15,874 research outputs found
Neural network modeling of memory deterioration in Alzheimer's disease
The clinical course of Alzheimer's disease (AD) is generally characterized by progressive gradual deterioration, although large clinical variability exists. Motivated by the recent quantitative reports of synaptic changes in AD, we use a neural network model to investigate how the interplay between synaptic deletion and compensation determines the pattern of memory deterioration, a clinical hallmark of AD. Within the model we show that the deterioration of memory retrieval due to synaptic deletion can be much delayed by multiplying all the remaining synaptic weights by a common factor, which keeps the average input to each neuron at the same level. This parallels the experimental observation that the total synaptic area per unit volume (TSA) is initially preserved when synaptic deletion occurs. By using different dependencies of the compensatory factor on the amount of synaptic deletion one can define various compensation strategies, which can account for the observed variation in the severity and progression rate of AD
Developing the Deutsch-Hayden approach to quantum mechanics
The formalism of Deutsch and Hayden is a useful tool for describing quantum
mechanics explicitly as local and unitary, and therefore quantum information
theory as concerning a "flow" of information between systems. In this paper we
show that these physical descriptions of flow are unique, and develop the
approach further to include the measurement interaction and mixed states. We
then give an analysis of entanglement swapping in this approach, showing that
it does not in fact contain non-local effects or some form of superluminal
signalling.Comment: 14 pages. Added section on entanglement swappin
Solution to the Equations of the Moment Expansions
We develop a formula for matching a Taylor series about the origin and an
asymptotic exponential expansion for large values of the coordinate. We test it
on the expansion of the generating functions for the moments and connected
moments of the Hamiltonian operator. In the former case the formula produces
the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We
choose the harmonic oscillator and a strongly anharmonic oscillator as
illustrative examples for numerical test. Our results reveal some features of
the connected-moments expansion that were overlooked in earlier studies and
applications of the approach
StemNet: An Evolving Service for Knowledge Networking in the Life Sciences
Up until now, crucial life science information resources, whether bibliographic or factual databases, are isolated from each other. Moreover, semantic metadata intended to structure their contents is supplied in a manual form only. In the StemNet project we aim at developing a framework for semantic interoperability for these resources. This will facilitate the extraction of relevant information from textual sources and the generation of semantic metadata in a fully automatic manner. In this way, (from a computational perspective) unstructured life science documents are linked to structured biological fact databases, in particular to the identifiers of genes, proteins, etc. Thus, life scientists will be able to seamlessly access information from a homogeneous platform, despite the fact that the original information was unlinked and scattered over the whole variety of heterogeneous life science information resources and, therefore, almost inaccessible for integrated systematic search by academic, clinical, or industrial users
Structural precursor to the metal-insulator transition in V_2O_3
The temperature dependence of the local structure of V_2O_3 in the vicinity
of the metal to insulator transition (MIT) has been investigated using hard
X-ray absorption spectroscopy. It is shown that the vanadium pair distance
along the hexagonal c-axis changes abruptly at the MIT as expected. However, a
continuous increase of the tilt of these pairs sets in already at higher
temperatures and reaches its maximum value at the onset of the electronic and
magnetic transition. These findings confirm recent theoretical results which
claim that electron-lattice coupling is important for the MIT in V_2O_3. Our
results suggest that interactions in the basal plane play a decisive role for
the MIT and orbital degrees of freedom drive the MIT via changes in
hybridization.Comment: 6 pages, 5 figures, 2 table
The - divergence and Mixing times of quantum Markov processes
We introduce quantum versions of the -divergence, provide a detailed
analysis of their properties, and apply them in the investigation of mixing
times of quantum Markov processes. An approach similar to the one presented in
[1-3] for classical Markov chains is taken to bound the trace-distance from the
steady state of a quantum processes. A strict spectral bound to the convergence
rate can be given for time-discrete as well as for time-continuous quantum
Markov processes. Furthermore the contractive behavior of the
-divergence under the action of a completely positive map is
investigated and contrasted to the contraction of the trace norm. In this
context we analyse different versions of quantum detailed balance and, finally,
give a geometric conductance bound to the convergence rate for unital quantum
Markov processes
Localizable Entanglement
We consider systems of interacting spins and study the entanglement that can
be localized, on average, between two separated spins by performing local
measurements on the remaining spins. This concept of Localizable Entanglement
(LE) leads naturally to notions like entanglement length and entanglement
fluctuations. For both spin-1/2 and spin-1 systems we prove that the LE of a
pure quantum state can be lower bounded by connected correlation functions. We
further propose a scheme, based on matrix-product states and the Monte Carlo
method, to efficiently calculate the LE for quantum states of a large number of
spins. The virtues of LE are illustrated for various spin models. In
particular, characteristic features of a quantum phase transition such as a
diverging entanglement length can be observed. We also give examples for pure
quantum states exhibiting a diverging entanglement length but finite
correlation length. We have numerical evidence that the ground state of the
antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum
channel. Furthermore, we apply the numerical method to mixed states and study
the entanglement as a function of temperature.Comment: 19 pages, modified definition of connected string order parameter,
updated reference
Singular value decomposition and matrix reorderings in quantum information theory
We review Schmidt and Kraus decompositions in the form of singular value
decomposition using operations of reshaping, vectorization and reshuffling. We
use the introduced notation to analyse the correspondence between quantum
states and operations with the help of Jamiolkowski isomorphism. The presented
matrix reorderings allow us to obtain simple formulae for the composition of
quantum channels and partial operations used in quantum information theory. To
provide examples of the discussed operations we utilize a package for the
Mathematica computing system implementing basic functions used in the
calculations related to quantum information theory.Comment: 11 pages, no figures, see
http://zksi.iitis.pl/wiki/projects:mathematica-qi for related softwar
Spectral Conditions on the State of a Composite Quantum System Implying its Separability
For any unitarily invariant convex function F on the states of a composite
quantum system which isolates the trace there is a critical constant C such
that F(w)<= C for a state w implies that w is not entangled; and for any
possible D > C there are entangled states v with F(v)=D. Upper- and lower
bounds on C are given. The critical values of some F's for qubit/qubit and
qubit/qutrit bipartite systems are computed. Simple conditions on the spectrum
of a state guaranteeing separability are obtained. It is shown that the thermal
equilbrium states specified by any Hamiltonian of an arbitrary compositum are
separable if the temperature is high enough.Comment: Corrects 1. of Lemma 2, and the (under)statement of Proposition 7 of
the earlier version
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