Discrete gradient methods for solving variational image regularisation models

Discrete gradient methods are well-known methods of geometric numerical integration, which preserve the dissipation of gradient systems. In this paper we show that this property of discrete gradient methods can be interesting in the context of variational models for image processing, that is where the processed image is computed as a minimiser of an energy functional. Numerical schemes for computing minimisers of such energies are desired to inherit the dissipative property of the gradient system associated to the energy and consequently guarantee a monotonic decrease of the energy along iterations, avoiding situations in which more computational work might lead to less optimal solutions. Under appropriate smoothness assumptions on the energy functional we prove that discrete gradient methods guarantee a monotonic decrease of the energy towards stationary states, and we promote their use in image processing by exhibiting experiments with convex and non-convex variational models for image deblurring, denoising, and inpainting

High order structure preserving explicit methods for solving linear-quadratic optimal control problems

[EN] We consider the numerical integration of linear-quadratic optimal control problems. This problem requires the solution of a boundary value problem: a non-autonomous matrix Riccati differential equation (RDE) with final conditions coupled with the state vector equation with initial conditions. The RDE has positive definite matrix solution and to numerically preserve this qualitative property we propose first to integrate this equation backward in time with a sufficiently accurate scheme. Then, this problem turns into an initial value problem, and we analyse splitting and Magnus integrators for the forward time integration which preserve the positive definite matrix solutions for the RDE. Duplicating the time as two new coordinates and using appropriate splitting methods, high order methods preserving the desired property can be obtained. The schemes make sequential computations and do not require the storrage of intermediate results, so the storage requirements are minimal. The proposed methods are also adapted for solving linear-quadratic N-player differential games. The performance of the splitting methods can be considerably improved if the system is a perturbation of an exactly solvable problem and the system is properly split. Some numerical examples illustrate the performance of the proposed methods.The author wishes to thank the University of California San Diego for its hospitality where part of this work was done. He also acknowledges the support of the Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03. The author also acknowledges the suggestions by the referees to improve the presentation of this work.Blanes Zamora, S. (2015). High order structure preserving explicit methods for solving linear-quadratic optimal control problems. 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Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms

This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators

Androgen receptor signalling in Vascular Endothelial cells is dispensable for spermatogenesis and male fertility

<p>Abstract</p> <p>Background</p> <p>Androgen signalling is essential both for male development and function of the male reproductive system in adulthood. Within the adult testis, Germ cells (GC) do not express androgen receptor (AR) suggesting androgen-mediated promotion of spermatogenesis must act via AR-expressing somatic cell-types. Several recent studies have exploited the Cre/lox system of conditional gene-targeting to ablate AR function from key somatic cell-types in order to establish the cell-specific role of AR in promotion of male fertility. In this study, we have used a similar approach to specifically ablate AR-signalling from Vascular Endothelial (VE) cells, with a view to defining the significance of androgen signalling within this cell-type on spermatogenesis.</p> <p>Findings</p> <p>AR expression in VE cells of the testicular vasculature was confirmed using an antibody against AR. A Cre-inducible fluorescent reporter line was used to empirically establish the utility of a mouse line expressing Cre Recombinase driven by the Tie2-Promoter, for targeting VE cells. Immunofluorescent detection revealed expression of YFP (and therefore Cre Recombinase function) limited to VE cells and an interstitial population of cells, believed to be macrophages, that did not express AR. Mating of Tie2-Cre males to females carrying a floxed AR gene produced Vascular Endothelial Androgen Receptor Knockout (VEARKO) mice and littermate controls. Ablation of AR from all VE cells was confirmed; however, no significant differences in bodyweight or reproductive tissue weights could be detected in VEARKO animals and spermatogenesis and fertility was unaffected.</p> <p>Conclusions</p> <p>We demonstrate the successful generation and empirical validation of a cell-specific knockout of AR from VE cells, and conclude that AR expression in VE cells is not essential for spermatogenesis or male fertility.</p

Mobile Phone Radiation Induces Reactive Oxygen Species Production and DNA Damage in Human Spermatozoa In Vitro

Background: In recent times there has been some controversy over the impact of electromagnetic radiation on human health. The significance of mobile phone radiation on male reproduction is a key element of this debate since several studies have suggested a relationship between mobile phone use and semen quality. The potential mechanisms involved have not been established, however, human spermatozoa are known to be particularly vulnerable to oxidative stress by virtue of the abundant availability of substrates for free radical attack and the lack of cytoplasmic space to accommodate antioxidant enzymes. Moreover, the induction of oxidative stress in these cells not only perturbs their capacity for fertilization but also contributes to sperm DNA damage. The latter has, in turn, been linked with poor fertility, an increased incidence of miscarriage and morbidity in the offspring, including childhood cancer. In light of these associations, we have analyzed the influence of RF-EMR on the cell biology of human spermatozoa in vitro. Principal Findings: Purified human spermatozoa were exposed to radio-frequency electromagnetic radiation (RF-EMR) tuned to 1.8 GHz and covering a range of specific absorption rates (SAR) from 0.4 W/kg to 27.5 W/kg. In step with increasing SAR, motility and vitality were significantly reduced after RF-EMR exposure, while the mitochondrial generation of reactive oxygen species and DNA fragmentation were significantly elevated (P<0.001). Furthermore, we also observed highly significant relationships between SAR, the oxidative DNA damage bio-marker, 8-OH-dG, and DNA fragmentation after RF-EMRexposure. Conclusions: RF-EMR in both the power density and frequency range of mobile phones enhances mitochondrial reactive oxygen species generation by human spermatozoa, decreasing the motility and vitality of these cells while stimulating DNA base adduct formation and, ultimately DNA fragmentation. These findings have clear implications for the safety of extensive mobile phone use by males of reproductive age, potentially affecting both their fertility and the health and wellbeing of their offspring

Lattice Boltzmann simulations of soft matter systems

This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview over the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures, 76 page

Role of PCSK5 Expression in Mouse Ovarian Follicle Development: Identification of the Inhibin α- and β-Subunits as Candidate Substrates

Inhibin and activin are essential dimeric glycoproteins belonging to the transforming growth factor-beta (TGFβ) superfamily. Inhibin is a heterodimer of α- and β-subunits, whereas activin is a homodimer of β-subunits. Production of inhibin is regulated during the reproductive cycle and requires the processing of pro-ligands to produce mature hormone. Furin is a subtilisin-like proprotein convertase (proconvertase) that activates precursor proteins by cleavage at basic sites during their transit through the secretory pathway and/or at the cell surface. We hypothesized that furin-like proconvertases are central regulators of inhibin α- and β-subunit processing within the ovary. We analyzed the expression of the proconvertases furin, PCSK5, PCSK6, and PCSK7 in the developing mouse ovary by real-time quantitative RT-PCR. The data showed that proconvertase enzymes are temporally expressed in ovarian cells. With the transition from two-layer secondary to pre-antral follicle, only PCSK5 mRNA was significantly elevated. Activin A selectively enhanced expression of PCSK5 mRNA and decreased expression of furin and PCSK6 in cultured two-layer secondary follicles. Inhibition of proconvertase enzyme activity by dec-RVKR-chloromethylketone (CMK), a highly specific and potent competitive inhibitor of subtilisin-like proconvertases, significantly impeded both inhibin α- and β-subunit maturation in murine granulosa cells. Overexpression of PC5/6 in furin-deficient cells led to increased inhibin α- and βB-subunit maturation. Our data support the role of proconvertase PCSK5 in the processing of ovarian inhibin subunits during folliculogenesis and suggest that this enzyme may be an important regulator of inhibin and activin bioavailability

Inter-Relationship between Testicular Dysgenesis and Leydig Cell Function in the Masculinization Programming Window in the Rat

The testicular dysgenesis syndrome (TDS) hypothesis proposes that maldevelopment of the testis, irrespective of cause, leads to malfunction of the somatic (Leydig, Sertoli) cells and consequent downstream TDS disorders. Studies in rats exposed in utero to di(n-butyl) phthalate (DBP) have strongly supported the TDS concept, but so far no direct evidence has been produced that links dysgenesis per se to somatic cell dysfunction, in particular to androgen production/action during the ‘masculinization programming window’ (MPW; e15.5–e18.5). Normal reproductive tract development and anogenital distance (AGD) are programmed within the MPW, and TDS disorders arise because of deficiencies in this programming. However, DBP-induced focal testicular dysgenesis (Leydig cell aggregation, ectopic Sertoli cells, malformed seminiferous cords) is not evident until after the MPW. Therefore, we used AGD as a read-out of androgen exposure in the MPW, and investigated if this measure was related to objectively quantified dysgenesis (Leydig cell aggregation) at e21.5 in male fetuses exposed to vehicle, DBP (500 or 750 mg/kg/day) or the synthetic glucocorticoid dexamethasone (Dex; alone or plus DBP-500) from e15.5–e18.5 (MPW), e13.5–e20.5 or e19.5–e20.5 (late window). Dysgenesis was found only in animals exposed to DBP during the MPW, and was negatively correlated (R2 = −0.5) with AGD at e21.5 and at postnatal day 8, irrespective of treatment period. Dysgenesis was also negatively correlated (R2 = –0.5) with intratesticular testosterone (ITT) at e21.5, but only when treatments in short windows (MPW, late window) were excluded; the same was true for correlation between AGD and ITT. We conclude that AGD, reflecting Leydig cell function solely within the MPW, is strongly related to focal dysgenesis. Our results point to this occurring because of a common early mechanism, targeted by DBP that determines both dysgenesis and early (during the MPW) fetal Leydig cell dysfunction. The findings provide strong validation of the TDS hypothesis