Complexified sigma model and duality

We show that the equations of motion associated with a complexified sigma-model action do not admit manifest dual SO(n,n) symmetry. In the process we discover new type of numbers which we called `complexoids' in order to emphasize their close relation with both complex numbers and matroids. It turns out that the complexoids allow to consider the analogue of the complexified sigma-model action but with (1+1)-worldsheet metric, instead of Euclidean-worldsheet metric. Our observations can be useful for further developments of complexified quantum mechanics.Comment: 15 pages, Latex, improved versio

Contextual planning for NASA - A second workbook of alternative future environments for mission analysis, volume 1 Interim report

Contextural planning for selecting alternate NASA program

Particle and particle pair dispersion in turbulence modeled with spatially and temporally correlated stochastic processes

In this paper we present a new model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use an Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid particles, which are modeled by stochastic processes correlated in time. We are able to reproduce the ballistic regime in the mean squared displacement of single particles and the transition to a normal diffusion regime for long times. For the dispersion of particle pairs we find a $t^{2}$-dependence of the mean squared separation at short times and a $t$-dependence for long ones. For intermediate times indications for a Richardson $t^{3}$ law are observed in certain situations. Finally the influence of inertia of real particles on the dispersion is investigated.Comment: 10 pages, 7 figures, 1 tabl

A novel protocol for the one-pot borylation/Suzuki reaction provides easy access to hinge-binding groups for kinase inhibitors

The one-pot borylation/Suzuki reaction is a very efficient means of accessing cross-coupling products of two aryl-halide partners that generally requires the use of specific catalysts or ligands and/or relatively long reaction times. This new microwave-assisted method provides a quick one-pot borylation/Suzuki reaction protocol that we applied to the synthesis of various bi- or poly-aryl scaffolds, including a variety of aryl and heteroaryl ring systems and the core frameworks of kinase inhibitors vemurafenib and GDC-0879

Black holes admitting a Freudenthal dual

The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the requirement that \tilde{x} be integer restricts us to the subset of black holes for which Delta(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a perfect cube, for which A**=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde

A unified approach on Springer fibers in the hook, two-row and two-column cases

We consider the Springer fiber over a nilpotent endomorphism. Fix a Jordan basis and consider the standard torus relative to this. We deal with the problem to describe the flags fixed by the torus which belong to a given component of the Springer fiber. We solve the problem in the hook, two-row and two-column cases. We provide two main characterizations which are common to the three cases, and which involve dominance relations between Young diagrams and combinatorial algorithms. Then, for these three cases, we deduce topological properties of the components and their intersections.Comment: 42 page

Arbitrarily large families of spaces of the same volume

In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these lattices with the help of Bruhat-Tits theory, using Prasad's volume formula to control their covolumes.Comment: 9 pages. Syntax corrected; one reference adde

Site Selective Antibody-Oligonucleotide Conjugation via Microbial Transglutaminase.

Nucleic Acid Therapeutics (NATs), including siRNAs and AntiSense Oligonucleotides (ASOs), have great potential to drug the undruggable genome. Targeting siRNAs and ASOs to specific cell types of interest has driven dramatic improvement in efficacy and reduction in toxicity. Indeed, conjugation of tris-GalNAc to siRNAs and ASOs has shown clinical efficacy in targeting diseases driven by liver hepatocytes. However, targeting non-hepatic diseases with oligonucleotide therapeutics has remained problematic for several reasons, including targeting specific cell types and endosomal escape. Monoclonal antibody (mAb) targeting of siRNAs and ASOs has the potential to deliver these drugs to a variety of specific cell and tissue types. However, most conjugation strategies rely on random chemical conjugation through lysine or cysteine residues resulting in conjugate heterogeneity and a distribution of Drug:Antibody Ratios (DAR). To produce homogeneous DAR-2 conjugates with two siRNAs per mAb, we developed a novel two-step conjugation procedure involving microbial transglutaminase (MTGase) tagging of the antibody C-terminus with an azide-functionalized linker peptide that can be subsequently conjugated to dibenzylcyclooctyne (DBCO) bearing oligonucleotides through azide-alkyne cycloaddition. Antibody-siRNA (and ASO) conjugates (ARCs) produced using this strategy are soluble, chemically defined targeted oligonucleotide therapeutics that have the potential to greatly increase the number of targetable cell types

Systematic Review – Final: Have arid land springs restoration projects been effective in restoring hydrology, geomorphology, and invertebrates and plant species composition comparable to natural springs with minimal anthropogenic disturbance?

The aim of this review is to examine the effectiveness of springs restoration projects in the southwestern United States in restoring hydrology, geomorphology, and plant and invertebrates species composition to condiitions comparable with natural springs with minimal anthropogenic disturbances