Extremal Segments in Random Sequences

We investigate the probability for the largest segment in with total displacement $Q$ in an $N$-step random walk to have length $L$. Using analytical, exact enumeration, and Monte Carlo methods, we reveal the complex structure of the probability distribution in the large $N$ limit. In particular, the size of the longest loop has a distribution with a square-root singularity at $\ell\equiv L/N=1$, an essential singularity at $\ell=0$, and a discontinuous derivative at $\ell=1/2$.Comment: 3 pages, REVTEX 3.0, with multicol.sty, epsf.sty and EPS figures appended via uufiles. (Email in case of trouble.) CHANGES: Missing figure added to figures.uu MIT-CMT-KE-94-

Statistics of Largest Loops in a Random Walk

We report further findings on the size distribution of the largest neutral segments in a sequence of N randomly charged monomers [D. Ertas and Y. Kantor, Phys. Rev. E53, 846 (1996); cond-mat/9507005]. Upon mapping to one--dimensional random walks (RWs), this corresponds to finding the probability distribution for the size L of the largest segment that returns to its starting position in an N--step RW. We primarily focus on the large N, \ell = L/N << 1 limit, which exhibits an essential singularity. We establish analytical upper and lower bounds on the probability distribution, and numerically probe the distribution down to \ell \approx 0.04 (corresponding to probabilities as low as 10^{-15}) using a recursive Monte Carlo algorithm. We also investigate the possibility of singularities at \ell=1/k for integer k.Comment: 5 pages and 4 eps figures, requires RevTeX, epsf and multicol. Postscript file also available at http://cmtw.harvard.edu/~deniz/publications.htm

A Model Ground State of Polyampholytes

The ground state of randomly charged polyampholytes is conjectured to have a structure similar to a necklace, made of weakly charged parts of the chain, compacting into globules, connected by highly charged stretched `strings'. We suggest a specific structure, within the necklace model, where all the neutral parts of the chain compact into globules: The longest neutral segment compacts into a globule; in the remaining part of the chain, the longest neutral segment (the 2nd longest neutral segment) compacts into a globule, then the 3rd, and so on. We investigate the size distributions of the longest neutral segments in random charge sequences, using analytical and Monte Carlo methods. We show that the length of the n-th longest neutral segment in a sequence of N monomers is proportional to N/(n^2), while the mean number of neutral segments increases as sqrt(N). The polyampholyte in the ground state within our model is found to have an average linear size proportional to sqrt(N), and an average surface area proportional to N^(2/3).Comment: 8 two-column pages. 5 eps figures. RevTex. Submitted to Phys. Rev.

Synergetic modelling of the Russian Federation’s energy system parameters

The energy system in any country is the basis of the whole economy. The level of its development largely determines the quantity and quality of economic entities, periods of economic growth, fall and stagnation. A high percentage of the power-deficient municipalities in the Russian Federation shows the substantive issues in this sphere that carries a threat to the energy security of the state. One of the promising trends for enhancing the energy security is the renewable energy sources (RES). Their use has the obvious benefits: it provides electricity to power-deficient and inaccessible areas, contributes to the introduction and spread of new technologies, thus solving the important social and economic problem. At that, it is important to determine the optimum ratio using of the recovery of renewable and conventional energy sources (CES). One of the main challenges in this regard is to build a model that adequately reflects the ratio of renewable and conventional energy sources in the Russian energy system. The paper presents the results of a synergistic approach to the construction of such a model. The Lotka- Volterra model was the main instrument used, which allowed to study a behavior pattern of the considered systems on the basis of the simplified regularities. It was found that the best possible qualitative “jump” in the Russian energy sector was in 2008. The calculations allowed to investigate the behavior of the Russian energy system with the variation of the initial conditions and to assess the validity of the targets for the share of electricity produced through the use of renewable energy in the total electric power of the country

Hydrogeological Investigations in the Pampa of Argentina

The author has identified the following significant results. Satellite imagery in combination with ground investigations allows the identification and delineation of the near surface ground water (depth to ground water, salinity). The degree of precision achieved is greater than that obtainable by conventional ground survey methods alone

Collapse of Randomly Linked Polymers

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N. This result is inconsistent with results obtained from free energy considerations by Brygelson and Thirumalai (PRL76, 542 (1996)).Comment: 1 page, 1 postscript figure, LaTe

La mise en oeuvre de la Liste unique des garanties.

L’élaboration, depuis le 1er janvier 2007, de la Liste unique des garanties éligibles aux opérations de refinancement de l’Eurosystème entraîne des adaptations dans les méthodes d’évaluation de la qualité des actifs remis en garantie.Eurosystème, Liste unique, garanties, collatéral, refinancement, qualité de signature, créances privées, actifs négociables.

A Census Of Highly Symmetric Combinatorial Designs

As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v,k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t > 2 most of these characterizations have remained longstanding challenging problems. Especially, the determination of all flag-transitive Steiner t-designs with 2 < t < 7 is of particular interest and has been open for about 40 years (cf. [11, p. 147] and [12, p. 273], but presumably dating back to 1965). The present paper continues the author's work [20, 21, 22] of classifying all flag-transitive Steiner 3-designs and 4-designs. We give a complete classification of all flag-transitive Steiner 5-designs and prove furthermore that there are no non-trivial flag-transitive Steiner 6-designs. Both results rely on the classification of the finite 3-homogeneous permutation groups. Moreover, we survey some of the most general results on highly symmetric Steiner t-designs.Comment: 26 pages; to appear in: "Journal of Algebraic Combinatorics