Distributed Feature Selection in Large n and Large p Regression Problems

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space), and the challenge arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. For sample space partitioning, I propose a MEdian Selection Subset AGgregation Estimator ({\em message}) algorithm for solving these issues. The algorithm applies feature selection in parallel for each subset using regularized regression or Bayesian variable selection method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in sample size, and has theoretical guarantees. I provide extensive experiments to show excellent performance in feature selection, estimation, prediction, and computation time relative to usual competitors.

While sample space partitioning is useful in handling datasets with large sample size, feature space partitioning is more effective when the data dimension is high. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In the thesis, I propose a new embarrassingly parallel framework named {\em DECO} for distributed variable selection and parameter estimation. In {\em DECO}, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

For datasets with both large sample sizes and high dimensionality, I propose a new "divided-and-conquer" framework {\em DEME} (DECO-message) by leveraging both the {\em DECO} and the {\em message} algorithm. The new framework first partitions the dataset in the sample space into row cubes using {\em message} and then partition the feature space of the cubes using {\em DECO}. This procedure is equivalent to partitioning the original data matrix into multiple small blocks, each with a feasible size that can be stored and fitted in a computer in parallel. The results are then synthezied via the {\em DECO} and {\em message} algorithm in a reverse order to produce the final output. The whole framework is extremely scalable.

SYSTEMS OF DIFFERENTIAL EQUATIONSTHAT ARE COMPETITIVE OR COOPERATIVE II:CONVERGENCE ALMOST EVERYWHERE*MORRIS W. HIRSCH

A vector field in n-space determines a competitive (or cooperative) system of differential equations provided all of the off-diagonal terms of its Jacobian matrix are nonpositive (or nonnegative). The main results in this article are the following. A cooperative system cannot have nonconstant attracting periodic solutions. In a cooperative system whose Jacobian matrices are irreducible the forward orbit converges for almost every point having compact forward orbit closure. In a cooperative system in 2 dimensions, every solution is eventually monotone.  Applications are made to generalizations of positive feedback loops.

Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the precompactness of sets in the Lebesgue spaces $L_p(\Rn)$, $1 \leq p < \infty$, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces $B^s_{p,q}(\Rn)$, $0

On the suboptimality of the p-version interior penalty discontinuous Galerkin method

We address the question of the rates of convergence of the p-version interior penalty discontinuous Galerkin method (p-IPDG) for second order elliptic problems with non-homogeneous Dirichlet boundary conditions. It is known that the p-IPDG method admits slightly suboptimal a-priori bounds with respect to the polynomial degree (in the Hilbertian Sobolev space setting). An example for which the suboptimal rate of convergence with respect to the polynomial degree is both proven theoretically and validated in practice through numerical experiments is presented. Moreover, the performance of p- IPDG on the related problem of p-approximation of corner singularities is assessed both theoretically and numerically, witnessing an almost doubling of the convergence rate of the p-IPDG method.

Almost Disjoint Families of Representing Sets

The thesis is concerned with a number of problems in Combinatorial Set Theory. The Generalized Continuum Hypothesis is assumed. Suppose X and K are non-zero cardinals. By successively identifying K with airwise disjoint sets of power K, a function/: X-*•K can be viewed as a transversal of a pairwise disjoint (X, K)family A . Questions about families of functions in K can thus bethought of as referring to families of transversals of A. We wish to consider generalizations of such questions to almost disjoint families; in particular we are interested in extensions of the following two problems: (i) What is the 'maximum' cardinality of an almost disjoint family of functions each mapping X into K? (ii) Describe the cardinalities of maximal almost disjoint families of functions each mapping X into K. Article in Bulletin of the Australian Mathematical Society 27(03):477 - 479 · June 1983  

Solderjet bumping technique used to manufacture a compact and robust green solid-state laser

Solder-joining using metallic solder alloys is an alternative to adhesive bonding. Laser-based soldering processes are especially well suited for the joining of optical components made of fragile and brittle materials such as glasses, ceramics and optical crystals due to a localized and minimized input of thermal energy. The Solderjet Bumping technique is used to assemble a miniaturized laser resonator in order to obtain higher robustness, wider thermal conductivity performance, higher vacuum and radiation compatibility, and better heat and long term stability compared with identical glued devices. The resulting assembled compact and robust green diode-pumped solid-state laser is part of the future Raman Laser Spectrometer designed for the Exomars European Space Agency (ESA) space mission 2018.

A functional representation of almost isometries

For each quasi-metric space X we consider the convex lattice SLip(1)(X) of all semi-Lipschitz functions on X with semi-Lipschitz constant not greater than 1. If X and Y are two complete quasi-metric spaces, we prove that every convex lattice isomorphism T from SLip(1)(Y) onto SLip(1)(X) can be written in the form Tf = c . (f o tau) + phi, where tau is an isometry, c > 0 and phi is an element of SLip(1)(X). As a consequence, we obtain that two complete quasi-metric spaces are almost isometric if, and only if, there exists an almost-unital convex lattice isomorphism between SLip(1)(X) and SLip(1) (Y).

Tid, rum och självbestämmande : Möjligheter och hinder i vardagen för äldre personer med intellektuell funktionsnedsättning på gruppboende

People with intellectual disability are living longer, which creates new demands for the support and care of this target group. Participation and autonomy at all ages, regardless of functional capacity, are cited in legislation and among the key objectives of disability policy. As a group, older people with intellectual disability have previously been almost invisible in both policy documents and research. Information regarding this group is thus limited, and more systematic knowledge is needed about older people with intellectual disability, their daily lives, and especially their opportunities for autonomy. The purpose of this thesis is to learn more about the role of influence and autonomy in everyday life from the perspective of older people with intellectual disability living in group homes. This will be achieved by studying situations in which opportunities and obstacles arise for these residents to exercise their autonomy in daily life, and identifying and analysing how autonomy is expressed in the meeting between residents and staff. The study applies an ethnographic approach, using methods including field studies with observations and videotaped meetings between residents and staff. The sample consists of residents aged 65 and over and staff at three group homes for people with intellectual disability. One resident at each group home is followed in greater depth. The analysis uses the time-geographic concepts of project, activity and restrictions in order to clarify where and when different projects are carried out, as well as who has the power to determine what is to be carried out. Interaction analysis is used to analyse the videotaped meetings between residents and staff. The analysis is based on Goffman’s interaction order and interaction rituals, theories about turntaking, both verbal and non-verbal, and theories about power and counter-power. In accordance with Goffman’s framework concept, the starting point is the concrete framework that reflects spatiality, which in turn becomes a way to place the more abstract framework of the situation into a specific context. Two major projects were identified: Sleep and Rest and Meals. The analysis reveals projects that are governed by the resident’s own preferences (individual projects) and projects that are governed to a greater degree by the staff’s objectives and opportunities (institutional projects). Some guidance also derives from municipal decisions and guidelines (organizational projects). Many projects were carried out based on staff decisions and objectives, but in actual practice many projects failed to get off the ground. Some projects were at risk of failure until something happened or someone intervened and thereby rescued the project so that it could be implemented. The interactional analysis perspective shows how autonomy is constructed in the meeting. Autonomy is situation-bound, and shifts more on the basis of context than in relation to specific individuals. The study includes decision situations mainly between autonomy and its opposite, paternalism, which are viewed as extremes on a continuum. However, certain factors lead to stronger autonomy in certain situations. When a resident can define the situation, they also have greater power to determine the outcome. In situations characterized by paternalism, the staff have a preferential right of interpretation and the power to decide, both on the basis of their knowledge and because of the asymmetrical interdependence that characterizes the resident-professional relationship. Such situations are also governed by the rules and procedures of the group home to a greater degree than those situations in which the resident exercises autonomy. The thesis discusses strategies that could increase the residents’ opportunities for autonomy. Greater communication skills among staff can be viewed as a step on the path toward greater autonomy for the residents. Staff have the potential to eliminate obstacles, to strengthen inadequate skills or create new ones by providing choices and assistive devices, and to exercise an affirmative approach.

Key performance indicators for measuring construction success

The construction industry is dynamic in nature. The concept of project success has remained ambiguously defined in the construction industry. Project success is almost the ultimate goal for every project. However, it means different things to different people. While some writers consider time, cost and quality as predominant criteria, others suggest that success is something more complex. The aim of this paper is to develop a framework for measuring success of construction projects. In this paper, a set of key performance indicators (KPIs), measured both objectively and subjectively are developed through a comprehensive literature review. The validity of the proposed KPIs is also tested by three case studies. Then, the limitations of the suggested KPIs are discussed. With the development of KPIs, a benchmark for measuring the performance of a construction project can be set. It also provides significant insights into developing a general and comprehensive base for further research.

Electronic states of trans-polyacetylene, poly(p-phenylene vinylene) and sp-hybridised carbon species in amorphous hydrogenated carbon probed by resonant Raman scattering

Inclusions of sp-hybridised, trans-polyacetylene [trans-(CH)x] and poly(p-phenylene vinylene) (PPV) chains are revealed using resonant Raman scattering (RRS) investigation of amorphous hydrogenated carbon (a-C:H) films in the near IR – UV range. The RRS spectra of trans-(CH)x core Ag modes and the PPV CC-H phenylene mode are found to transform and disperse as the laser excitation energy ћωL is increased from near IR through visible to UV, whereas sp-bonded inclusions only become evident in UV. This is attributed to ћωL probing of trans-(CH)x chain inhomogeneity and the distribution of chains with varying conjugation length; for PPV to the resonant probing of phelynene ring disorder; and for sp segments, to ћωL probing of a local band gap of end-terminated polyynes. The IR spectra analysis confirmed the presence of sp, trans-(CH)x and PPV inclusions. The obtained RRS results for a-C:H denote differentiation between the core Ag trans-(CH)x modes and the PPV phenylene mode. Furthermore, it was found that at various laser excitation energies the changes in Raman spectra features for trans-(CH)x segments included in an amorphous carbon matrix are the same as in bulk trans-polyacetylene. The latter finding can be used to facilitate identification of trans-(CH)x in the spectra of complex carbonaceous materials.