Statistical Properties of Single and Competing Non-Linear Fast-Slow Oscillators in Noise

Statistical properties offast-slow Ellias-Grossberg oscillators are studied in response to deterministic and noisy inputs. Oscillatory responses remain stable in noise due to the slow inhibitory variable, which establishes an adaptation level that centers the oscillatory responses of the fast excitatory variable to deterministic and noisy inputs. Competitive interactions between oscillators improve the stability in noise. Although individual oscillation amplitudes decrease with input amplitude, the average to'tal activity increases with input amplitude, thereby suggesting that oscillator output is evaluated by a slow process at downstream network sites.

A Neural Network Architecture for Autonomous Learning, Recognition, and Prediction in a Nonstationary World

In a constantly changing world, humans are adapted to alternate routinely between attending to familiar objects and testing hypotheses about novel ones. We can rapidly learn to recognize and narne novel objects without unselectively disrupting our memories of familiar ones. We can notice fine details that differentiate nearly identical objects and generalize across broad classes of dissimilar objects. This chapter describes a class of self-organizing neural network architectures--called ARTMAP-- that are capable of fast, yet stable, on-line recognition learning, hypothesis testing, and naming in response to an arbitrary stream of input patterns (Carpenter, Grossberg, Markuzon, Reynolds, and Rosen, 1992; Carpenter, Grossberg, and Reynolds, 1991). The intrinsic stability of ARTMAP allows the system to learn incrementally for an unlimited period of time. System stability properties can be traced to the structure of its learned memories, which encode clusters of attended features into its recognition categories, rather than slow averages of category inputs. The level of detail in the learned attentional focus is determined moment-by-moment, depending on predictive success: an error due to over-generalization automatically focuses attention on additional input details enough of which are learned in a new recognition category so that the predictive error will not be repeated. An ARTMAP system creates an evolving map between a variable number of learned categories that compress one feature space (e.g., visual features) to learned categories of another feature space (e.g., auditory features). Input vectors can be either binary or analog. Computational properties of the networks enable them to perform significantly better in benchmark studies than alternative machine learning, genetic algorithm, or neural network models. Some of the critical problems that challenge and constrain any such autonomous learning system will next be illustrated. Design principles that work together to solve these problems are then outlined. These principles are realized in the ARTMAP architecture, which is specified as an algorithm. Finally, ARTMAP dynamics are illustrated by means of a series of benchmark simulations.

Fusion ARTMAP: An Adaptive Fuzzy Network for Multi-Channel Classification

Fusion ARTMAP is a self-organizing neural network architecture for multi-channel, or multi-sensor, data fusion. Fusion ARTMAP generalizes the fuzzy ARTMAP architecture in order to adaptively classify multi-channel data. The network has a symmetric organization such that each channel can be dynamically configured to serve as either a data input or a teaching input to the system. An ART module forms a compressed recognition code within each channel. These codes, in turn, beco1ne inputs to a single ART system that organizes the global recognition code. When a predictive error occurs, a process called parallel match tracking simultaneously raises vigilances in multiple ART modules until reset is triggered in one of thmn. Parallel match tracking hereby resets only that portion of the recognition code with the poorest match, or minimum predictive confidence. This internally controlled selective reset process is a type of credit assignment that creates a parsimoniously connected learned network.

Fuzzy ART

Adaptive Resonance Theory (ART) models are real-time neural networks for category learning, pattern recognition, and prediction. Unsupervised fuzzy ART and supervised fuzzy ARTMAP synthesize fuzzy logic and ART networks by exploiting the formal similarity between the computations of fuzzy subsethood and the dynamics of ART category choice, search, and learning. Fuzzy ART self-organizes stable recognition categories in response to arbitrary sequences of analog or binary input patterns. It generalizes the binary ART 1 model, replacing the set-theoretic: intersection (∩) with the fuzzy intersection (∧), or component-wise minimum. A normalization procedure called complement coding leads to a symmetric: theory in which the fuzzy inter:>ec:tion and the fuzzy union (∨), or component-wise maximum, play complementary roles. Complement coding preserves individual feature amplitudes while normalizing the input vector, and prevents a potential category proliferation problem. Adaptive weights :otart equal to one and can only decrease in time. A geometric interpretation of fuzzy AHT represents each category as a box that increases in size as weights decrease. A matching criterion controls search, determining how close an input and a learned representation must be for a category to accept the input as a new exemplar. A vigilance parameter (p) sets the matching criterion and determines how finely or coarsely an ART system will partition inputs. High vigilance creates fine categories, represented by small boxes. Learning stops when boxes cover the input space. With fast learning, fixed vigilance, and an arbitrary input set, learning stabilizes after just one presentation of each input. A fast-commit slow-recode option allows rapid learning of rare events yet buffers memories against recoding by noisy inputs. Fuzzy ARTMAP unites two fuzzy ART networks to solve supervised learning and prediction problems. A Minimax Learning Rule controls ARTMAP category structure, conjointly minimizing predictive error and maximizing code compression. Low vigilance maximizes compression but may therefore cause very different inputs to make the same prediction. When this coarse grouping strategy causes a predictive error, an internal match tracking control process increases vigilance just enough to correct the error. ARTMAP automatically constructs a minimal number of recognition categories, or "hidden units," to meet accuracy criteria. An ARTMAP voting strategy improves prediction by training the system several times using different orderings of the input set. Voting assigns confidence estimates to competing predictions given small, noisy, or incomplete training sets. ARPA benchmark simulations illustrate fuzzy ARTMAP dynamics. The chapter also compares fuzzy ARTMAP to Salzberg's Nested Generalized Exemplar (NGE) and to Simpson's Fuzzy Min-Max Classifier (FMMC); and concludes with a summary of ART and ARTMAP applications.

Simulating Effects of Learning and Lesions with a Model of Intrinsic and Synaptically Gated Responses of Striatal Cholinergic Interneurons

The giant cholinergic interneurons of the striatum are tonically active neurons (TANs) that respond with characteristic pauses to novel events and to appetitive and aversive conditioned stimuli. Fluctuations in acetylcholine release by TANs modulate performance- and learning-related dynamics in the striatum. Whereas tonic activity emerges from intrinsic properties of these neurons, glutamatergic inputs from thalamic centromedian-parafascicular nuclei, and dopaminergic inputs from midbrain, are required for the generation of pause responses. No prior computational models encompass both intrinsic and synaptically-gated dynamics. We present a mathematical model that robustly accounts for behavior-related electrophysiological properties of TANs in terms of their intrinsic physiological properties and known afferents. In the model, balanced intrinsic hyperpolarizing and depolarizing currents engender tonic firing, and glutamatergic inputs from thalamus (and cortex) both directly excite and indirectly inhibit TANs. If the latter inhibition, presumably mediated by GABAergic interneurons, exceeds a threshold, its effect is amplified by a KIR current to generate a prolonged pause. In the model, the intrinsic mechanisms and external inputs are both modulated by learning-dependent dopamine (DA) signals and our simulations revealed that many learning-dependent behaviors of TANs are explicable without recourse to learning-dependent changes in synapses onto TANs. The "teaching signal" that modulates reinforcement learning at cortico-striatal synapses may be a sequence composed of an adaptively scaled DA burst, a brief ACh burst, and a scaled ACh pause. Such an interpretation is consistent with recent data on cholinergic control of LTD of cortical synapses onto striatal spiny projection neurons.

Texture Segregation By Visual Cortex: Perceptual Grouping, Attention, and Learning

A neural model is proposed of how laminar interactions in the visual cortex may learn and recognize object texture and form boundaries. The model brings together five interacting processes: region-based texture classification, contour-based boundary grouping, surface filling-in, spatial attention, and object attention. The model shows how form boundaries can determine regions in which surface filling-in occurs; how surface filling-in interacts with spatial attention to generate a form-fitting distribution of spatial attention, or attentional shroud; how the strongest shroud can inhibit weaker shrouds; and how the winning shroud regulates learning of texture categories, and thus the allocation of object attention. The model can discriminate abutted textures with blurred boundaries and is sensitive to texture boundary attributes like discontinuities in orientation and texture flow curvature as well as to relative orientations of texture elements. The model quantitatively fits a large set of human psychophysical data on orientation-based textures. Object boundar output of the model is compared to computer vision algorithms using a set of human segmented photographic images. The model classifies textures and suppresses noise using a multiple scale oriented filterbank and a distributed Adaptive Resonance Theory (dART) classifier. The matched signal between the bottom-up texture inputs and top-down learned texture categories is utilized by oriented competitive and cooperative grouping processes to generate texture boundaries that control surface filling-in and spatial attention. Topdown modulatory attentional feedback from boundary and surface representations to early filtering stages results in enhanced texture boundaries and more efficient learning of texture within attended surface regions. Surface-based attention also provides a self-supervising training signal for learning new textures. Importance of the surface-based attentional feedback in texture learning and classification is tested using a set of textured images from the Brodatz micro-texture album. Benchmark studies vary from 95.1% to 98.6% with attention, and from 90.6% to 93.2% without attention.

Working Memory Networks for Learning Temporal Order, with Application to 3-D Visual Object Recognition

Working memory neural networks are characterized which encode the invariant temporal order of sequential events. Inputs to the networks, called Sustained Temporal Order REcurrent (STORE) models, may be presented at widely differing speeds, durations, and interstimulus intervals. The STORE temporal order code is designed to enable all emergent groupings of sequential events to be stably learned and remembered in real time, even as new events perturb the system. Such a competence is needed in neural architectures which self-organize learned codes for variable-rate speech perception, sensory-motor planning, or 3-D visual object recognition. Using such a working memory, a self-organizing architecture for invariant 3-D visual object recognition is described. The new model is based on the model of Seibert and Waxman (1990a), which builds a 3-D representation of an object from a temporally ordered sequence of its 2-D aspect graphs. The new model, called an ARTSTORE model, consists of the following cascade of processing modules: Invariant Preprocessor --> ART 2 --> STORE Model --> ART 2 --> Outstar Network.

The development of a computer model to optimize the performance of a 50kWp photovoltaic system

A computer model has been developed to optimize the performance of a 50kWp photovoltaic system which supplies electrical energy to a dairy farm at Fota Island in Cork Harbour. Optimization of the system involves maximising the efficiency and increasing the performance and reliability of each hardware unit. The model accepts horizontal insolation, ambient temperature, wind speed, wind direction and load demand as inputs. An optimization program uses the computer model to simulate the optimum operating conditions. From this analysis, criteria are established which are used to improve the photovoltaic system operation. This thesis describes the model concepts, the model implementation and the model verification procedures used during development. It also describes the techniques which are used during system optimization. The software, which is written in FORTRAN, is structured in modular units to provide logical and efficient programming. These modular units may also be used in the modelling and optimization of other photovoltaic systems.

Modular average case analysis: Language implementation and extension

Motivated by accurate average-case analysis, MOdular Quantitative Analysis (MOQA) is developed at the Centre for Efficiency Oriented Languages (CEOL). In essence, MOQA allows the programmer to determine the average running time of a broad class of programmes directly from the code in a (semi-)automated way. The MOQA approach has the property of randomness preservation which means that applying any operation to a random structure, results in an output isomorphic to one or more random structures, which is key to systematic timing. Based on original MOQA research, we discuss the design and implementation of a new domain specific scripting language based on randomness preserving operations and random structures. It is designed to facilitate compositional timing by systematically tracking the distributions of inputs and outputs. The notion of a labelled partial order (LPO) is the basic data type in the language. The programmer uses built-in MOQA operations together with restricted control flow statements to design MOQA programs. This MOQA language is formally specified both syntactically and semantically in this thesis. A practical language interpreter implementation is provided and discussed. By analysing new algorithms and data restructuring operations, we demonstrate the wide applicability of the MOQA approach. Also we extend MOQA theory to a number of other domains besides average-case analysis. We show the strong connection between MOQA and parallel computing, reversible computing and data entropy analysis.

Hybrid integration and packaging of grating-coupled silicon photonics

This thesis covers both the packaging of silicon photonic devices with fiber inputs and outputs as well as the integration of laser light sources with these same devices. The principal challenge in both of these pursuits is coupling light into the submicrometer waveguides that are the hallmark of silicon-on-insulator (SOI) systems. Previous work on grating couplers is leveraged to design new approaches to bridge the gap between the highly-integrated domain of silicon, the Interconnected world of fiber and the active region of III-V materials. First, a novel process for the planar packaging of grating couplers with fibers is explored in detail. This technology allows the creation of easy-to-use test platforms for laser integration and also stands on its own merits as an enabling technology for next-generation silicon photonics systems. The alignment tolerances of this process are shown to be well-suited to a passive alignment process and for wafer-scale assembly. Furthermore, this technology has already been used to package demonstrators for research partners and is included in the offerings of the ePIXfab silicon photonics foundry and as a design kit for PhoeniX Software’s MaskEngineer product. After this, a process for hybridly integrating a discrete edge-emitting laser with a silicon photonic circuit using near-vertical coupling is developed and characterized. The details of the various steps of the design process are given, including mechanical, thermal, optical and electrical steps. The interrelation of these design domains is also discussed. The construction process for a demonstrator is outlined, and measurements are presented of a series of single-wavelength Fabry-Pérot lasers along with a two-section laser tunable in the telecommunications C-band. The suitability and potential of this technology for mass manufacture is demonstrated, with further opportunities for improvement detailed and discussed in the conclusion.

Control circuits for avalanche photodiodes

Avalanche Photodiodes (APDs) have been used in a wide range of low light sensing applications such as DNA sequencing, quantum key distribution, LIDAR and medical imaging. To operate the APDs, control circuits are required to achieve the desired performance characteristics. This thesis presents the work on development of three control circuits including a bias circuit, an active quench and reset circuit and a gain control circuit all of which are used for control and performance enhancement of the APDs. The bias circuit designed is used to bias planar APDs for operation in both linear and Geiger modes. The circuit is based on a dual charge pumps configuration and operates from a 5 V supply. It is capable of providing milliamp load currents for shallow-junction planar APDs that operate up to 40 V. With novel voltage regulators, the bias voltage provided by the circuit can be accurately controlled and easily adjusted by the end user. The circuit is highly integrable and provides an attractive solution for applications requiring a compact integrated APD device. The active quench and reset circuit is designed for APDs that operate in Geiger-mode and are required for photon counting. The circuit enables linear changes in the hold-off time of the Geiger-mode APD (GM-APD) from several nanoseconds to microseconds with a stable setting step of 6.5 ns. This facilitates setting the optimal `afterpulse-free' hold-off time for any GM-APD via user-controlled digital inputs. In addition this circuit doesn’t require an additional monostable or pulse generator to reset the detector, thus simplifying the circuit. Compared to existing solutions, this circuit provides more accurate and simpler control of the hold-off time while maintaining a comparable maximum count-rate of 35.2 Mcounts/s. The third circuit designed is a gain control circuit. This circuit is based on the idea of using two matched APDs to set and stabilize the gain. The circuit can provide high bias voltage for operating the planar APD, precisely set the APD’s gain (with the errors of less than 3%) and compensate for the changes in the temperature to maintain a more stable gain. The circuit operates without the need for external temperature sensing and control electronics thus lowering the system cost and complexity. It also provides a simpler and more compact solution compared to previous designs. The three circuits designed in this project were developed independently of each other and are used for improving different performance characteristics of the APD. Further research on the combination of the three circuits will produce a more compact APD-based solution for a wide range of applications.

The relationship between rural livelihoods and livestock keeping: the case of Sidama Zone, Southern Ethiopia

This study examines the relationship between rural livelihoods and livestock keeping in Sidama Zones, southern Ethiopia. The livelihood context, assets and strategies of households are the key features of rural livelihoods considered in the study; while households’ livestock ownership, dependence on livestock and livestock management are the main aspects of livestock keeping examined. The study used the sustainable livelihood approach as a framework for data collection and analysis. Describing the main features of rural livelihoods and livestock keeping, and the general pattern of relationship between them, this study mainly aims at identifying the main livelihood factors that determine livestock keeping in the study area. Descriptive statistics, pair wise correlations, mean comparisons and analysis of variance were used to describe rural livelihoods and livestock keeping as well as the relationship between them. Tobit regressions were used to examine the effect of the various livelihood factors on households’ livestock ownership and dependence; Poisson regressions are used to investigate the factors that influence the intensity of livestock management measured by the use of different technologies and inputs. The findings indicated that a number of livelihood factors - assets, livelihood strategies, livelihood shocks and institutional supports - significantly determine the different aspects of livestock keeping. These include: human assets such as age, education and family size; social assets such as membership to social groups; financial assets such as credit; natural assets such as land, and household physical assets; and livelihood strategies such as diversification into farm and nonfarm activities, and coping mechanisms. In addition the livelihood vulnerability context such as shocks and institutional support are among the main determinants of livestock keeping. The results, by and large, matched the findings of previous studies, and it is concluded that households livestock keeping depends on their livelihoods. Accordingly, it is recommended that policies aiming at livestock asset building and productivity improvement should take the livelihoods of rural households in to consideration. As such the study contribute to scholarly works in the area of rural livelihoods, in general, and livestock keeping, in particular. It also contributes to a better understanding of the problems of livestock keeping within the context of rural livelihoods in the country and to the formulation of appropriate policy for the development of the sector.

Networks versus vertical integration

We construct a theory to compare vertically integrated firms to networks of manufacturers and suppliers. Vertically integrated firms make their own specialized inputs. In networks, manufacturers procure specialized inputs from suppliers that, in turn, sell to several manufacturers. The analysis shows that networks can yield greater social welfare when manufacturers experience large idiosyncratic demand shocks. Individual firms may also have the incentive to form networks, despite the lack of long-term contracts. The analysis is supported by existing evidence and provides predictions as to the shape of different industries.

Serotonin synthesis, release and reuptake in terminals: a mathematical model.

BACKGROUND: Serotonin is a neurotransmitter that has been linked to a wide variety of behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and affective disorders. Full understanding of serotonergic systems in the central nervous system involves genomics, neurochemistry, electrophysiology, and behavior. Though associations have been found between functions at these different levels, in most cases the causal mechanisms are unknown. The scientific issues are daunting but important for human health because of the use of selective serotonin reuptake inhibitors and other pharmacological agents to treat disorders in the serotonergic signaling system. METHODS: We construct a mathematical model of serotonin synthesis, release, and reuptake in a single serotonergic neuron terminal. The model includes the effects of autoreceptors, the transport of tryptophan into the terminal, and the metabolism of serotonin, as well as the dependence of release on the firing rate. The model is based on real physiology determined experimentally and is compared to experimental data. RESULTS: We compare the variations in serotonin and dopamine synthesis due to meals and find that dopamine synthesis is insensitive to the availability of tyrosine but serotonin synthesis is sensitive to the availability of tryptophan. We conduct in silico experiments on the clearance of extracellular serotonin, normally and in the presence of fluoxetine, and compare to experimental data. We study the effects of various polymorphisms in the genes for the serotonin transporter and for tryptophan hydroxylase on synthesis, release, and reuptake. We find that, because of the homeostatic feedback mechanisms of the autoreceptors, the polymorphisms have smaller effects than one expects. We compute the expected steady concentrations of serotonin transporter knockout mice and compare to experimental data. Finally, we study how the properties of the the serotonin transporter and the autoreceptors give rise to the time courses of extracellular serotonin in various projection regions after a dose of fluoxetine. CONCLUSIONS: Serotonergic systems must respond robustly to important biological signals, while at the same time maintaining homeostasis in the face of normal biological fluctuations in inputs, expression levels, and firing rates. This is accomplished through the cooperative effect of many different homeostatic mechanisms including special properties of the serotonin transporters and the serotonin autoreceptors. Many difficult questions remain in order to fully understand how serotonin biochemistry affects serotonin electrophysiology and vice versa, and how both are changed in the presence of selective serotonin reuptake inhibitors. Mathematical models are useful tools for investigating some of these questions.

The role of tectonic uplift, climate, and vegetation in the long-term terrestrial phosphorous cycle

Phosphorus (P) is a crucial element for life and therefore for maintaining ecosystem productivity. Its local availability to the terrestrial biosphere results from the interaction between climate, tectonic uplift, atmospheric transport, and biotic cycling. Here we present a mathematical model that describes the terrestrial P-cycle in a simple but comprehensive way. The resulting dynamical system can be solved analytically for steady-state conditions, allowing us to test the sensitivity of the P-availability to the key parameters and processes. Given constant inputs, we find that humid ecosystems exhibit lower P availability due to higher runoff and losses, and that tectonic uplift is a fundamental constraint. In particular, we find that in humid ecosystems the biotic cycling seem essential to maintain long-term P-availability. The time-dependent P dynamics for the Franz Josef and Hawaii chronosequences show how tectonic uplift is an important constraint on ecosystem productivity, while hydroclimatic conditions control the P-losses and speed towards steady-state. The model also helps describe how, with limited uplift and atmospheric input, as in the case of the Amazon Basin, ecosystems must rely on mechanisms that enhance P-availability and retention. Our novel model has a limited number of parameters and can be easily integrated into global climate models to provide a representation of the response of the terrestrial biosphere to global change. © 2010 Author(s).