Two-dimensional infrared spectroscopy of azido-nicotinamide adenine dinucleotide in water

Mid-IR active analogs of enzyme cofactors have the potential to be important spectroscopic reporters of enzyme active site dynamics. Azido-nicotinamide adenine dinucleotide (NAD(+)), which has been recently synthesized in our laboratory, is a mid-IR active analog of NAD(+), a ubiquitous redox cofactor in biology. In this study, we measure the frequency-frequency time correlation function for the antisymmetric stretching vibration of the azido group of azido-NAD(+) in water. Our results are consistent with previous studies of pseudohalides in water. We conclude that azido-NAD(+) is sensitive to local environmental fluctuations, which, in water, are dominated by hydrogen-bond dynamics of the water molecules around the probe. Our results demonstrate the potential of azido-NAD(+) as a vibrational probe and illustrate the potential of substituted NAD(+)-analogs as reporters of local structural dynamics that could be used for studies of protein dynamics in NAD-dependent enzymes.     

Evidence for fully conjugated double-stranded cycles

A chain of circumstantial evidence for the existence of the first fully conjugated, double-stranded cycles is presented. The products have the structure of the belt-region of fullerene C(84)(D(2)) and carry either four hexyl chains or four phenyl groups. The unsubstituted parent cycle is also presented. The chain of evidence is mainly based on mass spectrometric analysis and trapping reactions, the latter being supported by quantum mechanical calculations. It is also of importance that the phenyl-substituted and unsubstituted products cannot undergo a [1,5] hydrogen shift, the only reasonable side-reaction that recently could not be excluded for the alkyl-substituted analogue. It is concluded that the fully aromatic targets truly exist in the gas phase. Whether they can be generated in solution under the applied conditions cannot yet be firmly decided; theoretical evidence speaks against.     

On the Homology of Completion and Torsion

Let A be a commutative ring, and ${\mathfrak{a}}$ a weakly proregular ideal in A. This includes the noetherian case: if A is noetherian then any ideal in it is weakly proregular; but there are other interesting examples. In this paper we prove the MGM equivalence, which is an equivalence between the category of cohomologically ${\mathfrak{a}}$ -adically complete complexes and the category of cohomologically ${\mathfrak{a}}$ -torsion complexes. These are triangulated subcategories of the derived category of A-modules. Our work extends earlier work by Alonso–Jeremias–Lipman, Schenzel and Dwyer–Greenlees.     

Dualizing complexes and perverse sheaves on noncommutative ringed schemes

A quasi-coherent ringed scheme is a pair (X, $$ \mathcal{A} $$), where X is a scheme, and $$ \mathcal{A} $$ is a noncomutative quasi-coherent $$ \mathcal{O}_X $$ -ring. We introduce dualizing complexes over quasi-coherent ringed schemes and study their properties. For a separated differential quasi-coherent ringed scheme of finite type over a field, we prove existence and uniqueness of a rigid dualizing complex. In the proof we use the theory of perverse coherent sheaves in order to glue local pieces of the rigid dualizing complex into a global complex.     

The NICS‐XY‐Scan: Identification of Local and Global Ring Currents in Multi‐Ring Systems

Nucleus‐independent chemical shift (NICS)‐based methods are very popular for the determination of the induced magnetic field under an external magnetic field. These methods are used mostly (but not only) for the determination of the aromaticity and antiaromaticity of molecules and ions, both qualitatively and quantitatively. The ghost atom that serves as the NICS probe senses the induced magnetic field and reports it in the form of an NMR chemical shift. However, the source of the field cannot be determined by NICS. Thus, in a multi‐ring system that may contain more than one induced current circuit (and therefore more than one source of the induced magnetic field) the NICS value may represent the sum of many induced magnetic fields. This may lead to wrong assignments of the aromaticity (and antiaromaticity) of the systems under study. In this paper, we present a NICS‐based method for the determination of local and global ring currents in conjugated multi‐ring systems. The method involves placing the NICS probes along the X axis, and if needed, along the Y axis, at a constant height above the system under study. Following the change in the induced field along these axes allows the identification of global and local induced currents. The best NICS type to use for these scans is NICS_πZZ, but it is shown that at a height of 1.7 Å above the molecular plane, NICS_ZZ provides the same qualitative picture. This method, namely the NICS‐XY‐scan, gives information equivalent to that obtained through current density analysis methods, and in some cases, provides even more details.     

Deformation quantization in algebraic geometry

We study deformation quantizations of the structure sheaf O_X of a smooth algebraic variety X in characteristic 0. Our main result is that when X is D-affine, any formal Poisson structure on X determines a deformation quantization of O_X (canonically, up to gauge equivalence). This is an algebro-geometric analogue of Kontsevich's celebrated result.     

Lossless Condensers,Unbalanced Expanders,And Extractors

Trevisan showed that many pseudorandom generator constructions give rise to constructions of explicit extractors. We show how to use such constructions to obtain explicit lossless condensers. A lossless condenser is a probabilistic map using only O(logn) additional random bits that maps n bits strings to poly(logK) bit strings, such that any source with support size K is mapped almost injectively to the smaller domain. Our construction remains the best lossless condenser to date. By composing our condenser with previous extractors, we obtain new, improved extractors. For small enough min-entropies our extractors can output all of the randomness with only O(logn) bits. We also obtain a new disperser that works for every entropy loss, uses an O(logn) bit seed, and has only O(logn) entropy loss. This is the best disperser construction to date, and yields other applications. Finally, our lossless condenser can be viewed as an unbalanced bipartite graph with strong expansion properties. * Much of this work was done while the author was in the Computer Science Division, University of California, Berkeley, and supported in part by a David and Lucile Packard Fellowship for Science and Engineering and NSF NYI Grant No. CCR-9457799. The work was also supported in part by an Alon fellowship and by the Israel Science Foundation. † Much of this work was done while the author was a graduate student in the Computer Science Division, University of California, Berkeley. Supported in part by NSF Grants CCR-9820897, CCF-0346991, and an Alfred P. Sloan Research Fellowship. ‡ Much of this work was done while the author was on leave at the Computer Science Division, University of California, Berkeley. Supported in part by a David and Lucile Packard Fellowship for Science and Engineering, NSF Grants CCR-9912428 and CCR-0310960, NSF NYI Grant CCR-9457799, and an Alfred P. Sloan Research Fellowship.     

On the width of the critical region in dilute magnets with long range percolation

The Ginzburg criterion is used to estimate the width of the critical region for a dilute magnet with a large range of interactionsR. This width decreases asR ^{–2d/(4–d)} at high temperature and asR ^{–2d/(6–d)} at very low temperatures, i.e. in the percolation limit. The crossover between the two regimes is discussed.