Quenched large deviation principle for words in a letter sequence

When we cut an i.i.d. sequence of letters into words according to an independent renewal process, we obtain an i.i.d. sequence of words. In the \emph{annealed} large deviation principle (LDP) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t. the reference law of words. In the present paper we consider the \emph{quenched} LDP, i.e., we condition on a typical letter sequence. We focus on the case where the renewal process has an \emph{algebraic} tail. The rate function turns out to be a sum of two terms, one being the annealed rate function, the other being proportional to the specific relative entropy of the observed law of letters w.r.t. the reference law of letters, with the former being obtained by concatenating the words and randomising the location of the origin. The proportionality constant equals the tail exponent of the renewal process. Earlier work by Birkner considered the case where the renewal process has an exponential tail, in which case the rate function turns out to be the first term on the set where the second term vanishes and to be infinite elsewhere. In a companion paper the annealed and the quenched LDP are applied to the collision local time of transient random walks, and the existence of an intermediate phase for a class of interacting stochastic systems is established.Comment: 41 pages, 2 figures. Acronym LDP spelled out in title, main result strengthened to cover more general "letter" spaces, application to collision local times removed (this part will become a separate manuscript

Copolymer with pinning: variational characterization of the phase diagram

This paper studies a polymer chain in the vicinity of a linear interface separating two immiscible solvents. The polymer consists of random monomer types, while the interface carries random charges. Both the monomer types and the charges are given by i.i.d. sequences of random variables. The configurations of the polymer are directed paths that can make i.i.d. excursions of finite length above and below the interface. The Hamiltonian has two parts: a monomer-solvent interaction ("copolymer") and a monomer-interface interaction ("pinning"). The quenched and the annealed version of the model each undergo a transition from a localized phase (where the polymer stays close to the interface) to a delocalized phase (where the polymer wanders away from the interface). We exploit the approach developed in [5] and [3] to derive variational formulas for the quenched and the annealed free energy per monomer. These variational formulas are analyzed to obtain detailed information on the critical curves separating the two phases and on the typical behavior of the polymer in each of the two phases. Our main results settle a number of open questions.Comment: 46 pages, 9 figure

The effect of disorder on the free-energy for the Random Walk Pinning Model: smoothing of the phase transition and low temperature asymptotics

We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in [5,6,7]. Given a fixed realization of a random walk Y$ on Z^d with jump rate rho (that plays the role of the random medium), we modify the law of a random walk X on Z^d with jump rate 1 by reweighting the paths, giving an energy reward proportional to the intersection time L_t(X,Y)=\int_0^t \ind_{X_s=Y_s}\dd s: the weight of the path under the new measure is exp(beta L_t(X,Y)), beta in R. As beta increases, the system exhibits a delocalization/localization transition: there is a critical value beta_c, such that if beta>beta_c the two walks stick together for almost-all Y realizations. A natural question is that of disorder relevance, that is whether the quenched and annealed systems have the same behavior. In this paper we investigate how the disorder modifies the shape of the free energy curve: (1) We prove that, in dimension d larger or equal to three 3, the presence of disorder makes the phase transition at least of second order. This, in dimension larger or equal to 4, contrasts with the fact that the phase transition of the annealed system is of first order. (2) In any dimension, we prove that disorder modifies the low temperature asymptotic of the free energy.Comment: 18 page

The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class

We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ universality class, not only as regards to scaling exponents but also as regards to the full probability distribution of the height in the long time limit.Comment: Proceedings StatPhys 2

Issues of Processing and Multiple Testing of SELDI-TOF MS Proteomic Data

A new data filtering method for SELDI-TOF MS proteomic spectra data is described. We examined technical repeats (2 per subject) of intensity versus m/z (mass/charge) of bone marrow cell lysate for two groups of childhood leukemia patients: acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL). As others have noted, the type of data processing as well as experimental variability can have a disproportionate impact on the list of interesting proteins (see Baggerly et al. (2004)). We propose a list of processing and multiple testing techniques to correct for 1) background drift; 2) filtering using smooth regression and cross-validated bandwidth selection; 3) peak finding; and 4) methods to correct for multiple testing (van der Laan et al. (2005)). The result is a list of proteins (indexed by m/z) where average expression is significantly different among disease (or treatment, etc.) groups. The procedures are intended to provide a sensible and statistically driven algorithm, which we argue provides a list of proteins that have a significant difference in expression. Given no sources of unmeasured bias (such as confounding of experimental conditions with disease status), proteins found to be statistically significant using this technique have a low probability of being false positives

An altered plasma lipidome-phenome network characterizes heart failure with preserved ejection fraction

AIMS: Heart failure with preserved ejection fraction (HFpEF) is a multifactorial, multisystemic syndrome that involves alterations in lipid metabolism. This study aimed to test whether distinct plasma lipid profiles or lipid entities or both are associated with clinical and functional echocardiographic parameters in HFpEF. METHODS AND RESULTS: We examined the human plasma lipidome in HFpEF patients (n = 18) with left ventricular ejection fraction =50% and N-terminal pro-brain natriuretic peptide (NT-proBNP) >125 pg/mL and control subjects (n = 12) using mass spectrometry-based shotgun lipidomics. The cohort included 8 women and 22 men with average age of 67.8 ± 8.6 SD. The control and disease groups were not significantly different with respect to age, body mass index, systolic and diastolic blood pressure, and waist-to-hip ratio. The disease group experienced more fatigue (P < 0.001), had more often coronary artery disease (P = 0.04), and received more medications (beta-blockers, P < 0.001). The disease group had significantly different levels of HFpEF-relevant parameters, including NT-proBNP (P < 0.001), left ventricular mass index (P = 0.005), left atrial volume index (P = 0.001), and left ventricular filling index (P < 0.001), and lower left ventricular end-diastolic diameter (P = 0.014), with no difference in left ventricular ejection fraction. Significant differences in lipid profiles between HFpEF patients and controls could not be detected, including no significant differences in abundance of circulating lipids binned by carbon chain length or by double bonds, nor at the level of individual lipid species. However, there was a striking correlation between selected lipids with smoking status that was independent of disease status, as well as between specific lipids and hyperlipidaemia [with corresponding significance of either false discovery rate (FDR) <0.1 or FDR < 0.01]. In an exploratory network analysis of correlations, we observed significantly stronger correlations within the HFpEF group between individual lipids from the cholesterol ester and phosphatidylcholine (PC) classes and clinical/echocardiographic parameters such as left atrial volume index, left ventricular end-diastolic diameters, and heart rate (FDR < 0.1). In contrast, the control group showed significantly stronger negative correlations (FDR < 0.1) between individual species from the PC and sphingomyelin classes and left ventricular mass index or systolic blood pressure. CONCLUSIONS: We did not find significant direct associations between plasma lipidomic parameters and HFpEF and therefore could not conclude that any specific lipids are biomarkers of HFpEF. The validation in larger cohort is needed to confidently conclude the absence of first-order associations

Source-Reconstruction of Event-Related Fields Reveals Hyperfunction and Hypofunction of Cortical Circuits in Antipsychotic-Naive, First-Episode Schizophrenia Patients during Mooney Face Processing

Schizophrenia is characterized by dysfunctions in neural circuits that can be investigated with electrophysiological methods, such as EEG and MEG. In the present human study, we examined event-related fields (ERFs), in a sample of medication-naive, first-episode schizophrenia (FE-ScZ) patients (n � 14) and healthy control participants (n � 17) during perception of Mooney faces to investigate the integrity of neuromagnetic responses and their experience-dependent modification. ERF responses were analyzed for M100, M170, and M250components at the sensor and source levels. In addition, we analyzed peak latency and adaptation effects due to stimulus repetition. FE-ScZ patients were characterized by significantly impaired sensory processing, as indicated by a reduced discrimination index (A�). At the sensor level, M100 and M170 responses in FE-ScZ were within the normal range, whereas the M250 response was impaired. However, source localization revealed widespread elevated activity for M100 and M170 in FE-ScZ and delayed peak latencies for the M100 and M250 responses. In addition, M170 source activity in FE-ScZ was not modulated by stimulus repetitions. The present findings suggest that neural circuits in FE-ScZ may be characterized by a disturbed balance between excitation and inhibition that could lead to a failure to gate information flow and abnormal spreading of activity, which is compatible with dysfunctional glutamatergic neurotransmission

Envisioning sustainable tourism futures: An evaluation of the futures wheel method

Methods for researching the future have grown both in variety and rigour, offering new opportunities for understanding sustainable tourism. This paper discusses the value of futures research as a tool for envisioning and planning sustainable tourism futures but observes that there is greater potential for the use of futures methods in tourism. The aim of this paper is to evaluate the usefulness of a particular method known as the futures wheel as a sustainable planning tool for tourism decision makers and researchers. The futures wheel method is combined with a grounded theory approach to capture and distil the tacit knowledge of three 'expert' think tanks. The evaluation suggests that the futures wheel is a useful tool for researching sustainable tourism futures but that its potential may be enhanced if it can be combined with other futures research methods

Tolerance induction through early feeding to prevent food allergy in infants with eczema (TEFFA): rationale, study design, and methods of a randomized controlled trial

BACKGROUND: Up to 8% of all children in industrialized countries suffer from food allergies, whereas children with atopic eczema are affected considerably more frequently. In addition, the type and starting time of weaning foods seem to influence the development of food allergies. However, data from interventional studies on weaning are controversial. The aim of this randomized-controlled clinical trial is to investigate, whether an early introduction of hen's egg (HE), cow's milk (CM), peanut (PN), and hazelnut (HN) in children with atopic eczema can reduce the risk for developing food allergies in the first year of life. METHODS: This is a protocol for a randomized, placebo controlled, double blind, single-center clinical trial. One hundred fifty infants with atopic eczema at 4-8 months of age will be randomized in a 2:1 manner into an active group that will receive rusk-like biscuit powder with HE, CM, PN, and HN (initially approximately 2 mg of each food protein) for 6-8 months or a placebo group, whose participants will receive the same rusk-like biscuit powder without HE, CM, PN, and HN on a daily basis. During the interventional period, the amount of allergens in the study product will be increased three times, each after 6 weeks. All study participants who are sensitized to HE, CM, PN, or HN at the end of the interventional period will undergo an oral food challenge to the respective food in a further visit. Primary endpoint is IgE-mediated food allergy to at least one of the four foods (HE, CM, PN or HN) after 6-8 months of intervention (i.e., at around 1 year of age). Secondary endpoints include multiple food allergies, severity of eczema, wheezing, and sensitization levels against food allergens. DISCUSSION: This clinical trial will assess whether an early introduction of allergenic foods into the diet of children with atopic eczema can prevent the development of food allergies. This trial will contribute to update food allergy prevention guidelines. TRIAL REGISTRATION: German Clinical Trials Register DRKS00016770 . Registered on 09 January 2020