94,307 research outputs found
Current results and open questions on PH and MAP characterization
Stochastic processes with matrix exponential kernels have a wide range
of applications due to the availability of efficient matrix analytic methods.
The characterization of these processes is in progress in recent years.
Basic questions like
the flexibility,
the degree of freedom,
the most efficient (canonical) representation of these models
are under study.
The presentation collects a set of available results and related open questions
Generalized Flow and Determinism in Measurement-based Quantum Computation
We extend the notion of quantum information flow defined by Danos and Kashefi
for the one-way model and present a necessary and sufficient condition for the
deterministic computation in this model. The generalized flow also applied in
the extended model with measurements in the X-Y, X-Z and Y-Z planes. We apply
both measurement calculus and the stabiliser formalism to derive our main
theorem which for the first time gives a full characterization of the
deterministic computation in the one-way model. We present several examples to
show how our result improves over the traditional notion of flow, such as
geometries (entanglement graph with input and output) with no flow but having
generalized flow and we discuss how they lead to an optimal implementation of
the unitaries. More importantly one can also obtain a better quantum
computation depth with the generalized flow rather than with flow. We believe
our characterization result is particularly essential for the study of the
algorithms and complexity in the one-way model.Comment: 16 pages, 10 figure
Generalized Flow and Determinism in Measurement-based Quantum Computation
We extend the notion of quantum information flow defined by Danos and Kashefi
for the one-way model and present a necessary and sufficient condition for the
deterministic computation in this model. The generalized flow also applied in
the extended model with measurements in the X-Y, X-Z and Y-Z planes. We apply
both measurement calculus and the stabiliser formalism to derive our main
theorem which for the first time gives a full characterization of the
deterministic computation in the one-way model. We present several examples to
show how our result improves over the traditional notion of flow, such as
geometries (entanglement graph with input and output) with no flow but having
generalized flow and we discuss how they lead to an optimal implementation of
the unitaries. More importantly one can also obtain a better quantum
computation depth with the generalized flow rather than with flow. We believe
our characterization result is particularly essential for the study of the
algorithms and complexity in the one-way model.Comment: 16 pages, 10 figure
Separability and distillability in composite quantum systems -a primer-
Quantum mechanics is already 100 years old, but remains alive and full of
challenging open problems. On one hand, the problems encountered at the
frontiers of modern theoretical physics like Quantum Gravity, String Theories,
etc. concern Quantum Theory, and are at the same time related to open problems
of modern mathematics. But even within non-relativistic quantum mechanics
itself there are fundamental unresolved problems that can be formulated in
elementary terms. These problems are also related to challenging open questions
of modern mathematics; linear algebra and functional analysis in particular.
Two of these problems will be discussed in this article: a) the separability
problem, i.e. the question when the state of a composite quantum system does
not contain any quantum correlations or entanglement and b) the distillability
problem, i.e. the question when the state of a composite quantum system can be
transformed to an entangled pure state using local operations (local refers
here to component subsystems of a given system).
Although many results concerning the above mentioned problems have been
obtained (in particular in the last few years in the framework of Quantum
Information Theory), both problems remain until now essentially open. We will
present a primer on the current state of knowledge concerning these problems,
and discuss the relation of these problems to one of the most challenging
questions of linear algebra: the classification and characterization of
positive operator maps.Comment: 11 pages latex, 1 eps figure. Final version, to appear in J. Mod.
Optics, minor typos corrected, references adde
Patient-centric trials for therapeutic development in precision oncology
An enhanced understanding of the molecular pathology of disease gained from genomic studies is facilitating the development of treatments that target discrete molecular subclasses of tumours. Considerable associated challenges include how to advance and implement targeted drug-development strategies. Precision medicine centres on delivering the most appropriate therapy to a patient on the basis of clinical and molecular features of their disease. The development of therapeutic agents that target molecular mechanisms is driving innovation in clinical-trial strategies. Although progress has been made, modifications to existing core paradigms in oncology drug development will be required to realize fully the promise of precision medicine
On quantum non-signalling boxes
A classical non-signalling (or causal) box is an operation on classical
bipartite input with classical bipartite output such that no signal can be sent
from a party to the other through the use of the box. The quantum counterpart
of such boxes, i.e. completely positive trace-preserving maps on bipartite
states, though studied in literature, have been investigated less intensively
than classical boxes. We present here some results and remarks about such maps.
In particular, we analyze: the relations among properties as causality,
non-locality and entanglement; the connection between causal and entanglement
breaking maps; the characterization of causal maps in terms of the
classification of states with fixed reductions. We also provide new proofs of
the fact that every non-product unitary transformation is not causal, as well
as for the equivalence of the so-called semicausality and semilocalizability
properties.Comment: 18 pages, 7 figures, revtex
Review of the Synergies Between Computational Modeling and Experimental Characterization of Materials Across Length Scales
With the increasing interplay between experimental and computational
approaches at multiple length scales, new research directions are emerging in
materials science and computational mechanics. Such cooperative interactions
find many applications in the development, characterization and design of
complex material systems. This manuscript provides a broad and comprehensive
overview of recent trends where predictive modeling capabilities are developed
in conjunction with experiments and advanced characterization to gain a greater
insight into structure-properties relationships and study various physical
phenomena and mechanisms. The focus of this review is on the intersections of
multiscale materials experiments and modeling relevant to the materials
mechanics community. After a general discussion on the perspective from various
communities, the article focuses on the latest experimental and theoretical
opportunities. Emphasis is given to the role of experiments in multiscale
models, including insights into how computations can be used as discovery tools
for materials engineering, rather than to "simply" support experimental work.
This is illustrated by examples from several application areas on structural
materials. This manuscript ends with a discussion on some problems and open
scientific questions that are being explored in order to advance this
relatively new field of research.Comment: 25 pages, 11 figures, review article accepted for publication in J.
Mater. Sc
Bifurcation currents and equidistribution on parameter space
In this paper we review the use of techniques of positive currents for the
study of parameter spaces of one-dimensional holomorphic dynamical systems
(rational mappings on P^1 or subgroups of the Moebius group PSL(2,C)). The
topics covered include: the construction of bifurcation currents and the
characterization of their supports, the equidistribution properties of
dynamically defined subvarieties on parameter space.Comment: Revised version, 46 pages, to appear in the proceedings of the
conference "Frontiers in complex dynamics (Celebrating John Milnor's 80th
birthday)
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