A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

The Presumption of Innocence: Patching the Tattered Cloak after Maryland v. Craig.

Over one hundred years ago, the United States Supreme Court recognized the importance of the presumption of innocence in a criminal justice system which is based on due process. The Court declared the presumption of innocence is “the undoubted law, axiomatic, and elementary, and its enforcements lies at the foundation … of our criminal law.” The Court’s changing view of the Sixth Amendment’s Confrontation Clause is the most recent contribution to the reduction in the practical value of the presumption of innocence. In Maryland v. Craig, the Court decided that while face-to-face confrontation forms the core of values furthered in Confrontation Clause, the use of closed-circuit television systems for testimony by children testifying in child sexual abuse cases did not violate the Sixth Amendment. In reaching this decision, the Court balanced the rights of the accused against the state’s interest in protecting an alleged victim from the trauma of testifying in the presence of an alleged perpetrator. The Court concluded traditional face-to-face confrontation requirements must give way to policy considerations when child sexual abuse victims are involved. While admirable in its desire to protect, Craig failed to address the damage its Sixth Amendment exceptions causes to the presumption of innocence. By making special accommodations for an alleged victim’s testimony, the trial judge sends a subtle signal to the jury endorsing the veracity of the witness. Accordingly, the use of alternative forms of testimony casts doubt on the presumption of innocence at the critical moment when the State’s key witness takes the stand. Because of the potentially negative impact which alternative forms of testimony have on the defendant’s presumption of innocence, courts should tailor the use of these procedures to ensure they further the narrow goals they are designed to serve

Modulating the Fibrillization of Parathyroid-Hormone (PTH) Peptides: Azo-Switches as Reversible and Catalytic Entities

We here report a novel strategy to control the bioavailability of the fibrillizing parathyroid hormone (PTH)-derived peptides, where the concentration of the bioactive form is controlled by an reversible, photoswitchable peptide. PTH1–84, a human hormone secreted by the parathyroid glands, is important for the maintenance of extracellular fluid calcium and phosphorus homeostasis. Controlling fibrillization of PTH1–84 represents an important approach for in vivo applications, in view of the pharmaceutical applications for this protein. We embed the azobenzene derivate 3-{[(4- aminomethyl)phenyl]diazenyl}benzoic acid (3,40-AMPB) into the PTH-derived peptide PTH25–37 to generate the artificial peptide AzoPTH25–37 via solid-phase synthesis. AzoPTH25–37 shows excellent photostability (more than 20 h in the dark) and can be reversibly photoswitched between its cis/trans forms. As investigated by ThT-monitored fibrillization assays, the trans-form of AzoPTH25–37 fibrillizes similar to PTH25–37, while the cis-form of AzoPTH25–37 generates only amorphous aggregates. Additionally, cis-AzoPTH25–37 catalytically inhibits the fibrillization of PTH25–37 in ratios of up to one-fifth. The approach reported here is designed to control the concentration of PTH-peptides, where the bioactive form can be catalytically controlled by an added photoswitchable peptide

Necrotic tumor growth: an analytic approach

The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute the solutions of the stationary linearized problem and comment on bifurcation.Comment: 14 pages, 3 figure

Aberrant splicing of U12-type introns is the hallmark of ZRSR2 mutant myelodysplastic syndrome.

Somatic mutations in the spliceosome gene ZRSR2-located on the X chromosome-are associated with myelodysplastic syndrome (MDS). ZRSR2 is involved in the recognition of 3'-splice site during the early stages of spliceosome assembly; however, its precise role in RNA splicing has remained unclear. Here we characterize ZRSR2 as an essential component of the minor spliceosome (U12 dependent) assembly. shRNA-mediated knockdown of ZRSR2 leads to impaired splicing of the U12-type introns and RNA-sequencing of MDS bone marrow reveals that loss of ZRSR2 activity causes increased mis-splicing. These splicing defects involve retention of the U12-type introns, while splicing of the U2-type introns remain mostly unaffected. ZRSR2-deficient cells also exhibit reduced proliferation potential and distinct alterations in myeloid and erythroid differentiation in vitro. These data identify a specific role for ZRSR2 in RNA splicing and highlight dysregulated splicing of U12-type introns as a characteristic feature of ZRSR2 mutations in MDS

The curvature of semidirect product groups associated with two-component Hunter-Saxton systems

In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(\S) with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page

Effects of Cr Doping and Water Content on the Crystal Structure Transitions of Ba2In2O5

Temperature dependent crystal structure alterations in the brownmillerite type material Ba2In2O5 play a fundamental role in its applications i photocatalytic CO2 conversion; ii oxygen transport membranes; and iii proton conduction. This is connected to a reversible uptake of up an equimolar amount of water. In this study, in situ X ray and neutron diffraction were combined with Raman spectroscopy and solid state nuclear magnetic resonance experiments to unravel the effects of Cr doping and water content on the crystal structure transitions of Ba2In2O5 H2O x over a wide temperature range 10 K lt; T lt; 1573 K, x lt; 1 . A mixture of isolated and correlated protons was identified, leading to a highly dynamic situation for the protons. Hence, localisation of the protons by diffraction techniques was not possible. Cr doping led to an overall higher degree of disorder and stabilisation of the tetragonal polymorph, even at 10 K. In contrast, a further disordering at high temperatures, leading to a cubic polymorph, was found at 1123 K. Cr doping in Ba2In2O5 resulted in severe structural changes and provides a powerful way to adjust its physical properties to the respective applicatio

Pain management procedures used by dental and maxillofacial surgeons: an investigation with special regard to odontalgia

BACKGROUND: Little is known about the procedures used by German dental and maxillofacial surgeons treating patients suffering from chronic orofacial pain (COP). This study aimed to evaluate the ambulatory management of COP. METHODS: Using a standardized questionnaire we collected data of dental and maxillofacial surgeons treating patients with COP. Therapists described variables as patients' demographics, chronic pain disorders and their aetiologies, own diagnostic and treatment principles during a period of 3 months. RESULTS: Although only 13.5% of the 520 addressed therapists returned completely evaluable questionnaires, 985 patients with COP could be identified. An orofacial pain syndrome named atypical odontalgia (17.0 %) was frequent. Although those patients revealed signs of chronification, pain therapists were rarely involved (12.5%). For assessing pain the use of Analogue Scales (7%) or interventional diagnostics (4.6%) was uncommon. Despite the fact that surgical procedures are cofactors of COP therapists preferred further surgery (41.9%) and neglected the prescription of analgesics (15.7%). However, most therapists self-evaluated the efficacy of their pain management as good (69.7 %). CONCLUSION: Often ambulatory dental and maxillofacial surgeons do not follow guidelines for COP management despite a high prevalence of severe orofacial pain syndromes