Nonlinear Schrödinger approximations for partial differential equations with quadratic and quasilinear terms

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrödinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrödinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale

Gun Ownership Rates and Opinions on Gun Control among Immigrants and Individuals Born in the United States.

This study will focus on gun ownership and opinions on gun control among immigrants and those born in the United States. Previous studies have shown that immigrants are less likely to commit crimes than US-born persons. The reasons for this are not well understood. One possible explanation is lower rates of gun ownership and attitudes supportive of gun control in this social group. However, previous studies have not looked at this issue. By utilizing publicly available data from the General Social Survey (GSS) – public opinion survey representative of all non-institutionalized adults in the United States - this study will fill this important gap in academic literature. Ordinary least square regression will be used to determine the relationship between immigrant generations and their likelihood of owning guns and their opinions on gun control. Results show that compared to first generation immigrants, second and third generation immigrants are more likely to own a gun and oppose gun permits

Optimization Of The GARCH Model Parameters Using A Genetic Algorithm

Financial time series are often characterized by nonlinearity and volatility bunching. Standard regression analysis models cannot capture changing volatilities, potentially leading to erroneous results. The need to more completely model the characteristic volatilities inherent to financial time series eventually led to the creation of the GARCH model. Typical GARCH parameters are (1,1) incorporating a 1-period lag of the regression residual as well as a 1-period lag of the regression volatility. The primary question investigated in this paper is whether the typical GARCH(1,1) parameters are in fact optimal over all time periods and attempts to improve on the typical parameters by minimizing a modified AIC value using a genetic algorithm

Hello World! I am Charlie, an Artificially Intelligent Conference Panelist

In recent years, advances in artificial intelligence (AI) have far outpaced our ability to understand and leverage them. In no domain has this been more true than in conversational agents (CAs). Transformer-based generative language models, such as GPT-2, significantly advance CAs\u27 ability to generate creative and relevant content. It is critical to start exploring collaboration with these CAs. In this paper, we focus on an initial step by enabling a human-augmented, AI-driven CA to contribute to a panel discussion. Key questions include training a transformer-based AI to talk like a panelist, effectively embodying the CA to interact with panel participants, and defining the operational requirements and challenges to a CA gaining acceptance from its peers. Our results highlight the benefits that varied training, equal and dynamic representation, and fluid operation can have for AI applications. While acknowledging limitations, we present a path forward to richer, more natural human-AI collaboration

SEARCH: Spatially Explicit Animal Response to Composition of Habitat.

Complex decisions dramatically affect animal dispersal and space use. Dispersing individuals respond to a combination of fine-scale environmental stimuli and internal attributes. Individual-based modeling offers a valuable approach for the investigation of such interactions because it combines the heterogeneity of animal behaviors with spatial detail. Most individual-based models (IBMs), however, vastly oversimplify animal behavior and such behavioral minimalism diminishes the value of these models. We present program SEARCH (Spatially Explicit Animal Response to Composition of Habitat), a spatially explicit, individual-based, population model of animal dispersal through realistic landscapes. SEARCH uses values in Geographic Information System (GIS) maps to apply rules that animals follow during dispersal, thus allowing virtual animals to respond to fine-scale features of the landscape and maintain a detailed memory of areas sensed during movement. SEARCH also incorporates temporally dynamic landscapes so that the environment to which virtual animals respond can change during the course of a simulation. Animals in SEARCH are behaviorally dynamic and able to respond to stimuli based upon their individual experiences. Therefore, SEARCH is able to model behavioral traits of dispersing animals at fine scales and with many dynamic aspects. Such added complexity allows investigation of unique ecological questions. To illustrate SEARCH\u27s capabilities, we simulated case studies using three mammals. We examined the impact of seasonally variable food resources on the weight distribution of dispersing raccoons (Procyon lotor), the effect of temporally dynamic mortality pressure in combination with various levels of behavioral responsiveness in eastern chipmunks (Tamias striatus), and the impact of behavioral plasticity and home range selection on disperser mortality and weight change in virtual American martens (Martes americana). These simulations highlight the relevance of SEARCH for a variety of applications and illustrate benefits it can provide for conservation planning

An analog approach for weather estimation using climate projections and reanalysis data

General circulation models (GCMs) are essential for projecting future climate; however, despite the rapid advances in their ability to simulate the climate system at increasing spatial resolution, GCMs cannot capture the local and regional weather dynamics necessary for climate impacts assessments. Temperature and precipitation, for which dense observational records are available, can be bias corrected and downscaled, but many climate impacts models require a larger set of variables such as relative humidity, cloud cover, wind speed and direction, and solar radiation. To address this need, we develop and demonstrate an analog-based approach, which we call a ‘‘weather estimator.’’ The weather estimator employs a highly generalizable structure, utilizing temperature and precipitation from previously downscaled GCMs to select analogs from a reanalysis product, resulting in a complete daily gridded dataset. The resulting dataset, constructed from the selected analogs, contains weather variables needed for impacts modeling that are physically, spatially, and temporally consistent. This approach relies on the weather variables’ correlation with temperature and precipitation, and our correlation analysis indicates that the weather estimator should best estimate evaporation, relative humidity, and cloud cover and do less well in estimating pressure and wind speed and direction. In addition, while the weather estimator has several user-defined parameters, a sensitivity analysis shows that the method is robust to small variations in important model parameters. The weather estimator recreates the historical distributions of relative humidity, pressure, evaporation, shortwave radiation, cloud cover, and wind speed well and outperforms a multiple linear regression estimator across all predictands

ULF waves in the low‐latitude boundary layer and their relationship to magnetospheric pulsations: A multisatellite observation

On April 30 (day 120), 1985, the magnetosphere was compressed at 0923 UT and the subsolar magnetopause remained near 7 REgeocentric for ∼2 hours, during which the four spacecraft Spacecraft Charging At High Altitude (SCATHA), GOES 5, GOES 6, and Active Magnetospheric Particle Tracer Explorers (AMPTE) CCE were all in the magnetosphere on the morning side. SCATHA was in the low-latitude boundary layer (LLBL) in the second half of this period. The interplanetary magnetic field was inferred to be northward from the characteristics of precipitating particle fluxes as observed by the low-altitude satellite Defense Meteorological Satellite Program (DMSP) F7 and also from absence of substorms. We used magnetic field and particle data from this unique interval to study ULF waves in the LLBL and their relationship to magnetic pulsations in the magnetosphere. The LLBL was identified from the properties of particles, including bidirectional field-aligned electron beams at ∼200 eV. In the boundary layer the magnetic field exhibited both a 5–10 min irregular compressional oscillation and a broadband (Δƒ/ƒ ∼ 1) primarily transverse oscillations with a mean period of ∼50 s and a left-hand sense of polarization about the mean field. The former can be observed by other satellites and is likely due to pressure variations in the solar wind, while the latter is likely due to a Kelvin-Helmholtz (K.-H.) instability occurring in the LLBL or on the magnetopause. Also, a strongly transverse ∼3-s oscillation was observed in the LLBL. The magnetospheric pulsations, which exhibited position dependent frequencies, may be explained in terms of field line resonance with a broadband source wave, that is, either the pressure-induced compressional wave or the K.-H. wave generated in or near the boundary layer

Virtual Lab Demonstrations Improve Students’ Mastery of Basic Biology Laboratory Techniques

Biology laboratory classes are designed to teach concepts and techniques through experiential learning. Students who have never performed a technique must be guided through the process, which is often difficult to standardize across multiple lab sections. Visual demonstration of laboratory procedures is a key element in teaching pedagogy. The main goals of the study were to create videos explaining and demonstrating a variety of lab techniques that would serve as teaching tools for undergraduate and graduate lab courses and to assess the impact of these videos on student learning. Demonstrations of individual laboratory procedures were videotaped and then edited with iMovie. Narration for the videos was edited with Audacity. Undergraduate students were surveyed anonymously prior to and following screening to assess the impact of the videos on student lab performance by completion of two Participant Perception Indicator surveys. A total of 203 and 171 students completed the pre- and posttesting surveys, respectively. Statistical analyses were performed to compare student perceptions of knowledge of, confidence in, and experience with the lab techniques before and after viewing the videos. Eleven demonstrations were recorded. Chi-square analysis revealed a significant increase in the number of students reporting increased knowledge of, confidence in, and experience with the lab techniques after viewing the videos. Incorporation of instructional videos as prelaboratory exercises has the potential to standardize techniques and to promote successful experimental outcomes