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

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

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

The fate of assimilated carbon during drought: impacts on respiration in Amazon rainforests

Interannual variations in CO2 exchange across Amazonia, as deduced from atmospheric inversions, correlate with El Niño occurrence. They are thought to result from changes in net ecosystem exchange and fire incidence that are both related to drought intensity. Alterations to net ecosystem production (NEP) are caused by changes in gross primary production (GPP) and ecosystem respiration (Reco). Here, we analyse observations of the components of Reco (leaves, live and dead woody tissue, and soil) to provide first estimates of changes in Reco during short-term (seasonal to interannual) moisture limitation. Although photosynthesis declines if moisture availability is limiting, leaf dark respiration is generally maintained, potentially acclimating upwards in the longer term. If leaf area is lost, then short-term canopy-scale respiratory effluxes from wood and leaves are likely to decline. Using a moderate short-term drying scenario where soil moisture limitation leads to a loss of 0.5 m2 m−2 yr−1 in leaf area index, we estimate a reduction in respiratory CO2 efflux from leaves and live woody tissue of 1.0 (±0.4) t C ha−1 yr−1. Necromass decomposition declines during drought, but mortality increases; the median mortality increase following a strong El Niño is 1.1% (n=46 tropical rainforest plots) and yields an estimated net short-term increase in necromass CO2 efflux of 0.13–0.18 t C ha−1 yr−1. Soil respiration is strongly sensitive to moisture limitation over the short term, but not to associated temperature increases. This effect is underestimated in many models but can lead to estimated reductions in CO2 efflux of 2.0 (±0.5) t C ha−1 yr−1. Thus, the majority of short-term respiratory responses to drought point to a decline in Reco, an outcome that contradicts recent regional-scale modelling of NEP. NEP varies with both GPP and Reco but robust moisture response functions are clearly needed to improve quantification of the role of Reco in influencing regional-scale CO2 emissions from Amazonia

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

A New Spin-Orbit Induced Universality Class in the Quantum Hall Regime ?

Using heuristic arguments and numerical simulations it is argued that the critical exponent $\nu$ describing the localization length divergence at the quantum Hall transition is modified in the presence of spin-orbit scattering with short range correlations. The exponent is very close to $\nu=4/3$, the percolation correlation length exponent, the prediction of a semi-classical argument. In addition, a region of weakly localized regime, where the localization length is exponentially large, is conjectured.Comment: 4 two-column pages including 4 eps figure

Interplay between Coulomb Blockade and Resonant Tunneling studied by the Keldysh Green's Function Method

A theory of tunneling through a quantum dot is presented which enables us to study combined effects of Coulomb blockade and discrete energy spectrum of the dot. The expression of tunneling current is derived from the Keldysh Green's function method, and is shown to automatically satisfy the conservation at DC current of both junctions.Comment: 4 pages, 3 figures(mail if you need), use revtex.sty, error corrected, changed titl