On the structure of non-full-rank perfect codes

The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code can be constructed by this combining construction is generalized to the $q$-ary case. Simply, every non-full-rank perfect code $C$ is the union of a well-defined family of $\mu$-components $K_\mu$, where $\mu$ belongs to an "outer" perfect code $C^*$, and these components are at distance three from each other. Components from distinct codes can thus freely be combined to obtain new perfect codes. The Phelps general product construction of perfect binary code from 1984 is generalized to obtain $\mu$-components, and new lower bounds on the number of perfect 1-error-correcting $q$-ary codes are presented.Comment: 8 page

Dirac fermions in a power-law-correlated random vector potential

We study localization properties of two-dimensional Dirac fermions subject to a power-law-correlated random vector potential describing, e.g., the effect of "ripples" in graphene. By using a variety of techniques (low-order perturbation theory, self-consistent Born approximation, replicas, and supersymmetry) we make a case for a possible complete localization of all the electronic states and compute the density of states.Comment: Latex, 4+ page

A Computational Approach to Multistationarity of Power-Law Kinetic Systems

This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the corresponding differential equations admit multiple positive steady states within a stoichiometric class. The approach, which is called the "Multistationarity Algorithm for PLK systems" (MSA), combines (i) the extension of the "higher deficiency algorithm" of Ji and Feinberg for mass action to PLK systems with reactant-determined interactions, and (ii) a method that transforms any PLK system to a dynamically equivalent one with reactant-determined interactions. Using this algorithm, we obtain two new results: the monostationarity of a popular model of anaerobic yeast fermentation pathway, and the multistationarity of a global carbon cycle model with climate engineering, both in the generalized mass action format of biochemical systems theory. We also provide examples of the broader scope of our approach for deficiency one PLK systems in comparison to the extension of Feinberg's "deficiency one algorithm" to such systems

Quartz Cherenkov Counters for Fast Timing: QUARTIC

We have developed particle detectors based on fused silica (quartz) Cherenkov radiators read out with micro-channel plate photomultipliers (MCP-PMTs) or silicon photomultipliers (SiPMs) for high precision timing (Sigma(t) about 10-15 ps). One application is to measure the times of small angle protons from exclusive reactions, e.g. p + p - p + H + p, at the Large Hadron Collider, LHC. They may also be used to measure directional particle fluxes close to external or stored beams. The detectors have small areas (square cm), but need to be active very close (a few mm) to the intense LHC beam, and so must be radiation hard and nearly edgeless. We present results of tests of detectors with quartz bars inclined at the Cherenkov angle, and with bars in the form of an "L" (with a 90 degree corner). We also describe a possible design for a fast timing hodoscope with elements of a few square mm.Comment: 24 pages, 14 figure

Statistical properties of contact vectors

We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n_i, representing the number of residues in contact with residue i. We study analytically (at mean-field level) and numerically the amount of structural information contained in a contact vector. Analytical calculations reveal that a large variance in the contact numbers reduces the degeneracy of the mapping between contact vectors and structures. Exact enumeration for lengths up to N=16 on the three dimensional cubic lattice indicates that the growth rate of number of contact vectors as a function of N is only 3% less than that for contact maps. In particular, for compact structures we present numerical evidence that, practically, each contact vector corresponds to only a handful of structures. We discuss how this information can be used for better structure prediction.Comment: 20 pages, 6 figure

Extremal dynamics model on evolving networks

We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly concentrated in the largest cluster. The time dependence of the number of units exhibits intermittent structure. The self-organized criticality is manifested by a power-law distribution of forward avalanches, but two regimes with distinct exponents tau = 1.98 +- 0.04 and tau^prime = 1.65 +- 0.05 are found. The distribution of extinction sizes obeys a power law with exponent 2.32 +- 0.05.Comment: 4 pages, 5 figure

Shortest paths and load scaling in scale-free trees

The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function (pdf) of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the m=1 case of the Barabasi-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows a demonstration of why the distribution approaches a Gaussian in the limit of N large. The load (betweenness), the number of shortest distance paths passing through any node, is discussed in the tree presentation.Comment: 8 pages, 8 figures; v2: load calculations extende