text:
• ### Low-temperature behavior of transmission phase shift across a Kondo correlated quantum dot(1608.05823)

Aug. 20, 2016 cond-mat.mes-hall
We study the transmission phase shift across a Kondo correlated quantum dot in a GaAs heterostructure at temperatures below the Kondo temperature ($T < T_{\rm K}$), where the phase shift is expected to show a plateau at $\pi/2$ for an ideal Kondo singlet ground state. Our device is tuned such that the ratio $\Gamma/U$ of level width $\Gamma$ to charging energy $U$ is quite large ($\lesssim 0.5$ rather than $\ll 1$). This situation is commonly used in GaAs quantum dots to ensure Kondo temperatures large enough ($\simeq 100$ mK here) to be experimentally accessible; however it also implies that charge fluctuations are more pronounced than typically assumed in theoretical studies focusing on the regime $\Gamma/U \ll 1$ needed to ensure a well-defined local moment. Our measured phase evolves monotonically by $\pi$ across the two Coulomb peaks, but without being locked at $\pi/2$ in the Kondo valley for $T \ll T_{\rm K}$, due to a significant influence of large $\Gamma/U$. Only when $\Gamma/U$ is reduced sufficiently does the phase start to be locked around $\pi/2$ and develops into a plateau at $\pi/2$. Our observations are consistent with numerical renormalization group calculations, and can be understood as a direct consequence of the Friedel sum rule that relates the transmission phase shift to the local occupancy of the dot, and thermal average of a transmission coefficient through a resonance level near the Fermi energy.
• ### Interleaved numerical renormalization group as an efficient multiband impurity solver(1602.02182)

June 7, 2016 cond-mat.str-el
Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a Wilson chain'. It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014)]. Here we systematically examine the accuracy and efficiency of the interleaved' NRG (iNRG) method in the context of the single impurity Anderson model, the two-channel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with `standard' NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are signifficantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.
• ### Thermalization and dynamics in the single impurity Anderson model(1507.03398)

We analyze the process of thermalization, dynamics and the eigenstate thermalization hypothesis (ETH) for the single impurity Anderson model, focusing on the Kondo regime. For this we construct the complete eigenbasis of the Hamiltonian using the numerical renormalization group (NRG) method in the language of the matrix product states. It is a peculiarity of the NRG that while the Wilson chain is supposed to describe a macroscopic bath, very few single particle excitations already suffice to essentially thermalize the impurity system at finite temperature, which amounts to having added a macroscopic amount of energy. Thus given an initial state of the system such as the ground state together with microscopic excitations, we calculate the spectral function of the impurity using the microcanonical and diagonal and grand canonical ensembles. By adding or removing particles at a certain Wilson energy shell on top of the ground state, we find qualitative agreement between the spectral functions calculated for different ensembles. This indicates that the system thermalizes in the long-time limit, and can be described by an appropriate statistical-mechanical ensemble. Moreover, by calculating the impurity spectral density at the Fermi level and the dot occupancy for energy eigenstates relevant for microcanonical ensemble, we find good support for ETH. The ultimate mechanism responsible for this effective thermalization within the NRG can be identified as Anderson orthogonality: the more charge that needs to flow to or from infinity after applying a local excitation within the Wilson chain, the more the system looks thermal afterwards at an increased temperature. For the same reason, however, thermalization fails if charge rearrangement after the excitation remains mostly local.
• ### DMFT+NRG study of spin-orbital separation in a three-band Hund's metal(1503.06467)

March 22, 2015 cond-mat.str-el
We show that the numerical renormalization group (NRG) is a viable multi-band impurity solver for Dynamical Mean Field Theory (DMFT), offering unprecedent real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund's metal problem for a three-orbital model with filling factor $n_d=2$. The ground state is a Fermi liquid. The one-particle spectral function has a strong particle-hole asymmetry, with a clear apparent power law for positive frequencies only. With increasing temperature it shows a coherence-incoherence crossover with spectral weight transfered from low to high energies and evolves qualitatively differently from a doped Mott insulator. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.
• ### Transmission Phase in the Kondo Regime Revealed in a Two-Path Interferometer(1311.6884)

Sept. 16, 2014 cond-mat.mes-hall
We report on the direct observation of the transmission phase shift through a Kondo correlated quantum dot by employing a new type of two-path interferometer. We observed a clear $\pi/2$-phase shift, which persists up to the Kondo temperature $T_{\rm K}$. Above this temperature, the phase shifts by more than $\pi/2$ at each Coulomb peak, approaching the behavior observed for the standard Coulomb blockade regime. These observations are in remarkable agreement with 2-level numerical renormalization group calculations. The unique combination of experimental and theoretical results presented here fully elucidates the phase evolution in the Kondo regime.
• ### Nonequilibrium dynamics in an optical transition from a neutral quantum dot to a correlated many-body state(1304.1745)

Nov. 4, 2013 quant-ph, cond-mat.mes-hall
We investigate the effect of many-body interactions on the optical absorption spectrum of a charge-tunable quantum dot coupled to a degenerate electron gas. A constructive Fano interference between an indirect path, associated with an intra dot exciton generation followed by tunneling, and a direct path, associated with the ionization of a valence-band quantum dot electron, ensures the visibility of the ensuing Fermi-edge singularity despite weak absorption strength. We find good agreement between experiment and renormalization group theory, but only when we generalize the Anderson impurity model to include a static hole and a dynamic dot-electron scattering potential. The latter highlights the fact that an optically active dot acts as a tunable quantum impurity, enabling the investigation of a new dynamic regime of Fermi-edge physics.
• ### Proposed Rabi-Kondo Correlated State in a Laser-Driven Semiconductor Quantum Dot(1211.6837)

Spin exchange between a single-electron charged quantum dot and itinerant electrons leads to an emergence of Kondo correlations. When the quantum dot is driven resonantly by weak laser light, the resulting emission spectrum allows for a direct probe of these correlations. In the opposite limit of vanishing exchange interaction and strong laser drive, the quantum dot exhibits coherent oscillations between the single-spin and optically excited states. Here, we show that the interplay between strong exchange and non-perturbative laser coupling leads to the formation of a new nonequilibrium quantum-correlated state, characterized by the emergence of a laser-induced secondary spin screening cloud, and examine the implications for the emission spectrum.
• ### Iron impurities in gold and silver: Comparison of transport measurements to numerical renormalization group calculations exploiting non-Abelian symmetries(1305.3551)

We consider iron impurities in the noble metals gold and silver and compare experimental data for the resistivity and decoherence rate to numerical renormalization group results. By exploiting non-Abelian symmetries we show improved numerical data for both quantities as compared to previous calculations [Costi et al., Phys. Rev. Lett. 102, 056802 (2009)], using the discarded weight as criterion to reliably judge the quality of convergence of the numerical data. In addition we also carry out finite-temperature calculations for the magnetoresistivity of fully screened Kondo models with S = 1/2, 1 and 3/2, and compare the results with available measurements for iron in silver, finding excellent agreement between theory and experiment for the spin-3/2 three-channel Kondo model. This lends additional support to the conclusion of Costi et al. that the latter model provides a good effective description of the Kondo physics of iron impurities in gold and silver.
• ### Quantum Corrections to the Polarizability and Dephasing in Isolated Disordered Metals(1304.4342)

July 15, 2013 cond-mat.mes-hall
We study the quantum corrections to the polarizability of isolated metallic mesoscopic systems using the loop-expansion in diffusive propagators. We show that the difference between connected (grand-canonical ensemble) and isolated (canonical ensemble) systems appears only in subleading terms of the expansion, and can be neglected if the frequency of the external field, $\omega$, is of the order of (or even slightly smaller than) the mean level spacing, $\Delta$. If $\omega \ll \Delta$, the two-loop correction becomes important. We calculate it by systematically evaluating the ballistic parts (the Hikami boxes) of the corresponding diagrams and exploiting electroneutrality. Our theory allows one to take into account a finite dephasing rate, $\gamma$, generated by electron interactions, and it is complementary to the non-perturbative results obtained from a combination of Random Matrix Theory (RMT) and the $\sigma$-model, valid at $\gamma \to 0$. Remarkably, we find that the two-loop result for isolated systems with moderately weak dephasing, $\gamma \sim \Delta$, is similar to the result of the RMT+$\sigma$-model even in the limit $\omega \to 0$. For smaller $\gamma$, we discuss the possibility to interpolate between the perturbative and the non-perturbative results. We compare our results for the temperature dependence of the polarizability of isolated rings to the experimental data of Deblock \emph{et al} [\prl \ {\bf 84}, 5379 (2000); \prb \ {\bf 65}, 075301 (2002)], and we argue that the elusive 0D regime of dephasing might have manifested itself in the observed magneto-oscillations. Besides, we thoroughly discuss possible future measurements of the polarizability, which could aim to reveal the existence of 0D dephasing and the role of the Pauli blocking at small temperatures.
• ### Thermal noise and dephasing due to electron interactions in non-trivial geometries(1105.0554)

Sept. 7, 2011 cond-mat.mes-hall
We study Johnson-Nyquist noise in macroscopically inhomogeneous disordered metals and give a microscopic derivation of the correlation function of the scalar electric potentials in real space. Starting from the interacting Hamiltonian for electrons in a metal and the random phase approximation, we find a relation between the correlation function of the electric potentials and the density fluctuations which is valid for arbitrary geometry and dimensionality. We show that the potential fluctuations are proportional to the solution of the diffusion equation, taken at zero frequency. As an example, we consider networks of quasi-1D disordered wires and give an explicit expression for the correlation function in a ring attached via arms to absorbing leads. We use this result in order to develop a theory of dephasing by electronic noise in multiply-connected systems.
• ### Universality of the Kondo effect in quantum dots with ferromagnetic leads(1104.5699)

April 29, 2011 cond-mat.mes-hall
We investigate quantum dots in clean single-wall carbon nanotubes with ferromagnetic PdNi-leads in the Kondo regime. In most odd Coulomb valleys the Kondo resonance exhibits a pronounced splitting, which depends on the tunnel coupling to the leads and an external magnetic field $B$, and only weakly on gate voltage. Using numerical renormalization group calculations, we demonstrate that all salient features of the data can be understood using a simple model for the magnetic properties of the leads. The magnetoconductance at zero bias and low temperature depends in a universal way on $g \mu_B (B-B_c) / k_B T_K$, where $T_K$ is the Kondo temperature and $B_c$ the external field compensating the splitting.
• ### Dimensional Crossover of the Dephasing Time in Disordered Mesoscopic Rings: From Diffusive through Ergodic to 0D Behavior(1001.0479)

Nov. 16, 2010 cond-mat.mes-hall
We analyze dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads, where we recently predicted a crossover for the dephasing time $\tPh(T)$ from diffusive or ergodic 1D ($\tPh^{-1} \propto T^{2/3}, T^{1}$) to $0D$ behavior ($\tPh^{-1} \propto T^{2}$) as $T$ drops below the Thouless energy $\ETh$. We provide a detailed derivation of our results, based on an influence functional for quantum Nyquist noise, and calculate all leading and subleading terms of the dephasing time in the three regimes. Explicitly taking into account the Pauli blocking of the Fermi sea in the metal allows us to describe the $0D$ regime on equal footing as the others. The crossover to $0D$, predicted by Sivan, Imry and Aronov for 3D systems, has so far eluded experimental observation. We will show that for $T \ll \ETh$, $0D$ dephasing governs not only the $T$-dependence for the smooth part of the magnetoconductivity but also for the amplitude of the Altshuler-Aronov-Spivak oscillations, which result only from electron paths winding around the ring. This observation can be exploited to filter out and eliminate contributions to dephasing from trajectories which do not wind around the ring, which may tend to mask the $T^{2}$ behavior. Thus, the ring geometry holds promise of finally observing the crossover to $0D$ experimentally.
• ### Dimensional Crossover of the Dephasing Time in Disordered Mesoscopic Rings(0905.1213)

We study dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads. We use an influence functional for quantum Nyquist noise to describe the crossover for the dephasing time $\Tph (T)$ from diffusive or ergodic 1D ($\Tph^{-1} \propto T^{2/3}, T^{1}$) to 0D behavior ($\Tph^{-1} \propto T^{2}$) as $T$ drops below the Thouless energy. The crossover to 0D, predicted earlier for 2D and 3D systems, has so far eluded experimental observation. The ring geometry holds promise of meeting this longstanding challenge, since the crossover manifests itself not only in the smooth part of the magnetoconductivity but also in the amplitude of Altshuler-Aronov-Spivak oscillations. This allows signatures of dephasing in the ring to be cleanly extracted by filtering out those of the leads.
• ### Shedding light on non-equilibrium dynamics of a spin coupled to fermionic reservoir(0907.3854)

A single confined spin interacting with a solid-state environment has emerged as one of the fundamental paradigms of mesoscopic physics. In contrast to standard quantum optical systems, decoherence that stems from these interactions can in general not be treated using the Born-Markov approximation at low temperatures. Here we study the non-equilibrium dynamics of a single-spin in a semiconductor quantum dot adjacent to a fermionic reservoir and show how the dynamics can be revealed in detail in an optical absorption experiment. We show that the highly asymmetrical optical absorption lineshape of the resulting Kondo exciton consists of three distinct frequency domains, corresponding to short, intermediate and long times after the initial excitation, which are in turn described by the three fixed points of the single-impurity Anderson Hamiltonian. The zero-temperature power-law singularity dominating the lineshape is linked to dynamically generated Kondo correlations in the photo-excited state. We show that this power-law singularity is tunable with gate voltage and magnetic field, and universal.
• ### Kondo decoherence: finding the right spin model for iron impurities in gold and silver(0810.1771)

We exploit the decoherence of electrons due to magnetic impurities, studied via weak localization, to resolve a longstanding question concerning the classic Kondo systems of Fe impurities in the noble metals gold and silver: which Kondo-type model yields a realistic description of the relevant multiple bands, spin and orbital degrees of freedom? Previous studies suggest a fully screened spin $S$ Kondo model, but the value of $S$ remained ambiguous. We perform density functional theory calculations that suggest $S = 3/2$. We also compare previous and new measurements of both the resistivity and decoherence rate in quasi 1-dimensional wires to numerical renormalization group predictions for $S=1/2,1$ and 3/2, finding excellent agreement for $S=3/2$.
• ### Mesoscopic Spin-Boson Models of Trapped Ions(0710.5145)

Oct. 28, 2007 quant-ph, cond-mat.mes-hall
Trapped ions arranged in Coulomb crystals provide us with the elements to study the physics of a single spin coupled to a boson bath. In this work we show that optical forces allow us to realize a variety of spin-boson models, depending on the crystal geometry and the laser configuration. We study in detail the Ohmic case, which can be implemented by illuminating a single ion with a travelling wave. The mesoscopic character of the phonon bath in trapped ions induces new effects like the appearance of quantum revivals in the spin evolution.
• ### Kondo quantum dot coupled to ferromagnetic leads: Numerical renormalization group study(0706.3997)

We systematically study the influence of ferromagnetic leads on the Kondo resonance in a quantum dot tuned to the local moment regime. We employ Wilson's numerical renormalization group method, extended to handle leads with a spin asymmetric density of states, to identify the effects of (i) a finite spin polarization in the leads (at the Fermi-surface), (ii) a Stoner splitting in the bands (governed by the band edges) and (iii) an arbitrary shape of the leads density of states. For a generic lead density of states the quantum dot favors being occupied by a particular spin-species due to exchange interaction with ferromagnetic leads leading to a suppression and splitting of the Kondo resonance. The application of a magnetic field can compensate this asymmetry restoring the Kondo effect. We study both the gate-voltage dependence (for a fixed band structure in the leads) and the spin polarization dependence (for fixed gate voltage) of this compensation field for various types of bands. Interestingly, we find that the full recovery of the Kondo resonance of a quantum dot in presence of leads with an energy dependent density of states is not only possible by an appropriately tuned external magnetic field but also via an appropriately tuned gate voltage. For flat bands simple formulas for the splitting of the local level as a function of the spin polarization and gate voltage are given.
• ### Dynamical conductance in the two-channel Kondo regime of a double dot system(0706.1558)

We study finite-frequency transport properties of the double-dot system recently constructed to observe the two-channel Kondo effect [R. M. Potok et al., Nature 446, 167 (2007)]. We derive an analytical expression for the frequency-dependent linear conductance of this device in the Kondo regime. We show how the features characteristic of the 2-channel Kondo quantum critical point emerge in this quantity, which we compute using the results of conformal field theory as well as numerical renormalization group methods. We determine the universal cross-over functions describing non-Fermi liquid vs. Fermi liquid cross-overs and also investigate the effects of a finite magnetic field.
• ### Mesoscopic to universal crossover of transmission phase of multi-level quantum dots(cond-mat/0609191)

Transmission phase \alpha measurements of many-electron quantum dots (small mean level spacing \delta) revealed universal phase lapses by \pi between consecutive resonances. In contrast, for dots with only a few electrons (large \delta), the appearance or not of a phase lapse depends on the dot parameters. We show that a model of a multi-level quantum dot with local Coulomb interactions and arbitrary level-lead couplings reproduces the generic features of the observed behavior. The universal behavior of \alpha for small \delta follows from Fano-type antiresonances of the renormalized single-particle levels.
• ### Phase lapses in transmission through interacting two-level quantum dots(cond-mat/0612490)

We investigate the appearance of pi lapses in the transmission phase theta of a two-level quantum dot with Coulomb interaction U. Using the numerical and functional renormalization group methods we study the entire parameter space for spin-polarized as well as spin-degenerate dots, modeled by spinless or spinful electrons, respectively. We investigate the effect of finite temperatures T. For small T and sufficiently small single-particle spacings delta of the dot levels we find pi phase lapses between two transmission peaks in an overwhelming part of the parameter space of the level-lead couplings. For large delta the appearance or not of a phase lapse between resonances depends on the relative sign of the level-lead couplings in analogy to the U=0 case. We show that this generic scenario is the same for spin-polarized and spin-degenerate dots. We emphasize that in contrast to dots with more levels, for a two-level dot with small delta and generic dot-lead couplings (that is up to cases with special symmetry) the "universal" phase lapse behavior is already established at U=0. The most important effect of the Coulomb interaction is to increase the separation of the transmission resonances. The relation of the appearance of phase lapses to the inversion of the population of the dot levels is discussed. For the spin-polarized case and low temperatures we compare our results to recent mean-field studies. For small delta correlations are found to strongly alter the mean-field picture.
• ### Comment on "Theoretical analysis of the transmission phase shift of a quantum dot in the presence of Kondo correlations"(cond-mat/0603073)

Recently, A. Jerez, P. Vitushinsky and M. Lavagna [Phys. Rev. Lett. 95, 127203 (2005)] claimed that the transmission phase through a quantum fot, as measured via the Aharonov-Bohm interferometer, differs from the phase which determines the corresponding conductance. Here we show that this claim is wrong for the single level Anderson model, which is usually used to describe the quantum dot. So far, there exists no derivation of this claim from any explicit theoretical model.
• ### Energy-resolved inelastic electron scattering off a magnetic impurity(cond-mat/0507431)

Feb. 9, 2006 cond-mat.str-el
We study inelastic scattering of energetic electrons off a Kondo impurity. If the energy E of the incoming electron (measured from the Fermi level) exceeds significantly the Kondo temperature T_K, then the differential inelastic cross-section \sigma (E,w), i.e., the cross-section characterizing scattering of an electron with a given energy transfer w, is well-defined. We show that \sigma (E,w) factorizes into two parts. The E-dependence of \sigma (E,w) is logarithmically weak and is due to the Kondo renormalization of the effective coupling. We are able to relate the w-dependence to the spin-spin correlation function of the magnetic impurity. Using this relation, we demonstrate that in the absence of magnetic field the dynamics of the impurity spin causes the electron scattering to be inelastic at any temperature. Quenching of the spin dynamics by an applied magnetic field results in a finite elastic component of the electron scattering cross-section. The differential scattering cross-section may be extracted from the measurements of relaxation of hot electrons injected in conductors containing localized spins.
• ### Frequency-dependent transport through a quantum dot in the Kondo regime(cond-mat/0406312)

May 24, 2005 cond-mat.str-el
We study the AC conductance and equilibrium current fluctuations of a Coulomb blockaded quantum dot. A relation between the equilibrium spectral function and the linear AC conductance is derived which is valid for frequencies well below the charging energy of the quantum dot. Frequency-dependent transport measurements can thus give experimental access to the Kondo peak in the equilibrium spectral function of a quantum dot. We illustrate this in detail for typical experimental parameters using the numerical renormalization group method in combination with the Kubo formalism.
• ### Absorption and Emission in quantum dots: Fermi surface effects of Anderson excitons(cond-mat/0502329)

Feb. 14, 2005 cond-mat.str-el
Recent experiments measuring the emission of exciton recombination in a self-organized single quantum dot (QD) have revealed that novel effects occur when the wetting layer surrounding the QD becomes filled with electrons, because the resulting Fermi sea can hybridize with the local electron levels on the dot. Motivated by these experiments, we study an extended Anderson model, which describes a local conduction band level coupled to a Fermi sea, but also includes a local valence band level. We are interested, in particular, on how many-body correlations resulting from the presence of the Fermi sea affect the absorption and emission spectra. Using Wilson's numerical renormalization group method, we calculate the zero-temperature absorption (emission) spectrum of a QD which starts from (ends up in) a strongly correlated Kondo ground state. We predict two features: Firstly, we find that the spectrum shows a power law divergence close to the threshold, with an exponent that can be understood by analogy to the well-known X-ray edge absorption problem. Secondly, the threshold energy $\omega_0$ - below which no photon is absorbed (above which no photon is emitted) - shows a marked, monotonic shift as a function of the exciton binding energy $U_{\rm exc}$
• ### One-dimensional density waves of ultracold bosons in an optical lattice(cond-mat/0411403)

Nov. 16, 2004 cond-mat.other
We investigate the propagation of density-wave packets in a Bose-Hubbard model using the adaptive time-dependent density-matrix renormalization group method. We discuss the decay of the amplitude with time and the dependence of the velocity on density, interaction strength and the height of the perturbation in a numerically exact way, covering arbitrary interactions and amplitudes of the perturbation. In addition, we investigate the effect of self-steepening due to the amplitude dependence of the velocity and discuss the possibilities for an experimental detection of the moving wave packet in time of flight pictures. By comparing the sound velocity to theoretical predictions, we determine the limits of a Gross-Pitaevskii or Bogoliubov type description and the regime where repulsive one-dimensional Bose gases exhibit fermionic behaviour.


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Chapter 30

INTRODUCTION

Neonatal jaundice, implying a yellow color of the skin and mucous membranes due to bilirubin deposition, occurs in about 60% of infants and even more often in those exclusively breast feeding. In most cases, the jaundice will be mild or moderate, and the total serum bilirubin (TSB) will not endanger the newborn infant. Occasionally, the TSB may increase to potentially dangerous levels and require treatment with phototherapy or rarely exchange transfusion to offset any further increase. Rarely, the TSB may rise to hazardous levels, at which bilirubin may cross the blood-brain barrier and enter the brain cells. The result will be the complication of acute bilirubin encephalopathy (ABE), in many cases with the devastating chronic sequela of choreoathetotic cerebral palsy known as kernicterus, or death. Despite attempts to eliminate this condition, kernicterus, although a rare condition, is still with us and accompanies us into the third millennium. Many cases should be preventable. Because the implications for affected individuals are lifelong, the public health aspects are necessarily of major importance. Understanding of the metabolism of bilirubin and the pathophysiology of hyperbilirubinemia are crucial to the prevention of this condition, as discussed in this chapter.

EPIDEMIOLOGY

Was There a Disappearance and Resurgence of Kernicterus?

Some authors refer to a disappearance and then resurgence of reported cases of kernicterus in Westernized countries during the last decades.1, 2, 3, and 4 Others opine that the condition never completely disappeared and is still being seen, both in countries with advanced medical systems and in developing countries.5 There can be no doubt that widespread use of the 2 mainstays of treatment of hyperbilirubinemia, exchange transfusion and phototherapy, along with immune prophylaxis of Rh isoimmunization, have prevented many cases of extreme hyperbilirubinemia. If the condition did indeed disappear, however, there can be no explanation for the cases of kernicterus still occurring due to conditions including glucose-6-phosphate dehydrogenase (G-6-PD) deficiency and direct antiglobulin titer (DAT) positive ABO isoimmunization, conditions that, in themselves, did not disappear.6,7

In favor of the resurgence theory, following a period during which few cases of kernicterus were reported, several case reports were published from the United States,8, 9, and 10 followed by reports of the US-based Kernicterus Registry.7,11 In Denmark, Ebbesen12 did find cases of bilirubin encephalopathy between 1994 and 2001, whereas in a nationwide search, he uncovered no cases during the 20 years preceding 1994.

On the other hand, in the United States, Burke et al reported a 70% decrease in the number of hospitalizations between 1988 and 2005 of neonates diagnosed with kernicterus.13 Brooks et al found a constant incidence of kernicterus in California occurring during 2 time epochs: 1988–1993 and 1994–1997.14 On a national US basis, mortality data due to kernicterus from the Centers for Disease Control and Prevention ...

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## A Bayesian Analysis in the Presence of Covariates for Multivariate Survival Data: An example of Application; Análisis bayesiano en presencia de covariables para datos de sobrevivencia multivariados: un ejemplo de aplicación

SANTOS, Carlos Aparecido; ACHCAR, Jorge Alberto
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
46.35%
In this paper, we introduce a Bayesian analysis for survival multivariate data in the presence of a covariate vector and censored observations. Different ""frailties"" or latent variables are considered to capture the correlation among the survival times for the same individual. We assume Weibull or generalized Gamma distributions considering right censored lifetime data. We develop the Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods.; En este artículo, se introduce un análisis bayesiano para datos multivariados de sobrevivencia en presencia de un vector de covariables y observaciones censuradas. Diferentes "fragilidades" o variables latentes son consideradas para capturar la correlación entre los tiempos de sobrevivencia para un mismo individuo. Asumimos distribuciones Weibull o Gamma generalizadas considerando datos de tiempo de vida a derecha. Desarrollamos el análisis bayesiano usando métodos Markov Chain Monte Carlo (MCMC).

## Modelagem espaço-temporal para dados de incidência de doenças em plantas.; Spatiotemporal modelling of plant disease incidence.

Lima, Renato Ribeiro de
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
46.31%

## Uma abordagem Bayesiana para o mapeamento de QTLs utilizando o método MCMC com saltos reversíveis; A Bayesian approach to detect quantitative trait loci using reversible-jump MCMC

Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
46.42%
A utilização de metodologias Bayesianas tem se tornado freqüuente nas aplicações em Genética, em particular em mapeamento de QTLs usando marcadores moleculares. Mapear um QTL implica em identificar sua posição no genoma, bem como seus efeitos genéticos. A abordagem Bayesiana combina, através do Teorema de Bayes, a verossimilhança dos dados fenotípicos com distribuições a priori atribuídas a todos os parâmetros desconhecidos (número, localização e efeito do QTL) induzindo distribuições a posteriori a respeito dessas quantidades. Métodos de mapeamento Bayesiano podem tratar o número desconhecido de QTLs como uma variável aleatória, resultando em complicações na obtençãao da amostra aleatória da distribuição conjunta a posteriori, uma vez que a dimensão do espaço do modelo pode variar. O Método MCMC com Saltos Reversíveis (MCMC-SR), proposto por Green(1995), é excelente para explorar distribuições a posteriori nesse contexto. O método proposto foi avaliado usando dados simulados no WinQTLCart, onde o maior objetivo foi avaliar diferentes prioris atribuídas para o número de QTLs.; The use of Bayesian methodology in genetical applications has grown increasingly popular, in particular in the analysis of quantitative trait loci (QTL) for studies using molecular markers. In such analyses the aim is mapping QTLs...

## Uso dos métodos clássico e bayesiano para os modelos não-lineares heterocedásticos simétricos; Use of the classical and bayesian methods for nonlinear heterocedastic symmetric models

Macêra, Márcia Aparecida Centanin
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
46.44%
Os modelos normais de regressão têm sido utilizados durante muitos anos para a análise de dados. Mesmo nos casos em que a normalidade não podia ser suposta, tentava-se algum tipo de transformação com o intuito de alcançar a normalidade procurada. No entanto, na prática, essas suposições sobre normalidade e linearidade nem sempre são satisfeitas. Como alternativas à técnica clássica, foram desenvolvidas novas classes de modelos de regressão. Nesse contexto, focamos a classe de modelos em que a distribuição assumida para a variável resposta pertence à classe de distribuições simétricas. O objetivo geral desse trabalho é a modelagem desta classe no contexto bayesiano, em particular a modelagem da classe de modelos não-lineares heterocedásticos simétricos. Vale ressaltar que esse trabalho tem ligação com duas linhas de pesquisa, a saber: a inferência estatística abordando aspectos da teoria assintótica e a inferência bayesiana considerando aspectos de modelagem e critérios de seleção de modelos baseados em métodos de simulação de Monte Carlo em Cadeia de Markov (MCMC). Uma primeira etapa consiste em apresentar a classe dos modelos não-lineares heterocedásticos simétricos bem como a inferência clássica dos parâmetros desses modelos. Posteriormente...

## Uso de Métodos Bayesianos para Confiabilidade de Redes; Using Bayesian methods for network reliability

Oliveira, Sandra Cristina de
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
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Neste trabalho apresentamos uma análise Bayesiana para confiabilidade de sistemas de redes usando métodos de simulação de Monte Carlo via Cadeias de Markov. Assumimos diferentes densidades a priori para as confiabilidades dos componentes individuais, com o objetivo de obtermos sumários de interesse. A metodologia é exemplificada condiderando um sistema de rede com sete componentes e um caso especial de sistema complexo composto por nove componentes. Consideramos ainda confiabilidade de redes tipo k-out--of-m com alguns exemplos numéricos; In this work we present a Bayesian approach for network reliability systems using Marov Chain Monte Carlo methods. We assume different prior densities for the individual component reliabilities th to get the posterior summaries of interest. The methodology is exemplified considering a network system with seven components and a special case of complex system with nine components. We also consider k-out-of-m system reliabiility with some numerical examples

## New volatility models under a Bayesian perspective: a case study

Cuervo,Edilberto Cepeda; Achcar,Jorge Alberto; Barossi-Filho,Milton
Tipo: Artigo de Revista Científica Formato: text/html
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In this paper, we present a brief description of ARCH, GARCH and EGARCH models. Usually, their parameter estimates are obtained using maximum likelihood methods. Considering new methodological processes to model the volatilities of time series, we need to use other inference approach to get estimates for the parameters of the models, since we can encouter great difficulties in obtaining the maximum likelihood estimates due to the complexity of the likelihood function. In this way, we obtain the inferences for the volatilities of time series under a Bayesian approach, especially using popular simulation algorithms such as the Markov Chain Monte Carlo (MCMC) methods. As an application to illustrate the proposed methodology, we analyze a financial time series of the Gillette Company ranging from January, 1999 to May, 2003.

## Comment on "Bayesian evidence: can we beat MultiNest using traditional MCMC methods", by Rutger van Haasteren (arXiv:0911.2150)

Feroz, F.; Hobson, M. P.; Trotta, R.
Tipo: Artigo de Revista Científica
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In arXiv:0911.2150, Rutger van Haasteren seeks to criticize the nested sampling algorithm for Bayesian data analysis in general and its MultiNest implementation in particular. He introduces a new method for evidence evaluation based on the idea of Voronoi tessellation and requiring samples from the posterior distribution obtained through MCMC based methods. He compares its accuracy and efficiency with MultiNest, concluding that it outperforms MultiNest in several cases. This comparison is completely unfair since the proposed method can not perform the complete Bayesian data analysis including posterior exploration and evidence evaluation on its own while MultiNest allows one to perform Bayesian data analysis end to end. Furthermore, their criticism of nested sampling (and in turn MultiNest) is based on a few conceptual misunderstandings of the algorithm. Here we seek to set the record straight.; Comment: 5 pages, 1 figure, added arXiv numbers to the references

## Non-asymptotic Error Bounds for Sequential MCMC Methods in Multimodal Settings

Schweizer, Nikolaus
Tipo: Artigo de Revista Científica
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We prove non-asymptotic error bounds for Sequential MCMC methods in the case of multimodal target distributions. Our bounds depend in an explicit way on upper bounds on relative densities, on constants associated with local mixing properties of the MCMC dynamics, namely, local spectral gaps and local hyperboundedness, and on the amount of probability mass shifted between effectively disconnected components of the state space.

## LISA Data Analysis using MCMC methods

Cornish, Neil J.; Crowder, Jeff
Tipo: Artigo de Revista Científica
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The Laser Interferometer Space Antenna (LISA) is expected to simultaneously detect many thousands of low frequency gravitational wave signals. This presents a data analysis challenge that is very different to the one encountered in ground based gravitational wave astronomy. LISA data analysis requires the identification of individual signals from a data stream containing an unknown number of overlapping signals. Because of the signal overlaps, a global fit to all the signals has to be performed in order to avoid biasing the solution. However, performing such a global fit requires the exploration of an enormous parameter space with a dimension upwards of 50,000. Markov Chain Monte Carlo (MCMC) methods offer a very promising solution to the LISA data analysis problem. MCMC algorithms are able to efficiently explore large parameter spaces, simultaneously providing parameter estimates, error analyses and even model selection. Here we present the first application of MCMC methods to simulated LISA data and demonstrate the great potential of the MCMC approach. Our implementation uses a generalized F-statistic to evaluate the likelihoods, and simulated annealing to speed convergence of the Markov chains. As a final step we super-cool the chains to extract maximum likelihood estimates...

## Efficient Bayesian inference for stochastic volatility models with ensemble MCMC methods

Shestopaloff, Alexander Y.; Neal, Radford M.
Tipo: Artigo de Revista Científica
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In this paper, we introduce efficient ensemble Markov Chain Monte Carlo (MCMC) sampling methods for Bayesian computations in the univariate stochastic volatility model. We compare the performance of our ensemble MCMC methods with an improved version of a recent sampler of Kastner and Fruwirth-Schnatter (2014). We show that ensemble samplers are more efficient than this state of the art sampler by a factor of about 3.1, on a data set simulated from the stochastic volatility model. This performance gain is achieved without the ensemble MCMC sampler relying on the assumption that the latent process is linear and Gaussian, unlike the sampler of Kastner and Fruwirth-Schnatter.

## CosmoHammer: Cosmological parameter estimation with the MCMC Hammer

Akeret, Joël; Seehars, Sebastian; Amara, Adam; Refregier, Alexandre; Csillaghy, André
Tipo: Artigo de Revista Científica
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We study the benefits and limits of parallelised Markov chain Monte Carlo (MCMC) sampling in cosmology. MCMC methods are widely used for the estimation of cosmological parameters from a given set of observations and are typically based on the Metropolis-Hastings algorithm. Some of the required calculations can however be computationally intensive, meaning that a single long chain can take several hours or days to calculate. In practice, this can be limiting, since the MCMC process needs to be performed many times to test the impact of possible systematics and to understand the robustness of the measurements being made. To achieve greater speed through parallelisation, MCMC algorithms need to have short auto-correlation times and minimal overheads caused by tuning and burn-in. The resulting scalability is hence influenced by two factors, the MCMC overheads and the parallelisation costs. In order to efficiently distribute the MCMC sampling over thousands of cores on modern cloud computing infrastructure, we developed a Python framework called CosmoHammer which embeds emcee, an implementation by Foreman-Mackey et al. (2012) of the affine invariant ensemble sampler by Goodman and Weare (2010). We test the performance of CosmoHammer for cosmological parameter estimation from cosmic microwave background data. While Metropolis-Hastings is dominated by overheads...

## Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems using MCMC Methods

Gilavert, Clément; Moussaoui, Saïd; Idier, Jérôme
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky factorization, induce an excessive numerical complexity and memory requirement, sequential coordinate sampling methods present a low rate of convergence. Based on the reversible jump Markov chain framework, this paper proposes an efficient Gaussian sampling algorithm having a reduced computation cost and memory usage. The main feature of the algorithm is to perform an approximate resolution of a linear system with a truncation level adjusted using a self-tuning adaptive scheme allowing to achieve the minimal computation cost. The connection between this algorithm and some existing strategies is discussed and its efficiency is illustrated on a linear inverse problem of image resolution enhancement.; Comment: 20 pages, 10 figures, under review for journal publication

## Complexity Analysis of Accelerated MCMC Methods for Bayesian Inversion

Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M.
Tipo: Artigo de Revista Científica
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We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior distribution, given data $\delta$. Particular attention is given to bounds on the overall work required to achieve a prescribed error level $\varepsilon$. Specifically, we first bound the computational complexity of "plain" MCMC, based on combining MCMC sampling with linear complexity multilevel solvers for elliptic PDE. Our (new) work versus accuracy bounds show that the complexity of this approach can be quite prohibitive. Two strategies for reducing the computational complexity are then proposed and analyzed: first, a sparse, parametric and deterministic generalized polynomial chaos (gpc) "surrogate" representation of the forward response map of the PDE over the entire parameter space, and, second, a novel Multi-Level Markov Chain Monte Carlo (MLMCMC) strategy which utilizes sampling from a multilevel discretization of the posterior and of the forward PDE. For both of these strategies we derive asymptotic bounds on work versus accuracy, and hence asymptotic bounds on the computational complexity of the algorithms. In particular we provide sufficient conditions on the regularity of the unknown coefficients of the PDE...

## MCMC methods for Gaussian process models using fast approximations for the likelihood

Tipo: Artigo de Revista Científica
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Gaussian Process (GP) models are a powerful and flexible tool for non-parametric regression and classification. Computation for GP models is intensive, since computing the posterior density, $\pi$, for covariance function parameters requires computation of the covariance matrix, C, a $pn^2$ operation, where p is the number of covariates and n is the number of training cases, and then inversion of C, an $n^3$ operation. We introduce MCMC methods based on the "temporary mapping and caching" framework, using a fast approximation, $\pi^*$, as the distribution needed to construct the temporary space. We propose two implementations under this scheme: "mapping to a discretizing chain", and "mapping with tempered transitions", both of which are exactly correct MCMC methods for sampling $\pi$, even though their transitions are constructed using an approximation. These methods are equivalent when their tuning parameters are set at the simplest values, but differ in general. We compare how well these methods work when using several approximations, finding on synthetic datasets that a $\pi^*$ based on the "Subset of Data" (SOD) method is almost always more efficient than standard MCMC using only $\pi$. On some datasets, a more sophisticated $\pi^*$ based on the "Nystr\"om-Cholesky" method works better than SOD.

## Markov Chain Monte Carlo methods applied to measuring the fine structure constant from quasar spectroscopy

King, Julian A.; Mortlock, Daniel J.; Webb, John K.; Murphy, Michael T.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Recent attempts to constrain cosmological variation in the fine structure constant, alpha, using quasar absorption lines have yielded two statistical samples which initially appear to be inconsistent. One of these samples was subsequently demonstrated to not pass consistency tests; it appears that the optimisation algorithm used to fit the model to the spectra failed. Nevertheless, the results of the other hinge on the robustness of the spectral fitting program VPFIT, which has been tested through simulation but not through direct exploration of the likelihood function. We present the application of Markov Chain Monte Carlo (MCMC) methods to this problem, and demonstrate that VPFIT produces similar values and uncertainties for (Delta alpha)/(alpha), the fractional change in the fine structure constant, as our MCMC algorithm, and thus that VPFIT is reliable.; Comment: IAU 2009 JD9 conference proceedings. 6 pages, 2 figures. MmSAI, vol. 80 in press Paolo Molaro & Elisabeth Vangioni eds

## Bayesian evidence: can we beat MultiNest using traditional MCMC methods?

van Haasteren, Rutger
Tipo: Artigo de Revista Científica
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Markov Chain Monte Carlo (MCMC) methods have revolutionised Bayesian data analysis over the years by making the direct computation of posterior probability densities feasible on modern workstations. However, the calculation of the prior predictive, the Bayesian evidence, has proved to be notoriously difficult with standard techniques. In this work a method is presented that lets one calculate the Bayesian evidence using nothing but the results from standard MCMC algorithms, like Metropolis-Hastings. This new method is compared to other methods like MultiNest, and greatly outperforms the latter in several cases. One of the toy problems considered in this work is the analysis of mock pulsar timing data, as encountered in pulsar timing array projects. This method is expected to be useful as well in other problems in astrophysics, cosmology and particle physics.; Comment: 9 pages, 8 figures, submitted to mnras

## MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster

Cotter, S. L.; Roberts, G. O.; Stuart, A. M.; White, D.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods, applicable whenever the target measure has density with respect to a Gaussian process or Gaussian random field reference measure, which ensures that their speed of convergence is robust under mesh refinement. Gaussian processes or random fields are fields whose marginal distributions, when evaluated at any finite set of $N$ points, are $\mathbb{R}^N$-valued Gaussians. The algorithmic approach that we describe is applicable not only when the desired probability measure has density with respect to a Gaussian process or Gaussian random field reference measure, but also to some useful non-Gaussian reference measures constructed through random truncation. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modelling strategy. These Gaussian-based reference measures are a very flexible modelling tool...

## MCMC Methods for Entropy Optimization and Nonlinear Network Coding

Tipo: Book Section; PeerReviewed Formato: application/pdf
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Although determining the space of entropic vectors for n random variables, denoted by Γ^*_n, is crucial for solving a large class of network information theory problems, there has been scant progress in explicitly characterizing Γ^*_n for n ≥ 4. In this paper, we present a certain characterization of quasi-uniform distributions that allows one to numerically stake out the entropic region via a random walk to any desired accuracy. When coupled with Monte Carlo Markov Chain (MCMC) methods, one may “bias” the random walk so as to maximize certain functions of the entropy vector. As an example, we look at maximizing the violation of the Ingleton inequality for four random variables and report a violation well in excess of what has been previously available in the literature. Inspired by the MCMC method, we also propose a framework for designing optimal nonlinear network codes via performing a random walk over certain truth tables. We show that the method can be decentralized and demonstrate its efficacy by applying it to the Vamos network and a certain storage problem from [1].

## Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods

O'Neill, Philip D; Balding, David; Becker, Niels; Eerola, Mervi; Mollison, Denis
Fonte: Blackwell Publishing Ltd Publicador: Blackwell Publishing Ltd
Tipo: Artigo de Revista Científica
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The analysis of infectious disease data presents challenges arising from the dependence in the data and the fact that only part of the transmission process is observable. These difficulties are usually overcome by making simplifying assumptions. The paper explores the use of Markov chain Monte Carlo (MCMC) methods for the analysis of infectious disease data, with the hope that they will permit analyses to be made under more realistic assumptions. Two important kinds of data sets are considered, containing temporal and non-temporal information, from outbreaks of measles and influenza. Stochastic epidemic models are used to describe the processes that generate the data. MCMC methods are then employed to perform inference in a Bayesian context for the model parameters. The MCMC methods used include standard algorithms, such as the Metropolis-Hastings algorithm and the Gibbs sampler, as well as a new method that involves likelihood approximation. It is found that standard algorithms perform well in some situations but can exhibit serious convergence difficulties in others. The inferences that we obtain are in broad agreement with estimates obtained by other methods where they are available. However, we can also provide inferences for parameters which have not been reported in previous analyses.

## Iterative Multiuser Detection based on Monte Carlo Probabilistic Data Association

Shi, Zhenning; Reed, Mark
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Conference paper
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Multiple-Access Interference (MAI) has been considered as a major performance-limiting factor in the next-generation CDMA systems. Multiuser detection (MUD) methods have been proposed to mitigate the MAI from the co-channel users by incoporating the cross-correlation properties between users. Recently, two classes of emerging techniques, probabilistic data association (PDA) and Markov Chain Monte Carlo (MCMC) methods, have been applied to the multiuser detection. In this paper, we present a new method, named Monte Carlo PDA (MC-PDA), that incorporates the concepts of both to give a more reliable inference of the CDMA symbols by appropriately modelling and updating the MAI. The methodology is general and can be applied to other communication channels.