This dissertation aims at theoretically studying a block of layers that is common in al- most all deep learning models. The block of layers of interest is the composition of an affine layer followed by a nonlinear activation that is followed by another affine layer. We study this block from three perspectives. (i) An Optimization Perspective. Is it possible that the output of the forward pass through this block is an optimal solution to a certain convex optimization problem? We show an equivalency between the forward pass through this block and a single iteration of deterministic and stochastic algorithms solving a ten- sor formulated convex optimization problem. As consequence, we derive for the first time a formula for computing the singular values of convolutional layers surpassing the need for the prohibitive construction of the underlying linear operator. Thereafter, we show that several deep networks can have this block replaced with the corresponding optimiza- tion algorithm predicted by our theory resulting in networks with improved generalization performance. (ii) A Probabilistic Perspective. Is it possible to analytically analyze the output of a deep network upon subjecting the input to Gaussian noise? To that regard, we derive analytical formulas for the first and second moments of this block under Gaussian input noise. We demonstrate that the derived expressions can be used to efficiently analyze the output of an arbitrary deep network in addition to constructing Gaussian adversarial attacks surpassing any need for prohibitive data augmentation procedures. (iii) A Tropi- cal Geometry Perspective. Is it possible to characterize the decision boundaries of this block as a geometric structure representing a solution set to a certain class of polynomials (tropical polynomials)? If so, then, is it possible to utilize this geometric representation of the decision boundaries for novel reformulations to classical computer vision and machine learning tasks on arbitrary deep networks? We show that the decision boundaries of this block are a subset of a tropical hypersurface, which is intimately related to a the polytope that is the convex hull of two zonotopes. We utilize this geometric characterization to shed lights on new perspectives of network pruning.

The earthquake source is routinely modeled by moment tensor description. In many cases we need more information about the source process and for that reason we occupy with higher degree moments. This approach allows us to esti- mate non-point characteristics (including some dynamic parameters): geometry of the source, duration of the source process, average slip on the fault, spatial and temporal centroid and rupture velocity vector within the point source ap- proach. This description includes 20 parameters - 6 parameters for standard moment tensor (MT) and 14 parameters for second degree moments (SDM). First, we studied synthetic tests. Large amount of significant earthquakes con- tains false non-DC component which can be caused by approximation finite source by point source. This hypothesis was proved on the case of unilateral rupture. Standard MT contains more than 20 % non-DC components which was reduced to 6 %. In the second part we applied this procedure to real data. We chose large earthquakes (Mw>6) with large non-DC component. We estimated second degree moments for them and compared them with previous studies. Moreover we restitute higher degree moments from data and proved that false non-DC component were caused by source finiteness. In the last part we applied this method to mining data and...

Some methods for generating scenarios from multidimensional distribution assume we are able to generate scenarios from the one-dimensional distribution. We dedicate chapter 3 to this problem. At the end of the chapter, we provide references for applicable algorithms. Chapter 4 is focused on selected methods for generating scenarios from multidimensional distributions. In chapter 4.3, we introduce an algorithm for generating scenarios, which do not use any assumption about the distribution, except the first four moments and correlations to be specified. A method of generating scenarios based on approximation of multivariate normal distribution by the binomial distribution is described in chapter 4.5. Dimension reduction technique using principal components is presented in chapter 4.4. The algorithm is presented under the assumption of normal distribution. In chapter 4.6, we introduce the basics of the copula theory and a method for generating scenarios by C-vine copula. In chapter 5, we implement selected methods for generating scenarios for the estimation of daily value at risk for selected indexes and we discuss the results. Powered by TCPDF (www.tcpdf.org)

Teachable moments (TMs) is a term that is used across various domains to refer to situations, occurrences, and/or events that present a potential opportunity to learn (Seals, 2018). TMs are recognized as important for educating others, as well as playing a role in professional and personal development. In sport contexts, TMs are a pathway for coaches to develop athletes (Hedlund, 1996). However, we do not fully understand what comprises TMs due to inconsistent usage of the term, and the paucity of sport-based, scholarly research on TMs. Much of our current understanding of TMs is based on studies from domains external to sport. This exploratory study aimed to (a) develop a broader conceptual understanding of how TMs occur between coaches and their athletes, and (b) explore university sports coaches’ perceptions of TMs with their athletes. In this study, data were collected through semi-structured interviews and a virtual TM recall document, whereby coaches logged events they perceived to be TMs with their athletes. Seven (7) university sports coaches completed an initial interview, while 5 of the 7 coaches completed between 4-8 recalls, as well as a second interview. A reflexive thematic analysis in combination with focused coding was applied, thus allowing us to develop a preliminary model of TMs in university sport contexts. In the first manuscript, titled ‘Teachable moments in university coaching: Exploring a coaching catchphrase,’we present our model, and outline the main qualities and conditions that support the occurrence of TMs. In the second manuscript, titled ‘Teachable moments: Practical examples from university sport,’ we elaborate on different forms of TMs that were developed in the findings, and provide concrete examples of TMs that coaches encountered in their day-to-day coaching practices. Throughout both manuscripts, we build our understanding of what comprises TMs in sport and discuss the implications for coaching practices and athlete development.

<div>Recently, researchers have pointed their attention toward Method of Moments (MoM)-based approaches to model low frequency magnetic devices (i.e. transformers and inductors). This has been prompted by the use of population-based design (PBD) methods wherein the performance of large numbers (on the order of millions) of candidate designs must be evaluated. MoM is attractive for such problems due to the fact that only the magnetic material is discretized. In addition, for the case in which the magnetic material is linear, only a surface mesh is required. In this research, point-matching and Galerkin-based MoM formulations are utilized for the design of electric machinery. In the formulations considered, the model inputs are the free currents of machine windings and the bound currents of permanent magnets. The unknowns are the magnetizations within the magnetic material which are used to compute winding inductance, electromagnetic torque, and core loss. </div><div><br></div><div>The proposed Galerkin formulation has been utilized in the PBD of a surface-mount permanent magnet machine with favorable results. Specifically, it is shown that a machine's performance can be evaluated on a time scale expected of a practical design tool. This is achieved in part through judicious exploitation of the periodic structure and excitation of machines to reduce the size of the system matrix. It is shown how the exploitation of periodic structure may be extended to the point-matching formulation for use in nonlinear analyses. Finally, alternative hybrid approaches that combine surface and volume meshing are explored for the analysis of an internal permanent magnet machine. It is shown that such a combination holds promise as a tool for rapid evaluation of machine performance.</div>

<div>In this research, the use of a Type-2 superconducting material (i.e. Yttrium Barium Copper Oxide) as a magnetic flux source within synchronous machines is considered. To do so, an analytical model is applied to predict the magnetic field and the currents that are induced within the material when it is magnetized to a mixed-state. These induced currents are then used to model the synchronous machine performance within a 2-dimensional Method of Moments (MoM) formulation. The MoM-based model is used in tandem with a thermal equivalent circuit to calculate the cooling required to keep the YBCO below its critical temperature. These are utilized within a genetic algorithm (GA) to evaluate the tradeoffs between mass and loss for several example electric drives ranging from 10 kW-20 MW. The expected mass and loss of the YBCO machines are compared to those of a standard permanent magnet synchronous machine (PMSM). Specifically, Pareto-optimal fronts are used to assess power levels where cryo-cooled YBCO materials may be warranted.<br></div>

High-quality lattice-matched LaNiO3/LaMnO3 superlattices with monolayer terrace structure have been grown on both (111)- and (001)-oriented SrTiO3 substrates by pulsed laser deposition. In contrast to the previously reported experiments, a magnetic exchange bias is observed that reproducibly occurs in both (111)- and (001)-oriented superlattices with the thin single layers of 5 and 7 unit cells, respectively. The exchange bias is theoretically explained by charge transfer-induced magnetic moments at Ni atoms. Furthermore, magnetization data at low temperature suggest two magnetic phases in the superlattices, with Néel temperature around 10 K. Electrical transport measurements reveal a metal-insulator transition with strong localization of electrons in the superlattices with the thin LaNiO3 layers of 4 unit cells, in which the electrical transport is dominated by two-dimensional variable range hopping.

An emerging branch of electronics, the optospintronics, would be highly boosted if the control of magnetic order by light is implemented in magnetic semiconductors’ nanostructures being compatible with the actual technology. Here, we show that the ferromagnetic magnetization of low Fe-doped ZnO nanowires prepared by carbothermal process is enhanced under illumination up to temperatures slightly below room temperature. This enhancement is related to the existence of an oxygen vacancy VO in the neighborhood of an antiferromagnetic superexchange Fe3+-Fe3+ pair. Under illumination, the VO is ionized to to V+O giving an electron to a closeFe3+ ion from the antiferromagnetic pair. This light excited electron transition allows the transition of Fe3+ to Fe2+ forming stable ferromagnetic double exchange pairs, increasing the total magnetization. The results presented here indicate an efficient way to influence the magnetic properties of ZnO based nanostructures by light illumination at high temperatures.

Magnetic spin structures in epitaxial BiFeO3 single layer and an epitaxial BaTiO3/BiFeO3 multilayer thin film have been studied by means of nuclear resonant scattering of synchrotron radiation. We demonstrate a spin reorientation in the 15 x[BaTiO3/BiFeO3] multilayer compared to the single BiFeO3 thin film. Where as in the BiFeO3 film, the net magnetic moment m→ lies in the (1–10) plane, identical to the bulk, m→ in the multilayer points to different polar and azimuthal directions. This spin reorientation indicates that strain and interfaces play a significant role in tuning the magnetic spin order. Furthermore, large difference in the magnetic field dependence of the magnetoelectric coefficient observed between the BiFeO3 single layer and multilayer can be associated with this magnetic spin reorientation.

Room temperature magnetoelectric BiFeO3-BaTiO3 superlattices with strong out-of-plane magnetic anisotropy have been prepared by pulsed laser deposition. We show that the out-ofplane magnetization component increases with the increasing number of double layers. Moreover, the magnetoelectric voltage coefficient can be tuned by varying the number of interfaces, reaching a maximum value of 29 V/cmOe for the20×BiFeO3-BaTiO3 superlattice. This enhancement is accompanied by a high degree of perpendicular magnetic anisotropy, making the latter an ideal candidate for the next generation of data storage devices.