Critical Gaussian multiplicative chaos: Convergence of the derivative martingale

In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching random walks, converges almost surely (in all dimensions) to a random measure with full support. We also show that the limiting measure has no atom. In connection with the derivative martingale, we write explicit conjectures about the glassy phase of log-correlated Gaussian potentials and the relation with the asymptotic expansion of the maximum of log-correlated Gaussian random variables.Comment: Published in at http://dx.doi.org/10.1214/13-AOP890 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Log-correlated Gaussian fields: an overview

We survey the properties of the log-correlated Gaussian field (LGF), which is a centered Gaussian random distribution (generalized function) $h$ on $\mathbb R^d$, defined up to a global additive constant. Its law is determined by the covariance formula $$\mathrm{Cov}\bigl[ (h, \phi_1), (h, \phi_2) \bigr] = \int_{\mathbb R^d \times \mathbb R^d} -\log|y-z| \phi_1(y) \phi_2(z)dydz$$ which holds for mean-zero test functions $\phi_1, \phi_2$. The LGF belongs to the larger family of fractional Gaussian fields obtained by applying fractional powers of the Laplacian to a white noise $W$ on $\mathbb R^d$. It takes the form $h = (-\Delta)^{-d/4} W$. By comparison, the Gaussian free field (GFF) takes the form $(-\Delta)^{-1/2} W$ in any dimension. The LGFs with $d \in \{2,1\}$ coincide with the 2D GFF and its restriction to a line. These objects arise in the study of conformal field theory and SLE, random surfaces, random matrices, Liouville quantum gravity, and (when $d=1$) finance. Higher dimensional LGFs appear in models of turbulence and early-universe cosmology. LGFs are closely related to cascade models and Gaussian branching random walks. We review LGF approximation schemes, restriction properties, Markov properties, conformal symmetries, and multiplicative chaos applications.Comment: 24 pages, 2 figure

Tatian and Basil: Differing Views Regarding the Pagan Educational System of Antiquity

Advanced education for Christians of antiquity was only available through schools which used classical Greek methodology. This included literature, poetry, and philosophy closely tied to polytheistic and pagan traditions. Christian families and leaders at that time had to consider the spiritual implications of participating in such a system. This article contrasts the opinion of Tatian with that of Basil of Caesarea regarding Christian participation in pagan education. Basil and Tatian had similar ascetic views, yet they differed on this issue. Tatian believed Christians should not take part in pagan education. Basil believed that Christians could benefit spiritually from this education if they experienced it selectively and wisely. I conclude that Basil’s view is the wiser choice

A Race of Headsmen: The Life and Mind of a Dynasty of French Executioners, 1688-1847

This thesis examines the memoirs, letters, public records, and legal records of the Sanson dynasty of executioners to understand the patterns of thought and behavior of the early modern headsman. While recent historians have acknowledged the social and political pressures of the profession, few have attempted to catalog the words and actions of the executioners themselves. The Sanson family is unique in their longevity and historical role in the French Revolution. Furthermore, their memoirs provide in their own words a direct understanding of their state of mind. With recent scholarship dedicated to the analysis of the “Age of Spectacular Punishment,” this thesis seeks to synthesize current historical interpretation with a microhistory of a single executioner family. This paper charts the rise and fall of the Sanson dynasty over seven generations from 1688-1857. While the Paris lineage is well documented, this paper also examines the executioner lines in Abbeville, Reims, and Rouen. It highlights the patterns of thought and behaviors caused by factors unique to the profession. The Sansons combated this trauma by targeting the social and professional factors that caused them. Members of the family worked to reform the penal code to restore their citizenship, pushed for the adoption of the guillotine to ease their workload and expenses, and wrote editorials to turn public perception of their profession from revulsion to respect. In highlighting the plight of the French headsman, this paper underscores the singular difficulties of a profession hitherto misunderstood by contemporary society

Strategies for Successful Long-Distance Mentoring

Mentorship offers benefits to both the mentee and mentor in terms of professional development and productivity. It can take many forms and is not limited to mentee-mentor pairs that are employed at the same institution. Mentoring relationships that span institutions offer an avenue for expanding one’s professional network beyond the local environment. We refer to this type of mentorship as “long-distance mentoring.” We offer four critical strategies and reflections for successful long-distance mentoring based on our experience in the AAHB Research Scholars Mentorship Program

Low-speed wind tunnel investigation of the static stability and control characteristics of an advanced turboprop configuration with the propellers placed over the tail

An exploratory wind tunnel investigation was performed in the 30 x 60 foot wind tunnel to determine the low speed static stability and control characteristics into the deep stall regime of an advanced turboprop aircraft with the propellers located over the horizontal tail. By this arrangement, the horizontal tail could potentially provide acoustic shielding to reduce the high community noise caused by the propeller blades. The current configuration was a generic turboprop model equipped with 1 foot diameter single rotating eight bladed propellers that were designed for efficient cruise operation at a Mach number of 0.8. The data presented is static force data. The effects of power on the configuration characteristics were generally favorable. An arrangement with the propellers rotating with the outboard blades moving down was found to have significantly higher installed thrust than an arrangement with the propellers rotating with the inboard blades moving down. The primary unfavorable effect was a large pitch trim change which occurred with power, but the trim change could be minimized with a proper configuration design

Intersectionality, Measurement, Methods, and Translation: Reflections on the 2023 AAHB Conference

Intersectionality is a critical yet understudied and often misused concept in health behavior research. To address this, the American Academy of Health Behavior organized its 2023 annual scientific conference held on March 12-15th, 2023 around issues of intersectionality conceptualization, measurement, and methods (San Francisco, California). The conference, titled “The science of identities: Measurement & methods for translational health behavior research,” brought together a diverse group of nearly 170 health behavior researchers from across the United States to highlight current research and challenges facing intersectionality. The conference included two invited keynotes and eight symposium presentations. Here, we highlight some of the research presented and key themes that emerged across presentations

Mi Cuerpo, Nuestra Responsabilidad: Using Photovoice to describe the assets and barriers to sexual and reproductive health among Latinos in North Carolina

Latinos in North Carolina experience disparities in sexual and reproductive health. To identify and explore assets for and barriers to sexual and reproductive health in the Latino community, an academic-community partnership engaged community health workers (CHW) in Photovoice, a participatory qualitative research methodology. Five sessions were completed in which CHW agreed on photo assignments and discussed the photos. Themes included the role of men, cultural taboos, and the effect of undocumented immigrant status on access to resources. Findings were presented at a community forum. Building on the strengths of CHW to reduce barriers to sexual and reproductive health is a viable strategy to address disparities

Ultra-low-cost logging anemometer for wind power generation feasibility surveys

We describe the design and implementation of a cup anemometer capable of logging average wind speed, maximum wind speed and seconds with wind above a criterion speed, on individual weeks. The instrument will operate for at least 54 weeks on two AA dry cells. The intention is that this instrument be deployed to ascertain whether it would be economical to install a wind generator, at a fraction of the cost of a multipurpose weather data logging station. It is designed around a $2 microcontroller that provides non-volatile memory. Provision has been made for using either a magnetic reed switch or the motor from a discarded hard disk drive to sense rotation. The latter enables the use of an otherwise worthless bearing and drive assembly to provide an especially frugal solution