Anomalous scaling due to correlations: Limit theorems and self-similar processes

We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling forms, justify their universal character, and specify universality domains in the spaces of joint probability density functions of the summand variables. These density functions are assumed to be invariant under arbitrary permutations of their arguments. Examples from the theory of critical phenomena are discussed. The novel notion of stability implied by the limit theorems also allows us to define sequences of random variables whose sum satisfies anomalous scaling for any finite number of summands. If regarded as developing in time, the stochastic processes described by these variables are non-Markovian generalizations of Gaussian processes with uncorrelated increments, and provide, e.g., explicit realizations of a recently proposed model of index evolution in finance.Comment: Through text revision. 15 pages, 3 figure

Branching Processes and Evolution at the Ends of a Food Chain

In a critically self--organized model of punctuated equilibrium, boundaries determine peculiar scaling of the size distribution of evolutionary avalanches. This is derived by an inhomogeneous generalization of standard branching processes, extending previous mean field descriptions and yielding $\nu=1/2$ together with $\tau'=7/4$, as distribution exponent of avalanches starting from species at the ends of a food chain. For the nearest neighbor chain one obtains numerically $\tau'=1.25 \pm 0.01$, and $\tau'_{first}=1.35 \pm 0.01$ for the first return times of activity, again distinct from bulk exponents.Comment: REVTex file, 12 pages, 2 figures in eps-files uuencoded, psfig.st

Adsorption-like Collapse of Diblock Copolymers

A linear copolymer made of two reciprocally attracting N-monomer blocks collapses to a compact phase through a novel transition, whose exponents are determined with extensive MC simulations in two and three dimensions. In the former case, an identification with the statistical geometry of suitable percolation paths allows to predict that the number of contacts between the blocks grows like $N^{9/16}$. In the compact phase the blocks are mixed and, in two dimensions, also zipped, in such a way to form a spiral, double chain structure.Comment: 4 pages, 5 Postscript figure

Direct and Regioselective Di-alpha-fucosylation on the Secondary Rim of beta-Cyclodextrin

A straightforward glycosylation method is described to regio- and stereoselectively introduce two alpha-L-fucose moieties directly to the secondary rim of beta-cyclodextrin. Using NMR and MS fragmentation studies, the nonasaccharide structure was determined, which was also visualized using molecular dynamics simulations. The reported glycosylation method proved to be robust on gram-scale, and may be generally applied to directly glycosylate beta-cyclodextrins to make well-defined multivalent glycoclusters.</p

Young pre-Low-Mass X-ray Binaries in propeller phase : Nature of the 6.7-hour periodic X-ray source 1E 161348-5055 in RCW 103

Discovery of the 6.7-hour periodicity in the X-ray source 1E 161348-5055 in RCW 103 has led to investigations of the nature of this periodicity. We explore a model for 1E 161348-5055, wherein a fast-spinning neutron star with a magnetic field $\sim 10^{12}$ G in a young pre-Low-Mass X-ray Binary (pre-LMXB) with an eccentric orbit of period 6.7 hr operates in the "propeller" phase. The 6.7-hr light curve of 1E 161348-5055 can be quantitatively accounted by a model of orbitally-modulated mass transfer through a viscous accretion disk and subsequent propeller emission (both Illarionov-Sunyaev type and Romanova-Lovelace et al type), and spectral and other properties are also in agreement. Formation and evolution of model systems are shown to be in accordance both with standard theories.Comment: 11 pages, 4 figures, accepted for publication in Astronomy and Astrophysics on 23/08/200

Classical and Quantum Solutions and the Problem of Time in R2R^2 Cosmology

We have studied various classical solutions in $R^2$ cosmology. Especially we have obtained general classical solutions in pure $R^2$\ cosmology. Even in the quantum theory, we can solve the Wheeler-DeWitt equation in pure $R^2$\ cosmology exactly. Comparing these classical and quantum solutions in $R^2$\ cosmology, we have studied the problem of time in general relativity.Comment: 17 pages, latex, no figure, one reference is correcte

The 2008 October Swift detection of X-ray bursts/outburst from the transient SGR-like AXP 1E 1547.0-5408

We report on the detailed study of the 2008 October outburst from the anomalous X-ray pulsar (AXP) 1E 1547.0-5408 discovered through the Swift/Burst Alert Telescope (BAT) detection of SGR-like short X-ray bursts on 2008 October 3. The Swift/X-ray Telescope (XRT) started observing the source after less than 100 s since the BAT trigger, when the flux (about 6E-11 erg/cm^2/s in the 2-10 keV range) was >50 times higher than its quiescent level. Swift monitored the outbursting activity of 1E 1547.0-5408 on a daily basis for approximately three weeks. This strategy allowed us to find a phase-coherent solution for the source pulsations after the burst, which, besides period and period derivative, requires a positive Period second derivative term (spin-down increase). The time evolution of the pulse shape is complex and variable, with the pulsed fraction increasing from 20% to 50% within the Swift observational window. The XRT spectra can be fitted well by means of a single component, either a power-law (PL) or a blackbody (BB). During the very initial phases of the outburst the spectrum is hard, with a PL photon index about 2 (or kT about 1.4 keV) which steepens to about 4 (or kT about 0.8 keV) within one day from the BAT trigger, though the two components are likely present simultaneously during the first day spectra. An INTEGRAL observation carried out five days after the trigger provided an upper limit of about 2E-11 erg/cm^2/s to the emission of 1E 1547.0-5408 in the 18-60 keV band.Comment: 10 pages, 2 tables, 6 figures; accepted for publication in MNRA

Boundary effects in a random neighbor model of earthquakes

We introduce spatial inhomogeneities (boundaries) in a random neighbor version of the Olami, Feder and Christensen model [Phys. Rev. Lett. 68, 1244 (1992)] and study the distributions of avalanches starting both from the bulk and from the boundaries of the system. Because of their clear geophysical interpretation, two different boundary conditions have been considered (named free and open, respectively). In both cases the bulk distribution is described by the exponent $\tau \simeq {3/2}$. Boundary distributions are instead characterized by two different exponents $\tau ' \simeq {3/2}$ and $\tau ' \simeq {7/4}$, for free and open boundary conditions, respectively. These exponents indicate that the mean-field behavior of this model is correctly described by a recently proposed inhomogeneous form of critical branching process.Comment: 6 pages, 2 figures ; to appear on PR