Mixed spatially varying L2L^2-BV regularization of inverse ill-posed problems

Several generalizations of the traditional Tikhonov-Phillips regularization method have been proposed during the last two decades. Many of these generalizations are based upon inducing stability throughout the use of different penalizers which allow the capturing of diverse properties of the exact solution (e.g. edges, discontinuities, borders, etc.). However, in some problems in which it is known that the regularity of the exact solution is heterogeneous and/or anisotropic, it is reasonable to think that a much better option could be the simultaneous use of two or more penalizers of different nature. Such is the case, for instance, in some image restoration problems in which preservation of edges, borders or discontinuities is an important matter. In this work we present some results on the simultaneous use of penalizers of $L^2$ and of bounded variation (BV) type. For particular cases, existence and uniqueness results are proved. Open problems are discussed and results to signal restoration problems are presented.Comment: 18 pages, 12 figure

On the existence of global saturation for spectral regularization methods with optimal qualification

A family of real functions {g_\alpha} defining a spectral regularization method with optimal qualification is considered. Sufficient condition on the family and on the optimal qualification guaranteeing the existence of saturation are established. Appropriate characterizations of both the saturation function and the saturation set are found and some examples are provided.Comment: 19 page

Existence, uniqueness and stability of solutions of generalized Tikhonov-Phillips functionals

The Tikhonov-Phillips method is widely used for regularizing ill-posed inverse problems mainly due to the simplicity of its formulation as an optimization problem. The use of different penalizers in the functionals associated to the corresponding optimization problems has originated a variety other methods which can be considered as "variants" of the traditional Tikhonov-Phillips method of order zero. Such is the case for instance of the Tikhonov-Phillips method of order one, the total variation regularization method, etc. In this article we find sufficient conditions on the penalizers in generalized Tikhonov-Phillips functionals which guarantee existence and uniqueness and stability of the minimizers. The particular cases in which the penalizers are given by the bounded variation norm, by powers of seminorms and by linear combinations of powers of seminorms associated to closed operators, are studied. Several examples are presented and a few results on image restoration are shown.Comment: 24 pages, 8 figure

Regularization Methods for Ill-Posed Problems in Multiple Hilbert Scales

Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases convergence is proved and orders and optimal orders of convergence are shown.Comment: 32 pages, 2 figure

Motives to use Facebook and problematic Facebook use in adolescents

Background and aims There is a growing body of evidence suggesting that problematic Facebook use (PFU) is an emerging problem, particularly among adolescents. Although a number of motivations explaining why people engage in frequent Facebook use have been identified, less is known about the specific psychological needs underlying PFU. The aim of this study is to test a model designed to assess the unique contribution of psychological motives for using Facebook to the different PFU dimensions in a sample of adolescents. Methods A total of 864 Italian adolescents participated in the study. Multivariate multiple regression was run to test whether the four motives were differently associated with problematic dimensions. Results The results showed that the two motives with negative valence (coping and conformity) were significantly linked to the five dimensions of PFU, whereas the two motives with positive valence (enhancement and social) appeared to be weaker predictors for three out of these five dimensions. Discussion and conclusion In conclusion, psychological motives for using Facebook appeared to significantly contribute to explaining PFU among adolescents, and should be considered by researchers and educational practitioners

Exploring hypotheses of the actions of TGF-beta 1 in epidermal wound healing using a 3D computational multiscale model of the human epidermis

In vivo and in vitro studies give a paradoxical picture of the actions of the key regulatory factor TGF-beta 1 in epidermal wound healing with it stimulating migration of keratinocytes but also inhibiting their proliferation. To try to reconcile these into an easily visualized 3D model of wound healing amenable for experimentation by cell biologists, a multiscale model of the formation of a 3D skin epithelium was established with TGF-beta 1 literature-derived rule sets and equations embedded within it. At the cellular level, an agent-based bottom-up model that focuses on individual interacting units ( keratinocytes) was used. This was based on literature-derived rules governing keratinocyte behavior and keratinocyte/ECM interactions. The selection of these rule sets is described in detail in this paper. The agent-based model was then linked with a subcellular model of TGF-beta 1 production and its action on keratinocytes simulated with a complex pathway simulator. This multiscale model can be run at a cellular level only or at a combined cellular/subcellular level. It was then initially challenged ( by wounding) to investigate the behavior of keratinocytes in wound healing at the cellular level. To investigate the possible actions of TGF-beta 1, several hypotheses were then explored by deliberately manipulating some of these rule sets at subcellular levels. This exercise readily eliminated some hypotheses and identified a sequence of spatial-temporal actions of TGF-beta 1 for normal successful wound healing in an easy-to-follow 3D model. We suggest this multiscale model offers a valuable, easy-to-visualize aid to our understanding of the actions of this key regulator in wound healing, and provides a model that can now be used to explore pathologies of wound healing

Genome-wide protein QTL mapping identifies human plasma kallikrein as a post-translational regulator of serum uPAR levels

The soluble cleaved urokinase plasminogen activator receptor (scuPAR) is a circulating protein detected in multiple diseases, including various cancers, cardiovascular disease, and kidney disease, where elevated levels of scuPAR have been associated with worsening prognosis and increased disease aggressiveness. We aimed to identify novel genetic and biomolecular mechanisms regulating scuPAR levels. Elevated serum scuPAR levels were identified in asthma (n=514) and chronic obstructive pulmonary disease (COPD; n=219) cohorts when compared to controls (n=96). In these cohorts, a genome-wide association study of serum scuPAR levels identified a human plasma kallikrein gene (KLKB1) promoter polymorphism (rs4253238) associated with serum scuPAR levels in a control/asthma population (P=1.17×10−7), which was also observed in a COPD population (combined P=5.04×10−12). Using a fluorescent assay, we demonstrated that serum KLKB1 enzymatic activity was driven by rs4253238 and is inverse to scuPAR levels. Biochemical analysis identified that KLKB1 cleaves scuPAR and negates scuPAR's effects on primary human bronchial epithelial cells (HBECs) in vitro. Chymotrypsin was used as a proproteolytic control, while basal HBECs were used as a control to define scuPAR-driven effects. In summary, we reveal a novel post-translational regulatory mechanism for scuPAR using a hypothesis-free approach with implications for multiple human diseases

Effect of dietary supplementation with ultramicronized palmitoylethanolamide in maintaining remission in cats with nonflea hypersensitivity dermatitis: a double-blind, multicentre, randomized, placebo-controlled study

Background Feline nonflea hypersensitivity dermatitis (NFHD) is a frequent cause of over-grooming, scratching and skin lesions. Multimodal therapy often is necessary. Hypothesis/Objectives To investigate the efficacy of ultramicronized palmitoylethanolamide (PEA-um) in maintaining methylprednisolone-induced remission in NFHD cats. Animals Fifty-seven NFHD cats with nonseasonal pruritus were enrolled originally, of which 25 completed all study requirements to be eligible for analysis. Methods and materials Cats were randomly assigned to PEA-um (15 mg/kg per os, once daily; n = 29) or placebo (n = 28) while receiving a 28 day tapering methylprednisolone course. Cats responding favourably to methylprednisolone were then administered only PEA-um (n = 21) or placebo (n = 23) for another eight weeks, followed by a four week long treatment-free period. Cats were maintained in the study until relapse or study end, whichever came first. Primary outcome was time to relapse. Secondary outcomes were pruritus Visual Analog Scale (pVAS), SCORing Feline Allergic Dermatitis scale (SCORFAD) and owner Global Assessment Score (GAS). Results Mean relapse time was 40.5 days (+/- 7.8 SE) in PEA-um treated cats (n = 13) and 22.2 days (+/- 3.7 SE) for placebo (n = 12; P = 0.04). On Day 28, the severity of pruritus was lower in the PEA-um treated cats compared to placebo (P = 0.03). Mean worsening of pruritus at the final study day was lower in the PEA-um group compared to placebo (P = 0.04), whereas SCORFAD was not different between groups. Mean owner GAS at the final study day was better in the PEA-um than the placebo-treated group (P = 0.05). Conclusion and clinical importance Ultramicronized palmitoylethanolamide could represent an effective and safe option to delay relapse in NFHD cats