Area limit laws for symmetry classes of staircase polygons

We derive area limit laws for the various symmetry classes of staircase polygons on the square lattice, in a uniform ensemble where, for fixed perimeter, each polygon occurs with the same probability. This complements a previous study by Leroux and Rassart, where explicit expressions for the area and perimeter generating functions of these classes have been derived.Comment: 18 pages, 3 figure

Spatiotemporally Complete Condensation in a Non-Poissonian Exclusion Process

We investigate a non-Poissonian version of the asymmetric simple exclusion process, motivated by the observation that coarse-graining the interactions between particles in complex systems generically leads to a stochastic process with a non-Markovian (history-dependent) character. We characterize a large family of one-dimensional hopping processes using a waiting-time distribution for individual particle hops. We find that when its variance is infinite, a real-space condensate forms that is complete in space (involves all particles) and time (exists at almost any given instant) in the thermodynamic limit. The mechanism for the onset and stability of the condensate are both rather subtle, and depends on the microscopic dynamics subsequent to a failed particle hop attempts.Comment: 5 pages, 5 figures. Version 2 to appear in PR

Discrete Spectra of Semirelativistic Hamiltonians

We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = \beta \sqrt{m^2 + p^2} + V(r) (w.l.o.g. in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation. Every Hamiltonian in this class of operators consists of the relativistic kinetic energy \beta \sqrt{m^2 + p^2} (where \beta > 0 allows for the possibility of more than one particles of mass m) and a spherically symmetric attractive potential V(r), r = |x|. In general, accurate eigenvalues of a nonlocal Hamiltonian operator can only be found by the use of a numerical approximation procedure. Our main emphasis, however, is on the derivation of rigorous semi-analytical expressions for both upper and lower bounds to the energy levels of such operators. We compare the bounds obtained within different approaches and present relationships existing between the bounds.Comment: 21 pages, 3 figure

Glass Transition Temperature Depression at the Percolation Threshold in Carbon Nanotube-Epoxy Resin and Polypyrrole-Epoxy Resin Composites

The glass transition temperatures of conducting composites, obtained by blending carbon nanotubes (CNTs) or polypyrrole (PPy) particles with epoxy resin, were investigated by using both differential scanning calorimetry (DSC) and dynamical mechanical thermal analysis (DMTA). For both composites, dc and ac conductivity measurements revealed an electrical percolation threshold at which the glass transition temperature and mechanical modulus of the composites pass through a minimum

Genome-wide profiling of chromosome interactions in Plasmodium falciparum characterizes nuclear architecture and reconfigurations associated with antigenic variation.

Spatial relationships within the eukaryotic nucleus are essential for proper nuclear function. In Plasmodium falciparum, the repositioning of chromosomes has been implicated in the regulation of the expression of genes responsible for antigenic variation, and the formation of a single, peri-nuclear nucleolus results in the clustering of rDNA. Nevertheless, the precise spatial relationships between chromosomes remain poorly understood, because, until recently, techniques with sufficient resolution have been lacking. Here we have used chromosome conformation capture and second-generation sequencing to study changes in chromosome folding and spatial positioning that occur during switches in var gene expression. We have generated maps of chromosomal spatial affinities within the P. falciparum nucleus at 25 Kb resolution, revealing a structured nucleolus, an absence of chromosome territories, and confirming previously identified clustering of heterochromatin foci. We show that switches in var gene expression do not appear to involve interaction with a distant enhancer, but do result in local changes at the active locus. These maps reveal the folding properties of malaria chromosomes, validate known physical associations, and characterize the global landscape of spatial interactions. Collectively, our data provide critical information for a better understanding of gene expression regulation and antigenic variation in malaria parasites

Antipersistent binary time series

Completely antipersistent binary time series are sequences in which every time that an $N$-bit string $\mu$ appears, the sequence is continued with a different bit than at the last occurrence of $\mu$. This dynamics is phrased in terms of a walk on a DeBruijn graph, and properties of transients and cycles are studied. The predictability of the generated time series for an observer who sees a longer or shorter time window is investigated also for sequences that are not completely antipersistent.Comment: 6 pages, 6 figure