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Crossing Minimization within Graph Embeddings

Shabbeer, Amina; Ozcaglar, Cagri; Bennett, Kristin P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/10/2012 Português
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We propose a novel optimization-based approach to embedding heterogeneous high-dimensional data characterized by a graph. The goal is to create a two-dimensional visualization of the graph structure such that edge-crossings are minimized while preserving proximity relations between nodes. This paper provides a fundamentally new approach for addressing the crossing minimization criteria that exploits Farkas' Lemma to re-express the condition for no edge-crossings as a system of nonlinear inequality constraints. The approach has an intuitive geometric interpretation closely related to support vector machine classification. While the crossing minimization formulation can be utilized in conjunction with any optimization-based embedding objective, here we demonstrate the approach on multidimensional scaling by modifying the stress majorization algorithm to include penalties for edge crossings. The proposed method is used to (1) solve a visualization problem in tuberculosis molecular epidemiology and (2) generate embeddings for a suite of randomly generated graphs designed to challenge the algorithm. Experimental results demonstrate the efficacy of the approach. The proposed edge-crossing constraints and penalty algorithm can be readily adapted to other supervised and unsupervised optimization-based embedding or dimensionality reduction methods. The constraints can be generalized to remove overlaps between any graph components represented as convex polyhedrons including node-edge and node-node intersections.; Comment: Previous versions of this paper are at http://cseweb.ucsd.edu/~lvdmaaten/workshops/nips2010/papers/bennett.pdf and http://www.cs.rpi.edu/research/pdf/11-03.pdf

The Physics of Living Neural Networks

Eckmann, Jean-Pierre; Feinerman, Ofer; Gruendlinger, Leor; Moses, Elisha; Soriano, Jordi; Tlusty, Tsvi
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/07/2010 Português
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Improvements in technique in conjunction with an evolution of the theoretical and conceptual approach to neuronal networks provide a new perspective on living neurons in culture. Organization and connectivity are being measured quantitatively along with other physical quantities such as information, and are being related to function. In this review we first discuss some of these advances, which enable elucidation of structural aspects. We then discuss two recent experimental models that yield some conceptual simplicity. A one-dimensional network enables precise quantitative comparison to analytic models, for example of propagation and information transport. A two-dimensional percolating network gives quantitative information on connectivity of cultured neurons. The physical quantities that emerge as essential characteristics of the network in vitro are propagation speeds, synaptic transmission, information creation and capacity. Potential application to neuronal devices is discussed.; Comment: PACS: 87.18.Sn, 87.19.La, 87.80.-y, 87.80.Xa, 64.60.Ak Keywords: complex systems, neuroscience, neural networks, transport of information, neural connectivity, percolation http://www.weizmann.ac.il/complex/tlusty/papers/PhysRep2007.pdf http://www.weizmann.ac.il/complex/EMoses/pdf/PhysRep-448-56.pdf

Reconstruction of Composite Events in Neutrino Telescopes

Ribordy, Mathieu
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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Neutrino telescopes detect the emission of Cherenkov light resulting from the tracks and showers of charged and neutral current neutrino interactions. These tracks or showers are reconstructed using a corresponding probability density function (PDF) which depends on measured time and location of the detected photo-electrons. We call a composite event the mixed detector response due to the juxtaposition of more than one Cherenkov light source (track or shower). This paper presents the construction of a generic PDF corresponding to a composite hypothesis. This composite PDF is therefore useful to reconstruct an arbitrary event topology and to favor or discard a given event topology hypothesis.; Comment: refeered version, accepted for publication, NIM A

A simple model for the distribution of quiet Sun magnetic field strengths

Almeida, J. Sanchez
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We derive a first order linear differential equation describing the shape of the probability density function of magnetic field strengths in the quiet Sun (PDF). The modeling is very schematic. It considers convective motions which continuously supply and withdraw magnetic structures. In addition, a magnetic amplification mechanism increases the field strength up to a threshold that cannot be exceeded. These three basic ingredients provide PDFs in good agreement with the PDFs produced by realistic numerical simulations of magneto convection, as well as with quiet Sun PDFs inferred from observations. In particular, the distribution is approximately lognormal, and it produces an excess of magnetic fields (i.e., a 'hump' in the distribution) right before the maximum field strength. The success of this simple model may indicate that only a few basic ingredients shape the quiet Sun PDF. Our approach provides a concise parametric representation of the PDF, as required to develop automatic methods of diagnostics.; Comment: Accepted for publication in ApJ. 7 pages and 3 figs

On the distribution of prime multiplets

Gepner, Doron
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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The probability of finding a prime multiplet, i.e., a sequence of primes $p$ and $p+a_i$, $i=1... m$, being all primes where $p$ is some prime less than the integer $n$ is naively $1/log(n)^{m+1}$. It is shown that, in reality, it is proportional to this probability by a constant factor which depends on $a_i$ and $m$ but not on $n$, for large $n$. These constants are appellated as PDF (prime distribution factors). Moreover, it is argued that the PDF depend on the $a_i$ in a "week" way, only on the prime factors of the differences $a_i-a_j$ and not on their exponents. For example $p$ and $p+2^s$ will have the exact same probability for all integer $s>0$. The exact formulae for the PDF ratios are given. Moreover, the actual 'basic' PDF's are calculated exactly and are shown to be bigger than 1, which indicates that primes 'repel' each other. An exact asymptotic formula for the number of basic multiplets is given.

A new phenomenological Investigation of $KMR$ and $MRW$ $unintegrated$ parton distribution functions

Modarres, Majid; Hossenikhani, Hossein; Olanj, Naeimeh; Masouminia, Mohammadreza
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/10/2015 Português
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The longitudinal proton structure function, $F_L(x,Q^2)$, from the $k_t$ factorization formalism by using the unintegrated parton distribution functions (UPDF) which are generated through the KMR and MRW procedures. The LO UPDF of the KMR prescription is extracted, by taking into account the PDF of Martin et al, i.e. MSTW2008-LO and MRST99-NLO and next, the NLO UPDF of the MRW scheme is generated through the set of MSTW2008-NLO PDF as the inputs. The different aspects of $F_L(x,Q^2)$ in the two approaches, as well as its perturbative and non-perturbative parts are calculated. Then the comparison of $F_L(x,Q^2)$ is made with the data given by the ZEUS and H1 collaborations. It is demonstrated that the extracted $F_L(x,Q^2)$ based on the UPDF of two schemes, are consistent to the experimental data, and by a good approximation, they are independent to the input PDF. But the one developed from the KMR prescription, have better agreement to the data with respect to that of MRW. As it has been suggested, by lowering the factorization scale or the Bjorken variable in the related experiments, it may be possible to analyze the present theoretical approaches more accurately.

Characteristic structure of star-forming clouds

Myers, Philip C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/05/2015 Português
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This paper gives a new way to diagnose the star-forming potential of a molecular cloud region from the probability density function of its column density (N-pdf). It gives expressions for the column density and mass profiles of a symmetric filament having the same N-pdf as a filamentary region. The central concentration of this characteristic filament can distinguish regions and can quantify their fertility for star formation. Profiles are calculated for N-pdfs which are pure lognormal, pure power law, or a combination. In relation to models of singular polytropic cylinders, characteristic filaments can be unbound, bound, or collapsing depending on their central concentration. Such filamentary models of the dynamical state of N-pdf gas are more relevant to star-forming regions than are models of spherical collapse. The star formation fertility of a bound or collapsing filament is quantified by its mean mass accretion rate when in radial free fall. For a given mass per length, the fertility increases with the filament mean column density and with its initial concentration. In selected regions the fertility of their characteristic filaments increases with the level of star formation.; Comment: accepted by The Astrophysical Journal

Strong Collapse Turbulence in Quintic Nonlinear Schr\"odinger Equation

Chung, Yeojin; Lushnikov, Pavel M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/04/2011 Português
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We consider the quintic one dimensional nonlinear Schr\"odinger equation with forcing and both linear and nonlinear dissipation. Quintic nonlinearity results in multiple collapse events randomly distributed in space and time forming forced turbulence. Without dissipation each of these collapses produces finite time singularity but dissipative terms prevents actual formation of singularity. In statistical steady state of the developed turbulence the spatial correlation function has a universal form with the correlation length determined by the modulational instability scale. The amplitude fluctuations at that scale are nearly-Gaussian while the large amplitude tail of probability density function (PDF) is strongly non-Gaussian with power-like behavior. The small amplitude nearly-Gaussian fluctuations seed formation of large collapse events. The universal spatio-temporal form of these events together with the PDF for their maximum amplitudes define the power-like tail of PDF for large amplitude fluctuations, i.e., the intermittency of strong turbulence.; Comment: 14 pages, 17 figures

Do measurements of the one-point distribution of aperture-mass improve constraints on cosmology ?

Munshi, Dipak; Valageas, Patrick
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/12/2005 Português
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We study the possibility of using the entire probability distribution function (PDF) of the aperture mass Map and its related cumulative probability distribution function (CPDF) to obtain meaningful constraints on cosmological parameters. Deriving completely analytic expressions for the associated covariance matrices, we construct the Fisher matrix and use it to estimate the accuracy with which various cosmological parameters can be recovered from future surveys using such statistics. This formalism also includes the effect of various noises such as intrinsic ellipticity distribution of galaxies and finite survey size. The estimation errors are then compared with the ones derived from low order moments of the PDF (variance and skewness) to check how efficiently the high Map tail can be used to constrain cosmological parameters such as Omega_m, sigma_8 and dark energy equation of state w_de. We find that for future surveys such as JDEM the full PDF does not bring significant tightening of constraints on cosmology beyond what is already achievable by the joint use of second and third order moments.; Comment: 5 pages, submitted

Intermittency, scaling and the Fokker-Planck approach to fluctuations of the solar wind bulk plasma parameters as seen by the WIND spacecraft

Hnat, Bogdan; Chapman, Sandra C.; Rowlands, George
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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The solar wind provides a natural laboratory for observations of MHD turbulence over extended temporal scales. Here, we apply a model independent method of differencing and rescaling to identify self-similarity in the Probability Density Functions (PDF) of fluctuations in solar wind bulk plasma parameters as seen by the WIND spacecraft. Whereas the fluctuations of speed v and IMF magnitude B are multi-fractal, we find that the fluctuations in the ion density rho, energy densities B^2 and rho v^2 as well as MHD-approximated Poynting flux vB^2 are mono-scaling on the timescales up to ~26 hours. The single curve, which we find to describe the fluctuations PDF of all these quantities up to this timescale, is non-Gaussian. We model this PDF with two approaches-- Fokker-Planck, for which we derive the transport coefficients and associated Langevin equation, and the Castaing distribution that arises from a model for the intermittent turbulent cascade.; Comment: 8 pages, 11 figures. APS format accepted to be published at PRE. Changes include the discussion of the functional form of tails for rescaled PDFs. Introductions has been modified as well. New figure 7 has been added

Using Drell-Yan $A_{FB}$ to constrain PDFs

Bodek, A.; Han, J. Y.; Khukhunaishvili, A.; Sakumoto, W.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/07/2015 Português
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We show that measurements of the forward-backward charge asymmetry ($A_{FB}(M,y)$) of Drell-Yan dilepton events produced at hadron colliders provide a new powerful tool to constrain Parton Distribution Functions (PDFs). PDF uncertainties are the dominant source of systematic error in precision measurements at hadron colliders (e.g. $\chi^2$ values of fits to extract $\sin^2\theta_{eff}^{lept}(M_Z)$ from $A_{FB}(M,y)$ with different PDF replicas can be used to place additional constraints on PDFs.In turn, using these constrained PDFs significantly reduces the PDF errors in precision measurements of electroweak parameters. The measurement of the on-shell $\sin^2\theta_{W}=1-M_W^2/M_Z^2$ is equivalent to an indirect measurement of the W mass. The errors in this indirect measurement of the W mass are competitive with direct measurements. For example, with 200 fb$^{-1}$ at 13 TeV, the expected error in the indirect measurement of the W mass is $\pm$9 MeV.; Comment: 6 pages, 2 Figures. Presented by A. Bodek at The XXIII International Workshop on Deep Inelastic Scattering and Related Subjects April 27 - May 1, 2015 Southern Methodist University, Dallas, Texas 75275, To be published in Proceedings

The nonlinear biasing of the 10k zCOSMOS galaxies up to z~1

Kovac, K.; Porciani, C.; Lilly, S. J.; Marinoni, C.; Guzzo, L.; Cucciati, O.; Zamorani, G.; Iovino, A.; Oesch, P.; Bolzonella, M.; Peng, Y.; Meneux, B.; Zucca, E.; Bardelli, S.; Carollo, C. M.; Contini, T.; Kneib, J. -P.; Fevre, O. Le; Mainieri, V.; Renzi
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/10/2009 Português
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We use the overdensity field reconstructed in the volume of the COSMOS area to study the nonlinear biasing of the zCOSMOS galaxies. The galaxy overdensity field is reconstructed using the current sample of ~8500 accurate zCOSMOS redshifts at I(AB)<22.5 out to z~1 on scales R from 8 to 12 Mpc/h. By comparing the probability distribution function (PDF) of galaxy density contrast delta_g to the lognormal approximation of the PDF of the mass density contrast delta, we obtain the mean biasing function b(delta,z,R) between the galaxy and matter overdensity field and its second moments b(hat) and b(tilde) up to z~1. Over the redshift interval 0.4 = b(delta,z,R) delta is of the following characteristic shape. The function vanishes in the most underdense regions and then sharply rises in a nonlinear way towards the mean densities. is almost a linear tracer of the matter in the overdense regions, up to the most overdense regions in which it is nonlinear again and the local effective slope of vs. delta is smaller than unity. The function is evolving only slightly over the redshift interval 0.4

Levy targeting and the principle of detailed balance

Garbaczewski, Piotr; Stephanovich, Vladimir
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/05/2011 Português
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We investigate confined L\'{e}vy flights under premises of the principle of detailed balance. The master equation admits a transformation to L\'{e}vy - Schr\"{o}dinger semigroup dynamics (akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation). We solve a stochastic targeting problem for arbitrary stability index $0<\mu <2$ of L\'{e}vy drivers: given an invariant probability density function (pdf), specify the jump - type dynamics for which this pdf is a long-time asymptotic target. Our ("$\mu$-targeting") method is exemplified by Cauchy family and Gaussian target pdfs. We solve the reverse engineering problem for so-called L\'{e}vy oscillators: given a quadratic semigroup potential, find an asymptotic pdf for the associated master equation for arbitrary $\mu$.

Molecular Orientation by Intense Single Cycle THz Pulses

Fleischer, Sharly; Zhou, Yan; Field, Robert W.; Nelson, Keith A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/05/2011 Português
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Intense single-cycle THz pulses resonantly interacting with molecular rotations are shown to induce significant field-free orientation under ambient conditions. We calculate and measure the angular distribution associated with THz-driven rotational motion and correlate the THz-induced orientation and alignment in an OCS gas sample.; Comment: 8 pages, 3 figures, presented at OTST 2011, presented at FRISNO 11 PDF available on FRISNO 11 website - http://www.weizmann.ac.il/conferences/frisno11/uploads/Fleischer_Zhou_Field_Nelson_frisno11_PDF.pdf

Local power fluctuations in two-dimensional turbulence

Bandi, M. M.; Connaughton, C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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The statistics of power fluctuations are studied in simulations of two-dimensional turbulence in both inverse (energy) and direct (enstrophy) cascade regimes from both Lagrangian and Eulerian perspectives. The probability density function (PDF) of the appropriately defined dimensionless power is strongly non-gaussian with asymmetric exponential tails. This distribution can be modeled by the distribution of the product of correlated normal variables allowing a derivation of the asymptotics of the tails. The PDF of the dimensionless power is shown to exhibit an empirical Fluctuation Relation. An expression for the entropy production rate is deduced from the asymptotic form of the power PDF and is found to agree very well with the measured entropy rate.; Comment: 5 Pages and 3 figures. Revised version contains additional results for Eulerian power fluctuations, better presentation of the data to facilitate easy comparison between different regimes and an explanation for the value of the entropy rate in the empirical Fluctuation Relation

Density PDFs of Super-Sonic Turbulence

Nordlund, AAke; Padoan, Paolo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/10/1998 Português
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The question of the shape of the density PDF for supersonic turbulence is addressed, using both analytical and numerical methods. For isothermal supersonic turbulence, the PDF is Log-Normal, with a width that scales approximately linearly with the Mach number. For a polytropic equation of state, with an effective gamma smaller than one, the PDF becomes skewed and reminiscent of (but not equal to) a power law on the high density side.; Comment: Interstellar Turbulence, Proceedings of the second Guillermo Haro Conference, held in Puebla, Mexico, Jan, 12-16, 1998, Eds.: Franco, J.; Carraminana, A., Cambridge University Press

The Omega dependence of the velocity divergence distribution

Bernardeau, F.; van de Weygaert, R.; Hivon, E.; Bouchet, F. R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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Analytical studies based on perturbative theory have shown that the moments of the Probability Distribution Function (PDF) of the local smoothed velocity divergence are expected to have a very specific dependence on the density parameter Omega in the quasi-linear regime. This dependence is particularly interesting as it does not involve the possible bias between the galaxy spatial distribution and the underlying mass distribution. This implies a new and promising method for determining a bias-independent value of Omega based on a reliable determination of the velocity divergence PDF. In this paper we study the Omega dependence of the velocity divergence PDF and its first moments in a set of N-body simulations, using the so-called Voronoi and Delaunay methods. We show that this dependence is in agreement with the theoretical prediction, even while the number density of velocity field tracers has been diluted to a value comparable to that available in current galaxy catalogues. In addition, we demonstrate that a sufficiently reliable determination of these statistical quantities is also possible when the measurement of the galaxy peculiar velocities is restricted to the one component along the line-of-sight. Under ideal, noise-free circumstances we can successfully discriminate between low and high Omega.; Comment: 12 pages...

The characteristic blue spectra of accretion disks in quasars as uncovered in the infrared

Kishimoto, Makoto; Antonucci, Robert; Blaes, Omer; Lawrence, Andy; Boisson, Catherine; Albrecht, Marcus; Leipski, Christian
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/07/2008 Português
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Quasars are thought to be powered by supermassive black holes accreting surrounding gas. Central to this picture is a putative accretion disk which is believed to be the source of the majority of the radiative output. It is well known, however, that the most extensively studied disk model -- an optically thick disk which is heated locally by the dissipation of gravitational binding energy -- is apparently contradicted by observations in a few major respects. In particular, the model predicts a specific blue spectral shape asymptotically from the visible to the near-infrared, but this is not generally seen in the visible wavelength region where the disk spectrum is observable. A crucial difficulty was that, toward the infrared, the disk spectrum starts to be hidden under strong hot dust emission from much larger but hitherto unresolved scales, and thus has essentially been impossible to observe. Here we report observations of polarized light interior to the dust-emiting region that enable us to uncover this near-infrared disk spectrum in several quasars. The revealed spectra show that the near-infrared disk spectrum is indeed as blue as predicted. This indicates that, at least for the outer near-infrared-emitting radii, the standard picture of the locally heated disk is approximately correct. The model problems at shorter wavelengths should then be directed toward a better understanding of the inner parts of the revealed disk. The newly uncovered disk emission at large radii...

On a new property of VC classes

Kwapien, Stanislaw
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We give an abstract approach to the results of Adams and Nobel, [1]. It allows to exhibit a new property of VC classes. It should be stressed that the basic ideas of proofs can be found in [1].; Comment: The paper has been withdrawn, because its content is completely coverd by two other articles cf http://www.unc.edu/ The paper has been withdrawn by the author because he was informed that its content is completely covered by two other papers: see http://www.unc.edu/`nobel/links/Papers/VC-Bracketing/pdf and http://arxiv.org/pdf/1009.4434.pdf

Prospects for improving the LHC W boson mass measurement with forward muons

Bozzi, Giuseppe; Citelli, Luca; Vesterinen, Mika; Vicini, Alessandro
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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Measurements of the $W$ boson mass are planned by the ATLAS and CMS experiments, but for the time being, these may be unable to compete with the current world average precision of 15~MeV, due to uncertainties in the PDFs. We discuss the potential of a measurement by the LHCb experiment based on the charged lepton transverse momentum $p_T^{\ell}$ spectrum in $W \to \mu\nu$ decays. The unique forward acceptance of LHCb means that the PDF uncertainties would be anti-correlated with those of $p_T^{\ell}$ based measurements by ATLAS and CMS. We compute an average of ATLAS, CMS and LHCb measurements of $m_W$ from the $p_T^{\ell}$ distribution. Considering PDF uncertainties, this average is a factor of 1.3 more precise than an average of ATLAS and CMS alone. Despite the relatively low rate of $W$ production in LHCb, we estimate that with the Run-II dataset, a measurement could be performed with sufficient experimental precision to exploit this anti-correlation in PDF uncertainties. The modelling of the lepton-pair transverse momentum distribution in the neutral current Drell-Yan process could be a limiting factor of this measurement and will deserve further studies.; Comment: 10 pages, 3 figures, submitted to EPJC