9,024 research outputs found
A quasi-Newton approach to optimization problems with probability density constraints
A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided
Mechanical Unfolding of a Simple Model Protein Goes Beyond the Reach of One-Dimensional Descriptions
We study the mechanical unfolding of a simple model protein. The Langevin
dynamics results are analyzed using Markov-model methods which allow to
describe completely the configurational space of the system. Using transition
path theory we also provide a quantitative description of the unfolding
pathways followed by the system. Our study shows a complex dynamical scenario.
In particular, we see that the usual one-dimensional picture: free-energy vs
end-to-end distance representation, gives a misleading description of the
process. Unfolding can occur following different pathways and configurations
which seem to play a central role in one-dimensional pictures are not the
intermediate states of the unfolding dynamics.Comment: 10 pages, 6 figure
Separable Measurement Estimation of Density Matrices and its Fidelity Gap with Collective Protocols
We show that there exists a gap between the performance of separable and
collective measurements in qubit mixed-state estimation that persists in the
large sample limit. We characterize such gap in terms of the corresponding
bounds on the mean fidelity. We present an adaptive protocol that attains the
separable-measurement bound. This (optimal separable) protocol uses von Neumann
measurements and can be easily implemented with current technology.Comment: version published in PR
Optimal full estimation of qubit mixed states
We obtain the optimal scheme for estimating unknown qubit mixed states when
an arbitrary number N of identically prepared copies is available. We discuss
the case of states in the whole Bloch sphere as well as the restricted
situation where these states are known to lie on the equatorial plane. For the
former case we obtain that the optimal measurement does not depend on the prior
probability distribution provided it is isotropic. Although the
equatorial-plane case does not have this property for arbitrary N, we give a
prior-independent scheme which becomes optimal in the asymptotic limit of large
N. We compute the maximum mean fidelity in this asymptotic regime for the two
cases. We show that within the pointwise estimation approach these limits can
be obtained in a rather easy and rapid way. This derivation is based on
heuristic arguments that are made rigorous by using van Trees inequalities. The
interrelation between the estimation of the purity and the direction of the
state is also discussed. In the general case we show that they correspond to
independent estimations whereas for the equatorial-plane states this is only
true asymptotically.Comment: 19 pages, no figure
Universal field equations for metric-affine theories of gravity
We show that almost all metric--affine theories of gravity yield Einstein
equations with a non--null cosmological constant . Under certain
circumstances and for any dimension, it is also possible to incorporate a Weyl
vector field and therefore the presence of an anisotropy. The viability
of these field equations is discussed in view of recent astrophysical
observations.Comment: 13 pages. This is a copy of the published paper. We are posting it
here because of the increasing interest in f(R) theories of gravit
How to hide a secret direction
We present a procedure to share a secret spatial direction in the absence of
a common reference frame using a multipartite quantum state. The procedure
guarantees that the parties can determine the direction if they perform joint
measurements on the state, but fail to do so if they restrict themselves to
local operations and classical communication (LOCC). We calculate the fidelity
for joint measurements, give bounds on the fidelity achievable by LOCC, and
prove that there is a non-vanishing gap between the two of them, even in the
limit of infinitely many copies. The robustness of the procedure under particle
loss is also studied. As a by-product we find bounds on the probability of
discriminating by LOCC between the invariant subspaces of total angular
momentum N/2 and N/2-1 in a system of N elementary spins.Comment: 4 pages, 1 figur
Mesoscopic Model for Free Energy Landscape Analysis of DNA sequences
A mesoscopic model which allows us to identify and quantify the strength of
binding sites in DNA sequences is proposed. The model is based on the
Peyrard-Bishop-Dauxois model for the DNA chain coupled to a Brownian particle
which explores the sequence interacting more importantly with open base pairs
of the DNA chain. We apply the model to promoter sequences of different
organisms. The free energy landscape obtained for these promoters shows a
complex structure that is strongly connected to their biological behavior. The
analysis method used is able to quantify free energy differences of sites
within genome sequences.Comment: 7 pages, 5 figures, 1 tabl
Temporal evolution of short-lived penumbral microjets
Context. Penumbral microjets are elongated jet-like brightenings observed in
the chromosphere above sunspot penumbrae. They are transient events that last
from a few seconds to several minutes and are thought to originate from
magnetic reconnection processes. Previous studies have mainly focused on their
morphological and spectral characteristics, and more recently on their
spectropolarimetric signals during the maximum brightness stage. Studies
addressing the temporal evolution of PMJs have also been carried out, but they
are based on spatial and spectral time variations only.
Aims. Here we investigate the temporal evolution of the polarization signals
produced by short-lived PMJs (lifetimes 2 minutes) to infer how the
magnetic field vector evolves in the upper photosphere and mid-chromosphere.
Methods. We use fast-cadence spectropolarimetric observations of the Ca II
854.2 nm line taken with the CRisp Imaging Spectropolarimeter at the Swedish
1-m Solar Telescope. The weak-field approximation (WFA) is used to estimate the
strength and inclination of the magnetic field vector.
Results. The WFA reveals larger magnetic field changes in the upper
photosphere than in the chromosphere during the PMJ maximum brightness stage.
In the photosphere, the magnetic field inclination and strength undergo a
transient increase for most PMJs, but in 25 of the cases the field strength
decreases during the brightening. In the chromosphere, the magnetic field tends
to be slightly stronger during the PMJs.
Conclusions. The propagation of compressive perturbation fronts followed by a
rarefaction phase in the aftershock region may explain the observed behavior of
the magnetic field vector. The fact that such behavior varies among the
analyzed PMJs could be a consequence of the limited temporal resolution of the
observations and the fast-evolving nature of the PMJs.Comment: Paper accepted for publication in section 9. The Sun and the
Heliosphere of Astronomy and Astrophysics. 18 pages, 21 figure
On the geometry of four qubit invariants
The geometry of four-qubit entanglement is investigated. We replace some of
the polynomial invariants for four-qubits introduced recently by new ones of
direct geometrical meaning. It is shown that these invariants describe four
points, six lines and four planes in complex projective space . For
the generic entanglement class of stochastic local operations and classical
communication they take a very simple form related to the elementary symmetric
polynomials in four complex variables. Moreover, their magnitudes are
entanglement monotones that fit nicely into the geometric set of -qubit ones
related to Grassmannians of -planes found recently. We also show that in
terms of these invariants the hyperdeterminant of order 24 in the four-qubit
amplitudes takes a more instructive form than the previously published
expressions available in the literature. Finally in order to understand two,
three and four-qubit entanglement in geometric terms we propose a unified
setting based on furnished with a fixed quadric.Comment: 19 page
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