Statistical mechanics analysis of LDPC coding in MIMO Gaussian channels

Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under low-density parity-check (LDPC) network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and symmetric and asymmetric interference. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases. © 2007 IOP Publishing Ltd.

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

The copper cladding of steel by the submerged arc welding method

The literature available on submerged arc welding of copper and copper alloys, submerged arc welding with strip electrodes, and related areas has been reviewed in depth. Copper cladding of mild steel substrates by deposition from strip electrodes using the submerged arc welding process has been successful. A wide range of parameters, and several fluxes have been investigated. The range of deposit compositions is 66.4% Cu to 95.7% Cu. The weld beads have been metallographically examined using optical and electron microscopy. Equating weld beads to a thermodynamical equivalent of iron has proven to be an accurate and simplified means of handling quantitative data for multicomponent welds. Empirical equations derived using theoretical considerations characterize the weld bead dimensions as functions of the welding parameters and hence composition. The melting rate for strip electrodes is dependent upon the current-voltage product. Weld nugget size is increased by increased thermal transfer efficiencies resulting from stirring which is current dependent. The presence of Fe2O3 in a flux has been demonstrated to diminish electrode melting rate and drastically increase penetration, making flux choice the prime consideration in cladding operations. A theoretical model for welding with strip electrodes and the submerged arc process is presented.

Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Measurement of single spin asymmetry and fifth structure function for the p( e&ar; ,e'K +)Λ reaction with CEBAF Large Acceptance Spectrometer (CLAS)

The single spin asymmetry, ALT ′, and the polarized structure function, σ LT′, for the p( e&ar; , e′K +)Λ reaction in the resonance region have been measured and extracted using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. Data were taken at an electron beam energy of 2.567 GeV. The large acceptance of CLAS allows for full azimuthal angle coverage over a large range of center-of-mass scattering angles. Results were obtained that span a range in Q 2 from 0.5 to 1.3 GeV2 and W from threshold up to 2.1 GeV and were compared to existing theoretical calculations. The polarized structure function is sensitive to the interferences between various resonant amplitudes, as well as to resonant and non-resonant amplitudes. This measurement is essential for understanding the structure of nucleons and searching for previously undetected nucleon excited states (resonances) predicted by quark models. The W dependence of the σ LT′ in the kinematic regions dominated by s and u channel exchange (cos qcmk = −0.50, −0.167, 0.167) indicated possible resonance structures not predicted by theoretical calculations. The σLT ′ behavior around W = 1.875 GeV could be the signature of a resonance predicted by the quark models and possibly seen in photoproduction. In the very forward angles where the reaction is dominated by the t-channel, the average σLT ′ was zero. There was no indication of the interference between resonances or resonant and non-resonant amplitudes. This might be indicating the dominance of a single t-channel exchange. Study of the sensitivity of the fifth structure function data to the resonance around 1900 MeV showed that these data were highly sensitive to the various assumptions of the models for the quantum number of this resonance. This project was part of a larger CLAS program to measure cross sections and polarization observables for kaon electroproduction in the nucleon resonance region. ^

Measurement of the induced polarization of Λ(1116) in kaon electroproduction with CLAS

The CLAS Collaboration is using the p(e, e&feet; K+ p)π- reaction to perform a measurement of the induced polarization of the electroproduced Λ(1116). The parity-violating weak decay of the Λ into pπ- (64%) allows extraction of the recoil polarization of the Λ. The present study uses the CEBAF Large Acceptance Spectrometer (CLAS) to detect the scattered electron, the kaon, and the decay proton. CLAS allows for a large kinematic acceptance in Q2 (0.8 ≤ Q2 ≤ 3.5 GeV2 ), W (1.6 ≤ W ≤ 3.0 GeV), as well as the kaon scattering angle. In this experiment a 5.499 GeV electron beam was incident upon an unpolarized liquid-hydrogen target. The goal is to map out the kinematic dependencies for this polarization observable to provide new constraints for theoretical models of the electromagnetic production of kaon-hyperon final states. Along with previously published photo- and electroproduction cross sections and polarization observables from CLAS, SAPHIR, and GRAAL, these data are needed in a coupled-channel analysis to identify previously unobserved s-channel resonances.^

Proton Form Factor Puzzle and the CEBAF Large Acceptance Spectrometer (CLAS) two-photon exchange experiment

The electromagnetic form factors are the most fundamental observables that encode information about the internal structure of the nucleon. The electric (GE) and the magnetic ( GM) form factors contain information about the spatial distribution of the charge and magnetization inside the nucleon. A significant discrepancy exists between the Rosenbluth and the polarization transfer measurements of the electromagnetic form factors of the proton. One possible explanation for the discrepancy is the contributions of two-photon exchange (TPE) effects. Theoretical calculations estimating the magnitude of the TPE effect are highly model dependent, and limited experimental evidence for such effects exists. Experimentally, the TPE effect can be measured by comparing the ratio of positron-proton elastic scattering cross section to that of the electron-proton [R = σ(e +p)/σ(e+p)]. The ratio R was measured over a wide range of kinematics, utilizing a 5.6 GeV primary electron beam produced by the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab. This dissertation explored dependence of R on kinematic variables such as squared four-momentum transfer (Q2) and the virtual photon polarization parameter (&epsis;). A mixed electron-positron beam was produced from the primary electron beam in experimental Hall B. The mixed beam was scattered from a liquid hydrogen (LH2) target. Both the scattered lepton and the recoil proton were detected by the CEBAF Large Acceptance Spectrometer (CLAS). The elastic events were then identified by using elastic scattering kinematics. This work extracted the Q2 dependence of R at high &epsis;(&epsis; > 0.8) and the $&epsis; dependence of R at ⟨Q 2⟩ approx 0.85 GeV2. In these kinematics, our data confirm the validity of the hadronic calculations of the TPE effect by Blunden, Melnitchouk, and Tjon. This hadronic TPE effect, with additional corrections contributed by higher excitations of the intermediate state nucleon, largely reconciles the Rosenbluth and the polarization transfer measurements of the electromagnetic form factors.

Desenvolvimento e validação do sistema de observação do clima de aula, em aulas de grupo de fitness: aplicação piloto em idosos

Dissertação com vista na obtenção no grau de mestre em Atividade Física em Populações Especiais

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Global relativistic folding optical potential and the relativistic Green's function model

Optical potentials provide critical input for calculations on a wide variety of nuclear reactions, in particular, for neutrino-nucleus reactions, which are of great interest in the light of the new neutrino oscillation experiments. We present the global relativistic folding optical potential (GRFOP) fits to elastic proton scattering data from C-12 nucleus at energies between 20 and 1040 MeV. We estimate observables, such as the differential cross section, the analyzing power, and the spin rotation parameter, in elastic proton scattering within the relativistic impulse approximation. The new GRFOP potential is employed within the relativistic Green's function model for inclusive quasielastic electron scattering and for (anti) neutrino-nucleus scattering at MiniBooNE kinematics.

Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.

Using Helix-coil Models to Study Protein Unfolded States

An abstract of a thesis devoted to using helix-coil models to study unfolded states.\\

Research on polypeptide unfolded states has received much more attention in the last decade or so than it has in the past. Unfolded states are thought to be implicated in various

misfolding diseases and likely play crucial roles in protein folding equilibria and folding rates. Structural characterization of unfolded states has proven to be

much more difficult than the now well established practice of determining the structures of folded proteins. This is largely because many core assumptions underlying

folded structure determination methods are invalid for unfolded states. This has led to a dearth of knowledge concerning the nature of unfolded state conformational

distributions. While many aspects of unfolded state structure are not well known, there does exist a significant body of work stretching back half a century that

has been focused on structural characterization of marginally stable polypeptide systems. This body of work represents an extensive collection of experimental

data and biophysical models associated with describing helix-coil equilibria in polypeptide systems. Much of the work on unfolded states in the last decade has not been devoted

specifically to the improvement of our understanding of helix-coil equilibria, which arguably is the most well characterized of the various conformational equilibria

that likely contribute to unfolded state conformational distributions. This thesis seeks to provide a deeper investigation of helix-coil equilibria using modern

statistical data analysis and biophysical modeling techniques. The studies contained within seek to provide deeper insights and new perspectives on what we presumably

know very well about protein unfolded states. \\

Chapter 1 gives an overview of recent and historical work on studying protein unfolded states. The study of helix-coil equilibria is placed in the context

of the general field of unfolded state research and the basics of helix-coil models are introduced.\\

Chapter 2 introduces the newest incarnation of a sophisticated helix-coil model. State of the art modern statistical techniques are employed to estimate the energies

of various physical interactions that serve to influence helix-coil equilibria. A new Bayesian model selection approach is utilized to test many long-standing

hypotheses concerning the physical nature of the helix-coil transition. Some assumptions made in previous models are shown to be invalid and the new model

exhibits greatly improved predictive performance relative to its predecessor. \\

Chapter 3 introduces a new statistical model that can be used to interpret amide exchange measurements. As amide exchange can serve as a probe for residue-specific

properties of helix-coil ensembles, the new model provides a novel and robust method to use these types of measurements to characterize helix-coil ensembles experimentally

and test the position-specific predictions of helix-coil models. The statistical model is shown to perform exceedingly better than the most commonly used

method for interpreting amide exchange data. The estimates of the model obtained from amide exchange measurements on an example helical peptide

also show a remarkable consistency with the predictions of the helix-coil model. \\

Chapter 4 involves a study of helix-coil ensembles through the enumeration of helix-coil configurations. Aside from providing new insights into helix-coil ensembles,

this chapter also introduces a new method by which helix-coil models can be extended to calculate new types of observables. Future work on this approach could potentially

allow helix-coil models to move into use domains that were previously inaccessible and reserved for other types of unfolded state models that were introduced in chapter 1.

On Provable Algorithms for Determination of Continuous Protein Interdomain Motions from Residual Dipolar Couplings

Dynamics of biomolecules over various spatial and time scales are essential for biological functions such as molecular recognition, catalysis and signaling. However, reconstruction of biomolecular dynamics from experimental observables requires the determination of a conformational probability distribution. Unfortunately, these distributions cannot be fully constrained by the limited information from experiments, making the problem an ill-posed one in the terminology of Hadamard. The ill-posed nature of the problem comes from the fact that it has no unique solution. Multiple or even an infinite number of solutions may exist. To avoid the ill-posed nature, the problem needs to be regularized by making assumptions, which inevitably introduce biases into the result.

Here, I present two continuous probability density function approaches to solve an important inverse problem called the RDC trigonometric moment problem. By focusing on interdomain orientations we reduced the problem to determination of a distribution on the 3D rotational space from residual dipolar couplings (RDCs). We derived an analytical equation that relates alignment tensors of adjacent domains, which serves as the foundation of the two methods. In the first approach, the ill-posed nature of the problem was avoided by introducing a continuous distribution model, which enjoys a smoothness assumption. To find the optimal solution for the distribution, we also designed an efficient branch-and-bound algorithm that exploits the mathematical structure of the analytical solutions. The algorithm is guaranteed to find the distribution that best satisfies the analytical relationship. We observed good performance of the method when tested under various levels of experimental noise and when applied to two protein systems. The second approach avoids the use of any model by employing maximum entropy principles. This 'model-free' approach delivers the least biased result which presents our state of knowledge. In this approach, the solution is an exponential function of Lagrange multipliers. To determine the multipliers, a convex objective function is constructed. Consequently, the maximum entropy solution can be found easily by gradient descent methods. Both algorithms can be applied to biomolecular RDC data in general, including data from RNA and DNA molecules.

When Consumption Embraces Faith: How Religious Beliefs and Practices Influence Consumption

Marketers have long looked for observables that could explain differences in consumer behavior. Initial attempts have centered on demographic factors, such as age, gender, and race. Although such variables are able to provide some useful information for segmentation (Bass, Tigert, and Longdale 1968), more recent studies have shown that variables that tap into consumers’ social classes and personal values have more predictive accuracy and also provide deeper insights into consumer behavior. I argue that one demographic construct, religion, merits further consideration as a factor that has a profound impact on consumer behavior. In this dissertation, I focus on two types of religious guidance that may influence consumer behaviors: religious teachings (being content with one’s belongings), and religious problem-solving styles (reliance on God).

Essay 1 focuses on the well-established endowment effect and introduces a new moderator (religious teachings on contentment) that influences both owner and buyers’ pricing behaviors. Through fifteen experiments, I demonstrate that when people are primed with religion or characterized by stronger religious beliefs, they tend to value their belongings more than people who are not primed with religion or who have weaker religious beliefs. These effects are caused by religious teachings on being content with one’s belongings, which lead to the overvaluation of one’s own possessions.

Essay 2 focuses on self-control behaviors, specifically healthy eating, and introduces a new moderator (God’s role in the decision-making process) that determines the relationship between religiosity and the healthiness of food choices. My findings demonstrate that consumers who indicate that they defer to God in their decision-making make unhealthier food choices as their religiosity increases. The opposite is true for consumers who rely entirely on themselves. Importantly, this relationship is mediated by the consumer’s consideration of future consequences. This essay provides an explanation to the existing mixed findings on the relationship between religiosity and obesity.