9,630 research outputs found
Stock mechanics: a general theory and method of energy conservation with applications on DJIA
A new method, based on the original theory of conservation of sum of kinetic
and potential energy defined for prices is proposed and applied on Dow Jones
Industrials Average (DJIA). The general trends averaged over months or years
gave a roughly conserved total energy, with three different potential energies,
i.e. positive definite quadratic, negative definite quadratic and linear
potential energy for exponential rises (and falls), sinusoidal oscillations and
parabolic trajectories, respectively. Corresponding expressions for force
(impact) are also given. Keywords:Comment: 14 pages, 3 figures, scehudled for IJMPC 17/ issue
The log-periodic-AR(1)-GARCH(1,1) model for financial crashes
This paper intends to meet recent claims for the attainment of more rigorous
statistical methodology within the econophysics literature. To this end, we
consider an econometric approach to investigate the outcomes of the
log-periodic model of price movements, which has been largely used to forecast
financial crashes. In order to accomplish reliable statistical inference for
unknown parameters, we incorporate an autoregressive dynamic and a conditional
heteroskedasticity structure in the error term of the original model, yielding
the log-periodic-AR(1)-GARCH(1,1) model. Both the original and the extended
models are fitted to financial indices of U. S. market, namely S&P500 and
NASDAQ. Our analysis reveal two main points: (i) the
log-periodic-AR(1)-GARCH(1,1) model has residuals with better statistical
properties and (ii) the estimation of the parameter concerning the time of the
financial crash has been improved.Comment: 17 pages, 4 figures, 12 tables, to appear in Europen Physical Journal
Stochastics theory of log-periodic patterns
We introduce an analytical model based on birth-death clustering processes to
help understanding the empirical log-periodic corrections to power-law scaling
and the finite-time singularity as reported in several domains including
rupture, earthquakes, world population and financial systems. In our
stochastics theory log-periodicities are a consequence of transient clusters
induced by an entropy-like term that may reflect the amount of cooperative
information carried by the state of a large system of different species. The
clustering completion rates for the system are assumed to be given by a simple
linear death process. The singularity at t_{o} is derived in terms of
birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge
Classification of Possible Finite-Time Singularities by Functional Renormalization
Starting from a representation of the early time evolution of a dynamical
system in terms of the polynomial expression of some observable f (t) as a
function of the time variable in some interval 0 < t < T, we investigate how to
extrapolate/forecast in some optimal stability sense the future evolution of
f(t) for time t>T. Using the functional renormalization of Yukalov and Gluzman,
we offer a general classification of the possible regimes that can be defined
based on the sole knowledge of the coefficients of a second-order polynomial
representation of the dynamics. In particular, we investigate the conditions
for the occurence of finite-time singularities from the structure of the time
series, and quantify the critical time and the functional nature of the
singularity when present. We also describe the regimes when a smooth extremum
replaces the singularity and determine its position and amplitude. This extends
previous works by (1) quantifying the stability of the functional
renormalization method more accurately, (2) introducing new global constraints
in terms of moments and (3) going beyond the ``mean-field'' approximation.Comment: Latex document of 18 pages + 7 ps figure
Invisible Higgs decay with B\to K\nu\bar{\nu} constraint
If the Higgs boson were the only particle within the LHC accessible range,
precision measurement of the Higgs's properties would play a unique role in
studying electroweak symmetry breaking as well as possible new physics. We try
to use low energy experiments such as rare B decay to constrain a challenging
decay mode of Higgs, in which a Higgs decays to a pair of light (\approx 1 \sim
2 GeV) SM singlet S and becomes invisible. By using the current experimental
bound of rare decay B\to K\nu\bar{\nu} and computing the contribution of B\to K
SS to (the) B\to K+\cancel{E}, we obtain an upper bound on the Higgs coupling
to such light singlet. It is interesting that the partial width of the
invisible decay mode h\to SS by taking the upper bound value of coupling is at
a comparable level with h\to WW/ZZ or WW^(*) decay modes, making the Higgs
identifiable but with a different predicted decay BR from the standard model
Higgs decay. It will then have an impact on precision measurement of the
Higgs's properties. We also study the implication for cosmology from such a
light singlet and propose a solution to the potential problem.Comment: 16 pages, 4 figures, the version to appear in Phys. Rev.
Log-periodic route to fractal functions
Log-periodic oscillations have been found to decorate the usual power law
behavior found to describe the approach to a critical point, when the
continuous scale-invariance symmetry is partially broken into a discrete-scale
invariance (DSI) symmetry. We classify the `Weierstrass-type'' solutions of the
renormalization group equation F(x)= g(x)+(1/m)F(g x) into two classes
characterized by the amplitudes A(n) of the power law series expansion. These
two classes are separated by a novel ``critical'' point. Growth processes
(DLA), rupture, earthquake and financial crashes seem to be characterized by
oscillatory or bounded regular microscopic functions g(x) that lead to a slow
power law decay of A(n), giving strong log-periodic amplitudes. In contrast,
the regular function g(x) of statistical physics models with
``ferromagnetic''-type interactions at equibrium involves unbound logarithms of
polynomials of the control variable that lead to a fast exponential decay of
A(n) giving weak log-periodic amplitudes and smoothed observables. These two
classes of behavior can be traced back to the existence or abscence of
``antiferromagnetic'' or ``dipolar''-type interactions which, when present,
make the Green functions non-monotonous oscillatory and favor spatial modulated
patterns.Comment: Latex document of 29 pages + 20 ps figures, addition of a new
demonstration of the source of strong log-periodicity and of a justification
of the general offered classification, update of reference lis
Fiber Orientation Estimation Guided by a Deep Network
Diffusion magnetic resonance imaging (dMRI) is currently the only tool for
noninvasively imaging the brain's white matter tracts. The fiber orientation
(FO) is a key feature computed from dMRI for fiber tract reconstruction.
Because the number of FOs in a voxel is usually small, dictionary-based sparse
reconstruction has been used to estimate FOs with a relatively small number of
diffusion gradients. However, accurate FO estimation in regions with complex FO
configurations in the presence of noise can still be challenging. In this work
we explore the use of a deep network for FO estimation in a dictionary-based
framework and propose an algorithm named Fiber Orientation Reconstruction
guided by a Deep Network (FORDN). FORDN consists of two steps. First, we use a
smaller dictionary encoding coarse basis FOs to represent the diffusion
signals. To estimate the mixture fractions of the dictionary atoms (and thus
coarse FOs), a deep network is designed specifically for solving the sparse
reconstruction problem. Here, the smaller dictionary is used to reduce the
computational cost of training. Second, the coarse FOs inform the final FO
estimation, where a larger dictionary encoding dense basis FOs is used and a
weighted l1-norm regularized least squares problem is solved to encourage FOs
that are consistent with the network output. FORDN was evaluated and compared
with state-of-the-art algorithms that estimate FOs using sparse reconstruction
on simulated and real dMRI data, and the results demonstrate the benefit of
using a deep network for FO estimation.Comment: A shorter version is accepted by MICCAI 201
Survival of the mm-cm size grain population observed in protoplanetary disks
Millimeter interferometry provides evidence for the presence of mm to cm size
"pebbles" in the outer parts of disks around pre-main-sequence stars. The
observations suggest that large grains are produced relatively early in disk
evolution (< 1 Myr) and remain at large radii for longer periods of time (5 to
10 Myr). Simple theoretical estimates of the radial drift time of solid
particles, however, imply that they would drift inward over a time scale of
less than 0.1 Myr. In this paper, we address this conflict between theory and
observation, using more detailed theoretical models, including the effects of
sedimentation, collective drag forces and turbulent viscosity. We find that,
although these effects slow down the radial drift of the dust particles, this
reduction is not sufficient to explain the observationally determined long
survival time of mm/cm-sized grains in protoplanetary disks. However, if for
some reason the gas to dust ratio in the disk is reduced by at least a factor
of 20 from the canonical value of 100 (for instance through photoevaporation of
the gas), then the radial drift time scales become sufficiently large to be in
agreement with observations.Comment: Accepted for publication in Astronomy and Astrophysic
Weak Measurements with Arbitrary Pointer States
The exact conditions on valid pointer states for weak measurements are
derived. It is demonstrated that weak measurements can be performed with any
pointer state with vanishing probability current density. This condition is
found both for weak measurements of noncommuting observables and for -number
observables. In addition, the interaction between pointer and object must be
sufficiently weak. There is no restriction on the purity of the pointer state.
For example, a thermal pointer state is fully valid.Comment: 4 page
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