Various algorithms for optimization and learning in adaptive systems

This thesis discusses various methods for learning and optimization in adaptive systems. Overall, it emphasizes the relationship between optimization, learning, and adaptive systems; and it illustrates the influence of underlying hardware upon the construction of efficient algorithms for learning and optimization. Chapter 1 provides a summary and an overview.

Chapter 2 discusses a method for using feed-forward neural networks to filter the noise out of noise-corrupted signals. The networks use back-propagation learning, but they use it in a way that qualifies as unsupervised learning. The networks adapt based only on the raw input data-there are no external teachers providing information on correct operation during training. The chapter contains an analysis of the learning and develops a simple expression that, based only on the geometry of the network, predicts performance.

Chapter 3 explains a simple model of the piriform cortex, an area in the brain involved in the processing of olfactory information. The model was used to explore the possible effect of acetylcholine on learning and on odor classification. According to the model, the piriform cortex can classify odors better when acetylcholine is present during learning but not present during recall. This is interesting since it suggests that learning and recall might be separate neurochemical modes (corresponding to whether or not acetylcholine is present). When acetylcholine is turned off at all times, even during learning, the model exhibits behavior somewhat similar to Alzheimer's disease, a disease associated with the degeneration of cells that distribute acetylcholine.

Chapters 4, 5, and 6 discuss algorithms appropriate for adaptive systems implemented entirely in analog hardware. The algorithms inject noise into the systems and correlate the noise with the outputs of the systems. This allows them to estimate gradients and to implement noisy versions of gradient descent, without having to calculate gradients explicitly. The methods require only noise generators, adders, multipliers, integrators, and differentiators; and the number of devices needed scales linearly with the number of adjustable parameters in the adaptive systems. With the exception of one global signal, the algorithms require only local information exchange.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

Fracture of materials undergoing solid-solid phase transformation

A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.

In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.

Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.

Learning and management skills: the internationalization of Grupo Arcor. Analysis from a process-based approach

This paper analyzes the path of the international expansion of Grupo Arcor, an Argentine multinational company specializing in confectionery. The objective is to entify corporate strategies and business learning that led this Latin American firm to establish itself as one of the leading manufacturers in confectionery industry ,particularly in the 21st Century. The analysis is primarily qualitative in order to identify the economic dimension as a determinant in the internationalization process; a processbased approach from the Uppsala Model is used for this. However, the study is also complemented with a regression analysis to test if the firm was driven to expand internationally by the expectations on the degree of globalization of the industry and the accumulation of experience in foreign markets, and if the company was influenced by psychic distance in choosing the location of its investment; given the influence of these variables in Grupo Arcor business strategies. Our findings suggest that Grupo Arcor, was able to become global due to strategies such as vertical integration, diversification of products and geographical markets (based on psychic distance) and indeed some strategies were consequence of the globalization of the sector and the accumulation of experience in foreign markets.

Interplay of martensitic phase transformation and plastic slip in polycrystals

Inspired by key experimental and analytical results regarding Shape Memory Alloys (SMAs), we propose a modelling framework to explore the interplay between martensitic phase transformations and plastic slip in polycrystalline materials, with an eye towards computational efficiency. The resulting framework uses a convexified potential for the internal energy density to capture the stored energy associated with transformation at the meso-scale, and introduces kinetic potentials to govern the evolution of transformation and plastic slip. The framework is novel in the way it treats plasticity on par with transformation.

We implement the framework in the setting of anti-plane shear, using a staggered implicit/explict update: we first use a Fast-Fourier Transform (FFT) solver based on an Augmented Lagrangian formulation to implicitly solve for the full-field displacements of a simulated polycrystal, then explicitly update the volume fraction of martensite and plastic slip using their respective stick-slip type kinetic laws. We observe that, even in this simple setting with an idealized material comprising four martensitic variants and four slip systems, the model recovers a rich variety of SMA type behaviors. We use this model to gain insight into the isothermal behavior of stress-stabilized martensite, looking at the effects of the relative plastic yield strength, the memory of deformation history under non-proportional loading, and several others.

We extend the framework to the generalized 3-D setting, for which the convexified potential is a lower bound on the actual internal energy, and show that the fully implicit discrete time formulation of the framework is governed by a variational principle for mechanical equilibrium. We further propose an extension of the method to finite deformations via an exponential mapping. We implement the generalized framework using an existing Optimal Transport Mesh-free (OTM) solver. We then model the $\alpha$--$\gamma$ and $\alpha$--$\varepsilon$ transformations in pure iron, with an initial attempt in the latter to account for twinning in the parent phase. We demonstrate the scalability of the framework to large scale computing by simulating Taylor impact experiments, observing nearly linear (ideal) speed-up through 256 MPI tasks. Finally, we present preliminary results of a simulated Split-Hopkinson Pressure Bar (SHPB) experiment using the $\alpha$--$\varepsilon$ model.

A model of the olfactory bulb and beyond

The olfactory bulb of mammals aids in the discrimination of odors. A mathematical model based on the bulbar anatomy and electrophysiology is described. Simulations of the highly non-linear model produce a 35-60 Hz modulated activity, which is coherent across the bulb. The decision states (for the odor information) in this system can be thought of as stable cycles, rather than as point stable states typical of simpler neuro-computing models. Analysis shows that a group of coupled non-linear oscillators are responsible for the oscillatory activities. The output oscillation pattern of the bulb is determined by the odor input. The model provides a framework in which to understand the transformation between odor input and bulbar output to the olfactory cortex. This model can also be extended to other brain areas such as the hippocampus, thalamus, and neocortex, which show oscillatory neural activities. There is significant correspondence between the model behavior and observed electrophysiology.

It has also been suggested that the olfactory bulb, the first processing center after the sensory cells in the olfactory pathway, plays a role in olfactory adaptation, odor sensitivity enhancement by motivation, and other olfactory psychophysical phenomena. The input from the higher olfactory centers to the inhibitory cells in the bulb are shown to be able to modulate the response, and thus the sensitivity, of the bulb to odor input. It follows that the bulb can decrease its sensitivity to a pre-existing and detected odor (adaptation) while remaining sensitive to new odors, or can increase its sensitivity to discover interesting new odors. Other olfactory psychophysical phenomena such as cross-adaptation are also discussed.

Otto Kelland’s Model Dories and the Digital Archives Initiative

Otto Kelland was a truly unique individual in Newfoundland. During his long life he had several careers from being a prison superintendant to being an instructor at Marine Institute. During his life Kelland made hundreds of wooden boat models. They are beautifuly hand-crafted and represented the type of watercraft used by fishermen in Newfoundland. The collection of boat models made by Otto Kelland and owned by Marine Institute made an ideal object to be digitalized. In particular the collection of dories was an ideal group to be digitized. They were housed in one cabinet and accompanied by hand-written documents describing each model. The Digital Archives Initiative (DAI) is a “gateway to the learning and research-based cultural resources held by Memorial University of Newfoundland and partnering organizations.” The DAI hosts a variety of collections which together reinforce the importance, past and present, of Newfoundland and Labrador's history and culture. I will give an oral presentation of the project followed by a demonstration of the Otto Kelland Dories exhibit on the Digital Archives Initiative (DAI) at Memorial University of Newfoundland. I will be happy to answer questions following my presentation.

Bertso transformation with pattern-based sampling

This paper presents a method to generate new melodies, based on conserving the semiotic structure of a template piece. A pattern discovery algorithm is applied to a template piece to extract significant segments: those that are repeated and those that are transposed in the piece. Two strategies are combined to describe the semiotic coherence structure of the template piece: inter-segment coherence and intra-segment coherence. Once the structure is described it is used as a template for new musical content that is generated using a statistical model created from a corpus of bertso melodies and iteratively improved using a stochastic optimization method. Results show that the method presented here effectively describes a coherence structure of a piece by discovering repetition and transposition relations between segments, and also by representing the relations among notes within the segments. For bertso generation the method correctly conserves all intra and inter-segment coherence of the template, and the optimization method produces coherent generated melodies.

Ensino e aprendizado em serviços de atenção básica do SUS: desafios da formação médica com a perspectiva da integralidade narrativas e tessituras

Esta investigação enfoca processos de ensino, aprendizagem e avaliação na graduação médica, que acontecem em serviços básicos do Sistema Único de Saúde (SUS), com ênfase nos entraves e potencialidades para a transformação das relações entre a formação e a assistência na perspectiva da integralidade, tendo como referência as Diretrizes Curriculares Nacionais para os Cursos de Graduação em medicina, homologadas pelo Conselho Nacional de Educação em 2001. Com uma abordagem metodológica qualitativa que reúne contribuições da etnografia, da pesquisa transdisciplinar e da cartografia, a pesquisadora propõe ao leitor um diálogo com os relatos de suas observações (de experiências formativas na atenção básica) e dados oriundos da sua própria preceptoria de estudantes de medicina envolvidos em atividades em um centro municipal de saúde. Aponta desafios que necessitam ser enfrentados como: a hegemonia da racionalidade biomédica na conformação do modelo tecnoassistencial e a necessidade de efetivar uma política de recursos humanos no setor que incentive a integração universidade-serviço-comunidade, na aproximação da graduação ao cotidiano do trabalho em saúde e à realidade de vida da população. Estas questões estão associadas ao atual debate sobre integração curricular , educação permanente visando uma práxis formativa criativa que envolva o desenvolvimento de competências (técnico-políticas) e o compromisso para com o cuidado no SUS. Conclui que é justamente na trama local cotidiana, na problematização e intercâmbio entre experiências, que afloram caminhos criativos na superação das rotinas e práticas mecanizadas . Estes processos transformadores são matérias de reflexão para que novos projetos de cuidado sejam construídos coletivamente, emergindo novos patamares na assistência e na formação.

A uniform phase representation for the harmonic model in speech synthesis applications

Feature-based vocoders, e.g., STRAIGHT, offer a way to manipulate the perceived characteristics of the speech signal in speech transformation and synthesis. For the harmonic model, which provide excellent perceived quality, features for the amplitude parameters already exist (e.g., Line Spectral Frequencies (LSF), Mel-Frequency Cepstral Coefficients (MFCC)). However, because of the wrapping of the phase parameters, phase features are more difficult to design. To randomize the phase of the harmonic model during synthesis, a voicing feature is commonly used, which distinguishes voiced and unvoiced segments. However, voice production allows smooth transitions between voiced/unvoiced states which makes voicing segmentation sometimes tricky to estimate. In this article, two-phase features are suggested to represent the phase of the harmonic model in a uniform way, without voicing decision. The synthesis quality of the resulting vocoder has been evaluated, using subjective listening tests, in the context of resynthesis, pitch scaling, and Hidden Markov Model (HMM)-based synthesis. The experiments show that the suggested signal model is comparable to STRAIGHT or even better in some scenarios. They also reveal some limitations of the harmonic framework itself in the case of high fundamental frequencies.

A Data Dropout Compensation Algorithm Based on the Iterative Learning Control Methodology for Discrete-Time Systems

This paper deals with the convergence of a remote iterative learning control system subject to data dropouts. The system is composed by a set of discrete-time multiple input-multiple output linear models, each one with its corresponding actuator device and its sensor. Each actuator applies the input signals vector to its corresponding model at the sampling instants and the sensor measures the output signals vector. The iterative learning law is processed in a controller located far away of the models so the control signals vector has to be transmitted from the controller to the actuators through transmission channels. Such a law uses the measurements of each model to generate the input vector to be applied to its subsequent model so the measurements of the models have to be transmitted from the sensors to the controller. All transmissions are subject to failures which are described as a binary sequence taking value 1 or 0. A compensation dropout technique is used to replace the lost data in the transmission processes. The convergence to zero of the errors between the output signals vector and a reference one is achieved as the number of models tends to infinity.

Structure learning in a sensorimotor association task.

Learning is often understood as an organism's gradual acquisition of the association between a given sensory stimulus and the correct motor response. Mathematically, this corresponds to regressing a mapping between the set of observations and the set of actions. Recently, however, it has been shown both in cognitive and motor neuroscience that humans are not only able to learn particular stimulus-response mappings, but are also able to extract abstract structural invariants that facilitate generalization to novel tasks. Here we show how such structure learning can enhance facilitation in a sensorimotor association task performed by human subjects. Using regression and reinforcement learning models we show that the observed facilitation cannot be explained by these basic models of learning stimulus-response associations. We show, however, that the observed data can be explained by a hierarchical Bayesian model that performs structure learning. In line with previous results from cognitive tasks, this suggests that hierarchical Bayesian inference might provide a common framework to explain both the learning of specific stimulus-response associations and the learning of abstract structures that are shared by different task environments.