On the dimension of a certain measure in the plane

We study the Hausdorff dimension of a measure related to a positive weak solution of a certain partial differential equation in a simply connected domain in the plane. Our work generalizes work of Lewis and coauthors when the measure is $p$ harmonic and also for $p=2$, the well known theorem of Makarov regarding the Hausdorff dimension of harmonic measure relative to a point in a simply connected domain.Comment: 26 page

Finance and macroeconomic volatility

Countries with more developed financial sectors, experience fewer fluctuations in real per capita output, consumption, and investment growth. But the manner in which the financial sector develops matters. The relative importance of banks in the financial system is important in explaining consumption, and investment volatility. The proportion of credit provided to the private sector, best explains volatility of consumption, and output. The authors generate their main results using fixed-effects estimates with panel data from seventy countries for the years 1956-98. Their general findings suggest that the risk management, and information processing provided by banks, maybe especially important in reducing consumption, and investment volatility. The simple availability of credit to the private sector, probably helps smooth consumption, and GDP.Economic Theory&Research,Inequality,Environmental Economics&Policies,Achieving Shared Growth,Financial Intermediation

On the probabilistic min spanning tree Problem

We study a probabilistic optimization model for min spanning tree, where any vertex vi of the input-graph G(V,E) has some presence probability pi in the final instance G′ ⊂ G that will effectively be optimized. Suppose that when this “real” instance G′ becomes known, a spanning tree T, called anticipatory or a priori spanning tree, has already been computed in G and one can run a quick algorithm (quicker than one that recomputes from scratch), called modification strategy, that modifies the anticipatory tree T in order to fit G ′. The goal is to compute an anticipatory spanning tree of G such that, its modification for any G ′ ⊆ G is optimal for G ′. This is what we call probabilistic min spanning tree problem. In this paper we study complexity and approximation of probabilistic min spanning tree in complete graphs under two distinct modification strategies leading to different complexity results for the problem. For the first of the strategies developed, we also study two natural subproblems of probabilistic min spanning tree, namely, the probabilistic metric min spanning tree and the probabilistic min spanning tree 1,2 that deal with metric complete graphs and complete graphs with edge-weights either 1, or 2, respectively

Coronavirus pandemic, remote learning and emerging education inequalities

Recent studies predict that the school closures and distance learning of the 2020 pandemic will lead to lower average education levels, but they may also result into greater and new education inequalities. Using PISA 2018 data from France, Germany, Italy, Spain and the United Kingdom, we find that, even before the pandemic, students lacking the resources needed to learn remotely – ICT resources at home, at school or a quiet place to study – experience strong and significant cognitive gaps with respect to their peers that, in mathematics, range from 70 percent of a school year in the United Kingdom, Germany and France to 25 percent in Spain. Gaps in reading are similar. With school closures and remote learning, these cognitive losses are predicted to increase. We find similar results by considering days of absence from school. In the longer run, students in Spain, Germany and Italy who cannot learn remotely are more likely to repeat grades and end their education early. Overall, cognitive gaps and school dropouts driven by a lack of ICT resources vary with countries’ educational systems and digital divides. Policies should aim to enhance the use of digital resources in education, and must be designed according to countries’ characteristics

Maximizing the Impact of Microphysiological Systems with in Vitro–in Vivo Translation

Microphysiological systems (MPS) hold promise for improving therapeutic drug approval rates by providing more physiological, human-based, in vitro assays for preclinical drug development activities compared to traditional in vitro and animal models. Here, we first summarize why MPSs are needed in pharmaceutical development, and examine how MPS technologies can be utilized to improve preclinical efforts. We then provide the perspective that the full impact of MPS technologies will be realized only when robust approaches for in vitro-in vivo (MPS-to-human) translation are developed and utilized, and explain how the burgeoning field of quantitative systems pharmacology (QSP) can fill that need

Two-scale convergence for locally-periodic microstructures and homogenization of plywood structures

The introduced notion of locally-periodic two-scale convergence allows to average a wider range of microstructures, compared to the periodic one. The compactness theorem for the locally-periodic two-scale convergence and the characterisation of the limit for a sequence bounded in $H^1(\Omega)$ are proven. The underlying analysis comprises the approximation of functions, which periodicity with respect to the fast variable depends on the slow variable, by locally-periodic functions, periodic in subdomains smaller than the considered domain, but larger than the size of microscopic structures. The developed theory is applied to derive macroscopic equations for a linear elasticity problem defined in domains with plywood structures.Comment: 22 pages, 4 figure

Rare Jarosite Detection in CRISM Imagery by Non-Parametric Bayesian Clustering

Discovery of rare phases on Mars is important as they serve as indicators of the geochemistry of the Mars surface and facilitate understanding of mineral assemblages within a geologic unit. Identification of rare minerals in high spatial and spectral resolution Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) visible/shortwave infrared (VSWIR) images has been a challenge due to the presence of both additive and multiplicative noise and other artifacts, affecting all collected images, in addition to the limited spatial extent of regions hosting these minerals. In an effort to automate this task we evaluate various clustering algorithms using the detection of rare jarosite, associated with spectrally similar minerals in CRISM imagery, as a case study. We compare nonparametric Bayesian and standard clustering algorithms and show that a recently developed doubly nonparametric Bayesian model could be effective for this task

Adams and Eves: The Gender Gap in Economics Majors

We investigate the gender gap in Economics among bachelor's and master's graduates in Italy between 2010 and 2019. First we establish that being female exerts a negative impact on the choice to major in Economics: at the bachelor level, only 73 women graduate in Economics for every 100 men, with the mathematical content of high school curricula as the key driver of the eect and a persistence of the gap at the master level. Second, within a full menu of major choices, Economics displays the largest gap, followed by STEM and then Business Economics. Third, decomposition analyses expose a unique role for the math background in driving the Economics gender gap relative to other elds. Fourth, a triple difference analysis of a high school reform shows that an increase in the math content of traditionally low math curricula caused an increase in the Economics gender gap among treated students

Adams and Eves: The Gender Gap in Economics Majors

We investigate the gender gap in Economics among bachelor’s and master’s graduates in Italy between 2010 and 2019. First we establish that being female exerts a negative impact on the choice to major in Economics: at the bachelor level, only 73 women graduate in Economics for every 100 men, with the mathematical content of high school curricula as the key driver of the effect and a persistence of the gap at the master level. Second, within a full menu of major choices, Economics displays the largest gap, followed by STEM and then Business Economics. Third, decomposition analyses expose a unique role for the math background in driving the Economics gender gap relative to other fields. Fourth, a triple difference analysis of a high school reform shows that an increase in the math content of traditionally low math curricula caused an increase in the Economics gender gap among treated students