Linked timestamping is a type of trusted timestamping where issued time-stamps are related to each other. Each time-stamp would contain data that authenticates the time-stamp before it, the authentication would be authenticating the entire message, including the previous time-stamps authentication, making a chain. This makes it impossible to add a time-stamp in to the middle of the chain, as any time-stamps afterwards would be different. == Description == Linked timestamping creates time-stamp tokens which are dependent on each other, entangled in some authenticated data structure. Later modification of the issued time-stamps would invalidate this structure. The temporal order of issued time-stamps is also protected by this data structure, making backdating of the issued time-stamps impossible, even by the issuing server itself. The top of the authenticated data structure is generally published in some hard-to-modify and widely witnessed media, like printed newspaper or public blockchain. There are no (long-term) private keys in use, avoiding PKI-related risks. Suitable candidates for the authenticated data structure include: Linear hash chain Merkle tree (binary hash tree) Skip list The simplest linear hash chain-based time-stamping scheme is illustrated in the following diagram: The linking-based time-stamping authority (TSA) usually performs the following distinct functions: Aggregation For increased scalability the TSA might group time-stamping requests together which arrive within a short time-frame. These requests are aggregated together without retaining their temporal order and then assigned the same time value. Aggregation creates a cryptographic connection between all involved requests; the authenticating aggregate value will be used as input for the linking operation. Linking Linking creates a verifiable and ordered cryptographic link between the current and already issued time-stamp tokens. Publishing The TSA periodically publishes some links, so that all previously issued time-stamp tokens depend on the published link and that it is practically impossible to forge the published values. By publishing widely witnessed links, the TSA creates unforgeable verification points for validating all previously issued time-stamps. == Security == Linked timestamping is inherently more secure than the usual, public-key signature based time-stamping. All consequential time-stamps "seal" previously issued ones - hash chain (or other authenticated dictionary in use) could be built only in one way; modifying issued time-stamps is nearly as hard as finding a preimage for the used cryptographic hash function. Continuity of operation is observable by users; periodic publications in widely witnessed media provide extra transparency. Tampering with absolute time values could be detected by users, whose time-stamps are relatively comparable by system design. Absence of secret keys increases system trustworthiness. There are no keys to leak and hash algorithms are considered more future-proof than modular arithmetic based algorithms, e.g. RSA. Linked timestamping scales well - hashing is much faster than public key cryptography. There is no need for specific cryptographic hardware with its limitations. The common technology for guaranteeing long-term attestation value of the issued time-stamps (and digitally signed data) is periodic over-time-stamping of the time-stamp token. Because of missing key-related risks and of the plausible safety margin of the reasonably chosen hash function this over-time-stamping period of hash-linked token could be an order of magnitude longer than of public-key signed token. == Research == === Foundations === Stuart Haber and W. Scott Stornetta proposed in 1990 to link issued time-stamps together into linear hash-chain, using a collision-resistant hash function. The main rationale was to diminish TSA trust requirements. Tree-like schemes and operating in rounds were proposed by Benaloh and de Mare in 1991 and by Bayer, Haber and Stornetta in 1992. Benaloh and de Mare constructed a one-way accumulator in 1994 and proposed its use in time-stamping. When used for aggregation, one-way accumulator requires only one constant-time computation for round membership verification. Surety started the first commercial linked timestamping service in January 1995. Linking scheme is described and its security is analyzed in the following article by Haber and Sornetta. Buldas et al. continued with further optimization and formal analysis of binary tree and threaded tree based schemes. Skip-list based time-stamping system was implemented in 2005; related algorithms are quite efficient. === Provable security === Security proof for hash-function based time-stamping schemes was presented by Buldas, Saarepera in 2004. There is an explicit upper bound N {\displaystyle N} for the number of time stamps issued during the aggregation period; it is suggested that it is probably impossible to prove the security without this explicit bound - the so-called black-box reductions will fail in this task. Considering that all known practically relevant and efficient security proofs are black-box, this negative result is quite strong. Next, in 2005 it was shown that bounded time-stamping schemes with a trusted audit party (who periodically reviews the list of all time-stamps issued during an aggregation period) can be made universally composable - they remain secure in arbitrary environments (compositions with other protocols and other instances of the time-stamping protocol itself). Buldas, Laur showed in 2007 that bounded time-stamping schemes are secure in a very strong sense - they satisfy the so-called "knowledge-binding" condition. The security guarantee offered by Buldas, Saarepera in 2004 is improved by diminishing the security loss coefficient from N {\displaystyle N} to N {\displaystyle {\sqrt {N}}} . The hash functions used in the secure time-stamping schemes do not necessarily have to be collision-resistant or even one-way; secure time-stamping schemes are probably possible even in the presence of a universal collision-finding algorithm (i.e. universal and attacking program that is able to find collisions for any hash function). This suggests that it is possible to find even stronger proofs based on some other properties of the hash functions. At the illustration above hash tree based time-stamping system works in rounds ( t {\displaystyle t} , t + 1 {\displaystyle t+1} , t + 2 {\displaystyle t+2} , ...), with one aggregation tree per round. Capacity of the system ( N {\displaystyle N} ) is determined by the tree size ( N = 2 l {\displaystyle N=2^{l}} , where l {\displaystyle l} denotes binary tree depth). Current security proofs work on the assumption that there is a hard limit of the aggregation tree size, possibly enforced by the subtree length restriction. == Standards == ISO 18014 part 3 covers 'Mechanisms producing linked tokens'. American National Standard for Financial Services, "Trusted Timestamp Management and Security" (ANSI ASC X9.95 Standard) from June 2005 covers linking-based and hybrid time-stamping schemes. There is no IETF RFC or standard draft about linking based time-stamping. RFC 4998 (Evidence Record Syntax) encompasses hash tree and time-stamp as an integrity guarantee for long-term archiving.
RIPAC (microprocessor)
RIPAC was a VLSI single-chip microprocessor designed for automatic recognition of the connected speech, one of the first of this use. The project of the microprocessor RIPAC started in 1984. RIPAC was aimed to provide efficient real-time speech recognition services to the italian telephone system provided by SIP. The microprocessor was presented in September 1986 at The Hague (Netherlands) at EUSPICO conference. It was composed of 70.000 transistors and structured as Harvard architecture. The name RIPAC is the acronym for "Riconoscimento del PArlato Connesso", that means "Recognition of the connected speech" in Italian. The microprocessor was designed by the Italian companies CSELT and ELSAG and was produced by SGS: a combination of Hidden Markov Model and Dynamic Time Warping algorithms was used for processing speech signals. It was able to do real-time speech recognition of Italian and many languages with a good affordability. The chip, issued by U.S. Patent No. 4,907,278, worked at first run.
Environmental informatics
Environmental informatics is the science of information applied to environmental science. As such, it provides the information processing and communication infrastructure to the interdisciplinary field of environmental sciences aiming at data, information and knowledge integration, the application of computational intelligence to environmental data as well as the identification of environmental impacts of information technology. Environmental informatics thus acts as a bridge, providing an interdisciplinary means of analysing, describing and understanding the complex interactions between humans, nature and technology. Since each field of applied computer science has its own subject matter, terminology and methods, specialised disciplines, such as environmental, bio- and geoinformatics have emerged, each of which combines computer science with a specific field of application such as environmental, bio- or geosciences. Environmental informatics, bioinformatics and geoinformatics all deal with computer-based processing of environmental phenomena. However, environmental informatics is the only field that pursues normative goals (e.g., political goals of environmental protection, environmental planning, and sustainability). This also influences the choice of methods. This also distinguishes it from application areas such as numerical weather prediction, which is considered an early and important example of computer simulation of environmental phenomena. The UK Natural Environment Research Council defines environmental informatics as the "research and system development focusing on the environmental sciences relating to the creation, collection, storage, processing, modelling, interpretation, display and dissemination of data and information." Kostas Karatzas defined environmental informatics as the "creation of a new 'knowledge-paradigm' towards serving environmental management needs." Karatzas argued further that environmental informatics "is an integrator of science, methods and techniques and not just the result of using information and software technology methods and tools for serving environmental engineering needs." Environmental informatics emerged in early 1990 in Central Europe. Current initiatives to effectively manage, share, and reuse environmental and ecological data are indicative of the increasing importance of fields like environmental informatics and ecoinformatics to develop the foundations for effectively managing ecological information. Examples of these initiatives are National Science Foundation Datanet projects, DataONE and Data Conservancy. == Subject matter and objectives == The subject of environmental informatics are environmental information systems (EIS). An EIS 'is a computer-based system that integrates and stores data collected about the natural environment and provides powerful methods for accessing and evaluating it.' This allows environmental data to be processed by computers for environmental protection, planning, research and technology. According to Jaeschke and Bossel, environmental informatics has three interrelated objectives: Environmental informatics serves to procure data and information for describing the state and development of the environment. Of particular importance is information that is needed to prevent or limit undesirable changes and to support desirable changes. Based on the evaluation and analysis of data, environmental informatics improves our understanding of the environment and the interactions between nature, technology and society. It thus supports environmentally relevant decisions. This enables the influence of development (system correction), the assessment of the effects and side effects of potential measures, and the creation of tools for the routine planning, implementation and monitoring of measures. == History == The simulation model World3, which formed the basis of the highly acclaimed study The Limits to Growth, is considered the starting point of environmental informatics. It incorporated environmental information, among other things, to calculate scenarios for global development. In the mid-1980s, interest grew in structuring environmental protection as an area of application for computer science. One of the first publications in German was the book Informatik im Umweltschutz. Anwendungen und Perspektiven (Computer science in environmental protection. Applications and perspectives) from 1986. The term 'environmental informatics' did not appear until around 1993, which is why the development of environmental informatics is usually referred to as having taken place in the 1990s. In 1993, the first university chair for environmental informatics was established in Cottbus. In 1994, the anthology Umweltinformatik. Informatikmethoden für Umweltschutz und Umweltforschung (Environmental Informatics: Informatics Methods for Environmental Protection and Environmental Research) was published. The development of environmental informatics was 'primarily initiated by German computer science.' In the English-speaking world, the volume Environmental Informatics was published in 1995, mainly based on the German anthology of 1994. An article in the conference proceedings of the World Computer Congress of the International Federation for Information Processing (IFIP) in Hamburg in 1994 describes the initial situation of environmental informatics as follows: 'On the one hand, we suffer from the huge amount of available data – people sometimes speak of data graveyards – on the other hand, the really relevant data may still be missing.' This statement indicates the need that led to the emergence of environmental informatics as a specialised discipline of applied computer science. Furthermore, the specific characteristics and processing requirements of environmental data necessitated the emergence of environmental informatics. The special features of environmental data include: The data structures required are highly heterogeneous due to specific processes and differing perspectives on environmental aspects (e.g., water protection, emission control, hazardous substances). In addition to the heterogeneity of the data, heterogeneous databases also play a role, as environmental data is often obtained and presented in an interdisciplinary manner. Obligations change frequently as a result of new legislation, whether regional (e.g. state regulations on water protection), national (e.g. federal emission control regulations) or international (e.g. Registration, Evaluation, Authorisation and Restriction of Chemicals|REACH). The objects represented are often multidimensional and, therefore, require complex geometric representation using curves or polygons. It is often necessary to process uncertain, imprecise or incomplete data, which is, for example, the result of extrapolations or forecasts. A new "knowledge paradigm" has emerged to meet the requirements of environmental management. Environmental informatics produces its own concepts, methods and techniques and is not merely the result of using information and communication technology methods and tools to meet environmental requirements. The development of environmental informatics since the 1990s has been significantly influenced by the newly established conferences EnviroInfo, ISESS and ITEE and is documented in the respective proceedings. Aspects of sustainability and sustainable development were increasingly integrated into environmental informatics after 2000, thereby expanding the field. In 2004, the Working Group on Sustainable Information Society of the Gesellschaft für Informatik e. V. (German Informatics Society, GI) published the Memorandum on a Sustainable Information Society, which formulates recommendations for an information society that is compatible with human, social and natural needs. Since 2007, environmental informatics has often been described in more detail as informatics for environmental protection, sustainable development and risk management. The increased focus on sustainability has also contributed to the formation of the research focus Information and Communications Technology for Sustainability (ICT4S) and to the emergence of the international conference ICT4S in 2013. ICT-ENSURE, the European Commission's funding measure for the establishment of a European research area on "ICT for Environmental Sustainability Research" (2008–2010), has also contributed to the structuring of environmental informatics. == Environmental informatics and sustainable development == Efforts to place environmental informatics within the context of sustainable development have been growing since 2000 and were significantly influenced by the Memorandum on a Sustainable Information Society. According to this Memorandum, the information society offers great but unevenly distributed opportunities for education, participation and intercultural understanding. In addition, the Memorandum highlighted the material and energy consumption of inf
Traité de Documentation
Traité de documentation: le livre sur le livre, théorie et pratique is a landmark book by Belgian author Paul Otlet, first published in 1934. == Legacy == The book is considered a landmark in the history of information science, with concepts predicting the rise of the World Wide Web and search engines. In [Otlet's] most famous publication of 1934, Traité de Documentation, he wrote of a desk in the form of a wheel from which different projects (workspaces) could be switched as they rotated — foreshadowing the multiple desktops and tabs of contemporary computer interfaces. Inspired by the arrival of radio, phonograph, cinema, and television, Otlet also posited that there were as yet many “inventions to be discovered,” including the reading and annotation of remote documents and computer speech.
Dependency network (graphical model)
Dependency networks (DNs) are graphical models, similar to Markov networks, wherein each vertex (node) corresponds to a random variable and each edge captures dependencies among variables. Unlike Bayesian networks, DNs may contain cycles. Each node is associated to a conditional probability table, which determines the realization of the random variable given its parents. == Markov blanket == In a Bayesian network, the Markov blanket of a node is the set of parents and children of that node, together with the children's parents. The values of the parents and children of a node evidently give information about that node. However, its children's parents also have to be included in the Markov blanket, because they can be used to explain away the node in question. In a Markov random field, the Markov blanket for a node is simply its adjacent (or neighboring) nodes. In a dependency network, the Markov blanket for a node is simply the set of its parents. == Dependency network versus Bayesian networks == Dependency networks have advantages and disadvantages with respect to Bayesian networks. In particular, they are easier to parameterize from data, as there are efficient algorithms for learning both the structure and probabilities of a dependency network from data. Such algorithms are not available for Bayesian networks, for which the problem of determining the optimal structure is NP-hard. Nonetheless, a dependency network may be more difficult to construct using a knowledge-based approach driven by expert-knowledge. == Dependency networks versus Markov networks == Consistent dependency networks and Markov networks have the same representational power. Nonetheless, it is possible to construct non-consistent dependency networks, i.e., dependency networks for which there is no compatible valid joint probability distribution. Markov networks, in contrast, are always consistent. == Definition == A consistent dependency network for a set of random variables X = ( X 1 , … , X n ) {\textstyle \mathbf {X} =(X_{1},\ldots ,X_{n})} with joint distribution p ( x ) {\displaystyle p(\mathbf {x} )} is a pair ( G , P ) {\displaystyle (G,P)} where G {\displaystyle G} is a cyclic directed graph, where each of its nodes corresponds to a variable in X {\displaystyle \mathbf {X} } , and P {\displaystyle P} is a set of conditional probability distributions. The parents of node X i {\displaystyle X_{i}} , denoted P a i {\displaystyle \mathbf {Pa_{i}} } , correspond to those variables P a i ⊆ ( X 1 , … , X i − 1 , X i + 1 , … , X n ) {\displaystyle \mathbf {Pa_{i}} \subseteq (X_{1},\ldots ,X_{i-1},X_{i+1},\ldots ,X_{n})} that satisfy the following independence relationships p ( x i ∣ p a i ) = p ( x i ∣ x 1 , … , x i − 1 , x i + 1 , … , x n ) = p ( x i ∣ x − x i ) . {\displaystyle p(x_{i}\mid \mathbf {pa_{i}} )=p(x_{i}\mid x_{1},\ldots ,x_{i-1},x_{i+1},\ldots ,x_{n})=p(x_{i}\mid \mathbf {x} -{x_{i}}).} The dependency network is consistent in the sense that each local distribution can be obtained from the joint distribution p ( x ) {\displaystyle p(\mathbf {x} )} . Dependency networks learned using large data sets with large sample sizes will almost always be consistent. A non-consistent network is a network for which there is no joint probability distribution compatible with the pair ( G , P ) {\displaystyle (G,P)} . In that case, there is no joint probability distribution that satisfies the independence relationships subsumed by that pair. == Structure and parameters learning == Two important tasks in a dependency network are to learn its structure and probabilities from data. Essentially, the learning algorithm consists of independently performing a probabilistic regression or classification for each variable in the domain. It comes from observation that the local distribution for variable X i {\displaystyle X_{i}} in a dependency network is the conditional distribution p ( x i | x − x i ) {\displaystyle p(x_{i}|\mathbf {x} -{x_{i}})} , which can be estimated by any number of classification or regression techniques, such as methods using a probabilistic decision tree, a neural network or a probabilistic support-vector machine. Hence, for each variable X i {\displaystyle X_{i}} in domain X {\displaystyle X} , we independently estimate its local distribution from data using a classification algorithm, even though it is a distinct method for each variable. Here, we will briefly show how probabilistic decision trees are used to estimate the local distributions. For each variable X i {\displaystyle X_{i}} in X {\displaystyle \mathbf {X} } , a probabilistic decision tree is learned where X i {\displaystyle X_{i}} is the target variable and X − X i {\displaystyle \mathbf {X} -X_{i}} are the input variables. To learn a decision tree structure for X i {\displaystyle X_{i}} , the search algorithm begins with a singleton root node without children. Then, each leaf node in the tree is replaced with a binary split on some variable X j {\displaystyle X_{j}} in X − X i {\displaystyle \mathbf {X} -X_{i}} , until no more replacements increase the score of the tree. == Probabilistic Inference == A probabilistic inference is the task in which we wish to answer probabilistic queries of the form p ( y ∣ z ) {\displaystyle p(\mathbf {y\mid z} )} , given a graphical model for X {\displaystyle \mathbf {X} } , where Y {\displaystyle \mathbf {Y} } (the 'target' variables) Z {\displaystyle \mathbf {Z} } (the 'input' variables) are disjoint subsets of X {\displaystyle \mathbf {X} } . One of the alternatives for performing probabilistic inference is using Gibbs sampling. A naive approach for this uses an ordered Gibbs sampler, an important difficulty of which is that if either p ( y ∣ z ) {\displaystyle p(\mathbf {y\mid z} )} or p ( z ) {\displaystyle p(\mathbf {z} )} is small, then many iterations are required for an accurate probability estimate. Another approach for estimating p ( y ∣ z ) {\displaystyle p(\mathbf {y\mid z} )} when p ( z ) {\displaystyle p(\mathbf {z} )} is small is to use modified ordered Gibbs sampler, where Z = z {\displaystyle \mathbf {Z=z} } is fixed during Gibbs sampling. It may also happen that y {\displaystyle \mathbf {y} } is rare, e.g. when Y {\displaystyle \mathbf {Y} } has many variables. So, the law of total probability along with the independencies encoded in a dependency network can be used to decompose the inference task into a set of inference tasks on single variables. This approach comes with the advantage that some terms may be obtained by direct lookup, thereby avoiding some Gibbs sampling. You can see below an algorithm that can be used for obtain p ( y | z ) {\displaystyle p(\mathbf {y|z} )} for a particular instance of y ∈ Y {\displaystyle \mathbf {y} \in \mathbf {Y} } and z ∈ Z {\displaystyle \mathbf {z} \in \mathbf {Z} } , where Y {\displaystyle \mathbf {Y} } and Z {\displaystyle \mathbf {Z} } are disjoint subsets. Algorithm 1: U := Y {\displaystyle \mathbf {U:=Y} } ( the unprocessed variables ) P := Z {\displaystyle \mathbf {P:=Z} } ( the processed and conditioning variables ) p := z {\displaystyle \mathbf {p:=z} } ( the values for P {\displaystyle \mathbf {P} } ) While U ≠ ∅ {\displaystyle \mathbf {U} \neq \emptyset } : Choose X i ∈ U {\displaystyle X_{i}\in \mathbf {U} } such that X i {\displaystyle X_{i}} has no more parents in U {\displaystyle U} than any variable in U {\displaystyle U} If all the parents of X {\displaystyle X} are in P {\displaystyle \mathbf {P} } p ( x i | p ) := p ( x i | p a i ) {\displaystyle p(x_{i}|\mathbf {p} ):=p(x_{i}|\mathbf {pa_{i}} )} Else Use a modified ordered Gibbs sampler to determine p ( x i | p ) {\displaystyle p(x_{i}|\mathbf {p} )} U := U − X i {\displaystyle \mathbf {U:=U} -X_{i}} P := P + X i {\displaystyle \mathbf {P:=P} +X_{i}} p := p + x i {\displaystyle \mathbf {p:=p} +x_{i}} Returns the product of the conditionals p ( x i | p ) {\displaystyle p(x_{i}|\mathbf {p} )} == Applications == In addition to the applications to probabilistic inference, the following applications are in the category of Collaborative Filtering (CF), which is the task of predicting preferences. Dependency networks are a natural model class on which to base CF predictions, once an algorithm for this task only needs estimation of p ( x i = 1 | x − x i = 0 ) {\displaystyle p(x_{i}=1|\mathbf {x} -{x_{i}}=0)} to produce recommendations. In particular, these estimates may be obtained by a direct lookup in a dependency network. Predicting what movies a person will like based on his or her ratings of movies seen; Predicting what web pages a person will access based on his or her history on the site; Predicting what news stories a person is interested in based on other stories he or she read; Predicting what product a person will buy based on products he or she has already purchased and/or dropped into his or her shopping basket. Another class of useful applications for dependency networks is related to data visualization, that is
NASA AI Assisted-Air Quality Monitoring Project
The NASA Expert-System Ion Trap Mass Spectrometer (ES-ITMS) Project was a public-private partnership to develop an artificial intelligence assisted, air quality monitoring system and was qualified for use on the Space Shuttle. The partnership was also the first cost and intellectual property shared public-partnership implemented by NASA, which used the commercial Research and Development Limited Partnership (RDLP) model that had been adopted by the Reagan Administration for Department of Defense semiconductor development, and recommended for use by NASA for space commercialization. The project partners included NASA, the University of Florida and Finnigan MAT Corporation, was organized and administered by the NASA Joint Enterprise Institute (subsequently NASA Joint Sponsored Program) and ran from 1988 through 1990. The partnership concluded final testing in 1991, generating four patents, expert system software and application protocol reports. The system was space qualified for use on the Shuttle and elements of the ES-ITMS system were integrated into the product Improvements for Finnigan MAT corporation. The success of the partnership lead NASA to create a pilot program to develop partnership business models as an ongoing management practice. == Purpose and objectives == The need to monitor air quality in confined spaces represented an increasing challenge for NASA's planned space missions and private sector facility managers facing the increased scrutiny of possible air contaminants. Up to the early 1980's, air quality monitors generally required large spaces and human technicians to interpret readings. This created a need for miniaturized air quality monitors that could generate reliable and accurate analytic results without on-site technician presence. NASA initiated projects to develop..."mobile and/or portable mass spectrometers" that evaluated the "tradeoff between instrumentation capabilities and space, weight and power considerations." NASA selected a "commercial ITMS instrument capable of generating electron ionization, chemical ionization and mass spectrometry data", to develop a linked expert system to accomplish analysis without human intervention. The commercial instrumentation was from Finnigan MAT corporation while the scientific expertise to support expert system development was available at the University of Florida. The project managers at NASA Ames created a single, integrated project using the RDLP model with objectives to: Develop AI/expert system software for instrument control (NASA's role) Expand sensitivity, selectivity and speed of the spectrometer (Univ Florida role) Expand the spectrometer analytic capability and automate the screening (Finnigan role) == Membership == The partnership included seven specialists from five member organizations: Federal Government National Aeronautics and Space Administration (NASA) NASA Ames Research Center (ARC) NASA Kennedy Space Center (KSC) Commercial Finnigan MAT Corporation (Thermo-Fisher Scientific) TGS Technology, Inc. Research Management University of Florida == Organization, management and administration == The technical project was organized into two development teams, one located in at the NASA Ames Research Center covering expert systems and analytic capabilities and one in Florida covering improved sensitivity and testing. The partnership management and administration was provided by a non-profit, partnership support organization: the Joint Enterprise Institute operating through San Francisco State University Foundation (SFSUF) with a NASA employee liaison, Syed Shariq. == Public-private partnership == The partnership structure was as a prototype test of a pilot NASA program to develop public-private partnership business models. The pilot program was known as the NASA Joint Sponsored Research Program (JSRP), which operated as the NASA Joint Enterprise Institute between 1988 and 1991. The partnership was the first public-private, research and development partnership implemented by NASA in response to national policy shifts to increase technology transfer and space commercialization. The partnership structure included a two year technology development and testing plan that cost $610,000, of which NASA funded $310,000, Finnigan $175,000 and the University of Florida $95,000. == Results and commercialization == The project generated patents (4), software (2) and application protocol reports (8). NASA gained use of the patents and jointly development software while Finnigan received commercial utilization rights. The results were commercialized within eighteen months of project completion. == Recognition == NASA recognized the project as a space qualified instrument. Its achievements were reported to the NASA Administrator, directly leading to establishment of the agency-wide Joint Sponsored Research Program.
Weak stability boundary
Weak stability boundary (WSB), including low-energy transfer, is a concept introduced by Edward Belbruno in 1987. The concept explained how a spacecraft could change orbits using very little fuel. Weak stability boundary is defined for the three-body problem. This problem considers the motion of a particle P of negligible mass moving with respect to two larger bodies, P1, P2, modeled as point masses, where these bodies move in circular or elliptical orbits with respect to each other, and P2 is smaller than P1. The force between the three bodies is the classical Newtonian gravitational force. For example, P1 is the Earth, P2 is the Moon and P is a spacecraft; or P1 is the Sun, P2 is Jupiter and P is a comet, etc. This model is called the restricted three-body problem. The weak stability boundary defines a region about P2 where P is temporarily captured. This region is in position-velocity space. Capture means that the Kepler energy between P and P2 is negative. This is also called weak capture. == Background == This boundary was defined for the first time by Edward Belbruno of Princeton University in 1987. He described a Low-energy transfer which would allow a spacecraft to change orbits using very little fuel. It was for motion about Moon (P2) with P1 = Earth. It is defined algorithmically by monitoring cycling motion of P about the Moon and finding the region where cycling motion transitions between stable and unstable after one cycle. Stable motion means P can completely cycle about the Moon for one cycle relative to a reference section, starting in weak capture. P needs to return to the reference section with negative Kepler energy. Otherwise, the motion is called unstable, where P does not return to the reference section within one cycle or if it returns, it has non-negative Kepler energy. The set of all transition points about the Moon comprises the weak stability boundary, W. The motion of P is sensitive or chaotic as it moves about the Moon within W. A mathematical proof that the motion within W is chaotic was given in 2004. This is accomplished by showing that the set W about an arbitrary body P2 in the restricted three-body problem contains a hyperbolic invariant set of fractional dimension consisting of the infinitely many intersections Hyperbolic manifolds. The weak stability boundary was originally referred to as the fuzzy boundary. This term was used since the transition between capture and escape defined in the algorithm is not well defined and limited by the numerical accuracy. This defines a "fuzzy" location for the transition points. It is also due the inherent chaos in the motion of P near the transition points. It can be thought of as a fuzzy chaos region. As is described in an article in Discover magazine, the WSB can be roughly viewed as the fuzzy edge of a region, referred to as a gravity well, about a body (the Moon), where its force of gravity becomes small enough to be dominated by force of gravity of another body (the Earth) and the motion there is chaotic. A much more general algorithm defining W was given in 2007. It defines W relative to n-cycles, where n = 1,2,3,..., yielding boundaries of order n. This gives a much more complex region consisting of the union of all the weak stability boundaries of order n. This definition was explored further in 2010. The results suggested that W consists, in part, of the hyperbolic network of invariant manifolds associated to the Lyapunov orbits about the L1, L2 Lagrange points near P2. The explicit determination of the set W about P2 = Jupiter, where P1 is the Sun, is described in "Computation of Weak Stability Boundaries: Sun-Jupiter Case". It turns out that a weak stability region can also be defined relative to the larger mass point, P1. A proof of the existence of the weak stability boundary about P1 was given in 2012, but a different definition is used. The chaos of the motion is analytically proven in "Geometry of Weak Stability Boundaries". The boundary is studied in "Applicability and Dynamical Characterization of the Associated Sets of the Algorithmic Weak Stability Boundary in the Lunar Sphere of Influence". == Applications == There are a number of important applications for the weak stability boundary (WSB). Since the WSB defines a region of temporary capture, it can be used, for example, to find transfer trajectories from the Earth to the Moon that arrive at the Moon within the WSB region in weak capture, which is called ballistic capture for a spacecraft. No fuel is required for capture in this case. This was numerically demonstrated in 1987. This is the first reference for ballistic capture for spacecraft and definition of the weak stability boundary. The boundary was operationally demonstrated to exist in 1991 when it was used to find a ballistic capture transfer to the Moon for Japan's Hiten spacecraft. Other missions have used the same transfer type as Hiten, including Grail, Capstone, Danuri, Hakuto-R Mission 1 and SLIM. The WSB for Mars is studied in "Earth-Mars Transfers with Ballistic Capture" and ballistic capture transfers to Mars are computed. The BepiColombo mission of ESA should achieve ballistic capture at the WSB of Mercury in November 2026. The WSB region can be used in the field of Astrophysics. It can be defined for stars within open star clusters. This is done in "Chaotic Exchange of Solid Material Between Planetary Systems: Implications for the Lithopanspermia Hypothesis" to analyze the capture of solid material that may have arrived on the Earth early in the age of the Solar System to study the validity of the lithopanspermia hypothesis. Numerical explorations of trajectories for P starting in the WSB region about P2 show that after the particle P escapes P2 at the end of weak capture, it moves about the primary body, P1, in a near resonant orbit, in resonance with P2 about P1. This property was used to study comets that move in orbits about the Sun in orbital resonance with Jupiter, which change resonance orbits by becoming weakly captured by Jupiter. An example of such a comet is 39P/Oterma. This property of change of resonance of orbits about P1 when P is weakly captured by the WSB of P2 has an interesting application to the field of quantum mechanics to the motion of an electron about the proton in a hydrogen atom. The transition motion of an electron about the proton between different energy states described by the Schrödinger equation is shown to be equivalent to the change of resonance of P about P1 via weak capture by P2 for a family of transitioning resonance orbits. This gives a classical model using chaotic dynamics with Newtonian gravity for the motion of an electron.