Zeta measures and Thermodynamic Formalism for temperature zero

We address the analysis of the following problem: given a real Hölder potential f defined on the Bernoulli space and μ _f its equilibrium state, it is known that this shift-invariant probability can be weakly approximated by probabilities in periodic orbits associated to certain zeta functions. Given a Hölder function f > 0 and a value s such that 0 < s < 1, we can associate a shift-invariant probability ν _s such that for each continuous function k we have $ \int {kd} v_s = \frac{{\sum\nolimits_{n = 1}^\infty {\sum\nolimits_{x \in Fix_n } {e^{sf^n (x) - nP(f)\frac{{k^n (x)}} {n}} } } }} {{\sum\nolimits_{n = 1}^\infty {\sum\nolimits_{x \in Fix_n } {e^{sf^n (x) - nP(f)} } } }}, $ , where P(f) is the pressure of f, Fix _n is the set of solutions of σ ⁿ (x) = x, for any n ∈ ?, and f ⁿ (x) = f(x) + f(σ (x)) + … + f(σ ^n?1(x)). We call νs a zeta probability for f and s, because it can be obtained in a natural way from the dynamical zeta-functions. From the work of W. Parry and M. Pollicott it is known that ν _s → µ _f , when s → 1. We consider for each value c the potential c f and the corresponding equilibrium state μ _cf . What happens with ν _s when c goes to infinity and s goes to one? This question is related to the problem of how to approximate the maximizing probability for f by probabilities on periodic orbits. We study this question and also present here the deviation function I and Large Deviation Principle for this limit c → ∞, s → 1. We will make an assumption: for some fixed L we have lim _{c→∞, s→1} c(1 ? s) = L > 0. We do not assume here the maximizing probability for f is unique in order to get the L.D.P.     

Evidence for partial rotation alignment in proton emitting Pr

Using nonadiabatic quasiparticle calculations we reproduce the experimental half-life for proton radioactivity in ¹²¹Pr assuming that the decaying state has angular momentum Jπ=7/²⁻$J^{\pi }=7/2^{-}$, thus showing for the first time clear evidence for partial rotation alignment in a proton emitting nucleus. The treatment of the pairing interaction in the BCS approach produces profound changes in the ordering of energy levels, and at high deformation, the state 7/²⁻$7/2^{-}$ coming from the h_11/2${\mathrm{h}}_{11/2}$ spherical shell becomes the bandhead.     

Volume quantification by fuzzy logic modelling in freehand ultrasound imaging

Introduction

Many algorithms exist for 3D reconstruction of data from freehand 2D ultrasound slices. These methods are based on interpolation techniques to fill the voxels from the pixels. For quantification purposes, segmentation is involved to delineate the structure of interest. However, speckle and partial volume effect errors can affect quantification.

Objective

This study aimed to assess the effect of the combination of a fuzzy model and 3D reconstruction algorithms of freehand ultrasound images on these errors.

Methods

We introduced a fuzzification step to correct the initial segmentation, by weighting the pixels by a distribution function, taking into account the local gray levels, the orientation of the local gradient, and the local contrast-to-noise ratio. We then used two of the most wide-spread reconstruction algorithms (pixel nearest neighbour (PNN) and voxel nearest neighbour (VNN)) to interpolate and create the volume of the structure. Finally, defuzzification was used to estimate the optimal volume.

Validation

B-scans were acquired using 5 MHz and 8 MHz ultrasound probes on ultrasound tissue-mimicking phantoms. Quantitative evaluation of the reconstructed structures was done by comparing the method output to the real volumes. Comparison was also done with classical PNN and VNN algorithms.

Results

With the fuzzy model quantification errors were less than 4.3%, whereas with classical algorithms, errors were larger (10.3% using PNN, 17.2% using VNN). Furthermore, for very small structures (0.5 cm³), errors reached 24.3% using the classical VNN algorithm, while they were about 9.6% with the fuzzy VNN model.

Conclusion

These experiments prove that the fuzzy model allows volumes to be determined with better accuracy and reproducibility, especially for small structures (<3 cm³).     

Crisis-induced unstable dimension variability in a dynamical system

Unstable dimension variability is an extreme form of non-hyperbolic behavior in chaotic systems whose attractors have periodic orbits with a different number of unstable directions. We propose a new mechanism for the onset of unstable dimension variability based on an interior crisis, or a collision between a chaotic attractor and an unstable periodic orbit. We give a physical example by considering a high-dimensional dissipative physical system driven by impulsive periodic forcing.     

Increase of temperature of an ideal nondegenerate quantum gas in a suddenly expanding box due to energy quantization

We show that due to energy quantization the temperature of an ideal nondegenerate quantum gas in a rectangular box always increases after a sudden expansion of the box and a subsequent thermalization. The maximal increment of temperature is proportional to the square root of the product of the initial absolute temperature by the energy of the first discrete quantum level, i.e., it is proportional to the first power of the Planck constant.     

Collective behavior in coupled chaotic map lattices with random perturbations

Numerical simulations of coupled map lattices with non-local interactions (i.e., the coupling of a given map occurs with all lattice sites) often involve a large computer time if the lattice size is too large. In order to study dynamical effects which depend on the lattice size we considered the use of small truncated lattices with random inputs at their boundaries chosen from a uniform probability distribution. This emulates a “thermal bath”, where deterministic degrees of freedom exhibiting chaotic behavior are replaced by random perturbations of finite amplitude. We demonstrate the usefulness of this idea to investigate the occurrence of completely synchronized chaotic states as the coupling parameters are varied. We considered one-dimensional lattices of chaotic logistic maps at outer crisis x→4x(1−x).     

Bursting synchronization in non-locally coupled maps

Neuron activity presents two timescales, a fast one related to action-potential spiking, and a slow timescale in which bursting takes place. Bursting activity in neuron ensembles can be synchronized, meaning the adjustment of the bursting phases due to coupling. We investigated bursting synchronization in a non-locally coupled lattice using a two-dimensional map to describe neuron activity. The coupling involves all sites in a lattice, the corresponding strength decreasing with the lattice distance in a power-law fashion. We observed bursting synchronization for wide intervals of the coupling parameters. We also investigated the bursting synchronization of the ensemble with an external time-periodic signal applied to one or more selected neurons.     

X-ray microfluorescence with synchrotron radiation applied in the analysis of pigments from ancient Egypt

In this work, X-ray microfluorescence with the synchrotron radiation technique was applied in the analysis of pigments found in decorative paintings in the sarcophagus of an Egyptian mummy. This female mummy, from the Roman Period, which was embalmed with the arms and legs swathed separately is considered one of the most important pieces of the Egyptian Collection from the National Museum (Rio de Janeiro, Brazil). The measurements were performed at the XRF beamline D09B of the Brazilian Synchrotron Light Laboratory (LNLS), using the white beam and a Si(Li) detector with resolution of 165 eV at 5.9 keV. The possible pigments found in the samples were: Egyptian blue, Egyptian green frit, green earth, verdigris, malachite, ochre, realgar, chalk, gypsum, bone white, ivory black and magnetite. Hierarchical cluster analysis (HCA) and principal component analysis (PCA) were applied to the results in order to verify if the samples belong to the same period of a linen wrapping fragment, whose provenance was well established. PACS 07.85.Nc; 07.85.Qe; 78.70.En     

Ethanol bone evaluation using 3D microtomography

The study of trabecular structures is important for understanding the mechanism of alcohol related to bone changes. Alcohol consumption can compromise the body mineral composition, affecting the bone metabolism and compromising the skeleton. The effects of the ethanol treatment on the internal microarchitecture of bone samples through 3D microcomputed tomography are shown in this study. The data was acquired from a radiographic system with a micro focus X-ray conic beam and it was used the Feldkamp's technique was used to carry out the 3D reconstructions. The measured microstructure parameters, which were based on stereological concepts, were bone volume fraction, relationship between bone surface and volume, trabecular number, separation and thickness. The results show that this technique is able to analyze these kinds of structures, especially rat bone, as these structures in rats (trabecular diameter) are thinner than in human bones.     

Exclusive branching-fraction measurements of semileptonic tau decays into three charged hadrons, into phipi(-)nu tau, and into phi K(-)nu tau

Using a data sample corresponding to an integrated luminosity of 342 fb(-1) collected with the BABAR detector at the SLAC PEP-II electron-positron storage ring operating at a center-of-mass energy near 10.58 GeV, we measure B(tau(-)--> pi(-)pi(-)pi+nu(tau)(ex.K(S0))=(8.83+/-0.01+/-0.13)%, B(tau(-) -->K(-)pi(-)pi+nu tau(ex.K(S0))=(0.273+/-0.002+/-0.009)%, B(tau(-) -->K(-)pi(-)K+nu tau)=(0.1346+/-0.0010+/-0.0036)%, and B(tau(-) -->K(-)K(-)K+nu tau)=(1.58+/-0.13+/-0.12)x10;{-5}, where the uncertainties are statistical and systematic, respectively. These include significant improvements over previous measurements and a first measurement of B(tau(-) -->K(-)K(-)K+nu tau) in which no resonance structure is assumed. We also report a first measurement of B(tau(-) -->var phi(-)nu tau)=(3.42+/-0.55+/-0.25)x10(-5), a new measurement of B(tau(-) -->var phi K(-)nu tau)=(3.39+/-0.20+/-0.28)x10(-5) and a first upper limit on B(tau(-) -->K(-)K(-)K+nu tau(ex.var phi)).