Grants

NSF

This program will create computer models of the very first galaxies and black holes to form in the Universe. New observations have discovered extremely distant galaxies, some of these galaxies appear more massive and evolved than expected by current models. Through computer simulations, this program will make an important contribution to establishing the new models needed to properly explain the recent observations of the most distant galaxies. To make the scientific results of this program available to everyone, the PIs will design and fabricate dozens of 3D-printed models from various simulated galaxies and any interesting structures within them. These 3D-printed models will be displayed in outreach events and art exhibits. This collaborative proposal will deliver theoretical and observational predictions for galaxy and Super-Massive Black Hole (SMBH) formation and growth during Cosmic Dawn with a particular focus on galaxies with overly massive black holes. Specifically, this proposal will investigate if galaxies in the early universe with and without a black hole seed can be distinguished observationally. Using the exascale-capable code Enzo-E, this program will carry out simulations of high-redshift galaxy formation, accounting for SMBH fueling, feedback models and their impact on the circumgalactic medium. The principal goal of this work is to determine the observational signatures of a galaxy that has hosted a massive black hole seed. This proposal will provide a basis for training astrophysical simulations enhanced by Artificial Intelligence. This proposed work will provide a breadth of research opportunities for the professional development of undergraduate and graduate students. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

This program will create computer models of the very first galaxies and black holes to form in the Universe. New observations have discovered extremely distant galaxies, some of these galaxies appear more massive and evolved than expected by current models. Through computer simulations, this program will make an important contribution to establishing the new models needed to properly explain the recent observations of the most distant galaxies. To make the scientific results of this program available to everyone, the PIs will design and fabricate dozens of 3D-printed models from various simulated galaxies and any interesting structures within them. These 3D-printed models will be displayed in outreach events and art exhibits. This collaborative proposal will deliver theoretical and observational predictions for galaxy and Super-Massive Black Hole (SMBH) formation and growth during Cosmic Dawn with a particular focus on galaxies with overly massive black holes. Specifically, this proposal will investigate if galaxies in the early universe with and without a black hole seed can be distinguished observationally. Using the exascale-capable code Enzo-E, this program will carry out simulations of high-redshift galaxy formation, accounting for SMBH fueling, feedback models and their impact on the circumgalactic medium. The principal goal of this work is to determine the observational signatures of a galaxy that has hosted a massive black hole seed. This proposal will provide a basis for training astrophysical simulations enhanced by Artificial Intelligence. This proposed work will provide a breadth of research opportunities for the professional development of undergraduate and graduate students. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

The investigators will carry out theoretical analysis and computer simulations of solar observations to test the hypothesis that heating in the coolest parts of the Sun’s atmosphere is caused by small-scale (meter-sized) slow-moving plasma processes referred to as the Thermal Farley-Buneman Instability. This may also occur in the atmospheres of other stars and planets, including the Earth. The researchers will train graduate, undergraduate, and high school students in methods of computational plasma physics. The student groups will include women and people from historically excluded populations. The team will constrain their models using data from the Interface Region Imaging Spectrograph (IRIS) on the NASA Solar Observation Satellite using the Mg II spectral lines in the NUV passband. They will use full-disk scans performed once month to capture a large variety of targets. They will also use Fe I 617.3 nm data with 1 arcsecond resolution obtained with the NASA Solar Dynamics Observatory’s Helioseismic and Magnetic Imager (SDO/HMI) instrument for measurements of the photospheric magnetic field. The work will include a series of multifluid and kinetic simulations to explore the nonlinear and thermal properties of the resulting turbulence and incorporate the electron heating into larger radiative magnetohydrodynamic codes. The models will also help understand observations from NSF’s new DKIST solar observatory. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Learning to innovate is crucial for preparing students to design and implement innovative solutions to social and technical problems upon graduation. However, students rarely receive opportunities to learn or practice the skills that drive innovation. Students need authentic project-based learning experiences, but also coaches who can help them develop regulation skills – namely, cognitive, metacognitive, motivational, emotional, and strategic behaviors for reaching desired goals and outcomes. Effective coaching can not only troubleshoot project issues, but help students understand and address underlying gaps in regulation skills that limit their effectiveness as innovators. However, even experienced coaches find it challenging to help students develop their regulation skills. This project aims to improve regulation skills in college students by advancing computational tools and techniques to create tailored practice opportunities for coaches and students. Students can struggle to understand and articulate the underlying causes beneath their project struggles, and coaches challenged by the need to elicit, model, and facilitate effective practices and provide tailored feedback to large numbers of students. This project aims to overcome these challenges by developing Situated Practice Systems, a new intelligent coaching tool that (1) computationally encodes learners’ regulation behaviors across coaching sessions; (2) uses Artificial Intelligence practice agents to provide learners with tailored reminders and feedback on regulation skills between coaching sessions; and (3) leverages Large Language Models, machine learning and case libraries to provide tailored practice support to students. This research uses a design-based research approach to generate empirically validated principles that advance our understanding of learning to innovate. This project is funded by the Research on Innovative Technologies for Enhanced Learning (RITEL) program that supports early-stage exploratory research in emerging technologies for teaching and learning. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Being able to predict behaviors of other people is important to successfully navigate the social world. Prior research shows that one major way to achieve this is by learning about other people’s personality traits. This project explores how individuals learn not only about others’ personality traits but also about the situations that inform people’s actions, and in turn use situational learning in decision making. Impacts of this project include research training opportunities for graduate and undergraduate students, and dissemination of findings to the public. This project aims to characterize how individuals learn about situations and explore how different life experiences influence this process. The research team leverages behavioral methods, advanced neuroimaging techniques and computational modeling to (1) identify the neural and cognitive mechanisms involved in situational and trait learning and to (2) examine the role that situational and trait learning play in reasoning and decision-making across different contexts. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Being able to predict behaviors of other people is important to successfully navigate the social world. Prior research shows that one major way to achieve this is by learning about other people’s personality traits. This project explores how individuals learn not only about others’ personality traits but also about the situations that inform people’s actions, and in turn use situational learning in decision making. Impacts of this project include research training opportunities for graduate and undergraduate students, and dissemination of findings to the public. This project aims to characterize how individuals learn about situations and explore how different life experiences influence this process. The research team leverages behavioral methods, advanced neuroimaging techniques and computational modeling to (1) identify the neural and cognitive mechanisms involved in situational and trait learning and to (2) examine the role that situational and trait learning play in reasoning and decision-making across different contexts. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Learning-enabled autonomous systems operating in unfamiliar or unprecedented environments pose new foundational challenges for their safety assessment and subsequent risk management. In this context, the system-level safety means the complicated behaviors created by the interactions between multiple learning components and the physical world satisfy the safety requirements, protecting the system from accidental failures to avoid hazards such as collisions to other vehicles, bicycles and pedestrians. The qualitative and quantitative methodologies envisioned to complement each other by providing both 'yes' or 'no' binary decisions and numerical measures of safety, which allow for a thorough understanding of safety concerns and enable effective safety verification in uncertain environments. This project targets the foundational challenges of developing qualitative and quantitative safety assessment methods capable of capturing uncertainties from environments and providing timely, comprehensive, and accurate safety evaluations at the system level. The outcomes are expected to boost the trustworthiness and adaptability of learning-enabled systems to the unknown world and facilitate their safe integration into various domains, such as autonomous vehicles, robotics, or industrial automation. Educational and outreach activities are well-integrated into the research, including curriculum development, K-12 STEM outreach, and industrial engagement activities. The designed activities are uniquely positioned to promote diversity throughout this project by giving priority consideration, mentoring, and working with students in underrepresented minority groups. The proposed research efforts will be directed toward building the foundations of end-to-end qualitative and quantitative safety assessment of learning-enabled autonomous systems. This project will develop the probabilistic star temporal logic specification language. The new specification language offers a formalism for expressive modeling of learning process uncertainty and complex temporal behaviors, and supports both qualitative and quantitative reasoning. Efficient computation methods and tools will be developed to verify probabilistic star temporal logic specifications for learning-enabled deep neural network components. The verification methods and tools are centered on enhancing their scalability and resource efficiency. This project will develop system-level qualitative and quantitative safety assessment methods and tools that can handle the interplay of various learning-enabled components in a system under different availability of environment information. Learning-enabled F1Tenth testbed, a small-scale system of real autonomous vehicles and its simulator, will be used to create multiple real-world autonomous driving scenarios to validate and evaluate the applicability, scalability and reliability of the proposed methods and tools. This research is supported by a partnership between the National Science Foundation and Open Philanthropy. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Whole numbers are among the most practical and most important mathematical objects. Humans have studied them for millennia. Number theory aims to understand patterns possessed by whole numbers. Fundamental questions revolve around multiplication: how often are numbers in some sequence even (i.e. divisible by two)? Divisible by three? Or five? Nineteenth century researchers introduced symmetry actions to reveal hidden patterns in numbers. And, in the 1970's, Robert Langlands made far-reaching conjectures on symmetry. These conjectures have occupied number theorists ever since. They predict patterns seen by symmetry actions will arise equally from the calculus of complex numbers ("modular forms"). A pattern appearing in two places is an example of a mathematical reciprocity. This project will refine Langlands' reciprocity prediction. The new tool is geometric spaces of symmetry actions, constructed by Emerton and Gee over the past fifteen years. These spaces are believed to convert reciprocity questions into geometrical ones. This project establishes instances of this belief. It will connect divisibility patterns from the world of modular forms to geometrical theorems on Emerton and Gee's spaces. The project has substantial broader impacts. Computational data will be included in the widely-used L-functions and Modular Forms Database. The project also develops computational tools for teaching. Open education resources (OERs) are learning materials placed in the public domain. Their primary benefit is providing learning experiences at low costs. They can be adapted to fit a diversity of learning environments. The project develops OERs for computer-based learning of number theory and abstract algebra. The project supports education and outreach in two more ways. First, Math Circles will be run in public schools. Second, research projects will be developed to support the Program in Mathematics for Young Scientists. Finally, the project plans two research workshops in number theory. Both aim to disseminate new advances in number theory and reciprocity. The more detailed aim is a new study of p-adic slopes of modular forms and Galois representations. The p-adic slope of a modular form is how often its p-th Hecke eigenvalue is divisible by a fixed prime p. Predictions and theorems on slopes have been around since the 1980's. Seven years ago, Bergdall and Pollack proposed a way ("the ghost conjecture") to unify almost all prior ideas. The ghost conjecture's input is a congruence class of modular forms. The output is an elementary recipe for slopes in the class. The main caveat is the ghost conjecture only applies to "regular" classes. But, assuming regularity, Liu, Truong, Xiao, and Zhao (LTXZ) recently established the conjecture. The current project removes the regular assumption in the ghost conjecture. The new tool is Emerton and Gee's (EG) moduli stack of Galois representations. In Galois terms, regularity is a generic property on the EG stack. The project's technical innovation is thus deforming slope questions over the stack. A geometrical reformulation will open the door to generalizing the LTXZ proof. It will also create space for novel studies of Hilbert modular forms or higher rank automorphic forms. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

AC motor drives are widely utilized in many on-the-move energy technologies (e.g., electric vehicles and industrial or medical robots) to control the speed or position of a mechanical scheme. The industry is constantly seeking lightweight, efficient, and reliable solutions for these high-performance AC motor drives. Recent advancements in semiconductor materials have enabled electrical engineers to design ultrafast switches and motor drive systems with higher efficiency and power density. However, the ultrafast switches can cause severe voltage stress on the motor stator winding insulation, reducing the motor lifetime and eventually leading to unexpected shutdowns. This collaborative research will address such reliability concerns through developing the technology of smart coils. Since the proposed technology avoids the conventional bulky and lossy filters, it will advance the compactness of high-performance motor drive systems. In this project, innovative educational modules will also be collaboratively developed to inspire prospective undergraduate and graduate students to pursue education and careers in applications of control theories in power electronics and motor drives. This project aims to develop the technology of smart coils for AC motor drives. The envisioned smart coil technology will make the surge impedance of the motor windings adaptively vary by the sharpness of the voltage pulses which are produced by a drive, travel along cables, and reach the motor terminals. The evolving technology of ultrafast wide bandgap semiconductor switches enhances the efficiency and power density of AC motor drives by minimizing the size of passive components and cooling apparatuses. However, the sharpness of the generated voltage pulses can induce reflected waves in the cable and overvoltages at the motor terminals. The smart coil technology can mitigate the overvoltage stress caused by the reflected wave phenomena regardless of the length of the power cables. Unlike conventional approaches for mitigating reflected wave phenomena that use bulky and lossy passive filters, the smart coil technology will enable AC motors much more compatible with the emerging wide bandgap-based fast-switching drives. This technology can also lead to more electric powertrains with high efficiency, high power density, and high reliability. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

PUBLIC ABSTRACT This project will reveal how venom complexity has evolved in association with sociality in spiders. The evolution of sociality is associated with a redistribution of efforts among group-mates to accomplish collective tasks. However, how social groups of predators optimize the distribution of weaponry used to subdue prey remains unknown. Venomous predatory spiders represent a powerful system to address this gap in knowledge because both social and solitary spiders use venom for defense and prey capture. This project explores how venom – a critical tool for defense and hunting – is shaped not only by an animal’s biology, but also by the microbes (the “microbiome”) that live within it. Researchers will study how venom composition, including both toxins and microbial communities, has changed across multiple independent origins of social living in spiders. By comparing venom traits in social spiders and their solitary relatives, the team will examine whether social living drives changes in venom that help divide labor among individuals. This work is significant because it brings together tools from evolutionary biology, toxinology, and microbiome science to ask how cooperation in nature evolves, and if this evolution is repeatable. It also has real-world relevance in that spider venom and venom microbes may hold clues for developing new natural products or medicines, including treatments for chronic pain and infections. The researchers will share their discoveries, as well as educational resources for inspiring students to apply the scientific method to both basic and applied research questions, with students from local communities in both Florida and Puerto Rico. This research investigates how venom complexity – defined here as the combined diversity of venom toxins and venom-associated microbial communities – has evolved in association with three independent origins of sociality in spiders. Using complementary multi-omics techniques, the research team will quantify two components of venom composition, toxin diversity and venom microbial community diversity, to assess within- and between-species differences in venom complexity. Three research objectives will be addressed: the team will (1) determine differences in venom toxin composition between social and solitary predators, (2) identify differences in venom microbiomes between social and solitary predators, and (3) establish the degree to which individual venom composition coincides with behavioral task differentiation. This proposal expands the traditional view of venom evolution to encompass the functional role of venom-associated microbes across multiple scales: from individuals to social groups to populations to species. Using Stegodyphus social spiders as a test system allows us to address the parallel evolution of two key innovations (sociality and venom use) across multiple origins of sociality. Few systems exist in which these key innovations are genetically tractable, allowing for the mapping of precise mutational pathways and revealing underlying microevolutionary processes. From a biotechnology perspective, venom peptides provide a large untapped potential for therapeutic discoveries, including treatments for chronic pain and parasite infection. Characterization of the venom microbiome has high potential to yield novel taxa of biomedical importance because this microbial community inhabits venom-gland environments known for their antimicrobial properties. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

PUBLIC ABSTRACT This project will reveal how venom complexity has evolved in association with sociality in spiders. The evolution of sociality is associated with a redistribution of efforts among group-mates to accomplish collective tasks. However, how social groups of predators optimize the distribution of weaponry used to subdue prey remains unknown. Venomous predatory spiders represent a powerful system to address this gap in knowledge because both social and solitary spiders use venom for defense and prey capture. This project explores how venom – a critical tool for defense and hunting – is shaped not only by an animal’s biology, but also by the microbes (the “microbiome”) that live within it. Researchers will study how venom composition, including both toxins and microbial communities, has changed across multiple independent origins of social living in spiders. By comparing venom traits in social spiders and their solitary relatives, the team will examine whether social living drives changes in venom that help divide labor among individuals. This work is significant because it brings together tools from evolutionary biology, toxinology, and microbiome science to ask how cooperation in nature evolves, and if this evolution is repeatable. It also has real-world relevance in that spider venom and venom microbes may hold clues for developing new natural products or medicines, including treatments for chronic pain and infections. The researchers will share their discoveries, as well as educational resources for inspiring students to apply the scientific method to both basic and applied research questions, with students from local communities in both Florida and Puerto Rico. This research investigates how venom complexity – defined here as the combined diversity of venom toxins and venom-associated microbial communities – has evolved in association with three independent origins of sociality in spiders. Using complementary multi-omics techniques, the research team will quantify two components of venom composition, toxin diversity and venom microbial community diversity, to assess within- and between-species differences in venom complexity. Three research objectives will be addressed: the team will (1) determine differences in venom toxin composition between social and solitary predators, (2) identify differences in venom microbiomes between social and solitary predators, and (3) establish the degree to which individual venom composition coincides with behavioral task differentiation. This proposal expands the traditional view of venom evolution to encompass the functional role of venom-associated microbes across multiple scales: from individuals to social groups to populations to species. Using Stegodyphus social spiders as a test system allows us to address the parallel evolution of two key innovations (sociality and venom use) across multiple origins of sociality. Few systems exist in which these key innovations are genetically tractable, allowing for the mapping of precise mutational pathways and revealing underlying microevolutionary processes. From a biotechnology perspective, venom peptides provide a large untapped potential for therapeutic discoveries, including treatments for chronic pain and parasite infection. Characterization of the venom microbiome has high potential to yield novel taxa of biomedical importance because this microbial community inhabits venom-gland environments known for their antimicrobial properties. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Public Safety Systems (PSS) deal with victims, first responders, and emergency control centers (ECCs) that coordinate the rescue missions during and aftermath of a disaster. Currently, there is limited understanding of how humans make decisions to utilize personal and shared resources in the wake of disasters; moreover, the existing models are mostly qualitative. Limited information availability in disaster scenarios and resource uncertainty in PSSs pose two major challenges: (1) how to achieve the victims’ satisfaction accounting for their risk-aware (autonomous) decision-making characteristics about dynamic resource orchestration? and (2) how to design a resilient disaster response system incentivizing the victims’ participation in crowdsourcing? The innovative SOTERIA project addresses these challenges by proposing a novel behavioral decision-making model that captures humans’ decision-making characteristics under risk, stemming from uncertain availability of resources. It introduces a new field in game theory, called Satisfaction Games that aims to satisfy the victims’ minimum service requirements rather than maximizing their overall satisfaction, addressing the resource management problems in PSSs. A novel bio-inspired Disaster Response Network (DRN) is also proposed that mimics the inherent robustness of biological networks of living organisms, to support the victims’ participation in reliable crowdsourcing, while the truthfulness and quality of the collected information are evaluated based on the newly invented Bayesian Prospect Theory. The proposed methods and the system will be evaluated using real-world field data. The SOTERIA project will create new distributed control, optimization, and scalable resource management techniques in PSSs. The novelty lies in the integrated approach to efficiently managing resources considering human behavior and Tragedy of the Commons phenomena about shared resources, thus enhancing the victim’s satisfaction instead of utility maximization. To deal with incomplete information about resource availability, the proposed reinforcement learning techniques will enhance the victim’s decision-making capability in real time. Research outcomes of this project have tremendous potential for supporting ECC activities and saving peoples’ lives and infrastructures during and after disasters, by designing robust situation-aware disaster response networks and advancing state of the art research in Prospect Theory, Tragedy of the Commons, and Satisfaction Games. The project will train undergraduate and graduate students and the research findings will be disseminated via a project website and high-quality publications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

A research collaboration between Georgia State University, Bridgewater State University and Southern Connecticut State University will observe a sample of nearly 5000 stars across the entire sky using a technique called speckle imaging. The observations will focus on two volume-limited, volume-complete samples of K dwarf stars within 40 parsecs of the Sun and M dwarf stars within 20 parsecs, our Sun’s nearest stellar neighbors. The choice of nearby stars will enable imaging of their stellar environments down to separations smaller than the distance of Mercury to the Sun. This will allow them to discover how unusual our Sun is in its stellar solitude and provide a list of stars around which other solar systems might be found because they lack close companion stars. The project is student-intensive, with graduate and undergraduate students carrying out the work at three universities, including an outreach effort entitled “Why Resolution Matters.” The project provides opportunities to gain expertise in (1) science — astronomy and physics, (2) mathematics — intensive data acquisition and reduction, with statistical treatments of results involving large databases, and (3) engineering — using some of the U.S.’s premier telescopes equipped with state-of-the-art instruments. This work will allow the researchers to detect stellar companions and provide benchmark measurements of their (1) luminosity function, (2) mass function, (3) multiplicity rates, (4) masses, (5) mass-luminosity relations, and (6) orbital architectures. The survey will comprise legacy samples that will continue to be the subject of ground-based and spaced-base efforts. The speckle imaging surveys will be carried out primarily at the APO 3.5m telescope with DSSI in the northern hemisphere and the SOAR 4.1m telescope with HRCam+SAM in the south. The speckle surveys are particularly relevant to exoplanet work, because they sample scales of 0.1–100 AU around the stars, similar to where planets are found in our Solar System. The results will be combined with a sweep of wide-field companions found in Gaia for larger separations and companions at small separations found via previous high-resolution efforts and in radial velocity surveys that are sensitive to lower-mass objects. The orbital architectures of companions to K and M dwarfs will be compared directly to planets reported to be orbiting stars in the same samples. A third sample of AFG stars will serve as a comparison to higher mass stars, with a nod toward lower metallicities to investigate dependences on how stars form in different historical environments. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

This project focuses on developing new mathematical techniques that help us analyze signals more effectively by carefully isolating their distinct parts, whether in time, space, or frequency, without interference. Tackling this challenge enables researchers and engineers to build practical tools that clean up noisy signals and reveal essential details. These improvements directly enhance everyday technologies, such as delivering sharper and clearer MRI scans, boosting the reliability of our wireless communications, and speeding up accurate data reconstruction. By making these technologies better, the project not only pushes the boundaries of science and engineering but also makes real-world differences, improving healthcare diagnostics, ensuring emergency messages get through reliably, and enhancing national defense capabilities. Additionally, the project emphasizes education and community outreach, providing valuable research experience to undergraduate and graduate students in science and technology. Public workshops and outreach activities are planned to inspire broader interest in mathematics, encouraging future generations to pursue scientific careers and ultimately contributing to a stronger scientific workforce. This project aims to improve our understanding of special mathematical tools known as spatio-spectral limiting operators (SSLOs), which help analyze signals precisely in both space (or time) and frequency. Although mathematicians have thoroughly studied these tools in one dimension, the more complex case involving multiple dimensions still has many unanswered questions. Addressing these questions is important because it can significantly improve technologies that impact everyday life, such as MRI machines, wireless communication, and scientific imaging techniques. The research team will develop and study Gaussian wave packet systems, an advanced version of traditional tools like wavelets and Gabor systems. The use of these new systems will effectively manage the challenges of multi-dimensional signals by incorporating translations, modulations, and dilations. They will investigate how the properties of these mathematical tools change, particularly when dealing with regularly shaped domains like balls or other smooth geometric shapes, and how stable these properties are when applied to more complicated shapes, including those with small holes or gaps. To enable practical computation, they will specifically focus on radial wave packets for simple shapes like discs, making it easier and faster to perform analysis essential to signal processing tasks, such as interpolating and integrating data. Finally, the research team will extend these mathematical ideas to discrete-time scenarios, offering valuable insights useful in various applications, from digital signal processing to advanced imaging techniques. Overall, the project’s results will offer significant advances in mathematics while providing practical tools that enhance medical imaging, improve communications technologies, and enable more accurate scientific data analysis. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

This project focuses on developing new mathematical techniques that help us analyze signals more effectively by carefully isolating their distinct parts, whether in time, space, or frequency, without interference. Tackling this challenge enables researchers and engineers to build practical tools that clean up noisy signals and reveal essential details. These improvements directly enhance everyday technologies, such as delivering sharper and clearer MRI scans, boosting the reliability of our wireless communications, and speeding up accurate data reconstruction. By making these technologies better, the project not only pushes the boundaries of science and engineering but also makes real-world differences, improving healthcare diagnostics, ensuring emergency messages get through reliably, and enhancing national defense capabilities. Additionally, the project emphasizes education and community outreach, providing valuable research experience to undergraduate and graduate students in science and technology. Public workshops and outreach activities are planned to inspire broader interest in mathematics, encouraging future generations to pursue scientific careers and ultimately contributing to a stronger scientific workforce. This project aims to improve our understanding of special mathematical tools known as spatio-spectral limiting operators (SSLOs), which help analyze signals precisely in both space (or time) and frequency. Although mathematicians have thoroughly studied these tools in one dimension, the more complex case involving multiple dimensions still has many unanswered questions. Addressing these questions is important because it can significantly improve technologies that impact everyday life, such as MRI machines, wireless communication, and scientific imaging techniques. The research team will develop and study Gaussian wave packet systems, an advanced version of traditional tools like wavelets and Gabor systems. The use of these new systems will effectively manage the challenges of multi-dimensional signals by incorporating translations, modulations, and dilations. They will investigate how the properties of these mathematical tools change, particularly when dealing with regularly shaped domains like balls or other smooth geometric shapes, and how stable these properties are when applied to more complicated shapes, including those with small holes or gaps. To enable practical computation, they will specifically focus on radial wave packets for simple shapes like discs, making it easier and faster to perform analysis essential to signal processing tasks, such as interpolating and integrating data. Finally, the research team will extend these mathematical ideas to discrete-time scenarios, offering valuable insights useful in various applications, from digital signal processing to advanced imaging techniques. Overall, the project’s results will offer significant advances in mathematics while providing practical tools that enhance medical imaging, improve communications technologies, and enable more accurate scientific data analysis. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Topological insulators are a class of materials that are insulators in their bulk and that nevertheless allow wave propagation along their edge. Such materials are at the forefront of the rapidly developing industry of low-energy consumption electronics technologies as they yield a fundamentally new type of electronic transport with ultra-low resistance. Mathematically, such transport is modeled by wave functions corresponding to the eigenvalues appearing, after introduction of a boundary, in a gap of the spectrum of the material without boundary. The principal goal of the project is to develop mathematical methods for measuring the number of such states based on readily computable information about the physical models of the corresponding material. The principal investigators investigate discrete boundary value problems for the tight-binding Hamiltonians describing electronic transport in topological insulators. One of the main themes is the derivation of explicit formulas for the number of eigenvalues in the gaps of the essential spectrum, which correspond to edge states localizing along the boundary. The formulas are expressed through mathematical tools stemming from symplectic geometry, such as the Maslov index and its discretization, the Duistermaat index, with the latter being particularly amenable to numerical computation. In addition to eigenvalues in the gaps, the new formulas give access to the integrated density of states (in the bands of the continuous spectrum) and shed new light on the bulk-boundary correspondence by connecting the gap indices with the band indices. The discrete boundary value problems are described using the theory of boundary triplets of non-densely defined symmetric operators. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Topological insulators are a class of materials that are insulators in their bulk and that nevertheless allow wave propagation along their edge. Such materials are at the forefront of the rapidly developing industry of low-energy consumption electronics technologies as they yield a fundamentally new type of electronic transport with ultra-low resistance. Mathematically, such transport is modeled by wave functions corresponding to the eigenvalues appearing, after introduction of a boundary, in a gap of the spectrum of the material without boundary. The principal goal of the project is to develop mathematical methods for measuring the number of such states based on readily computable information about the physical models of the corresponding material. The principal investigators investigate discrete boundary value problems for the tight-binding Hamiltonians describing electronic transport in topological insulators. One of the main themes is the derivation of explicit formulas for the number of eigenvalues in the gaps of the essential spectrum, which correspond to edge states localizing along the boundary. The formulas are expressed through mathematical tools stemming from symplectic geometry, such as the Maslov index and its discretization, the Duistermaat index, with the latter being particularly amenable to numerical computation. In addition to eigenvalues in the gaps, the new formulas give access to the integrated density of states (in the bands of the continuous spectrum) and shed new light on the bulk-boundary correspondence by connecting the gap indices with the band indices. The discrete boundary value problems are described using the theory of boundary triplets of non-densely defined symmetric operators. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Rainfall during the Asian summer monsoon (ASM) is a critical water resource for human use, ecosystems, agriculture, energy and industry. The behavior of the ASM varies regionally, and there is a gap in understanding of the variability through time of ASM and the Asian Winter Monsoon (AWM) in mainland Southeast Asia (MSEA), where a greater proportion of rainfall is during the autumn and winter months. This project will reconstruct rainfall intensity on timescales of decades to tens of thousands of years through geochemical measurements of cave deposits from Laos and Vietnam. These measurements, along will climate model simulations, will improve understanding the mechanisms that drive variability of the ASM and AWM, and how this system responds to climate variations through time. This project will use oxygen, carbon, calcium stable isotope ratios and trace elements measured in speleothems, cave monitoring, and hydrogeochemical modeling to reconstruct ASM and autumn/winter monsoon AWM circulation and regional precipitation patterns in MSEA over the last 200 ky. These new data will be synthesized with existing data and isotope-enabled and high-resolution climate model simulations to determine drivers of MSEA hydroclimate variability on millennial to orbital timescales and characterize decadal scale hydroclimate variability and the impacts of coupled ocean-atmosphere dynamics and hydrological extremes on ASM and AWM in different climate states. The project includes support for undergraduate students and PhD students and K-12 outreach events. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Rainfall during the Asian summer monsoon (ASM) is a critical water resource for human use, ecosystems, agriculture, energy and industry. The behavior of the ASM varies regionally, and there is a gap in understanding of the variability through time of ASM and the Asian Winter Monsoon (AWM) in mainland Southeast Asia (MSEA), where a greater proportion of rainfall is during the autumn and winter months. This project will reconstruct rainfall intensity on timescales of decades to tens of thousands of years through geochemical measurements of cave deposits from Laos and Vietnam. These measurements, along will climate model simulations, will improve understanding the mechanisms that drive variability of the ASM and AWM, and how this system responds to climate variations through time. This project will use oxygen, carbon, calcium stable isotope ratios and trace elements measured in speleothems, cave monitoring, and hydrogeochemical modeling to reconstruct ASM and autumn/winter monsoon AWM circulation and regional precipitation patterns in MSEA over the last 200 ky. These new data will be synthesized with existing data and isotope-enabled and high-resolution climate model simulations to determine drivers of MSEA hydroclimate variability on millennial to orbital timescales and characterize decadal scale hydroclimate variability and the impacts of coupled ocean-atmosphere dynamics and hydrological extremes on ASM and AWM in different climate states. The project includes support for undergraduate students and PhD students and K-12 outreach events. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

This project investigates how the rapid evolution of an agricultural pest makes it more difficult to control using natural means. People think of evolution occurring in geological time, with eras like the Dinosaur Age populated with different organisms from what we have on Earth today. Most studies of evolution, however, look at changes that occur in days or years in organisms that are all around us today. Scientists are realizing that rapid evolution is common and affects all organisms. For example, many agricultural pests in the USA are controlled by predators that attack and kill them, making insecticides unnecessary. Pea aphids represent a great example of this, because they are kept in check by predators. However, pea aphids can evolve resistance to predators. This rapid evolution raises the risk of greater crop damage. Despite their ability to evolve resistance, all the pea aphids do not become resistance to predators. There are also some that remain susceptible, creating a balance between resistance and susceptibility. This project aims to uncover how this balance is maintained, and how agricultural management practices can reduce the risks of agricultural pests becoming resistant. Understanding this balance will help to develop strategies to make US agriculture more resilient and increase the security and sustainability of our bioeconomy. The project will also provide hands-on research experiences to students with no prior experience. Public outreach events will engage farmers to share the results of the research broadly. The research investigates the ecological-evolutionary dynamics of pea aphids and their parasitoid wasp, Aphidius ervi. Aphidius ervi was deliberately introduced to North America as a biocontrol agent of pea aphids, particularly to control pea aphids as pests of alfalfa crops. Pea aphids are a leading model for investigating the evolutionary and ecological consequences of symbiosis because all populations harbor heritable symbionts that provide well-documented benefits. The most common and best studied facultative symbiont, Hamiltonella defensa, confers resistance against A. ervi. Although evolutionary theory predicts that resistance traits will often be bimodal (either susceptible or highly resistant), pea aphids exhibit a full spectrum of resistance through different symbiont variants. Although the prevalences of different symbiont variants fluctuate (reflecting the intensity of parasitism and selection), the collective of symbionts across the spectrum of resistance appears to be stable. Furthermore, the ecological interactions between pea aphids and A. ervi are stable, in the sense that A. ervi is always present but abundances never get high enough to extirpate pea aphids. This ecological stability of A. ervi-pea aphid interactions may itself be the product of the evolutionary stability of the symbionts that confer pea aphid resistance to A. ervi. The research will use field experiments, lab experiments and mathematical modeling to examine both the evolutionary and ecological stability of A. ervi-pea aphid interactions, and whether this stability is generated by the interconnections between evolutionary and ecological dynamics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

This project investigates how the rapid evolution of an agricultural pest makes it more difficult to control using natural means. People think of evolution occurring in geological time, with eras like the Dinosaur Age populated with different organisms from what we have on Earth today. Most studies of evolution, however, look at changes that occur in days or years in organisms that are all around us today. Scientists are realizing that rapid evolution is common and affects all organisms. For example, many agricultural pests in the USA are controlled by predators that attack and kill them, making insecticides unnecessary. Pea aphids represent a great example of this, because they are kept in check by predators. However, pea aphids can evolve resistance to predators. This rapid evolution raises the risk of greater crop damage. Despite their ability to evolve resistance, all the pea aphids do not become resistance to predators. There are also some that remain susceptible, creating a balance between resistance and susceptibility. This project aims to uncover how this balance is maintained, and how agricultural management practices can reduce the risks of agricultural pests becoming resistant. Understanding this balance will help to develop strategies to make US agriculture more resilient and increase the security and sustainability of our bioeconomy. The project will also provide hands-on research experiences to students with no prior experience. Public outreach events will engage farmers to share the results of the research broadly. The research investigates the ecological-evolutionary dynamics of pea aphids and their parasitoid wasp, Aphidius ervi. Aphidius ervi was deliberately introduced to North America as a biocontrol agent of pea aphids, particularly to control pea aphids as pests of alfalfa crops. Pea aphids are a leading model for investigating the evolutionary and ecological consequences of symbiosis because all populations harbor heritable symbionts that provide well-documented benefits. The most common and best studied facultative symbiont, Hamiltonella defensa, confers resistance against A. ervi. Although evolutionary theory predicts that resistance traits will often be bimodal (either susceptible or highly resistant), pea aphids exhibit a full spectrum of resistance through different symbiont variants. Although the prevalences of different symbiont variants fluctuate (reflecting the intensity of parasitism and selection), the collective of symbionts across the spectrum of resistance appears to be stable. Furthermore, the ecological interactions between pea aphids and A. ervi are stable, in the sense that A. ervi is always present but abundances never get high enough to extirpate pea aphids. This ecological stability of A. ervi-pea aphid interactions may itself be the product of the evolutionary stability of the symbionts that confer pea aphid resistance to A. ervi. The research will use field experiments, lab experiments and mathematical modeling to examine both the evolutionary and ecological stability of A. ervi-pea aphid interactions, and whether this stability is generated by the interconnections between evolutionary and ecological dynamics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Variability in winds and sea surface temperature in the tropical Pacific produces the cycle of El Niño and La Niña events. These events produce both powerful storms and droughts, but their cycling is irregular and difficult to predict. The isotopic composition of oxygen preserved in fossil corals is one of the best tools scientists have for understanding how El Niño and La Niña have changed in the past. The composition is influenced by temperature but also by the salinity of seawater. Their respective influences must be separated to understand the magnitude of past El Niño and La Niña events and their impacts on the global water cycle. The proposed research combines analysis of rain and seawater, climate models, and fossil coral data to address this scientific question. The researchers will create a detailed map, or “isoscape,” showing how oxygen isotope values in seawater and rainfall vary across the modern tropical Pacific during El Niño and La Niña events. This map will be coupled with simulations from an ocean model. As a result of this work, scientists will have a more comprehensive understanding of how the intensity of past El Niño and La Niña events are recorded in coral oxygen isotope values. The proposed research will advance understanding of how El Niño-Southern Oscillation (ENSO)-related hydrologic anomalies may be inferred from oxygen isotope (delta-18O) values in tropical Pacific seawater. The researchers will utilize samples from long-running seawater and precipitation collection sites across the tropical Pacific and create a new isotope-enabled ocean reanalysis product for the Pacific basin at high spatial resolution. This combination will allow, for the first time, a direct assessment of the simultaneous isotopic anomalies associated with ENSO phases across multiple sites. The results will enable researchers to quantify the contributions of ocean circulation, atmospheric moisture balance, and precipitation delta-18O to seawater delta-18O values during different phases of ENSO. Results will also quantify seawater delta-18O and temperature influences on coral delta-18O values and reveal whether coral records of seawater delta-18O indicate stronger ENSO-related hydroclimate variability in recent decades, which is critical to inform planning for the impacts of ENSO events. The temporal continuity of the dataset, capturing ENSO phases across the basin, will enhance the community’s ability to interpret paleoclimate information of past tropical Pacific climate change. The project will support training for a graduate student, a postdoctoral scientist, and high school students. A new educational module on stable isotopes and the water cycle will be developed for 6th grade students. This module will involve hands-on learning and stable isotope analysis of local water samples, with assessment based on pre- and post-tests to measure educational outcomes and student understanding. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

Variability in winds and sea surface temperature in the tropical Pacific produces the cycle of El Niño and La Niña events. These events produce both powerful storms and droughts, but their cycling is irregular and difficult to predict. The isotopic composition of oxygen preserved in fossil corals is one of the best tools scientists have for understanding how El Niño and La Niña have changed in the past. The composition is influenced by temperature but also by the salinity of seawater. Their respective influences must be separated to understand the magnitude of past El Niño and La Niña events and their impacts on the global water cycle. The proposed research combines analysis of rain and seawater, climate models, and fossil coral data to address this scientific question. The researchers will create a detailed map, or “isoscape,” showing how oxygen isotope values in seawater and rainfall vary across the modern tropical Pacific during El Niño and La Niña events. This map will be coupled with simulations from an ocean model. As a result of this work, scientists will have a more comprehensive understanding of how the intensity of past El Niño and La Niña events are recorded in coral oxygen isotope values. The proposed research will advance understanding of how El Niño-Southern Oscillation (ENSO)-related hydrologic anomalies may be inferred from oxygen isotope (delta-18O) values in tropical Pacific seawater. The researchers will utilize samples from long-running seawater and precipitation collection sites across the tropical Pacific and create a new isotope-enabled ocean reanalysis product for the Pacific basin at high spatial resolution. This combination will allow, for the first time, a direct assessment of the simultaneous isotopic anomalies associated with ENSO phases across multiple sites. The results will enable researchers to quantify the contributions of ocean circulation, atmospheric moisture balance, and precipitation delta-18O to seawater delta-18O values during different phases of ENSO. Results will also quantify seawater delta-18O and temperature influences on coral delta-18O values and reveal whether coral records of seawater delta-18O indicate stronger ENSO-related hydroclimate variability in recent decades, which is critical to inform planning for the impacts of ENSO events. The temporal continuity of the dataset, capturing ENSO phases across the basin, will enhance the community’s ability to interpret paleoclimate information of past tropical Pacific climate change. The project will support training for a graduate student, a postdoctoral scientist, and high school students. A new educational module on stable isotopes and the water cycle will be developed for 6th grade students. This module will involve hands-on learning and stable isotope analysis of local water samples, with assessment based on pre- and post-tests to measure educational outcomes and student understanding. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

NSF

This project will test how savanna ecosystems respond to the removal of invasive species. Invasive species are introduced from outside their natural range that rapidly expand across areas where they were introduced. Invasive species negatively affect the economy and can change ecosystems in undesirable ways. Because of these negative effects, many restoration efforts involve removing invasive species. The project will test if ecosystems are resilient and can return to their original state after invasive species are removed. This project will also examine how long it takes for ecosystems to return to their original state once invasive species are removed. Both questions will be answered by experiments done in central Kenya, where an invasive ant has displaced native ants that defend Acacia trees against elephants and other browsing mammals. In invaded areas, browsing on trees is common, transforming savanna woodlands into open landscapes with few trees. Through targeted removal of the invasive ant, the project will discover whether invaded areas can be returned to their original state. Removal of invasive ants may restore the partnership between trees and native ants and reduce browsing by elephants. Across much of East Africa, Acacia trees are critical to the bioeconomy because they provide food for black rhinoceros, giraffe, and other animals. These trees are also used for fuel by humans. This project provides an opportunity to answer important questions about ecosystem resilience. Research in this system will address conservation issues that are relevant for land managers and restoration planning. This project will test the hypothesis that a foundational ant-Acacia mutualism responsible for giving rise to near monocultures of the whistling-thorn tree is resilient following the removal of the invasive big-headed ant. Invasion fronts occur along a rainfall gradient, providing an opportunity to quantify whether and under what contexts the ant-acacia mutualism is resilient to removal of big-headed ants. Specifically, this project will answer two questions: (1) following big-headed at removal, how faithfully do stability-promoting feedbacks return to approximate those from uninvaded areas (i.e., is the foundational ant-acacia mutualism resilient)? (2) does resilience hinge on time since invasion, rainfall, or both? To answer these questions, the project will employ large-scale removal of big-headed ants, assays of photosynthesis, and demographic modeling to quantify the restoration of feedback loops involving symbiotic ant activity, elephant browsing, and whole tree photosynthesis. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.