68 research outputs found
The Convex Geometry of Linear Inverse Problems
In applications throughout science and engineering one is often faced with
the challenge of solving an ill-posed inverse problem, where the number of
available measurements is smaller than the dimension of the model to be
estimated. However in many practical situations of interest, models are
constrained structurally so that they only have a few degrees of freedom
relative to their ambient dimension. This paper provides a general framework to
convert notions of simplicity into convex penalty functions, resulting in
convex optimization solutions to linear, underdetermined inverse problems. The
class of simple models considered are those formed as the sum of a few atoms
from some (possibly infinite) elementary atomic set; examples include
well-studied cases such as sparse vectors and low-rank matrices, as well as
several others including sums of a few permutations matrices, low-rank tensors,
orthogonal matrices, and atomic measures. The convex programming formulation is
based on minimizing the norm induced by the convex hull of the atomic set; this
norm is referred to as the atomic norm. The facial structure of the atomic norm
ball carries a number of favorable properties that are useful for recovering
simple models, and an analysis of the underlying convex geometry provides sharp
estimates of the number of generic measurements required for exact and robust
recovery of models from partial information. These estimates are based on
computing the Gaussian widths of tangent cones to the atomic norm ball. When
the atomic set has algebraic structure the resulting optimization problems can
be solved or approximated via semidefinite programming. The quality of these
approximations affects the number of measurements required for recovery. Thus
this work extends the catalog of simple models that can be recovered from
limited linear information via tractable convex programming
Serotonin controlling feeding and satiety
Serotonin has been implicated in the control of satiety for almost four decades. Historically, the insight that the appetite suppressant effect of fenfluramine is linked to serotonin has stimulated interest in and research into the role of this neurotransmitter in satiety. Various rodent models, including transgenic models, have been developed to identify the involved 5-HT receptor subtypes. This approach also required the availability of receptor ligands of different selectivity, and behavioural techniques had to be developed simultaneously which allow differentiating between unspecific pharmacological effects of these ligands and ‘true’ satiation and satiety. Currently, 5-HT1B, 5-HT2C and 5-HT6 receptors have been identified to mediate serotonergic satiety in different ways. The recently approved anti-obesity drug lorcaserin is a 5-HT2C receptor agonist. In brain, both hypothalamic (arcuate nucleus, paraventricular nucleus) and extrahypothalamic sites (parabrachial nucleus, nucleus of the solitary tract) have been identified to mediate the serotonergic control of satiety. Serotonin interacts within the hypothalamus with endogenous orexigenic (Neuropeptide Y/Agouti related protein) and anorectic (α-melanocyte stimulating hormone) peptides. In the nucleus of the solitary tract serotonin integrates peripheral satiety signals. Here, the 5-HT3, but possibly also the 5-HT2C receptor play a role. It has been found that 5-HT acts in concert with such peripheral signals as cholecystokinin and leptin. Despite the recent advances of our knowledge, many of the complex interactions between 5-HT and other satiety factors are not fully understood yet. Further progress in research will also advance the development of new serotonergic anti-obesity drugs
Disease: A Hitherto Unexplored Constraint on the Spread of Dogs (Canis lupus familiaris) in Pre-Columbian South America
A comparative study of nitrate leaching from soils of differing textures under similar climatic and cropping conditions
A comparative study of nitrate leaching from soils of differing textures under similar climatic and cropping conditions
Factors affecting N immobilisation/mineralisation kinetics for cellulose, glucose and straw amended sandy soils.
DNA damage and susceptibility to oxidative damage in lymphocytes: effects of carotenoids in vitro and in vivo
Protective effects of long-term bradycardial pacing against catecholamine-induced myocardial damage in rabbit hearts.
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