New fermionic formula for unrestricted Kostka polynomials

A new fermionic formula for the unrestricted Kostka polynomials of type $A_{n-1}^{(1)}$ is presented. This formula is different from the one given by Hatayama et al. and is valid for all crystal paths based on Kirillov-Reshetihkin modules, not just for the symmetric and anti-symmetric case. The fermionic formula can be interpreted in terms of a new set of unrestricted rigged configurations. For the proof a statistics preserving bijection from this new set of unrestricted rigged configurations to the set of unrestricted crystal paths is given which generalizes a bijection of Kirillov and Reshetikhin.Comment: 35 pages; reference adde

N=2 Supersymmetry and Bailey Pairs

We demonstrate that the Bailey pair formulation of Rogers-Ramanujan identities unifies the calculations of the characters of $N=1$ and $N=2$ supersymmetric conformal field theories with the counterpart theory with no supersymmetry. We illustrate this construction for the $M(3,4)$ (Ising) model where the Bailey pairs have been given by Slater. We then present the general unitary case. We demonstrate that the model $M(p,p+1)$ is derived from $M(p-1,p)$ by a Bailey renormalization flow and conclude by obtaining the $N=1$ model $SM(p,p+2)$ and the unitary $N=2$ model with central charge $c=3(1-2/p).$Comment: 32 pages in harvmac, no figure

A generalization of the q-Saalschutz sum and the Burge transform

A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A_1^{(1)} string functions.Comment: 18 pages, AMSLaTe

The perturbations ϕ2,1\phi_{2,1} and ϕ1,5\phi_{1,5} of the minimal models M(p,p′)M(p,p') and the trinomial analogue of Bailey's lemma

We derive the fermionic polynomial generalizations of the characters of the integrable perturbations $\phi_{2,1}$ and $\phi_{1,5}$ of the general minimal $M(p,p')$ conformal field theory by use of the recently discovered trinomial analogue of Bailey's lemma. For $\phi_{2,1}$ perturbations results are given for all models with $2p>p'$ and for $\phi_{1,5}$ perturbations results for all models with ${p'\over 3}<p< {p'\over 2}$ are obtained. For the $\phi_{2,1}$ perturbation of the unitary case $M(p,p+1)$ we use the incidence matrix obtained from these character polynomials to conjecture a set of TBA equations. We also find that for $\phi_{1,5}$ with $2<p'/p < 5/2$ and for $\phi_{2,1}$ satisfying $3p<2p'$ there are usually several different fermionic polynomials which lead to the identical bosonic polynomial. We interpret this to mean that in these cases the specification of the perturbing field is not sufficient to define the theory and that an independent statement of the choice of the proper vacuum must be made.Comment: 34 pages, 15 figures, harvmac. References added and the TBA conjecture refine

New Finite Rogers-Ramanujan Identities

We present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson's transformation formula by specialization or through Bailey's method, the second similar formula can be proved either by using the first formula and the q-Gosper algorithm, or through the so-called Bailey lattice.Comment: 19 pages. to appear in Ramanujan

Capsular polysaccharide production and serum survival of Vibrio vulnificus are dependent on antitermination control by RfaH

© 2016 Federation of European Biochemical Societies The human pathogen Vibrio vulnificus undergoes phase variation among colonial morphotypes, including a virulent opaque form which produces capsular polysaccharide (CPS) and a translucent phenotype that produces little or no CPS and is attenuated. Here, we found that a V. vulnificus mutant defective for RfaH antitermination control showed a diminished capacity to undergo phase variation and displayed significantly reduced distal gene expression within the Group I CPS operon. Moreover, the rfaH mutant produced negligible CPS and was highly sensitive to killing by normal human serum, results which indicate that RfaH is likely essential for virulence in this bacterium

RfaH Suppresses Small RNA MicA Inhibition of fimB Expression in Escherichia coli K-12

The phase variation (reversible on-off switching) of the type 1 fimbrial adhesin of Escherichia coli involves a DNA inversion catalyzed by FimB (switching in either direction) or FimE (on-to-off switching). Here, we demonstrate that RfaH activates expression of a FimB-LacZ protein fusion while having a modest inhibitory effect on a comparable fimB-lacZ operon construct and on a FimE-LacZ protein fusion, indicating that RfaH selectively controls fimB expression at the posttranscriptional level. Further work demonstrates that loss of RfaH enables small RNA (sRNA) MicA inhibition of fimB expression even in the absence of exogenous inducing stress. This effect is explained by induction of σE , and hence MicA, in the absence of RfaH. Additional work con- firms that the procaine-dependent induction of micA requires OmpR, as reported previously (A. Coornaert et al., Mol. Microbiol. 76:467–479, 2010, doi:10.1111/j.1365-2958.2010.07115.x), but also demonstrates that RfaH inhibition of fimB transcription is enhanced by procaine independently of OmpR. While the effect of procaine on fimB transcription is shown to be independent of RcsB, it was found to require SlyA, another known regulator of fimB transcription. These results demonstrate a complex role for RfaH as a regulator of fimB expression

Testing "microscopic" theories of glass-forming liquids

We assess the validity of "microscopic" approaches of glass-forming liquids based on the sole k nowledge of the static pair density correlations. To do so we apply them to a benchmark provided by two liquid models that share very similar static pair density correlation functions while disp laying distinct temperature evolutions of their relaxation times. We find that the approaches are unsuccessful in describing the difference in the dynamical behavior of the two models. Our study is not exhausti ve, and we have not tested the effect of adding corrections by including for instance three-body density correlations. Yet, our results appear strong enough to challenge the claim that the slowd own of relaxation in glass-forming liquids, for which it is well established that the changes of the static structure factor with temperature are small, can be explained by "microscopic" appr oaches only requiring the static pair density correlations as nontrivial input.Comment: 10 pages, 7 figs; Accepted to EPJE Special Issue on The Physics of Glasses. Arxiv version contains an addendum to the appendix which does not appear in published versio

Integration of Genome Scale Metabolic Networks and gene regulation of metabolic enzymes with Physiologically Based Pharmacokinetics

The scope of Physiologically Based Pharmacokinetic (PBPK) modelling can be expanded by assimilation of the mechanistic models of intracellular processes from Systems Biology field. Genome Scale Metabolic Networks (GSMNs) represent a whole set of metabolic enzymes expressed in human tissues. Dynamic models of the gene regulation of key drug metabolism enzymes are available. Here, we introduce GSMNs and review ongoing work on integration of PBPK, GSMNs and metabolic gene regulation. We demonstrate example models

Computational Design of Auxotrophy-Dependent Microbial Biosensors for Combinatorial Metabolic Engineering Experiments

Combinatorial approaches in metabolic engineering work by generating genetic diversity in a microbial population followed by screening for strains with improved phenotypes. One of the most common goals in this field is the generation of a high rate chemical producing strain. A major hurdle with this approach is that many chemicals do not have easy to recognize attributes, making their screening expensive and time consuming. To address this problem, it was previously suggested to use microbial biosensors to facilitate the detection and quantification of chemicals of interest. Here, we present novel computational methods to: (i) rationally design microbial biosensors for chemicals of interest based on substrate auxotrophy that would enable their high-throughput screening; (ii) predict engineering strategies for coupling the synthesis of a chemical of interest with the production of a proxy metabolite for which high-throughput screening is possible via a designed bio-sensor. The biosensor design method is validated based on known genetic modifications in an array of E. coli strains auxotrophic to various amino-acids. Predicted chemical production rates achievable via the biosensor-based approach are shown to potentially improve upon those predicted by current rational strain design approaches. (A Matlab implementation of the biosensor design method is available via http://www.cs.technion.ac.il/~tomersh/tools)