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

Magnon Condensation in a Dense Nitrogen-Vacancy Spin Ensemble

The feasibility of creating a Bose-Einstein condensate of magnons using a dense ensemble of nitrogen-vacancy spin defects in diamond is investigated. Through assessing a density-dependent spin exchange interaction strength and the magnetic phase transition temperature ($T_c$) using the Sherrington-Kirkpatrick model, the minimum temperature-dependent concentration for magnetic self-ordering is estimated. For a randomly dispersed spin ensemble, the calculated average exchange constant exceeds the average dipole interaction strengths for concentrations approximately greater than 70 ppm, while $T_c$ is estimated to exceed 10 mK beyond 90 ppm, reaching 300 K at a concentration of approximately 450 ppm. On this basis, the existence of dipole-exchange spin waves and their plane-wave dispersion is postulated and estimated using a semiclassical magnetostatic description. This is discussed along with a $T_c$-based estimate of the four-magnon scattering rate, which indicates magnons and their condensation may be detectable in thin films for concentrations greater than 90 ppm.Comment: 14 pages, 6 figure

Enhancing IT investments productivity: Integrating network QOS and it indirect costs

Increasing productivity is considered one of the major driving factors for a successful business. From an Information Technology (IT) infrastructure perspective, obtaining an optimised performance of resources is expected to improve productivity. From a technical viewpoint, the introduction of Quality of Service (QoS) models have been perceived to optimise the performance of the organisation network backbone. These models aim to provide an acceptable level of service assurance to the newly introduced applications and services such as voice and video. From a management viewpoint, the proper management of IT investments indirect costs can lead to a reduction of the overall cost portfolio. Consequently, both benefits and productivity increase are likely to be realised. This paper introduces network QoS strategy within the hierarchy of business infrastructure. In addition, it aims to identify the relationship between network QoS and IT indirect costs. Such integration demonstrates how network QoS strategy can be used to control IT indirect costs as well as enhancing network performance

Freshwater security, conflict and cooperation: the case of the Red Sea-Dead Sea conduit project

This study examines the challenge of freshwater security faced by Israel, Jordan and Palestine, and mechanisms for multilateral collaboration that have been developed in order to create a Red Sea-Dead Sea Conduit. This paper outlines the proposed conduit as a major collaborative project which hinges on the engagement of both state and non-state stakeholders. The argument presented here is that the feasibility and planning process has so far been successful and that the mechanisms for collaboration developed as part of this project are the reason why. Overall conclusions suggest that the importance of freshwater security and the agency of international state and non-state actors are largely responsible for these collaborative successes

Presenting Schur superalgebras

We provide a presentation of the Schur superalgebra and its quantum analogue which generalizes the work of Doty and Giaquinto for Schur algebras. Our results include a basis for these algebras and a presentation using weight idempotents in the spirit of Lusztig's modified quantum groups.Comment: 28 pages, to appear in the Pacific Journal of Mathematic

Artinian Gorenstein algebras with linear resolutions

Fix a pair of positive integers d and n. We create a ring R and a complex G of R-modules with the following universal property. Let P be a polynomial ring in d variables over a field and let I be a grade d Gorenstein ideal in P which is generated by homogeneous forms of degree n. If the resolution of P/I by free P-modules is linear, then there exists a ring homomorphism from R to P such that P tensor G is a minimal homogeneous resolution of P/I by free P-modules. Our construction is coordinate free