6,369 research outputs found
Face tracking using a hyperbolic catadioptric omnidirectional system
In the first part of this paper, we present a brief review on catadioptric omnidirectional
systems. The special case of the hyperbolic omnidirectional system is analysed in depth.
The literature shows that a hyperboloidal mirror has two clear advantages over alternative
geometries. Firstly, a hyperboloidal mirror has a single projection centre [1]. Secondly, the
image resolution is uniformly distributed along the mirror’s radius [2].
In the second part of this paper we show empirical results for the detection and tracking
of faces from the omnidirectional images using Viola-Jones method. Both panoramic and
perspective projections, extracted from the omnidirectional image, were used for that purpose.
The omnidirectional image size was 480x480 pixels, in greyscale. The tracking method used
regions of interest (ROIs) set as the result of the detections of faces from a panoramic projection
of the image. In order to avoid losing or duplicating detections, the panoramic projection was
extended horizontally. Duplications were eliminated based on the ROIs established by previous
detections. After a confirmed detection, faces were tracked from perspective projections (which
are called virtual cameras), each one associated with a particular face. The zoom, pan and tilt
of each virtual camera was determined by the ROIs previously computed on the panoramic
image.
The results show that, when using a careful combination of the two projections, good frame
rates can be achieved in the task of tracking faces reliably
Equations of the reaction-diffusion type with a loop algebra structure
A system of equations of the reaction-diffusion type is studied in the
framework of both the direct and the inverse prolongation structure. We find
that this system allows an incomplete prolongation Lie algebra, which is used
to find the spectral problem and a whole class of nonlinear field equations
containing the original ones as a special case.Comment: 16 pages, LaTex. submitted to Inverse Problem
Large Firm Dynamics and the Business Cycle
Do large firm dynamics drive the business cycle? We answer this question by developing a quantitative theory of aggregate fluctuations caused by firm-level disturbances alone. We show that a standard heterogeneous firm dynamics setup already contains in it a theory of the business cycle, without appealing to aggregate shocks. We offer a complete analytical characterization of the law of motion of the aggregate state in this class of models – the firm size distribution – and show that the resulting closed form solutions for aggregate output and productivity dynamics display: (i) persistence, (ii) volatility and (iii) time-varying second moments. We explore the key role of moments of the firm size distribution – and, in particular, the role of large firm dynamics – in shaping aggregate fluctuations, theoretically, quantitatively and in the data
Non-equilibrated post freeze out distributions
We discuss freeze out on the hypersurface with time-like normal vector,
trying to answer how realistic is to assume thermal post freeze out
distributions for measured hadrons. Using simple kinetic models for gradual
freeze out we are able to generate thermal post FO distribution, but only in
highly simplified situation. In a more advanced model, taking into account
rescattering and re-thermalization, the post FO distribution gets more
complicated. The resulting particle distributions are in qualitative agreement
with the experimentally measured pion spectra. Our study also shows that the
obtained post FO distribution functions, although analytically very different
from the Juttner distribution, do look pretty much like thermal distributions
in some range of parameters.Comment: 14 pages, 2 figures, EPJ style, submitted to EPJ
Continuous approximation of binomial lattices
A systematic analysis of a continuous version of a binomial lattice,
containing a real parameter and covering the Toda field equation as
, is carried out in the framework of group theory. The
symmetry algebra of the equation is derived. Reductions by one-dimensional and
two-dimensional subalgebras of the symmetry algebra and their corresponding
subgroups, yield notable field equations in lower dimensions whose solutions
allow to find exact solutions to the original equation. Some reduced equations
turn out to be related to potentials of physical interest, such as the
Fermi-Pasta-Ulam and the Killingbeck potentials, and others. An instanton-like
approximate solution is also obtained which reproduces the Eguchi-Hanson
instanton configuration for . Furthermore, the equation under
consideration is extended to --dimensions. A spherically symmetric form
of this equation, studied by means of the symmetry approach, provides
conformally invariant classes of field equations comprising remarkable special
cases. One of these enables us to establish a connection with the
Euclidean Yang-Mills equations, another appears in the context of Differential
Geometry in relation to the socalled Yamabe problem. All the properties of the
reduced equations are shared by the spherically symmetric generalized field
equation.Comment: 30 pages, LaTeX, no figures. Submitted to Annals of Physic
Freeze out of the expanding system
The freeze out (FO) of the expanding systems, created in relativistic heavy
ion collisions, is discussed. We start with kinetic FO model, which realizes
complete physical FO in a layer of given thickness, and then combine our
gradual FO equations with Bjorken type system expansion into a unified model.
We shall see that the basic FO features, pointed out in the earlier works, are
not smeared out by the expansion.Comment: 3 pages, 2 figure
A bound on 6D N=1 supergravities
We prove that there are only finitely many distinct semi-simple gauge groups
and matter representations possible in consistent 6D chiral (1,0) supergravity
theories with one tensor multiplet. The proof relies only on features of the
low-energy theory; the consistency conditions we impose are that anomalies
should be cancelled by the Green-Schwarz mechanism, and that the kinetic terms
for all fields should be positive in some region of moduli space. This result
does not apply to the case of the non-chiral (1,1) supergravities, which are
not constrained by anomaly cancellation.Comment: 23 pages, no figures; two paragraphs added to the proof in Appendix A
covering the SU(2) and SU(3) case, other minor correction
Picard group of hypersurfaces in toric 3-folds
We show that the usual sufficient criterion for a generic hypersurface in a
smooth projective manifold to have the same Picard number as the ambient
variety can be generalized to hypersurfaces in complete simplicial toric
varieties. This sufficient condition is always satisfied by generic K3 surfaces
embedded in Fano toric 3-folds.Comment: 14 pages. v2: some typos corrected. v3: Slightly changed title. Final
version to appear in Int. J. Math., incorporates many (mainly expository)
changes suggested by the refere
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