A Non-Convex Relaxation for Fixed-Rank Approximation

This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear norm typically work well and come with theoretical performance guarantees. On the other hand these formulations suffer from a shrinking bias that can severely degrade the solution in the presence of noise. In this theoretical paper we study an alternative non-convex relaxation that in contrast to the nuclear norm does not penalize the leading singular values and thereby avoids this bias. We show that despite its non-convexity the proposed formulation will in many cases have a single local minimizer if a RIP holds. Our numerical tests show that our approach typically converges to a better solution than nuclear norm based alternatives even in cases when the RIP does not hold

The Aq,t\mathbb{A}_{q,t} algebra and parabolic flag Hilbert schemes

The earlier work of the first and the third named authors introduced the algebra $\mathbb{A}_{q,t}$ and its polynomial representation. In this paper we construct an action of this algebra on the equivariant K-theory of certain smooth strata in the flag Hilbert schemes of points on the plane. In this presentation, the fixed points of torus action correspond to generalized Macdonald polynomials and the the matrix elements of the operators have explicit combinatorial presentation.Comment: 26 pages, no figure

Comparison of Sprinkler Activation in Flat and Sloping Ceilings using FDS 6

The purpose of this report is to investigate the implications of installing sprinkler systems in ceilings with a ceiling slope exceeding the maximum permitted by NFPA 13, being 9.5 ° or 18.44 ° depending on the type of sprinkler system. The objective of the report is to present a comparison and analysis of sprinkler activation times and patterns for sprinkler systems installed in ceilings with different slope angles, using Fire Dynamics Simulator version 6 Release Candidate 1. The problem has been defined as: how does the ceiling slope angle where sprinklers are provided affect the activation of sprinklers? It has been demonstrated that a ceiling slope of up to 26.57 ° may not affect the sprinkler activation pattern. It has also been demonstrated that the increased sprinkler activation times and changed patterns exhibited for sprinkler systems in sloping ceilings may be a result of a combination of excessive ceiling height and ceiling slope angle, subject to discussion. Reduced Response Time Index and activation temperature can reduce activation pattern discrepancies and reduce activation times. The intent of the sprinkler system may not be compromised when ceiling slopes exceeding those specified in NFPA 13 are introduced

Fertility Intentions across Immigrant Generations in Sweden: Do Patterns of Adaptation Differ by Gender and Origin?

In being representative of individuals' demographic value orientations, fertility preferences provide information about immigrants' adaptation to family formation patterns in the destination country at a deeper, ideational level than actual fertility does. Using data from Wave 1 of the Swedish GGS from 2012/2013 (n=3,932), this study compares the first, 1.5, and second generations with either one or two foreign-born parent(s) to Swedes without an immigrant background by gender and across origins. Binary logistic regression is used to compare the propensity to state a positive fertility intention, and partial proportional odds models are used to analyse differences across four ordinal intention categories (definitely/probably yes/no). Results show a general tendency towards convergence from the relatively positive intentions of the first generation to levels closer to non-immigrants in later generations, although complete convergence is only found for the second generation with one foreign-born parent. There are gender differences, with women being similar to non-immigrants by the 1.5 generation, while there is no clear intergenerational trend for men. Among origin groups, convergence is evident among Eastern Europeans and "other non-Europeans", while Westerners already are similar to non-immigrants in the first generation, and Middle Easterners/North Africans display no clear intergenerational trend. This study contributes to the understanding of immigrant fertility by showing that there often is intergenerational adaptation at the ideational (i.e. preference) level, that the pace and extent of convergence vary by gender and across origins, and that group-level patterns found for fertility intentions do not always match those found in earlier research on fertility behaviour