Khasawneh F.A.,SUNY Polytechnic Institute |
Munch E.,University at Albany
Mechanical Systems and Signal Processing | Year: 2016
This paper describes a new approach for ascertaining the stability of stochastic dynamical systems in their parameter space by examining their time series using topological data analysis (TDA). We illustrate the approach using a nonlinear delayed model that describes the tool oscillations due to self-excited vibrations in turning. Each time series is generated using the Euler-Maruyama method and a corresponding point cloud is obtained using the Takens embedding. The point cloud can then be analyzed using a tool from TDA known as persistent homology. The results of this study show that the described approach can be used for analyzing datasets of delay dynamical systems generated both from numerical simulation and experimental data. The contributions of this paper include presenting for the first time a topological approach for investigating the stability of a class of nonlinear stochastic delay equations, and introducing a new application of TDA to machining processes. © 2015 Elsevier Ltd. Source
Agency: NSF | Branch: Continuing grant | Program: | Phase: INSTRUMENTAT & INSTRUMENT DEVP | Award Amount: 399.69K | Year: 2015
An award is made to the University at Albany (SUNY) and several collaborating organizations, including two other SUNY campuses (SUNY Polytechnic Institute and SUNY College of Environmental Science and Forestry) and Boston University, to construct and test an aphid-like nanobiosensor whose purpose is to enable real-time monitoring of sugars in living plant tissues. Graduate and undergraduate students will participate in the development of NANAPHID technology. The results obtained in the process of NANAPHID development will be disseminated to the community through lectures, student laboratory exercises and field trips. The project will include a unique Website used to broadcast webinars addressing NANAPHID design, its capabilities, and the latest research results. The NANAPHID will make routine measurements of sugars that will benefit many biological research communities including plant ecologists, investigators at NSF-funded Long Term Ecological Research (LTER) sites, and scientists involved in a broad range of experimental and modelling studies of terrestrial carbon cycling. Applications in crop plant research and management are also promising. For example, the sensor has the potential to replace refractometry as the method of choice for volumetric analysis of sugars.
Non-structural carbohydrates (NSCs) are the currency of energy and growth allocation within plants. These products of photosynthesis are circulated as soluble sugars, whose concentrations are estimated using destructive analytical techniques that have difficulties distinguishing sugars in plant sap from associated cellular materials that get mixed into samples. NANAPHID technology will make real-time in situ measurements of NSC using concentrations in stems, roots, and branches and provide biologists with many new opportunities to monitor critical changes in resource allocation in plants. Tracking these changes in living plants is necessary for directly testing the effect of many environmental changes such as climate, diseases, atmospheric nutrient loads, and acidic deposition.
Agency: NSF | Branch: Standard Grant | Program: | Phase: CDS&E-MSS | Award Amount: 93.11K | Year: 2016
Objects whose state changes over time, known as dynamical systems, describe a large number of natural and engineered processes; therefore, developing a deeper understanding of their behavior is of great importance. While sometimes it is possible to derive mathematical models that describe the evolution of a dynamical system, these models are almost always an abstraction of the physical system and, therefore, have a limited ability to predict how the system will change in time. Further, when the system under investigation is large or too complicated with several factors influencing its behavior, it may simply be impossible to describe the system with the corresponding descriptive equations. Consequently, in the absence of adequate analytical models it becomes necessary to instrument the dynamical system with sensors and use the resulting data to understand its characteristics. Specifically, the change in the state of a dynamic system is often governed by an underlying skeleton that gives the overall behavior a shape, and thus the shape of the skeleton directly governs the system behavior. Most of the time, this shape of the underlying skeleton is unknown and can be easily masked by the complicated and rich system signals. The emergent field of topological data analysis (TDA), a branch of mathematics that quantifies the shape of data, is capable of revealing information that is invisible to other existing methods by providing a high level X-ray of the skeleton governing the dynamics. However, the information-rich structures provided by TDA still need to be interpreted in order to classify the dynamics and predict future outcomes. To accomplish this, the principal investigators will leverage ideas from machine learning, a field of study that investigates algorithms that can learn from the data and use the acquired knowledge for classification and prediction. However, the mathematical theory that elucidates how machine learning can operate on the features extracted using TDA currently does not exist. Hence, this work will develop the necessary, novel mathematical and computational tools at the intersection of topological data analysis (TDA), dynamical systems, and machine learning.
The principal investigators seek to understand and formulate the foundations of machine learning when the important features of a dynamical system are summarized by descriptors generated with topological data analysis (TDA). Although these signatures provide an information-rich structure for the evolution of the dynamics, current literature has only been utilizing a fraction of the available information in order to identify, predict, and classify different dynamic behavior. One of the current impediments to further exploring the relationship between TDA and dynamical systems is the lack of machine learning theory that can operate on these structures. Therefore, the success of our effort will lead to (1) the establishment of a novel, general, and robust machine learning framework for studying dynamic signals via topological signatures, (2) better understanding of the relationship between TDA and dynamical systems via the use of these methods on real and synthetic data, and (3) the integration of the new knowledge into the investigators educational programs, which will provide timely training of well-equipped next generation scientists and engineers.
Agency: NSF | Branch: Standard Grant | Program: | Phase: Exploiting Parallel&Scalabilty | Award Amount: 84.90K | Year: 2014
The transistor density of integrated circuits has been doubling approximately every two years for about four decades. This exponential rise in the computational power of the integrated circuit has driven the information technology revolution that has transformed every aspect of our society - from personal entertainment devices to high-assurance intelligent cyber-physical systems. However, the growth in transistor density is now slowing down, and new technological breakthroughs are urgently needed to sustain the ongoing information technology revolution.
This project creates a new memristor-based nano-computing architecture that circumvents the fabrication density problems associated with traditional transistor-based integrated circuits. The project investigates the fundamental principles of memristor-based nano-computing and designs efficient memristor-based nano-crossbar circuits that can execute elementary bit-vector mathematical and logical computations. The project pursues a transformative agenda for next-generation extreme-scale computing involving two design principles: (1) the use of memristors as distributed asynchronous digital switches and continuous-valued non-volatile nano-stores of input data and intermediate results, and (2) the use of sneak-paths in nano-crossbars as fundamental computational primitives that pool together results of intermediate computations from distributed memristor nano-stores.
The memristor-based nano-computing architecture developed in the project will enable the execution of legacy programs on low-energy ultra-dense memristive nano-crossbar circuits and will facilitate the design of domain-specific parallel execution engines that combine storage and computation on the same chip - thereby nullifying the traditional barrier between the memory and the microprocessor.
Agency: National Science Foundation | Branch: | Program: STTR | Phase: Phase I | Award Amount: 225.00K | Year: 2015
The broader impact/commercial potential of this Small Business Technology Transfer (STTR) project will be the development of a testing system that will facilitate glaucoma drug development in a more cost-effective manner. This will enable better treatment of glaucoma and ultimately prevention of vision loss. This work will overcome a major limiting factor for glaucoma drug discovery, and provide scientists and doctors with a unique tool to understand the physiology of the human eye as related to glaucoma. Commercially, this project will allow for high-throughput testing of new glaucoma therapies, making this technology highly desirable to the pharmaceutical industry. Longer term, this technology has the potential to provide a healthy transplantable tissue that can cure glaucoma. This STTR Phase I project proposes to address the lack of effective in vitro model for testing targeted glaucoma therapies. This work will be the first-of-its-kind, exploring the feasibility to bioengineer a physiologically-relevant 3D human trabecular outflow tract utilizing co-culture and cell differentiation methods along with microfabrication techniques. It is based on the development of a custom-built system that will incorporate the bioengineered tissue into a platform that mimics the flow of aqueous humor and pressure changes in the human eye. At the conclusion of this project, it is anticipated that the bioengineered tissue will behave similarly to its in vivo counterpart, and be usable as higher throughput testing platform for drugs affecting the outflow physiology of the human trabecular outflow tract. In addition, this project will lead to a platform that could be used by other scientists to study and understand the biology of the human trabecular outflow tract.