L1-determined ideals in group algebras of exponential Lie groups

A locally compact group $G$ is said to be $\ast$-regular if the natural map \Psi:\Prim C^\ast(G)\to\Prim_{\ast} L^1(G) is a homeomorphism with respect to the Jacobson topologies on the primitive ideal spaces \Prim C^\ast(G) and \Prim_{\ast} L^1(G). In 1980 J. Boidol characterized the $\ast$-regular ones among all exponential Lie groups by a purely algebraic condition. In this article we introduce the notion of $L^1$-determined ideals in order to discuss the weaker property of primitive $\ast$-regularity. We give two sufficient criteria for closed ideals $I$ of $C^\ast(G)$ to be $L^1$-determined. Herefrom we deduce a strategy to prove that a given exponential Lie group is primitive $\ast$-regular. The author proved in his thesis that all exponential Lie groups of dimension $\le 7$ have this property. So far no counter-example is known. Here we discuss the example $G=B_5$, the only critical one in dimension $\le 5$

Comprehensive molecular pharmacology screening reveals potential new receptor interactions for clinically relevant opioids

Most clinically used opioids are thought to induce analgesia through activation of the mu opioid receptor (MOR). However, disparities have been observed between the efficacy of opioids in activating the MOR in vitro and in inducing analgesia in vivo. In addition, some clinically used opioids do not produce cross-tolerance with each other, and desensitization produced in vitro does not match tolerance produced in vivo. These disparities suggest that some opioids could be acting through other targets in vivo, but this has not been comprehensively tested. We thus screened 9 clinically relevant opioids (buprenorphine, hydrocodone, hydromorphone, morphine, 0-desmethyl-tramadol, oxycodone, oxymorphone, tapentadol, tramadol) against 9 pain-related receptor targets (MOR, delta opioid receptor [DOR], kappa opioid receptor [KOR], nociceptin receptor [NOP], cannabinoid receptor type 1 [CB1], sigma-1 receptor [al R], and the monoamine transporters [NET/SERT/DAT]) expressed in cells using radioligand binding and functional activity assays. We found several novel interactions, including monoamine transporter activation by buprenorphine and al R binding by hydrocodone and tapentadol. Tail flick anti-nociception experiments with CD-1 mice demonstrated that the monoamine transporter inhibitor duloxetine selectively promoted buprenorphine anti-nociception while producing no effects by itself or in combination with the most MOR-selective drug oxymorphone, providing evidence that these novel interactions could be relevant in vivo. Our findings provide a comprehensive picture of the receptor interaction profiles of clinically relevant opioids, which has not previously been performed. Our findings also suggest novel receptor interactions for future investigation that could explain some of the disparities observed between opioid performance in vitro and in vivo.Depomed, Inc.; University of ArizonaOpen access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Recoil Correction to Hydrogen Energy Levels: A Revision

Recent calculations of the order (Z\alpha)^4(m/M)Ry pure recoil correction to hydrogen energy levels are critically revised. The origins of errors made in the previous works are elucidated. In the framework of a successive approach, we obtain the new result for the correction to S levels. It amounts to -16.4 kHz in the ground state and -1.9 kHz in the 2S state.Comment: 15 pages, Latex, no figure

Treatment Guidelines for Rare, Early-Onset Conditions Associated with Epileptic Seizures: A Literature Review on Rett Syndrome and Tuberous Sclerosis Complex

Background Rett syndrome (RTT) and tuberous sclerosis complex (TSC) are two rare disorders presenting with a range of different epileptic seizures. Seizure management requires careful therapy selection, thereby necessitating development of high-quality treatment guidelines. This targeted literature review (TLR) aimed to characterise country-specific and international treatment guidelines available for pharmacological management of seizures in RTT and TSC.Methods A TLR was performed between 25-Jan and 11-Mar 2021. Manual searches of online rare disease and guideline databases, and websites of national heath technology assessment bodies were conducted for the following countries: Australia, Canada, France, Germany, Israel, Italy, Japan, Spain, Switzerland, UK, and US as defined by pre-specified eligibility criteria. Search terms were developed for each condition and translated into local languages where appropriate. Eligible publications were defined as guidelines/guidance reporting pharmacological management of seizures in patients with RTT and TSC. Guideline development methodology, geographical focus, author information and treatment recommendations were extracted from guidelines. An author map was generated using R version 3.5.1 to visualise extent of collaboration between authors. Results24 total guidelines were included, of which three and six contained only recommendations for RTT and TSC, respectively (some provided recommendations for ≥1 condition). Guideline development processes were poorly described (50% [12 guidelines] had unclear/absent literature review methodologies); reported methodologies were variable, including systematic literature reviews (SLRs)/TLRs and varying levels of expert consultation. Most (83% [20/24]) were country-specific, with guideline authors predominantly publishing in contained national groups; four guidelines were classified as ‘International,’ linking author groups in the US, UK, Italy and France. High levels of heterogeneity were observed in the availability of treatment recommendations across indications, with 13 and 67 recommendations found for RTT and TSC, respectively. For RTT, all treatment recommendations were positive and sodium valproate had the highest number of positive recommendations (3). All TSC treatments (21 medications) received either exclusively negative (2) or positive (65) recommendations; vigabatrin received the highest number of positive recommendations (21). ConclusionsThis review highlights the need for the development of international high-quality and comprehensive consensus-based guidance for the management of seizures with pharmacological therapy in RTT and TSC. <br/

General Framework for phase synchronization through localized sets

We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs, these observations give rise to a localized set. Our result provides a general and easy way to identify PS, which can also be used to oscillators that possess multiple time scales. We illustrate our approach in networks of chemically coupled neurons. We show that clusters of phase synchronous neurons may emerge before the onset of phase synchronization in the whole network, producing a suitable environment for information exchanging. Furthermore, we show the relation between the localized sets and the amount of information that coupled chaotic oscillator can exchange

On the Complex Network Structure of Musical Pieces: Analysis of Some Use Cases from Different Music Genres

This paper focuses on the modeling of musical melodies as networks. Notes of a melody can be treated as nodes of a network. Connections are created whenever notes are played in sequence. We analyze some main tracks coming from different music genres, with melodies played using different musical instruments. We find out that the considered networks are, in general, scale free networks and exhibit the small world property. We measure the main metrics and assess whether these networks can be considered as formed by sub-communities. Outcomes confirm that peculiar features of the tracks can be extracted from this analysis methodology. This approach can have an impact in several multimedia applications such as music didactics, multimedia entertainment, and digital music generation.Comment: accepted to Multimedia Tools and Applications, Springe

Positronium S state spectrum: analytic results at O(m alpha^6)

We present an analytic calculation of the O(m alpha^6) recoil and radiative recoil corrections to energy levels of positronium nS states and their hyperfine splitting. A complete analytic formula valid to O(m alpha^6) is given for the spectrum of S states. Technical aspects of the calculation are discussed in detail. Theoretical predictions are given for various energy intervals and compared with experimental results.Comment: 29 pages, revte

Evolving networks with disadvantaged long-range connections

We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at distance $d$ is proportional to $d^{-\alpha}$, where $\alpha$ is a tunable parameter of the model. We show that the properties of the networks grown with $\alpha <1$ are close to those of the genuine scale-free construction, while for $\alpha >1$ the structure of the network is vastly different. Thus, in this regime, the node degree distribution is no more a power law, and it is well-represented by a stretched exponential. On the other hand, the small-world property of the growing networks is preserved at all values of $\alpha$.Comment: REVTeX, 6 pages, 5 figure