A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks

Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the moment-closure approach used to obtain such approximations, calling it an ad-hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems. We use mixtures of product-Poisson distributions to obtain a flexible parametric family which solves the commonly observed problem of divergences at low system sizes. We also extend the recently introduced entropic matching approach to arbitrary ansatz distributions and Markov processes, demonstrating that it is a special case of variational moment closure. This provides us with a particularly principled approximation method. Finally, we extend the above approaches to cover the approximation of multi-time joint distributions, resulting in a viable alternative to process-level approximations which are often intractable.Comment: Minor changes and clarifications; corrected some typo

Interference effects in the counting statistics of electron transfers through a double quantum dot

We investigate the effect of quantum interferences and Coulomb interaction on the counting statistics of electrons crossing a double quantum dot in a parallel geometry using a generating function technique based on a quantum master equation approach. The skewness and the average residence time of electrons in the dots are shown to be the quantities most sensitive to interferences and Coulomb coupling. The joint probabilities of consecutive electron transfer processes show characteristic temporal oscillations due to interference. The steady-state fluctuation theorem which predicts a universal connection between the number of forward and backward transfer events is shown to hold even in the presence of Coulomb coupling and interference.Comment: 11 pages, 12 figure

Learning SO(3) Equivariant Representations with Spherical CNNs

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.Comment: Camera-ready. Accepted to ECCV'18 as oral presentatio

Evolution of cosmological constant in effective gravity

In contrast to the phenomenon of nullification of the cosmological constant in the equilibrium vacuum, which is the general property of any quantum vacuum, there are many options in modifying the Einstein equation to allow the cosmological constant to evolve in a non-equilibrium vacuum. An attempt is made to extend the Einstein equation in the direction suggested by the condensed-matter analogy of the quantum vacuum. Different scenarios are found depending on the behavior of and the relation between the relaxation parameters involved, some of these scenarios having been discussed in the literature. One of them reproduces the scenario in which the effective cosmological constant emerges as a constant of integration. The second one describes the situation, when after the cosmological phase transition the cosmological constant drops from zero to the negative value; this scenario describes the relaxation from this big negative value back to zero and then to a small positive value. In the third example the relaxation time is not a constant but depends on matter; this scenario demonstrates that the vacuum energy (or its fraction) can play the role of the cold dark matter.Comment: LaTeX file, 5 pages, no figures, version submitted to JETP Letter

The 30/20 GHz flight experiment system, phase 2. Volume 2: Experiment system description

A detailed technical description of the 30/20 GHz flight experiment system is presented. The overall communication system is described with performance analyses, communication operations, and experiment plans. Hardware descriptions of the payload are given with the tradeoff studies that led to the final design. The spacecraft bus which carries the payload is discussed and its interface with the launch vehicle system is described. Finally, the hardwares and the operations of the terrestrial segment are presented

The 30/20 GHz flight experiment system, phase 2. Volume 1: Executive summary

Summary information on the final communication system design, communication payload, space vehicle, and development plan for the 30/20 GHz flight experiment will be installed on the LEASAT spacecraft which will be placed into orbit from the space shuttle cargo bay. The communication concept has two parts: a truck service and a customer premise service (CPS). The trucking system serves four spot beams which are interconnected in a satellite switched time division multiple access mode by an IF switch matrix. The CPS covers two large areas of the eastern United States with a pair of scanning beams

The 30/20 GHz flight experiment system, phase 2. Volume 3: Experiment system requirement document

An approach to the requirements document to be used to procure the system by NASA is presented. The basic approach is similar to the requirements document used in the commercial communication satellite. Enough detail requirements are given to define the system without tight constraints