Generation of folk song melodies using Bayes transforms

The paper introduces the `Bayes transform', a mathematical procedure for putting data into a hierarchical representation. Applicable to any type of data, the procedure yields interesting results when applied to sequences. In this case, the representation obtained implicitly models the repetition hierarchy of the source. There are then natural applications to music. Derivation of Bayes transforms can be the means of determining the repetition hierarchy of note sequences (melodies) in an empirical and domain-general way. The paper investigates application of this approach to Folk Song, examining the results that can be obtained by treating such transforms as generative models

Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries

Using exact computations we study the classical hard-core monomer-dimer models on m x n plane lattice strips with free boundaries. For an arbitrary number v of monomers (or vacancies), we found a logarithmic correction term in the finite-size correction of the free energy. The coefficient of the logarithmic correction term depends on the number of monomers present (v) and the parity of the width n of the lattice strip: the coefficient equals to v when n is odd, and v/2 when n is even. The results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers.Comment: 4 pages, 2 figure

A study of the in vitro initiation of adenovirus DNA replication

The development of systems in which adenovirus DNA can be replicated in vitro has led to the elucidation of the sequences essential for origin function and to the identification of the proteins required for viral DNA replication. Much of the information currently available has been derived from investigations carried out using adenovirus types 2 and 5 which in addition to the viral proteins, adenovirus DNA polymerase, precursor terminal protein and DNA binding protein, require cellular proteins nuclear factor I and nuclear factor III for efficient initiation of DNA replication. In contrast adenovirus type 4 replicates Its DNA efficiently without these cellular proteins. Correspondingly its minimal origin of replication is remarkably simple in structure, consisting of only the terminal 18bp of the adenovirus genome ('the core sequence'). The effect of point mutations in the core region on adenovirus type 4 DNA replication in vitro was investigated and it was found that mutations within two discrete domains had a married deleterious effect on initiation of DNA replication. The crude Ad4 infected cell extracts initially used for in vitro DNA replication were fractionated and it was found that only four detectable proteins, three of which were identified as viral DNA polymerase, precursor terminal protein and DNA binding protein gave efficient DNA replication in vitro and furthermore behaved similarly to unfractionated infected cell extracts in the presence of template which contained point mutations. To examine a possible role of the core region of the origin as containing sites for specific interactions with viral replication proteins, purified adenovirus type 5 precursor terminal protein and DNA polymerase were assayed for their ability to recognise the terminal 1-18 sequence. It was found that both proteins independently and as a heterodimer bound specifically to a sequence corresponding to the core origin of replication, suggesting that sequences within this region are important for localisation of DNA replication proteins at the origin via a sequence specific DNA-protein interaction

Vacancy localization in the square dimer model

We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this formalism, we can address the question of the possible motion of the vacancy induced by dimer slidings. We find a probability 57/4-10Sqrt[2] for the vacancy to be strictly jammed in an infinite system. More generally, the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9/8. On a finite system, the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent 1/4. The resultant weak localization of vacancies still allows for unbounded diffusion, characterized by a diffusion exponent that we relate to that of diffusion on spanning trees. We also implement numerical simulations of the model with both free and periodic boundary conditions.Comment: 35 pages, 24 figures. Improved version with one added figure (figure 9), a shift s->s+1 in the definition of the tree size, and minor correction

A Corpus-Based, Pilot Study of Lexical Stress Variation in American English

Phonological free variation describes the phenomenon of there being more than one pronunciation for a word without any change in meaning (e.g. because, schedule, vehicle). The term also applies to words that exhibit different stress patterns (e.g. academic, resources, comparable) with no change in meaning or grammatical category. A corpus-based analysis of free variation is a useful tool for testing the validity of surveys of speakers' pronunciation preferences for certain variants. The current paper presents the results of a corpus-based pilot study of American English, in an attempt to replicate Mompéan's 2009 study of British English

Phase Transition in a Self-repairing Random Network

We consider a network, bonds of which are being sequentially removed; that is done at random, but conditioned on the system remaining connected (Self-Repairing Bond Percolation SRBP). This model is the simplest representative of a class of random systems for which forming of isolated clusters is forbidden. It qualitatively describes the process of fabrication of artificial porous materials and degradation of strained polymers. We find a phase transition at a finite concentration of bonds $p=p_c$, at which the backbone of the system vanishes; for all $p<p_c$ the network is a dense fractal.Comment: 4 pages, 4 figure

Density functional theory for nearest-neighbor exclusion lattice gasses in two and three dimensions

To speak about fundamental measure theory obliges to mention dimensional crossover. This feature, inherent to the systems themselves, was incorporated in the theory almost from the beginning. Although at first it was thought to be a consistency check for the theory, it rapidly became its fundamental pillar, thus becoming the only density functional theory which possesses such a property. It is straightforward that dimensional crossover connects, for instance, the parallel hard cube system (three-dimensional) with that of squares (two-dimensional) and rods (one-dimensional). We show here that there are many more connections which can be established in this way. Through them we deduce from the functional for parallel hard (hyper)cubes in the simple (hyper)cubic lattice the corresponding functionals for the nearest-neighbor exclusion lattice gases in the square, triangular, simple cubic, face-centered cubic, and body-centered cubic lattices. As an application, the bulk phase diagram for all these systems is obtained.Comment: 13 pages, 13 figures; needs revtex

Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer

The number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory. In this paper, solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by Monte Carlo simulations using Wang-Landau sampling method for integers up to 8000. It is shown that, for large n, ln[p(n)]/n^(3/4) = 1.79 \pm 0.01, where p(n) is the number of solid partitions of the integer n. This result strongly suggests that the MacMahon conjecture for solid partitions, though not exact, could still give the correct leading asymptotic behaviour.Comment: 6 pages, 4 figures, revtex

Exact solution of A-D Temperley-Lieb Models

We solve for the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups {\cal U}_q(X_n } for X_n = A_1,B_n,C_n$and$D_n$. We employ a generalization of the coordinate Bethe-Ansatz developed previously for the deformed biquadratic spin one chain. As expected, all these models have equivalent spectra, i.e. they differ only in the degeneracy of their eigenvalues. This is true for finite length and open boundary conditions. For periodic boundary conditions the spectra of the lower dimensional representations are containded entirely in the higher dimensional ones. The Bethe states are highest weight states of the quantum group, except for some states with energy zero

The duality relation between Glauber dynamics and the diffusion-annihilation model as a similarity transformation

In this paper we address the relationship between zero temperature Glauber dynamics and the diffusion-annihilation problem in the free fermion case. We show that the well-known duality transformation between the two problems can be formulated as a similarity transformation if one uses appropriate (toroidal) boundary conditions. This allow us to establish and clarify the precise nature of the relationship between the two models. In this way we obtain a one-to-one correspondence between observables and initial states in the two problems. A random initial state in Glauber dynamics is related to a short range correlated state in the annihilation problem. In particular the long-time behaviour of the density in this state is seen to depend on the initial conditions. Hence, we show that the presence of correlations in the initial state determine the dependence of the long time behaviour of the density on the initial conditions, even if such correlations are short-ranged. We also apply a field-theoretical method to the calculation of multi-time correlation functions in this initial state.Comment: 15 pages, Latex file, no figures. To be published in J. Phys. A. Minor changes were made to the previous version to conform with the referee's Repor