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A Hopf-algebraic structure on a vector space which has as basis a family of trees is described. Some applications of this structure to combinatorics and to differential operators are surveyed. Some possible future directions for this work are indicated.
An attempt is made to show that the combination of data with models leads to a sequence of conventionally ill-posed problems which can be treated in a systematic and practical way by control-theory techniques. The illustrative approach is to exploit the very great mathematical simplifications which result when the methods of finite dimensional vector spaces are used, thus reducing a lot of difficult mathematics to classical least squares. The immediate motivation for this study comes from ocean acoustic tomography.
A method was developed to plan feasible and obstacle-avoiding paths for two spatial robots working cooperatively in a known static environment. Cooperating spatial robots as referred to herein are robots which work in 6D task space while simultaneously grasping and manipulating a common, rigid payload. The approach is configuration space (c-space) based and performs selective rather than exhaustive c-space mapping. No expensive precomputations are required. A novel, divide-and-conquer type of heuristic is used to guide the selective mapping process. The heuristic does not involve any robot, environment, or task specific assumptions. A technique was also developed which enables solution of the cooperating redundant robot path planning problem without requiring the use of inverse kinematics for a redundant robot. The path planning strategy involves first attempting to traverse along the configuration space vector from the start point towards the goal point. If an unsafe region is encountered, an intermediate via point is identified by conducting a systematic search in the hyperplane orthogonal to and bisecting the unsafe region of the vector. This process is repeatedly applied until a solution to the global path planning problem is obtained. The basic concept behind this strategy is that better local decisions at the beginning of the trouble region may be made if a possible way around the 'center' of the trouble region is known. Thus, rather than attempting paths which look promising locally (at the beginning of a trouble region) but which may not yield overall results, the heuristic attempts local strategies that appear promising for circumventing the unsafe region.
This paper summarizes the author's advances in the design of dense processor networks. Within is reported a collection of recent constructions of dense symmetric networks that provide the largest know values for the number of nodes that can be placed in a network of a given degree and diameter. The constructions are in the range of current potential engineering significance and are based on groups of automorphisms of finite-dimensional vector spaces.
This note is concerned with the explicit symbolic computation of expressions involving differential operators and their actions on functions. The derivation of specialized numerical algorithms, the explicit symbolic computation of integrals of motion, and the explicit computation of normal forms for nonlinear systems all require such computations. More precisely, if R = k(x(sub 1),...,x(sub N)), where k = R or C, F denotes a differential operator with coefficients from R, and g member of R, we describe data structures and algorithms for efficiently computing g. The basic idea is to impose a multiplicative structure on the vector space with basis the set of finite rooted trees and whose nodes are labeled with the coefficients of the differential operators. Cancellations of two trees with r + 1 nodes translates into cancellation of O(N(exp r)) expressions involving the coefficient functions and their derivatives.
A new algorithm, called the CDF-Inversion Algorithm, is described. Using it, one can efficiently learn a probability distribution over a finite set to a specified accuracy and confidence. The algorithm can be extended to learn joint distributions over a vector space. Some implementation results are described.
Fractional-Order systems, or systems containing fractional derivatives and integrals, have been studied by many in the engineering area. Additionally, very readable discussions, devoted specifically to the subject, are presented by Oldham and Spanier, Miller and Ross, and Pudlubny (1999a). It should be noted that there are a growing number of physical systems whose behavior can be compactly described using fractional system theory. Of specific interest to electrical engineers are long lines, electrochemical processes, dielectric polarization, colored noise, viscoelastic materials, and chaos. With the growing number of applications, it is important to establish a theory of control for these fractional-order systems, and for the potential use of fractional-order systems as feedback compensators. This topic is addressed in this paper. The first section discusses the control of fractional-order systems using a vector space representation, where initialization is included in the discussion. It should be noted that Bagley and Calico and Padovan and Sawicki both present a fractional state-space representation, which do not include the important historic effects. Incorporation of these effects based on the initialized fractional calculus is presented . The control methods presented in this paper are based on the initialized fractional order system theory. The second section presents an input-output approach. Some of the problems encountered in these sections are: a) the need to introduce a new complex plane to study the dynamics of fractional-order systems, b) the need to properly define the Laplace transform of the fractional derivative, and c) the proper inclusion of the initialization response in the system and control formulation. Following this, the next section generalizes the proportional-plus-integral-control (PI-control) and PID-control (PI-plus- derivative) concepts using fractional integrals. This is then further generalized using general fractional- order compensators. Finally the compensator concept is generalized by the use of a continuum of fractions in the compensator via the concept of order-distributions. The last section introduces fractional feedback in discrete-time.
We present the user evaluation of two recommendation server methodologies implemented for the NASA Technical Report Server (NTRS). One methodology for generating recommendations uses log analysis to identify co-retrieval events on full-text documents. For comparison, we used the Vector Space Model (VSM) as the second methodology. We calculated cosine similarities and used the top 10 most similar documents (based on metadata) as 'recommendations'. We then ran an experiment with NASA Langley Research Center (LaRC) staff members to gather their feedback on which method produced the most 'quality' recommendations. We found that in most cases VSM outperformed log analysis of co-retrievals. However, analyzing the data revealed the evaluations may have been structurally biased in favor of the VSM generated recommendations. We explore some possible methods for combining log analysis and VSM generated recommendations and suggest areas of future work.
We present the user evaluation of two recommendation server methodologies implemented for the NASA Technical Report Server (NTRS). One methodology for generating recommendations uses log analysis to identify co-retrieval events on full-text documents. For comparison, we used the Vector Space Model (VSM) as the second methodology. We calculated cosine similarities and used the top 10 most similar documents (based on metadata) as recommendations . We then ran an experiment with NASA Langley Research Center (LaRC) staff members to gather their feedback on which method produced the most quality recommendations. We found that in most cases VSM outperformed log analysis of co-retrievals. However, analyzing the data revealed the evaluations may have been structurally biased in favor of the VSM generated recommendations. We explore some possible methods for combining log analysis and VSM generated recommendations and suggest areas of future work.
Methods and systems for determining if one or more target molecules are present in a gas, by exposing a functionalized carbon nanostructure (CNS) to the gas and measuring an electrical parameter value EPV(n) associated with each of N CNS sub-arrays. In a first embodiment, a most-probable concentration value C(opt) is estimated, and an error value, depending upon differences between the measured values EPV(n) and corresponding values EPV(n;C(opt)) is computed. If the error value is less than a first error threshold value, the system interprets this as indicating that the target molecule is present in a concentration C.apprxeq.C(opt). A second embodiment uses extensive statistical and vector space analysis to estimate target molecule concentration.
In recent years the methodology proposed for conversion of light elements into energy via fusion has made steady progress. Scientific studies and engineering efforts in advanced fusion systems designs have introduced some new concepts with unique aspects including consideration of Aneutronic fuels. The plant parameters for harnessing aneutronic fusion appear more exigent than those required for the conventional fusion fuel cycle. However aneutronic fusion propulsion plants for Space deployment will ultimately offer the possibility of enhanced performance from nuclear gain as compared to existing ionic engines as well as providing a clean solution to Planetary Protection considerations and requirements. Proton triggered 11Boron fuel (p- 11B) will produce abundant ion kinetic energy for In-Space vectored thrust. Thus energetic alpha particles "exhaust" momentum can be used directly to produce high ISP thrust and also offer possibility of power conversion into electricity. p- 11B is an advanced fusion plant fuel with well understood reaction kinematics but will require some new conceptual thinking as to the most effective implementation.
This research is a follow on to the "Optimal Control Prediction Method for Control Allocation" paper in which the Prediction Method iterative algorithm was introduced. Previously, the Prediction Method was shown to provide optimal control allocation solutions over the entire Attainable Moment Set for the Moore-Penrose and the generalized (weighted) inverse. As an extension to the Prediction Method, this paper introduces a family of Moore Penrose Affine Generalized Inverses, applicable for all moments, which compute control allocation solutions using a constant matrix and fixed null-space vector. The Moore-Penrose Affine Generalized Inverse is proven to yield equivalent solutions to those of the Prediction Method and therefore is guaranteed to yield Moore-Penrose optimal control allocation solutions. While the Prediction Method is applicable for any moment along an a priori specified moment direction, the Affine Generalized Inverse is shown to yield optimal control allocation solutions in a neighborhood of the given moment which is not restricted to a specified moment direction. Furthermore, the Affine Generalized Inverse is shown to provide the time derivative of optimal control allocation solutions and to facilitate maintaining solutions within control effector rate limitations. The Moore-Penrose Affine Generalized Inverse is broadened to encompass any arbitrary (weighted) Affine Generalized Inverse. Finally, a method of creating a moment lookup table is outlined to utilize the Affine Generalized Inverse as an offline control allocation solution for all moments in the Attainable Moment Set.
A method for projecting flight configuration eigenvectors onto the vector space of the test configuration eigenvectors is proposed. The underlying concept of the proposed method is that any flight configuration eigenvectors that can be replicated by a linear combination of test configuration eigenvectors, is correlated, if the constituent test eigenvectors are themselves correlated. Therefore, the modal test target mode shapes should be those test modes that combine to form the important modes of the flight configurations. This approach also recognizes that it is the deformed shapes that dictate what sections of the structure are “highly strained” (in a relative sense, within each mode shape), and that it is these highly strained sections that require an accurate stiffness representation to achieve an accurate model correlation.
A method for projecting flight configuration eigenvectors onto the vector space of the test configuration eigenvectors is proposed. The underlying concept of the proposed method is that any flight configuration eigenvectors that can be replicated by a linear combination of test configuration eigenvectors, is correlated, if the constituent test eigenvectors are themselves correlated. Therefore, the modal test target mode shapes should be those test modes that combine to form the important modes of the flight configurations. This approach also recognizes that it is the deformed shapes that dictate what sections of the structure are “highly strained” (in a relative sense, within each mode shape), and that these “highly strained” sections require an accurate stiffness representation to achieve an accurate model correlation.
A method for projecting flight configuration eigenvectors onto the vector space of the test configuration eigenvectors is proposed. The underlying concept of the proposed method is that any flight configuration eigenvectors (that can be replicated by a linear combination of test configuration eigenvectors) is correlated if the constituent test eigenvectors are themselves correlated. Therefore, the modal test target mode shapes should be those test modes that combine to form the important modes of the flight configurations. This approach also recognizes that it is the deformed shapes that dictate what sections of the structure are “highly strained” (in a relative sense, within each mode shape), and that these “highly strained” sections require an accurate stiffness representation to achieve an accurate model correlation.
The National Airspace System (NAS) is constantly evolving as air traffic continues to ramp up to pre-pandemic numbers and projected to grow to unprecedented levels in the coming years. As well as increasing demand to the current system, emerging operations such as Unmanned Autonomous Systems are also expected to add to complexity in the airspace. To address these issues, the industry and government agencies supporting the NAS will need to rely upon additional automation and new technologies to address future operational requirements, while continuing to be a world-leading safe transportation system. As these new technologies are implemented, the system continues to rely on human pilots and controllers in the loop to monitor the system and intervene in situations the automation cannot handle. The goal of proactively addressing safety is of foremost concern to ensure passenger confidence. The industry has implemented various Safety Monitoring Systems to identify safety risks and proactively address them before they result in a serious incident or accident. One such program is the Aviation Safety Reporting System (ASRS). ASRS is a long-established system where pilots and controllers voluntarily and anonymously report safety incidents they experienced and observed during line operations by providing rich text narratives describing the events, the environment, and conditions leading to the safety event of concern. These narratives provide insight and context around events of interest and can be used to identify emerging problems. They can trigger investigations within Flight Operational Quality Assurance or Flight Data Monitoring programs. However, this process typically focuses on the adverse events and the unsafe aspects of the operations surrounding the reported or detected events. This perspective of investigating factors that went wrong around an adverse event is commonly referred to as Safety I. Alternatively, characterizing successful actions that operators perform every day under varying conditions that keep the system within safe operating bounds is a concept referred to as Safety II. The benefit of the Safety II view is that the scope is much larger than that of Safety I since a vast majority of the operations result in successful flights. Many of the successful techniques used to manage operational threats are not documented in standard operating procedures or taught during training. They are typically acquired over time by working with experienced pilots during line operations or in many cases after experiencing a problem for the first time and reacting to it in situ, drawing from years of experience to manage the threat. In an attempt to quantify these positive actions, we are proposing an approach to extracting key behaviors within ASRS reports that can support the Safety II concept. Our analysis assumes that ASRS reports contain some descriptions of corrective actions that operators performed to prevent a situation from leading to an accident. Leveraging recent advances in Natural Language Process modeling, we have developed an approach to extract positive sentiment from reports, embed these positive statements in a vector space where they can be numerically analyzed, and clustering these statements into similar contextual categories. From these contextualized categories we can attempt to summarized and distilled aspects of the positive behavior. The goal is to identify categories of behavior that describe consistent operator techniques that supports the Safety II concept. With this information, airlines may enable learning from these positive actions, or address procedures that need to be changed to avoid having pilots implement a workaround. These insights can provide a lens into what is “going right” in the operations that may otherwise not be known widely within the community. It is envisioned that this approach can be extended to other narrative programs such as Line Operation Safety Audit or Learning Improvement Team reports where similar observed behavior can be analyzed to extract positive actions and inform the overall operations.
The National Airspace System (NAS) is constantly evolving as air traffic continues to ramp up to pre-pandemic numbers and projected to grow to unprecedented levels in the coming years. As well as increasing demand to the current system, emerging operations such as Unmanned Autonomous Systems are also expected to add to complexity in the airspace. To address these issues, the industry and government agencies supporting the NAS will need to rely upon additional automation and new technologies to address future operational requirements, while continuing to be a world-leading safe transportation system. As these new technologies are implemented, the system continues to rely on human pilots and controllers in the loop to monitor the system and intervene in situations the automation cannot handle. The goal of proactively addressing safety is of foremost concern to ensure passenger confidence. The industry has implemented various Safety Monitoring Systems to identify safety risks and proactively address them before they result in a serious incident or accident. One such program is the Aviation Safety Reporting System (ASRS). ASRS is a long-established system where pilots and controllers voluntarily and anonymously report safety incidents they experienced and observed during line operations by providing rich text narratives describing the events, the environment, and conditions leading to the safety event of concern. These narratives provide insight and context around events of interest and can be used to identify emerging problems. They can trigger investigations within Flight Operational Quality Assurance or Flight Data Monitoring programs. However, this process typically focuses on the adverse events and the unsafe aspects of the operations surrounding the reported or detected events. This perspective of investigating factors that went wrong around an adverse event is commonly referred to as Safety I. Alternatively, characterizing successful actions that operators perform every day under varying conditions that keep the system within safe operating bounds is a concept referred to as Safety II. The benefit of the Safety II view is that the scope is much larger than that of Safety I since a vast majority of the operations result in successful flights. Many of the successful techniques used to manage operational threats are not documented in standard operating procedures or taught during training. They are typically acquired over time by working with experienced pilots during line operations or in many cases after experiencing a problem for the first time and reacting to it in situ, drawing from years of experience to manage the threat. In an attempt to quantify these positive actions, we are proposing an approach to extracting key behaviors within ASRS reports that can support the Safety II concept. Our analysis assumes that ASRS reports contain some descriptions of corrective actions that operators performed to prevent a situation from leading to an accident. Leveraging recent advances in Natural Language Process modeling, we have developed an approach to extract positive sentiment from reports, embed these positive statements in a vector space where they can be numerically analyzed, and clustering these statements into similar contextual categories. From these contextualized categories we can attempt to summarized and distilled aspects of the positive behavior. The goal is to identify categories of behavior that describe consistent operator techniques that supports the Safety II concept. With this information, airlines may enable learning from these positive actions, or address procedures that need to be changed to avoid having pilots implement a workaround. These insights can provide a lens into what is “going right” in the operations that may otherwise not be known widely within the community. It is envisioned that this approach can be extended to other narrative programs such as Line Operation Safety Audit or Learning Improvement Team reports where similar observed behavior can be analyzed to extract positive actions and inform the overall operations.
The National Airspace System (NAS) is constantly evolving as air traffic continues to ramp up to pre-pandemic numbers and projected to grow to unprecedented levels in the coming years. As well as increasing demand to the current system, emerging operations such as Unmanned Autonomous Systems are also expected to add to complexity in the airspace. To address these issues, the industry and government agencies supporting the NAS will need to rely upon additional automation and new technologies to address future operational requirements, while continuing to be a world-leading safe transportation system. As these new technologies are implemented, the system continues to rely on human pilots and controllers in the loop to monitor the system and intervene in situations the automation cannot handle. The goal of proactively addressing safety is of foremost concern to ensure passenger confidence. The industry has implemented various Safety Monitoring Systems to identify safety risks and proactively address them before they result in a serious incident or accident. One such program is the Aviation Safety Reporting System (ASRS). ASRS is a long-established system where pilots and controllers voluntarily and anonymously report safety incidents they experienced and observed during line operations by providing rich text narratives describing the events, the environment, and conditions leading to the safety event of concern. These narratives provide insight and context around events of interest and can be used to identify emerging problems. They can trigger investigations within Flight Operational Quality Assurance or Flight Data Monitoring programs. However, this process typically focuses on the adverse events and the unsafe aspects of the operations surrounding the reported or detected events. This perspective of investigating factors that went wrong around an adverse event is commonly referred to as Safety I. Alternatively, characterizing successful actions that operators perform every day under varying conditions that keep the system within safe operating bounds is a concept referred to as Safety II. The benefit of the Safety II view is that the scope is much larger than that of Safety I since a vast majority of the operations result in successful flights. Many of the successful techniques used to manage operational threats are not documented in standard operating procedures or taught during training. They are typically acquired over time by working with experienced pilots during line operations or in many cases after experiencing a problem for the first time and reacting to it in situ, drawing from years of experience to manage the threat. In an attempt to quantify these positive actions, we are proposing an approach to extracting key behaviors within ASRS reports that can support the Safety II concept. Our analysis assumes that ASRS reports contain some descriptions of corrective actions that operators performed to prevent a situation from leading to an accident. Leveraging recent advances in Natural Language Process modeling, we have developed an approach to extract positive sentiment from reports, embed these positive statements in a vector space where they can be numerically analyzed, and clustering these statements into similar contextual categories. From these contextualized categories we can attempt to summarized and distilled aspects of the positive behavior. The goal is to identify categories of behavior that describe consistent operator techniques that supports the Safety II concept. With this information, airlines may enable learning from these positive actions, or address procedures that need to be changed to avoid having pilots implement a workaround. These insights can provide a lens into what is “going right” in the operations that may otherwise not be known widely within the community. It is envisioned that this approach can be extended to other narrative programs such as Line Operation Safety Audit or Learning Improvement Team reports where similar observed behavior can be analyzed to extract positive actions and inform the overall operations.