The Weyl bound for triple product L-functions

Let $\pi_1, \pi_2, \pi_3$ be three cuspidal automorphic representations for the group ${\rm SL}(2, \Bbb{Z})$, where $\pi_1$ and $\pi_2$ are fixed and $\pi_3$ has large conductor. We prove a subconvex bound for $L(1/2, \pi_1 \otimes \pi_2 \otimes \pi_3)$ of Weyl-type quality. Allowing $\pi_3$ to be an Eisenstein series we also obtain a Weyl-type subconvex bound for $L(1/2 + it, \pi_1 \otimes \pi_2)$.Comment: 37 page

Carbon taxes and the composition of new passenger car sales in Europe

This paper examines the effectiveness of implementing carbon taxes to reduce carbon dioxide emissions from transport. Using the system Generalized Method of Moments estimator, we utilize cross-country analysis for the first time to study the impact of carbon taxes on the composition of petrol versus diesel passenger cars sold in 17 countries over the period 2013-2017. The results suggest that increasing carbon taxes affects consumer behavior, causing a significant shift from petrol to diesel fuel vehicles, controlling for factors such as the price of passenger cars, fuel price, interest rates, income level, population density, inflation, and vehicle stock. © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).Grant Agency Academia aurea (GA AA) [GA/16/2019]; Internal Grant Agency of the Tomas Bata University in Zlin [IGA/FaME/2020/001

White-tailed Deer and Cattle Interactions in Southeastern Oklahoma

Wildlife Ecolog

Psychopathy, Empathy, and Perspective -Taking Ability in a Community Sample: Implications for the Successful Psychopathy Concept

This study examined the relationship between psychopathy and two components of empathy including a cognitive component (e.g., perspective-taking ability) and an affective component (e.g., compassion) in a community sample. The Psychopathic Personality Inventory Short Form was used to assess psychopathy and several psychological measures were used to test empathy including the Interpersonal Reactivity Index, the Diagnostic Analysis of Nonverbal Accuracy-2, and the Test of Self Conscious Affect -3. Across instruments, psychopathy (as a unitary construct) appeared to be negligibly correlated with perspective-taking scales and negatively correlated with the affective components of empathy. Findings indicated that the emotional deficits were noted most prominently for the behavioral component of psychopathy. Results also showed that higher psychopathy scores in community participants were linked to higher levels of antisocial conduct

The impact of confounding on the associations of different adiposity measures with the incidence of cardiovascular disease: a cohort study of 296 535 adults of white European descent

Aims: The data regarding the associations of body mass index (BMI) with cardiovascular (CVD) risk, especially for those at the low categories of BMI, are conflicting. The aim of our study was to examine the associations of body composition (assessed by five different measures) with incident CVD outcomes in healthy individuals. Methods and results: A total of 296 535 participants (57.8% women) of white European descent without CVD at baseline from the UK biobank were included. Exposures were five different measures of adiposity. Fatal and non-fatal CVD events were the primary outcome. Low BMI (≤18.5 kg m−2) was associated with higher incidence of CVD and the lowest CVD risk was exhibited at BMI of 22–23 kg m−2 beyond, which the risk of CVD increased. This J-shaped association attenuated substantially in subgroup analyses, when we excluded participants with comorbidities. In contrast, the associations for the remaining adiposity measures were more linear; 1 SD increase in waist circumference was associated with a hazard ratio of 1.16 [95% confidence interval (CI) 1.13–1.19] for women and 1.10 (95% CI 1.08–1.13) for men with similar magnitude of associations for 1 SD increase in waist-to-hip ratio, waist-to-height ratio, and percentage body fat mass. Conclusion: Increasing adiposity has a detrimental association with CVD health in middle-aged men and women. The association of BMI with CVD appears more susceptible to confounding due to pre-existing comorbidities when compared with other adiposity measures. Any public misconception of a potential ‘protective’ effect of fat on CVD risk should be challenged

Adventures in Supersingularland

In this paper, we study isogeny graphs of supersingular elliptic curves. Supersingular isogeny graphs were introduced as a hard problem into cryptography by Charles, Goren, and Lauter for the construction of cryptographic hash functions [CGL06]. These are large expander graphs, and the hard problem is to find an efficient algorithm for routing, or path-finding, between two vertices of the graph. We consider four aspects of supersingular isogeny graphs, study each thoroughly and, where appropriate, discuss how they relate to one another. First, we consider two related graphs that help us understand the structure: the `spine' $\mathcal{S}$, which is the subgraph of $\mathcal{G}_\ell(\overline{\mathbb{F}_p})$ given by the $j$-invariants in $\mathbb{F}_p$, and the graph $\mathcal{G}_\ell(\mathbb{F}_p)$, in which both curves and isogenies must be defined over $\mathbb{F}_p$. We show how to pass from the latter to the former. The graph $\mathcal{S}$ is relevant for cryptanalysis because routing between vertices in $\mathbb{F}_p$ is easier than in the full isogeny graph. The $\mathbb{F}_p$-vertices are typically assumed to be randomly distributed in the graph, which is far from true. We provide an analysis of the distances of connected components of $\mathcal{S}$. Next, we study the involution on $\mathcal{G}_\ell(\overline{\mathbb{F}_p})$ that is given by the Frobenius of $\mathbb{F}_p$ and give heuristics on how often shortest paths between two conjugate $j$-invariants are preserved by this involution (mirror paths). We also study the related question of what proportion of conjugate $j$-invariants are $\ell$-isogenous for $\ell = 2,3$. We conclude with experimental data on the diameters of supersingular isogeny graphs when $\ell = 2$ and compare this with previous results on diameters of LPS graphs and random Ramanujan graphs.Comment: 46 pages. Comments welcom

Quantum fluctuations as deviation from classical dynamics of ensemble of trajectories parameterized by unbiased hidden random variable

A quantization method based on replacement of c-number by c-number parameterized by an unbiased hidden random variable is developed. In contrast to canonical quantization, the replacement has straightforward physical interpretation as statistical modification of classical dynamics of ensemble of trajectories, and implies a unique operator ordering. We then apply the method to develop quantum measurement without wave function collapse \'a la pilot-wave theory.Comment: 14 pages, accepted in Physica