Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Local operator multipliers and positivity

We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators. We apply these results to study positivity for Schur multipliers. We characterise positive local Schur multipliers, and provide a description of positive local Schur multipliers of Toeplitz type. We introduce local operator multipliers as a non-commutative analogue of local Schur multipliers, and characterise them extending both the characterisation of operator multipliers from [16] and that of local Schur multipliers from [27]. We provide a description of the positive local operator multipliers in terms of approximation by elements of canonical positive cones.

Towards Organic Electronic Materials for Electrically Stimulated Gene Delivery

The cell-specific delivery of polynucleic acids (e.g., DNA, RNA), gene therapy, has the potential to treat various diseases. In this chapter we discuss the use of organic electronic materials as non-viral gene delivery vectors and the great potential for electrochemically triggered gene delivery. We highlight some examples in this chapter based on fullerenes (bucky balls and carbon nanotubes), graphenes and electroactive polymers, particularly those that include experiments in vivo.

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

We consider the non-equilibrium dynamics of a simple system consisting of interacting spin-1/2 particles subjected to a collective damping. The model is close to situations that can be engineered in hybrid electro/opto-mechanical settings. Making use of large-deviation theory, we find a Gallavotti-Cohen symmetry in the dynamics of the system as well as evidence for the coexistence of two dynamical phases with different activity levels. We show that additional damping processes smooth out this behavior. Our analytical results are backed up by Monte Carlo simulations that reveal the nature of the trajectories contributing to the different dynamical phases.

Bioactive Gyroid Scaffolds Formed by Sacrificial Templating of Nanocellulose and Nanochitin Hydrogels as Instructive Platforms for Biomimetic Tissue Engineering

A sacrificial templating process using lithographically printed minimal surface structures allows complex de novo geometries of delicate hydrogel materials. The hydrogel scaffolds based on cellulose and chitin nanofibrils show differences in terms of attachment of human mesenchymal stem cells, and allow their differentiation into osteogenic outcomes. The approach here serves as a first example toward designer hydrogel scaffolds viable for biomimetic tissue engineering.

Coherent and stochastic contributions of compound resonances in atomic processes: Electron recombination, photoionization, and scattering

In open-shell atoms and ions, processes such as photoionization, combination (Raman) scattering, electron scattering, and recombination are often mediated by many-electron compound resonances. We show that their interference (neglected in the independent-resonance approximation) leads to a coherent contribution, which determines the energy-averaged total cross sections of electron- and photon-induced reactions obtained using the optical theorem. In contrast, the partial cross sections (e.g., electron recombination or photon Raman scattering) are dominated by the stochastic contributions. Thus, the optical theorem provides a link between the stochastic and coherent contributions of the compound resonances. Similar conclusions are valid for reactions via compound states in molecules and nuclei.

The prevalence of pica in tuberous sclerosis complex

Background: Pica and Tuberous sclerosis complex (TSC) are rare disorders. We carried out a population survey of pica in our TSC patient population.

Findings: Pica was identified in four percent of cases of TSC. It was associated with adult onset or persistence into adulthood, epilepsy, severe learning difficulties and anaemia.

Conclusions: Pica in TSC is a rare disorder and a coherent history may be difficult to obtain from patients. The prevalence of pica is likely to be underdiagnosed. Pica is a recognised feature in adults with TSC and prompt recognition of this disorder should allow better management of patients with TSC.

Total eclipse of the heart: the AM CVn Gaia14aae/ASSASN-14cn

We report the discovery and characterization of a deeply eclipsing AM CVn-system, Gaia14aae (=ASSASN-14cn). Gaia14aae was identified independently by the All-Sky Automated Survey for Supernovae (ASAS-SN; Shappee et al.) and by the Gaia Science Alerts project, during two separate outbursts. A third outburst is seen in archival Pan-STARRS-1 (PS1; Schlafly et al.; Tonry et al.; Magnier et al.) and ASAS-SN data. Spectroscopy reveals a hot, hydrogen-deficient spectrum with clear double-peaked emission lines, consistent with an accreting double-degenerate classification. We use follow-up photometry to constrain the orbital parameters of the system. We find an orbital period of 49.71 min, which places Gaia14aae at the long period extremum of the outbursting AM CVn period distribution. Gaia14aae is dominated by the light from its accreting white dwarf (WD). Assuming an orbital inclination of 90° for the binary system, the contact phases of the WD lead to lower limits of 0.78 and 0.015 M⊙ on the masses of the accretor and donor, respectively, and a lower limit on the mass ratio of 0.019. Gaia14aae is only the third eclipsing AM CVn star known, and the first in which the WD is totally eclipsed. Using a helium WD model, we estimate the accretor's effective temperature to be 12 900 ± 200 K. The three outburst events occurred within four months of each other, while no other outburst activity is seen in the previous 8 yr of Catalina Real-time Transient Survey (CRTS; Drake et al.), Pan-STARRS-1 and ASAS-SN data. This suggests that these events might be rebrightenings of the first outburst rather than individual events.

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.

Comments on “Wirtinger-based integral inequality: Application to time-delay systems [Automatica 49 (2013) 2860–2866]”

In a recent paper (Automatica 49 (2013) 2860–2866), the Wirtinger-based inequality has been introduced to derive tractable stability conditions for time-delay or sampled-data systems. We point out that there exist two errors in Theorem 8 for the stability analysis of sampled-data systems, and the correct theorem is presented.

Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks

We present a general method to undertake a thorough analysis of the thermodynamics of the quantum jump trajectories followed by an arbitrary quantum harmonic network undergoing linear and bilinear dynamics. The approach is based on the phase-space representation of the state of a harmonic network. The large deviation function associated with this system encodes the full counting statistics of exchange and also allows one to deduce for fluctuation theorems obeyed by the dynamics. We illustrate the method showing the validity of a local fluctuation theorem about the exchange of excitations between a restricted part of the environment (i.e., a local bath) and a harmonic network coupled with different schemes.

Hydrogel-forming microneedle arrays made from light-responsive materials for on-demand transdermal drug delivery

We describe, for the first time, stimuli-responsive hydrogel-forming microneedle (MN) arrays that enable delivery of a clinically-relevant model drug (ibuprofen) upon application of light. MN arrays were prepared using a polymer prepared from 2-hydroxyethyl methacrylate (HEMA) and ethylene glycol dimethacrylate (EGDMA) by micromolding. The obtained MN arrays showed good mechanical properties. The system was loaded with up to 5% (w/w) ibuprofen included in a light-responsive 3,5-dimethoxybenzoin conjugate. Raman spectroscopy confirmed the presence of the conjugate inside the polymeric MN matrix. In vitro, this system was able to deliver up to three doses of 50 mg of ibuprofen upon application of an optical trigger over a prolonged period of time (up to 160 hours). This makes the system appealing as a controlled release device for prolonged periods of time. We believe that this technology has potential for use in ?on-demand? delivery of a wide range of drugs in a variety of applications relevant to enhanced patient care.

Abdominal Aortic Aneurysm Genetic Associations: Mostly False? A Systematic Review and Meta-analysis

OBJECTIVE/BACKGROUND: Many associations between abdominal aortic aneurysm (AAA) and genetic polymorphisms have been reported. It is unclear which are genuine and which may be caused by type 1 errors, biases, and flexible study design. The objectives of the study were to identify associations supported by current evidence and to investigate the effect of study design on reporting associations.

METHODS: Data sources were MEDLINE, Embase, and Web of Science. Reports were dual-reviewed for relevance and inclusion against predefined criteria (studies of genetic polymorphisms and AAA risk). Study characteristics and data were extracted using an agreed tool and reports assessed for quality. Heterogeneity was assessed using I(2) and fixed- and random-effects meta-analyses were conducted for variants that were reported at least twice, if any had reported an association. Strength of evidence was assessed using a standard guideline.

RESULTS: Searches identified 467 unique articles, of which 97 were included. Of 97 studies, 63 reported at least one association. Of 92 studies that conducted multiple tests, only 27% corrected their analyses. In total, 263 genes were investigated, and associations were reported in polymorphisms in 87 genes. Associations in CDKN2BAS, SORT1, LRP1, IL6R, MMP3, AGTR1, ACE, and APOA1 were supported by meta-analyses.

CONCLUSION: Uncorrected multiple testing and flexible study design (particularly testing many inheritance models and subgroups, and failure to check for Hardy-Weinberg equilibrium) contributed to apparently false associations being reported. Heterogeneity, possibly due to the case mix, geographical, temporal, and environmental variation between different studies, was evident. Polymorphisms in nine genes had strong or moderate support on the basis of the literature at this time. Suggestions are made for improving AAA genetics study design and conduct.

Exact and numerical solutions for diffusio-reaction equations with convection term

Esta dissertação estuda essencialmente dois problemas: (A) uma classe de equações unidimensionais de reacção-difusão-convecção em meios não uniformes (dependentes do espaço), e (B) um problema elíptico não-linear e paramétrico ligado a fenómenos de capilaridade. A Análise de Perturbação Singular e a dinâmica de Hamilton-Jacobi são utilizadas na obtenção de expressões assimptóticas para a solução (com comportamento de frente) e para a sua velocidade de propagação. Os seguintes três métodos de decomposição, Adomian Decomposition Method (ADM), Decomposition Method based on Infinite Products (DIP), e New Iterative Method (NIM), são apresentados e brevemente comparados. Adicionalmente, condições suficientes para a convergência da solução em série, obtida pelo ADM, e uma aplicação a um problema da Telecomunicações por Fibras Ópticas, envolvendo EDOs não-lineares designadas equações de Raman, são discutidas. Um ponto de vista mais abrangente que unifica os métodos de decomposição referidos é também apresentado. Para subclasses desta EDP são obtidas soluções numa forma explícita, para diferentes tipos de dados e usando uma variante do método de simetrias de Bluman-Cole. Usando Teoria de Pontos Críticos (o teorema usualmente designado mountain pass) e técnicas de truncatura, prova-se a existência de duas soluções não triviais (uma positiva e uma negativa) para o problema elíptico não-linear e paramétrico (B). A existência de uma terceira solução não trivial é demonstrada usando Grupos Críticos e Teoria de Morse.

A generalization of fiedler's lemma and some applications

In a previous paper [M. Robbiano, E.A. Martins, and I. Gutman, Extending a theorem by Fiedler and applications to graph energy, MATCH Commun. Math. Comput. Chem. 64 (2010), pp. 145-156], a lemma by Fiedler was used to obtain eigenspaces of graphs, and applied to graph energy. In this article Fiedler's lemma is generalized and this generalization is applied to graph spectra and graph energy. © 2011 Taylor & Francis.