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Using citation data, this article examines the pattern of diffusion in the academic literatures of science, the social sciences, and the arts and humanities. An examination of the citations from a given year to the year in which the cited article was published shows that the initial level of citations starts out small and then increases, reaching a peak in less than two years. It then gradually decreases as articles age. A mathematical model is developed to describe this pattern, which is compared to a linear model. The model explains between 97.2% and 99.2% of the variance, depending on the data set, with the parameters for science and the social sciences being remarkably similar. Based on this model, we find that the age at which citation reaches a maximum is lowest for the arts and humanities, next for science, and last for the social sciences. The peak in the proportion of citations is greatest for science, followed by the social sciences and the arts and humanities. Problems in the model led to an examination of one source of historical change in citation practice. We find that the number of citations per article per year has increased systematically over time. Diffusion research is discussed in light of the utility of the citation model.

Mathematical models describing relationships in a group of individuals are known for a long time. The basic idea underlying these models can be described as follows. There are affective (emotionally colored) not necessarily symmetrical relationships between any two members of the group. In general, these relationships vary over time and can be described by numerical functions of time. The value of the corresponding function is positive if the first individual has a positive attitude toward the second one and negative if the attitude is negative. While interacting, two individuals share their views on other members of the group. It affects the dynamics of group relationships. At the same time, the model uses principles such as "if the person whom I dislike says something unpleasant about a third person then I improve my opinion of this third person." This paper also deals with the modeling of group interactions, with the difference that the considered interactions have features of mass (not paired) communications, i.e., the opinion of each individual is equally available to all the others (at the same time, affective relations are paired). This situation occurs, for example, in communities of users of internet forums and blogging platforms. Another important difference is due to the fact that individuals do not discuss other members of the group, but discuss various issues on the topic (e.g., political) of interest to all members of the group. The results of numerical experiments for the system are presented and a number of substantial conclusions are formulated. DOI:10.5901/mjss.2013.v4n10p380

Secular cycles are 2-3 century oscillations in population associated with periodic state breakdown. Turchin and Nefedov (2009) find two secular cycles in England: the Plantagenet (1150–1485) and Tudor-Stuart (1485–1730). This paper proposes modified dating for these cycles (1070–1485 and 1485–1690) and two adjacent cycles: Anglo-Saxon (ca. 880–1070) and mercantile (1690–undetermined). Several mathematical models for secular cycles were investigated for their ability to model trends in population, state strength, elite number and internal instability during the Plantagenet and Tudor-Stuart cycles with the modified dating. The demographic-fiscal model (Turchin 2003) uses just six adjustable parameters and gave as good a fit to the population data as a polynomial model with ten parameters. Sociopolitical instability has been proposed as the primary factor in delayed population recovery following secular decline. This did not seem to be the case for England, at least when instability was measured in terms of large-scale events. For such events the dominant pattern was the fathers and sons cycle, not the much longer secular cycle.

The rat is one of the most widely used laboratory animal species. Therefore development of mathematical models aimed to analyze electromechanical coupling in the rat myocardium is a matter of top interest. We have developed a novel model of excitation-contraction coupling in the rat cardiomyocyte. This model combines equations from the Pandit electrophysiological model and Hinch model of calcium handling with equations describing myofilament mechanical activity from the 'Ekaterinburg-Oxford' mathematical model. The model reproduces both fast and slow responses to mechanical interventions in rat myocardium. © 2018 Creative Commons Attribution. ; Russian Foundation for Basic Research, RFBR: 18-01-00059 ; The work is performed in the frameworks of IIP UrB RAS projects (Nos. AAAA-A18-118020590031-8, АААА-А18-118020590134-6), and supported by RFBR (No. 18-01-00059), by Act 211 Government of the Russian Federation, contract No. 02.A03.21.0006.

ObjectivesThis article examines the comparative effectiveness of different types of social ties used by a job seeker and proposes an explanation for the inconsistency in empirical evidence for strength‐of‐weak‐ties hypothesis.MethodsGranovetter's strength‐of‐weak‐ties hypothesis predicted that in a job search, weak ties (acquaintances) are a more valuable source of information as compared to strong ties (close friends or relatives). However, subsequent empirical research has provided ambiguous support for this hypothesis. To sort out the conflicting results, a mathematical model of the transmission of job information through a contact network has been constructed. Along with the strength of tie, a widely used characteristic of contact, the model also incorporates the work relation of tie.ResultsThe model has numerous implications with strong empirical support, as well as propositions going beyond the findings of prior empirical work, which can be evaluated in subsequent studies. It is shown that the effectiveness of a certain type of contact depends on both the ego's status (weak and work‐related contacts are more advantageous for higher‐status workers) and the composition of the ego's network (work‐related contacts promote the effectiveness of weak ties, while strong‐tie contacts hinder the effectiveness of work‐related ties). In particular, it implies that the inconsistency in empirical evidence for the strength‐of‐weak‐ties hypothesis can be explained by the differences in status or the proportion of work‐related contacts in the samples examined.ConclusionWork‐related ties play a significant role in the analysis of informal job‐search methods; their incorporation into the model allows one to account for a number of previously unexplained empirical results.

A modern competition theory deals with a single-level B2C market involving product vendors (i.e., its manufacturers) and innumerable quantity of ultimate buyers. Also, several researchers study B2B competition. However, nobody has taken a shot at study of systemic interrelationship of various market levels as yet. This the first paper in this regard. It represents successive description of approaches, methods and models of various market levels and relevant competition. A cri­tical constructive analysis of modern tool base of the competition theory is performed. The paper demonstrates several ways of its advance and development by modification of existing models and coefficients, as well as application of new ones.