808 research outputs found
A tensor analysis improved genetic algorithm for online bin packing
Mutation in a Genetic Algorithm is the key variation operator adjusting the genetic diversity in a population throughout the evolutionary process. Often, a fixed mutation probability is used to perturb the value of a gene. In this study, we describe a novel data science approach to adaptively generate the mutation probability for each locus. The trail of high quality candidate solutions obtained during the search process is represented as a 3rd order tensor. Factorizing that tensor captures the common pattern between those solutions, identifying the degree of mutation which is likely to yield improvement at each locus. An online bin packing problem is used as an initial case study to investigate the proposed approach for generating locus dependent mutation probabilities. The empirical results show that the tensor approach improves the performance of a standard Genetic Algorithm on almost all classes of instances, significantly
Smoothed Analysis of Tensor Decompositions
Low rank tensor decompositions are a powerful tool for learning generative
models, and uniqueness results give them a significant advantage over matrix
decomposition methods. However, tensors pose significant algorithmic challenges
and tensors analogs of much of the matrix algebra toolkit are unlikely to exist
because of hardness results. Efficient decomposition in the overcomplete case
(where rank exceeds dimension) is particularly challenging. We introduce a
smoothed analysis model for studying these questions and develop an efficient
algorithm for tensor decomposition in the highly overcomplete case (rank
polynomial in the dimension). In this setting, we show that our algorithm is
robust to inverse polynomial error -- a crucial property for applications in
learning since we are only allowed a polynomial number of samples. While
algorithms are known for exact tensor decomposition in some overcomplete
settings, our main contribution is in analyzing their stability in the
framework of smoothed analysis.
Our main technical contribution is to show that tensor products of perturbed
vectors are linearly independent in a robust sense (i.e. the associated matrix
has singular values that are at least an inverse polynomial). This key result
paves the way for applying tensor methods to learning problems in the smoothed
setting. In particular, we use it to obtain results for learning multi-view
models and mixtures of axis-aligned Gaussians where there are many more
"components" than dimensions. The assumption here is that the model is not
adversarially chosen, formalized by a perturbation of model parameters. We
believe this an appealing way to analyze realistic instances of learning
problems, since this framework allows us to overcome many of the usual
limitations of using tensor methods.Comment: 32 pages (including appendix
The Superconducting Transition Temperatures of Fe1+xSe1--y, Fe1+xSe1--yTey and (K/Rb/Cs)zFe2--xSe2
In a recent contribution to this journal, it was shown that the transition
temperatures of optimal high-Tc compounds obey the algebraic relation, Tc0 =
kB-1{\beta}/\ell{\zeta}, where \ell is related to the mean spacing between
interacting charges in the layers, {\zeta} is the distance between interacting
electronic layers, {\beta} is a universal constant and kB is Boltzmann's
constant. The equation was derived assuming pairing based on interlayer Coulomb
interactions between physically separated charges. This theory was initially
validated for 31 compounds from five different high-Tc families (within an
accuracy of \pm1.37 K). Herein we report the addition of Fe1+xSe1-y and
Fe1+xSe1-yTey (both optimized under pressure) and AzFe2-xSe2 (for A = K, Rb, or
Cs) to the growing list of Coulomb-mediated superconducting compounds in which
Tc0 is determined by the above equation. Doping in these materials is
accomplished through the introduction of excess Fe and/or Se deficiency, or a
combination of alkali metal and Fe vacancies. Consequently, a very small number
of vacancies or interstitials can induce a superconducting state with a
substantial transition temperature. The confirmation of the above equation for
these Se-based Fe chalcogenides increases to six the number of superconducting
families for which the transition temperature can be accurately predicted.Comment: 16 pages, 54 references 3 figures 1 tabl
An efficient and general approach for implementing thermodynamic phase equilibria information in geophysical and geodynamic studies
We present a flexible, general, and efficient approach for implementing thermodynamic phase equilibria information (in the form of sets of physical parameters) into geophysical and geodynamic studies. The approach is based on Tensor Rank Decomposition methods, which transform the original multidimensional discrete information into a separated representation that contains significantly fewer terms, thus drastically reducing the amount of information to be stored in memory during a numerical simulation or geophysical inversion. Accordingly, the amount and resolution of the thermodynamic information that can be used in a simulation or inversion increases substantially. In addition, the method is independent of the actual software used to obtain the primary thermodynamic information, and therefore, it can be used in conjunction with any thermodynamic modeling program and/or database. Also, the errors associated with the decomposition procedure are readily controlled by the user, depending on her/his actual needs (e.g., preliminary runs versus full resolution runs). We illustrate the benefits, generality, and applicability of our approach with several examples of practical interest for both geodynamic modeling and geophysical inversion/modeling. Our results demonstrate that the proposed method is a competitive and attractive candidate for implementing thermodynamic constraints into a broad range of geophysical and geodynamic studies. MATLAB implementations of the method and examples are provided as supporting information and can be downloaded from the journal's website.Peer ReviewedPostprint (author's final draft
Poincare Semigroup Symmetry as an Emergent Property of Unstable Systems
The notion that elementary systems correspond to irreducible representations
of the Poincare group is the starting point for this paper, which then goes on
to discuss how a semigroup for the time evolution of unstable states and
resonances could emerge from the underlying Poincare symmetry. Important tools
in this analysis are the Clebsch-Gordan coefficients for the Poincare group.Comment: 17 pages, 1 figur
Theory of High-Tc Superconductivity: Accurate Predictions of Tc
The superconducting transition temperatures of high-Tc compounds based on
copper, iron, ruthenium and certain organic molecules are discovered to be
dependent on bond lengths, ionic valences, and Coulomb coupling between
electronic bands in adjacent, spatially separated layers [1]. Optimal
transition temperature, denoted as T_c0, is given by the universal expression
; is the spacing between interacting
charges within the layers, \zeta is the distance between interacting layers and
\Lambda is a universal constant, equal to about twice the reduced electron
Compton wavelength (suggesting that Compton scattering plays a role in
pairing). Non-optimum compounds in which sample degradation is evident
typically exhibit Tc < T_c0. For the 31+ optimum compounds tested, the
theoretical and experimental T_c0 agree statistically to within +/- 1.4 K. The
elemental high Tc building block comprises two adjacent and spatially separated
charge layers; the factor e^2/\zeta arises from Coulomb forces between them.
The theoretical charge structure representing a room-temperature superconductor
is also presented.Comment: 7 pages 5 references, 6 figures 1 tabl
An Evolutionary No Man’s Land and Reply from L. G. Harshman and A. A. Hoffmann
The gap between evolutionary studies in laboratory versus natural populations is a persistent problem
About the maximal rank of 3-tensors over the real and the complex number field
High dimensional array data, tensor data, is becoming important in recent
days. Then maximal rank of tensors is important in theory and applications. In
this paper we consider the maximal rank of 3 tensors. It can be attacked from
various viewpoints, however, we trace the method of Atkinson-Stephens(1979) and
Atkinson-Lloyd(1980). They treated the problem in the complex field, and we
will present various bounds over the real field by proving several lemmas and
propositions, which is real counterparts of their results.Comment: 13 pages, no figure v2: correction and improvemen
Understanding entangled spins in QED
The stability of two entangled spins dressed by electrons is studied by
calculating the scattering phase shifts. The interaction between electrons is
interpreted by fully relativistic QED and the screening effect is described
phenomenologically in the Debye exponential form . Our results
show that if the (Einstein-Podolsky-Rosen-) EPR-type states are kept stable
under the interaction of QED, the spatial wave function must be
parity-dependent. The spin-singlet state and the polarized state along the z-axis\QTR{bf}{\}give rise to two
different kinds of phase shifts\QTR{bf}{.} Interestingly, the interaction
between electrons in the spin-singlet pair is found to be attractive. Such an
attraction could be very useful when we extract the entangled spins from
superconductors. A mechanism to filter the entangled spins is also discussed.Comment: 6 pages, 3 figures. changes adde
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