Combinatorial Markov chains on linear extensions

We consider generalizations of Schuetzenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other has a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence L=S_n is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is R-trivial and then using Steinberg's extension of Brown's theory for Markov chains on left regular bands to R-trivial monoids.Comment: 35 pages, more examples of promotion, rephrased the main theorems in terms of discrete time Markov chain

QCD Strings as Constrained Grassmannian Sigma Model:

We present calculations for the effective action of string world sheet in R3 and R4 utilizing its correspondence with the constrained Grassmannian sigma model. Minimal surfaces describe the dynamics of open strings while harmonic surfaces describe that of closed strings. The one-loop effective action for these are calculated with instanton and anti-instanton background, reprsenting N-string interactions at the tree level. The effective action is found to be the partition function of a classical modified Coulomb gas in the confining phase, with a dynamically generated mass gap.Comment: 22 pages, Preprint: SFU HEP-116-9

Reexamination of the long-range Potts model: a multicanonical approach

We investigate the critical behavior of the one-dimensional q-state Potts model with long-range (LR) interaction $1/r^{d+\sigma}$, using a multicanonical algorithm. The recursion scheme initially proposed by Berg is improved so as to make it suitable for a large class of LR models with unequally spaced energy levels. The choice of an efficient predictor and a reliable convergence criterion is discussed. We obtain transition temperatures in the first-order regime which are in far better agreement with mean-field predictions than in previous Monte Carlo studies. By relying on the location of spinodal points and resorting to scaling arguments, we determine the threshold value $\sigma_c(q)$ separating the first- and second-order regimes to two-digit precision within the range $3 \leq q \leq 9$. We offer convincing numerical evidence supporting $\sigma_c(q)Comment: 18 pages, 18 figure

On 'Light' Fermions and Proton Stability in 'Big Divisor' D3/D7 Swiss Cheese Phenomenology

Building up on our earlier work [1,2], we show the possibility of generating "light" fermion mass scales of MeV-GeV range (possibly related to first two generations of quarks/leptons) as well as eV (possibly related to first two generations of neutrinos) in type IIB string theory compactified on Swiss-Cheese orientifolds in the presence of a mobile space-time filling D3-$brane restricted to (in principle) stacks of fluxed D7-branes wrapping the "big" divisor \Sigma_B. This part of the paper is an expanded version of the latter half of section 3 of a published short invited review [3] written up by one of the authors [AM]. Further, we also show that there are no SUSY GUT-type dimension-five operators corresponding to proton decay, as well as estimate the proton lifetime from a SUSY GUT-type four-fermion dimension-six operator to be 10^{61} years. Based on GLSM calculations in [1] for obtaining the geometric Kaehler potential for the "big divisor", using further the Donaldson's algorithm, we also briefly discuss in the first of the two appendices, obtaining a metric for the Swiss-Cheese Calabi-Yau used, that becomes Ricci flat in the large volume limit.Comment: v2: 1+25 pages, Title modified and text thoroughly expanded including a brief discussion on obtaining Ricci-flat Swiss Cheese Calabi-Yau metrics using the Donaldson's algorithm, references added, to appear in EPJ

Salerno's model of DNA reanalysed: could solitons have biological significance?

We investigate the sequence-dependent behaviour of localised excitations in a toy, nonlinear model of DNA base-pair opening originally proposed by Salerno. Specifically we ask whether ``breather'' solitons could play a role in the facilitated location of promoters by RNA polymerase. In an effective potential formalism, we find excellent correlation between potential minima and {\em Escherichia coli} promoter recognition sites in the T7 bacteriophage genome. Evidence for a similar relationship between phage promoters and downstream coding regions is found and alternative reasons for links between AT richness and transcriptionally-significant sites are discussed. Consideration of the soliton energy of translocation provides a novel dynamical picture of sliding: steep potential gradients correspond to deterministic motion, while ``flat'' regions, corresponding to homogeneous AT or GC content, are governed by random, thermal motion. Finally we demonstrate an interesting equivalence between planar, breather solitons and the helical motion of a sliding protein ``particle'' about a bent DNA axis.Comment: Latex file 20 pages, 5 figures. Manuscript of paper to appear in J. Biol. Phys., accepted 02/09/0

Can forest management based on natural disturbances maintain ecological resilience?

Given the increasingly global stresses on forests, many ecologists argue that managers must maintain ecological resilience: the capacity of ecosystems to absorb disturbances without undergoing fundamental change. In this review we ask: Can the emerging paradigm of natural-disturbance-based management (NDBM) maintain ecological resilience in managed forests? Applying resilience theory requires careful articulation of the ecosystem state under consideration, the disturbances and stresses that affect the persistence of possible alternative states, and the spatial and temporal scales of management relevance. Implementing NDBM while maintaining resilience means recognizing that (i) biodiversity is important for long-term ecosystem persistence, (ii) natural disturbances play a critical role as a generator of structural and compositional heterogeneity at multiple scales, and (iii) traditional management tends to produce forests more homogeneous than those disturbed naturally and increases the likelihood of unexpected catastrophic change by constraining variation of key environmental processes. NDBM may maintain resilience if silvicultural strategies retain the structures and processes that perpetuate desired states while reducing those that enhance resilience of undesirable states. Such strategies require an understanding of harvesting impacts on slow ecosystem processes, such as seed-bank or nutrient dynamics, which in the long term can lead to ecological surprises by altering the forest's capacity to reorganize after disturbance

Gene Regulation in the Pi Calculus: Simulating Cooperativity at the Lambda Switch

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4230).Also part of the Lecture Notes in Bioinformatics book sub series (volume 4230).International audienceWe propose to model the dynamics of gene regulatory networks as concurrent processes in the stochastic pi calculus. As a first case study, we show how to express the control of transcription initiation at the lambda switch, a prototypical example where cooperative enhancement is crucial. This requires concurrent programming techniques that are new to systems biology, and necessitates stochastic parameters that we derive from the literature. We test all components of our model by exhaustive stochastic simulations. A comparison with previous results reported in the literature, experimental and simulation based, confirms the appropriateness of our modeling approach