The ee-vector of a simplicial complex

We study the exponential Hilbert series (both coarsely- and finely-graded) of the Stanley-Reisner ring of an abstract simplicial complex, $\Delta$, and we introduce the $e$-vector of $\Delta$, which relates to the coefficients of the exponential Hilbert series. We explore the relationship of the $e$-vector with the classical $f$-vector and $h$-vector of $\Delta$ while simultaneously investigating the geometric information that the $e$-vector encodes about $\Delta$. We then prove a simple combinatorial identity for the $e$-vector in the case where $\Delta$ is an Eulerian manifold

One pot ‘click’ reactions: tandem enantioselective biocatalytic epoxide ring opening and [3+2] azide alkyne cycloaddition

Halohydrin dehalogenase (HheC) can perform enantioselective azidolysis of aromatic epoxides to 1,2-azido alcohols which are subsequently ligated to alkynes producing chiral hydroxy triazoles in a one-pot procedure with excellent enantiomeric excess.

Magnetization dynamics down to zero field in dilute (Cd,Mn)Te quantum wells

The evolution of the magnetization in (Cd,Mn)Te quantum wells after a short pulse of magnetic field was determined from the giant Zeeman shift of spectroscopic lines. The dynamics in absence of magnetic field was found to be up to three orders of magnitude faster than that at 1 T. Hyperfine interaction and strain are mainly responsible for the fast decay. The influence of a hole gas is clearly visible: at zero field anisotropic holes stabilize the system of Mn ions, while in a magnetic field of 1 T they are known to speed up the decay by opening an additional relaxation channel

Structural and paramagnetic properties of dilute Ga1-xMnxN

Systematic investigations of the structural and magnetic properties of single crystal (Ga,Mn)N films grown by metal organic vapor phase epitaxy are presented. High resolution transmission electron microscopy, synchrotron x-ray diffraction, and extended x-ray absorption fine structure studies do not reveal any crystallographic phase separation and indicate that Mn occupies Ga-substitutional sites in the Mn concentration range up to 1%. The magnetic properties as a function of temperature, magnetic field and its orientation with respect to the c-axis of the wurtzite structure can be quantitatively described by the paramagnetic theory of an ensemble of non-interacting Mn$^{3+}$ ions in the relevant crystal field, a conclusion consistent with the x-ray absorption near edge structure analysis. A negligible contribution of Mn in the 2+ charge state points to a low concentration of residual donors in the studied films. Studies on modulation doped p-type (Ga,Mn)N/(Ga,Al)N:Mg heterostructures do not reproduce the high temperature robust ferromagnetism reported recently for this system.Comment: 15 pages, 14 figure

On the structure of the set of bifurcation points of periodic solutions for multiparameter Hamiltonian systems

This paper deals with periodic solutions of the Hamilton equation with many parameters. Theorems on global bifurcation of solutions with periods $2\pi/j,$ $j\in\mathbb{N},$ from a stationary point are proved. The Hessian matrix of the Hamiltonian at the stationary point can be singular. However, it is assumed that the local topological degree of the gradient of the Hamiltonian at the stationary point is nonzero. It is shown that (global) bifurcation points of solutions with given periods can be identified with zeros of appropriate continuous functions on the space of parameters. Explicit formulae for such functions are given in the case when the Hessian matrix of the Hamiltonian at the stationary point is block-diagonal. Symmetry breaking results concerning bifurcation of solutions with different minimal periods are obtained. A geometric description of the set of bifurcation points is given. Examples of constructive application of the theorems proved to analytical and numerical investigation and visualization of the set of all bifurcation points in given domain are provided. This paper is based on a part of the author's thesis [W. Radzki, ``Branching points of periodic solutions of autonomous Hamiltonian systems'' (Polish), PhD thesis, Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, Toru\'{n}, 2005].Comment: 35 pages, 4 figures, PDFLaTe

NA61/SHINE facility at the CERN SPS: beams and detector system

NA61/SHINE (SPS Heavy Ion and Neutrino Experiment) is a multi-purpose experimental facility to study hadron production in hadron-proton, hadron-nucleus and nucleus-nucleus collisions at the CERN Super Proton Synchrotron. It recorded the first physics data with hadron beams in 2009 and with ion beams (secondary 7Be beams) in 2011. NA61/SHINE has greatly profited from the long development of the CERN proton and ion sources and the accelerator chain as well as the H2 beamline of the CERN North Area. The latter has recently been modified to also serve as a fragment separator as needed to produce the Be beams for NA61/SHINE. Numerous components of the NA61/SHINE set-up were inherited from its predecessors, in particular, the last one, the NA49 experiment. Important new detectors and upgrades of the legacy equipment were introduced by the NA61/SHINE Collaboration. This paper describes the state of the NA61/SHINE facility - the beams and the detector system - before the CERN Long Shutdown I, which started in March 2013

Combined In Silico, In Vivo, and In Vitro Studies Shed Insights into the Acute Inflammatory Response in Middle-Aged Mice

We combined in silico, in vivo, and in vitro studies to gain insights into age-dependent changes in acute inflammation in response to bacterial endotoxin (LPS). Time-course cytokine, chemokine, and NO2-/NO3- data from "middle-aged" (6-8 months old) C57BL/6 mice were used to re-parameterize a mechanistic mathematical model of acute inflammation originally calibrated for "young" (2-3 months old) mice. These studies suggested that macrophages from middle-aged mice are more susceptible to cell death, as well as producing higher levels of pro-inflammatory cytokines, vs. macrophages from young mice. In support of the in silico-derived hypotheses, resident peritoneal cells from endotoxemic middle-aged mice exhibited reduced viability and produced elevated levels of TNF-α, IL-6, IL-10, and KC/CXCL1 as compared to cells from young mice. Our studies demonstrate the utility of a combined in silico, in vivo, and in vitro approach to the study of acute inflammation in shock states, and suggest hypotheses with regard to the changes in the cytokine milieu that accompany aging. © 2013 Namas et al

Irradiated Esophageal Cells are Protected from Radiation-Induced Recombination by MnSOD Gene Therapy

Radiation-induced DNA damage is a precursor to mutagenesis and cytotoxicity. During radiotherapy, exposure of healthy tissues can lead to severe side effects. We explored the potential of mitochondrial SOD (MnSOD) gene therapy to protect esophageal, pancreatic and bone marrow cells from radiation-induced genomic instability. Specifically, we measured the frequency of homologous recombination (HR) at an integrated transgene in the Fluorescent Yellow Direct Repeat (FYDR) mice, in which an HR event can give rise to a fluorescent signal. Mitochondrial SOD plasmid/liposome complex (MnSOD-PL) was administered to esophageal cells 24 h prior to 29 Gy upper-body irradiation. Single cell suspensions from FYDR, positive control FYDR-REC, and negative control C57BL/6NHsd (wild-type) mouse esophagus, pancreas and bone marrow were evaluated by flow cytometry. Radiation induced a statistically significant increase in HR 7 days after irradiation compared to unirradiated FYDR mice. MnSOD-PL significantly reduced the induction of HR by radiation at day 7 and also reduced the level of HR in the pancreas. Irradiation of the femur and tibial marrow with 8 Gy also induced a significant increase in HR at 7 days. Radioprotection by intraesophageal administration of MnSOD-PL was correlated with a reduced level of radiation-induced HR in esophageal cells. These results demonstrate the efficacy of MnSOD-PL for suppressing radiation-induced HR in vivo.National Institutes of Health (U.S.) (NIH Grant R01-CA83876-8)National Institute of Allergy and Infectious Diseases (U.S.) (NIH grant U19A1068021)National Institutes of Health (U.S.) (Grant T32-ES07020)United States. Dept. of Energy (DOE DE-FG01-04ER04)National Institutes of Health (U.S.) (NIH P01-CA26735