Analysis of Basis Pursuit Via Capacity Sets

Finding the sparsest solution $\alpha$ for an under-determined linear system of equations $D\alpha=s$ is of interest in many applications. This problem is known to be NP-hard. Recent work studied conditions on the support size of $\alpha$ that allow its recovery using L1-minimization, via the Basis Pursuit algorithm. These conditions are often relying on a scalar property of $D$ called the mutual-coherence. In this work we introduce an alternative set of features of an arbitrarily given $D$, called the "capacity sets". We show how those could be used to analyze the performance of the basis pursuit, leading to improved bounds and predictions of performance. Both theoretical and numerical methods are presented, all using the capacity values, and shown to lead to improved assessments of the basis pursuit success in finding the sparest solution of $D\alpha=s$

Landscape genetics reveal broad and fine‐scale population structure due to landscape features and climate history in the northern leopard frog (Rana pipiens) in North Dakota

Prehistoric climate and landscape features play large roles structuring wildlife populations. The amphibians of the northern Great Plains of North America present an opportunity to investigate how these factors affect colonization, migration, and current population genetic structure. This study used 11 microsatellite loci to genotype 1,230 northern leopard frogs (Rana pipiens) from 41 wetlands (30 samples/wetland) across North Dakota. Genetic structure of the sampled frogs was evaluated using Bayesian and multivariate clustering methods. All analyses produced concordant results, identifying a major east–west split between two R. pipiens population clusters separated by the Missouri River. Substructuring within the two major identified population clusters was also found. Spatial principal component analysis (sPCA) and variance partitioning analysis identified distance, river basins, and the Missouri River as the most important landscape factors differentiating R. pipiens populations across the state. Bayesian reconstruction of coalescence times suggested the major east– west split occurred ~13–18 kya during a period of glacial retreat in the northern Great Plains and substructuring largely occurred ~5–11 kya during a period of extreme drought cycles. A range‐wide species distribution model (SDM) for R. pipiens was developed and applied to prehistoric climate conditions during the Last Glacial Maximum (21 kya) and the mid‐Holocene (6 kya) from the CCSM4 climate model to identify potential refugia. The SDM indicated potential refugia existed in South Dakota or further south in Nebraska. The ancestral populations of R. pipiens in North Dakota may have inhabited these refugia, but more sampling outside the state is needed to reconstruct the route of colonization. Using microsatellite genotype data, this study determined that colonization from glacial refugia, drought dynamics in the northern Great Plains, and major rivers acting as barriers to gene flow were the defining forces shaping the regional population structure of R. pipiens in North Dakota

Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to $\ell_1$-constraints, using a gradient method, with projection on $\ell_1$-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration.Comment: 24 pages, 5 figures. v2: added reference, some amendments, 27 page

Diseases of winter linseed : occurrence, effects and importance

In 1998, a survey of the incidence and severity of diseases was carried out on 30 crops of winter linseed at early flowering and again at crop maturity. Five crops each were selected in south west, east, east Midlands, west Midlands and north of England and from Scotland. Crops were predominantly cv. Oliver (90% crops), grown from certified seed (83%) and sown in September (97%). Pasmo (Mycosphaerella) was the most important disease, affecting leaves of 73% crops at early flowering and 90% crops at maturity. Powdery mildew (70% crops), Alternaria (30% crops) on leaves and Botrytis on capsules (70% crops) were also common. Regional differences were apparent for powdery mildew, which was present in all regions except the southwest, whilst Alternaria predominated in the Midlands. Half of the crops surveyed had received fungicide sprays, but this appeared to have made limited impact on disease severity. Pasmo is a new threat to UK linseed crops and this raises concerns about the threat it poses to spring linsee

Journal Staff

This book constitutes the refereed proceedings of the 18th Scandinavian Conference on Image Analysis, SCIA 2013, held in Espoo, Finland, in June 2013. The 67 revised full papers presented were carefully reviewed and selected from 132 submissions. The papers are organized in topical sections on feature extraction and segmentation, pattern recognition and machine learning, medical and biomedical image analysis, faces and gestures, object and scene recognition, matching, registration, and alignment, 3D vision, color and multispectral image analysis, motion analysis, systems and applications, human-centered computing, and video and multimedia analysis

A discrete systems approach to cardinal spline Hermite interpolation

AbstractA cardinal spline Hermite interpolation problem is posed by specifying values, and m−1 derivatives, m⩾1, at uniformly spaced knots tk; it may be solved by means of a generalized spline function w(t) (a standard spline function when m=1), piecewise a polynomial of degree n−1=2m+p−1, p⩾0, with w(j)(t) continuous across the knots for j=0,1,2,…,m+p−1. The problem is studied here for p>0 in the context of an (m+p)-dimensional system of linear recursion equations satisfied by the values of the m-th through m+p−1-st derivatives of w(t) at the knots, whose homogeneous term involves a p×p matrix A . In the case m=1 we relate the characteristic polynomial of A and certain controllability notions to the standard B-spline and we proceed to show how systems-theoretic ideas can be used to generate systems of basis splines for higher values of m

Low-lying excitations of a trapped rotating Bose-Einstein condensate

We investigate the low-lying excitations of a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation, in the limit where the angular mometum $L$ of the system is much less than the number of the atoms $N$ in the trap. We show that in the asymptotic limit $N \to \infty$ the excitation energy, measured from the energy of the lowest state, is given by $27 N_{3}(N_{3}-1) v_0 /68$, where $N_{3}$ is the number of octupole excitations and $v_{0}$ is the unit of the interaction energy.Comment: 3 pages, RevTex, 2 ps figures, submitted to PR

Student–teacher relationships in elementary school: The unique role of shyness, anxiety, and emotional problems

This study explored the unique contributions of students' self-reported internalizing behaviors (shyness, anxiety, and emotional problems) to teachers' perceptions of the quality of student–teacher relationships (closeness, conflict, and dependency). In total, 269 third-to-sixth grade students (50.9% girls) and 35 teachers (74.7% females) from 8 Dutch regular elementary schools participated in this study. Teachers filled out questionnaires about their background characteristics and the affective quality of their relationship with individual students, and students answered questions about their demographics and internalizing behaviors. Multilevel models revealed significant negative associations of student-perceived shyness with teacher-perceived closeness and conflict in the student–teacher relationship. Additionally, students' anxiety was positively associated with conflict and dependency in the relationship. Students' emotional problems, however, were not associated with student–teacher relationship quality. These findings suggest that different types of internalizing student behavior may play a differential role in the quality of the student–teacher relationship