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Analysis-by-synthesis: Pedestrian tracking with crowd simulation models in a multi-camera video network
For tracking systems consisting of multiple cameras with overlapping field-of-views, homography-based approaches are widely adopted to significantly reduce occlusions among pedestrians by sharing information among multiple views. However, in these approaches, the usage of information under real-world coordinates is only at a preliminary level. Therefore, in this paper, a multi-camera tracking system with integrated crowd simulation is proposed in order to explore the possibility to make homography information more helpful. Two crowd simulators with different simulation strategies are used to investigate the influence of the simulation strategy on the final tracking performance. The performance is evaluated by multiple object tracking precision and accuracy (MOTP and MOTA) metrics, for all the camera views and the results obtained under real-world coordinates. The experimental results demonstrate that crowd simulators boost the tracking performance significantly, especially for crowded scenes with higher density. In addition, a more realistic simulation strategy helps to further improve the overall tracking result
Recovering the potential and order in one-dimensional time-fractional diffusion with unknown initial condition and source *
This paper is concerned with an inverse problem of recovering a potential term and fractional order in a one-dimensional subdiffusion problem, which involves a Djrbashian–Caputo fractional derivative of order α ∈ (0, 1) in time, from the lateral Cauchy data. In the model, we do not assume a full knowledge of the initial data and the source term, since they might be unavailable in some practical applications. We prove the unique recovery of the spatially-dependent potential coefficient and the order α of the derivation simultaneously from the measured trace data at one end point, when the model is equipped with a boundary excitation with a compact support away from t = 0. One of the initial data and the source can also be uniquely determined, provided that the other is known. The analysis employs a representation of the solution and the time analyticity of the associated function. Further, we discuss a two-stage procedure, directly inspired by the analysis, for the numerical identification of the order and potential coefficient, and illustrate the feasibility of the recovery with several numerical experiments
Thermodynamics of lattice QCD with 2 flavours of colour-sextet quarks: A model of walking/conformal Technicolor
QCD with two flavours of massless colour-sextet quarks is considered as a
model for conformal/walking Technicolor. If this theory possess an infrared
fixed point, as indicated by 2-loop perturbation theory, it is a
conformal(unparticle) field theory. If, on the other hand, a chiral condensate
forms on the weak-coupling side of this would-be fixed point, the theory
remains confining. The only difference between such a theory and regular QCD is
that there is a range of momentum scales over which the coupling constant runs
very slowly (walks). In this first analysis, we simulate the lattice version of
QCD with two flavours of staggered quarks at finite temperatures on lattices of
temporal extent and 6. The deconfinement and chiral-symmetry
restoration couplings give us a measure of the scales associated with
confinement and chiral-symmetry breaking. We find that, in contrast to what is
seen with fundamental quarks, these transition couplings are very different.
for each of these transitions increases significantly from
and as expected for the finite temperature transitions of an
asymptotically-free theory. This suggests a walking rather than a conformal
behaviour, in contrast to what is observed with Wilson quarks. In contrast to
what is found for fundamental quarks, the deconfined phase exhibits states in
which the Polyakov loop is oriented in the directions of all three cube roots
of unity. At very weak coupling the states with complex Polyakov loops undergo
a transition to a state with a real, negative Polyakov loop.Comment: 21 pages, 9 figures, Revtex with postscript figures. One extra
reference was added; text is unchanged. Corrected typographical erro
Two fully discrete schemes for fractional diffusion and diffusion-wave equations with nonsmooth data
We consider initial/boundary value problems for the subdiffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two fully discrete schemes based on the piecewise linear Galerkin finite element method in space and convolution quadrature in time with the generating function given by the backward Euler method/second-order backward difference method, and establish error estimates optimal with respect to the regularity of problem data. These two schemes are first- and second-order accurate in time for both smooth and nonsmooth data. Extensive numerical experiments for two-dimensional problems confirm the convergence analysis and robustness of the schemes with respect to data regularity.
Read More: http://epubs.siam.org/doi/10.1137/14097956
Nonlinear Dynamics in the Resonance Lineshape of NbN Superconducting Resonators
In this work we report on unusual nonlinear dynamics measured in the
resonance response of NbN superconducting microwave resonators. The nonlinear
dynamics, occurring at relatively low input powers (2-4 orders of magnitude
lower than Nb), and which include among others, jumps in the resonance
lineshape, hysteresis loops changing direction and resonance frequency shift,
are measured herein using varying input power, applied magnetic field, white
noise and rapid frequency sweeps. Based on these measurement results, we
consider a hypothesis according to which local heating of weak links forming at
the boundaries of the NbN grains are responsible for the observed behavior, and
we show that most of the experimental results are qualitatively consistent with
such hypothesis.Comment: Updated version (of cond-mat/0504582), 16 figure
Thermodynamics of lattice QCD with 2 sextet quarks on N_t=8 lattices
We continue our lattice simulations of QCD with 2 flavours of colour-sextet
quarks as a model for conformal or walking technicolor. A 2-loop perturbative
calculation of the -function which describes the evolution of this
theory's running coupling constant predicts that it has a second zero at a
finite coupling. This non-trivial zero would be an infrared stable fixed point,
in which case the theory with massless quarks would be a conformal field
theory. However, if the interaction between quarks and antiquarks becomes
strong enough that a chiral condensate forms before this IR fixed point is
reached, the theory is QCD-like with spontaneously broken chiral symmetry and
confinement. However, the presence of the nearby IR fixed point means that
there is a range of couplings for which the running coupling evolves very
slowly, i.e. it 'walks'. We are simulating the lattice version of this theory
with staggered quarks at finite temperature studying the changes in couplings
at the deconfinement and chiral-symmetry restoring transitions as the temporal
extent () of the lattice, measured in lattice units, is increased. Our
earlier results on lattices with show both transitions move to weaker
couplings as increases consistent with walking behaviour. In this paper
we extend these calculations to . Although both transition again move to
weaker couplings the change in the coupling at the chiral transition from
to is appreciably smaller than that from to .
This indicates that at we are seeing strong coupling effects and that
we will need results from to determine if the chiral-transition
coupling approaches zero as , as needed for the theory
to walk.Comment: 21 pages Latex(Revtex4) source with 4 postscript figures. v2: added 1
reference. V3: version accepted for publication, section 3 restructured and
interpretation clarified. Section 4 future plans for zero temperature
simulations clarifie
Inverse Problems for Subdiffusion from Observation at an Unknown Terminal Time
Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source, or potential coefficient in a subdiffusion model from the terminal observation have been extensively studied in recent years. However, all existing studies have assumed that the terminal time at which one takes the observation is exactly known. In this work, we present uniqueness and stability results for three canonical inverse problems, e.g., backward problem, inverse source, and inverse potential problems from the terminal observation at an unknown time. The subdiffusive nature of the problem indicates that one can simultaneously determine the terminal time and space-dependent parameter. The analysis is based on explicit solution representations, asymptotic behavior of the Mittag-Leffler function, and mild regularity conditions on the problem data. Further, we present several one- and two-dimensional numerical experiments to illustrate the feasibility of the approach
On the Saturation Phenomenon of Stochastic Gradient Descent for Linear Inverse Problems
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems due to its excellent scalability with respect to data size. The current mathematical theory in the lens of regularization theory predicts that SGD with a polynomially decaying stepsize schedule may suffer from an undesirable saturation phenomenon; i.e., the convergence rate does not further improve with the solution regularity index when it is beyond a certain range. In this work, we present a refined convergence rate analysis of SGD and prove that saturation actually does not occur if the initial stepsize of the schedule is sufficiently small. Several numerical experiments are provided to complement the analysis
On the convergence of stochastic gradient descent for nonlinear inverse problems
In this work, we analyze the regularizing property of the stochastic gradient descent for the numerical solution of a class of nonlinear ill-posed inverse problems in Hilbert spaces. At each step of the iteration, the method randomly chooses one equation from the nonlinear system to obtain an unbiased stochastic estimate of the gradient and then performs a descent step with the estimated gradient. It is a randomized version of the classical Landweber method for nonlinear inverse problems, and it is highly scalable to the problem size and holds significant potential for solving large-scale inverse problems. Under the canonical tangential cone condition, we prove the regularizing property for a priori stopping rules and then establish the convergence rates under a suitable sourcewise condition and a range invariance condition
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