328 research outputs found
Linear orbits of arbitrary plane curves
The `linear orbit' of a plane curve of degree is its orbit in
under the natural action of \PGL(3). In this paper we obtain
an algorithm computing the degree of the closure of the linear orbit of an
arbitrary plane curve, and give explicit formulas for plane curves with
irreducible singularities. The main tool is an intersection@-theoretic study of
the projective normal cone of a scheme determined by the curve in the
projective space of matrices; this expresses the degree of
the orbit closure in terms of the degrees of suitable loci related to the
limits of the curve. These limits, and the degrees of the corresponding loci,
have been established in previous work.Comment: 33 pages, AmS-TeX 2.
Mach Bands: How Many Models are Possible? Recent Experiemental Findings and Modeling Attempts
Mach bands are illusory bright and dark bands seen where a luminance plateau meets a ramp, as in half-shadows or penumbras. A tremendous amount of work has been devoted to studying the psychophysics and the potential underlying neural circuitry concerning this phenomenon. A number of theoretical models have also been proposed, originating in the seminal studies of Mach himself. The present article reviews the main experimental findings after 1965 and the main recent theories of early vision that have attempted to discount for the effect. It is shown that the different theories share working principles and can be grouped in three clsses: a) feature-based; b) rule-based; and c) filling-in. In order to evaluate individual proposals it is necessary to consider them in the larger picture of visual science and to determine how they contribute to the understanding of vision in general.Air Force Office of Scientific Research (F49620-92-J-0334); Office of Naval Research (N00014-J-4100); COPPE/UFRJ, Brazi
Detecting quantum critical points at finite temperature via quantum teleportation: further models
In [Phys. Rev. A 107, 052420 (2023)] we showed that the quantum teleportation
protocol can be used to detect quantum critical points (QCPs) associated with a
couple of different classes of quantum phase transitions, even when the system
is away from the absolute zero temperature (T=0). Here, working in the
thermodynamic limit (infinite chains), we extend the previous analysis for
several other spin-1/2 models. We investigate the usefulness of the quantum
teleportation protocol to detect the QCPs of those models when the temperature
is either zero or greater than zero. The spin chains we investigate here are
described by the XXZ model, the XY model, and the Ising model, all of them
subjected to an external magnetic field. Specifically, we use a pair of nearest
neighbor qubits from an infinite spin chain at thermal equilibrium with a
reservoir at temperature T as the resource to execute the quantum teleportation
protocol. We show that the ability of this pair of qubits to faithfully
teleport an external qubit from the chain is dramatically affected as we cross
the QCPs related to the aforementioned models. The results here presented
together with the ones of [Phys. Rev. A 107, 052420 (2023)] suggest that the
quantum teleportation protocol is a robust and quite universal tool to detect
QCPs even when the system of interest is far from the absolute zero
temperature.Comment: 15 pages, 23 figures, double column, RevTex4; v2: published versio
Binary differential equations at parabolic and umbilical points for -parameter families of surfaces
We determine local topological types of binary differential equations of
asymptotic curves at parabolic and flat umbilical points for generic
-parameter families of surfaces in by comparing our projective
classification of Monge forms and classification of general BDE obtained by
Tari and Oliver. In particular, generic bifurcations of the parabolic curve are
classified. The flecnodal curve is also examined by direct computations, and we
present new bifurcation diagrams in typical examples.Comment: 20 page
Determining Critical Points of Handwritten Mathematical Symbols Represented as Parametric Curves
We consider the problem of computing critical points of plane curves represented in a finite orthogonal polynomial basis. This is motivated by an approach to the recognition of hand-written mathematical symbols in which the initial data is in such an orthogonal basis and it is desired to avoid ill-conditioned basis conversions. Our main contribution is to assemble the relevant mathematical tools to perform all the necessary operations in the orthogonal polynomial basis. These include implicitization, differentiation, root finding and resultant computation
Gravitational Nanolensing from Subsolar Mass Dark Matter Halos
We investigate the feasibility of extracting the gravitational nanolensing
signal due to the presence of subsolar mass halos within galaxy-sized dark
matter halos. We show that subsolar mass halos in a lensing galaxy can cause
strong nanolensing events with shorter durations and smaller amplitudes than
microlensing events caused by stars. We develop techniques that can be used in
future surveys such as Pan-STARRS, LSST and OMEGA to search for the nanolensing
signal from subsolar mass halos.Comment: 12 pages, 10 figures. Replaced with version accepted for publication
in ApJ. Very minor changes from version
On the Characterization Diagrams of Planar Cubic Hybrid Hyperbolic Polynomial Curve
根据文献[9](WAng g z,yAng Q M.PlAnAr CubIC HybrId HyPErbOlIC POlynOMIAl CurVE And ITS SHAPE ClASSIfICATIOn.PrOgrESS In nATurAl SCIEnCE,2004,14(1):41-46)中提出的H-曲线带奇点或拐点的条件,利用H-曲线奇点、拐点的仿射不变性,给出H-曲线几何特征图的判别法,并找到了不同特征图在三维空间中的关系.该判别法完善了H-曲线的奇异点检测理论,提升了几何特征图维数.In this paper,we propose the geometric characterization diagrams of planar cubic H-curves based on the conditions of singularities for planar cubic H-curves presented by Reference(Wang G Z,Yang Q M.Planar cubic hybrid hyperbolic polynomial curve and its shape classification.Progress In Natural Science,2004,14(1): 41-46) Since inflection points and singularities(loops or cusps) of curves are affinely invariant,we find out the geometrically intuitive relationship of these different geometric characterization diagrams in a common 3-dimension characterization space.This approach completes the theory of detecting singularities of H-curves in the point of elevating geometric characterization diagrams dimension.国家自然科学基金(60773179;60970079;60933008
Phase transitions in rotating neutron stars cores: back bending, stability, corequakes and pulsar timing
The back-bending phenomenon for compact stars is studied by means of
analytical equations of state, for both constant-pressure phase transitions and
the transitions through the mixed-phase region. We restrict ourselves to the
case of normal rotating configurations, with baryon mass below the maximum
allowable baryon mass for non-rotating stars. We use high-precision 2-D
multi-domain spectral code LORENE to search the parameter space for possible
instability regions, and possible changes in the stability character of
rotating stars with phase transitions in their cores. Conditions on the density
jump in constant-pressure phase transitions, leading to the existence of the
unstable segments in the evolutionary sequences of spinning down isolated
normal neutron stars, are derived. Conjectures concerning the existence of two
disjoint families of non-rotating and rotating stationary configurations of
neutron stars are formulated. Particular case of EOSs leading to marginal
instability of static and rotating configurations is also studied: marginal
instability point in non-rotating configurations continues to exist in all
evolutionary spin-down tracks. The fate of rotating stars entering the region
of instability is discussed. The change in radius, energy release, and spin-up
associated with the corequake in rotating neutron star, triggered by the
instability, are calculated. The energy release is found to be very weakly
dependent on the angular momentum of collapsing star.Comment: 13 pages, 15 figures, accepted by A&
PTOPO: A Maple package for the topology of parametric curves
International audiencePTOPO is a MAPLE package computing the topology and describing the geometry of a parametric plane curve. The algorithm behind PTOPO constructs an abstract graph that is isotopic to the curve. PTOPO exploits the benefits of the parametric representation and performs all computations in the parameter space using exact computing. PTOPO computes the topology and visualizes the curve in less than a second for most examples in the literature
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