Sharp decay estimates for critical Dirac equations

We prove sharp pointwise decay estimates for critical Dirac equations on $\mathbb{R}^n$ with $n\geq 2$. They appear for instance in the study of critical Dirac equations on compact spin manifolds, describing blow-up profiles, and as effective equations in honeycomb structures. For the latter case, we find excited states with an explicit asymptotic behavior. Moreover, we provide some classification results both for ground states and for excited states.Comment: Final version to appear in Trans. Amer. Math. So

A Sequential Quadratic Programming Approach to the Solution of Open-Loop Generalized Nash Equilibria

Dynamic games can be an effective approach to modeling interactive behavior between multiple non-cooperative agents and they provide a theoretical framework for simultaneous prediction and control in such scenarios. In this work, we propose a numerical method for the solution of local generalized Nash equilibria (GNE) for the class of open-loop general-sum dynamic games for agents with nonlinear dynamics and constraints. In particular, we formulate a sequential quadratic programming (SQP) approach which requires only the solution of a single convex quadratic program at each iteration. Central to the robustness of our approach is a non-monotonic line search method and a novel merit function for SQP step acceptance. We show that our method achieves linear convergence in the neighborhood of local GNE and we derive an update rule for the merit function which helps to improve convergence from a larger set of initial conditions. We demonstrate the effectiveness of the algorithm in the context of car racing, where we show up to 32\% improvement of success rate when comparing against a state-of-the-art solution approach for dynamic games. \url{https://github.com/zhu-edward/DGSQP}

Diagnosis of centrocestus formosanus infection in zebrafish (Danio rerio) in Italy: A window to a new globalization-derived invasive microorganism

Centrocestus formosanus is a digenetic trematode with a complex life cycle, involving invertebrate and vertebrate hosts, humans included. In particular, it causes gill lesions and mortality in freshwater fish species, and gastrointestinal symptoms in infected humans. Here, we describe the occurrence of C. formosanus infection in zebrafish imported in Italy and propose a newly designed species-specific primer pair to ameliorate the diagnostic investigations for C. formosanus. Gill arches of 30 zebrafish were examined for the presence of encysted metacercariae under a stereomicroscope and processed through molecular analyses targeting the ribosomal internal transcribed sequence 2 (ITS2). Although C. formosanus distribution was originally restricted to Asia, it has been subsequently reported in new countries, revealing itself as an invasive species and raising important concerns for biodiversity, economy, scientific research, as well as animal and public health. Given the crucial role played by the ornamental fish industry in spreading this parasite, there is an urgent need for control measures to prevent the introduction and establishment of C. formosanus in non-endemic areas, including Europe. We also suggest developing new strategies in microbiology and epidemiology to better explore this new globalization-derived invasive species

Ion-Exchanged Waveguides in Glass Doped with PbS Quantum Dots

The lowest-loss (≤1 dB/cm) ion-exchanged waveguides in glass doped with PbS quantum dots are presented. Near-field mode profile and refractive index profile using the refracted near-field technique were measured for these waveguides. We demonstrate that the optical properties of this glass unchanged during the ion-exchange process

A Note on the Dirac Operator with Kirchoff-Type Vertex Conditions on Metric Graphs

In this note we present some properties of the Dirac operator on noncompact metric graphs with Kirchoff-type vertex conditions. In particular, we discuss its spectral features and describe the associated quadratic form

Energy balance of five fodder cropping systems in the irrigated lowlands of Northern Italy

Extensification has recently become an important option in Western European agriculture, driven both by economic considerations (product surpluses together with the fact that developed countries cropping systems have been heavily relying on fossil energy) and growing public concern on the possible adverse effects of intensive farming on the environment and human health. The adoption of rational fodder crop rotations, with the rediscovery of the beneficial effect of the meadow, is viewed as a possible mean to reduce the impact of farming systems in the lowlands of northern Italy, characterised by highly intensive cropping and animal husbandry. For this reason our study examines the effects of crop rotation on the energy balance during 1985-2007 period in a long-term crop rotation trial in Northern Italy comparing five fodder crop systems, different in the degree of crop intensification and for the presence or absence of the meadow: a 1-year continuous cereal double cropping (R1); a 3-year rotation (R3); a 6-year rotation (R6); a permanent meadow (PM); and a continuous grain maize cropping (CM). Each rotation was subjected to two input treatments, defined as high (mostly used in lowlands of northern Italy) and low (input reduction of ca. 30%) respectively, in terms of nutrient levels, herbicide doses, and soil tillage methods. The crop rotations exerted a marked influence on the energy balance. The most efficient rotations in terms of net energy production energy efficiency have been characterized by reduced length and presence of maize and catch-crops

Learning Model Predictive Control with Error Dynamics Regression for Autonomous Racing

This work presents a novel Learning Model Predictive Control (LMPC) strategy for autonomous racing at the handling limit that can iteratively explore and learn unknown dynamics in high-speed operational domains. We start from existing LMPC formulations and modify the system dynamics learning method. In particular, our approach uses a nominal, global, nonlinear, physics-based model with a local, linear, data-driven learning of the error dynamics. We conduct experiments in simulation, 1/10th scale hardware, and deployed the proposed LMPC on a full-scale autonomous race car used in the Indy Autonomous Challenge (IAC) with closed loop experiments at the Putnam Park Road Course in Indiana, USA. The results show that the proposed control policy exhibits improved robustness to parameter tuning and data scarcity. Incremental and safety-aware exploration toward the limit of handling and iterative learning of the vehicle dynamics in high-speed domains is observed both in simulations and experiments.Comment: Submitted to ICRA 202

The Relationship Antecedents of Smoking (RAS) Scale: A new scale to assess couple-focused triggers to smoke.

The purpose of this pilot study is to assess the reliability and construct validity of a measure of relationship-focused antecedents for smoking (RAS). The scale includes both positively-valenced items (e.g.. “I feel like smoking when I am relaxing with my partner”) and negatively-valenced items (e.g., “I feel like smoking when my partner criticizes me”). Participants included 123 individuals who smoke cigarettes with co-habitating smoking (n=63) or non-smoking (n=60) romantic partners. Participants completed the RAS and a series of measures associated with smoking outcomes. Principal component analysis with varimax rotation resulted in a 2-component solution. The RAS showed excellent internal consistency for the total scale (α=.96) and for the positive (α=.88) and negative (α=.97) subscales. Higher positive subscale scores were associated with lower motivation to quit while higher negative scores were associated with lower relationship satisfaction and dyadic efficacy to quit. Higher scores on both subscales were related to higher social motives, dependence motives, and social outcome expectances. Participants with smoking partners reported higher positive subscale scores and lower negative subscale scores. The RAS may be helpful in the design of smoking cessation interventions for couples