No-splitting property and boundaries of random groups

We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.Comment: 20 page

Property (T)(T) for noncommutative universal lattices

We establish a new spectral criterion for Kazhdan's property $(T)$ which is applicable to a large class of discrete groups defined by generators and relations. As the main application, we prove property $(T)$ for the groups $EL_n(R)$, where $n\geq 3$ and $R$ is an arbitrary finitely generated associative ring. We also strengthen some of the results on property $(T)$ for Kac-Moody groups from a paper of Dymara and Januszkiewicz (Invent. Math 150 (2002)).Comment: 47 pages; final versio

Isoperimetric Inequalities in Simplicial Complexes

In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high dimensional Laplacian defined by Eckmann. In particular, we present a Cheeger-type inequality, and a high-dimensional Expander Mixing Lemma. As a corollary, using the work of Pach, we obtain a connection between spectral properties of complexes and Gromov's notion of geometric overlap. Using the work of Gunder and Wagner, we give an estimate for the combinatorial expansion and geometric overlap of random Linial-Meshulam complexes

Finite covers of random 3-manifolds

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this model of random 3-manifold, we are able to compute the probabilities that the resulting manifolds have finite covers of particular kinds. Our results contrast with the analogous probabilities for groups coming from random balanced presentations, giving quantitative theorems to the effect that 3-manifold groups have many more finite quotients than random groups. The next natural question is whether these covers have positive betti number. For abelian covers of a fixed type over 3-manifolds of Heegaard genus 2, we show that the probability of positive betti number is 0. In fact, many of these questions boil down to questions about the mapping class group. We are lead to consider the action of mapping class group of a surface S on the set of quotients pi_1(S) -> Q. If Q is a simple group, we show that if the genus of S is large, then this action is very mixing. In particular, the action factors through the alternating group of each orbit. This is analogous to Goldman's theorem that the action of the mapping class group on the SU(2) character variety is ergodic.Comment: 60 pages; v2: minor changes. v3: minor changes; final versio

A simplified formula to calculate fractional flow reserve in sequential lesions circumventing the measurement of coronary wedge pressure: The APIS-S pilot study

Background: A simplified formula to calculate the predicted fractional flow reserve (FFR) in sequen­tial coronary stenosis without balloon inflation is hereby proposed. Methods: In patients with an indication for FFR and sequential coronary stenosis, FFR was recorded distally and between the lesions. The predicted FFR for each stenosis was calculated with a novel formu­la. While treating one of the lesions, wedge pressure was measured during balloon inflation to calculate Pijls’ formula. FFR of the remaining lesion was finally recorded (measured FFR). Results: Forty patients were enrolled in the study, 4 (10.0%) had a distal FFR > 0.80 and were excluded from the main analysis. In the remaining 36 patients, the novel formula and Pijls’ formula showed virtually absolute agreement (ICCa 0.999, R2 = 0.997 for the proximal lesion, R2 = 0.999 for the distal lesion, kappa 1.000, Se 100%, Sp 100%). The agreement between predicted and measured FFR was good (ICCa 0.820; 0.640–0.909, R2 = 0.717, intercept = 0.05, slope = 0.92, kappa 0.748, Se 75%, Sp 96%). In 19 (47.5%) cases the use of the formula enabled the operator to freely decide which lesion should be treated first, an option not available if the percutaneous coronary intervention (PCI) were guided by the largest pressure drop across each lesion. Conclusions: The predicted FFR for each lesion in sequential coronary stenosis can be accurately calculated by a simplified formula circumventing the need for balloon inflation. This approach provides the operator upfront, with detailed information on physiology, thus having a potentially high impact on the corresponding PCI strategy

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Addressing climate change with behavioral science: a global intervention tournament in 63 countries

Effectively reducing climate change requires marked, global behavior change. However, it is unclear which strategies are most likely to motivate people to change their climate beliefs and behaviors. Here, we tested 11 expert-crowdsourced interventions on four climate mitigation outcomes: beliefs, policy support, information sharing intention, and an effortful tree-planting behavioral task. Across 59,440 participants from 63 countries, the interventions’ effectiveness was small, largely limited to nonclimate skeptics, and differed across outcomes: Beliefs were strengthened mostly by decreasing psychological distance (by 2.3%), policy support by writing a letter to a future-generation member (2.6%), information sharing by negative emotion induction (12.1%), and no intervention increased the more effortful behavior—several interventions even reduced tree planting. Last, the effects of each intervention differed depending on people’s initial climate beliefs. These findings suggest that the impact of behavioral climate interventions varies across audiences and target behaviors