Elimination for Systems of Algebraic Differential Equations

We develop new upper bounds for several effective differential elimination techniques for systems of algebraic ordinary and partial differential equations. Differential elimination, also known as decoupling, is the process of eliminating a fixed subset of unknown functions from a system of differential equations in order to obtain differential algebraic consequences of the original system that do not depend on that fixed subset of unknowns. A special case of differential elimination, which we study extensively, is the question of consistency, that is, if the given system of differential equations has a solution. We first look solely at the ``algebraic data of the system of differential equations through the theory of differential kernels to provide a new upper bound for proving the consistency of the system. We then prove a new upper bound for the effective differential Nullstellensatz, which determines a sufficient number of times to differentiate the original system in order to prove its inconsistency. Finally, we study the Rosenfeld-Gröbner algorithm, which approaches differential elimination by decomposing the given system of differential equations into simpler systems. We analyze the complexity of the Rosenfeld-Gröbner algorithm by computing an upper bound for the orders of the derivatives in all intermediate steps and in the output of the algorithm

Laplacians of Covering Complexes

The Laplace operator on a simplicial complex encodes information about the adjacencies between simplices. A relationship between simplicial complexes does not always translate to a relationship between their Laplacians. In this paper we look at the case of covering complexes. A covering of a simplicial complex is built from many copies of simplices of the original complex, maintaining the adjacency relationships between simplices. We show that for dimension at least one, the Laplacian spectrum of a simplicial complex is contained inside the Laplacian spectrum of any of its covering complexes

A reduction algorithm for Volterra integral equations

An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specifically an algorithm that reduces any separable Volterra integral equation into an equivalent one in operator-linear form, i.e. one that only contains iterated integrals. This serves to standardize the presentation of such integral equations so as to only consider those containing iterated integrals. We use the algebraic object of the integral operator, the twisted Rota-Baxter identity, and vertex-edge decorated rooted trees to construct our algorithm.Comment: 18 page

Coherent matter wave inertial sensors for precision measurements in space

We analyze the advantages of using ultra-cold coherent sources of atoms for matter-wave interferometry in space. We present a proof-of-principle experiment that is based on an analysis of the results previously published in [Richard et al., Phys. Rev. Lett., 91, 010405 (2003)] from which we extract the ratio h/m for 87Rb. This measurement shows that a limitation in accuracy arises due to atomic interactions within the Bose-Einstein condensate

Evidence for an Excess of Soft Photons in Hadronic Decays of Z^0

Soft photons inside hadronic jets converted in front of the DELPHI main tracker (TPC) in events of qqbar disintegrations of the Z^0 were studied in the kinematic range 0.2 < E_gamma < 1 GeV and transverse momentum with respect to the closest jet direction p_T < 80 MeV/c. A clear excess of photons in the experimental data as compared to the Monte Carlo predictions is observed. This excess (uncorrected for the photon detection efficiency) is (1.17 +/- 0.06 +/- 0.27) x 10^{-3} gamma/jet in the specified kinematic region, while the expected level of the inner hadronic bremsstrahlung (which is not included in the Monte Carlo) is (0.340 +/- 0.001 +/- 0.038) x 10^{-3} gamma/jet. The ratio of the excess to the predicted bremsstrahlung rate is then (3.4 +/- 0.2 +/- 0.8), which is similar in strength to the anomalous soft photon signal observed in fixed target experiments with hadronic beams.Comment: 37 pages, 9 figures, Accepted by Eur. Phys. J.

Glucagon-like peptide-1 and its class B G protein-coupled receptors: A long march to therapeutic successes

Theglucagon-likepeptide (GLP)-1receptor (GLP-1R) is a class B G protein-coupled receptor (GPCR) that mediates the action of GLP-1, a peptide hormone secretedfromthreemajor tissues inhumans,enteroendocrine L cells in the distal intestine, a cells in the pancreas, and the central nervous system, which exerts important actions useful in the management of type 2 diabetes mellitus and obesity, including glucose homeostasis and regulation of gastric motility and food intake. Peptidic analogs of GLP-1 have been successfully developed with enhanced bioavailability and pharmacological activity. Physiologic and biochemical studies with truncated, chimeric, and mutated peptides and GLP-1R variants, together with ligand-bound crystal structures of the extracellular domain and the first three-dimensional structures of the 7-helical transmembrane domain of class B GPCRs, have provided the basis for a twodomain-binding mechanism of GLP-1 with its cognate receptor. Although efforts in discovering therapeutically viable nonpeptidicGLP-1R agonists have been hampered, small-moleculemodulators offer complementary chemical tools to peptide analogs to investigate ligand-directed biased cellular signaling of GLP-1R. The integrated pharmacological and structural information of different GLP-1 analogs and homologous receptors give new insights into the molecular determinants of GLP-1R ligand selectivity and functional activity, thereby providing novel opportunities in the design and development of more efficacious agents to treat metabolic disorders

Author Correction:Study of 300,486 individuals identifies 148 independent genetic loci influencing general cognitive function

Christina M. Lill, who contributed to analysis of data, was inadvertently omitted from the author list in the originally published version of this article. This has now been corrected in both the PDF and HTML versions of the article