Exact solution of the Bernoulli matching model of sequence alignment

Through a series of exact mappings we reinterpret the Bernoulli model of sequence alignment in terms of the discrete-time totally asymmetric exclusion process with backward sequential update and step function initial condition. Using earlier results from the Bethe ansatz we obtain analytically the exact distribution of the length of the longest common subsequence of two sequences of finite lengths $X,Y$. Asymptotic analysis adapted from random matrix theory allows us to derive the thermodynamic limit directly from the finite-size result.Comment: 13 pages, 4 figure

Transfer matrices for the totally asymmetric exclusion process

We consider the totally asymmetric simple exclusion process (TASEP) on a finite lattice with open boundaries. We show, using the recursive structure of the Markov matrix that encodes the dynamics, that there exist two transfer matrices $T_{L-1,L}$ and $\tilde{T}_{L-1,L}$ that intertwine the Markov matrices of consecutive system sizes: $\tilde{T}_{L-1,L}M_{L-1}=M_{L}T_{L-1,L}$. This semi-conjugation property of the dynamics provides an algebraic counterpart for the matrix-product representation of the steady state of the process.Comment: 7 page

Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model

By using the fact that Polychronakos-like models can be obtained through the `freezing limit' of related spin Calogero models, we calculate the exact spectrum as well as partition function of SU(m|n) supersymmetric Polychronakos (SP) model. It turns out that, similar to the non-supersymmetric case, the spectrum of SU(m|n) SP model is also equally spaced. However, the degeneracy factors of corresponding energy levels crucially depend on the values of bosonic degrees of freedom (m) and fermionic degrees of freedom (n). As a result, the partition functions of SP models are expressed through some novel q-polynomials. Finally, by interchanging the bosonic and fermionic degrees of freedom, we obtain a duality relation among the partition functions of SP models.Comment: Latex, 20 pages, no figures, minor typos correcte

Distribution and conservation status of two endemic Tasmanian crustaceans, Allanaspides hickmani and Allanaspides helonomus (Syncarida: anaspididae)

Extant representatives of the ancient crustacean family Anaspididae (Syncarida) are restricted to the island state of Tasmania, Australia. The most recently described species, Allanaspides helonomus Swain, Wilson, Hickman & Ong, 1970 and A. hickmani Swain, Wilson & Ong, 1971, were described from buttongrass moorland in southwestern Tasmania. Large areas of their habitat were subsequently inundated for hydroelectric power generation. We surveyed the extant distributions of A. hickmani and A. helonomus, assessed potential threats to the species, and reviewed their conservation status against state, national and international criteria. A. hickmani is restricted to a single catchment and occurs in a very small number (<10) of highly fragmented subpopulations on the margins of two hydroelectric impoundments. A. helonomus has a substantially larger range and Area of Occupancy spanning three separate catchments, and is now known to also occur in the Lake Pedder hydro-electric impoundment. Both species are listed as vulnerable on the IUCN Red List. This listing appears warranted for A. hickmani based on its restricted Area of Occupancy and the small number of extant subpopulations. However, A. helonomus no longer appears to fulfil the IUCN criterion for vulnerable. Neither species appears to be eligible for listing as vulnerable under the Australian Environment Protection and Biodiversity Conservation Act 1999 and the Tasmanian Threatened Species Protection Act 1995. The current listing of A. hickmani as rare under the Tasmanian Threatened Species Protection Act 1995 appears warranted as extant subpopulations may be at risk of extinction. The level of risk for A. helonomus is considerably lower than is the case for A. hickmani, and A. helonomus may not be eligible for listing as rare. The potential impacts of climate change on buttongrass moorland may present the most serious long-term threat to the two Allanaspides species

Matrix product solution to an inhomogeneous multi-species TASEP

We study a multi-species exclusion process with inhomogeneous hopping rates. This model is equivalent to a Markov chain on the symmetric group that corresponds to a random walk in the affine braid arrangement. We find a matrix product representation for the stationary state of this model. We also show that it is equivalent to a graphical construction proposed by Ayyer and Linusson, which generalizes Ferrari and Martin's construction

Novel Quantum States of the Rational Calogero Models Without the Confining Interaction

We show that the N-particle A_{N-1} and B_N rational Calogero models without the harmonic interaction admit a new class of bound and scattering states. These states owe their existence to the self-adjoint extensions of the corresponding Hamiltonians, labelled by a real parameter z. It is shown that the new states appear for all values of N and for specific ranges of the coupling constants. Moreover, they are shown to exist even in the excited sectors of the Calogero models. The self-adjoint extension generically breaks the classical scaling symmetry, leading to quantum mechanical scaling anomaly. The scaling symmetry can however be restored for certain values of the parameter z. We also generalize these results for many particle systems with classically scale invariant long range interactions in arbitrary dimensions.Comment: Latex file, 21 pages; minor changes in text, some references added, to appear in Nucl. Phys.

Formulation and in vitro Evaluation of Eudragit® Microspheres of Stavudine

Purpose: The aim of this study was to formulate and evaluate microencapsulated controlled release preparations of a highly water-soluble drug, stavudine, using Copolymers synthesized from acrylic and methacrylic acid esters (Eudragit RS 100 and RL 100) as the retardant material. . Methods: Microspheres were prepared by solvent evaporation method using an acetone / liquid paraffin system. Magnesium stearate was used as the droplet stabilizer and n-hexane was added to harden the microspheres. The prepared microspheres were characterized for their micromeritic properties and drug loading, as well by fourier transform infrared spectroscopy (FTIR), differential scanning calorimetry, x-ray powder diffractometry and scanning electron microscopy. The in vitro release studies were performed in pH 6.8, phosphate buffer. Results: The prepared microspheres were white, free flowing and spherical in shape. The drug-loaded microspheres showed 67-91% of entrapment and release was extended upto 6 to 8 h. The infrared spectra and differential scanning calorimetry thermographs showed stable character of stavudine in the drug-loaded microspheres and revealed the absence of drug-polymer interactions. X-ray diffraction patterns showed that there was decrease in crystallinity of the drug. Scanning electron microscopy study revealed that the microspheres were spherical and porous in nature. Conclusion: The best-fit release kinetics was achieved with Higuchi plot followed by zero order and First order. The release of stavudine was influenced by the drug to polymer ratio and particle size & was found to be diffusion controlled. Keywords: Stavudine, Eudragit, microspheres, controlled release, polymethacrylate > Tropical Journal of Pharmaceutical Research Vol. 4 (1) 2005: pp. 369-37

Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries

The one-dimensional partially asymmetric simple exclusion process with open boundaries is considered. The stationary state, which is known to be constructed in a matrix product form, is studied by applying the theory of q-orthogonal polynomials. Using a formula of the q-Hermite polynomials, the average density profile is computed in the thermodynamic limit. The phase diagram for the correlation length, which was conjectured in the previous work[J. Phys. A {\bf 32} (1999) 7109], is confirmed.Comment: 24 pages, 6 figure