866 research outputs found
Playing a quantum game with a corrupted source
The quantum advantage arising in a simplified multi-player quantum game, is
found to be a disadvantage when the game's qubit-source is corrupted by a noisy
"demon". Above a critical value of the corruption-rate, or noise-level, the
coherent quantum effects impede the players to such an extent that the optimal
choice of game changes from quantum to classical.Comment: This version will appear in PRA (Rapid Comm.
Eigenvalues of p-summing and lp-type operators in Banach spaces
AbstractThis paper is a study of the distribution of eigenvalues of various classes of operators. In Section 1 we prove that the eigenvalues (λn(T)) of a p-absolutely summing operator, p ⩾ 2, satisfy ∑n∈N|λn(T)|p1p⩽πp(T). This solves a problem of A. Pietsch. We give applications of this to integral operators in Lp-spaces, weakly singular operators, and matrix inequalities.In Section 2 we introduce the quasinormed ideal Π2(n), P = (p1, …, pn) and show that for T ∈ Π2(n), 2 = (2, …, 2) ∈ Nn, the eigenvalues of T satisfy ∑i∈N|λi(T)|2nn2⩽πn2(T). More generally, we show that for T ∈ Πp(n), P = (p1, …, pn), pi ⩾ 2, the eigenvalues are absolutely p-summable, 1p=∑i=1n1pi and ∑n∈N|λn(T)|p1p⩽CpπnP(T).We also consider the distribution of eigenvalues of p-nuclear operators on Lr-spaces.In Section 3 we prove the Banach space analog of the classical Weyl inequality, namely ∑n∈N|λn(T)|p ⩽ Cp∑n∈N αn(T)p, 0 < p < ∞, where αn denotes the Kolmogoroff, Gelfand of approximation numbers of the operator T. This solves a problem of Markus-Macaev.Finally we prove that Hilbert space is (isomorphically) the only Banach space X with the property that nuclear operators on X have absolutely summable eigenvalues. Using this result we show that if the nuclear operators on X are of type l1 then X must be a Hilbert space
Crop and Soil Productivity Response to Corn Residue Removal: A Literature Review
Society is facing three related issues: over-reliance on imported fuel, increasing levels of greenhouse gases in the atmosphere, and producing sufficient food for a growing world population. The U.S. Department of Energy and private enterprise are developing technology necessary to use high-cellulose feedstock, such as crop residues, for ethanol production. Corn (Zea mays L.) residue can provide about 1.7 times more C than barley (Hordeum vulgare L.), oat (Avena sativa L.), sorghum [Sorghum bicolor (L.) Moench], soybean [Glycine max L.) Merr.], sunflower (Helianthus annuus L.), and wheat (Triticum aestivum L.) residues based on production levels. Removal of crop residue from the field must be balanced against impacting the environment (soil erosion), maintaining soil organic matter levels, and pre- serving or enhancing productivity. Our objective is to summarize published works for potential impacts of wide-scale, corn stover collection on corn production capacity in Corn Belt soils. We address the issue crop yield (sustainability) and related soil processes directly. However, scarcity of data requires us to deal with the issue of greenhouse gases indirectly and by inference. All ramifications of new management practices and crop uses must be explored and evaluated fully before industry is established. Our conclusion is that within limits, corn stover can be harvested for ethanol production to provide a renewable, domestic source of energy that reduces greenhouse gases. Recommendation for removal rates will vary based on regional yield, climatic conditions, and cultural practices. Agronomists are challenged to develop a procedure (tool) for recommending maximum permissible removal rates that ensure sustained soil productivity
Random forests with random projections of the output space for high dimensional multi-label classification
We adapt the idea of random projections applied to the output space, so as to
enhance tree-based ensemble methods in the context of multi-label
classification. We show how learning time complexity can be reduced without
affecting computational complexity and accuracy of predictions. We also show
that random output space projections may be used in order to reach different
bias-variance tradeoffs, over a broad panel of benchmark problems, and that
this may lead to improved accuracy while reducing significantly the
computational burden of the learning stage
Coarse and uniform embeddings between Orlicz sequence spaces
We give an almost complete description of the coarse and uniform
embeddability between Orlicz sequence spaces. We show that the embeddability
between two Orlicz sequence spaces is in most cases determined only by the
values of their upper Matuszewska-Orlicz indices. On the other hand, we present
examples which show that sometimes the embeddability is not determined by the
values of these indices.Comment: 12 pages. This is the final version. To appear in Mediterr. J. Mat
Continuous time dynamics of the Thermal Minority Game
We study the continuous time dynamics of the Thermal Minority Game. We find
that the dynamical equations of the model reduce to a set of stochastic
differential equations for an interacting disordered system with non-trivial
random diffusion. This is the simplest microscopic description which accounts
for all the features of the system. Within this framework, we study the phase
structure of the model and find that its macroscopic properties strongly depend
on the initial conditions.Comment: 4 pages, 4 figure
Influence of external information in the minority game
The influence of a fixed number of agents with the same fixed behavior on the
dynamics of the minority game is studied. Alternatively, the system studied can
be considered the minority game with a change in the comfort threshold away
from half filling. Agents in the frustrated, non ergodic phase tend to
overreact to the information provided by the fixed agents, leading not only to
large fluctuations, but to deviations of the average occupancies from their
optimal values. Agents which discount their impact on the market, or which use
individual strategies reach equilibrium states, which, unlike in the absence of
the external information provided by the fixed agents, do not give the highest
payoff to the collective.Comment: 8 pages, 6 figure
A nonparametric urn-based approach to interacting failing systems with an application to credit risk modeling
In this paper we propose a new nonparametric approach to interacting failing
systems (FS), that is systems whose probability of failure is not negligible in
a fixed time horizon, a typical example being firms and financial bonds. The
main purpose when studying a FS is to calculate the probability of default and
the distribution of the number of failures that may occur during the
observation period. A model used to study a failing system is defined default
model. In particular, we present a general recursive model constructed by the
means of inter- acting urns. After introducing the theoretical model and its
properties we show a first application to credit risk modeling, showing how to
assess the idiosyncratic probability of default of an obligor and the joint
probability of failure of a set of obligors in a portfolio of risks, that are
divided into reliability classes
Density functional theory of phase coexistence in weakly polydisperse fluids
The recently proposed universal relations between the moments of the
polydispersity distributions of a phase-separated weakly polydisperse system
are analyzed in detail using the numerical results obtained by solving a simple
density functional theory of a polydisperse fluid. It is shown that universal
properties are the exception rather than the rule.Comment: 10 pages, 2 figures, to appear in PR
A characterization of Schauder frames which are near-Schauder bases
A basic problem of interest in connection with the study of Schauder frames
in Banach spaces is that of characterizing those Schauder frames which can
essentially be regarded as Schauder bases. In this paper, we give a solution to
this problem using the notion of the minimal-associated sequence spaces and the
minimal-associated reconstruction operators for Schauder frames. We prove that
a Schauder frame is a near-Schauder basis if and only if the kernel of the
minimal-associated reconstruction operator contains no copy of . In
particular, a Schauder frame of a Banach space with no copy of is a
near-Schauder basis if and only if the minimal-associated sequence space
contains no copy of . In these cases, the minimal-associated
reconstruction operator has a finite dimensional kernel and the dimension of
the kernel is exactly the excess of the near-Schauder basis. Using these
results, we make related applications on Besselian frames and near-Riesz bases.Comment: 12 page
- …