Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information and statistical distribution theory. The results presented in the essay cover a period of time in Mathai's research from 1982 to 2008 and are all related to the thematic area of the gravitationally stabilized solar fusion reactor and fractional reaction-diffusion, taking into account concepts of non-extensive statistical mechanics. The time period referred to above coincides also with Mathai's exceptional contributions to the establishment and operation of the Centre for Mathematical Sciences, India, as well as the holding of the United Nations (UN)/European Space Agency (ESA)/National Aeronautics and Space Administration (NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA) Workshops on basic space science and the International Heliophysical Year 2007, around the world. Professor Mathai's contributions to the latter, since 1991, are a testimony for his social con-science applied to international scientific activity.

On Root Arrangements of Polynomial-Like Functions and their Derivatives

2000 Mathematics Subject Classification: 12D10.

Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points

2000 Mathematics Subject Classification: 60J60, 62M99.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Global Waves with Non-Positive Energy in General Relativity

2000 Mathematics Subject Classification: 35Lxx, 35Pxx, 81Uxx, 83Cxx.

Limit Theorems for Non-Critical Branching Processes with Continuous State Space

2000 Mathematics Subject Classification: Primary 60J80, Secondary 60G99.

Bayesian Prediction of Weibull Distribution Based on Fixed and Random Sample Size

2000 Mathematics Subject Classification: 62E16, 65C05, 65C20.

Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.

Intensity dynamics and statistical properties of random distributed feedback fiber laser

We present first experimental investigation of fast-intensity dynamics of random distributed feedback (DFB) fiber lasers. We found that the laser dynamics are stochastic on a short time scale and exhibit pronounced fluctuations including generation of extreme events. We also experimentally characterize statistical properties of radiation of random DFB fiber lasers. We found that statistical properties deviate from Gaussian and depend on the pump power.

The special case of self-perspective inhibition in mental, but not non-mental, representation

The ventrolateral prefrontal cortex (vlPFC) has been implicated in studies of both executive and social functions. Recent meta-analyses suggest that vlPFC plays an important but little understood role in Theory of Mind (ToM). Converging neuropsychological and functional Magnetic Resonance Imaging (fMRI) evidence suggests that this may reflect inhibition of self-perspective. The present study adapted an extensively published ToM localizer to evaluate the role of vlPFC in inhibition of self-perspective. The classic false belief, false photograph vignettes that comprise the localizer were modified to generate high and low salience of self-perspective. Using a factorial design, the present study identified a behavioural and neural cost associated with having a highly salient self-perspective that was incongruent with the representational content. Importantly, vlPFC only differentiated between high versus low salience of self-perspective when representing mental state content. No difference was identified for non-mental representation. This result suggests that different control processes are required to represent competing mental and non-mental content.

Binding of small molecules to DNA junctions

Previous results in our laboratory suggest that the (CG) 4 segments whether present in a right-handed or a left-handed conformation form distinctive junctions with adjacent random sequences. These junctions and their associated sequences have unique structural and thermodynamic properties that may be recognized by DNA-binding molecules. This study probes these sequences by using the following small ligands: actinomycin D, 1,4-bis(((di(aminoethyl)amino)ethyl)amino)anthracene-9,10-dione, ametantrone, and tris(phenanthroline)ruthenium (II). These ligands may recognize the distinctive features associated to the (CG)4 segment and its junctions and thus interact preferentially near these sequences. Restriction enzyme inhibition assays were used to determine whether or not binding interactions took place, and to approximate locations of these interactions. These binding studies are first carried out using two small synthetic oligomers BZ-III and BZ-IV. The (5meCG)4 segment present in BZ-III adopts the Z-conformation in the presence of 50 m M Co(NH3)63+. In BZ-IV, the unmethylated (CG)4 segment changes to a non-B conformation in the presence of 50 m M Co(NH3)63+. BZ-IV, containing the (CG)4 segment, was inserted into a clone plasmid then digested with the restriction enzyme Hinf I to produce a larger fragment that contains the (CG)4 segment. The results obtained on the small oligomers and on the larger fragment for restriction enzyme Mbo I indicate that 1,4-bis(((di(aminoethyl)amino)ethyl)amino)anthracene-9,10-dione binds more efficiently at or near the (CG)4 segment. Restriction enzymes EcoRV, Sac I and Not I with cleavage sites upstream and downstream of the (CG)4 insert were used to further localize binding interactions in the vicinity of the (CG)4 insert. RNA polymerase activity was studied in a plasmid which contained the (CG)4 insert downstream from the promoter sites of SP6 and T7 RNA polymerases. Activities of these two polymerases were studied in the presence of each one of the ligands used throughout the study. Only actinomycin D and spider, which bind at or near the (CG)4 segment, alter the activities of SP6 and T7 RNA polymerases. Surprisingly, enhancement of polymerase activity was observed in the presence of very low concentrations of actinomycin D. These results suggest that the conformational features of (CG) segments may serve in regulatory functions of DNA. ^

Law Enforcement Actions in Urban Spaces Governed by Violent Non-State Entities: Lessons from Latin America

In response to a crime epidemic afflicting Latin America since the early 1990s, several countries in the region have resorted to using heavy-force police or military units to physically retake territories de facto controlled by non-State criminal or insurgent groups. After a period of territory control, the heavy forces hand law enforcement functions in the retaken territories to regular police officers, with the hope that the territories and their populations will remain under the control of the state. To a varying degree, intensity, and consistency, Brazil, Colombia, Mexico, and Jamaica have adopted such policies since the mid-1990s. During such operations, governments need to pursue two interrelated objectives: to better establish the state’s physical presence and to realign the allegiance of the population in those areas toward the state and away from the non-State criminal entities. From the perspective of law enforcement, such operations entail several critical decisions and junctions, such as: Whether or not to announce the force insertion in advance. The decision trades off the element of surprise and the ability to capture key leaders of the criminal organizations against the ability to minimize civilian casualties and force levels. The latter, however, may allow criminals to go to ground and escape capture. Governments thus must decide whether they merely seek to displace criminal groups to other areas or maximize their decapitation capacity. Intelligence flows rarely come from the population. Often, rival criminal groups are the best source of intelligence. However, cooperation between the State and such groups that goes beyond using vetted intelligence provided by the groups, such as a State tolerance for militias, compromises the rule-of-law integrity of the State and ultimately can eviscerate even public safety gains. Sustaining security after initial clearing operations is at times even more challenging than conducting the initial operations. Although unlike the heavy forces, traditional police forces, especially if designed as community police, have the capacity to develop trust of the community and ultimately focus on crime prevention, developing such trust often takes a long time. To develop the community’s trust, regular police forces need to conduct frequent on-foot patrols with intensive nonthreatening interactions with the population and minimize the use of force. Moreover, sufficiently robust patrol units need to be placed in designated beats for substantial amount of time, often at least over a year. Establishing oversight mechanisms, including joint police-citizens’ boards, further facilities building trust in the police among the community. After disruption of the established criminal order, street crime often significantly rises and both the heavy-force and community-police units often struggle to contain it. The increase in street crime alienates the population of the retaken territory from the State. Thus developing a capacity to address street crime is critical. Moreover, the community police units tend to be vulnerable (especially initially) to efforts by displaced criminals to reoccupy the cleared territories. Losing a cleared territory back to criminal groups is extremely costly in terms of losing any established trust and being able to recover it. Rather than operating on a priori determined handover schedule, a careful assessment of the relative strength of regular police and criminal groups post-clearing operations is likely to be a better guide for timing the handover from heavy forces to regular police units. Cleared territories often experience not only a peace dividend, but also a peace deficit – in the rise new serious crime (in addition to street crime). Newly – valuable land and other previously-inaccessible resources can lead to land speculation and forced displacement; various other forms of new crime can also significantly rise. Community police forces often struggle to cope with such crime, especially as it is frequently linked to legal business. Such new crime often receives little to no attention in the design of the operations to retake territories from criminal groups. But without developing an effective response to such new crime, the public safety gains of the clearing operations can be altogether lost.

Non -traded goods, product differentiation and integration of factor markets

This research sought to determine the implications of a non-traded differentiated commodity produced with increasing returns to scale, for the welfare of countries that allowed free international migration. We developed two- and three-country Ricardian models in which labor was the only factor of production. The countries traded freely in homogeneous goods produced with constant returns to scale. Each also had a non-traded differentiated good sector where production took place using increasing returns to scale technology. Then we allowed for free international migration between two of the countries and observed what happened to welfare in both countries as indicated by their per capita utilities in the new equilibrium relative to their pre-migration utilities. ^ Preferences of consumers were represented by a two-tier utility function [Dixit and Stiglitz 1977]. As migration took place it impacted utility in two ways. The expanding country enjoyed the positive effect of increased product diversity in the non-traded good sector. However, it also suffered adverse terms-of-trade as its production cost declined. The converse was true for the contracting country. To determine the net impact on welfare we derived indirect per capita utility functions of the countries algebraically and graphically. Then we juxtaposed the graphs of the utility functions to obtain possible general equilibria. These we used to observe the welfare outcomes. ^ We found that the most likely outcomes were either that both countries gained, or one country lost while the other gained. We were, however, able to generate cases where both countries lost as a result of allowing free inter-country migration. This was most likely to happen when the shares of income spent on each country's export good differed significantly. In the three country world when we allowed two of the countries to engage in preferential trading arrangements while imposing a prohibitive tariff on imports from the third country welfare of the partner countries declined. When inter-union migration was permitted welfare declined even further. This we showed was due to the presence of the non-traded good sector. ^

O paradoxo da superdifusão de uma caminhada aleatória com memória exponencial

The random walk models with temporal correlation (i.e. memory) are of interest in the study of anomalous diffusion phenomena. The random walk and its generalizations are of prominent place in the characterization of various physical, chemical and biological phenomena. The temporal correlation is an essential feature in anomalous diffusion models. These temporal long-range correlation models can be called non-Markovian models, otherwise, the short-range time correlation counterparts are Markovian ones. Within this context, we reviewed the existing models with temporal correlation, i.e. entire memory, the elephant walk model, or partial memory, alzheimer walk model and walk model with a gaussian memory with profile. It is noticed that these models shows superdiffusion with a Hurst exponent H > 1/2. We study in this work a superdiffusive random walk model with exponentially decaying memory. This seems to be a self-contradictory statement, since it is well known that random walks with exponentially decaying temporal correlations can be approximated arbitrarily well by Markov processes and that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. The solution to the apparent paradox is that the model is genuinely non-Markovian, due to a time-dependent decay constant associated with the exponential behavior. In the end, we discuss ideas for future investigations.

Executive functions predict conceptual learning of science

Peer reviewed