COMPLEXITY MEASURE: A QUANTUM INFORMATION APPROACH

In the past decades, all of the efforts at quantifying systems complexity with a general tool has usually relied on using Shannon's classical information framework to address the disorder of the system through the Boltzmann-Gibbs-Shannon entropy, or one of its extensions. However, in recent years, there were some attempts to tackle the quantification of algorithmic complexities in quantum systems based on the Kolmogorov algorithmic complexity, obtaining some discrepant results against the classical approach. Therefore, an approach to the complexity measure is proposed here, using the quantum information formalism, taking advantage of the generality of the classical-based complexities, and being capable of expressing these systems' complexity on other framework than its algorithmic counterparts. To do so, the Shiner-Davison-Landsberg (SDL) complexity framework is considered jointly with linear entropy for the density operators representing the analyzed systems formalism along with the tangle for the entanglement measure. The proposed measure is then applied in a family of maximally entangled mixed state.

Entanglement of two-qubit photon beam by magnetic field.

We have studied the possibility of affecting the entanglement measure of 2-qubit system consisting of two photons with different fi xed frequencies but with two arbitrary linear polarizations, moving in the same direction, by the help of an applied external magnetic field. The interaction between the magnetic fi eld and the photons in our model is achieved through intermediate electrons that interact with both the photons and the magnetic fi eld. The possibility of exact theoretical analysis of this scheme is based on known exact solutions that describe the interaction of an electron subjected to an external magnetic fi eld (or a medium of electrons not interacting with each other) with a quantized field of two photons. We adapt these exact solutions to the case under consideration. Using explicit wave functions for the resulting electromagnetic fi eld, we calculate the entanglement measure of the photon beam as a function of the applied magnetic field and parameters of the electron medium.

High-throughput non-destructive nuclear magnetic resonance method to measure intramuscular fat content in beef

High intake of saturated fat from meats has been associated with cardiovascular disease, cancer, diabetes, and others diseases. In this paper, we are introducing a simple, high-throughput, and non-destructive low-resolution nuclear magnetic resonance method that has the potential to analyze the intramuscular fat content (IMF) in more than 1,000 beef portions per hour. The results can be used in nutritional fact labels, replacing the currently used average value. The method is based on longitudinal (T(1)) and transverse (T(2)) relaxation time information obtained by a continuous wave-free precession (CWFP) sequence. CWFP yields a higher correlation coefficient (r=0.9) than the conventional Carr-Purcell-Meiboom- Gill (CPMG) method (r=-0.25) for IMF in beef and is just as fast and a simpler pulse sequence than CPMG. The method can also be applied to other meat products.

Measure functional differential equations and functional dynamic equations on time scales

We study measure functional differential equations and clarify their relation to generalized ordinary differential equations. We show that functional dynamic equations on time scales represent a special case of measure functional differential equations. For both types of equations, we obtain results on the existence and uniqueness of solutions, continuous dependence, and periodic averaging.

Quantum entanglement of bound particles under free center of mass dispersion

On the basis of the full analytical solution of the overall unitary dynamics, the time evolution of entanglement is studied in a simple bipartite model system evolving unitarily from a pure initial state. The system consists of two particles in one spatial dimension bound by harmonic forces and having its free center of mass initially localized in space in a minimum uncertainty wavepacket. The existence of such initial states in which the bound particles are not entangled is discussed. Galilean invariance of the system ensures that the dynamics of entanglement between the two particles is independent of the wavepacket mean momentum. In fact, as shown, it is driven by the dispersive center of mass free dynamics, and evolves in a time scale that depends on the interparticle interaction in an essential way.

Semi-supervised learning guided by the modularity measure in complex networks

Semi-supervised learning techniques have gained increasing attention in the machine learning community, as a result of two main factors: (1) the available data is exponentially increasing; (2) the task of data labeling is cumbersome and expensive, involving human experts in the process. In this paper, we propose a network-based semi-supervised learning method inspired by the modularity greedy algorithm, which was originally applied for unsupervised learning. Changes have been made in the process of modularity maximization in a way to adapt the model to propagate labels throughout the network. Furthermore, a network reduction technique is introduced, as well as an extensive analysis of its impact on the network. Computer simulations are performed for artificial and real-world databases, providing a numerical quantitative basis for the performance of the proposed method.

Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

Motor function measure scale, steroid therapy and patients with Duchenne muscular dystrophy

Objective: To assess the evolution of motor function in patients with Duchenne muscular dystrophy (DMD) treated with steroids (prednisolone or deflazacort) through the Motor Function Measure (MFM), which evaluates three dimensions of motor performance (D1, D2, D3). Methods: Thirty-three patients with DMD (22 ambulant, 6 non-ambulant and 5 who lost the capacity to walk during the period of the study) were assessed using the MFM scale six times over a period of 18 months. Results: All the motor functions remained stable for 14 months in all patients, except D1 for those who lost their walking ability. In ambulant patients, D2 (axial and proximal motor capacities) motor functions improved during six months; an improvement in D3 (distal motor capacity) was noted during the total follow-up. D1 (standing posture and transfers) and total score were useful to predict the loss of the ability to walk. Conclusions: The use of the MFM in DMD patients confirms the benefits of the steroid treatment for slowing the progression of the disease.

Cosmological measure with volume averaging and the vacuum energy problem

In this paper, we give a possible solution to the cosmological constant problem. It is shown that the traditional approach, based on volume weighting of probabilities, leads to an incoherent conclusion: the probability that a randomly chosen observer measures Lambda = 0 is exactly equal to 1. Using an alternative, volume averaging measure, instead of volume weighting can explain why the cosmological constant is non-zero.

Entanglement of excited states in critical spin chains

Renyi and von Neumann entropies quantifying the amount of entanglement in ground states of critical spin chains are known to satisfy a universal law which is given by the conformal field theory (CFT) describing their scaling regime. This law can be generalized to excitations described by primary fields in CFT, as was done by Alcaraz et al in 2011 (see reference [1], of which this work is a completion). An alternative derivation is presented, together with numerical verifications of our results in different models belonging to the c = 1, 1/2 universality classes. Oscillations of the Renyi entropy in excited states are also discussed.

Speech Graphs Provide a Quantitative Measure of Thought Disorder in Psychosis

Background: Psychosis has various causes, including mania and schizophrenia. Since the differential diagnosis of psychosis is exclusively based on subjective assessments of oral interviews with patients, an objective quantification of the speech disturbances that characterize mania and schizophrenia is in order. In principle, such quantification could be achieved by the analysis of speech graphs. A graph represents a network with nodes connected by edges; in speech graphs, nodes correspond to words and edges correspond to semantic and grammatical relationships. Methodology/Principal Findings: To quantify speech differences related to psychosis, interviews with schizophrenics, manics and normal subjects were recorded and represented as graphs. Manics scored significantly higher than schizophrenics in ten graph measures. Psychopathological symptoms such as logorrhea, poor speech, and flight of thoughts were grasped by the analysis even when verbosity differences were discounted. Binary classifiers based on speech graph measures sorted schizophrenics from manics with up to 93.8% of sensitivity and 93.7% of specificity. In contrast, sorting based on the scores of two standard psychiatric scales (BPRS and PANSS) reached only 62.5% of sensitivity and specificity. Conclusions/Significance: The results demonstrate that alterations of the thought process manifested in the speech of psychotic patients can be objectively measured using graph-theoretical tools, developed to capture specific features of the normal and dysfunctional flow of thought, such as divergence and recurrence. The quantitative analysis of speech graphs is not redundant with standard psychometric scales but rather complementary, as it yields a very accurate sorting of schizophrenics and manics. Overall, the results point to automated psychiatric diagnosis based not on what is said, but on how it is said.

A simple method to measure critical angles for high-sensitivity differential refractometry

A total internal reflection-based differencial refractometer, capable of measuring the real and imaginary parts of the complex refractive index in real time, is presented. The device takes advantage of the phase difference acquired by s- and p-polarized light to generate an easily detectable minimum at the reflected profile. The method allows to sensitively measuring transparent and turbid liquid samples. (C)2012 Optical Society of America

Entanglement entropy in long-range harmonic oscillators

We study the Von Neumann and Renyi entanglement entropy of long-range harmonic oscillators (LRHO) by both theoretical and numerical means. We show that the entanglement entropy in massless harmonic oscillators increases logarithmically with the sub-system size as S - c(eff)/3 log l. Although the entanglement entropy of LRHO's shares some similarities with the entanglement entropy at conformal critical points we show that the Renyi entanglement entropy presents some deviations from the expected conformal behaviour. In the massive case we demonstrate that the behaviour of the entanglement entropy with respect to the correlation length is also logarithmic as the short-range case. Copyright (c) EPLA, 2012

Use of Carr-Purcell pulse sequence with low refocusing flip angle to measure T-1 and T-2 in a single experiment

The Carr-Purcell pulse sequence, with low refocusing flip angle, produces echoes midway between refocusing pulses that decay to a minimum value dependent on T*(2). When the refocusing flip angle was pi/2 (CP90) and tau > T*(2), the signal after the minimum value, increased to reach a steady-state free precession regime (SSFP), composed of a free induction decay signal after each pulse and an echo, before the next pulse. When tau < T*(2), the signal increased from the minimum value to the steady-state regime with a time constant (T*) = 2T(1)T(2)/(T-1 + T-2). identical to the time constant observed in the SSFP sequence, known as the continuous wave free precession (CWFP). The steady-state amplitude obtained with M-cp90 = M0T2/(T-1+T-2) was identical to CWFP. Therefore, this sequence was named CP-CWFP because it is a Carr-Purcell sequence that produces results similar to the CWFP. However, CP-CWFP is a better sequence for measuring the longitudinal and transverse relaxation times in single scan, when the sample exhibits T-1 similar to T-2. Therefore, this sequence can be a useful method in time domain NMR and can be widely used in the agriculture, food and petrochemical industries because those samples tend to have similar relaxation times in low magnetic fields. (C) 2011 Elsevier Inc. All rights reserved.