A Deformation Quantization Theory for Non-Commutative Quantum Mechanics

We show that the deformation quantization of non-commutative quantum mechanics previously considered by Dias and Prata can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined, and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef.Comment: Submitted for publicatio

Triaza-based amphiphilic chelators : synthetic route, in vitro characterization and in vivo studies of their Ga(III) and Al(III) chelates

Radiogalium chelates are important for diagnostic imaging in nuclear medicine (PET and ƴ-scintigraphy). Micelles are adequate colloidal vehicles for the delivery of therapeutic and diagnostic agents to organs and tissues. In this paper we describe the synthesis and in vitro and in vivo studies of a series of micelles-forming Ga(III) chelates targeted for the liver. The amphiphilic ligands are based on NOTA (NOTA = 1,4,7-triazacyclonoane-N,N’N’’-triacetic acid) and bear a α-alkyl chain in one of the pendant acetate arms (the size of the chain changes from four to fourteen carbon atoms). A multinuclear NMR study (1H, 13C, 27Al and 71Ga) gave some insights into the structure and dynamics of the metal chelates in solution, consistent with their rigidity and octahedral or pseudo-octahedral geometry. The critical micellar concentration of the chelates was determined using a fluorescence method and 27Al NMR spectroscopy (Al(III) was used as a surrogate of Ga(III)), both showing similar results and suggesting that the chelates of NOTAC6 form pre-micellar aggregates. The logP (octanol-water) determination showed enhancement of the lipophilic character of the Ga(III) chelates with the increase of the number of carbons in the α-alkyl chain. Biodistribution and Ƴ-scintigraphic studies of the 67Ga(III) labeled chelates were performed on Wistar rats, showing higher liver uptake for [67Ga](NOTAC8) in comparison to [67Ga](NOTAC6), consistent with a longer α-alkyl chain and a higher lipophilicity. After 24 hours both chelates were completely cleared off from the tissues and organs with no deposition in the bones and liver/spleen. [67Ga](NOTAC8) showed high kinetic stability in blood serum.Fundação para a Ciência e a Tecnologia (FCT

Ga(III) chelates of amphiphilic DOTA-based ligands : synthetic route and in vitro and in vivo studies

In this work we report a synthetic strategy of amphiphilic DOTA-based chelators bearing a variable size α-alkyl chain at one of the pendant acetate arms (from six to fourteen carbon atoms), compatible with their covalent coupling to amine-bearing biomolecules. The amphiphilic behavior of the micelles-forming Ga(III) chelates (critical micelle concentration), their stability in blood serum and their lipophilicity (logP) were investigated. Biodistribution studies with the 67Ga-labeled chelates were performed in Wistar rats showing a predominant liver uptake with almost no traces of the radiochelates in the body after 24 hours.Fundação para a Ciência e a Tecnologia (FCT

Entropic Gravity, Phase-Space Noncommutativity and the Equivalence Principle

We generalize E. Verlinde's entropic gravity reasoning to a phase-space noncommutativity set-up. This allow us to impose a bound on the product of the noncommutative parameters based on the Equivalence Principle. The key feature of our analysis is an effective Planck's constant that naturally arises when accounting for the noncommutative features of the phase-space.Comment: 12 pages. Version to appear at the Classical and Quantum Gravit

Gallium labeled NOTA-based conjugates for peptide receptor-mediated medical imaging

We report a straightforward and efficient synthetic strategy for the synthesis of three model glycine-arginine-glycine-aspartic-glycine (GRGDG) conjugates based on derivatives of NOTA and of their Ga(III) complexes targeted to the integrin αѵβ₃receptor. 71Ga NMR spectroscopy showed that the Ga(III)-labeled conjugates are highly stable in aqueous solution. The 67Ga-labeled conjugates proved to have high kinetic stability and showed a weak but specific binding to the receptors in a U87MG-glioblastoma cell line.Fundação para a Ciência e a Tecnologia (FCT

Features of Moyal Trajectories

We study the Moyal evolution of the canonical position and momentum variables. We compare it with the classical evolution and show that, contrary to what is commonly found in the literature, the two dynamics do not coincide. We prove that this divergence is quite general by studying Hamiltonians of the form $p^2 /2m + V(q)$. Several alternative formulations of Moyal dynamics are then suggested. We introduce the concept of starfunction and use it to reformulate the Moyal equations in terms of a system of ordinary differential equations on the noncommutative Moyal plane. We then use this formulation to study the semiclassical expansion of Moyal trajectories, which is cast in terms of a (order by order in $\hbar$) recursive hierarchy of i) first order partial differential equations as well as ii) systems of first order ordinary differential equations. The latter formulation is derived independently for analytic Hamiltonians as well as for the more general case of smooth local integrable ones. We present various examples illustrating these results

Ga[NO2A-N-(alfa-amino)propionate] chelates: synthesis and evaluation as potential tracers for 68Ga3+ PET

The availability of commercial 68Ge/68Ga cyclotron-independent 68Ga3+ generators is making Positron Emission Tomography (PET) accessible to most hospitals, which is generating a surge of interest in the design and synthesis of bi-functional chelators for Ga3+. In this work we introduce the NO2A-N-(alfa-amino)propionic acid family of chelators based on the triazacyclononane scaffold. Complexation of the parent NO2A-N-(alfa-amino)propionic acid chelator and of a low molecular weight (model) amide conjugate with Ga3+ was studied by 1H and 71Ga NMR. The Ga3+ chelate of the amide conjugate shows pH-independent N3O3 coordination in the pH range 3-10 involving the carboxylate group of the pendant propionate arm in a 6 member chelate. For the Ga[NO2A-N-(alfa-amino)propionate] chelate, a reversible pH-triggered switch from Ga3+ coordination to the carboxylate group to coordination to the amine group of the propionate arm, was observed upon pH increase/decrease in the pH range 4-6. This phenomenon can conceivably constitute the basis of a physiological pH sensor. Both complexes are stable in the physiological range. The [67Ga][NO2A-N-(alfa-benzoylamido)propionate] chelate was found to be stable in human serum. Biodistribution studies of the 67Ga3+-labeled pyrene butyric acid conjugate NO2A-N-(alfa-pyrenebutanamido)propionic acid revealed that, despite its high lipophilicity and concentration-dependent aggregation properties, the chelate follows mainly renal elimination with very low liver/spleen accumulation and no activity deposition in bones after 24 hours. Facile synthesis of amide conjugates of the NO2A-N-(alfa-amino)propionic acid chelator, serum stability of the Ga3+chelates and fast renal elimination warrant further evaluation of this novel class of chelators for PET applications.This work was financially supported by Fundação para a Ciência e Tecnologia, Portugal: PEst-C/QUI/UI0686/2013; FCOMP-01-0124-FEDER-037302; PTDC/QUI/70063/2006; grant SFRH/BD/63994/2009 to Miguel Ferreira and sabbatical grant SFRH/BSAB/1328/2013 to J. A. Martins; Rede Nacional de RMN (REDE/1517/RMN/2005) for the acquisition of the Varian VNMRS 600 NMR spectrometer at the University of Coimbra and the Bruker Avance-3 400 Plus at the University of Minho in Braga. We also acknowledge the COST Action TD1004 “Theragnostics Imaging and Therapy”

Modular coherent photonic-aided payload receiver for communications satellites

Ubiquitous satellite communications are in a leading position for bridging the digital divide. Fulfilling such a mission will require satellite services on par with fibre services, both in bandwidth and cost. Achieving such a performance requires a new generation of communications payloads powered by large-scale processors, enabling a dynamic allocation of hundreds of beams with a total capacity beyond 1 Tbit s−1. The fact that the scale of the processor is proportional to the wavelength of its signals has made photonics a key technology for its implementation. However, one last challenge hinders the introduction of photonics: while large-scale processors demand a modular implementation, coherency among signals must be preserved using simple methods. Here, we demonstrate a coherent photonic-aided receiver meeting such demands. This work shows that a modular and coherent photonic-aided payload is feasible, making way to an extensive introduction of photonics in next generation communications satellites