Statistical Thermodynamics of Clustered Populations

We present a thermodynamic theory for a generic population of $M$ individuals distributed into $N$ groups (clusters). We construct the ensemble of all distributions with fixed $M$ and $N$, introduce a selection functional that embodies the physics that governs the population, and obtain the distribution that emerges in the scaling limit as the most probable among all distributions consistent with the given physics. We develop the thermodynamics of the ensemble and establish a rigorous mapping to thermodynamics. We treat the emergence of a so-called "giant component" as a formal phase transition and show that the criteria for its emergence are entirely analogous to the equilibrium conditions in molecular systems. We demonstrate the theory by an analytic model and confirm the predictions by Monte Carlo simulation.Comment: Minor edits to tex

Attainment of reproductive competence, phase transition, and quantification of juvenility in mutant genetic screens

Plant development between seedling emergence and flowering is characterized by a series of successive qualitative phases: (1) a post embryonic photoperiodinsensitive phase, during which plants are insensitive to photoperiod; (2) a photoperiod- sensitive inductive phase, in which plants require a number of short day (SD) or long day (LD) inductive cycles, depending on their age for rapid flowering, and (3) a photoperiod-insensitive post-inductive phase, in which plant development is no longer influenced by photoperiod (Figure 1; Matsoukas et al., 2013)

Quantum Probability and the Born Ensemble

We formulate a discrete two-state stochastic model with elementary rules that give rise to Born statistics and reproduce the probabilities of the Schrodinger equation under an associated Hamiltonian matrix, which we identify. We define the probability to observe a state, classical or quantum, in proportion to the number of events at that state--number of ways the walker may materialize at a point of observation at time t, starting from known initial state at t=0. The quantum stochastic process differs from its classical counterpart in that the quantum walker is a pair of qubits, each transmitted independently through all possible paths to a point of observation, and whose recombination may produce a positive or negative event. We represent the state of the walker via a square matrix of recombination events, interpret the indeterminacy of the qubit state as rotations of this matrix, and show that the Born rule counts the number elements on this matrix that remain invariant over a full rotation.Comment: 13 pages including appendi

Extensive in-silico analysis of cis-acting DNA sequences in 5’ regulatory regions of sucrose synthase, cell wall invertase and sucrose transporter gene families

Cis-acting regulatory elements are important molecular switches involved in the temporal and spatial expression of a dynamic network of gene activities. This network control hormone responses, abiotic stress responses and developmental events such as juvenility, floral signal transduction and senescence. In this analysis, a particular emphasis was placed on cis-acting regulatory elements present within the 5’ regulatory region of sucrose synthase (SuSy), cell wall invertase (CWI) and sucrose transporter (SUT) gene families in Arabidopsis thaliana and Oryza sativa. The potential cis-acting regulatory elements were predicted by scanning 1.5 kbp of 5’ regulatory regions of the SUT, CWI and SuSy genes translational start sites, using various resources for cis-element bioinformatics. Cis-elements associated with hormone responsiveness, light responsiveness, elicitor responsiveness and abiotic stress were predicted in varying frequencies within the 1.5 kbp of 5’ regulatory sequences. In addition, cis-elements involved in sugar repression, mineral responses, and cold- and light-inducible gene expression were also identified. Some of the predicted cis-elements have experimental precedent, but many are novel and encourage further exploration. This analysis provides a basis for elucidating transcription regulatory interactions of SUT, CWI and SUSY gene families during development or under abiotic stress conditions