16,238 research outputs found
Comment on `About the magnetic field of a finite wire'
A flaw is pointed out in the justification given by Charitat and Graner [2003
Eur. J. Phys. vol. 24, 267] for the use of the Biot--Savart law in the
calculation of the magnetic field due to a straight current-carrying wire of
finite length.Comment: REVTeX, 3 pages. A slightly expanded version that has been accepted
for publication by Eur. J. Phy
Combining Thesaurus Knowledge and Probabilistic Topic Models
In this paper we present the approach of introducing thesaurus knowledge into
probabilistic topic models. The main idea of the approach is based on the
assumption that the frequencies of semantically related words and phrases,
which are met in the same texts, should be enhanced: this action leads to their
larger contribution into topics found in these texts. We have conducted
experiments with several thesauri and found that for improving topic models, it
is useful to utilize domain-specific knowledge. If a general thesaurus, such as
WordNet, is used, the thesaurus-based improvement of topic models can be
achieved with excluding hyponymy relations in combined topic models.Comment: Accepted to AIST-2017 conference (http://aistconf.ru/). The final
publication will be available at link.springer.co
Correlation inequalities for noninteracting Bose gases
For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0
independent of the number of particles we derive the inequalities _N <
_{N+1}, _N _N _N for i\neq j, \partial
_N/\partial \beta >0 and ^+_N _N. Here N_i is the occupation
number of the ith eigenstate of H^0, \beta is the inverse temperature and the
superscript + refers to adding an extra level to those of H^0. The results
follow from the convexity of the N-particle free energy as a function of N.Comment: a further inequality adde
Collision of High Frequency Plane Gravitational and Electromagnetic Waves
We study the head-on collision of linearly polarized, high frequency plane
gravitational waves and their electromagnetic counterparts in the
Einstein-Maxwell theory. The post-collision space-times are obtained by solving
the vacuum Einstein-Maxwell field equations in the geometrical optics
approximation. The head-on collisions of all possible pairs of these systems of
waves is described and the results are then generalised to non-linearly
polarized waves which exhibit the maximum two degrees of freedom of
polarization.Comment: Latex file, 17 pages, accepted for publication in International
Journal of Modern Physics
The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3
We consider an Euclidean supersymmetric field theory in given by a
supersymmetric perturbation of an underlying massless Gaussian measure
on scalar bosonic and Grassmann fields with covariance the Green's function of
a (stable) L\'evy random walk in . The Green's function depends on the
L\'evy-Khintchine parameter with . For
the interaction is marginal. We prove for
sufficiently small and initial
parameters held in an appropriate domain the existence of a global
renormalization group trajectory uniformly bounded on all renormalization group
scales and therefore on lattices which become arbitrarily fine. At the same
time we establish the existence of the critical (stable) manifold. The
interactions are uniformly bounded away from zero on all scales and therefore
we are constructing a non-Gaussian supersymmetric field theory on all scales.
The interest of this theory comes from the easily established fact that the
Green's function of a (weakly) self-avoiding L\'evy walk in is a second
moment (two point correlation function) of the supersymmetric measure governing
this model. The control of the renormalization group trajectory is a
preparation for the study of the asymptotics of this Green's function. The
rigorous control of the critical renormalization group trajectory is a
preparation for the study of the critical exponents of the (weakly)
self-avoiding L\'evy walk in .Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition
of norms involving fermions to ensure uniqueness. 2. change in the definition
of lattice blocks and lattice polymer activities. 3. Some proofs have been
reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos
corrected.This is the version to appear in Journal of Statistical Physic
Finding Your (3D) Center: 3D Object Detection Using a Learned Loss
Massive semantically labeled datasets are readily available for 2D images, however, are much harder to achieve for 3D scenes. Objects in 3D repositories like ShapeNet are labeled, but regrettably only in isolation, so without context. 3D scenes can be acquired by range scanners on city-level scale, but much fewer with semantic labels. Addressing this disparity, we introduce a new optimization procedure, which allows training for 3D detection with raw 3D scans while using as little as 5% of the object labels and still achieve comparable performance. Our optimization uses two networks. A scene network maps an entire 3D scene to a set of 3D object centers. As we assume the scene not to be labeled by centers, no classic loss, such as Chamfer can be used to train it. Instead, we use another network to emulate the loss. This loss network is trained on a small labeled subset and maps a non-centered 3D object in the presence of distractions to its own center. This function is very similar – and hence can be used instead of – the gradient the supervised loss would provide. Our evaluation documents competitive fidelity at a much lower level of supervision, respectively higher quality at comparable supervision. Supplementary material can be found at: dgriffiths3.github.io
Positionally dependent ^(15)N fraction factors in the UV photolysis of N_2O determined by high resolution FTIR spectroscopy
Positionally dependent fractionation factors for the photolysis of isotopomers of N_2O in natural abundance have been determined by high resolution FTIR spectroscopy at three photolysis wavelengths. Fractionation factors show clear 15N position and photolysis wavelength dependence and are in qualitative agreement with theoretical models but are twice as large. The fractionation factors increase with photolysis wavelength from 193 to 211 nm, with the fractionation factors at 207.6 nm for ^(14)N^(15)N^916)O, ^(15)N^(14)N^(16)O and ^(14)N^(14)N^(18)O equal to −66.5±5‰,−27.1±6‰ and −49±10‰, respectively
Subtleties on energy calculations in the image method
In this pedagogical work we point out a subtle mistake that can be done by
undergraduate or graduate students in the computation of the electrostatic
energy of a system containing charges and perfect conductors if they naively
use the image method. Specifically, we show that the naive expressions for the
electrostatic energy for these systems obtained directly from the image method
are wrong by a factor 1/2. We start our discussion with well known examples,
namely, point charge-perfectly conducting wall and point charge-perfectly
conducting sphere and then proceed to the demonstration of general results,
valid for conductors of arbitrary shapes.Comment: 9 pages, 2 figures; Major change in this version: subsection added to
Sect.4 (theorem generalization). Minor changes: title replaced; corrections
to the English; some explanatory comments adde
A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks
Understanding how the dynamics of a neural network is shaped by the network
structure, and consequently how the network structure facilitates the functions
implemented by the neural system, is at the core of using mathematical models
to elucidate brain functions. This study investigates the tracking dynamics of
continuous attractor neural networks (CANNs). Due to the translational
invariance of neuronal recurrent interactions, CANNs can hold a continuous
family of stationary states. They form a continuous manifold in which the
neural system is neutrally stable. We systematically explore how this property
facilitates the tracking performance of a CANN, which is believed to have clear
correspondence with brain functions. By using the wave functions of the quantum
harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is
decomposed into different motion modes, corresponding to distortions in the
amplitude, position, width or skewness of the network state. We then develop a
perturbative approach that utilizes the dominating movement of the network's
stationary states in the state space. This method allows us to approximate the
network dynamics up to an arbitrary accuracy depending on the order of
perturbation used. We quantify the distortions of a Gaussian bump during
tracking, and study their effects on the tracking performance. Results are
obtained on the maximum speed for a moving stimulus to be trackable and the
reaction time for the network to catch up with an abrupt change in the
stimulus.Comment: 43 pages, 10 figure
Weibull Modulus Estimated by the Non-linear Least Squares Method: A Solution to Deviation Occurring in Traditional Weibull Estimation
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