Spinal cord injury therapy through active learning

Therapy employing epidural electrostimulation holds great potential for improving therapy for patients with spinal cord injury (SCI) (Harkema et al., 2011). Further promising results from combined therapies using electrostimulation have also been recently obtained (e.g., van den Brand et al., 2012). The devices being developed to deliver the stimulation are highly flexible, capable of delivering any individual stimulus among a combinatorially large set of stimuli (Gad et al., 2013). While this extreme flexibility is very useful for ensuring that the device can deliver an appropriate stimulus, the challenge of choosing good stimuli is quite substantial, even for expert human experimenters. To develop a fully implantable, autonomous device which can provide useful therapy, it is necessary to design an algorithmic method for choosing the stimulus parameters. Such a method can be used in a clinical setting, by caregivers who are not experts in the neurostimulator's use, and to allow the system to adapt autonomously between visits to the clinic. To create such an algorithm, this dissertation pursues the general class of active learning algorithms that includes Gaussian Process Upper Confidence Bound (GP-UCB, Srinivas et al., 2010), developing the Gaussian Process Batch Upper Confidence Bound (GP-BUCB, Desautels et al., 2012) and Gaussian Process Adaptive Upper Confidence Bound (GP-AUCB) algorithms. This dissertation develops new theoretical bounds for the performance of these and similar algorithms, empirically assesses these algorithms against a number of competitors in simulation, and applies a variant of the GP-BUCB algorithm in closed-loop to control SCI therapy via epidural electrostimulation in four live rats. The algorithm was tasked with maximizing the amplitude of evoked potentials in the rats' left tibialis anterior muscle. These experiments show that the algorithm is capable of directing these experiments sensibly, finding effective stimuli in all four animals. Further, in direct competition with an expert human experimenter, the algorithm produced superior performance in terms of average reward and comparable or superior performance in terms of maximum reward. These results indicate that variants of GP-BUCB may be suitable for autonomously directing SCI therapy.

Neural network design for switching network control

A neural network is a highly interconnected set of simple processors. The many connections allow information to travel rapidly through the network, and due to their simplicity, many processors in one network are feasible. Together these properties imply that we can build efficient massively parallel machines using neural networks. The primary problem is how do we specify the interconnections in a neural network. The various approaches developed so far such as outer product, learning algorithm, or energy function suffer from the following deficiencies: long training/ specification times; not guaranteed to work on all inputs; requires full connectivity.

Alternatively we discuss methods of using the topology and constraints of the problems themselves to design the topology and connections of the neural solution. We define several useful circuits-generalizations of the Winner-Take-All circuitthat allows us to incorporate constraints using feedback in a controlled manner. These circuits are proven to be stable, and to only converge on valid states. We use the Hopfield electronic model since this is close to an actual implementation. We also discuss methods for incorporating these circuits into larger systems, neural and nonneural. By exploiting regularities in our definition, we can construct efficient networks. To demonstrate the methods, we look to three problems from communications. We first discuss two applications to problems from circuit switching; finding routes in large multistage switches, and the call rearrangement problem. These show both, how we can use many neurons to build massively parallel machines, and how the Winner-Take-All circuits can simplify our designs.

Next we develop a solution to the contention arbitration problem of high-speed packet switches. We define a useful class of switching networks and then design a neural network to solve the contention arbitration problem for this class. Various aspects of the neural network/switch system are analyzed to measure the queueing performance of this method. Using the basic design, a feasible architecture for a large (1024-input) ATM packet switch is presented. Using the massive parallelism of neural networks, we can consider algorithms that were previously computationally unattainable. These now viable algorithms lead us to new perspectives on switch design.

Design of a timber Howe truss highway bridge

The span of the bridge was assumed as 100 feet. The type of bridge used is the timber Howe Truss. The height of truss was taken as 20 feet between center lines of top and bottom chords. The width was taken as 18 feet center to center of trusses. The truss was divided up into five panels 20 feet long.

It was designed according to the "General Specifications for Steel Highway Bridges" by Ketchum. For the live load for the floor and its supports, a load of 80 pounds per square foot of total floor surface or a 15 ton traction engine with axles 10 feet centers and 6 feet gage, two thirds of load to be carried by rear axles.

For the truss a load of 75 pounds per square foot of floor surface.

For the wind load the bottom lateral bracing is to be designed to resist a lateral wind load of 300 pounds per foot of span; 150 pounds of this to be treated as a moving load.

The top lateral bracing is to be designed to resist a lateral wind force of 150 pounds per foot of span.

The timber to be used in the bridge is to be Douglas fir.

The unit stresses used for timber are those of the American Railway Engineering Association.

Design, Synthesis, and Study of Novel Platforms for Iron-N2 Chemistry and Photoinduced, Copper-mediated C-N Bond Formation

Several new ligand platforms designed to support iron dinitrogen chemistry have been developed. First, we report Fe complexes of a tris(phosphino)alkyl (CP^iPr₃) ligand featuring an axial carbon donor intended to conceptually model the interstitial carbide atom of the nitrogenase iron-molybdenum cofactor (FeMoco). It is established that in this scaffold, the iron center binds dinitrogen trans to the C_alkyl anchor in three structurally characterized oxidation states. Fe-C_alkyl lengthening is observed upon reduction, reflective of significant ionic character in the Fe-C_alkyl interaction. The anionic (CP^iPr₃)FeN₂^- species can be functionalized by a silyl electrophile to generate (CP^iPr₃)Fe-N₂SiR₃. This species also functions as a modest catalyst for the reduction of N₂ to NH₃. Next, we introduce a new binucleating ligand scaffold that supports an Fe(μ-SAr)Fe diiron subunit that coordinates dinitrogen (N₂-Fe(μ-SAr)Fe-N₂) across at least three oxidation states (Fe^IIFe^II, Fe^IIFe^I, and Fe^IFe^I). Despite the sulfur-rich coordination environment of iron in FeMoco, synthetic examples of transition metal model complexes that bind N₂ and also feature sulfur donor ligands remain scarce; these complexes thus represent an unusual series of low-valent diiron complexes featuring thiolate and dinitrogen ligands. The (N₂-Fe(μ-SAr)Fe-N₂) system undergoes reduction of the bound N₂ to produce NH₃ (~50% yield) and can efficiently catalyze the disproportionation of N₂H₄ to NH₃ and N₂. The present scaffold also supports dinitrogen binding concomitant with hydride as a co-ligand. Next, inspired by the importance of secondary-sphere interactions in many metalloenzymes, we present complexes of iron in two new ligand scaffolds ([SiP^NMe₃] and [SiP^iPr₂P^NMe]) that incorporate hydrogen-bond acceptors (tertiary amines) which engage in interactions with nitrogenous substrates bound to the iron center (NH₃ and N₂H₄). Cation binding is also facilitated in anionic Fe(0)-N₂ complexes. While Fe-N₂ complexes of a related ligand ([SiP^iPr₃]) lacking hydrogen-bond acceptors produce a substantial amount of ammonia when treated with acid and reductant, the presence of the pendant amines instead facilitates the formation of metal hydride species.

Additionally, we present the development and mechanistic study of copper-mediated and copper-catalyzed photoinduced C-N bond forming reactions. Irradiation of a copper-amido complex, ((m-tol)₃P)₂Cu(carbazolide), in the presence of aryl halides furnishes N-phenylcarbazole under mild conditions. The mechanism likely proceeds via single-electron transfer from an excited state of the copper complex to the aryl halide, generating an aryl radical. An array of experimental data are consistent with a radical intermediate, including a cyclization/stereochemical investigation and a reactivity study, providing the first substantial experimental support for the viability of a radical pathway for Ullmann C-N bond formation. The copper complex can also be used as a precatalyst for Ullmann C-N couplings. We also disclose further study of catalytic C_alkyl-N couplings using a CuI precatalyst, and discuss the likely role of [Cu(carbazolide)₂]^- and [Cu(carbazolide)₃]^- species as intermediates in these reactions.

Finally, we report a series of four-coordinate, pseudotetrahedral P₃Fe^II-X complexes supported by tris(phosphine)borate ([PhBP₃Fe^R]^-) and phosphiniminato X-type ligands (-N=PR'₃) that in combination tune the spin-crossover behavior of the system. Low-coordinate transition metal complexes such as these that undergo reversible spin-crossover remain rare, and the spin equilibria of these systems have been studied in detail by a suite of spectroscopic techniques.