Entropy, independent sets and antichains: A new approach to Dedekind's problem

For -regular, -vertex bipartite graphs with bipartition , a precise bound is given for the sum over independent sets of the quantity . (In other language, this is bounding the partition function for certain instances of the hard-core model.) This result is then extended to graded partially ordered sets, which in particular provides a simple proof of a well-known bound for Dedekind's Problem given by Kleitman and Markowsky in 1975.

     

Broken symmetries and pattern formation in two-frequency forced faraday waves

We exploit the approximate (broken) symmetries of time translation, time reversal, and Hamiltonian structure to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Using explicit parameter symmetries we determine, for the case of two-frequency forcing, how the strength of observed three-wave interactions depends on the frequency ratio and on the relative phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments.     

Synthetic gene network for entraining and amplifying cellular oscillations

We present a model for a synthetic gene oscillator and consider the coupling of the oscillator to a periodic process that is intrinsic to the cell. We investigate the synchronization properties of the coupled system, and show how the oscillator can be constructed to yield a significant amplification of cellular oscillations. We reduce the driven oscillator equations to a normal form, and analytically determine the amplification as a function of the strength of the cellular oscillations. The ability to couple naturally occurring genetic oscillations to a synthetically designed network could lead to possible strategies for entraining and/or amplifying oscillations in cellular protein levels.     

Dynamics of entanglement transfer from radiation modes to localized qubits

We address the dynamics of entanglement transfer from two radiation modes to a pair of localized qubits implemented as atoms flying through or trapped in separated cavities. We first generalize previous results to include radiation in entangled mixed states and to describe the effect of cavity mirror transmittance. Then we investigate the transfer process by Monte Carlo Wave Function approach, which allows us to solve the whole system dynamics including cavity mode and atomic decays. We focus on flying modes prepared in coherently correlated states and we find realistic conditions for efficient entanglement transfer out of the weak and strong coupling regimes in the perspective of quantum memories realization.     

Pions as spin waves: Chiral symmetry breaking in lattice gauge theory

In hamiltonian lattice gauge theory, the fermion vacuum at lowest order in 1/g² can be determined from degenerate perturbation theory plus mean field-spin wave techniques. Using compact QED as an example, we show that: (i) chiral symmetry is spontaneously broken; and (ii) $\text{m}{}_{\mathrm{<mtext>pseudoGoldstone</mtext>}}{}^2\text{∝ m}{}_{\mathrm{<mtext>fermion</mtext>}}\text{〈}\text{ψ}\text{ψ〉}$. The pseudoscalar pseudoGoldstone particles—the “pions” of this abelian theory—correspond to antiferromagnetic spin wave excitations of the fermion vacuum.     

Mimicking dihydroxy acetone phosphate-utilizing aldolases through organocatalysis: a facile route to carbohydrates and aminosugars

[reaction: see text] A practical and environmentally friendly organocatalytic strategy designed to mimic the DHAP aldolases has been developed and shown to be effective in the preparation of carbohydrates and aminosugars. (S)-Proline and (S)-2-pyrrolidine-tetrazole catalyzed the aldol reaction between dihydroxy acetone variants such as 1,3-dioxan-5-one and 2,2-dimethyl-1,3-dioxan-5-one with aldehydes to give the corresponding polyols in good yields with very high ees.