Geodesics in the Brownian map: Strong confluence and geometric structure

We study geodesics in the Brownian map $(\mathcal{S},d,\nu)$, the random metric measure space which arises as the Gromov-Hausdorff scaling limit of uniformly random planar maps. Our results apply to all geodesics including those between exceptional points. First, we prove a strong and quantitative form of the confluence of geodesics phenomenon which states that any pair of geodesics which are sufficiently close in the Hausdorff distance must coincide with each other except near their endpoints. Then, we show that the intersection of any two geodesics minus their endpoints is connected, the number of geodesics which emanate from a single point and are disjoint except at their starting point is at most $5$, and the maximal number of geodesics which connect any pair of points is $9$. For each $1\le k \le 9$, we obtain the Hausdorff dimension of the pairs of points connected by exactly $k$ geodesics. For $k=7,8,9$, such pairs have dimension zero and are countably infinite. Further, we classify the (finite number of) possible configurations of geodesics between any pair of points in $\mathcal{S}$, up to homeomorphism, and give a dimension upper bound for the set of endpoints in each case. Finally, we show that every geodesic can be approximated arbitrarily well and in a strong sense by a geodesic connecting $\nu$-typical points. In particular, this gives an affirmative answer to a conjecture of Angel, Kolesnik, and Miermont that the geodesic frame of $\mathcal{S}$, the union of all of the geodesics in $\mathcal{S}$ minus their endpoints, has dimension one, the dimension of a single geodesic.Comment: 86 pages, 31 figures. We have added a matching lower bound for 5 geodesics, and showed that the set of points connected by 7,8 geodesics is countably infinit

Using Acoustic Emission to Quantify Freeze–Thaw Damage of Mortar Saturated with NaCl Solutions

Mortar samples were saturated with NaCl solutions of various concentrations and subjected to freeze– thaw cycles. Passive and active acoustic emission (AE) testing was conducted. The freezing temperature of the NaCl solutions in mortar corresponded with the sudden observation of passive AE events. The acoustic energy and damage parameter were calculated to evaluate the extent of freeze–thaw damage. The influence of the NaCl solution concentration and whether the solution freezes on freeze–thaw damage are discussed

Who Survives on Death Row? An Individual and Contextual Analysis

What are the relationships between death row offender attributes, social arrangements, and executions? Partly because public officials control executions, theorists view this sanction as intrinsically political. Although the literature has focused on offender attributes that lead to death sentences, the post-sentencing stage is at least as important. States differ sharply in their willingness to execute and less than 10 percent of those given a death sentence are executed. To correct the resulting problems with censored data, this study uses a discrete-time event history analysis to detect the individual and state-level contextual factors that shape execution probabilities. The findings show that minority death row inmates convicted of killing whites face higher execution probabilities than other capital offenders. Theoretically relevant contextual factors with explanatory power include minority presence in nonlinear form, political ideology, and votes for Republican presidential candidates. Inasmuch as there is little or no systematic research on the individual and contextual factors that influence execution probabilities, these findings fill important gaps in the literature

The geodesics in Liouville quantum gravity are not Schramm–Loewner evolutions

Funder: University of CambridgeAbstract: We prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necessarily singular with respect to the law of any type of SLEκ. These hypotheses are satisfied by the LQG metric for γ=8/3 constructed by the first author and Sheffield, and subsequent work by Gwynne and the first author has shown that there is a unique metric which satisfies these hypotheses for each γ∈(0, 2). As a consequence of our analysis, we also establish certain regularity properties of LQG geodesics which imply, among other things, that they are conformally removable

The geodesics in Liouville quantum gravity are not Schramm–Loewner evolutions

Funder: University of CambridgeAbstract: We prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necessarily singular with respect to the law of any type of SLEκ. These hypotheses are satisfied by the LQG metric for γ=8/3 constructed by the first author and Sheffield, and subsequent work by Gwynne and the first author has shown that there is a unique metric which satisfies these hypotheses for each γ∈(0, 2). As a consequence of our analysis, we also establish certain regularity properties of LQG geodesics which imply, among other things, that they are conformally removable

Two potential hookworm DAF-16 target genes, SNR-3 and LPP-1: gene structure, expression profile, and implications of a cis-regulatory element in the regulation of gene expression

Background Hookworms infect nearly 700 million people, causing anemia and developmental stunting in heavy infections. Little is known about the genomic structure or gene regulation in hookworms, although recent publication of draft genome assemblies has allowed the first investigations of these topics to be undertaken. The transcription factor DAF-16 mediates multiple developmental pathways in the free living nematode Caenorhabditis elegans, and is involved in the recovery from the developmentally arrested L3 in hookworms. Identification of downstream targets of DAF-16 will provide a better understanding of the molecular mechanism of hookworm infection. Methods Genomic Fragment 2.23 containing a DAF-16 binding element (DBE) was used to identify overlapping complementary expressed sequence tags (ESTs). These sequences were used to search a draft assembly of the Ancylostoma caninum genome, and identified two neighboring genes, snr-3 and lpp-1, in a tail-to-tail orientation. Expression patterns of both genes during parasitic development were determined by qRT-PCR. DAF-16 dependent cis-regulatory activity of fragment 2.23 was investigated using an in vitro reporter system. Results The snr-3 gene spans approximately 5.6 kb in the genome and contains 3 exons and 2 introns, and contains the DBE in its 3′ untranslated region. Downstream from snr-3 in a tail-to-tail arrangement is the gene lpp-1. The lpp-1 gene spans more than 6 kb and contains 10 exons and 9 introns. The A. caninum genome contains 2 apparent splice variants, but there are 7 splice variants in the A. ceylanicum genome. While the gene order is similar, the gene structures of the hookworm genes differ from their C. elegans orthologs. Both genes show peak expression in the late L4 stage. Using a cell culture based expression system, fragment 2.23 was found to have both DAF-16-dependent promoter and enhancer activity that required an intact DBE. Conclusions Two putative DAF-16 targets were identified by genome wide screening for DAF-16 binding elements. Aca-snr-3 encodes a core small nuclear ribonucleoprotein, and Aca-lpp-1 encodes a lipid phosphate phosphohydrolase. Expression of both genes peaked at the late L4 stage, suggesting a role in L4 development. The 3′-terminal genomic fragment of the snr-3 gene displayed Ac-DAF-16-dependent cis-regulatory activity

Mechanism of action of VP1-001 in cryAB(R120G)-associated and age-related cataracts

PurposeWe previously identified an oxysterol, VP1-001 (also known as compound 29), that partially restores the transparency of lenses with cataracts. To understand the mechanism of VP1-001, we tested the ability of its enantiomer, ent-VP1-001, to bind and stabilize αB-crystallin (cryAB) in vitro and to produce a similar therapeutic effect in cryAB(R120G) mutant and aged wild-type mice with cataracts. VP1-001 and ent-VP1-001 have identical physicochemical properties. These experiments are designed to critically evaluate whether stereoselective binding to cryAB is required for activity.MethodsWe compared the binding of VP1-001 and ent-VP1-001 to cryAB using in silico docking, differential scanning fluorimetry (DSF), and microscale thermophoresis (MST). Compounds were delivered by six topical administrations to mouse eyes over 2 weeks, and the effects on cataracts and lens refractive measures in vivo were examined. Additionally, lens epithelial and fiber cell morphologies were assessed via transmission electron microscopy.ResultsDocking studies suggested greater binding of VP1-001 into a deep groove in the cryAB dimer compared with ent-VP1-001. Consistent with this prediction, DSF and MST experiments showed that VP1-001 bound cryAB, whereas ent-VP1-001 did not. Accordingly, topical treatment of lenses with ent-VP1-001 had no effect, whereas VP1-001 produced a statistically significant improvement in lens clarity and favorable changes in lens morphology.ConclusionsThe ability of VP1-001 to bind native cryAB dimers is important for its ability to reverse lens opacity in mouse models of cataracts

Fully-inverted piezoresponse hysteresis loops mediated by charge injection in 0.29Pb(In1/2Nb1/2)O3–0.44Pb(Mg1/3Nb2/3)O3–0.27PbTiO3 single crystals

The domain structure and local switching behavior of ternary relaxor (001) 0.29Pb(In1/2Nb1/2)O3–0.44Pb(Mg1/3Nb2/3)O3–0.27PbTiO3single crystals are studied using piezoresponse force microscopy. The as-grown crystals exhibit a labyrinthine domain pattern similar to other relaxor-based ferroelectrics. Abnormally switched domains are observed for both positive and negative tip-voltages, with sign-dependent thresholds and growth rates on the poled crystals. Further piezoresponse hysteresis loop measurements show that fully inverted loops can be observed under high switching voltages, mediated by injected charge fields. The dynamic behavior of the observed abnormal switching is qualitatively analyzed and the underlying mechanisms discussed.Q.L., Y.L., and R.L.W. acknowledge financial support from the Australian Research Council ARC in the form of an ARC Discovery Grant No. DP0877069