Nonlinear indicial response of complex nonstationary oscillations as pulmonary hypertension responding to step hypoxia

This paper is devoted to the quantization of the degree of nonlinearity of the relationship between two biological variables when one of the variables is a complex nonstationary oscillatory signal. An example of the situation is the indicial responses of pulmonary blood pressure (P) to step changes of oxygen tension (ΔpO2) in the breathing gas. For a step change of ΔpO2 beginning at time t1, the pulmonary blood pressure is a nonlinear function of time and ΔpO2, which can be written as P(t-t1 | ΔpO2). An effective method does not exist to examine the nonlinear function P(t-t1 | ΔpO2). A systematic approach is proposed here. The definitions of mean trends and oscillations about the means are the keys. With these keys a practical method of calculation is devised. We fit the mean trends of blood pressure with analytic functions of time, whose nonlinearity with respect to the oxygen level is clarified here. The associated oscillations about the mean can be transformed into Hilbert spectrum. An integration of the square of the Hilbert spectrum over frequency yields a measure of oscillatory energy, which is also a function of time, whose mean trends can be expressed by analytic functions. The degree of nonlinearity of the oscillatory energy with respect to the oxygen level also is clarified here. Theoretical extension of the experimental nonlinear indicial functions to arbitrary history of hypoxia is proposed. Application of the results to tissue remodeling and tissue engineering of blood vessels is discussed.

Quantisation of the bosonic string

In this work we review the basic principles of the theory of the relativistic bosonic string through the study of the action functionals of Nambu-Goto and Polyakov and the techniques required for their canonical, light-cone, and path-integral quantisation. For this purpose, we briefly review the main properties of the gauge symmetries and conformal field theory involved in the techniques studied.

Equações de onda generalizadas e quantização funtorial para teorias de campo escalar livre

Nesta dissertação apresentamos um método de quantização matemática e conceitualmente rigoroso para o campo escalar livre de interações. Trazemos de início alguns aspéctos importantes da Teoria de Distribuições e colocamos alguns pontos de geometria Lorentziana. O restante do trabalho é dividido em duas partes: na primeira, estudamos equações de onda em variedades Lorentzianas globalmente hiperbólicas e apresentamos o conceito de soluções fundamentais no contexto de equações locais. Em seguida, progressivamente construímos soluções fundamentais para o operador de onda a partir da distribuição de Riesz. Uma vez estabelecida uma solução para a equação de onda em uma vizinhança de um ponto da variedade, tratamos de construir uma solução global a partir da extensão do problema de Cauchy a toda a variedade, donde as soluções fundamentais dão lugar aos operadores de Green a partir da introdução de uma condição de contorno. Na última parte do trabalho, apresentamos um mínimo da Teoria de Categorias e Funtores para utilizar esse formalismo na contrução de um funtor de segunda quantização entre a categoria de variedades Lorentzianas globalmente hiperbólicas e a categoria de redes de álgebras C* satisfazendo os axiomas de Haag-Kastler. Ao fim, retomamos o caso particular do campo escalar quântico livre.

Evolution of conducting channels in metallic atomic contacts under elastic deformation

We investigate both experimentally and theoretically the evolution of conductance in metallic one-atom contacts under elastic deformation. While simple metals like Au exhibit almost constant conductance plateaus, Al and Pb show inclined plateaus with positive and negative slopes. It is shown how these behaviors can be understood in terms of the orbital structure of the atoms forming the contact. This analysis provides further insight into the issue of conductance quantization in metallic contacts revealing important aspects of their atomic and electronic structures.

Spin-filtered edge states in graphene

Spin–orbit coupling changes graphene, in principle, into a two-dimensional topological insulator, also known as quantum spin Hall insulator. One of the expected consequences is the existence of spin-filtered edge states that carry dissipationless spin currents and undergo no backscattering in the presence of non-magnetic disorder, leading to quantization of conductance. Whereas, due to the small size of spin–orbit coupling in graphene, the experimental observation of these remarkable predictions is unlikely, the theoretical understanding of these spin-filtered states is shedding light on the electronic properties of edge states in other two-dimensional quantum spin Hall insulators. Here we review the effect of a variety of perturbations, like curvature, disorder, edge reconstruction, edge crystallographic orientation, and Coulomb interactions on the electronic properties of these spin filtered states.

Anisotropic intrinsic spin relaxation in graphene due to flexural distortions

We propose an intrinsic spin scattering mechanism in graphene originated by the interplay of atomic spin-orbit interaction and the local curvature induced by flexural distortions of the atomic lattice. Starting from a multiorbital tight-binding Hamiltonian with spin-orbit coupling considered nonperturbatively, we derive an effective Hamiltonian for the spin scattering of the Dirac electrons due to flexural distortions. We compute the spin lifetime due to both flexural phonons and ripples and we find values in the microsecond range at room temperature. Interestingly, this mechanism is anisotropic on two counts. First, the relaxation rate is different for off-plane and in-plane spin quantization axis. Second, the spin relaxation rate depends on the angle formed by the crystal momentum with the carbon-carbon bond. In addition, the spin lifetime is also valley dependent. The proposed mechanism sets an upper limit for spin lifetimes in graphene and will be relevant when samples of high quality can be fabricated free of extrinsic sources of spin relaxation.

Quantum Hall effect in gapped graphene heterojunctions

We model the quantum Hall effect in heterostructures made of two gapped graphene stripes with different gaps, Δ1 and Δ2. We consider two main situations, Δ1=0,Δ2≠0, and Δ1=−Δ2. They are different in a fundamental aspect: only the latter features kink states that, when intervalley coupling is absent, are protected against backscattering. We compute the two-terminal conductance of heterostructures with channel length up to 430 nm, in two transport configurations, parallel and perpendicular to the interface. By studying the effect of disorder on the transport along the boundary, we quantify the robustness of kink states with respect to backscattering. Transport perpendicular to the boundary shows how interface states open a backscattering channel for the conducting edge states, spoiling the perfect conductance quantization featured by the homogeneously gapped graphene Hall bars. Our results can be relevant for the study of graphene deposited on hexagonal boron-nitride, as well as to model graphene with an interaction-driven gapped phase with two equivalent phases separated by a domain wall.

Quantum anomalous Hall effect in graphene coupled to skyrmions

Skyrmions are topologically protected spin textures, characterized by a topological winding number N, that occur spontaneously in some magnetic materials. Recent experiments have demonstrated the capability to grow graphene on top Fe/Ir, a system that exhibits a two-dimensional skyrmion lattice. Here we show that a weak exchange coupling between the Dirac electrons in graphene and a two-dimensional skyrmion lattice withN = ±1 drives graphene into a quantum anomalous Hall phase, with a band gap in bulk, a Chern number C = 2N, and chiral edge states with perfect quantization of conductance G = 2N e2 h . Our findings imply that the topological properties of the skyrmion lattice can be imprinted in the Dirac electrons of graphene.

Boston, Massachusetts Region, Digital Elevation Model with Bathymetry

This raster layer represents surface elevation and bathymetry data for the Boston Region, Massachusetts. It was created by merging portions of MassGIS Digital Elevation Model 1:5,000 (2005) data with NOAA Estuarine Bathymetric Digital Elevation Models (30 m.) (1998). DEM data was derived from the digital terrain models that were produced as part of the MassGIS 1:5,000 Black and White Digital Orthophoto imagery project. Cellsize is 5 meters by 5 meters. Each cell has a floating point value, in meters, which represents its elevation above or below sea level.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

Low bit-rate speech encoding for digital mobile radio

The need for low bit-rate speech coding is the result of growing demand on the available radio bandwidth for mobile communications both for military purposes and for the public sector. To meet this growing demand it is required that the available bandwidth be utilized in the most economic way to accommodate more services. Two low bit-rate speech coders have been built and tested in this project. The two coders combine predictive coding with delta modulation, a property which enables them to achieve simultaneously the low bit-rate and good speech quality requirements. To enhance their efficiency, the predictor coefficients and the quantizer step size are updated periodically in each coder. This enables the coders to keep up with changes in the characteristics of the speech signal with time and with changes in the dynamic range of the speech waveform. However, the two coders differ in the method of updating their predictor coefficients. One updates the coefficients once every one hundred sampling periods and extracts the coefficients from input speech samples. This is known in this project as the Forward Adaptive Coder. Since the coefficients are extracted from input speech samples, these must be transmitted to the receiver to reconstruct the transmitted speech sample, thus adding to the transmission bit rate. The other updates its coefficients every sampling period, based on information of output data. This coder is known as the Backward Adaptive Coder. Results of subjective tests showed both coders to be reasonably robust to quantization noise. Both were graded quite good, with the Forward Adaptive performing slightly better, but with a slightly higher transmission bit rate for the same speech quality, than its Backward counterpart. The coders yielded acceptable speech quality of 9.6kbps for the Forward Adaptive and 8kbps for the Backward Adaptive.

Neural population coding is optimized by discrete tuning curves

The sigmoidal tuning curve that maximizes the mutual information for a Poisson neuron, or population of Poisson neurons, is obtained. The optimal tuning curve is found to have a discrete structure that results in a quantization of the input signal. The number of quantization levels undergoes a hierarchy of phase transitions as the length of the coding window is varied. We postulate, using the mammalian auditory system as an example, that the presence of a subpopulation structure within a neural population is consistent with an optimal neural code.

A hierarchy of phase transitions in optimal neuronal coding:from binary to M-ary discrete optimal codes

We have investigated how optimal coding for neural systems changes with the time available for decoding. Optimization was in terms of maximizing information transmission. We have estimated the parameters for Poisson neurons that optimize Shannon transinformation with the assumption of rate coding. We observed a hierarchy of phase transitions from binary coding, for small decoding times, toward discrete (M-ary) coding with two, three and more quantization levels for larger decoding times. We postulate that the presence of subpopulations with specific neural characteristics could be a signiture of an optimal population coding scheme and we use the mammalian auditory system as an example.

Quantum Mechanics of Guiding Center Motion in Strong Magnetic Field (Coherent State Path Integral Approach)

A new approach is proposed for the quantum mechanics of guiding center motion in strong magnetic field. This is achieved by use of the coherent state path integral for the coupled systems of the cyclotron and the guiding center motion. We are specifically concerned with the effective action for the guiding center degree, which can be used to get the Bohr- Sommerfeld quantization scheme. The quantization rule is similar to the one for the vortex motion as a dynamics of point particles.