Modulated Branching Processes, Origins of Power Laws and Queueing Duality

Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological and technological areas. In many of the observations, e.g., city populations and sizes of living organisms, the objects of interest evolve due to the replication of their many independent components, e.g., births-deaths of individuals and replications of cells. Furthermore, the rates of the replication are often controlled by exogenous parameters causing periods of expansion and contraction, e.g., baby booms and busts, economic booms and recessions, etc. In addition, the sizes of these objects often have reflective lower boundaries, e.g., cities do not fall bellow a certain size, low income individuals are subsidized by the government, companies are protected by bankruptcy laws, etc. Hence, it is natural to propose reflected modulated branching processes as generic models for many of the preceding observations. Indeed, our main results show that the proposed mathematical models result in power law distributions under quite general polynomial Gartner-Ellis conditions, the generality of which could explain the ubiquitous nature of power law distributions. In addition, on a logarithmic scale, we establish an asymptotic equivalence between the reflected branching processes and the corresponding multiplicative ones. The latter, as recognized by Goldie (1991), is known to be dual to queueing/additive processes. We emphasize this duality further in the generality of stationary and ergodic processes.Comment: 36 pages, 2 figures; added references; a new theorem in Subsection 4.

Characterizing Heavy-Tailed Distributions Induced by Retransmissions

Consider a generic data unit of random size L that needs to be transmitted over a channel of unit capacity. The channel availability dynamics is modeled as an i.i.d. sequence {A, A_i},i>0 that is independent of L. During each period of time that the channel becomes available, say A_i, we attempt to transmit the data unit. If L<A_i, the transmission was considered successful; otherwise, we wait for the next available period and attempt to retransmit the data from the beginning. We investigate the asymptotic properties of the number of retransmissions N and the total transmission time T until the data is successfully transmitted. In the context of studying the completion times in systems with failures where jobs restart from the beginning, it was shown that this model results in power law and, in general, heavy-tailed delays. The main objective of this paper is to uncover the detailed structure of this class of heavy-tailed distributions induced by retransmissions. More precisely, we study how the functional dependence between P[L>x] and P[A>x] impacts the distributions of N and T. In particular, we discover several functional criticality points that separate classes of different functional behavior of the distribution of N. We also discuss the engineering implications of our results on communication networks since retransmission strategy is a fundamental component of the existing network protocols on all communication layers, from the physical to the application one.Comment: 39 pages, 2 figure

Information Ranking and Power Laws on Trees

We study the situations when the solution to a weighted stochastic recursion has a power law tail. To this end, we develop two complementary approaches, the first one extends Goldie's (1991) implicit renewal theorem to cover recursions on trees; and the second one is based on a direct sample path large deviations analysis of weighted recursive random sums. We believe that these methods may be of independent interest in the analysis of more general weighted branching processes as well as in the analysis of algorithms

The socialist Yugoslav paradox: Documentary cinema exhibition opportunities and the meaning of ‘Dissent’

This article will examine the position of critical cinema in socialist Yugoslavia by analysing the archives of the only documentary festival in the country, the Yugoslav Documentary and Short Film Festival in Belgrade (founded in 1954). It will compare the festival’s most prosperous years, when a series of internationally acclaimed Black Wave films were screened (late 60 s/early 70 s), and its final socialist phase, when a series of ‘patriotic’ films, mostly seen as uninteresting by international programmers, were shown (late 80 s/early 90 s). Analysing the ideological change in the festival’s programming, the article will show how Yugoslav documentary moved from a critique within a socialist perspective in the 60 s to the promotion of a predominantly anti-socialist and nationalist perspective in the 80 s. In doing so, it will demonstrate that although often regarded as ‘the’ dissident cinema of Yugoslavia, the Black Wave was in its essence in dialectical dialog with the socialist state, unlike the critical films of the late 80 s and early 90 s, which were arguing for regime change in favour of a nation-state. The article will shed light on the paradoxes of Yugoslav censorship and film exhibition opportunities, in the specific context of the only European country that was ruled by a communist government but that was outside of the Eastern Bloc

Allchar Deposit in Republic of Macedonia – Petrology and Age Determination

The Allchar Sb-As-Tl-Au volcanogenic hydrothermal deposit is situated at the northwestern margins of Kožuf Mts. (Republic of Macedonia), close to the border between Republic of Macedonia and Greece (Fig.1). From the geotectonic point of view, ore mineralization is related to a Pliocene volcano-intrusive complex located between the rigid Pellagonian block in the west, and the labile Vardar zone in the east. From the metallogenic point of view, the Allchar deposit belongs to the Kožuf ore district as part of the Serbo-Macedonian metallogenetic province

Cytogenetics of Vitis III. Partially fertile F1 diploid hybrids between V. vinifera L. x V. rotundifolia MICHX.

An unusual, partially-fertile population of diploid Vitis vinifera x V. rotundifolia F1 hybrids is described. These hybrids are partially fertile with varieties of both parental species.It is suggested that the success of hybridization, as measured by the fertility of the F1 hybrids, depends on the V. vinifera clone originally used as a female parent.In meiosis of these F1 plants, average bivalent formation varies from 13.1 to 15.6 per cell at MI. There is a correlation in the diploid VR hybrids between chromosomal pairing at MI and fertility of the vines.Some V. rotundifolia characters are dominant in diploid F1 hybrids.In regard to crossability, the F1 hybrids are reciprocally crossable with V. vinifera varieties, but can only serve as female parents with V. rotundifolia. Evidence from breeding tests indicates that incompatibility between V. rotundifolia x V. vinifera is not due to cytoplasmic inheritance, but is caused by nuclear factors