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Wilmington, North Carolina once had a thriving Black middle class and an elected interracial government. In 1898 white supremacists used violence to overthrow that government, kill Black residents and drive many others from the city.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
Adaptive resonance theory (ART) is a theory developed by Stephen Grossberg and Gail Carpenter on aspects of how the brain processes information. It describes a number of artificial neural network models which use supervised and unsupervised learning methods, and address problems such as pattern recognition and prediction.
The primary intuition behind the ART model is that object identification and recognition generally occur as a result of the interaction of 'top-down' observer expectations with 'bottom-up' sensory information. The model postulates that 'top-down' expectations take the form of a memory template or prototype that is then compared with the actual features of an object as detected by the senses. This comparison gives rise to a measure of category belongingness. As long as this difference between sensation and expectation does not exceed a set threshold called the 'vigilance parameter', the sensed object will be considered a member of the expected class. The system thus offers a solution to the 'plasticity/stability' problem, i.e. the problem of acquiring new knowledge without disrupting existing knowledge that is also called incremental learning.
The basic ART system is an unsupervised learning model. It typically consists of a comparison field and a recognition field composed of neurons, a vigilance parameter (threshold of recognition), and a reset module.
There are two basic methods of training ART-based neural networks: slow and fast. In the slow learning method, the degree of training of the recognition neuron's weights towards the input vector is calculated to continuous values with differential equations and is thus dependent on the length of time the input vector is presented. With fast learning, algebraic equations are used to calculate degree of weight adjustments to be made, and binary values are used. While fast learning is effective and efficient for a variety of tasks, the slow learning method is more biologically plausible and can be used with continuous-time networks (i.e. when the input vector can vary continuously).
ART 1[1][2] is the simplest variety of ART networks, accepting only binary inputs. ART 2[3] extends network capabilities to support continuous inputs. ART 2-A[4] is a streamlined form of ART-2 with a drastically accelerated runtime, and with qualitative results being only rarely inferior to the full ART-2 implementation. ART 3[5] builds on ART-2 by simulating rudimentary neurotransmitter regulation of synaptic activity by incorporating simulated sodium (Na+) and calcium (Ca2+) ion concentrations into the system's equations, which results in a more physiologically realistic means of partially inhibiting categories that trigger mismatch resets.
ARTMAP[6] also known as Predictive ART, combines two slightly modified ART-1 or ART-2 units into a supervised learning structure where the first unit takes the input data and the second unit takes the correct output data, then used to make the minimum possible adjustment of the vigilance parameter in the first unit in order to make the correct classification.
Fuzzy ART[7] implements fuzzy logic into ART's pattern recognition, thus enhancing generalizability. An optional (and very useful) feature of fuzzy ART is complement coding, a means of incorporating the absence of features into pattern classifications, which goes a long way toward preventing inefficient and unnecessary category proliferation. The applied similarity measures are based on the L1 norm. Fuzzy ART is known to be very sensitive to noise.
Fuzzy ARTMAP[8] is merely ARTMAP using fuzzy ART units, resulting in a corresponding increase in efficacy.
Simplified Fuzzy ARTMAP (SFAM)[9] constitutes a strongly simplified variant of fuzzy ARTMAP dedicated to classification tasks.
Gaussian ART[10] and Gaussian ARTMAP[10] use Gaussian activation functions and computations based on probability theory. Therefore, they have some similarity with Gaussian mixture models. In comparison to fuzzy ART and fuzzy ARTMAP, they are less sensitive to noise. But the stability of learnt representations is reduced which may lead to category proliferation in open-ended learning tasks.
Fusion ART and related networks[11][12][13] extend ART and ARTMAP to multiple pattern channels. They support several learning paradigms, including unsupervised learning, supervised learning and reinforcement learning.
TopoART[14] combines fuzzy ART with topology learning networks such as the growing neural gas. Furthermore, it adds a noise reduction mechanism. There are several derived neural networks which extend TopoART to further learning paradigms.
Hypersphere ART[15] and Hypersphere ARTMAP[15] are closely related to fuzzy ART and fuzzy ARTMAP, respectively. But as they use a different type of category representation (namely hyperspheres), they do not require their input to be normalised to the interval [0, 1]. They apply similarity measures based on the L2 norm.
LAPART[16] The Laterally Primed Adaptive Resonance Theory (LAPART) neural networks couple two Fuzzy ART algorithms to create a mechanism for making predictions based on learned associations. The coupling of the two Fuzzy ARTs has a unique stability that allows the system to converge rapidly towards a clear solution. Additionally, it can perform logical inference and supervised learning similar to fuzzy ARTMAP.
It has been noted that results of Fuzzy ART and ART 1 (i.e., the learnt categories) depend critically upon the order in which the training data are processed. The effect can be reduced to some extent by using a slower learning rate, but is present regardless of the size of the input data set. Hence Fuzzy ART and ART 1 estimates do not possess the statistical property of consistency.[17] This problem can be considered as a side effect of the respective mechanisms ensuring stable learning in both networks.
More advanced ART networks such as TopoART and Hypersphere TopoART that summarise categories to clusters may solve this problem as the shapes of the clusters do not depend on the order of creation of the associated categories. (cf. Fig. 3(g, h) and Fig. 4 of [18])
Wasserman, Philip D. (1989), Neural computing: theory and practice, New York: Van Nostrand Reinhold, ISBN 0-442-20743-3
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
Adaptive resonance theory (ART) is a theory developed by Stephen Grossberg and Gail Carpenter on aspects of how the brain processes information. It describes a number of artificial neural network models which use supervised and unsupervised learning methods, and address problems such as pattern recognition and prediction. The primary intuition behind the ART model is that object identification and recognition generally occur as a result of the interaction of 'top-down' observer expectations with 'bottom-up' sensory information. The model postulates that 'top-down' expectations take the form of a memory template or prototype that is then compared with the actual features of an object as detected by the senses. This comparison gives rise to a measure of category belongingness. As long as this difference between sensation and expectation does not exceed a set threshold called the 'vigilance parameter', the sensed object will be considered a member of the expected class. The system thus offers a solution to the 'plasticity/stability' problem, i.e. the problem of acquiring new knowledge without disrupting existing knowledge that is also called incremental learning.
Fusion adaptive resonance theory (fusion ART) is a generalization of self-organizing neural networks known as the original Adaptive Resonance Theory models for learning recognition categories across multiple pattern channels. There is a separate stream of work on fusion ARTMAP, that extends fuzzy ARTMAP consisting of two fuzzy ART modules connected by an inter-ART map field to an extended architecture consisting of multiple ART modules. Fusion ART unifies a number of neural model designs and supports a myriad of learning paradigms, notably unsupervised learning, supervised learning, reinforcement learning, multimodal learning, and sequence learning. In addition, various extensions have been developed for domain knowledge integration, memory representation, and modelling of high level cognition.
Gail Alexandra Carpenter is an American cognitive scientist, neuroscientist and mathematician, known for her work with Stephen Grossberg developing adaptive resonance theory, a theory of how the human brain processes information, and for her work on the Hodgkin–Huxley model of how neurons operate. She is a professor emerita of mathematics and statistics at Boston University, where she was also a professor of cognitive and neural systems.
In computational chemistry, natural resonance theory (NRT) is an iterative, variational functional embedded into the natural bond orbital (NBO) program, commonly run in Gaussian, GAMESS, ORCA, Ampac and other software packages. NRT was developed in 1997 by Frank A. Weinhold and Eric D. Glendening, chemistry professors at University of Wisconsin-Madison and Indiana State University, respectively. Given a list of NBOs for an idealized natural Lewis structure, the NRT functional creates a list of Lewis resonance structures and calculates the resonance weights of each contributing resonance structure. Structural and chemical properties, such as bond order, valency, and bond polarity, may be calculated from resonance weights. Specifically, bond orders may be divided into their covalent and ionic contributions, while valency is the sum of bond orders of a given atom. This aims to provide quantitative results that agree with qualitative notions of chemical resonance. In contrast to the "wavefunction resonance theory" (i.e., the superposition of wavefunctions), NRT uses the density matrix resonance theory, performing a superposition of density matrices to realize resonance. NRT has applications in ab initio calculations, including calculating the bond orders of intra- and intermolecular interactions and the resonance weights of radical isomers.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Brown v. Board of Education in 1954.