Creating Common Ground: Architecture For Tactical Learning and Creative Convergence

Certain environments can inhibit learning and stifle enthusiasm, while others enhance learning or stimulate curiosity. Furthermore, in a world where technological change is accelerating we could ask how might architecture connect resource abundant and resource scarce innovation environments? Innovation environments developed out of necessity within urban villages and those developed with high intention and expectation within more institutionalized settings share a framework of opportunity for addressing change through learning and education. This thesis investigates formal and informal learning environments and how architecture can stimulate curiosity, enrich learning, create common ground, and expand access to education. The reason for this thesis exploration is to better understand how architects might design inclusive environments that bring people together to build sustainable infrastructure encouraging innovation and adaptation to change for years to come. The context of this thesis is largely based on Colin McFarlane’s theory that the “city is an assemblage for learning” The socio-spatial perspective in urbanism, considers how built infrastructure and society interact. Through the urban realm, inhabitants learn to negotiate people, space, politics, and resources affecting their daily lives. The city is therefore a dynamic field of emergent possibility. This thesis uses the city as a lens through which the boundaries between informal and formal logics as well as the public and private might be blurred. Through analytical processes I have examined the environmental devices and assemblage of factors that consistently provide conditions through which learning may thrive. These parameters that make a creative space significant can help suggest the design of common ground environments through which innovation is catalyzed.

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.