Diastereoselective self-condensation of dihydroxyfumaric Acid in water: potential route to sugars

Jack of all trades: Water-soluble salts of DHF underwent self-condensation to afford the threo diastereomer of pentulosonic acid, through differing reaction pathways contingent on the metal salt used. This transformation exemplifies the diverging roles of DHF as a nucleophile (a synthon for α-hydroxyacetyl anion) and an electrophile (an α-carboxyglycolaldehyde equivalent).     

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.     

Fractional integral operators in the complex matrix variate case

A formal definition of fractional integrals in the complex matrix variate case is given here. This definition will encompass all the various fractional integral operators introduced by various authors in the real scalar and matrix cases. The new definition is introduced in terms of M-convolutions of products and ratios of matrices in the complex domain. Their connections to statistical distribution theory, Mellin convolutions, M-transforms and Mellin transform are pointed out. Some basic properties are given and a pathway extension of the new definition is also given. The pathway extension will provide a switching mechanism to move among three different families of functions.     

Generalized Boltzmann factors induced by Weibull-type distributions

The inverse Mellin transform technique is utilized to obtain closed form representations of the generalized Boltzmann factors associated with several Weibull-type models such as the generalized gamma, Maxwell, Rayleigh and half-normal distributions. The results complement those already available in the Physics literature in connection with the distribution of certain variables affecting the behavior of nonequilibrium systems subject to complex dynamics, which include for instance computable expressions for the generalized Boltzmann factors induced by the gamma, F$F$, uniform and lognormal statistical models.     

T-Duality Simplifies Bulk–Boundary Correspondence: Some Higher Dimensional Cases

Recently we introduced T-duality in the study of topological insulators, and used it to show that T-duality transforms the bulk–boundary homomorphism into a simpler restriction map in two dimensions. In this paper, we partially generalize these results to higher dimensions in both the complex and real cases, and briefly discuss the 4D quantum Hall effect.     

Nonassociative Tori and Applications to T-Duality

In this paper, we initiate the study of C^*-algebras endowed with a twisted action of a locally compact abelian Lie group , and we construct a twisted crossed product , which is in general a nonassociative, noncommutative, algebra. The duality properties of this twisted crossed product algebra are studied in detail, and are applied to T-duality in Type II string theory to obtain the T-dual of a general principal torus bundle with general H-flux, which we will argue to be a bundle of noncommutative, nonassociative tori. Nonassociativity is interpreted in the context of monoidal categories of modules. We also show that this construction of the T-dual includes the other special cases already analysed in a series of papers.     

Robust free space board-to-board optical interconnect with closed loop MEMS tracking

We present a free-space optical interconnect system capable of dynamic closed-loop optical alignment using a microlens scanner with a proportional integral and derivative controller. Electrostatic microlens scanners based on combdrive actuators are designed and characterized with vertical cavity surface emitting lasers (VCSELs) for adaptive optical beam tracking in the midst of mechanical vibration noise. The microlens scanners are fabricated on silicon-on-insulator wafers with a bulk micromachining process using deep reactive ion etching. We demonstrate dynamic optical beam positioning with a 700 Hz bandwidth and a maximum noise reduction of approximately 40 dB. Eye diagrams with a 1 Gb/s modulation rate are presented to demonstrate the improved optical link in the presence of mechanical noise.     

Integrated receiver architectures for board-to-board free-space optical interconnects

In many computer and server communications copper cables and wires are currently being used for data transmission and interconnects. However, due to significant shortcomings, such as long transmission time, high noise level, unstable electrical properties, and high power consumption for cooling, researchers are increasingly turning their research interests toward alternatives, such as fiber optic interconnects and free-space optical communication technologies. In this paper, we present design considerations for an integrated receiver for high-speed free-space line-of-sight optical interconnects for distortion-free data transmission in an environment with mechanical vibrations and air turbulences. The receiver consists of an array of high-speed photodiodes for data communication and an array of quadrant photodiodes for real-time beam tracking in order to compensate for the beam misalignment caused by vibrations in servers. Different configurations for spatially positioning the quadrant and data photodiodes are discussed for 4×4 and 9×9 multielement optical detector arrays. We also introduce a new beam tracking device, termed the strip quadrant photodiodes, in order to accurately track highly focused optical beams with very small beam diameter.     

Approximating Spectral Invariants of Harper Operators on Graphs

We study Harper operators and the closely related discrete magnetic Laplacians (DML) on a graph with a free action of a discrete group, as defined by Sunada (Sun). A main result in this paper is that the spectral density function of DMLs associated to rational weight functions on graphs with a free action of an amenable discrete group can be approximated by the average spectral density function of the DMLs on a regular exhaustion, with either Dirichlet or Neumann boundary conditions. This then gives a criterion for the existence of gaps in the spectrum of the DML, as well as other interesting spectral properties of such DMLs. The technique used incorporates some results of algebraic number theory.