University of Pittsburgh
universityPittsburgh, PA
Total disclosed
$34,166,173
Award count
76
Distinct programs
1
First → last award
2024 → 2031
Disclosed awards
Showing 1–25 of 76. Public data only — SR&ED tax credits are confidential and not shown.
NSF Awards · FY 2026 · 2026-07
Incompressible fluid flows on curved surfaces govern a wide range of phenomena central to biotechnology, biomedical engineering, and advanced materials. Examples include biological membranes, drug-delivery vesicles, the fluid coating the air sacs in the lungs, biofilms, and fluid transport along complex interfaces. As computational modeling becomes increasingly indispensable for biotechnology innovation, biomanufacturing, and health technologies, there is a growing need for accurate and reliable simulation tools for these systems. However, existing computational methods for these surface-flow models often rely on artificial stabilization parameters that can compromise robustness and predictive capability. This project develops next-generation mathematical and algorithmic tools for simulating incompressible flows on surfaces using structure-preserving computational methods that exactly preserve key physical laws such as mass conservation. The resulting algorithms will improve the reliability and accuracy of simulations central to biotechnology research and advanced engineering applications, while reducing dependence on ad hoc numerical tuning. The research develops structure-preserving finite element methods for incompressible surface PDEs through two complementary directions. First, it constructs divergence-free and tangential surface finite element spaces based on classical Euclidean pairs such as Scott-Vogelius and adapted to surfaces using novel Piola-type mappings. These spaces exactly enforce tangentiality and incompressibility, maintain weak interelement continuity, and achieve optimal-order convergence without requiring superparametric geometry approximations. Second, the project develops a divergence-free unfitted TraceFEM for incompressible viscous surface flows using bulk divergence-free finite element pairs and a modified continuity equation to enforce surface incompressibility exactly, thereby ensuring pressure robustness and avoiding pressure stabilization while retaining the geometric flexibility of TraceFEM. These methods are designed to be accurate, parameter-free, robust, and applicable to high-fidelity simulations in biophysics, materials science, and fluid mechanics. The algorithms will be implemented in open-source software. The project will support graduate and undergraduate training, contribute to PhD dissertation work, and motivate a new graduate course on numerical methods for surface PDEs at the University of Pittsburgh. 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 Awards · FY 2026 · 2026-06
Tiny electrodes placed in the brain can help doctors treat conditions like Parkinson's disease, epilepsy, and paralysis. These devices, called brain-computer interfaces (BCIs), can let a paralyzed person move a robotic arm or speak through a computer. For BCIs to function, the tissue around the newly implanted electrode must heal and form a stable connection with it. Half of the BCIs stop functioning within a year because brain tissue around the device does not heal and becomes inflamed. Electrode insertion leaves behind cellular debris such as damaged cells, blood, and fragments of the fatty coating that wraps neurons. Brain cells have built-in cleanup systems driven by organelles inside cells called lysosomes that act as recycling centers and break down this debris. However, after an electrode is implanted, lysosomes become overwhelmed and are unable to remove the cellular debris. This causes inflammation in the brain and the contact between the electrode and the brain tissue slowly fails. This project will test a new approach that uses safe gene therapy tools to boost the brain's lysosomes and help tissue heal, enabling brain implants to last for many years. The project will also support workforce development by providing internships to Pittsburgh high school students. Further, the work will enable hands-on learning for undergraduates in bioengineering and cell biology to design better brain electrodes. The work will be disseminated on a public website with demos and articles to engage the public in understanding how brain devices work. Chronic intracortical electrodes fail in nearly half of implants within one year, limiting the translation potential of BCI and neuroprosthetics. Implantation deposits cellular debris, ruptured vasculature, and myelin fragments that overwhelm the lysosomal-autophagic clearance machinery. This process produces a feed-forward cycle of stalled debris removal, persistent neuroinflammation and oligodendrocyte loss, and progressive recording degradation. This project will test the hypothesis that lysosomal capacity is the rate-limiting step in chronic implant failure and that restoring lysosomal biogenesis, and fusion competence will resolve the clearance bottleneck and improve long-term neural interface performance. The project will map the cell-type-specific evolution of lysosomal pH, autophagic flux, and lysosomal calcium dynamics in microglia, oligodendrocytes, and neurons. Further, the team will test adeno-associated virus delivery of constitutively active transcription factor EB (TFEB) to drive lysosomal biogenesis. Finally, by combining longitudinal two-photon imaging, multiplex immunohistochemistry, and chronic awake electrophysiology, the project will dissect transient receptor potential mucolipin 1 (TRPML1)-mediated lysosomal fusion through genetic knockouts in murine models. The outcomes of this work will have a significant impact in our understanding of lysosomal sufficiency as a therapeutic axis and provide design principles for next-generation implantation technology that integrates engineering and gene therapy. 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 Awards · FY 2026 · 2026-06
This grant award provides support for the 2026, 2027, and 2028 Annual Phenomenology (PHENO) Symposia at the University of Pittsburgh, Pennsylvania, under the direction of Professor Tao Han. The purpose of the Annual Phenomenology (PHENO) Symposia is to present and discuss state-of-the-art results in theoretical and experimental particle physics; to stimulate new ideas in cutting-edge research and foster collaborations among physicists; and to encourage the participation of junior physicists and nurture their career development. In recent years, the annual PHENO conferences have been devoted, in large part, to studying the physics emerging from the Large Hadron Collider (LHC) at CERN, the European Laboratory for Particle Physics in Geneva, Switzerland, and to the connections between these experimental results and results from other collider- and non-collider-based experiments in both elementary particle physics and astrophysics and cosmology. An increasing component of the annual PHENO Symposia concerns the connections between traditional high-energy physics and cosmology and emerging disciplines such as AI/machine learning as well as Quantum Information Science. Junior physicists are especially encouraged to attend the PHENO Symposia. Indeed, a characteristic feature of the PHENO Conferences is the significant involvement of junior physicists (graduate students, postdocs, and beginning faculty) attending from many institutions in the US. As a result, the PHENO Conferences have become nothing less than the largest professional student meetings in high-energy physics in the United States. As such, this grant serves the national interest by supporting the development of a cutting-edge scientific infrastructure in the United States and the training of junior physicists to take part in the most current research developments. 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 Awards · FY 2026 · 2026-06
Embryos are masterful bioengineers, with the ability to build every organ of the body from a single fertilized egg. This process demands astonishing coordination— millions of cells taking on specialized functions in precisely the right locations— yet embryos build healthy organisms with near perfect regularity. This project aims to understand the origins of this reliability: how do embryos prevent, recognize and correct mistakes before they cause birth defects? The work will be broken up into three interconnected parts. First, the investigators will build and experimentally test a new mathematical theory to explain how embryos communicate error-free instructions to their cells. Second, the investigators will develop and deploy a new microscope technology to observe developmental errors with unprecedented depth and accuracy. Finally, the investigators will engage Pittsburgh-area high school students in experiments to determine how embryos compensate for unexpected changes in external conditions. Over the long run, this work aims to discover new principles that enable bioengineers to build replacement tissues with the reliability and precision of an embryo. Additionally, it aims to inspire the next generation of biologists by providing cutting-edge research experience to high school students. Embryos must communicate precise instructions to their cells. Clear communication is no easy feat, however. An unpredictable environment, random mutations and even noisy intracellular chemistry all threaten to derail orderly development. The principles that enable embryos to function reliably—to be ‘robust’— in the face of such unexpected perturbations remain poorly understood. This study will investigate the origins of robustness in the context of embryo patterning by the Nodal signaling pathway. In previous work, the investigators demonstrated that the zebrafish Nodal patterning system uses signaling feedback to correct perturbations. This project aims to uncover the quantitative principles underlying this correction and determine how variability in cell fate specification is resolved after patterning. In Objective 1, a new, control-theoretic model that explains how signaling feedback implements robust patterning will be formulated and tested. In Objective 2, the investigators develop and apply a new high-throughput imaging approach to measure developmental variability throughout embryogenesis. This work will enhance societal well-being and economic competitiveness by inspiring the next generation of tissue engineering strategies. Further, the high-throughput imaging approach developed in Objective 2 will accelerate the impact of AI on developmental biology and tissue engineering by making it possible to image embryos and organoids at the massive scale required to train cutting-edge deep learning models. Finally, the project will contribute to a globally competitive STEM workforce by inspiring pre-college students with engaging research experiences. 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/BIO-UKRI/BBSRC: Comparing ultrastructure measures across multiscale electron microscopies$1,065,000
NSF Awards · FY 2026 · 2026-06
Imaging biological structures across scales, from individual molecules up to complex organs is possible using electron microscopy (EM). Two EM technologies have advanced rapidly in the past decade: 1) cryo-electron tomography (cryoET), which resolves molecules inside cells at near-atomic detail, and 2) volume electron microscopy (VEM), which maps cellular architecture of tissues across millimeter scales. Used together, they could reveal how molecules are organized from cells to tissues to support essential processes and functions. However, cryoET and VEM have evolved within separate research communities supported by incompatible software and data standards. The absence of a shared framework prevents connecting observations across different scales, leaving the field unable to construct integrated, multiscale models of tissue organization. This project will develop the imaging datasets, computational tools, standardized analysis pipelines, and unified metadata framework needed to close this gap. The approach combines artificial intelligence (AI)-enabled segmentation and classification with state-of-the-art cryoET and VEM imaging of tissues of organs central to neurological, metabolic, and cardiovascular health. The project will also produce the first publicly available multiscale 3D reference image libraries for these tissues, establishing open benchmark resources for the global research community. This work will build partnerships that unite US investigators at the University of Pittsburgh with UK partners at the Science and Technology Facilities Council. Together, the findings will accelerate biological discovery; train a new generation of researchers in skills at the interface of biology, AI, and data science; and strengthen research infrastructure, contributing to American leadership in biotechnology. This research project will establish a quantitative computational framework linking ultrastructural measurements made by cryoET, serial cryo-volume EM (cryo-VEM), and room-temperature volume EM (rtVEM) of the same tissue types. Although the field has cataloged ultrastructural features at each individual scale, the correspondences between molecular-resolution and tissue-scale measurements remain largely unexplored. Four coordinated aims address this gap. Aim 1 will generate systematic multiscale 3D reference image libraries from brain, pancreas, and heart tissue, with paired stimulated and unstimulated conditions. Aim 2 will develop cryoET analysis pipelines for automated segmentation, particle detection, and geometric quantification within the established Collaborative Computational Project for Electron cryo-Microscopy (CCP-EM) framework. This will include adoption of AI-based classification and structured metadata output. Aim 3 will develop VEM analysis pipelines for consensus segmentation, feature classification, and morphometric quantification, coordinating with the Collaborative Computational Project for Volume EM (CCP-volumeEM). Aim 4 will integrate cryoET and VEM measurements for cross-scale comparisons and use this correspondence to build multiscale models that incorporate molecular-resolution detail within tissue-scale anatomical contexts. Expected outcomes include validated multiscale benchmark datasets, AI-driven analytical tools released openly through CCP-EM, and development of a potentially transformative foundation for novel multiscale structural biology investigations that integrate molecular organization and tissue-level architecture. By developing this infrastructure for the biological sciences community, the project advances NSF priorities in Biotechnology and Artificial Intelligence. This award is made possible through the NSF-UKRI lead agency opportunity. 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 Awards · FY 2026 · 2026-05
The core objective of the project will be to conduct fundamental studies to understand the process-structure-properties relationship for a groundbreaking manufacturing process that uses a complex (dusty) plasma to bond dissimilar metals. These materials that can withstand extreme service conditions, such as high temperature and corrosive environments, while retaining strength and thermal conductivity, are crucial for advanced energy and aerospace applications, including structural components for future fusion reactors and shielding materials for hypersonic aviation. The project’s outcome will be knowledge on a process that significantly reduces energy use and shortens production time in the high-throughput manufacturing of these materials. This project aims to enhance U.S. competitiveness in advanced manufacturing and, potentially, create new domestic STEM career opportunities, thereby contributing to economic and national security. The project will also strengthen the STEM workforce by engaging thirty high school science teachers from northwestern Pennsylvania in three annual hybrid summer workshops. Through these workshops, teachers will gain hands‑on experience and foundational knowledge of how electromagnetic microwaves interact with different materials. This broader‑impact effort supports STEM education and enhances public understanding of the science underlying the project’s emerging manufacturing technology. The overall objective of this research is to understand a high‑throughput, complex‑plasma‑based process for manufacturing bonded dissimilar metallic materials. In this method, stable or semi‑stable plasma generated by microwave radiation near bulk and powder metals creates thermodynamic conditions that promote strong interfacial bonding. Preliminary work shows that this process can join similar and dissimilar metals while reducing manufacturing time by two orders of magnitude and lowering the carbon footprint compared to conventional diffusion bonding. The central hypothesis is that microwave‑metal interactions generate a complex plasma containing liquid and solid metal particles that react with the substrate surface, forming both mechanical and chemical bonds. The first research aim is to study how material parameters, including metal types (ferromagnetic, paramagnetic, and diamagnetic), their apparent density and geometry (shape and size), together with process parameters, including the radiation time and power of a multi‑mode 2.45 GHz microwave, affect the radiation‑induced electrical discharge required to sustain the complex plasma. Building on the findings from the first research aim, the second aim is to investigate the process–structure–property relationships for the dusty‑plasma‑based joining process. For the second aim, the work will focus on studying the formation, microstructure, and impression‑creep behavior of the interface between similar and dissimilar metals joined via microwave‑assisted bonding. 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 Awards · FY 2026 · 2026-05
This award supports participation of US-based researchers in the international workshop on Nonlinear Partial Differential Equations and Stochastic Methods held June 9-12, 2026 at the University of Jyväskylä, Finland. Partial differential equations (PDE) and stochastic analysis, including stochastic games, are the foundational mathematical pillars for artificial intelligence and machine learning. This project contributes to the education of the next generation of US-based research mathematicians in the theory and applications of nonlinear PDE, including regularity, homogenization, and data science. In addition to the research presentations, there will be several background lectures aimed at graduate students and other early-career researchers. The award will help cover the travel expenses of graduate students and postdoctoral researchers from institutions in the United States. The local expenses of US-based participants supported by this project are covered by the local organizers at the University of Jyväskylä. The themes of the workshop are nonlinear elliptic and parabolic equations, homogenization, stochastic games methods in PDE, as well as applications to data analysis and machine learning. For example, semi-supervised learning can be articulated and analyzed with the help of discrete PDE on graphs. In addition, the theoretical underpinnings of data science and machine learning are becoming increasingly relevant, as these are foundational pillars for artificial intelligence applications and machine learning. Information about the workshop is available at https://www.jyu.fi/en/events/workshop-on-nonlinear-pdes-and-stochastic-methods. 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 Awards · FY 2026 · 2026-05
Sensors with high resolution and detection capabilities have the potential to transform applications in many facets of Americans' lives, including enabling new cancer screenings, earthquake early warnings, and expanding the lifetime of next-generation aircraft. Advances in these areas can be enabled by nonlinear dynamic behavior—sharp state transitions, threshold sensitivity, and multi-stable response that exceed what linear designs can achieve. While decades of research have produced deep understanding of these phenomena, the corresponding design question remains open: given a desired nonlinear response, how should a system be configured to produce it? This Faculty Early Career Development Program (CAREER) grant supports research answering this question by establishing mathematical and computational foundations for bifurcation engineering—the systematic design of the qualitative transitions governing when systems switch equilibrium states, lose stability, or exhibit the sharp responses central to precision measurement and control. By converting nonlinear device development from a specialist craft into a transferable methodology and providing open-source tools, this research advances the national health, prosperity, and welfare by accelerating innovations in environmental monitoring, medical diagnostics, and infrastructure resilience. Integrated with these research activities, this grant supports educational initiatives engaging K-12 students and the general public through science center and library exhibits, enriching undergraduate and graduate curricula with nonlinear design methods, and broadening participation in STEM through layered mentorship spanning multiple educational levels. Although powerful tools exist for characterizing nonlinear dynamical systems, they have not yet been extended to the inverse problem of designing systems that achieve specified response characteristics. Doing so requires overcoming interrelated challenges: responses depend sensitively on parameters, undergo qualitative changes at critical parameter values, and involve multiple coexisting solutions whose selection depends on history. This research develops a unified framework for inverse design via bifurcation engineering, organized around three thrusts. The first formulates mathematical representations treating bifurcation locations, types, and stability properties, as well as overall response curve shape, as explicit design objectives within continuation-based optimization. The second extends sensitivity analysis to solution families defined implicitly as curves and surfaces in parameter space, enabling efficient gradient-based tailoring of dynamic response to engineering specifications. The third develops shape-aware metrics based on differentiable time-series alignment and graph neural networks for quantifying response similarity when exact point-by-point matching is neither achievable nor physically meaningful. Contributions will be validated through numerical implementation and experimental demonstration of optimization and system identification tasks on microelectromechanical resonator systems and aeroelastic structures. The resulting open-source tools and design principles apply broadly to energy harvesting, neuromorphic computing, and any engineered system whose performance depends on nonlinear dynamic behavior. 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 Awards · FY 2026 · 2026-03
Despite significant public investment, innovations arising from early-stage discovery research often fails to reach the market, limiting their potential societal and economic impacts. While existing federal programs have improved aspects of the innovation pipeline, persistent systemic barriers remain. These translational "leaks" stem from complex challenges in technology transfer, commercialization pathways, inter-sector coordination, and a lack of appropriately targeted funding mechanisms. Addressing these gaps in the research-to-translation pipeline is critical to preventing promising discoveries from stalling before they reach real-world use. By identifying and closing gaps in areas such as industrial engagement, standards readiness, workforce capacity, and regulatory alignment, stakeholders can accelerate adoption and improve the return on public research investments. The workshop, Gaps and Barriers to Translating Research to Practice, examines three stages of the early-stage, discovery-driven innovation lifecycle. The workshop first examines mechanisms to incentivize academic and non-profit researchers to consider market needs early in their process, with the goal of increasing their participation in commercialization activities. Next, the workshop seeks approaches for proactive technology curation to facilitate investment in the de-risking required to bridge the gap between basic research and commercial viability. Finally, the workshop evaluates traditional technology transfer models and proposes alternative approaches to reduce commercialization barriers. This systems-level approach treats the innovation process as non-linear, interconnected steps rather than a series of silos. The two-day workshop gathers diverse experts from academia, government, and industry to move beyond problem identification and collaboratively devise actionable solutions for the entire lab-to-market pathway. 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 Awards · FY 2026 · 2026-02
The Workshop on Harmonic Analysis and Partial Differential Equations is a three-day research conference hosted by the Department of Mathematics at the University of Pittsburgh on November 14-16, 2025. The workshop is bringing together researchers at various career stages working at the intersection of harmonic analysis, geometric measure theory, and partial differential equations. The event aims to highlight recent advances in the field, foster new collaborations, and stimulate scientific exchange. This award supports the travel expenses for graduate students and other early-career participants from universities across the United States. The website for the meeting is: https://sites.google.com/view/hapdes-workshop/home. The workshop focuses on recent developments at the intersection of harmonic analysis, geometric measure theory, and partial differential equations, with particular emphasis on applications to elliptic partial differential equations. The program features invited lectures by leading experts alongside presentations by early-career researchers and includes a research poster session devoted to highlighting recent work by early-career participants, thus enabling their full participation in the scientific program. 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 Awards · FY 2026 · 2026-02
As famously stated by the Nobel laureate Richard Feynman: “…turbulence is the most important unsolved problem of classical physics….” This statement is still true today despite more than a century of research devoted to turbulence. The complicated structure of turbulent flow at small and large scales makes analysis of turbulence notoriously difficult. This proposal explores whether quantum mechanics can provide an effective framework for addressing this classical problem. The project will adapt two methods – tensor networks and analog quantum simulators - that have been used in quantum mechanics for use in computational fluid dynamics. A variety of challenging turbulent flows will be simulated, and results will be compared with those obtained using classical computational methods. The research will be integrated with education and industrial collaborations to help establish a self-sustaining ecosystem to accelerate the development of quantum technologies to solve classical problems. To leverage hybrid quantum-classical computing for addressing the complex problem of turbulence, the research will proceed along two parallel directions. First, tensor network methods will be implemented to classically simulate flows as governed by the Navier-Stokes and Fickian-Fourier reaction-convection-diffusion equations. When the classical computational complexity becomes prohibitive, the tensor networks will be uploaded to digital quantum computers, where variational quantum algorithms will be utilized. Second, an analog quantum solver based on the Koopman-von Neumann formalism will be developed to encode nonlinear partial differential equations into interacting bosonic systems. The solution of these equations will be extracted from measurements of the bosonic degrees of freedom. This approach is promising for solving the Navier-Stokes equations. Simulations of reacting flows spanning a broad range of Reynolds, Péclet, Mach, and Damköler numbers will be conducted. The extent to which the hybrid methods yield quantum advantage will be systematically assessed. 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 Awards · FY 2026 · 2026-02
Turbulent motion of fluids appears in many important settings, including weather systems, ocean currents, aircraft flows, wind energy, and industrial mixing. Turbulence looks extremely complicated with swirls of many different sizes. This project addresses a fundamental puzzle: why does violent, intense turbulence often result in little net energy transfer between swirls of different sizes? The reason is that energy does not move one way. Instead, it moves forward and backward between large and small swirls, resembling a tug-of-war where both sides pull hard, but the rope barely moves. The detailed mechanisms of energy transfer are not captured in simplified statistical tools often used to study turbulence. By analyzing large amounts of data from lab experiments and computer simulations with data-enabled learning, this research will uncover the hidden rules that control this balance. The results will help build better models for predicting weather and designing safer engineering systems. The project will also train students in engineering, data science and physics, and provide free software tools to the public. The project will support the use of AI and machine learning in fluid dynamics and will benefit advanced manufacturing of transportation vehicles. Current turbulence theory relies on simplified statistical tools, leaving the mechanisms of energy transfer across scales only partially understood. To address this critical gap, this project develops a data-enabled, physics-guided framework to uncover and model the processes controlling the cascade. The research focuses on two fundamental but unresolved phenomena: "self-competition," where strong physical-space advection paradoxically suppresses scale-to-scale energy transfer, and "weak asymmetry," where intense forward and backward flux events nearly cancel to produce a weak net cascade. The overarching goal is to quantify these mechanisms and translate this physical understanding into improved predictive models for Large Eddy Simulation. To achieve this, the project will analyze large, time-resolved datasets from three-dimensional Direct Numerical Simulations and high-resolution two-dimensional laboratory experiments. The methodology employs advanced data-driven diagnostics to identify the origins of the net energy flux. These insights will then be operationalized in a diagnostic-aware spatio-temporal Graph Neural Network framework to create accurate, interpretable subgrid-scale closures. Results will reveal a mechanistic understanding of “self-competition” and “weak asymmetry” phenomena and provide a principled pathway to regularize turbulence models. The project will produce open software and curated datasets, train graduate and undergraduate students at the interface of physics and data science and deliver transferable methods for other complex multiscale systems in engineering, physics, and beyond. 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.
- ENG-SEMICON: Quantum inspired ab initio simulation of thermal transport near heterojunctions$449,998
NSF Awards · FY 2025 · 2025-12
A major challenge in designing modern semiconductor devices is removing heat they generate during routine operations. Heat accumulation reduces device performance, shortens its lifespan, and increases the energy required for cooling. This project will examine heat accumulation near “heterojunctions,” which are tiny nanometer-scale regions where different materials connect to each other. There is an extra thermal resistance at heterojunctions, which makes removing heat there especially difficult. Simulation tools are often used to analyze the motion of heat-carrying particles, but these tools are not sufficiently accurate to describe heat transfer at heterojunctions. This project will develop a new simulation tool inspired by methods from quantum mechanics. By providing a more accurate prediction of heat transport at the nanoscale, this research will enable the design of more powerful, durable, and energy efficient semiconductor devices. The project will also include undergraduate research programs, which will help train the future workforce in applying quantum methods to conventional modeling and simulation. The central goal of this research is to develop and validate a novel computational framework for solving the Boltzmann transport equation with high predictive power. The Boltzmann transport equation accurately describes the transport of heat carrying particles, but its high-dimensional nature has traditionally made it computationally prohibitive to solve without significant simplifications. This project addresses this “curse of dimensionality” by employing a quantum algorithm that can efficiently compress the solution space of the Boltzmann transport equation. A significant reduction in computational cost is expected, making it feasible to use energy dispersion and scattering matrices from first principles, and thereby enabling the high-fidelity simulation. The framework will then be applied to uncover the fundamental aspects of thermal transport in power transistors. The research will focus on the detailed energy transport processes among different heat carriers near the heterojunction, with the ultimate goal of developing new engineering strategies for improved thermal management of electronic devices. 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 Awards · FY 2025 · 2025-12
This REU site will train undergraduate students in the learning sciences, an interdisciplinary field that aims to translate knowledge on the science of learning into educational practice. Training in an interdisciplinary research context provides a unique opportunity to learn about complementary perspectives and approaches to address scientific challenges to understanding human learning and how to facilitate it in educational contexts. The site is housed within a large interdisciplinary center that brings together multiple disciplinary fields, including psychology, computer science, artificial intelligence, and education, with the ultimate goal of translating scientific knowledge into educational practice and advancing learning technologies. This REU will provide formative opportunities to gain direct experience alongside faculty experts conducting leading-edge learning research in an interdisciplinary environment. REU students will work alongside faculty, research staff, graduate students, and postdoctoral fellows to identify and co-create research projects. They will generate their own research questions, develop hypotheses, conduct coding and data analytics, interpret data, and disseminate and present the findings at a research symposium. This work will be scaffolded through training activities, including learning science and professional development workshops, and meetings with the co-directors, lab group, primary faculty mentor, and external mentors. Our strengths-based training program is based on the cognitive apprenticeship model of science and scholarship and community mentorship. Students will participate in a series of workshops that provide an overview of the theoretical frameworks and approaches of the learning sciences and professional development seminars to support the students' educational and career trajectories. This REU will establish a community of practice aimed at fostering innovation and advancing discoveries in the learning sciences. 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 Awards · FY 2025 · 2025-11
Deep inside every drop of water lie tiny signatures from rare forms of hydrogen and oxygen, known as isotopes. These isotopes contain different numbers of neutrons and act like nature’s recorder, revealing where water vapor came from and how it traveled across the globe and formed precipitation. Sensitive to both temperature and humidity along their pathways, these isotopes are stored in natural archives such as ice cores, lake beds, and cave formations. Scientists can read them like time capsules, unlocking stories of Earth’s past climate: how hot it was, how much it rained, and how climate patterns shifted over thousands of years. These records also help scientists evaluate and improve water cycles in climate models, offering insights into how our planet may change in the future. However, adding isotopes into today’s complex climate models requires cutting-edge scientific and engineering expertise and vast amounts of computing power. The goal of this project is to build a smart shortcut based on machine learning: an “emulator” that can predict water isotope patterns from climate variables in existing climate simulations quickly and efficiently. This is a powerful step forward for climate science, hydrology, and understanding our planet’s past and future. The project fosters interdisciplinary collaboration between climate scientists and AI experts. Its success could lead to new ways of modeling other passive tracers in the Earth system. The project products such as code and data will be open to the community, and results will be shared through university courses, training programs, and K-12 outreach at NSF NCAR, Pitt, and UMD. Using simulations from fully-coupled global climate models (GCMs) with isotope capabilities, such as the isotope-enabled Community Earth System Model (iCESM1), this project aims to build a machine-learning-based emulator that learns a mapping from climate fields to water isotope fields. This mapping can then be applied to other GCMs that lack built-in isotope capabilities, enabling cost-efficient generation of isotopic outputs. Scientifically, the project will improve understanding of the leading drivers of isotopic variability, enhance model–data comparison using both modern and paleoclimate observations, and support isotope-enabled climate model development. It also contributes to ongoing (paleo)climate data assimilation efforts in the broader community, where the lack of isotopic prior simulations has been a limiting factor. 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 Awards · FY 2025 · 2025-10
This project will realize nanoscale amplifier devices tailored for the rapidly advancing quantum technology. These amplifiers will work in the microwave frequency range where quantum devices are typically operated. Quantum parametric amplifiers are prominently featured in applications such as quantum-limited detection, as well as coupling of distant quantum circuits. The amplifiers will be built out of a combination of superconductor and semiconductor materials and will use nanowires as their core elements. The project will improve the nanowire growth to attain defect-free, epitaxial growth which is believed to directly translate into the performance of quantum devices. The amplifiers will be compatible with large magnetic fields which will open their use in several quantum technologies such as quantum dot spin qubits and prospective topological qubits. This project will support a collaboration between researchers in the United States and France that will both explore and enhance the potential of nanowire-based devices for quantum information science. The project will design, create, and characterize nanowire-based quantum-limited nonlinear quantum circuits such as parametric amplifiers that leverage the unique features of the hybrid materials platform. The devices will offer unique operational advantages such as large gate-tunability exceeding 1 GHz, gains of up to 20 dB, dynamic bandwidth of order 40 MHz, and magnetic field compatibility up to 1 Tesla. The applications of these devices include pump-efficient quantum-limited amplification, as well as potential use in novel two-qubit gate schemes. Magnetic field compatibility offers opportunities for integration into spin qubit and future topological quantum computing platforms. Device design will be based on the unconventional Josephson effects such as non-inversion symmetric current-phase relations. Intrinsic spin-orbit interaction and large effective Landé g-factors in InAs will be used to induce strong third-order nonlinearities in Josephson inductive elements, realizing in a single junction the equivalent of quantum circuits such as the Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL). 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 Awards · FY 2025 · 2025-10
This research project will deliver tools to obtain accurate and broad statistical conclusions from data that are subject to privacy constraints. Differential Privacy is an increasingly adopted technique to protect data within government and industry, such as in the US 2020 Decennial Census. However, privacy protection comes at a cost in terms of accuracy of the analysis run on these data, sometimes drastically affecting the decisions and conclusions that entail. While employing and training graduate students from diverse backgrounds, this project will use computer-simulation techniques to tackle a wide range of statistical tasks under these privacy settings. The increased accuracy from these new tools will allow for the wider adoption of Differential Privacy and increase the possibility of sharing data with reduced risks of privacy violations. This will guarantee broader access to essential and reliable information for decision-making bodies as well as for researchers in the social sciences and other fields of academic research. Results will be disseminated through a series of publications in journals and conference proceedings in the fields of statistics and computer science, as well as through presentations at national and international scientific conferences and workshops. Open-source software packages will be developed and made available to the broader community. This research project will deliver both theoretical and practical tools for the advancement of statistical approaches in complex parametric settings such as those entailed by the added noise of Differential Privacy mechanisms. Differential Privacy protects the private information of individuals included in the data by introducing calibrated noise (randomness) into the data. The idea behind this mechanism is that even a highly informed attacker/hacker will not be able to detect whether changes in outputs are due to a particular individual's response or are simply due to randomness. However, these noise-addition techniques also introduce additional bias and variance into the analyses made by researchers who will want to use these data for the advancement of knowledge in government, industry, and academia. This project will deliver more accurate analytical techniques by relying on simulation-based statistical methods, such as co-sufficient sampling and indirect inference. While preserving the same level of privacy, this approach will take into account the noise mechanisms used to privatize the data. The tools to be developed will improve estimation and statistical inference on noisy privatized data by correcting bias of estimators and delivering reliable confidence intervals and hypothesis tests for a wide range of statistical methods. The project will establish some of the first links between statistical privacy and simulation-based inference techniques and will expand the field of robust statistics. 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.
- Collaborative Research: DMREF: NSF-BSF: Moire-Engineered Oxide Membrane Heterostructures by Design$480,000
NSF Awards · FY 2025 · 2025-10
Non-technical description: Twisted oxide heterostructures are artificial materials made by stacking two or more complex oxide thin layers on top of each other with a twist angle — meaning one layer is rotated relative to the other. This twist creates a moiré pattern at the interface — a repeating interference pattern that changes the local atomic arrangement and the electronic environment. This can dramatically alter the material’s properties and create novel functionalities useful for applications. This Designing Materials to Revolutionize and Engineer our Future (DMREF) project aims to design, create, and understand novel electronic, magnetic, and structural phases emerging in free-standing oxide membranes assembled into twisted heterostructures. The research combines advanced characterization techniques with theoretical modeling and data analytics to accelerate the discovery and development of new materials with engineered properties. The project leverages an iterative feedback loop between theory, synthesis, and characterization and involves the U.S.-Israel collaboration supported by Binational Science Foundation (BSF). Educational and outreach activities within this project are targeted at advancing workforce development through interdisciplinary training of graduate students and postdoctoral researchers in integrated experimental and theoretical approaches to materials research. Technical description: This DMREF project aims to explore fundamental phenomena emerging in oxide moiré heterostructures, including structured two-dimensional polarization-vortex crystals, topological spin textures at twisted oxide interfaces, oxide flat-band systems at large twist angles, coupled quantum dot arrays, and dynamically strained interfacial electron and hole gases. The project introduces moiré periodicity and modulated intra-moiré-cell atomic registry as new design parameters in thin-film oxides. The strong interlayer coupling in oxide systems generates a strong periodic potential, enabling robust quantum states and new physical phenomena through the interplay between intrinsic oxide properties and moiré-engineered periodicity. The research combines state-of-the-art theoretical modeling approaches, advanced synthesis techniques for creating oxide membranes, and unique characterization methods, particularly Quantum Twisting Microscopy, which enables momentum-resolved spectroscopy with nanoscale spatial resolution. The education/outreach component of this project includes DMREF Workshops providing training experience for students and postdoctoral researchers, collaboration with secondary school teachers from Puerto Rico and Wisconsin to develop teaching modules incorporating DMREF principles, and integration of the undergraduate research with a First Experiences in Quantum program. 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 Awards · FY 2025 · 2025-09
This project aims to advance student engagement and achievement in high-enrollment STEM courses by substantively improving and evaluating CourseMIRROR, a mobile learning environment that delivers real-time, AI-guided reflection support. Powered by state-of-the-art natural language processing, CourseMIRROR prompts learners to reflect on what interests or confuses them, provides immediate feedback that spurs deeper thinking, and compiles class-wide insights for instructors. Partnering with universities and community colleges, the project reaches hundreds of students each semester and equips faculty with scalable, evidence-based practices that require no extra grading. By expanding access to effective study strategies and informing national priorities in AI-enabled education, the goal is to have broad benefits for retention and workforce readiness in science and engineering. Guided by the Reflection-Informed Learning and Instruction model and a Self-Regulated Learning (SRL) theory of change, the research pursues three integrated aims. First, adaptive prompts, motivational nudges, and automated reflection summaries are engineered and optimized through iterative usability and feasibility tests. Second, the effects of these features on motivation, emotion, SRL processes, and course performance are explored through field experiments across multiple introductory courses at multiple institutions. Third, multimodal data, including Motivated Strategies for Learning Questionnaire subscales, fine-grained app logs, micro-analytic interviews, and graded assessments, are analyzed with multilevel models and structural-equation mediation tests to determine whether SRL gains explain achievement improvements. The multidisciplinary approach bridges natural language processing, human-computer interaction, and learning sciences, yielding transferable design principles for AI-enabled educational tools and aims to open new research directions at the intersection of emerging technologies and STEM learning. 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 Awards · FY 2025 · 2025-09
The final stages in the evolution of the most massive stars play a crucial role in astrophysics, injecting energy and enriched metals into the interstellar medium, and producing compact objects – neutron stars, black holes, and the wide range of transient phenomena associated with them. The predictive power of theoretical models for massive stars, however, is severely limited by the large uncertainties associated with this regime of stellar evolution. The project will constrain some of the most uncertain processes in massive stellar evolution, such as the efficiency of mass loss and the impact of supernova kicks. This project will develop new tools that can maximize the science extracted from the wealth of data on resolved stellar populations and object catalogs that will be available in the coming decade with the advent of facilities, like the Vera C. Rubin Observatory. The project will also broaden the impact of the research through a mixture of new and well-established outreach projects designed to foster engagement by educators and students in science. The spatially resolved stellar populations in Local Group galaxies will be used to place unprecedented constraints on the evolution of the most massive stars. To this end, the investigators will precisely measure the formation efficiencies and evolutionary timescales (i.e., the delay time distributions, or DTDs), for the main outcomes of massive stellar evolution: Wolf-Rayet and Intermediate Mass Stripped Stars, Blue, Yellow and Red Supergiants, X-ray Binaries, and Supernova Remnants. The investigators will model each of these DTDs using the state-of-the-art population synthesis code COSMIC. A systematic comparison between measured DTDs and COSMIC predictions will therefore constrain some of the most uncertain processes in massive stellar evolution, such as the efficiency of mass loss, the effects of the common envelope phase, and the impact of supernova kicks. These constraints will provide a new level of detail in our ability to trace and quantify the energetics and enrichment from the progenitors of many astrophysical transients and gravitational wave sources. 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 Awards · FY 2025 · 2025-09
Many natural microorganisms, such as bacteria and fungi, can be used to degrade toxic pollutants and remediate contaminated sites. These microorganisms use a series of enzymes, called cascade enzymes, to break down pollutants step by step into less toxic end products. However, this process is slow and often allows toxic intermediates to accumulate. The goal of this CAREER project is to make biodegradation more efficient. The project will develop a new biotechnology, called protein nano-compartment (PNC)-based cargo encapsulation. Cascade enzymes will be encapsulated within PNCs, which will enable the enzymes to degrade pollutants and intermediates at similar rates. Toxic intermediates will not accumulate in the environment. The research will be integrated with education of students from middle schools and colleges. Successful completion of this project will create a more efficient, robust, and faster environmental remediation technology to protect human and environmental health. This CAREER project plans to apply PNC-based enzyme co-localization to accelerate biodegradation efficiency in removing organic water contaminants. The central hypothesis is that attaching enzymes with affinity tags of varying molecular properties will allow their tunable co-localization within PNCs, thereby enabling optimization and enhancement of the kinetics and stability of enzyme cascades for contaminant degradation. The study will integrate techniques in biodegradation, synthetic biology, and metabolic flux analysis to systematically characterize the effect of PNC co-localization on enzyme cascade efficiency. The proposed work will establish quantitative correlations between affinity tag properties and enzyme encapsulation efficiency. Building on these correlations, the study will explore how to strategically control the co-localization of biodegradative cascade enzymes within PNCs and analyze how this co-localization affects their kinetics in contaminant removal and stability against environmental factors under controlled in vitro conditions. Lastly, the PNC co-localization of biodegradative cascade enzymes will be assessed under cellular environments, and isotope-labeled metabolic flux analysis will be employed to develop a fundamental understanding of how the in vivo co-localization affects the rate, flux, and specificity of organic contaminant biodegradation in cells. The project includes an education plan aiming to 1) foster the education of college students in STEM and their participation in environmental engineering; 2) educate and train next-generation environmental engineers on the fundamentals, real-world applications, and opportunities of PNC encapsulation and biodegradation; and 3) promote public awareness and understanding of biodegradation as a sustainable solution for environmental protection and remediation. These educational activities will be integrated throughout to improve academic success and broaden participation of college students in research, stimulate STEM interest in 6-12 graders, train a future workforce on biodegradation through research projects, and build a biodegradation website for public education and outreach. 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 Awards · FY 2025 · 2025-09
This three-year REU Site, Particle-Based Functional Materials for Energy, Sustainability, and Biomedicine, will support ten undergraduate students each summer (2026-8) in a ten-week immersive research experience. The program recruits students from institutions with limited research opportunities – particularly those majoring in engineering, chemistry, physics, or mathematics – who are interested in exploring research as a pathway to graduate studies. Participants (REU Fellows) will join engineering research groups and conduct independent projects that deepen their disciplinary knowledge while developing the ability to integrate concepts across fields. In addition to hands-on research, fellows will engage in structured professional development activities designed to strengthen their communication skills, understanding of research ethics, career planning, and their growth mindset. Modern scientific and engineering breakthroughs increasingly occur at the intersection of disciplines – particularly in biomedicine, sustainability, and energy. This program centers on Particle-Based Functional Materials (PFM), an interdisciplinary domain that involves both computational and experimental studies of materials designed to perform specific functions. These functions arise from the intrinsic properties of particles or the influence of particles on larger material structures. PFM applications are broad and impactful, encompassing self-healing materials, controlled therapeutic delivery, smart catalysis, and advanced particle separations, among others. This program prepares students to navigate these cross-cutting areas, emphasizing the need for future engineers to be nimble thinkers capable of working across traditional disciplinary boundaries. The PFM REU Site is grounded in the belief that future success in engineering and science requires both technical expertise and the ability to synthesize knowledge across domains. To cultivate these skills, this program integrates traditional research experiences with a customized workshop series that emphasizes knowledge integration and mindset development. By blending technical training with professional growth, the team aims to prepare students not only for graduate education but also for leadership in a rapidly evolving technological landscape. 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.
- Collaborative Research: Building AI Models to Help Middle School Students Interpret Science Diagrams$299,990
NSF Awards · FY 2025 · 2025-09
Representations such as diagrams, graphs, and charts are central to science and science education. However, learners often struggle with how to interpret science representations. The goal of this project is to develop, implement, and test a new AI assistant, the Representational Reasoning Assistant (RRA), to help middle school students interpret representations in their science classrooms. The AI assistant will draw on cutting edge Generative AI technologies to engage learners in conversations about the representations assigned by their teachers, ask the learners guiding questions, and offer suggestions about where to look in order to make sense of the representations. A key component of the design is to enable teachers to modify the AI assistant easily based on knowledge of their students and on the tasks which they set as priorities for their students. The project will help advance interdisciplinary research and practices in AI, computer science, learning sciences, and STEM learning. Throughout the three years of the project, teachers and students will be recruited from urban, suburban, and rural schools. The sequence of research and development activities reflects an integrated effort between the learning sciences and computer science teams. The project consists of iterative cycles of exploration, development, pilot and model refinements of the AI assistant, focusing on the types of representations teachers use in science activities and the types of feedback they give to students. Multimodal Large Language Models (MLLMs) will be adapted to be visually focused, supportive of pedagogical intent for young learners, and include innovations in rapid training to support a wide range of classroom topics and contexts. Early rounds of the piloting will gather teacher feedback on initial models and versions of the AI assistant. The AI assistant interface will then be fine-tuned based on teachers and students' feedback as well as measurements of students' engagement and learning. 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 Awards · FY 2025 · 2025-08
The 17th International Workshop on Bio-Design Automation (IWBDA) brings together researchers from electronic design automation and synthetic biology to tackle challenges in biology and medicine. Electronic design automation is the practice of using computer software to build complex electronics and synthetic biology is the forward design of novel biological systems using engineering principles. The goal of IWBDA is to make biology more easily, robustly, reliably, and predictably engineered which will lead to advances in biology and medicine including advances in disease diagnosis, treatment and prevention. The topics that IWBDA covers include design methodologies for synthetic biology, standardization of biological components, biosecurity in lab automation processes, bio-preparedness through bio-design automation, artificial intelligence and machine learning in synthetic biology, computer-aided design tools and automation for engineering biology, biofoundries and their impact on synthetic biology, synthetic biology education and outreach. This award provides travel assistance for ten undergraduate and graduate students to attend this workshop to present research, participate in a computer programming competition, and network with a large community of industrial and academic researchers. The supported students will go on to form the foundation of the field in the future and strengthen the US biotechnology industry. IWBDA 2025 takes place in Worcester, Massachusetts from September 7th to September 10th. The students supported will join a variety of researchers from electronic design automation and synthetic biology, engaging in activities that do not exist elsewhere. They will have access to between twelve and fifteen technical talks over three days, two invited lectures, ten to twenty posters, multiple group discussion sessions, and a featured student programming competition (BDAthlon). 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 Awards · FY 2025 · 2025-08
Plants associate with beneficial bacteria that help protect them from pathogens and facilitate nutrient uptake. As a result, they have the potential to supplement pesticides and fertilizers for use in agriculture. However, attempts to use beneficial bacteria in agriculture have had limited success, often due to poor survival of introduced strains. This project will enhance our understanding of the ecological, molecular, genetic, and genomic mechanisms that make some beneficial bacteria strong colonizers of plants and the mechanisms by which they protect plants from pathogens. The project will use synthetic microbial communities consisting of closely related plant-beneficial and pathogenic strains of bacteria, coupled with genetic and genomic approaches to find the molecular mechanisms that allow some beneficial microbes to successfully colonize plants and exclude pathogens. The use of established microbial communities, genome-sequenced community members and high throughput assays will enable rapid screening of many combinations of microbes. The project will also provide training opportunities for a breadth of career stages including graduate students and postdoctoral fellows, as well as undergraduate students through course-based research experiences. With the rise of emergent pathogens, understanding the mechanisms by which bacteria facilitate or prevent disease will aid in rapid and cost-effective solutions. Microbiome community engineering has proven difficult, in part, due to priority effects where existing communities result in poor invasion of introduced strains. The goal of this project is to facilitate understanding of the molecular, ecological, genetic, and genomic mechanisms that allow or prevent microbial community invasion. The project uses synthetic communities to understand the mechanisms that allow beneficial strains to exclude pathogens and invade a community via three objectives that query the molecular and genomic rules driving priority effects and microbial community assembly. First, strains that show strong priority effects and strains that can invade a community will be identified to determine the ecological and genomic features that contribute to priority effects. Comparative genomics will then be used to identify genes and traits that allow or prevent community invasion. Second, mechanisms by which a beneficial strain can exclude a closely related opportunistic pathogen will be examined using a pathogen-beneficial strain pair. A genetic screen will be used to identify novel genes required for plant colonization and pathogen exclusion. Genes essential for pathogen exclusion will be identified and tested in the presence of complex synthetic communities. Finally, genetic strategies for community invasion and overcoming priority effects will be engineered by building a Pseudomonas fosmid library containing large inserts representing the Pseudomonas pan-genome and iteratively passaging engineered P. fluorescens on roots of pathogen-infected plants. Collectively, these objectives will reveal the mechanisms by which communities exclude invaders and allow a beneficial strain to compete with an existing community. 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.