Bounding Embeddings of VC Classes into Maximum Classes

One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinality for their VC dimension. The most promising approach to positively resolving the conjecture is by embedding general VC classes into maximum classes without super-linear increase to their VC dimensions, as such embeddings would extend the known compression schemes to all VC classes. We show that maximum classes can be characterised by a local-connectivity property of the graph obtained by viewing the class as a cubical complex. This geometric characterisation of maximum VC classes is applied to prove a negative embedding result which demonstrates VC-d classes that cannot be embedded in any maximum class of VC dimension lower than 2d. On the other hand, we show that every VC-d class C embeds in a VC-(d+D) maximum class where D is the deficiency of C, i.e., the difference between the cardinalities of a maximum VC-d class and of C. For VC-2 classes in binary n-cubes for 4 <= n <= 6, we give best possible results on embedding into maximum classes. For some special classes of Boolean functions, relationships with maximum classes are investigated. Finally we give a general recursive procedure for embedding VC-d classes into VC-(d+k) maximum classes for smallest k.Comment: 22 pages, 2 figure

NSSDC Conference on Mass Storage Systems and Technologies for Space and Earth Science Applications, volume 1

Papers and viewgraphs from the conference are presented. This conference served as a broad forum for the discussion of a number of important issues in the field of mass storage systems. Topics include magnetic disk and tape technologies, optical disks and tape, software storage and file management systems, and experiences with the use of a large, distributed storage system. The technical presentations describe, among other things, integrated mass storage systems that are expected to be available commercially. Also included is a series of presentations from Federal Government organizations and research institutions covering their mass storage requirements for the 1990's

Rigorous Derivation of the Gross-Pitaevskii Equation

The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short scale correlation structure in the condensate.Comment: 4 pages, 1 figur

Comment on ``Scaling Laws for a System with Long-Range Interactions within Tsallis Statistics''

In their recent Letter [Phys. Rev. Lett. 83, 4233 (1999)], Salazar and Toral (ST) study numerically a finite Ising chain with non-integrable interactions decaying like 1/r^(d+sigma) where -d <= sigma <= 0 (like ST, we discuss general dimensionality d). In particular, they explore a presumed connection between non-integrable interactions and Tsallis's non-extensive statistics. We point out that (i) non-integrable interactions provide no more motivation for Tsallis statistics than do integrable interactions, i.e., Gibbs statistics remain meaningful for the non-integrable case, and in fact provide a {\em complete and exact treatment}; and (ii) there are undesirable features of the method ST use to regulate the non-integrable interactions.Comment: Accepted for publication in Phys. Rev. Let

A Pyrrole-Based Triazolium-Phane with Nh and Cationic Ch Donor Groups as a Receptor for Tetrahedral Oxyanions that Functions in Polar Media

The pyrrole-based triazolium-phane 1(4+)center dot 4BF(4)(-) has been prepared via the tetraalkylation of a macrocycle originally prepared via click chemistry. It displays a high selectivity for tetrahedral oxyanions relative to various test monoanions and trigonal planar anions in mixed polar organic-aqueous media. This selectivity is solvent dependent and is less pronounced in acetonitrile. Theoretical calculations were carried out in with the chloride anion in an effort to understand the influence of solvent on the intrinsic hydrogen bonding ability of the donor groups (pyrrole N-H, benzene C-H and triazolium C-H). The host-guest interactions between receptor 1(4+)center dot 4BF(4)(-) and representative tetrahedral oxyanions were further analysed by H-1 NMR spectroscopy, and the findings proved consistent with the differences in the intrinsic strength of the various H-bond donor groups inferred from the electronic structure calculations carried out in methanol, namely that (CH)(+)-anion interactions are less important in an energetic sense than neutral CH-anion interactions in polar media. Single crystal X-ray diffraction analyses of the mixed salts 1(4+)center dot HP2O73-center dot BF4- and 31(4+)center dot 4H(2)PO(4)(-)center dot 8BF(4)(-) confirmed that receptor 1(4+) can bind the pyrophosphate and phosphate anions in the solid state.Cai, Jiajia, Benjamin P. Hay, Neil J. Young, Xiaoping Yang, and Jonathan L. Sessler. "A pyrrole-based triazolium-phane with NH and cationic CH donor groups as a receptor for tetrahedral oxyanions that functions in polar media." Chemical Science 4, no. 4 (Jan., 2013): 1560-1567.Chemistr

Modulational Instability and Complex Dynamics of Confined Matter-Wave Solitons

We study the formation of bright solitons in a Bose-Einstein condensate of $^7$Li atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment (Nature {\bf 417}, 150 (2002)). The numerical simulations are performed by using the 3D Gross-Pitaevskii equation (GPE) with a dissipative three-body term. We show that a number of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent macroscopic wave function of the Bose condensate. In particular, we derive a simple formula for the number of solitons that is in good agreement with the numerical results of 3D GPE. By investigating the long time evolution of the soliton train solving the 1D GPE with three-body dissipation we find that adjacent solitons repel each other due to their phase difference. In addition, we find that during the motion of the soliton train in an axial harmonic potential the number of solitonic peaks changes in time and the density of individual peaks shows an intermittent behavior. Such a complex dynamics explains the ``missing solitons'' frequently found in the experiment.Comment: to be published in Phys. Rev. Let

INCORPORATION OF WITHIN-SEASON YIELD GROWTH INTO A MATHEMATICAL PROGRAMMING SUGARCANE HARVEST SCHEDULING MODEL

This study focuses on the development of a optimal harvest scheduling mathematical programming model which incorporates within-season changes in perennial crop yields. Daily crop yield prediction models are estimated econometrically for major commercially grown sugarcane cultivars. This information is incorporated into a farm-level harvest scheduling linear programming model. The harvest scheduling model solves for an optimal daily harvest schedule which maximizes whole farm net returns above harvesting costs. Model results are compared for a commercial sugarcane farm in Louisiana.sugarcane, harvest scheduling, within-season yield growth, Crop Production/Industries,

Single-Species Three-Particle Reactions in One Dimension

Renormalization group calculations for fluctuation-dominated reaction-diffusion systems are generally in agreement with simulations and exact solutions. However, simulations of the single-species reactions 3A->(0,A,2A) at their upper critical dimension d_c=1 have found asymptotic densities argued to be inconsistent with renormalization group predictions. We show that this discrepancy is resolved by inclusion of the leading corrections to scaling, which we derive explicitly and show to be universal, a property not shared by the A+A->(0,A) reactions. Finally, we demonstrate that two previous Smoluchowski approaches to this problem reduce, with various corrections, to a single theory which yields, surprisingly, the same asymptotic density as the renormalization group.Comment: 8 pages, 5 figs, minor correction

Unconventional magnetism in imbalanced Fermi systems with magnetic dipolar interactions

We study the magnetic structure of the ground state of an itinerant Fermi system of spin-\nicefrac{1}{2} particles with magnetic dipole-dipole interactions. We show that, quite generally, the spin state of particles depend on its momentum, i.e., spin and orbital degrees of freedom are entangled and taken separately are not ``good'' quantum numbers. Specifically, we consider a uniform system with non-zero magnetization at zero temperature. Assuming the magnetization is along $z$-axis, the quantum spin states are $\v{k}$-dependent linear combinations of eigenstates of the $\sigma_z$ Pauli matrix. This leads to novel spin structures in \textit{momentum space} and to the fact that the Fermi surfaces for ``up'' and ``down'' spins are not well defined. The system still has a cylindrical axis of symmetry along the magnetization axis. We also show that the self energy has a universal structure which we determine based on the symmetries of the dipolar interaction and we explicitly calculated it in the Hartree-Fock approximation. We show that the bare magnetic moment of particles is renormalized due to particle-particle interactions and we give order of magnitude estimates of this renormalization effect. We estimate that the above mentioned dipolar effects are small but we discuss possible scenarios where this physics may be realized in future experiments.Comment: 10 pages, 6 figures(2 subfigures); 4 appendices. Version published in Physical Review

The Dynamics of Galaxy Pairs in a Cosmological Setting

We use the Millennium Simulation, and an abundance-matching framework, to investigate the dynamical behaviour of galaxy pairs embedded in a cosmological context. Our main galaxy-pair sample, selected to have separations under 250 kpc/h, consists of over 1.3 million pairs at redshift z = 0, with stellar masses greater than 10^9 Msun, probing mass ratios down to 1:1000. We use dark matter halo membership and energy to classify our galaxy pairs. In terms of halo membership, central-satellite pairs tend to be in isolation (in relation to external more massive galaxies), are energetically- bound to each other, and are also weakly-bound to a neighbouring massive galaxy. Satellite-satellite pairs, instead, inhabit regions in close proximity to a more massive galaxy, are energetically-unbound, and are often bound to that neighbour. We find that 60% of our paired galaxies are bound to both their companion and to a third external object. Moreover, only 9% of our pairs resemble the kind of systems described by idealised binary merger simulations in complete isolation. In sum, we demonstrate the importance of properly connecting galaxy pairs to the rest of the Universe.Comment: 25 pages, 14 figures, accepted by MNRA