957 research outputs found
An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota
We sketch the outlines of Gian Carlo Rota's interaction with the ideas that
Hermann Grassmann developed in his Ausdehnungslehre of 1844 and 1862, as
adapted and explained by Giuseppe Peano in 1888. This leads us past what Rota
variously called 'Grassmann-Cayley algebra', or 'Peano spaces', to the Whitney
algebra of a matroid, and finally to a resolution of the question "What,
really, was Grassmann's regressive product?". This final question is the
subject of ongoing joint work with Andrea Brini, Francesco Regonati, and
William Schmitt.
The present paper was presented at the conference "The Digital Footprint of
Gian-Carlo Rota: Marbles, Boxes and Philosophy" in Milano on 17 Feb 2009. It
will appear in proceedings of that conference, to be published by Springer
Verlag.Comment: 28 page
Precise Critical Exponents for the Basic Contact Process
We calculated some of the critical exponents of the directed percolation
universality class through exact numerical diagonalisations of the master
operator of the one-dimensional basic contact process. Perusal of the power
method together with finite-size scaling allowed us to achieve a high degree of
accuracy in our estimates with relatively little computational effort. A simple
reasoning leading to the appropriate choice of the microscopic time scale for
time-dependent simulations of Markov chains within the so called quantum chain
formulation is discussed. Our approach is applicable to any stochastic process
with a finite number of absorbing states.Comment: LaTeX 2.09, 9 pages, 1 figur
Looking backward: From Euler to Riemann
We survey the main ideas in the early history of the subjects on which
Riemann worked and that led to some of his most important discoveries. The
subjects discussed include the theory of functions of a complex variable,
elliptic and Abelian integrals, the hypergeometric series, the zeta function,
topology, differential geometry, integration, and the notion of space. We shall
see that among Riemann's predecessors in all these fields, one name occupies a
prominent place, this is Leonhard Euler. The final version of this paper will
appear in the book \emph{From Riemann to differential geometry and relativity}
(L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017
Cognitive Information Processing
Contains reports on six research projects.National Institutes of Health (Grant 1 PO1 GM-14940-01)National Institutes of Health (Grant 1 PO1 GM-15006-01)Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E)Project MAC, an M. I. T. research programAdvanced Research Projects Agency, Department of Defense, under Office of Naval Research Contract Nonr-4102-(01
Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution
A birth-death process is a continuous-time Markov chain that counts the
number of particles in a system over time. In the general process with
current particles, a new particle is born with instantaneous rate
and a particle dies with instantaneous rate . Currently no robust and
efficient method exists to evaluate the finite-time transition probabilities in
a general birth-death process with arbitrary birth and death rates. In this
paper, we first revisit the theory of continued fractions to obtain expressions
for the Laplace transforms of these transition probabilities and make explicit
an important derivation connecting transition probabilities and continued
fractions. We then develop an efficient algorithm for computing these
probabilities that analyzes the error associated with approximations in the
method. We demonstrate that this error-controlled method agrees with known
solutions and outperforms previous approaches to computing these probabilities.
Finally, we apply our novel method to several important problems in ecology,
evolution, and genetics
Mutation Spectrum of the ABCA4 Gene in 335 Stargardt Disease Patients From a Multicenter German Cohort-Impact of Selected Deep Intronic Variants and Common SNPs
PURPOSE. Stargardt disease (STGD1) is an autosomal recessive retinopathy, caused by mutations in the retina-specific ATP-binding cassette transporter (ABCA4) gene. To establish the mutational spectrum and to assess effects of selected deep intronic and common genetic variants on disease, we performed a comprehensive sequence analysis in a large cohort of German STGD1 patients. METHODS. DNA samples of 335 STGD1 patients were analyzed for ABCA4 mutations in its 50 coding exons and adjacent intronic sequences by resequencing array technology or next generation sequencing (NGS). Parts of intron 30 and 36 were screened by Sanger chain-terminating dideoxynucleotide sequencing. An in vitro splicing assay was used to test selected variants for their splicing behavior. By logistic regression analysis we assessed the association of common ABCA4 alleles while a multivariate logistic regression model calculated a genetic risk score (GRS). RESULTS. Our analysis identified 148 pathogenic or likely pathogenic mutations, of which 48 constitute so far unpublished ABCA4-associated disease alleles. Four rare deep intronic variants were found once in 472 alleles analyzed. In addition, we identified six risk-modulating common variants. Genetic risk score estimates suggest that defined common ABCA4 variants influence disease risk in carriers of a single pathogenic ABCA4 allele. CONCLUSIONS. Our study adds to the mutational spectrum of the ABCA4 gene. Moreover, in our cohort, deep intronic variants in intron 30 and 36 likely play no or only a minor role in disease pathology. Of note, our findings demonstrate a possible modifying effect of common sequence variants on ABCA4-associated disease
Teleportation of geometric structures in 3D
Simplest quantum teleportation algorithms can be represented in geometric
terms in spaces of dimensions 3 (for real state-vectors) and 4 (for complex
state-vectors). The geometric representation is based on geometric-algebra
coding, a geometric alternative to the tensor-product coding typical of quantum
mechanics. We discuss all the elementary ingredients of the geometric version
of the algorithm: Geometric analogs of states and controlled Pauli gates. Fully
geometric presentation is possible if one employs a nonstandard representation
of directed magnitudes, formulated in terms of colors defined via stereographic
projection of a color wheel, and not by means of directed volumes.Comment: typos corrected, one plot remove
Search for Chargino-Neutralino Associated Production at the Fermilab Tevatron Collider
We have searched in collisions at = 1.8 TeV for events
with three charged leptons and missing transverse energy. In the Minimal
Supersymmetric Standard Model, we expect trilepton events from
chargino-neutralino (\chione \chitwo) pair production, with subsequent decay
into leptons. We observe no candidate , ,
or events in 106 pb integrated
luminosity. We present limits on the sum of the branching ratios times cross
section for the four channels: \sigma_{\chione\chitwo}\cdot
BR(\chione\chitwo\to 3\ell+X) 81.5 \mgev\sp and
M_\chitwo > 82.2 \mgev\sp for , ~\mgev\sp and
M_\squark= M_\gluino.Comment: 9 pages and 3 figure
Search for charged Higgs decays of the top quark using hadronic tau decays
We present the result of a search for charged Higgs decays of the top quark,
produced in collisions at 1.8 TeV. When the charged
Higgs is heavy and decays to a tau lepton, which subsequently decays
hadronically, the resulting events have a unique signature: large missing
transverse energy and the low-charged-multiplicity tau. Data collected in the
period 1992-1993 at the Collider Detector at Fermilab, corresponding to
18.70.7~pb, exclude new regions of combined top quark and charged
Higgs mass, in extensions to the standard model with two Higgs doublets.Comment: uuencoded, gzipped tar file of LaTeX and 6 Postscript figures; 11 pp;
submitted to Phys. Rev.
Inclusive jet cross section in collisions at TeV
The inclusive jet differential cross section has been measured for jet
transverse energies, , from 15 to 440 GeV, in the pseudorapidity region
0.10.7. The results are based on 19.5 pb of data
collected by the CDF collaboration at the Fermilab Tevatron collider. The data
are compared with QCD predictions for various sets of parton distribution
functions. The cross section for jets with GeV is significantly
higher than current predictions based on O() perturbative QCD
calculations. Various possible explanations for the high- excess are
discussed.Comment: 8 pages with 2 eps uu-encoded figures Submitted to Physical Review
Letter
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