Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems.

Fast scrambling, quantified by the exponential initial growth of out-of-time-ordered correlators (OTOCs), is the ability to efficiently spread quantum correlations among the degrees of freedom of interacting systems and constitutes a characteristic signature of local unstable dynamics. As such, it may equally manifest both in systems displaying chaos or in integrable systems around criticality. Here we go beyond these extreme regimes with an exhaustive study of the interplay between local criticality and chaos right at the intricate phase-space region where the integrability-chaos transition first appears.

Statistical Topology-Distribution and Density Correlations of Winding Numbers in Chiral Systems.

Statistical Topology emerged as topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of universalities. Here, the statistics of winding numbers and of winding number densities are addressed.

Hilbert space average of transition probabilities.

The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition probabilities. In this context we also find that the transition probability of two random uniformly distributed states is connected to the spectral statistics of the considered operator.

Transition from quantum chaos to localization in spin chains.

Recent years have seen an increasing interest in quantum chaos and related aspects of spatially extended systems, such as spin chains. However, the results are strongly system dependent: generic approaches suggest the presence of many-body localization, while analytical calculations for certain system classes, here referred to as the "self-dual case," prove adherence to universal (chaotic) spectral behavior. We address these issues studying the level statistics in the vicinity of the latter case, thereby revealing transitions to many-body localization as well as the appearance of several nonstandard random-matrix universality classes.

Definition of Naturally Processed Peptides Reveals Convergent Presentation of Autoantigenic Topoisomerase I Epitopes in Scleroderma.

Objective: Autoimmune responses to DNA topoisomerase I (topo I) are found in a subset of scleroderma patients who are at high risk for interstitial lung disease (ILD) and mortality. Anti-topo I antibodies (ATAs) are associated with specific HLA-DRB1 alleles, and the frequency of HLA-DR-restricted topo I-specific CD4+ T cells is associated with the presence, severity, and progression of ILD. Although this strongly implicates the presentation of topo I peptides by HLA-DR in scleroderma pathogenesis, the processing and presentation of topo I has not been studied.

Multivariate analysis of short time series in terms of ensembles of correlation matrices.

When dealing with non-stationary systems, for which many time series are available, it is common to divide time in epochs, i.e. smaller time intervals and deal with short time series in the hope to have some form of approximate stationarity on that time scale.

Impact and recovery process of mini flash crashes: An empirical study.

In an Ultrafast Extreme Event (or Mini Flash Crash), the price of a traded stock increases or decreases strongly within milliseconds. We present a detailed study of Ultrafast Extreme Events in stock market data. In contrast to popular belief, our analysis suggests that most of the Ultrafast Extreme Events are not necessarily due to feedbacks in High Frequency Trading: In at least 60 percent of the observed Ultrafast Extreme Events, the largest fraction of the price change is due to a single market order.

Dimeric IgG complexes from IVIg are incapable of inducing in vitro neutrophil degranulation or complement activation.

Purpose: Intravenous immunoglobulin (IVIg) products contain various amounts of dimeric IgG complexes. Current insights into the possible biological activities of these dimers remain controversial, and both immunemodulating and immune-activating effects have been reported. Here, we analyzed the putative immune-activating effects of dimers isolated from IVIg.

Concurrent credit portfolio losses.

We consider the problem of concurrent portfolio losses in two non-overlapping credit portfolios. In order to explore the full statistical dependence structure of such portfolio losses, we estimate their empirical pairwise copulas. Instead of a Gaussian dependence, we typically find a strong asymmetry in the copulas.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison.

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering.

Semiclassical Identification of Periodic Orbits in a Quantum Many-Body System.

While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems feasible, which is nontrivial due to the exponential proliferation of orbits with increasing particle number. Employing a recently discovered duality relation, we focus on the collective, coherent motion that together with the also present incoherent one typically leads to a mixture of regular and chaotic dynamics.

Exact spectral densities of complex noise-plus-structure random matrices.

We use supersymmetry to calculate exact spectral densities for a class of complex random matrix models having the form M=S+LXR, where X is a random noise part X, and S,L,R are fixed structure parts. This is a certain version of the "external field" random matrix models. We find twofold integral formulas for arbitrary structural matrices.

Compounding approach for univariate time series with nonstationary variances.

A defining feature of nonstationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for long time horizons, however, averages over the time-dependent variances.

A methodology for exploring biomarker--phenotype associations: application to flow cytometry data and systemic sclerosis clinical manifestations.

Background: This work seeks to develop a methodology for identifying reliable biomarkers of disease activity, progression and outcome through the identification of significant associations between high-throughput flow cytometry (FC) data and interstitial lung disease (ILD) - a systemic sclerosis (SSc, or scleroderma) clinical phenotype which is the leading cause of morbidity and mortality in SSc. A specific aim of the work involves developing a clinically useful screening tool that could yield accurate assessments of disease state such as the risk or presence of SSc-ILD, the activity of lung involvement and the likelihood to respond to therapeutic intervention. Ultimately this instrument could facilitate a refined stratification of SSc patients into clinically relevant subsets at the time of diagnosis and subsequently during the course of the disease and thus help in preventing bad outcomes from disease progression or unnecessary treatment side effects.

Completing the picture for the smallest eigenvalue of real Wishart matrices.

Rectangular real N×(N+ν) matrices W with a Gaussian distribution appear very frequently in data analysis, condensed matter physics, and quantum field theory. A central question concerns the correlations encoded in the spectral statistics of WW^{T}. The extreme eigenvalues of WW^{T} are of particular interest.

Spectral properties and dynamical tunneling in constant-width billiards.

We determine with unprecedented accuracy the lowest 900 eigenvalues of two quantum constant-width billiards from resonance spectra measured with flat, superconducting microwave resonators. While the classical dynamics of the constant-width billiards is unidirectional, a change of the direction of motion is possible in the corresponding quantum system via dynamical tunneling. This becomes manifest in a splitting of the vast majority of resonances into doublets of nearly degenerate ones.

A random matrix approach to credit risk.

We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero.

Distribution of the smallest eigenvalue in the correlated Wishart model.

Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex and in the real case, we calculate it exactly for arbitrary empirical eigenvalues, i.

Distribution of scattering matrix elements in quantum chaotic scattering.

Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory, the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic scattering systems. To model the universal properties, stochasticity is introduced to the scattering matrix on the level of the Hamiltonian by using random matrices.

Identifying states of a financial market.

The understanding of complex systems has become a central issue because such systems exist in a wide range of scientific disciplines. We here focus on financial markets as an example of a complex system. In particular we analyze financial data from the S&P 500 stocks in the 19-year period 1992-2010.

Use of a human recombinant immunoglobulin G1 CH3 domain as a probe for detecting alternatively folded human IgG in intravenous Ig products.

It has been previously reported that intravenous immunoglobulin (IVIg) contains alternatively folded (aggregation-prone) monomeric immunoglobulin (Ig) G molecules. These alternatively folded IgG molecules may act as precursors for Fc-Fc-mediated dimerization and/or aggregation in IVIg. To study this phenomenon, we set up a fluid-phase binding assay using an acid-shocked (pH 2.

Enrichment of sialylated IgG by lectin fractionation does not enhance the efficacy of immunoglobulin G in a murine model of immune thrombocytopenia.

Intravenous immunoglobulin G (IVIg) is widely used against a range of clinical symptoms. For its use in immune modulating therapies such as treatment of immune thrombocytopenic purpura high doses of IVIg are required. It has been suggested that only a fraction of IVIg causes this anti immune modulating effect.

Eigenvalue densities of real and complex Wishart correlation matrices.

Wishart correlation matrices are the standard model for the statistical analysis of time series. The ensemble averaged eigenvalue density is of considerable practical and theoretical interest. For complex time series and correlation matrices, the eigenvalue density is known exactly.

Exact fidelity and full fidelity statistics in regular and chaotic surroundings.

For a prepared state exact expressions for the time-dependent mean fidelity as well as for the mean inverse participation ratio are obtained analytically. The prepared state is taken as an eigenstate of the unperturbed system, and the studied fidelity is identical to the survival probability. The full distribution functions of fidelity in the long-time limit and of inverse participation ratio are studied numerically and analytically.

Observation of periodic orbits on curved two-dimensional geometries.

We measure elastomechanical spectra for a family of thin shells. We show that these spectra can be described by a "semiclassical" trace formula comprising periodic orbits on geodesics, with the periods of these orbits consistent with those extracted from experiment. The influence of periodic orbits on spectra in the case of two-dimensional curved geometries is thereby demonstrated, where the parameter corresponding to Planck's constant in quantum systems involves the wave number and the curvature radius.