Input Sparsity and Hardness for Robust Subspace Approximation

In the subspace approximation problem, we seek a k-dimensional subspace F of R^d that minimizes the sum of p-th powers of Euclidean distances to a given set of n points a_1, ..., a_n in R^d, for p >= 1. More generally than minimizing sum_i dist(a_i,F)^p,we may wish to minimize sum_i M(dist(a_i,F)) for some loss function M(), for example, M-Estimators, which include the Huber and Tukey loss functions. Such subspaces provide alternatives to the singular value decomposition (SVD), which is the p=2 case, finding such an F that minimizes the sum of squares of distances. For p in [1,2), and for typical M-Estimators, the minimizing $F$ gives a solution that is more robust to outliers than that provided by the SVD. We give several algorithmic and hardness results for these robust subspace approximation problems. We think of the n points as forming an n x d matrix A, and letting nnz(A) denote the number of non-zero entries of A. Our results hold for p in [1,2). We use poly(n) to denote n^{O(1)} as n -> infty. We obtain: (1) For minimizing sum_i dist(a_i,F)^p, we give an algorithm running in O(nnz(A) + (n+d)poly(k/eps) + exp(poly(k/eps))), (2) we show that the problem of minimizing sum_i dist(a_i, F)^p is NP-hard, even to output a (1+1/poly(d))-approximation, answering a question of Kannan and Vempala, and complementing prior results which held for p >2, (3) For loss functions for a wide class of M-Estimators, we give a problem-size reduction: for a parameter K=(log n)^{O(log k)}, our reduction takes O(nnz(A) log n + (n+d) poly(K/eps)) time to reduce the problem to a constrained version involving matrices whose dimensions are poly(K eps^{-1} log n). We also give bicriteria solutions, (4) Our techniques lead to the first O(nnz(A) + poly(d/eps)) time algorithms for (1+eps)-approximate regression for a wide class of convex M-Estimators.Comment: paper appeared in FOCS, 201

The Alaska Marriage Amendment: The People’s Choice on the Last Frontier

I Sverige beräknas 17 % av befolkningen ha en hörselnedsättning, vilket innebär att det är den vanligaste sensoriska funktionsnedsättningen. Idag finns det en mängd studier som visar att hörselnedsättning är relaterat till sämre psykisk hälsa. Acceptans av sin hörselnedsättning har visat sig vara positivt för hörselnedsatta och samvarierar med hjälpsökande. Acceptance and commitment therapy (ACT) är en transdiagnostisk behandling där psykopatologi antas bero på en hög grad av upplevelsemässigt undvikande och fusion med tankar. Målet i ACT är att öka psykologisk flexibilitet där acceptans är en betydande komponent. Denna explorativa studie undersökte förändringsprocesser i ACT för personer med hörselnedsättning där utfallet var känslomässig och social anpassning för hörselnedsättningen (HHIE-S). De förändringsprocesser som prövades var acceptans (HAQ), som tidigare visat på medierande effekt för ACT, samt två alternativa förändringsprocesser; self-efficacy (HSE-4) och upplevd stress (PSS-4). Behandlingen bestod av åtta internetadministrerade moduler givna med behandlarstöd där veckovisa mätningar av förändringsprocesser och utfall användes. Studiens resultat visar att behandlingsgruppen upplevde marginellt signifikant mindre problem med känslomässig och social anpassning för hörselnedsättningen (HHIE-S). Studiens resultat pekar på att hörselrelaterad acceptans (HAQ) och self- efficacy (HSE-4) medierar behandlingens effekt på deltagarnas känslomässiga och sociala anpassning för hörselnedsättning (HHIE-S). Således tillför denna studie ytterligare belägg för acceptans som förändringsprocess i ACT. Även self-efficacy kan vara en intressant mediator att beakta i fortsatt forskning.

Study of pion-proton backward elastic scattering in the centre of mass energy range 2.1 to 2.4 GeV

SIGLELD:D45266/83 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Issues facing Southland’s wetlands— recommendations for future management

This report summarises our experiences and recommendations from a weeklong series of fieldtrips and workshops focused on Southland’s wetlands. Our major recommendations are: • Priorities must be developed for wetland protection and restoration, according to which wetland systems have suffered the greatest losses and which are least represented in the reserves network. • The development of educational and interpretive resources and programmes will help to raise the level of awareness of the unique values of Southland’s wetlands amongst landowners, local authorities and the public, and will provide opportunities for regional promotion and ecotourism. • There is a need for more research to: increase levels of understanding of wetland development and function; threats from weed invasion and effective control methods; and to design and monitor effective restoration efforts. Some of this research could be achieved thorough ongoing communication with PGSF-funded research organisations and universities, eg. BSc (Hons) and MSc thesis topics. • Protect the hydrological functioning of wetlands, by developing guidelines for drainage practices in land adjacent to wetlands, and reducing nutrient loading of surface and groundwaters flowing into wetlands. • Incorporate principles of wetland protection into regional and district plans

The use of chronosequences in studies of ecological succession and soil development

1. Chronosequences and associated space-for-time substitutions are an important and often necessary tool for studying temporal dynamics of plant communities and soil development across multiple time-scales. However, they are often used inappropriately, leading to false conclusions about ecological patterns and processes, which has prompted recent strong criticism of the approach. Here, we evaluate when chronosequences may or may not be appropriate for studying community and ecosystem development. 2. Chronosequences are appropriate to study plant succession at decadal to millennial time-scales when there is evidence that sites of different ages are following the same trajectory. They can also be reliably used to study aspects of soil development that occur between temporally linked sites over time-scales of centuries to millennia, sometimes independently of their application to shorter-term plant and soil biological communities. 3. Some characteristics of changing plant and soil biological communities (e.g. species richness, plant cover, vegetation structure, soil organic matter accumulation) are more likely to be related in a predictable and temporally linear manner than are other characteristics (e.g. species composition and abundance) and are therefore more reliably studied using a chronosequence approach. 4. Chronosequences are most appropriate for studying communities that are following convergent successional trajectories and have low biodiversity, rapid species turnover and low frequency and severity of disturbance. Chronosequences are least suitable for studying successional trajectories that are divergent, species-rich, highly disturbed or arrested in time because then there are often major difficulties in determining temporal linkages between stages. 5. Synthesis. We conclude that, when successional trajectories exceed the life span of investigators and the experimental and observational studies that they perform, temporal change can be successfully explored through the judicious use of chronosequences

The cosmological gravitational wave background from primordial density perturbations

We discuss the gravitational wave background generated by primordial density perturbations evolving during the radiation era. At second-order in a perturbative expansion, density fluctuations produce gravitational waves. We calculate the power spectra of gravitational waves from this mechanism, and show that, in principle, future gravitational wave detectors could be used to constrain the primordial power spectrum on scales vastly different from those currently being probed by large-scale structure. As examples we compute the gravitational wave background generated by both a power-law spectrum on all scales, and a delta-function power spectrum on a single scale.Comment: 8 Page

Novel muon imaging techniques

Owing to the high penetrating power of high-energy cosmic ray muons, muon imaging techniques can be used to image large bulky objects, especially objects with heavy shielding. Muon imaging systems work just like CT scanners in the medical imaging field—that is, they can reveal information inside of a target. There are two forms of muon imaging techniques: muon absorption imaging and muon multiple scattering imaging. The former is based on the flux attenuation of muons, and the latter is based on the multiple scattering of muons in matter. The muon absorption imaging technique is capable of imaging very large objects such as volcanoes and large buildings, and also smaller objects like spent fuel casks; the muon multiple scattering imaging technique is best suited to inspect smaller objects such as nuclear waste containers. Muon imaging techniques can be applied in a broad variety of fields, i.e. from measuring the magma thickness of volcanoes to searching for secret cavities in pyramids, and from monitoring the borders of countries checking for special nuclear materials to monitoring the spent fuel casks for nuclear safeguards applications. In this paper, the principles of muon imaging are reviewed. Image reconstruction algorithms such as Filtered Back Projection and Maximum Likelihood Expectation Maximization are discussed. The capability of muon imaging techniques is demonstrated through a Geant4 simulation study for imaging a nuclear spent fuel cask