46,134 research outputs found
Statistical properties for directional alignment and chasing of players in football games
Focusing on motion of two interacting players in football games, two velocity
vectors for the pair of one player and the nearest opponent player exhibit
strong alignment. Especially, we find that there exists a characteristic
interpersonal distance cm below which the circular variance for
their alignment decreases rapidly. By introducing the order parameter in order to measure degree of alignment of players' velocity vectors, we also
find that the angle distribution between the nearest players' velocity vectors
becomes wrapped Cauchy () and the mixture of von Mises and
wrapped Cauchy distributions (), respectively. To
understand these findings, we construct a simple model for the motion of the
two interacting players with the following rules: chasing between the players
and the reset of the chasing. We numerically show that our model successfully
reproduce the results obtained from the actual data. Moreover, from the
numerical study, we find that there is another characteristic distance cm below which player's chasing starts.Comment: 16pages, 12 figures, 3 table
On high-dimensional sign tests
Sign tests are among the most successful procedures in multivariate
nonparametric statistics. In this paper, we consider several testing problems
in multivariate analysis, directional statistics and multivariate time series
analysis, and we show that, under appropriate symmetry assumptions, the
fixed- multivariate sign tests remain valid in the high-dimensional case.
Remarkably, our asymptotic results are universal, in the sense that, unlike in
most previous works in high-dimensional statistics, may go to infinity in
an arbitrary way as does. We conduct simulations that (i) confirm our
asymptotic results, (ii) reveal that, even for relatively large , chi-square
critical values are to be favoured over the (asymptotically equivalent)
Gaussian ones and (iii) show that, for testing i.i.d.-ness against serial
dependence in the high-dimensional case, Portmanteau sign tests outperform
their competitors in terms of validity-robustness.Comment: Published at http://dx.doi.org/10.3150/15-BEJ710 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
A framework for quantification and physical modeling of cell mixing applied to oscillator synchronization in vertebrate somitogenesis
In development and disease, cells move as they exchange signals. One example is found in vertebrate development, during which the timing of segment formation is set by a ‘segmentation clock’, in which oscillating gene expression is synchronized across a population of cells by Delta-Notch signaling. Delta-Notch signaling requires local cell-cell contact, but in the zebrafish embryonic tailbud, oscillating cells move rapidly, exchanging neighbors. Previous theoretical studies proposed that this relative movement or cell mixing might alter signaling and thereby enhance synchronization. However, it remains unclear whether the mixing timescale in the tissue is in the right range for this effect, because a framework to reliably measure the mixing timescale and compare it with signaling timescale is lacking. Here, we develop such a framework using a quantitative description of cell mixing without the need for an external reference frame and constructing a physical model of cell movement based on the data. Numerical simulations show that mixing with experimentally observed statistics enhances synchronization of coupled phase oscillators, suggesting that mixing in the tailbud is fast enough to affect the coherence of rhythmic gene expression. Our approach will find general application in analyzing the relative movements of communicating cells during development and disease.Fil: Uriu, Koichiro. Kanazawa University; JapónFil: Bhavna, Rajasekaran. Max Planck Institute of Molecular Cell Biology and Genetics; Alemania. Max Planck Institute for the Physics of Complex Systems; AlemaniaFil: Oates, Andrew C.. Francis Crick Institute; Reino Unido. University College London; Reino UnidoFil: Morelli, Luis Guillermo. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigación en Biomedicina de Buenos Aires - Instituto Partner de la Sociedad Max Planck; Argentina. Max Planck Institute for Molecular Physiology; Alemania. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de FÃsica; Argentin
Random Spin-orbit Coupling in Spin Triplet Superconductors: Stacking Faults in Sr_2RuO_4 and CePt_3Si
The random spin-orbit coupling in multicomponent superconductors is
investigated focusing on the non-centrosymmetric superconductor CePt_3Si and
the spin triplet superconductor Sr_2RuO_4. We find novel manifestations of the
random spin-orbit coupling in the multicomponent superconductors with
directional disorders, such as stacking faults. The presence of stacking faults
is indicated for the disordered phase of CePt_3Si and Sr_2RuO_4. It is shown
that the d-vector of spin triplet superconductivity is locked to be d = k_y x -
k_x y with the anisotropy \Delta T_c/T_c0 \sim \bar{\alpha}^2/T_c0 W_z, where
\bar{\alpha}, T_c0, and W_z are the mean square root of random spin-orbit
coupling, the transition temperature in the clean limit, and the kinetic energy
along the c-axis, respectively. This anisotropy is much larger (smaller) than
that in the clean bulk Sr_2RuO_4 (CePt_3Si). These results indicate that the
helical pairing state d = k_y x - k_x y in the eutectic crystal
Sr_2RuO_4-Sr_3Ru_2O_7 is stabilized in contrast to the chiral state d = (k_x
\pm i k_y) z in the bulk Sr_2RuO_4. The unusual variation of T_c in CePt_3Si is
resolved by taking into account the weak pair-breaking effect arising from the
uniform and random spin-orbit couplings. These superconductors provide a basis
for discussing recent topics on Majorana fermions and non-Abelian statistics.Comment: J. Phys. Soc. Jpn. 79 (2010) 08470
Directed expected utility networks
A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, such as, for example, conditional utility independence and generalized additive independence, have more recently started to appear. In this paper, we define a new graphical model, called a directed expected utility network, whose edges depict both probabilistic and utility conditional independences. These embed a very flexible class of utility models, much larger than those usually conceived in standard influence diagrams. Our graphical representation and various transformations of the original graph into a tree structure are then used to guide fast routines for the computation of a decision problem’s expected utilities. We show that our routines generalize those usually utilized in standard influence diagrams’ evaluations under much more restrictive conditions. We then proceed with the construction of a directed expected utility network to support decision makers in the domain of household food security
Connectedness of Poisson cylinders in Euclidean space
We consider the Poisson cylinder model in , . We show
that given any two cylinders and in the
process, there is a sequence of at most other cylinders creating a
connection between and . In particular, this
shows that the union of the cylinders is a connected set, answering a question
appearing in a previous paper. We also show that there are cylinders in the
process that are not connected by a sequence of at most other cylinders.
Thus, the diameter of the cluster of cylinders equals .Comment: 30 page
Probing anisotropies of gravitational-wave backgrounds with a space-based interferometer: geometric properties of antenna patterns and their angular power
We discuss the sensitivity to anisotropies of stochastic gravitational-wave
backgrounds (GWBs) observed via space-based interferometer. In addition to the
unresolved galactic binaries as the most promising GWB source of the planned
Laser Interferometer Space Antenna (LISA), the extragalactic sources for GWBs
might be detected in the future space missions. The anisotropies of the GWBs
thus play a crucial role to discriminate various components of the GWBs. We
study general features of antenna pattern sensitivity to the anisotropies of
GWBs beyond the low-frequency approximation. We show that the sensitivity of
space-based interferometer to GWBs is severely restricted by the data
combinations and the symmetries of the detector configuration. The spherical
harmonic analysis of the antenna pattern functions reveals that the angular
power of the detector response increases with frequency and the detectable
multipole moments with effective sensitivity h_{eff} \sim 10^{-20} Hz^{-1/2}
may reach 8-10 at mHz in the case of the single
LISA detector. However, the cross correlation of optimal interferometric
variables is blind to the monopole (\ell=0) intensity anisotropy, and also to
the dipole (\ell=1) in some case, irrespective of the frequency band. Besides,
all the self-correlated signals are shown to be blind to the odd multipole
moments (\ell=odd), independently of the frequency band.Comment: RevTex4, 22 pages, 6 figures (low resolution), typos correcte
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