The Kontsevich constants for the volume of the moduli of curves and topological recursion

We give an Eynard-Orantin type topological recursion formula for the canonical Euclidean volume of the combinatorial moduli space of pointed smooth algebraic curves. The recursion comes from the edge removal operation on the space of ribbon graphs. As an application we obtain a new proof of the Kontsevich constants for the ratio of the Euclidean and the symplectic volumes of the moduli space of curves.Comment: 37 pages with 20 figure

The Compositional Structure of the Asteroid Belt

The past decade has brought major improvements in large-scale asteroid discovery and characterization with over half a million known asteroids and over 100,000 with some measurement of physical characterization. This explosion of data has allowed us to create a new global picture of the Main Asteroid Belt. Put in context with meteorite measurements and dynamical models, a new and more complete picture of Solar System evolution has emerged. The question has changed from "What was the original compositional gradient of the Asteroid Belt?" to "What was the original compositional gradient of small bodies across the entire Solar System?" No longer is the leading theory that two belts of planetesimals are primordial, but instead those belts were formed and sculpted through evolutionary processes after Solar System formation. This article reviews the advancements on the fronts of asteroid compositional characterization, meteorite measurements, and dynamical theories in the context of the heliocentric distribution of asteroid compositions seen in the Main Belt today. This chapter also reviews the major outstanding questions relating to asteroid compositions and distributions and summarizes the progress and current state of understanding of these questions to form the big picture of the formation and evolution of asteroids in the Main Belt. Finally, we briefly review the relevance of asteroids and their compositions in their greater context within our Solar System and beyond.Comment: Accepted chapter in Asteroids IV in the Space Science Series to be published Fall 201

On Optimizing the Conditional Value-at-Risk of a Maximum Cost for Risk-Averse Safety Analysis

The popularity of Conditional Value-at-Risk (CVaR), a risk functional from finance, has been growing in the control systems community due to its intuitive interpretation and axiomatic foundation. We consider a non-standard optimal control problem in which the goal is to minimize the CVaR of a maximum random cost subject to a Borel-space Markov decision process. The objective takes the form $\text{CVaR}_{\alpha}(\max_{t=0,1,\dots,N} C_t)$, where $\alpha$ is a risk-aversion parameter representing a fraction of worst cases, $C_t$ is a stage or terminal cost, and $N \in \mathbb{N}$ is the length of a finite discrete-time horizon. The objective represents the maximum departure from a desired operating region averaged over a given fraction $\alpha$ of worst cases. This problem provides a safety criterion for a stochastic system that is informed by both the probability and severity of the potential consequences of the system's trajectory. In contrast, existing safety analysis frameworks apply stage-wise risk constraints (i.e., $\rho(C_t)$ must be small for all $t$, where $\rho$ is a risk functional) or assess the probability of constraint violation without quantifying its possible severity. To the best of our knowledge, the problem of interest has not been solved. To solve the problem, we propose and study a family of stochastic dynamic programs on an augmented state space. We prove that the optimal CVaR of a maximum cost enjoys an equivalent representation in terms of the solutions to this family of dynamic programs under appropriate assumptions. We show the existence of an optimal policy that depends on the dynamics of an augmented state under a measurable selection condition. Moreover, we demonstrate how our safety analysis framework is useful for assessing the severity of combined sewer overflows under precipitation uncertainty.Comment: A shorter version is under review for IEEE Transactions on Automatic Control, submitted December 202

What Do We Know About What to Do With Dams? How Knowledge Shapes Public Opinion About Their Removal in New Hampshire

In this brief, authors Simone Chapman, Catherine Ashcraft, Lawrence Hamilton, and Kevin Gardner report the results of an October 2018 Granite State Poll that asked 607 New Hampshire residents how much they have heard, and their thoughts, concerning the question of whether older dams on New Hampshire rivers should be removed for ecological or safety reasons, or whether the dams should be kept. Most people admitted they have not heard or read about this issue, but at the same time they agreed that dams could be removed in at least some cases. The more people heard or read about the issue of dam removal, the more likely they were to support removal in some or most cases. These survey results highlight the need for communicating sound information to the public concerning the costs and benefits of possible dam management options— whether doing nothing, repairs and maintenance, or removal

DATA SHARING TO DRIVE THE IMPROVEMENT OF TEACHER PREPARATION PROGRAMS

Background/Context: Teacher preparation programs (TPPs) face increasing pressure from the federal government, states, and accreditation agencies to improve the quality of their practices and graduates, yet they often do not possess enough data to make evidence-based reforms. Purpose/Objective: This manuscript has four objectives: (a) to present the strengths and shortcomings of accountability-based TPP evaluation systems; (b) to detail the individual-level data being shared with TPPs at public universities in North Carolina; (c) to describe how data sharing can lead to TPP improvement and the challenges that programs will need to overcome; and (d) to detail how three TPPs are using the data for program improvement. Setting: North Carolina public schools and schools of education at public universities in North Carolina. Importantly, this individual-level data sharing system can be instituted among TPPs in other states. Population/Participants/Subjects: Teachers initially-prepared b

Orbital Dimer Model for Spin-Glass State in Y2_2Mo2_2O7_7

The formation of a spin glass usually requires both structural disorder and frustrated magnetic interactions. Consequently, the origin of spin-glass behaviour in Y$_2$Mo$_2$O$_7$ $-$ in which magnetic Mo$^{4+}$ ions occupy a frustrated pyrochlore lattice with minimal compositional disorder $-$ has been a longstanding question. Here, we use neutron and X-ray pair-distribution function (PDF) analysis to develop a disorder model that resolves apparent incompatibilities between previously-reported PDF, EXAFS and NMR studies and provides a new and physical mechanism for spin-glass formation. We show that Mo$^{4+}$ ions displace according to a local "2-in/2-out" rule on each Mo$_4$ tetrahedron, driven by orbital dimerisation of Jahn-Teller active Mo$^{4+}$ ions. Long-range orbital order is prevented by the macroscopic degeneracy of dimer coverings permitted by the pyrochlore lattice. Cooperative O$^{2-}$ displacements yield a distribution of Mo$-$O$-$Mo angles, which in turn introduces disorder into magnetic interactions. Our study demonstrates experimentally how frustration of atomic displacements can assume the role of compositional disorder in driving a spin-glass transition.Comment: 6 pages, 3 figure

Continuous Spikes and Waves during Sleep: Electroclinical Presentation and Suggestions for Management

Continuous spikes and waves during sleep (CSWS) is an epileptic encephalopathy characterized in most patients by (1) difficult to control seizures, (2) interictal epileptiform activity that becomes prominent during sleep leading to an electroencephalogram (EEG) pattern of electrical status epilepticus in sleep (ESES), and (3) neurocognitive regression. In this paper, we will summarize current epidemiological, clinical, and EEG knowledge on CSWS and will provide suggestions for treatment. CSWS typically presents with seizures around 2–4 years of age. Neurocognitive regression occurs around 5-6 years of age, and it is accompanied by subacute worsening of EEG abnormalities and seizures. At approximately 6–9 years of age, there is a gradual resolution of seizures and EEG abnormalities, but the neurocognitive deficits persist in most patients. The cause of CSWS is unknown, but early developmental lesions play a major role in approximately half of the patients, and genetic associations have recently been described. High-dose benzodiazepines and corticosteroids have been successfully used to treat clinical and electroencephalographic features. Corticosteroids are often reserved for refractory disease because of adverse events. Valproate, ethosuximide, levetiracetam, sulthiame, and lamotrigine have been also used with some success. Epilepsy surgery may be considered in a few selected patients

NMP-7 inhibits chronic inflammatory and neuropathic pain via block of Cab3.2 T-type calcium channels and activation of CB2 receptors

Background: T-type calcium channels and cannabinoid receptors are known to play important roles in chronic pain, making them attractive therapeutic targets. We recently reported on the design, synthesis and analgesic properties of a novel T-type channel inhibitor (NMP-7), which also shows mixed agonist activity on CB1 and CB2 receptors in vitro. Here, we analyzed the analgesic effect of systemically delivered NMP-7 (intraperitoneal (i.p.) or intragstric (i.g.) routes) on mechanical hypersensitivity in inflammatory pain induced by Complete Freund’s Adjuvant (CFA) and neuropathic pain induced by sciatic nerve injury. Results: NMP-7 delivered by either i.p. or i.g. routes produced dose-dependent inhibition of mechanical hyperalgesia in mouse models of inflammatory and neuropathic pain, without altering spontaneous locomotor activity in the open-field test at the highest active dose. Neither i.p. nor i.g. treatment reduced peripheral inflammation per se, as evaluated by examining paw edema and myeloperoxidase activity. The antinociception produced by NMP-7 in the CFA test was completely abolished in CaV3.2-null mice, confirming CaV3.2 as a key target. The analgesic action of intraperitoneally delivered NMP-7 was not affected by pretreatment of mice with the CB1 antagonist AM281, but was significantly attenuated by pretreatment with the CB2 antagonist AM630, suggesting that CB2 receptors, but not CB1 receptors are involved in the action of NMP-7 in vivo. Conclusions: Overall, our work shows that NMP-7 mediates a significant analgesic effect in a model of persistent inflammatory and chronic neuropathic pain by way of T-type channel modulation and CB2 receptor activation. Thus, this study provides a novel therapeutic avenue for managing chronic pain conditions via mixed CB ligands/ T-type channel blockers

The 3-D kinematics of water masers around the semiregular variable RT Virginis

We report observations of water masers around the semiregular variable RT Virginis (RT Vir), which have been made with the Very Long Baseline Array (VLBA) of the National Radio Astronomy Observatory (NRAO) at five epochs, each separated by three weeks of time. We detected about 60 maser features at each epoch. Overall, 61 features, detected at least twice, were tracked by their radial velocities and proper motions. The 3-D maser kinematics exhibited a circumstellar envelope that is expanding roughly spherically with a velocity of about 8 km/s. Asymmetries in both the spatial and velocity distributions of the maser features were found in the envelope, but less significant than that found in other semiregular variables. Systematic radial-velocity drifts of individual maser features were found with amplitudes of <= 2 km/s/yr. For one maser feature, we found a quadratic position shift with time along a straight line on the sky. This apparent motion indicates an acceleration with an amplitude of 33 km/s/yr, implying the passage of a shock wave driven by the stellar pulsation of RT Vir. The acceleration motion is likely seen only on the sky plane because of a large velocity gradient formed in the accelerating maser region. We estimated the distance to RT Vir to be about 220 pc on the basis of both the statistical parallax and model-fitting methods for the maser kinematics.Comment: 18 pages, 8 figures. Accepted to appear in the Astrophysical Journa