Lecture Hall Partitions

We prove a finite version of the well-known theorem that says that the number of partitions of an integer N into distinct parts is equal to the number of partitions of N into odd parts. Our version says that the number of lecture hall partitions of length n of N equals the number of partitions of N into small odd parts: 1,3,5, ldots, 2n-1 . We give two proofs: one via Bott's formula for the Poincaré series of the affine Coxeter group , and one direct proof.     

On the origin of residual dipolar couplings from denatured proteins

Effects of steric obstruction on random flight chains are examined. Spatial probability distributions are elaborated to calculate residual dipolar couplings and residual chemical shift anisotropy, parameters that are acquired by NMR spectroscopy from solutes dissolved in dilute liquid crystals. Calculations yield chain length and residue position-dependent values in good agreement with simulations to provide understanding of recently acquired data from denatured proteins.     

Kinetic transport theory with quantum coherence

We derive transport equations for fermions and bosons in spatially or temporally varying backgrounds with special symmetries, by use of the Schwinger-Keldysh formalism. In a noninteracting theory the coherence information is shown to be encoded in new singular shells for the 2-point function. Imposing this phase space structure to the interacting theory leads to a a self-consistent equation of motion for a physcial density matrix, including coherence and a well defined collision integral. The method is applied e.g. to demonstrate how an initially coherent out-of-equlibrium state approaches equlibrium through decoherence and thermalization.     

Critical behavior of non-order-parameter fields

We show that all of the relevant features of a phase transition can be determined using a non-order-parameter field which is a physical state of the theory. This fact allows us to describe the deconfining transition of the pure Yang-Mills theory via the physical excitations rather than using the Polyakov loop.     

Strongly first order electroweak phase transition induced by primordial hypermagnetic fields

We consider the effect of the presence of a hypermagnetic field at the electroweak phase transition. Screening of the Z-component inside a bubble of the broken phase delays the phase transition and makes it stronger first order. We show that the sphaleron constraint can be evaded for m_H up to 100 GeV if a B_Y0.3T² exists at the time of the EW phase transition, thus resurrecting the possibility for baryogenesis within the minimal standard model (provided enough CP violation can be obtained). We estimate that for m_H100 GeV the Higgs condensate behaves like a type II superconductor with Z-vortices penetrating the bubble. Also, for such high Higgs masses the minimum B_Y field required for a strong first order phase transition is large enough to render the W-field unstable towards forming a condensate which changes the simple picture of the symmetry breaking.     

Prenatal stress and subsequent exposure to chronic mild stress influence dendritic spine density and morphology in the rat medial prefrontal cortex

Background  

Both prenatal stress (PS) and postnatal chronic mild stress (CMS) are associated with behavioral and mood disturbances in humans and rodents. The aim of this study was to reveal putative PS- and/or CMS-related changes in basal spine morphology and density of pyramidal neurons in the rat medial prefrontal cortex (mPFC).     

Spectral and network methods in the analysis of correlation matrices of stock returns

Correlation matrices inferred from stock return time series contain information on the behaviour of the market, especially on clusters of highly correlating stocks. Here we study a subset of New York Stock Exchange (NYSE) traded stocks and compare three different methods of analysis: (i) spectral analysis, i.e. investigation of the eigenvalue-eigenvector pairs of the correlation matrix, (ii) asset trees, obtained by constructing the maximal spanning tree of the correlation matrix, and (iii) asset graphs, which are networks in which the strongest correlations are depicted as edges. We illustrate and discuss the localisation of the most significant modes of fluctuation, i.e. eigenvectors corresponding to the largest eigenvalues, on the asset trees and graphs.     

A novel particle sampling system for physico-chemical and toxicological characterization of emissions

Several studies have shown that combustion-derived fine particles cause adverse health effects. Previous toxicological studies on combustion-derived fine particles have rarely involved multiple endpoints and a detailed characterization of chemical composition. In this study, we developed a novel particle sampling system for toxicological and chemical characterization (PSTC), consisting of the Dekati Gravimetric Impactor (DGI) and a porous tube diluter. Physico-chemical and toxicological properties of the particles emitted from various combustion sources were evaluated in two measurement campaigns. First, the DGI was compared with the High-Volume Cascade Impactor (HVCI) and to the Dekati Low-Pressure Impactor (DLPI), using the same dilution system and the same sampling conditions. Only small differences were observed in the mass size distributions, total particulate matter (PM), and particulate matter with diameter smaller than 1 um (PM(1)) concentrations and geometric mass mean diameters (GMMD) between these three impactors. Second, the PSTC was compared with the HVCI sampling system, which has been optimal for collection of particulate samples for toxicological and chemical analyses. Differences were observed in the mass size distributions, total PM and PM(1) emissions, and GMMDs, probably due to the different sampling and dilution methods as well as different sampling substrates which affected the behavior of semi-volatile and volatile organic compounds. However, no significant differences were detected in the in vitro measurements of cytotoxicity between the samples collected with the PSTC and the HVCI systems. In measurements of genotoxicity, significant differences between the two sampling systems were seen only with the particles emitted from the sauna stove. In conclusion, due to compact size, PSTC is an applicable method for use in particle sampling as part of the toxicological and chemical characterization of particulate emissions from different combustion sources. It offers some advantages compared to the previously used high-volume sampling methods including compactness for field measurements, simple preparation of sample substrates and high extraction efficiency.     

Kinetics of photoinduced electron transfer in polythiophene-porphyrin-fullerene molecular films

Photoinduced electron transfer (ET) processes were studied by the time-resolved Maxwell displacement charge (TRMDC) method in bilayer structures consisting of an electron donor-acceptor and conductive polymer monolayers, porphyrin-fullerene dyad and polyhexylthiophene, respectively, both layers prepared by the Langmuir-Blodgett (LB) method. The charge separation involves two fast steps: an intramolecular ET in the dyad molecule followed by an interlayer ET from the polymer to the formed porphyrin radical cation. These fast vertical intra- and interlayer processes could not be time-resolved by the TRMDC method. The lifetime of the charge separated state in the system was extended to hundreds of milliseconds by lateral electron and hole transfers in fullerene and polymer sublayers. The kinetics of the system was described by a model involving two long-living energetically different complete charge separated states. The data analysis indicates that the charge separation has a recombination time of 0.5 s. This is a promising result for possible applications.     

Measured Composite Collision Models: Quantum Trajectory Purities and Channel Divisibility

We investigate a composite quantum collision model with measurements on the memory part, which effectively probe the system. The framework allows us to adjust the measurement strength, thereby tuning the dynamical map of the system. For a two-qubit setup with a symmetric and informationally complete measurement on the memory, we study the divisibility of the resulting dynamics in dependence of the measurement strength. The measurements give rise to quantum trajectories of the system and we show that the average asymptotic purity depends on the specific form of the measurement. With the help of numerical simulations, we demonstrate that the different performance of the measurements is generic and holds for almost all interaction gates between the system and the memory in the composite collision model. The discrete model is then extended to a time-continuous limit.