Modified linear dependence and the capacity of a cyclic graph

AbstractIn 1956 Shannon raised a problem in information theory, which amounts to this geometric question: How many n-dimensional cubes of width 2 can be packed in the n-dimensional torus described by the nth power of the cyclic group Cm? The present paper examines this question in the special circumstance that the set of centers of the cubes form a subgroup—that is, a lattice packing. In this case, the machinery of vector spaces is available when m is a prime. This approach introduces a modified definition of linear independence, obtains some known results with its aid, and suggests a promising direction for future computation and theory. The paper concludes by showing that, in return, combinatorial information can yield results about finite vector spaces

Two combinatorial covering theorems

AbstractA theorem in convex bodies (in fact, measure theory) and a theorem about translates of sets of integers are generalized to coverings by subsets of a finite set. These theorems are then related to quasigroups and (0, 1)-matrices

Non-linear feedback effects in coupled Boson-Fermion systems

We address ourselves to a class of systems composed of two coupled subsystems without any intra-subsystem interaction: itinerant Fermions and localized Bosons on a lattice. Switching on an interaction between the two subsystems leads to feedback effects which result in a rich dynamical structure in both of them. Such feedback features are studied on the basis of the flow equation technique - an infinite series of infinitesimal unitary transformations - which leads to a gradual elimination of the inter-subsystem interaction. As a result the two subsystems get decoupled but their renormalized kinetic energies become mutually dependent on each other. Choosing for the inter - subsystem interaction a charge exchange term (the Boson-Fermion model) the initially localized Bosons acquire itinerancy through their dependence on the renormalized Fermion dispersion. This latter evolves from a free particle dispersion into one showing a pseudogap structure near the chemical potential. Upon lowering the temperature both subsystems simultaneously enter a macroscopic coherent quantum state. The Bosons become superfluid, exhibiting a soundwave like dispersion while the Fermions develop a true gap in their dispersion. The essential physical features described by this technique are already contained in the renormalization of the kinetic terms in the respective Hamiltonians of the two subsystems. The extra interaction terms resulting in the process of iteration only strengthen this physics. We compare the results with previous calculations based on selfconsistent perturbative approaches.Comment: 14 pages, 16 figures, accepted for publication in Phys. Rev.

Untangling polygons and graphs

Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at least \Omega(n^{2/3}) vertices fixed. For any graph G, we also present an upper bound on the number of fixed vertices in the worst case. The bound is a function of the number of vertices, maximum degree and diameter of G. One of its consequences is the upper bound O((n log n)^{2/3}) for all 3-vertex-connected planar graphs.Comment: 11 pages, 3 figure

Genome-Wide Studies Reveal that H3K4me3 Modification in Bivalent Genes Is Dynamically Regulated during the Pluripotent Cell Cycle and Stabilized upon Differentiation

Indexación: Web of Science; Scopus.Stem cell phenotypes are reflected by posttranslational histone modifications, and this chromatin-related memory must be mitotically inherited to maintain cell identity through proliferative expansion. In human embryonic stem cells (hESCs), bivalent genes with both activating (H3K4me3) and repressive (H3K27me3) histone modifications are essential to sustain pluripotency. Yet, the molecular mechanisms by which this epigenetic landscape is transferred to progeny cells remain to be established. By mapping genomic enrichment of H3K4me3/H3K27me3 in pure populations of hESCs in G2, mitotic, and G1 phases of the cell cycle, we found striking variations in the levels of H3K4me3 through the G2-M-G1 transition. Analysis of a representative set of bivalent genes revealed that chromatin modifiers involved in H3K4 methylation/demethylation are recruited to bivalent gene promoters in a cell cycle-dependent fashion. Interestingly, bivalent genes enriched with H3K4me3 exclusively during mitosis undergo the strongest upregulation after induction of differentiation. Furthermore, the histone modification signature of genes that remain bivalent in differentiated cells resolves into a cell cycle-independent pattern after lineage commitment. These results establish a new dimension of chromatin regulation important in the maintenance of pluripotencyhttp://mcb.asm.org/content/36/4/61

Stokes Diagnostis of 2D MHD-simulated Solar Magnetogranulation

We study the properties of solar magnetic fields on scales less than the spatial resolution of solar telescopes. A synthetic infrared spectropolarimetric diagnostics based on a 2D MHD simulation of magnetoconvection is used for this. We analyze two time sequences of snapshots that likely represent two regions of the network fields with their immediate surrounding on the solar surface with the unsigned magnetic flux density of 300 and 140 G. In the first region we find from probability density functions of the magnetic field strength that the most probable field strength at logtau_5=0 is equal to 250 G. Weak fields (B < 500 G) occupy about 70% of the surface, while stronger fields (B 1000 G) occupy only 9.7% of the surface. The magnetic flux is -28 G and its imbalance is -0.04. In the second region, these parameters are correspondingly equal to 150 G, 93.3 %, 0.3 %, -40 G, and -0.10. We estimate the distribution of line-of-sight velocities on the surface of log tau_5=-1. The mean velocity is equal to 0.4 km/s in the first simulated region. The averaged velocity in the granules is -1.2 km/s and in the intergranules is 2.5 km/s. In the second region, the corresponding values of the mean velocities are equal to 0, -1.8, 1.5 km/s. In addition we analyze the asymmetry of synthetic Stokes-V profiles of the Fe I 1564.8 nm line. The mean values of the amplitude and area asymmetry do not exceed 1%. The spatially smoothed amplitude asymmetry is increased to 10% while the area asymmetry is only slightly varied.Comment: 24 pages, 12 figure

Determination of the high-twist contribution to the structure function xF3νNxF^{\nu N}_3

We extract the high-twist contribution to the neutrino-nucleon structure function $xF_3^{(\nu+\bar{\nu})N}$ from the analysis of the data collected by the IHEP-JINR Neutrino Detector in the runs with the focused neutrino beams at the IHEP 70 GeV proton synchrotron. The analysis is performed within the infrared renormalon (IRR) model of high twists in order to extract the normalization parameter of the model. From the NLO QCD fit to our data we obtained the value of the IRR model normalization parameter $\Lambda^2_{3}=0.69\pm0.37~({\rm exp})\pm0.16~({\rm theor})~{\rm GeV}^2$. We also obtained $\Lambda^2_{3}=0.36\pm0.22~({\rm exp})\pm0.12~({\rm theor})~{\rm GeV}^2$ from a similar fit to the CCFR data. The average of both results is $\Lambda^2_{3}=0.44\pm0.19~({\rm exp})~{\rm GeV}^2$.Comment: preprint IHEP-01-18, 7 pages, LATEX, 1 figure (EPS

Multiscale magnetic underdense regions on the solar surface: Granular and Mesogranular scales

The Sun is a non-equilibrium dissipative system subjected to an energy flow which originates in its core. Convective overshooting motions create temperature and velocity structures which show a temporal and spatial evolution. As a result, photospheric structures are generally considered to be the direct manifestation of convective plasma motions. The plasma flows on the photosphere govern the motion of single magnetic elements. These elements are arranged in typical patterns which are observed as a variety of multiscale magnetic patterns. High resolution magnetograms of quiet solar surface revealed the presence of magnetic underdense regions in the solar photosphere, commonly called voids, which may be considered a signature of the underlying convective structure. The analysis of such patterns paves the way for the investigation of all turbulent convective scales from granular to global. In order to address the question of magnetic structures driven by turbulent convection at granular and mesogranular scales we used a "voids" detection method. The computed voids distribution shows an exponential behavior at scales between 2 and 10 Mm and the absence of features at 5-10 Mm mesogranular scales. The absence of preferred scales of organization in the 2-10 Mm range supports the multiscale nature of flows on the solar surface and the absence of a mesogranular convective scale

A Method for Assaying Deubiquitinating Enzymes

A general method for the assay of deubiquitinating enzymes was described in detail using (125)I-labeled ubiquitin-fused αNH-MHISPPEPESEEEEEHYC (referred to as Ub-PESTc) as a substrate. Since the tyrosine residue in the PESTc portion of the fusion protein was almost exclusively radioiodinated under a mild labeling condition, such as using IODO-BEADS, the enzymes could be assayed directly by simple measurement of the radioactivity released into acid soluble products. Using this assay protocol, we could purify six deubiquitinating enzymes from chick skeletal muscle and yeast and compare their specific activities. Since the extracts of E. coli showed little or no activity against the substrate, the assay protocol should be useful for identification and purification of eukaryotic deubiquitinating enzymes cloned and expressed in the cells

Sequential design of computer experiments for the estimation of a probability of failure

This paper deals with the problem of estimating the volume of the excursion set of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold, under a probability measure on $\mathbb{R}^d$ that is assumed to be known. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of $f$ and aim at performing evaluations of $f$ as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.Comment: This is an author-generated postprint version. The published version is available at http://www.springerlink.co