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Disease modelling using evolved discriminate function
Precocious diagnosis increases the survival time and patient quality of life. It is a binary classification, exhaustively studied in the literature. This paper innovates proposing the application of genetic programming to obtain a discriminate function. This function contains the disease dynamics used to classify the patients with as little false negative diagnosis as possible. If its value is greater than zero then it means that the patient is ill, otherwise healthy. A graphical representation is proposed to show the influence of each dataset attribute in the discriminate function. The experiment deals with Breast Cancer and Thrombosis & Collagen diseases diagnosis. The main conclusion is that the discriminate function is able to classify the patient using numerical clinical data, and the graphical representation displays patterns that allow understanding of the model
The Vacuum Structure of Light-Front -Theory
We discuss the vacuum structure of -theory in 1+1 dimensions
quantised on the light-front . To this end, one has to solve a
non-linear, operator-valued constraint equation. It expresses that mode of the
field operator having longitudinal light-front momentum equal to zero, as a
function of all the other modes in the theory. We analyse whether this zero
mode can lead to a non-vanishing vacuum expectation value of the field
and thus to spontaneous symmetry breaking. In perturbation theory, we get no
symmetry breaking. If we solve the constraint, however, non-perturbatively,
within a mean-field type Fock ansatz, the situation changes: while the vacuum
state itself remains trivial, we find a non-vanishing vacuum expectation value
above a critical coupling. Exactly the same result is obtained within a
light-front Tamm-Dancoff approximation, if the renormalisation is done in the
correct way.Comment: 28 pages LaTeX, 1 Postscript figur
The topological classification of one-dimensional symmetric quantum walks
We give a topological classification of quantum walks on an infinite 1D
lattice, which obey one of the discrete symmetry groups of the tenfold way,
have a gap around some eigenvalues at symmetry protected points, and satisfy a
mild locality condition. No translation invariance is assumed. The
classification is parameterized by three indices, taking values in a group,
which is either trivial, the group of integers, or the group of integers modulo
2, depending on the type of symmetry. The classification is complete in the
sense that two walks have the same indices if and only if they can be connected
by a norm continuous path along which all the mentioned properties remain
valid. Of the three indices, two are related to the asymptotic behaviour far to
the right and far to the left, respectively. These are also stable under
compact perturbations. The third index is sensitive to those compact
perturbations which cannot be contracted to a trivial one. The results apply to
the Hamiltonian case as well. In this case all compact perturbations can be
contracted, so the third index is not defined. Our classification extends the
one known in the translation invariant case, where the asymptotic right and
left indices add up to zero, and the third one vanishes, leaving effectively
only one independent index. When two translationally invariant bulks with
distinct indices are joined, the left and right asymptotic indices of the
joined walk are thereby fixed, and there must be eigenvalues at or
(bulk-boundary correspondence). Their location is governed by the third index.
We also discuss how the theory applies to finite lattices, with suitable
homogeneity assumptions.Comment: 36 pages, 7 figure
Propagation and spectral properties of quantum walks in electric fields
We study one-dimensional quantum walks in a homogeneous electric field. The
field is given by a phase which depends linearly on position and is applied
after each step. The long time propagation properties of this system, such as
revivals, ballistic expansion and Anderson localization, depend very
sensitively on the value of the electric field , e.g., on whether
is rational or irrational. We relate these properties to the
continued fraction expansion of the field. When the field is given only with
finite accuracy, the beginning of the expansion allows analogous conclusions
about the behavior on finite time scales.Comment: 7 pages, 4 figure
Estimating entanglement measures in experiments
We present a method to estimate entanglement measures in experiments. We show
how a lower bound on a generic entanglement measure can be derived from the
measured expectation values of any finite collection of entanglement witnesses.
Hence witness measurements are given a quantitative meaning without the need of
further experimental data. We apply our results to a recent multi-photon
experiment [M. Bourennane et al., Phys. Rev. Lett. 92, 087902 (2004)], giving
bounds on the entanglement of formation and the geometric measure of
entanglement in this experiment.Comment: 4 pages, 1 figure, v2: final versio
Nuclear binding energies: Global collective structure and local shell-model correlations
Nuclear binding energies and two-neutron separation energies are analyzed
starting from the liquid-drop model and the nuclear shell model in order to
describe the global trends of the above observables. We subsequently
concentrate on the Interacting Boson Model (IBM) and discuss a new method in
order to provide a consistent description of both, ground-state and
excited-state properties. We address the artefacts that appear when crossing
mid-shell using the IBM formulation and perform detailed numerical calculations
for nuclei situated in the 50-82 shell. We also concentrate on local deviations
from the above global trends in binding energy and two-neutron separation
energies that appear in the neutron-deficient Pb region. We address possible
effects on the binding energy, caused by mixing of low-lying intruder
states into the ground state, using configuration mixing in the IBM framework.
We also study ground-state properties using a deformed mean-field approach.
Detailed comparisons with recent experimental data in the Pb region are amply
discussed.Comment: 69 pages, TeX (ReVTeX). 23 eps figures. 1 table. Modified version.
Accepted in Nucl. Phys.
Complete homotopy invariants for translation invariant symmetric quantum walks on a chain
We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, translation invariance, a gap condition, and some symmetry of the tenfold way. The classification largely matches the one recently obtained (arXiv: 1611.04439) for a similar setting leaving out translation invariance. However, the translation invariant case has some finer distinctions, because some walks may be connected only by breaking translation invariance along the way, retaining only invariance by an even number of sites. Similarly, if walks are considered equivalent when they differ only by adding a trivial walk, i.e., one that allows no jumps between cells, then the classification collapses also to the general one. The indices of the general classification can be computed in practice only for walks closely related to some translation invariant ones. We prove a completed collection of simple formulas in terms of winding numbers of band structures covering all symmetry types. Furthermore, we determine the strength of the locality conditions, and show that the continuity of the band structure, which is a minimal requirement for topological classifications in terms of winding numbers to make sense, implies the compactness of the commutator of the walk with a half-space projection, a condition which was also the basis of the general theory. In order to apply the theory to the joining of large but finite bulk pieces, one needs to determine the asymptotic behaviour of a stationary Schrodinger equation. We show exponential behaviour, and give a practical method for computing the decay constants
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