Finite dimensional representations and subgroup actions on homogeneous spaces

LetH be an ℝ-subgroup of a ℚ-algebraic groupG. We study the connection between the dynamics of the subgroup action ofH onG/G _ℤ and the representation-theoretic properties ofH being observable and epimorphic inG. We show that ifH is a ℚ-subgroup thenH is observable inG if and only if a certainH orbit is closed inG/G _ℤ; that ifH is epimorphic inG then the action ofH onG/G _ℤ is minimal, and that the converse holds whenH is a ℚ-subgroup ofG; and that ifH is a ℚ-subgroup ofG then the closure of the orbit underH of the identity coset image inG/G _ℤ is the orbit of the same point under the observable envelope ofH inG. Thus in subgroup actions on homogeneous spaces, closures of ‘rational orbits’ (orbits in which everything which can be defined over ℚ, is defined over ℚ) are always submanifolds.     

Increasing the efficacy of bioorthogonal click reactions for bioconjugation: a comparative study

Raising the bar: The efficacy of bioorthogonal reactions for bioconjugation has been thoroughly evaluated in four different biological settings. Powered by the development of new biocompatible ligands, the copper-catalyzed azide-alkyne cycloaddition has brought about unsurpassed bioconjugation efficiency, and thus it holds great promise as a highly potent and adaptive tool for a broader spectrum of biological applications.     

Probing conformational variations at the ATPase site of the RNA helicase DbpA by high-field electron-nuclear double resonance spectroscopy

The RNA helicase DbpA promotes RNA remodeling coupled to ATP hydrolysis. It is unique because of its specificity to hairpin 92 of 23S rRNA (HP92). Although DbpA kinetic pathways leading to ATP hydrolysis and RNA unwinding have been recently elucidated, the molecular (atomic) basis for the coupling of ATP hydrolysis to RNA remodeling remains unclear. This is, in part, due to the lack of detailed structural information on the ATPase site in the presence and absence of RNA in solution. We used high-field pulse ENDOR (electron-nuclear double resonance) spectroscopy to detect and analyze fine conformational changes in the protein's ATPase site in solution. Specifically, we substituted the essential Mg(2+) cofactor in the ATPase active site for paramagnetic Mn(2+) and determined its close environment with different nucleotides (ADP, ATP, and the ATP analogues ATPγS and AMPPnP) in complex with single- and double-stranded RNA. We monitored the Mn(2+) interactions with the nucleotide phosphates through the (31)P hyperfine couplings and the coordination by protein residues through (13)C hyperfine coupling from (13)C-enriched DbpA. We observed that the nucleotide binding site of DbpA adopts different conformational states upon binding of different nucleotides. The ENDOR spectra revealed a clear distinction between hydrolyzable and nonhydrolyzable nucleotides prior to RNA binding. Furthermore, both the (13)C and the (31)P ENDOR spectra were found to be highly sensitive to changes in the local environment of the Mn(2+) ion induced by the hydrolysis. More specifically, ATPγS was efficiently hydrolyzed upon binding of RNA, similar to ATP. Importantly, the Mn(2+) cofactor remains bound to a single protein side chain and to one or two nucleotide phosphates in all complexes, whereas the remaining metal coordination positions are occupied by water. The conformational changes in the protein's ATPase active site associated with the different DbpA states occur in remote coordination shells of the Mn(2+) ion. Finally, a competitive Mn(2+) binding site was found for single-stranded RNA construct.     

Dubrovin's duality for F-manifolds with eventual identities

A vector field E on an F-manifold (M,°,e) is an eventual identity if it is invertible and the multiplication X?Y:=X°Y°E−1 defines a new F-manifold structure on M. We give a characterization of such eventual identities, this being a problem raised by Manin (2005) [12]. We develop a duality between F-manifolds with eventual identities and we show that this duality is compatible with the local irreducible decomposition of F-manifolds and preserves the class of Riemannian F-manifolds. We find necessary and sufficient conditions on the eventual identity which ensure that the classes of harmonic Higgs bundles, DChk-structures and weak CV-structures are preserved by our duality. Examples of such structures are given in the case of a semi-simple multiplication. We use eventual identities to construct compatible pairs of metrics.     

Free resolutions over short Gorenstein local rings

Let R be a local ring with maximal ideal ${\mathfrak{m}}$ admitting a non-zero element ${a\in\mathfrak{m}}$ for which the ideal (0 : a) is isomorphic to R/aR. We study minimal free resolutions of finitely generated R-modules M, with particular attention to the case when ${\mathfrak{m}^4=0}$ . Let e denote the minimal number of generators of ${\mathfrak{m}}$ . If R is Gorenstein with ${\mathfrak{m}^4=0}$ and e ?? 3, we show that ${{\rm P}_{M}^{R}(t)}$ is rational with denominator H _R (?t) =?1 ? et?+?et ² ? t ³, for each finitely generated R-module M. In particular, this conclusion applies to generic Gorenstein algebras of socle degree 3.     

Nuclear threat detection with mobile distributed sensor networks

The ability to track illicit radioactive source in an urban environment is critical in national security applications. To this end, two modes of operation are common: positioning individual portal monitors, and deploying a network of distributed sensors. We address here the use of multiple detectors, mounted on moving vehicles, for the purpose of detecting nuclear threats. An example scenario is that of multiple taxi cabs each carrying a detector. The detectors’ positions are known in real-time as these are continuously reported from GPS data. The level of detected risk is then reported from each detector at each position. The problem is to delineate the presence of a potentially dangerous source and its approximate location by identifying a small area that has an elevated concentration of reported risk. This problem of using spatially deployed mobile detector networks to identify and locate risks is modeled and formulated here. The problem is shown to be solvable in polynomial time and with a combinatorial network flow algorithm. The efficiency of the algorithm enable its use in real time, and in areas containing a large number of deployed detectors. A simulation study, that takes into account false-positive and false-negatives reports from individual sensors, demonstrates the effectiveness of the algorithm in using the sensor network’s detection capabilities.     

Diverging rabi oscillations in subwavelength photonic lattices

We show that Rabi oscillations between Bloch modes of an optical waveguide array with subwavelength periodicity diverge, both in frequency and in field amplitude, when the optical wavelength approaches a mathematical exceptional point at which the Bloch mode becomes self-orthogonal.     

The Raman Spectrum of Mercury (II) Iodide in High Temperature Solvents

Abstract

The Raman spectrum of mercury(II) iodide was observed in cesium nitrate at 430°C and in meta- and para-terphenyl at 235 and 240°C, respectively. A single strong polarized line was found at 148. 5 cm^?1, width at half height 15 cm^?1 in cesium nitrate, and a single line at 154. 0 cm^?1 width at half height 7 cm^?1 in the terphenyls. The observed spectra are not consistent with interactions of the solute and the solvents involving bonds of highly covalent character, but do not exclude other interactions.

In the course of an investigation on the nature of mercury (II) iodide species in solution in molten alkali metal nitrates, by its distribution between the salt melts and terphenyl melts^{1, 2}, it became of interest to study by means of Raman spectroscopy the mercury (II) iodide species formed. Several such studies at lower temperatures have already been made: in the gas phase³, in a krypton matrix⁴, in alcohols⁵, tributy phosphate⁶ and dioxame⁷, and in molten mercury(II) iodide⁸, chloride⁹, and bromide⁹. The reason for looking at the Raman spectrum in yetfurther media was the suggestion made on the basis of thermodynamic and kinetic data^2,10 that the mercury(II) iodide species in the alkali mitrate melts are solvated by nitrate anions, and that possiby the mixed anion terrahedral species HgI₂(NO₃)₂ is formed. Recent Ranan sepctrophotometric data on mixed halide anionic complexes of mercury₁₁ identified prominent lines of the spectrum of the species HgBr_nI^2– _4–n, including HGBr₂I₂ ^2–, so that a comparison could be made. The solubility of mercury (II) iodide in molten alkali metal nitrates is rather small, expect for cesium nitrate¹², Where the solubility should be sufficent for the Raman spectrum to be recorded. Also, it was comcluded from vapor pressure osmometric data in aromatic solvents that demiric species of mercury(II) halides (even a trimeric species of the iodide) are found, in which the mercury has a distorted octahedral coordination, with three halogen atoms bonded to a mercury atom in the dimer¹³. In terphenyl melts, the solubility     

Comparison between multi-echo T2* with and without fat saturation pulse for quantification of liver iron overload

Purpose

To test a magnetic resonance image (MRI) technique that uses an additional pulse in multi-echo T2* sequence that works to suppress the fat signal, in subjects with liver iron overload and concomitant presence of fat in the liver, which have been revealed as a major drawback that compromises the correct iron quantification by MRI.

Materials and Methods

Fifty magnetic resonance images of the liver (1.5 T scanner) of individuals with blood ferritin increases were retrospectively reviewed for the presence of steatosis, using the sequence in and out of phase, and iron overloading, using two sequences T2 * multi-echo: one standard and other with additional fat suppression pulse. T2 * values and their standard deviations were analyzed statistically.

Results

Our results showed that a significantly lower standard deviation of T2* values is obtained when the fat saturation pulse is applied in patients with steatosis. We found that modulation of fat signal on liver iron overload resulted in a different categorization of some patients. In one case, the patient was re-classified within normal levels of liver iron.

Conclusion

Our findings may contribute to a better measure of liver iron overload with relevant implications for patient treatment and care.     

Fuzzy turnover rate chance constraints portfolio model

One concern of many investors is to own the assets which can be liquidated easily. Thus, in this paper, we incorporate portfolio liquidity in our proposed model. Liquidity is measured by an index called turnover rate. Since the return of an asset is uncertain, we present it as a trapezoidal fuzzy number and its turnover rate is measured by fuzzy credibility theory. The desired portfolio turnover rate is controlled through a fuzzy chance constraint. Furthermore, to manage the portfolios with asymmetric investment return, other than mean and variance, we also utilize the third central moment, the skewness of portfolio return. In fact, we propose a fuzzy portfolio mean–variance–skewness model with cardinality constraint which combines assets limitations with liquidity requirement. To solve the model, we also develop a hybrid algorithm which is the combination of cardinality constraint, genetic algorithm, and fuzzy simulation, called FCTPM.