Explicit Learning Curves for Transduction and Application to Clustering and Compression Algorithms

Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are given to the learner prior to learning. Although transduction seems at the outset to be an easier task than induction, there have not been many provably useful algorithms for transduction. Moreover, the precise relation between induction and transduction has not yet been determined. The main theoretical developments related to transduction were presented by Vapnik more than twenty years ago. One of Vapnik's basic results is a rather tight error bound for transductive classification based on an exact computation of the hypergeometric tail. While tight, this bound is given implicitly via a computational routine. Our first contribution is a somewhat looser but explicit characterization of a slightly extended PAC-Bayesian version of Vapnik's transductive bound. This characterization is obtained using concentration inequalities for the tail of sums of random variables obtained by sampling without replacement. We then derive error bounds for compression schemes such as (transductive) support vector machines and for transduction algorithms based on clustering. The main observation used for deriving these new error bounds and algorithms is that the unlabeled test points, which in the transductive setting are known in advance, can be used in order to construct useful data dependent prior distributions over the hypothesis space

Kondo effect in complex mesoscopic structures

We study the Kondo effect of a quantum dot placed in a complex mesoscopic structure. Assuming that electronic interactions are taking place solely on the dot, and focusing on the infinite Hubbard interaction limit, we use a decoupling scheme to obtain an explicit analytic approximate expression for the dot Green function, which fulfills certain Fermi-liquid relations at zero temperature. The details of the complex structure enter into this expression only via the self-energy for the non-interacting case. The effectiveness of the expression is demonstrated for the single impurity Anderson model and for the T-shaped network.Comment: 12 pages 6 figure

Andreev Tunneling in Strongly Interacting Quantum Dots

We review recent work on resonant Andreev tunneling through a strongly interacting quantum dot connected to a normal and to a superconducting lead. We derive a general expression for the current flowing in the structure and discuss the linear and non-linear transport in the nonperturbative regime. New effects associated to the Kondo resonance combined with the two-particle tunneling arise. The Kondo anomaly in the $I-V$ characteristics depends on the relative size of the gap energy and the Kondo temperature.Comment: 8 pages, 4 figures; submitted to Superlattices and Microstructure

The Effects of Resonant Tunneling on Magnetoresistance through a Q uantum Dot

The effect of resonant tunneling on magnetoresistance (MR) is studied theoretically in a double junction system. We have found that the ratio of the MR of the resonant peak current is reduced more than that of the single junction, whereas that of the valley current is enhanced depending on the change of the discrete energy-level under the change of magnetic field. We also found that the peak current-valley current (PV) ratio decreases when the junction conductance increases.Comment: 11 pages, 3 figures(mail if you need), use revtex.st

Anomalous magnetic splitting of the Kondo resonance

The splitting of the Kondo resonance in the density of states of an Anderson impurity in finite magnetic field is calculated from the exact Bethe-ansatz solution. The result gives an estimate of the electron spectral function for nonzero magnetic field and Kondo temperature, with consequences for transport experiments on quantum dots in the Kondo regime. The strong correlations of the Kondo ground state cause a significant low-temperature reduction of the peak splitting. Explicit formulae are found for the shift and broadening of the Kondo peaks. A likely cause of the problems of large-N approaches to spin-1/2 impurities at finite magnetic field is suggested.Comment: 4 pages, 2 eps figures; published versio

Three-compartment body composition changes in elite rugby league players during a super league season, measured by dual-energy X-ray absorptiometry.

This study investigated the acute changes in body composition that occur over the course of a competitive season in elite rugby league players. Twenty elite senior players from an English Super League rugby league team underwent a total-body dual-energy X-ray absorptiometry scan at 3 phases of a competitive season: preseason (February), midseason (June), and postseason (September). Body mass (BM), fat mass (FM), lean mass, percentage body fat, and bone mineral content (BMC) were reported at each phase. Between the start and midpoint of the season, BM, lean mass, FM, and body fat percentage showed no significant change (p > 0.05); however, BMC was significantly increased (+0.71%; 30.70 ± 38.00 g; p 0.05); however, significant changes were observed in lean mass (-1.54%; 1.19 ± 1.43 kg), FM (+4.09%; 0.57 ± 1.10 kg), and body fat percentage (+4.98%; 0.78 ± 1.09%; p < 0.05). The significant changes in body composition seen over the latter stages of the competitive season may have implications for performance capabilities at this important stage of competition. An increase in FM and decrease in lean mass may have a negative effect on the power/BM ratio, and therefore may be a cause for concern for playing, coaching, and medical staff. Coaching and strength and conditioning staff should aim to prescribe appropriate training and nutritional practices with the aim of maintaining the players' optimal body composition until the conclusion of the competitive season, in order that performance capabilities are maximized over the entire competition period

Transmission Phase Shift of a Quantum Dot with Kondo Correlations

We study the effects of Kondo correlations on the transmission phase shift of a quantum dot in an Aharonov-Bohm ring. We predict in detail how the development of a Kondo resonance should affect the dependence of the phase shift on transport voltage, gate voltage and temperature. This system should allow the first direct observation of the well-known scattering phase shift of pi/2 expected (but not directly measurable in bulk systems) at zero temperature for an electron scattering off a spin-1/2 impurity that is screened into a singlet.Comment: 4 pages Revtex, 4 figures, final published versio

Gauge factor of thick film resistors: outcomes of the variable range hopping model

Despite a large amount of data and numerous theoretical proposals, the microscopic mechanism of transport in thick film resistors remains unclear. However, recent low temperature measurements point toward a possible variable range hopping mechanism of transport. Here we examine how such a mechanism affects the gauge factor of thick film resistors. We find that at sufficiently low temperatures $T$, for which the resistivity follows the Mott's law $R(T)\sim \exp(T_0/T)^{1/4}$, the gauge factor GF is proportional to $(T_0/T)^{1/4}$. Moreover, the inclusion of Coulomb gap effects leads to ${\rm GF}\sim (T_0'/T)^{1/2}$ at lower temperatures. In addition, we study a simple model which generalizes the variable range hopping mechanism by taking into account the finite mean inter-grain spacing. Our results suggest a possible experimental verification of the validity of the variable range hopping in thick film resistors.Comment: 7 pages, 3 eps figures, submitted to Journal of Applied Physic

Reply to Comment on "Exact analytic solution for the generalized Lyapunov exponent of the 2-dimensional Anderson localization"

We reply to comments by P.Marko$\breve{s}$, L.Schweitzer and M.Weyrauch [preceding paper] on our recent paper [J. Phys.: Condens. Matter 63, 13777 (2002)]. We demonstrate that our quite different viewpoints stem for the different physical assumptions made prior to the choice of the mathematical formalism. The authors of the Comment expect \emph{a priori} to see a single thermodynamic phase while our approach is capable of detecting co-existence of distinct pure phases. The limitations of the transfer matrix techniques for the multi-dimensional Anderson localization problem are discussed.Comment: 4 pages, accepted for publication in J.Phys.: Condens. Mat