A review on sparse solutions in optimal control of partial differential equations

In this paper a review of the results on sparse controls for partial differential equations is presented. There are two different approaches to the sparsity study of control problems. One approach consists of taking functions to control the system, putting in the cost functional a convenient term that promotes the sparsity of the optimal control. A second approach deals with controls that are Borel measures and the norm of the measure is involved in the cost functional. The use of measures as controls allows to obtain optimal controls supported on a zero Lebesgue measure set, which is very interesting for practical implementation. If the state equation is linear, then we can carry out a complete analysis of the control problem with measures. However, if the equation is nonlinear the use of measures to control the system is still an open problem, in general, and the use of functions to control the system seems to be more appropriate.This work was partially supported by the Spanish Ministerio de Economía y Competitividad under project MTM2014-57531-P

Myristic acid potentiates palmitic acid-induced lipotoxicity and steatohepatitis associated with lipodystrophy by sustaning de novo ceramide synthesis.

Palmitic acid (PA) induces hepatocyte apoptosis and fuels de novo ceramide synthesis in the endoplasmic reticulum (ER). Myristic acid (MA), a free fatty acid highly abundant in copra/palmist oils, is a predictor of nonalcoholic steatohepatitis (NASH) and stimulates ceramide synthesis. Here we investigated the synergism between MA and PA in ceramide synthesis, ER stress, lipotoxicity and NASH. Unlike PA, MA is not lipotoxic but potentiated PA-mediated lipoapoptosis, ER stress, caspase-3 activation and cytochrome c release in primary mouse hepatocytes (PMH). Moreover, MA kinetically sustained PA-induced total ceramide content by stimulating dehydroceramide desaturase and switched the ceramide profile from decreased to increased ceramide 14:0/ceramide16:0, without changing medium and long-chain ceramide species. PMH were more sensitive to equimolar ceramide14:0/ceramide16:0 exposure, which mimics the outcome of PA plus MA treatment on ceramide homeostasis, than to either ceramide alone. Treatment with myriocin to inhibit ceramide synthesis and tauroursodeoxycholic acid to prevent ER stress ameliorated PA plus MA induced apoptosis, similar to the protection afforded by the antioxidant BHA, the pan-caspase inhibitor z-VAD-Fmk and JNK inhibition. Moreover, ruthenium red protected PMH against PA and MA-induced cell death. Recapitulating in vitro findings, mice fed a diet enriched in PA plus MA exhibited lipodystrophy, hepatosplenomegaly, increased liver ceramide content and cholesterol levels, ER stress, liver damage, inflammation and fibrosis compared to mice fed diets enriched in PA or MA alone. The deleterious effects of PA plus MA-enriched diet were largely prevented by in vivo myriocin treatment. These findings indicate a causal link between ceramide synthesis and ER stress in lipotoxicity, and imply that the consumption of diets enriched in MA and PA can cause NASH associated with lipodystrophy

Topical application of ALA and ALA hexyl ester on a subcutaneous murine mammary adenocarcinoma: tissue distribution

Although 5-aminolevulinic acid (ALA)-based photodynamic therapy (PDT) has proven to be clinically beneficial for the treatment of certain cancers, including a variety of skin cancers, optimal tissue localisation still remains a problem. An approach to improve the bioavailability of protoporphyrin IX (PpIX) is the use of ALA derivatives instead of ALA. In this work, we employed a subcutaneous murine mammary adenocarcinoma to study the tissue distribution pattern of the ALA hexyl ester (He-ALA) in comparison with ALA after their topical application in different vehicles. He-ALA induced porphyrin synthesis in the skin overlying the tumour (SOT), but it did not reach the tumour tissue as efficiently. Only 5 h after He-ALA lotion application, tumour porphyrin levels surpassed control values. He-ALA delivered in cream induced a substantially lower porphyrin synthesis in SOT, reinforcing the importance of the vehicle in the use of topical PDT. Porphyrin levels in internal organs remained almost within control values when He-ALA was employed. The addition of DMSO to ALA formulation slightly increased tumour and SOT porphyrin biosynthesis, but it did not when added to He-ALA lotion

Overview of (pro-)Lie group structures on Hopf algebra character groups

Character groups of Hopf algebras appear in a variety of mathematical and physical contexts. To name just a few, they arise in non-commutative geometry, renormalisation of quantum field theory, and numerical analysis. In the present article we review recent results on the structure of character groups of Hopf algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild assumptions on the Hopf algebra or the target algebra the character groups possess strong structural properties. Moreover, these properties are of interest in applications of these groups outside of Lie theory. We emphasise this point in the context of two main examples: The Butcher group from numerical analysis and character groups which arise from the Connes--Kreimer theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on "New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai

Magnetic connectivity of the ecliptic plane within 0.5 AU : PFSS modeling of the first PSP encounter

We compare magnetic field measurements taken by the FIELDS instrument on Parker Solar Probe (PSP) during its first solar encounter to predictions obtained by Potential Field Source Surface (PFSS) modeling. Ballistic propagation is used to connect the spacecraft to the source surface. Despite the simplicity of the model, our results show striking agreement with PSPs first observations of the heliospheric magnetic field from 0.5 AU (107.5 Rs) down to 0.16 AU (35.7 Rs). Further, we show the robustness of the agreement is improved both by allowing the photospheric input to the model to vary in time, and by advecting the field from PSP down to the PFSS model domain using in situ PSP/SWEAP measurements of the solar wind speed instead of assuming it to be constant with longitude and latitude. We also explore the source surface height parameter (RSS) to the PFSS model finding that an extraordinarily low source surface height (1.3-1.5Rs) predicts observed small scale polarity inversions which are otherwise washed out with regular modeling parameters. Finally, we extract field line traces from these models. By overlaying these on EUV images we observe magnetic connectivity to various equatorial and mid-latitude coronal holes indicating plausible magnetic footpoints and offering context for future discussions of sources of the solar wind measured by PSP

Flavor Physics in an SO(10) Grand Unified Model

In supersymmetric grand-unified models, the lepton mixing matrix can possibly affect flavor-changing transitions in the quark sector. We present a detailed analysis of a model proposed by Chang, Masiero and Murayama, in which the near-maximal atmospheric neutrino mixing angle governs large new b -> s transitions. Relating the supersymmetric low-energy parameters to seven new parameters of this SO(10) GUT model, we perform a correlated study of several flavor-changing neutral current (FCNC) processes. We find the current bound on B(tau -> mu gamma) more constraining than B(B -> X_s gamma). The LEP limit on the lightest Higgs boson mass implies an important lower bound on tan beta, which in turn limits the size of the new FCNC transitions. Remarkably, the combined analysis does not rule out large effects in B_s-B_s-bar mixing and we can easily accomodate the large CP phase in the B_s-B_s-bar system which has recently been inferred from a global analysis of CDF and DO data. The model predicts a particle spectrum which is different from the popular Constrained Minimal Supersymmetric Standard Model (CMSSM). B(tau -> mu gamma) enforces heavy masses, typically above 1 TeV, for the sfermions of the degenerate first two generations. However, the ratio of the third-generation and first-generation sfermion masses is smaller than in the CMSSM and a (dominantly right-handed) stop with mass below 500 GeV is possible.Comment: 44 pages, 5 figures. Footnote and references added, minor changes, Fig. 2 corrected; journal versio

A Comprehensive Association Analysis of Homocysteine Metabolic Pathway Genes in Singaporean Chinese with Ischemic Stroke

10.1371/journal.pone.0024757PLoS ONE69

The correlation between reading and mathematics ability at age twelve has a substantial genetic component

Dissecting how genetic and environmental influences impact on learning is helpful for maximizing numeracy and literacy. Here we show, using twin and genome-wide analysis, that there is a substantial genetic component to children’s ability in reading and mathematics, and estimate that around one half of the observed correlation in these traits is due to shared genetic effects (so-called Generalist Genes). Thus, our results highlight the potential role of the learning environment in contributing to differences in a child’s cognitive abilities at age twelve

Cross-cultural neuropsychological assessment in Europe: Position statement of the European Consortium on Cross-Cultural Neuropsychology (ECCroN)

Over the past decades European societies have become increasingly diverse. This diversity in culture, education, and language significantly impacts neuropsychological assessment. Although several initiatives are under way to overcome these barriers - e.g. newly developed and validated test batteries - there is a need for more collaboration in the development and implementation of neuropsychological tests, such as in the domains of social cognition and language. To address these gaps in cross-cultural neuropsychological assessment in Europe, the European Consortium on Cross-Cultural Neuropsychology (ECCroN) was established in 2019. ECCroN recommends taking a broad range of variables into account, such as linguistic factors, literacy, education, migration history, acculturation and other cultural factors. We advocate against race-based norms as a solution to the challenging interpretation of group differences on neuropsychological tests, and instead support the development, validation, and standardization of more widely applicable/cross-culturally applicable tests that take into account interindividual variability. Last, ECCroN advocates for an improvement in the clinical training of neuropsychologists in culturally sensitive neuropsychological assessment, and the development and implementation of guidelines for interpreter-mediated neuropsychological assessment in diverse populations in Europe. ECCroN may impact research and clinical practice by contributing to existing theoretical frameworks and by improving the assessment of diverse individuals across Europe through collaborations on test development, collection of normative data, cross-cultural clinical training, and interpreter-mediated assessment

Type II Secretory Phospholipase A2 and Prognosis in Patients with Stable Coronary Heart Disease: Mendelian Randomization Study

Serum type II secretory phospholipase A(2) (sPLA(2)-IIa) has been found to be predictive of adverse outcomes in patients with stable coronary heart disease. Compounds targeting sPLA(2)-IIa are already under development. This study investigated if an association of sPLA(2)-IIa with secondary cardiovascular disease (CVD) events may be of causal nature or mainly a matter of confounding by correlated cardiovascular risk markers.Eight-year follow-up data of a prospective cohort study (KAROLA) of patients who underwent in-patient rehabilitation after an acute cardiovascular event were analysed. Associations of polymorphisms (SNP) in the sPLA(2)-IIa-coding gene PLA2G2A with serum sPLA(2)-IIa and secondary fatal or non-fatal CVD events were examined by multiple regression. Hazard ratios (HR) were compared with those expected if the association between sPLA(2)-IIa and CVD were causal. The strongest determinants of sPLA(2)-IIa (rs4744 and rs10732279) were associated with an increase of serum concentrations by 81% and 73% per variant allele. HRs (95% confidence intervals) estimating the associations of the SNPs with secondary CVD events were increased, but not statistically significant (1.16 [0.89-1.51] and 1.18 [0.91-1.52] per variant allele, respectively). However, these estimates were very similar to those expected when assuming causality (1.18 and 1.17), based on an association of natural log-transformed sPLA(2)-IIa concentration with secondary events with HR = 1.33 per unit.The present findings regarding genetic polymorphisms, determination of serum sPLA(2)-IIa, and prognosis in CVD patients are consistent with a genuine causal relationship and thus might point to a valid drug target for prevention of secondary CVD events