154 research outputs found
The Bregman chord divergence
Distances are fundamental primitives whose choice significantly impacts the
performances of algorithms in machine learning and signal processing. However
selecting the most appropriate distance for a given task is an endeavor.
Instead of testing one by one the entries of an ever-expanding dictionary of
{\em ad hoc} distances, one rather prefers to consider parametric classes of
distances that are exhaustively characterized by axioms derived from first
principles. Bregman divergences are such a class. However fine-tuning a Bregman
divergence is delicate since it requires to smoothly adjust a functional
generator. In this work, we propose an extension of Bregman divergences called
the Bregman chord divergences. This new class of distances does not require
gradient calculations, uses two scalar parameters that can be easily tailored
in applications, and generalizes asymptotically Bregman divergences.Comment: 10 page
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When optimal foragers meet in a game theoretical conflict: A model of kleptoparasitism
Kleptoparasitism can be considered as a game theoretical problem and a foraging tactic at the same time, so the aim of this paper is to combine the basic ideas of two research lines: evolutionary game theory and optimal foraging theory. To unify these theories, firstly, we take into account the fact that kleptoparasitism between foragers has two consequences: the interaction takes time and affects the net energy intake of both contestants. This phenomenon is modeled by a matrix game under time constraints. Secondly, we also give freedom to each forager to avoid interactions, since in optimal foraging theory foragers can ignore each food type (we have two prey types: either a prey item in possession of another predator or a free prey individual is discovered). The main question of the present paper is whether the zero-one rule of optimal foraging theory (always or never select a prey type) is valid or not, in the case where foragers interact with each other?
In our foraging game we consider predators who engage in contests (contestants) and those who never do (avoiders), and in general those who play a mixture of the two strategies. Here the classical zero-one rule does not hold. Firstly, the pure avoider phenotype is never an ESS. Secondly, the pure contestant can be a strict ESS, but we show this is not necessarily so. Thirdly, we give an example when there is mixed ESS
Continuity of the Maximum-Entropy Inference
We study the inverse problem of inferring the state of a finite-level quantum
system from expected values of a fixed set of observables, by maximizing a
continuous ranking function. We have proved earlier that the maximum-entropy
inference can be a discontinuous map from the convex set of expected values to
the convex set of states because the image contains states of reduced support,
while this map restricts to a smooth parametrization of a Gibbsian family of
fully supported states. Here we prove for arbitrary ranking functions that the
inference is continuous up to boundary points. This follows from a continuity
condition in terms of the openness of the restricted linear map from states to
their expected values. The openness condition shows also that ranking functions
with a discontinuous inference are typical. Moreover it shows that the
inference is continuous in the restriction to any polytope which implies that a
discontinuity belongs to the quantum domain of non-commutative observables and
that a geodesic closure of a Gibbsian family equals the set of maximum-entropy
states. We discuss eight descriptions of the set of maximum-entropy states with
proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
We extend the mathematical theory of quantum hypothesis testing to the
general -algebraic setting and explore its relation with recent
developments in non-equilibrium quantum statistical mechanics. In particular,
we relate the large deviation principle for the full counting statistics of
entropy flow to quantum hypothesis testing of the arrow of time.Comment: 60 page
Unified criterion for security of secret sharing in terms of violation of Bell inequality
In secret sharing protocols, a secret is to be distributed among several
partners so that leaving out any number of them, the rest do not have the
complete information. Strong multiqubit correlations in the state by which
secret sharing is carried out, had been proposed as a criterion for security of
such protocols against individual attacks by an eavesdropper. However we show
that states with weak multiqubit correlations can also be used for secure
secret sharing. That our state has weak multiqubit correlations, is shown from
the perspective of violation of local realism, and also by showing that its
higher order correlations are described by lower ones. We then present a
unified criterion for security of secret sharing in terms of violation of local
realism, which works when the secret sharing state is the
Greenberger-Horne-Zeilinger state (with strong multiqubit correlations), as
well as states of a different class (with weak multiqubit correlations).Comment: 7 pages, no figures, RevTeX
Phenotyping shows improved physiological traits and seed yield of transgenic wheat plants expressing the alfalfa aldose reductase under permanent drought stress
Members of the aldo-keto reductase family including aldose reductases are involved in antioxidant defense by metabolizing a wide range of lipid peroxidation-derived cytotoxic compounds. Therefore, we produced transgenic wheat genotypes over-expressing the cDNA of alfalfa aldose reductase gene. These plants consequently exhibit 1.5-4.3 times higher detoxification activity for the aldehyde substrate. Permanent drought stress was generated in the greenhouse by growing wheat plants in soil with 20 % water capacity. The control and stressed plants were monitored by a semi automatic phenotyping platform providing computer-controlled watering, digital and thermal imaging. Calculation of biomass values was based on the correlation (R2 = 0.7556) between fresh weight and green pixel-based shoot surface area. The green biomass production by plants of the three transgenic lines was 12-26-41 % higher than the non-transgenic plants' grown under water limitation. Thermal imaging of stressed non-transgenic plants indicated an elevation in the leaf temperature. The thermal status of transformants was similar at both normal and suboptimal water regime. In drought, the transgenic plants used more water during the growing season. The described phenotyping platform provided a comprehensive data set demonstrating the improved physiological condition of the drought stressed transgenic wheat plants in the vegetative growth phase. In soil with reduced water capacity two transgenic genotypes showed higher seed weight per plant than the control non-transgenic one. Limitation of greenhouse-based phenotyping in analysis of yield potential is discussed. © 2013 The Author(s)
Quantum cryptography with 3-state systems
We consider quantum cryptographic schemes where the carriers of information
are 3-state particles. One protocol uses four mutually unbiased bases and
appears to provide better security than obtainable with 2-state carriers.
Another possible method allows quantum states to belong to more than one basis.
The security is not better, but many curious features arise.Comment: 11 pages Revte
Group entropies, correlation laws and zeta functions
The notion of group entropy is proposed. It enables to unify and generalize
many different definitions of entropy known in the literature, as those of
Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals
are presented, related to nontrivial correlation laws characterizing
universality classes of systems out of equilibrium, when the dynamics is weakly
chaotic. The associated thermostatistics are discussed. The mathematical
structure underlying our construction is that of formal group theory, which
provides the general structure of the correlations among particles and dictates
the associated entropic functionals. As an example of application, the role of
group entropies in information theory is illustrated and generalizations of the
Kullback-Leibler divergence are proposed. A new connection between statistical
mechanics and zeta functions is established. In particular, Tsallis entropy is
related to the classical Riemann zeta function.Comment: to appear in Physical Review
Secret Sharing over Fast-Fading MIMO Wiretap Channels
Secret sharing over the fast-fading MIMO wiretap channel is considered. A
source and a destination try to share secret information over a fast-fading
MIMO channel in the presence of a wiretapper who also makes channel
observations that are different from but correlated to those made by the
destination. An interactive authenticated unrestricted public channel is also
available for use by the source and destination in the secret sharing process.
This falls under the "channel-type model with wiretapper" considered by
Ahlswede and Csiszar. A minor extension of their result (to continuous channel
alphabets) is employed to evaluate the key capacity of the fast-fading MIMO
wiretap channel. The effects of spatial dimensionality provided by the use of
multiple antennas at the source, destination, and wiretapper are then
investigated.Comment: Revision submitted to EURASIP Journal on Wireless Communications and
Networking, Special Issue on Wireless Physical Layer Security, Sept. 2009.
v.3: Fixes to proofs. Matthieu Bloch added as co-author for contributions to
proof
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