networks, where the formalization proposed by the authors scales the depicted sizes of nodes and branches of the model in accordance with the values of resources or potentials of its elements. In fact, a graph (map) of the network landscape under study is obtained, in which information circulates. In the case of the introduction of the malware, the map components are colored taking into account the dosage of its presence in them, where the topological basis is the “stars” of the network. For this purpose, the authors propose the corresponding analytical expressions.

The Relevance of Aristophanes: a New Look at Clouds

1988 ◽  
Vol 35 (1) ◽  
pp. 23-28
Author(s):  
Raymond K. Fisher
Keyword(s):  
Everyday Life ◽  
Contemporary Society ◽  
Power Politics ◽  
Original Intention ◽  
Current Affairs ◽  
Battle Of The Sexes ◽  
Classical Author ◽  
Wide Range ◽  
Insight Into ◽  
New Look

My aim in this paper is to discover in what sense, if any, Aristophanes can be considered relevant to our society in the 1980s. If we call a classical author relevant to contemporary society, we may mean that he or she presents issues and problems for which we can find modern parallels and from which we may gain a deeper insight into our own current affairs. Aristophanes deals with a wide range of social and political problems of the kind which recur in all cultures, as well as with the practicalities of everyday life, so that when dealing with these problems he is ostensibly as relevant now as he was in his own day. But is there anything in the nature of Aristophanic comedy which constrains us from making the kind of modern connections which we might wish to make? L. Spatz says ‘Aristophanes speaks directly to us through such topical themes as the battle of the sexes, the scandals of power politics, and the underdog's need to strike back at his oppressors. But sometimes this relevance results in a misunderstanding of his original intention.’

Human Population Genetics, 1961

1962 ◽  
Vol 11 (3) ◽  
pp. 263-268
Author(s):  
James V. Neel
Keyword(s):  
Population Genetics ◽  
Genetic Polymorphisms ◽  
Human Population ◽  
Genetic Locus ◽  
Classical Model ◽  
Optimum Level ◽  
Mutation Pressure ◽  
Genetic Traits ◽  
Human Population Genetics ◽  
Insight Into

The more significant developments in the field of human population genetics during the past decade can for the most part be subsumed under three headings, as follows:1. The recognition of an increasing number of genetic traits capable of serving as analytic tools in population studies.2. The recognition that many of these traits attain frequencies, although some only in limited areas, such that they have to be labelled genetic polymorphisms. Table 1 is an attempt to list the presently recognized human polymorphisms for which the genetic basis seems clear.3. The emergence of at least a few clues as to the factors responsible for the maintenance of some of the plymorphisms, although it must be confessed that for the majority of the traits listed in Table 1, there is as yet no real insight into their role in populations.As is well known from the contributions of Fisher, Wright, Dobzhansky, Lerner, Crow, Kimura, and others, genetic polymorphisms have the property of acting as stabilizing mechanisms in maintaining certain aspects of the fitness of populations. Consequently, whereas what we may term the “classical model” of the dynamics of a genetic locus in a population looked to mutation pressure as the source of the impairment of population fitness which could be traced to that locus, the “polymorphic model” views that impairment as in part a price a population pays for the maintenance of an optimum level of heterozygosity at that locus. The two models have such profoundly different practical and philosophical consequences that it is small wonder that in recent years the running discussion of their relative merits and roles has generated a degree of heat matched by few other current biological questions.

scholarly journals Antilinear symmetry and the ghost problem in quantum field theory

2021 ◽  
Vol 2038 (1) ◽  
pp. 012018
Author(s):  
Philip D. Mannheim
Keyword(s):  
Hilbert Space ◽  
Inner Product ◽  
Underlying Structure ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Theories ◽  
Inner Products ◽  
Hermitian Conjugate ◽  
Theories Of Gravity ◽  
Insight Into

Abstract The recognition that the eigenvalues of a non-Hermitian Hamiltonian could all be real if the Hamiltonian had an antilinear symmetry such as PT stimulated new insight into the underlying structure of quantum mechanics. Specifically, it led to the realization that Hilbert space could be richer than the established Dirac approach of constructing inner products out of ket vectors and their Hermitian conjugate bra vectors. With antilinear symmetry one must instead build inner products out of ket vectors and their antilinear conjugates, and it is these inner products that would be time independent in the non-Hermitian but antilinearly symmetric case even as the standard Dirac inner products would not be. Moreover, and in a sense quite remarkably, antilinear symmetry could address not only the temporal behavior of the inner product but also the issue of its overall sign, with antilinear symmetry being capable of yielding a positive inner product in situations such as fourth-order derivative quantum field theories where the standard Dirac inner product is found to have ghostlike negative signature. Antilinear symmetry thus solves the ghost problem in such theories by showing that they are being formulated in the wrong Hilbert space, with antilinear symmetry providing a Hilbert space that is ghost free. Antilinear symmetry does not actually get rid of the ghost states. Rather, it shows that the reasoning that led one to think that ghosts were present in the first place is faulty. Implications of our results for constructing unitary quantum theories of gravity are presented.

Sign in / Sign up

Export Citation Format

Share Document