On the Skitovich–Darmois theorem for some locally compact Abelian groups

Let X be a locally compact Abelian group, \(\alpha _{j}, \beta _j\) be topological automorphisms of X. Let \(\xi _1, \xi _2\) be independent random variables with values in X and distributions \(\mu _j\) with non-vanishing characteristic functions. It is known that if X contains no subgroup topologically isomorphic to the circle group \(\mathbb {T}\), then the independence of the linear forms \(L_1=\alpha _1\xi _1+\alpha _2\xi _2\) and \(L_2=\beta _1\xi _1+\beta _2\xi _2\) implies that \(\mu _j\) are Gaussian distributions. We prove that if X contains no subgroup topologically isomorphic to \(\mathbb {T}^2\), then the independence of \(L_1\) and \(L_2\) implies that \(\mu _j\) are either Gaussian distributions or convolutions of Gaussian distributions and signed measures supported in a subgroup of X generated by an element of order 2. The proof is based on solving the Skitovich–Darmois functional equation on some locally compact Abelian groups.     

A genetic algorithm with local search strategy for improved detection of community structure

On the basis of modularity optimization, a genetic algorithm is proposed to detect community structure in networks by defining a local search operator. The local search operator emphasizes two features: one is that the connected nodes in a network should be located in the same community, while the other is “local selection” inspired by the mechanisms of efficient message delivery underlying the small‐world phenomenon. The results of community detection for some classic networks, such as Ucinet and Pajek networks, indicate that our algorithm achieves better community structure than other methodologies based on modularity optimization, such as the algorithms based on betweenness analysis, simulated annealing, or Tasgin and Bingol's genetic algorithm. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Testing Lorentz invariance and CPT conservation with NuMI neutrinos in the MINOS near detector

A search for a sidereal modulation in the MINOS near detector neutrino data was performed. If present, this signature could be a consequence of Lorentz and CPT violation as predicted by the effective field theory called the standard-model extension. No evidence for a sidereal signal in the data set was found, implying that there is no significant change in neutrino propagation that depends on the direction of the neutrino beam in a sun-centered inertial frame. Upper limits on the magnitudes of the Lorentz and CPT violating terms in the standard-model extension lie between 10(-4) and 10(-2) of the maximum expected, assuming a suppression of these signatures by a factor of 10(-17).     

Quantum phase transition between a Luttinger liquid and a gas of cold molecules

We consider cold polar molecules confined in a helical optical lattice similar to those used in holographic microfabrication. An external electric field polarizes molecules along the axis of the helix. The large-distance intermolecular dipolar interaction is attractive but the short-scale interaction is repulsive due to geometric constraints and thus prevents collapse. The interaction strength depends on the electric field. We show that a zero-temperature second-order liquid-gas transition occurs at a critical field. It can be observed under experimentally accessible conditions.     

Compton scattering from deuterium and the polarizabilities of the neutron

A new program of Compton scattering on deuterium is under way at the tagged-photon facility at MAX-Lab in Lund, Sweden. We will measure differential cross sections between 60° and 150° over the photon energy range 60–115?MeV in 5?MeV steps, with the ultimate goal of obtaining new precision information on the electric and magnetic polarizabilities of the neutron.     

Tobramycin and Nebramine as Pseudo‐oligosaccharide Scaffolds for the Development of Antimicrobial Cationic Amphiphiles

Antimicrobial cationic amphiphiles derived from aminoglycoside pseudo‐oligosaccharide antibiotics interfere with the structure and function of bacterial membranes and offer a promising direction for the development of novel antibiotics. Herein, we report the design and synthesis of cationic amphiphiles derived from the pseudo‐trisaccharide aminoglycoside tobramycin and its pseudo‐disaccharide segment nebramine. Antimicrobial activity, membrane selectivity, mode of action, and structure–activity relationships were studied. Several cationic amphiphiles showed marked antimicrobial activity, and one amphiphilic nebramine derivative proved effective against all of the tested strains of bacteria; furthermore, against several of the tested strains, this compound was well over an order of magnitude more potent than the parent antibiotic tobramycin, the membrane‐targeting antimicrobial peptide mixture gramicidin D, and the cationic lipopeptide polymyxin B, which are in clinical use.     

On a Characterization Theorem on a -adic Solenoids

Doklady Mathematics - According to the Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form in independent...