Reversed Radial SLE and the Brownian Loop Measure

The Brownian loop measure is a conformally invariant measure on loops in the plane that arises when studying the Schramm–Loewner evolution (SLE). When an SLE curve in a domain evolves from an interior point, it is natural to consider the loops that hit the curve and leave the domain, but their measure is infinite. We show that there is a related normalized quantity that is finite and invariant under Möbius transformations of the plane. We estimate this quantity when the curve is small and the domain simply connected. We then use this estimate to prove a formula for the Radon–Nikodym derivative of reversed radial SLE with respect to whole-plane SLE.     

Quantum order by disorder in frustrated diamond lattice antiferromagnets

We present a quantum theory of frustrated diamond lattice antiferromagnets. Considering quantum fluctuations as the predominant mechanism relieving spin frustration, we find a rich phase diagram comprising of six phases with coplanar spiral ordering in addition to the Néel phase. By computing the specific heat of these ordered phases, we obtain a remarkable agreement between (k, k, 0) spiral ordering and the experimental specific heat data for the diamond lattice spinel compounds MnSc2S4, Co3O4, and CoRh2O4, i.e., specific heat data is a strong evidence for (k, k, 0) spiral ordering in all of these materials. This prediction can be tested in future neutron scattering experiments on Co3O4 and CoRh2O4, and is consistent with existing neutron scattering data on MnSc2S4. Based on this agreement, we infer a monotonically increasing relationship between frustration and the strength of quantum fluctuations.     

Random walk loop soup

The Brownian loop soup introduced by Lawler and Werner (2004) is a Poissonian realization from a -finite measure on unrooted loops. This measure satisfies both conformal invariance and a restriction property. In this paper, we define a random walk loop soup and show that it converges to the Brownian loop soup. In fact, we give a strong approximation result making use of the strong approximation result of Komlós, Major, and Tusnády. To make the paper self-contained, we include a proof of the approximation result that we need.

     

Spectroscopic imaging STM studies of broken electronic symmetries in underdoped cuprates

We use spectroscopic imaging scanning tunneling microscopy (SI-STM) to visualize the spatial symmetries of the electronic states that occur at the pseudogap energy scale in underdoped cuprates. We find evidence for the local intra-unit-cell electronic nematicity—by which we mean the disordered breaking of C_4v symmetry within each CuO₂ unit cell [1]. We also find that the coexisting incommensurate (smectic) electronic modulations couple to the intra-unit-cell nematicity through their 2π$2\mathrm{\pi }$ topological defects [2].     

Nanosecond time-resolved EPR spectroscopy: time profiles via integration of free induction decays

Tune dependence of transient magnetization can be sampled by using a single microwave pulse and observing the intensity of free induction decay (FID). The FID method is illustrated and compared to the two-pulse electron spin echo (ESE) technique. The time pronies of the hydrogen atoms created by electron beam pulse radiolysis or acidic water are used to illustrate the advantages of the FID method. Superior signal to noise and better effective response time of the F ID method makes it an ideal tool for the study of fast reacting radicals in liquids.     

On the critical exponent for random walk intersections

The exponent _d for the probability of nonintersection of two random walks starting at the same point is considered. It is proved that 1/2<₂3/4. Monte Carlo simulations are done to suggest ₂=0.61 and ₃0.29.     

Regio- and diastereoselective rhodium-catalyzed allylic substitution with acyclic alpha-alkoxy-substituted copper(I) enolates: stereodivergent approach to 2,3,6-trisubstituted dihydropyrans

The regio- and diastereoselective transition metal-catalyzed allylic alkylation using alpha-heteroatom-substituted ketones and carboxylic acid derivatives represents a challenging and important synthetic transformation. We have developed a regio- and diastereoselective rhodium-catalyzed allylic alkylation reaction utilizing the copper(I) enolates derived from alkyl protected acyclic alpha-alkoxy aryl ketones. This study suggests that the ability to form a chelated enolate intermediate is crucial for obtaining high diastereoselectivity, whereas excellent regioselectivity is obtained regardless of the substituent. Hence, the excellent selectivity coupled with the synthetic utility of alpha-alkoxy aryl ketone enolates makes this an important new method for the construction of acyclic adjacent ternary stereogenic centers. Finally, the synthetic utility of this protocol was highlighted through the conversion of the aryl ketone to the ester and the development of a stereodivergent approach to 2,3,6-trisubstituted dihydropyrans relevant to target-directed synthesis.     

Synthesis of N3- and 2-NH2-substituted 6,7-diphenylpterins and their use as intermediates for the preparation of oligonucleotide conjugates designed to target photooxidative damage on single-stranded DNA representing the bcr-abl chimeric gene

Two 17-mer oligodeoxynucleotide-5'-linked-(6,7-diphenylpterin) conjugates, 2 and 3, were prepared as photosensitisers for targeting photooxidative damage to a 34-mer DNA oligodeoxynucleotide (ODN) fragment 1 representing the chimeric bcr-abl gene that is implicated in the pathogenesis of chronic myeloid leukaemia (CML). The base sequence in the 17-mer was 3'G G T A G T T A T T C C T T C T T5'. In the first of these ODN conjugates (2) the pterin was attached at its N3 atom, via a -(CH2)3OPO(OH)- linker, to the 5'-OH group of the ODN. Conjugate 2 was prepared from 2-amino-3-(3-hydroxypropyl)-6,7-diphenyl-4(3H)-pteridinone 10, using phosphoramidite methodology. Starting material 10 was prepared from 5-amino-7-methylthiofurazano[3,4-d]pyrimidine 4 via an unusual highly resonance stabilised cation 8, incorporating the rare 2H,6H-pyrimido[6,1-b][1,3]oxazine ring system. In the characterisation of 10 two pteridine phosphazenes, 15 and 29, were obtained, as well as new products containing two uncommon tricyclic ring systems, namely pyrimido[2,1-b]pteridine (20 and 24) and pyrimido[1,2-c]pteridine (27). In the second ODN conjugate the linker was -(CH2)5CONH(CH2)6OPO(OH)- and was attached to the 2-amino group of the pterin. In the preparation of 3, the N-hydroxysuccinimide ester 37 of 2-(5-carboxypentylamino)-6,7-diphenyl-4(3H)-pteridinone was condensed with the hexylamino-modified 17-mer. Excitation of 36 with near UV light in the presence of the single-stranded target 34-mer, 5'T G A C C A T C A A T A A G14 G A A G18 A A G21 C C C T T C A G C G G C C3' 1 caused oxidative damage at guanine bases, leading to alkali-labile sites which were monitored by polyacrylamide gel electrophoresis. Cleavage was observed at all guanine sites with a marked preference for cleavage at G14. In contrast, excitation of ODN-pteridine conjugate 2 in the presence of 1 caused oxidation of the latter predominantly at G18, with a smaller extent of cleavage at G15 and G14 (in the double-stranded portion) and G21. These results contrast with our previous observation of specific cleavage at G21 with ruthenium polypyridyl sensitisers, and suggest that a different mechanism, probably one involving Type 1 photochemical electron transfer, is operative. Much lower yields were found with the ODN-pteridine conjugate 3, perhaps as a consequence of the longer linker between the ODN and the pteridine in this case.     

Universality for conformally invariant intersection exponents

We construct a class of conformally invariant measures on sets (or paths) and we study the critical exponents called intersection exponents associated to these measures. We show that these exponents exist and that they correspond to intersection exponents between planar Brownian motions. More precisely, using the definitions and results of our paper [27], we show that any set defined under such a conformal invariant measure behaves exactly as a pack (containing maybe a non-integer number) of Brownian motions as far as all intersection exponents are concerned. We show how conjectures about exponents for two-dimensional self-avoiding walks and critical percolation clusters can be reinterpreted in terms of conjectures on Brownian exponents. Received June 4, 1999 / final version received June 20, 2000?Published online September 7, 2000