Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage ...and selection operator (LASSO), wavelet-based deconvolution and reconstruction, and compressed sensing (CS) are a few well-known areas in which problems of this type appear. One standard approach is to minimize an objective function that includes a quadratic ( lscr 2 ) error term added to a sparsity-inducing (usually lscr 1 ) regularizater. We present an algorithmic framework for the more general problem of minimizing the sum of a smooth convex function and a nonsmooth, possibly nonconvex regularizer. We propose iterative methods in which each step is obtained by solving an optimization subproblem involving a quadratic term with diagonal Hessian (i.e., separable in the unknowns) plus the original sparsity-inducing regularizer; our approach is suitable for cases in which this subproblem can be solved much more rapidly than the original problem. Under mild conditions (namely convexity of the regularizer), we prove convergence of the proposed iterative algorithm to a minimum of the objective function. In addition to solving the standard lscr 2 -lscr 1 case, our framework yields efficient solution techniques for other regularizers, such as an lscr infin norm and group-separable regularizers. It also generalizes immediately to the case in which the data is complex rather than real. Experiments with CS problems show that our approach is competitive with the fastest known methods for the standard lscr 2 -lscr 1 problem, as well as being efficient on problems with other separable regularization terms.
Standard formulations of image/signal deconvolution under wavelet-based priors/regularizers lead to very high-dimensional optimization problems involving the following difficulties: the non-Gaussian ...(heavy-tailed) wavelet priors lead to objective functions which are nonquadratic, usually nondifferentiable, and sometimes even nonconvex; the presence of the convolution operator destroys the separability which underlies the simplicity of wavelet-based denoising. This paper presents a unified view of several recently proposed algorithms for handling this class of optimization problems, placing them in a common majorization-minimization (MM) framework. One of the classes of algorithms considered (when using quadratic bounds on nondifferentiable log-priors) shares the infamous ¿singularity issue¿ (SI) of ¿iteratively re weighted least squares¿ (IRLS) algorithms: the possibility of having to handle infinite weights, which may cause both numerical and convergence issues. In this paper, we prove several new results which strongly support the claim that the SI does not compromise the usefulness of this class of algorithms. Exploiting the unified MM perspective, we introduce a new algorithm, resulting from using bounds for nonconvex regularizers; the experiments confirm the superior performance of this method, when compared to the one based on quadratic majorization. Finally, an experimental comparison of the several algorithms, reveals their relative merits for different standard types of scenarios.
Interactions between fungi and plants, including parasitism, mutualism, and saprotrophy, have been invoked as key to their respective macroevolutionary success. Here we evaluate the origins of ...plant-fungal symbioses and saprotrophy using a time-calibrated phylogenetic framework that reveals linked and drastic shifts in diversification rates of each kingdom. Fungal colonization of land was associated with at least two origins of terrestrial green algae and preceded embryophytes (as evidenced by losses of fungal flagellum, ca. 720 Ma), likely facilitating terrestriality through endomycorrhizal and possibly endophytic symbioses. The largest radiation of fungi (Leotiomyceta), the origin of arbuscular mycorrhizae, and the diversification of extant embryophytes occurred ca. 480 Ma. This was followed by the origin of extant lichens. Saprotrophic mushrooms diversified in the Late Paleozoic as forests of seed plants started to dominate the landscape. The subsequent diversification and explosive radiation of Agaricomycetes, and eventually of ectomycorrhizal mushrooms, were associated with the evolution of Pinaceae in the Mesozoic, and establishment of angiosperm-dominated biomes in the Cretaceous.
This paper investigates the problem of determining a binary-valued function through a sequence of strategically selected queries. The focus is an algorithm called Generalized Binary Search (GBS). GBS ...is a well-known greedy algorithm for determining a binary-valued function through a sequence of strategically selected queries. At each step, a query is selected that most evenly splits the hypotheses under consideration into two disjoint subsets, a natural generalization of the idea underlying classic binary search. This paper develops novel incoherence and geometric conditions under which GBS achieves the information-theoretically optimal query complexity; i.e., given a collection of N hypotheses, GBS terminates with the correct function after no more than a constant times logN queries. Furthermore, a noise-tolerant version of GBS is developed that also achieves the optimal query complexity. These results are applied to learning halfspaces, a problem arising routinely in image processing and machine learning.
Madagascar is one of the world's hottest biodiversity hot spots due to its diverse, endemic, and highly threatened biota. This biota shows a distinct signature of evolution in isolation, both in the ...high levels of diversity within lineages and in the imbalance of lineages that are represented. For example, chameleon diversity is the highest of any place on Earth, yet there are no salamanders. These biotic enigmas have inspired centuries of speculation relating to the mechanisms by which Madagascar's biota came to reside there. The two most probable causal factors are Gondwanan vicariance and/or Cenozoic dispersal. By reviewing a comprehensive sample of phylogenetic studies of Malagasy biota, we find that the predominant pattern is one of sister group relationships to African taxa. For those studies that include divergence time analysis, we find an overwhelming indication of Cenozoic origins for most Malagasy clades. We conclude that most of the present-day biota of Madagascar is comprised of the descendents of Cenozoic dispersers, predominantly with African origins.
Arsenic trioxide (ATO) is presently the most active single agent in the treatment of acute promyelocytic leukemia (APL). This review provides insights into the mode of action and the pharmacological ...properties of ATO, and summarizes the most relevant results of more than 20 treatment studies in relapsed or newly diagnosed APL published between 1997 and 2011. ATO acts by targeting multiple pathways in APL leading to apoptosis and myeloid differentiation. It induces complete remission without myelosuppression and causes only few adverse effects. In relapsed APL, ATO-based salvage therapy has been able to induce long-lasting remissions and possible cure in 50-81% of patients. In newly diagnosed APL, two main strategies are currently pursued. ATO is either included into induction therapy with the aim to minimize or eliminate chemotherapy, or it is incorporated as an additive into established first-line concepts with all-trans-retinoic acid and chemotherapy to reinforce their anti-leukemic efficacy. Recent results suggest a high efficacy of ATO in both concepts. In conclusion, experimental research and clinical studies have made contributions toward a better understanding of the molecular mechanisms induced by ATO in APL cells and have established this historic substance as an important candidate for the further improvement of APL therapy.
Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in ...minimizing an objective function which includes a quadratic (squared ) error term combined with a sparseness-inducing regularization term. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution, and compressed sensing are a few well-known examples of this approach. This paper proposes gradient projection (GP) algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems. We test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method. Computational experiments show that these GP approaches perform well in a wide range of applications, often being significantly faster (in terms of computation time) than competing methods. Although the performance of GP methods tends to degrade as the regularization term is de-emphasized, we show how they can be embedded in a continuation scheme to recover their efficient practical performance.
This paper presents the impact of microwave penetration depth on the process of heating the moulding sand with sodium silicate. For each material it is affected by: the wavelength in vacuum and the ...real and imaginary components of the relative complex electrical permittivity ε
for a selected measurement frequency. Since the components are not constant values and they change depending on the electrical parameters of materials and the frequency of the electromagnetic wave, it is indispensable to carry out laboratory measurements to determine them. Moreover, the electrical parameters of materials are also affected by: temperature, packing degree, humidity and conductivity. The measurements of the dielectric properties of moulding sand with sodium silicate was carried out using the perturbation method on a stand of waveguide resonance cavity. The real and imaginary components of the relative complex electrical permittivity was determined for moulding sand at various contents of sodium silicate and at various packing degrees of the samples. On the basis of the results the microwave penetration depth of moulding sand with sodium silicate was established. Relative literature contains no such data that would be essential to predicting an effective process of microwave heating of moulding sand with sodium silicate. Both the packing degree and the amount of sodium silicate in moulding sand turned out to affect the penetration depth, which directly translates into microwave power density distribution in the process of microwave heating of moulding sand with sodium silicate.
Biominerals, such as nacreous bivalve shells, are important archives of environmental information. Most marine calcifiers form their shells from amorphous calcium carbonate, hypothesised to occur via ...particle attachment and stepwise crystallisation of metastable precursor phases. However, the mechanism of this transformation, including the incorporation of trace elements used for environmental reconstructions, are poorly constrained. Here, using shells of the Mediterranean mussel, we explore the formation of nacre from the meso- to the atomic scale. We use a combination of strontium pulse-chase labelling experiments in aquaculture and correlated micro- to sub-nanoscale analysis to show that nacre grows in a dynamic two-step process with extensional and space-filling growth components. Furthermore, we show that nacre crystallizes via localised dissolution and reprecipitation within nanogranules. Our findings elucidate how stepwise crystallization pathways affect trace element incorporation in natural biominerals, while preserving their intricate hierarchical ultrastructure.
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