ncRNA-mediated bistability in the synthesis of hundreds of distinct mRNAs and proteins

The kinetics of gene expression can be bistable due to the feedback between the mRNA and protein formation. In eukaryotic cells, the interplay between mRNAs and proteins can be influenced by non-coding RNAs. Some of these RNAs, e.g., microRNAs, may target hundreds of distinct mRNAs. The model presented here shows how a non-coding RNA can be used as a mediator in order to involve numerous mRNAs and proteins into a bistable network.     

Quantum entanglement of a large number of photons

A bipartite multiphoton entangled state is created through stimulated parametric down-conversion of strong laser pulses in a nonlinear crystal. It is shown how detectors that do not resolve the photon number can be used to analyze such multiphoton states. Entanglement of up to 12 photons is detected using both the positivity of the partially-transposed density matrix and a newly derived criteria. Furthermore, evidence is provided for entanglement of up to 100 photons. The multiparticle quantum state is such that even in the case of an overall photon collection and detection efficiency as low as a few percent, entanglement remains and can be detected.     

Instabilities in complex mixtures with a large number of components

Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterize all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the conditions under which the mixtures phase separate. The approach approximates the matrix of second-virial coefficients of the mixture by a random matrix, and determines the stability of the mixture from the spectrum of such random matrices.     

Gentile statistics with a large maximum occupation number

In Gentile statistics the maximum occupation number can take on unrestricted integers: 1<n<∞. It is usually believed that Gentile statistics will reduce to Bose-Einstein statistics when n equals the total number of particles in the system N. In this paper, we will show that this statement is valid only when the fugacity z<1; nevertheless, if z>1 the Bose-Einstein case is not recovered from Gentile statistics as n goes to N. Attention is also concentrated on the contribution of the ground state which was ignored in related literature. The thermodynamic behavior of a ν-dimensional Gentile ideal gas of particle of dispersion E=p^s/2m, where ν and s are arbitrary, is analyzed in detail. Moreover, we provide an alternative derivation of the partition function for Gentile statistics.     

Two-component Bose-Einstein condensates with a large number of vortices

We consider the condensate wave function of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine states of (87)Rb or (23)Na) we find that the two components contain identical rectangular vortex lattices, where the unit cell has an aspect ratio of sqrt[3], and one lattice is displaced to the center of the unit cell of the other. Our results are based on an exact evaluation of the vortex lattice energy in the large angular momentum (or quantum Hall) regime.     

Vicious random walkers in the limit of a large number of walkers

The vicious random walker problem on a line is studied in the limit of a large number of walkers. The multidimensional integral representing the probability that thep walkers will survive a timet (denotedP _t ^(p) ) is shown to be analogous to the partition function of a particular one-component Coulomb gas. By assuming the existence of the thermodynamic limit for the Coulomb gas, one can deduce asymptotic formulas forP _t ^(p) in the large-p, large-t limit. A straightforward analysis gives rigorous asymptotic formulas for the probability that after a timet the walkers are in their initial configuration (this event is termed a reunion). Consequently, asymptotic formulas for the conditional probability of a reunion, given that all walkers survive, are derived. Also, an asymptotic formula for the conditional probability density that any walker will arrive at a particular point in timet, given that allp walkers survive, is calculated in the limittp.     

Asymptotic relaxation of a system of a large number of interacting particles

A model of an open relaxing system of scalar bosons with one state and random interaction, described by a system of linking equations for the moments, is considered in a Markov approximation. It is shown that in the self-consistent field limit the equations for the first moments are equations of the characteristics with respect to the equation for the generating functions of the system. They can be understood as the scalar analog of a quasilinear Schrödinger equation with a purely imaginary Hamiltonian describing non-Hamiltonian dynamics of an open system of randomly interacting quantum particles. By virtue of the assumption made about the nature of the interaction, the equations of the characteristics obtained differ from those presented earlier, where the means are solutions of linearized relaxation equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 89–92, October, 1988.In conclusion, I am grateful to V. P. Belavkin for formulating the problems and useful discussions.     

Generalized large number hypothesis and cosmological constant

By generalizing Dirac's large number hypothesis we infer that the cosmological constant varies witht ^–2, as expected from earlier studies.     

On the expected number of distinct points in a subset visited by anN-step random walk

Many investigators have calculated asymptotically valid expressions for the expected number of distinct points visited by ann-step random walk on a lattice. In this note we point out that the same formalism can be used to study the expected number of distinct points in a subset of lattice points. We also calculate the expected occupancy of the subset and give sufficient conditions for the ratio of the two calculated quantities to have the same asymptotic time dependence as for the full lattice. Specific examples are considered.     

Anomalous characteristics of lasers with a large number of quantum wells

Semiconductor lasers with an active region containing six quantum wells are investigated experimentally. The temperature dependences of working characteristics (threshold current density, external differential quantum efficiency, and directional pattern) are analyzed. Anomalous behavior of the temperature dependence of the threshold current and external differential quantum efficiency, associated with a negative characteristic temperature and a decrease in the quantum efficiency of radiation upon a decrease in temperature, is detected. A narrowing of the directional patterns in the plane perpendicular to the p-n junction upon an increase in temperature is revealed.     

Substituting a qubit for an arbitrarily large number of classical bits

We show that a qubit can be used to substitute for a classical analog system requiring an arbitrarily large number of classical bits to represent digitally. Let a physical system S interact locally with a classical field varphi(x) as S travels directly from point A to point B. Our task is to use S to answer a simple yes/no question about varphi(x). If S is a qubit, the task can be done perfectly. We show that any classical system S must encode an arbitrarily large number of classical bits to solve the same task. This result implies a large quantum advantage in the memory size necessary for some computations. We also show that no finite amount of one-way classical communication can perfectly simulate the effect of quantum entanglement.     

Scaling in large Prandtl number turbulent thermal convection

We study the scaling properties of heat transfer Nu in turbulent thermal convection at large Prandtl number Pr using a quasi-linear theory. We show that two regimes arise, depending on the Reynolds number Re. At low Reynolds number, NuPr ^-1/2 and Re are a function of RaPr ^-3/2. At large Reynolds number NuPr ^1/3 and RePr are function only of RaPr ^2/3 (within logarithmic corrections). In practice, since Nu is always close to Ra ^1/3, this corresponds to a much weaker dependence of the heat transfer in the Prandtl number at low Reynolds number than at large Reynolds number. This difference may solve an existing controversy between measurements in SF₆ (large Re) and in alcohol/water (lower Re). We link these regimes with a possible global bifurcation in the turbulent mean flow. We further show how a scaling theory could be used to describe these two regimes through a single universal function. This function presents a bimodal character for intermediate range of Reynolds number. We explain this bimodality in term of two dissipation regimes, one in which fluctuation dominate, and one in which mean flow dominates. Altogether, our results provide a six parameters fit of the curve Nu(Ra, Pr) which may be used to describe all measurements at Pr≥0.7. Received 27 February 2002 / Received in final form 29 May 2002 Published online 31 July 2002     

Bose-Einstein condensates with large number of vortices

We show that as the number of vortices in a three dimensional Bose-Einstein condensate increases, the system reaches a "quantum Hall" regime where the density profile is a Gaussian in the xy plane and an inverted parabolic profile along z. The angular momentum of the system increases as the vortex lattice shrinks. However, Coriolis force prevents the unit cell of the vortex lattice from shrinking beyond a minimum size. Although the recent MIT experiment is not exactly in the quantum Hall regime, it is close enough for the present results to be used as a guide. The quantum Hall regime can be easily reached by moderate changes of the current experimental parameters.     

Confinement of a large number of antiprotons and production of an ultraslow antiproton beam

We have used a radio frequency quadrupole decelerator to decelerate antiprotons emerging from the CERN Antiproton Decelerator from MeV- to keV-scale energy, and collected five decelerated pulses in a multiring trap. Some 5 x 10(6) antiprotons were stacked in this way. Cooling of the trapped antiprotons by a simultaneously trapped electron plasma was studied nondestructively via shifts in plasma mode frequencies. We have also demonstrated the first step in extracting a 10-500 eV antiproton beam from the trap.