Community structure and modularity in networks of correlated brain activity

Functional connectivity patterns derived from neuroimaging data may be represented as graphs or networks, with individual image voxels or anatomically-defined structures representing the nodes, and a measure of correlation between the responses in each pair of nodes determining the edges. This explicit network representation allows network-analysis approaches to be applied to the characterization of functional connections within the brain. Much recent research in complex networks has focused on methods to identify community structure, i.e. cohesive clusters of strongly interconnected nodes. One class of such algorithms determines a partition of a network into 'sub-networks' based on the optimization of a modularity parameter, thus also providing a measure of the degree of segregation versus integration in the full network. Here, we demonstrate that a community structure algorithm based on the maximization of modularity, applied to a functional connectivity network calculated from the responses to acute fluoxetine challenge in the rat, can identify communities whose distributions correspond to anatomically meaningful structures and include compelling functional subdivisions in the brain. We also discuss the biological interpretation of the modularity parameter in terms of segregation and integration of brain function.     

On a Recent Proposal of Faster than Light Quantum Communication

In a recent paper, A.Y. Shiekh has discussed an experimental set-up which, in his opinion, should make possible faster-than-light communication using the collapse of the quantum wave function. Contrary to the many proposals which have been presented in the past, he does not resort to an entangled state of two systems but he works with a single particle in a superposition of two states—corresponding to its propagation in opposite directions—one of which goes through an appropriate interferometer. The possibility for an observer near the interferometer to introduce or not, at his free will, a phase shifter along one of the paths should allow to change instantaneously the probability of finding the particle in the far-away region corresponding to the other state of the superposition and, correspondingly, to change the intensity of a beam of particles reaching a distant observer. In this paper we show a flaw in the argument: once more, as it has been proved in full generality a long time ago, the process of wave packet reduction cannot be used for superluminal communication.     

Fast perturbation Monte Carlo method for photon migration in heterogeneous turbid media

We present a two-step Monte Carlo (MC) method that is used to solve the radiative transfer equation in heterogeneous turbid media. The method exploits the one-to-one correspondence between the seed value of a random number generator and the sequence of random numbers. In the first step, a full MC simulation is run for the initial distribution of the optical properties and the "good" seeds (the ones leading to detected photons) are stored in an array. In the second step, we run a new MC simulation with only the good seeds stored in the first step, i.e., we propagate only detected photons. The effect of a change in the optical properties is calculated in a short time by using two scaling relationships. By this method we can increase the speed of a simulation up to a factor of 1300 in typical situations found in near-IR tissue spectroscopy and diffuse optical tomography, with a minimal requirement for hard disk space. Potential applications of this method for imaging of turbid media and the inverse problem are discussed.     

New search for processes violating the Pauli exclusion principle in sodium and in iodine

In this paper a new search for non-Paulian nuclear processes, i.e. processes normally forbidden by the Pauli Exclusion Principle (PEP), is presented. It has been carried out at the Gran Sasso National Laboratory of the INFN by means of the highly radiopure DAMA/LIBRA set-up (sensitive mass of about 250 kg highly radiopure NaI(Tl)). In particular, a new improved upper limit for the spontaneous non-Paulian emission rate of protons with energy E _p ≥ 10 MeV in ²³Na and ¹²⁷I has been obtained: 1.63 × 10⁻³³ s⁻¹ (90% C.L.). The corresponding limit on the relative strength (δ ²) for the searched non-Paulian transition is δ ²≲(3–4)×10⁻⁵⁵ (90% C.L.). Moreover, PEP-violating electron transitions in iodine atoms have also been investigated. Lifetimes shorter than 4.7×10³⁰ s are excluded at 90% C.L.; this allows us to derive the limit δ _e ²<1.28×10⁻⁴⁷ (90% C.L.). This latter limit can also be related to a possible finite size of the electron in composite models of quarks and leptons providing superficial violation of the PEP; the obtained upper limit on the electron size is r ₀<5.7×10⁻¹⁸ cm (energy scale of E≳3.5 TeV).     

Painleve' analysis of a variable coefficient Sine-Gordon equation

In this paper we study a variable coefficient Sine-Gordon (vSG) equation given by theta(tt)-theta(xx)+F(x,t)sin theta=0 where F(x,t) is a real function. To establish if it may be integrable we have performed the standard test of Weiss, Tabor, and Carnevale (WTC). We have got that the (vSG) equation has the Painleve' property (Pp) if the function F(x,t) satisfies a well-defined nonlinear partial differential equation. We have found the general solution of this last equation and, consequently, the functions F(x,t) such that the (vSG) equation possesses the (Pp), are given by F(x,t)=F(1)(x+t)F(2)(x-t) where F(1)(x+t) and F(2)(x-t) are arbitrary functions. Using this last result we have obtained some particular solutions of the vSG equation. (c) 1995 American Institute of Physics.     

Angular Momentum Effects in Michelson–Morley Type Experiments

The effect of the angular momentum density of a gravitational source on the times of flight of light rays in an interferometer is analyzed. The calculation is made imagining that the interferometer is at the equator of an axisymmetric steadily rotating gravity source. In order to evaluate the size of the effect in the case of the Earth a weak field approximation for the metric elements is introduced. For laboratory scales and non-geodesic paths the correction due to the angular momentum turns out to be comparable with the sensitivity expected in gravitational waves interferometric detectors, whereas it drops under the threshold of detectability when using free (geodesic) light rays.     

On continuation of inviscid vortex patches

This investigation concerns solutions of the steady-state Euler equations in two dimensions featuring finite area regions with constant vorticity embedded in a potential flow. Using elementary methods of the functional analysis we derive precise conditions under which such solutions can be uniquely continued with respect to their parameters, valid also in the presence of the Kutta condition concerning a fixed separation point. Our approach is based on the Implicit Function Theorem and perturbation equations derived using shape-differentiation methods. These theoretical results are illustrated with careful numerical computations carried out using the Steklov–Poincaré method which show the existence of a global manifold of solutions connecting the point vortex and the Prandtl–Batchelor solution, each of which satisfies the Kutta condition.     

Gas-phase pyrolysis mechanism and kinetics of 3-t-butoxyquadricyclane

The gas-phase pyrolysis of 3-t-butoxyquadricyclane [1] was investigated over the temperature range 511–542 K at one atm in helium. The initial pyrolysis step is the isomerization of 3-t-butoxyquadricyclane to 7-t-butoxynorbornadiene (Ea = 38.49 ± 0.85 kcal/mole, log A = 15.44 ± 0.35). 7-t-butoxynorbornadiene exhibits a single unimolecular reaction pathway which produces a mixture of t-butoxycycloheptatrienes (Ea = 38.44 ± 0.63 kcal/mole, log A = 15.05 ± 0.26). This two-step mechanism affords fewer reactions than unsubstituted quadricyclane in the gas phase and could be useful for its reduced sooting potential. © 1996 John Wiley & Sons, Inc.