Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second part, see math-ph/0105046. To appear in Reviews in Mathematical Physic

Synchronous visual analysis and editing of RNA sequence and secondary structure alignments using 4SALE

<p>Abstract</p> <p>Background</p> <p>The function of a noncoding RNA sequence is mainly determined by its secondary structure and therefore a family of noncoding RNA sequences is much more conserved on the structural level than on the sequence level. Understanding the function of noncoding RNA sequence families requires two things: a hand-crafted or hand-improved alignment and detailed analyses of the secondary structures. There are several tools available that help performing these tasks, but all of them are specialized and focus on only one aspect, editing the alignment or plotting the secondary structure. The problem is both these tasks need to be performed simultaneously.</p> <p>Findings</p> <p>4SALE is designed to handle sequence and secondary structure information of RNAs synchronously. By including a complete new method of simultaneous visualization and editing RNA sequences and secondary structure information, 4SALE enables to improve and understand RNA sequence and secondary structure evolution much more easily.</p> <p>Conclusion</p> <p>4SALE is a step further for simultaneously handling RNA sequence and secondary structure information. It provides a complete new way of visual monitoring different structural aspects, while editing the alignment. The software is freely available and distributed from its website at <url>http://4sale.bioapps.biozentrum.uni-wuerzburg.de/</url></p

4SALE – A tool for synchronous RNA sequence and secondary structure alignment and editing

BACKGROUND: In sequence analysis the multiple alignment builds the fundament of all proceeding analyses. Errors in an alignment could strongly influence all succeeding analyses and therefore could lead to wrong predictions. Hand-crafted and hand-improved alignments are necessary and meanwhile good common practice. For RNA sequences often the primary sequence as well as a secondary structure consensus is well known, e.g., the cloverleaf structure of the t-RNA. Recently, some alignment editors are proposed that are able to include and model both kinds of information. However, with the advent of a large amount of reliable RNA sequences together with their solved secondary structures (available from e.g. the ITS2 Database), we are faced with the problem to handle sequences and their associated secondary structures synchronously. RESULTS: 4SALE fills this gap. The application allows a fast sequence and synchronous secondary structure alignment for large data sets and for the first time synchronous manual editing of aligned sequences and their secondary structures. This study describes an algorithm for the synchronous alignment of sequences and their associated secondary structures as well as the main features of 4SALE used for further analyses and editing. 4SALE builds an optimal and unique starting point for every RNA sequence and structure analysis. CONCLUSION: 4SALE, which provides an user-friendly and intuitive interface, is a comprehensive toolbox for RNA analysis based on sequence and secondary structure information. The program connects sequence and structure databases like the ITS2 Database to phylogeny programs as for example the CBCAnalyzer. 4SALE is written in JAVA and therefore platform independent. The software is freely available and distributed from the website a

State-level trends in sudden unexpected infant death and immunization in the United States: an ecological study

Background: Sudden unexpected infant death (SUID) continues to be a major contributor to infant mortality in the United States. The objective was to analyze time trends in SUID and their association with immunization coverage. Methods: The number of deaths and live births per year and per state (1992-2015) was obtained from the Centers for Disease Control and Prevention (CDC). We calculated infant mortality rates (i.e., deaths below one year of age) per 1000 live births for SUID. We obtained data on immunization in children aged 19-35 months with three doses or more of diphtheria-tetanus-pertussis (3+ DTP), polio (3+ Polio), and Haemophilus influenzae type b (3+ Hib) as well as four doses or more of DTP (4+ DTP) from the National Immunization Survey, and data on infant sleep position from the Pregnancy Risk Assessment Monitoring System (PRAMS) Study. Data on poverty and race were derived from the Current Population and American Community Surveys of the U.S. Census Bureau. We calculated mean SUID mortality rates with 95% confidence interval (CI) as well as the annual percentage change using breakpoint analysis. We used Poisson regression with random effects to examine the dependence of SUID rates on immunization coverage, adjusting for sleep position and poverty (1996-2015). In a second model, we additionally adjusted for race (2000-2015). Results: Overall, SUID mortality decreased in the United States. The mean annual percent change was - 9.6 (95% CI = - 10.5, - 8.6) between 1992 and 1996, and - 0.3 (95% CI = - 0.4, - 0.1) from 1996 onwards. The adjusted rate ratios for SUID mortality were 0.91 (95% CI = 0.80, 1.03) per 10% increase for 3+ DTP, 0.88 (95% CI = 0.83, 0.95) for 4+ DTP, 1.00 (95% CI = 0.90, 1.10) for 3+ polio, and 0.95 (95% CI = 0.89, 1.02) for 3+ Hib. After additionally adjusting for race, the rate ratios were 0.76 (95% CI = 0.67, 0.85) for 3+ DTP, 0.83 (95% CI = 0.78, 0.89) for 4+ DTP, 0.81 (95% CI = 0.73, 0.90) for 3+ polio, and 0.94 (95% CI = 0.88, 1.00) for 3+ Hib. Conclusions: SUID mortality is decreasing, and inversely related to immunization coverage. However, since 1996, the decline has slowed down

Classical Spin Clusters: Integrability and Dynamical Properties

A pair of exchange‐coupled classical spins with biaxial exchange and single‐site anisotropy represents a Hamiltonian system with two degrees of freedom for which the integrability question is nontrivial. We have found that such a system is completely integrable if the model parameters satisfy a certain condition. For the integrable cases, the second integral of the motion (in addition to the Hamiltonian), which guarantees integrability, is determined explicitly. It can be reconstructed numerically by means of time averages of dynamical variables over all trajectories. In the nonintegrable cases, the existence of the time averages is still guaranteed, but they no longer define an analytic invariant, and their determination is subject to long‐time anomalies. Our numerical calculation of time averages for two lines of initial conditions reveals a number of interesting features of such nonanalytic invariants

Microbial approaches for the assessment of toothpaste efficacy against oral species: A method comparison

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Electro‐Olefination—A Catalyst Free Stereoconvergent Strategy for the Functionalization of Alkenes

Conventional methods carrying out C(sp2)−C(sp2) bond formations are typically mediated by transition‐metal‐based catalysts. Herein, we conceptualize a complementary avenue to access such bonds by exploiting the potential of electrochemistry in combination with organoboron chemistry. We demonstrate a transition metal catalyst‐free electrocoupling between (hetero)aryls and alkenes through readily available alkenyl‐tri(hetero)aryl borate salts (ATBs) in a stereoconvergent fashion. This unprecedented transformation was investigated theoretically and experimentally and led to a library of functionalized alkenes. The concept was then carried further and applied to the synthesis of the natural product pinosylvin and the derivatization of the steroidal dehydroepiandrosterone (DHEA) scaffold