Limit analysis based upon the theory of plasticity is one of the very useful numerical techniques to determine the failure loads of different civil and mechanical engineering structures for a material following an associated flow rule. The limiting values of the collapse loads, namely, lower and upper bounds, can be bracketed quite accurately with the application of the lower and upper bound theorems of the limit analysis. With the advancement of the finite elements and different robust optimization techniques, the numerical limit analysis approach in association with finite elements is becoming very popular to assess the stability of various complicated structures. Although two different optimization methods, namely, linear programming and nonlinear programming, have been both successfully implemented by various researchers for solving different stability problems in geomechanics, the linear programming method is employed in the present thesis due to its inherent advantage in implementation and ease in achieving the convergence. The objectives of the present thesis are (i) to improve upon the existing lower bound limit analysis method, in combination with finite elements and linear programming, with an intention of reducing the computational time and the associated memory requirement, and (ii) to apply the existing lower bound finite element limit analysis to various important planar stability problems in geotechnical engineering. With reference to the first objective of the thesis, two new methods have been introduced in this thesis to improve upon the existing computational procedure while solving the geomechanics stability problem with the usage of the limit analysis, finite elements and linear programming. In the first method, namely, the method-I, the order of the yield polygon within the chosen domain is varied, based on the proximity of the stress state to the yield, such that a higher order polygon needs not to be used everywhere in the problem domain. In the second method, the method-II, it has been intended to use only a few selected sides, but not all, of the higher order yield polygon which are being used to linearize the Mohr-Coulomb yield function. The proposed two methods have been applied to compute the ultimate bearing capacity of smooth as well as rough strip footings for various soil frictional angles. It has been noticed that both the proposed new methods reduce the CPU time and the total number of inequality constraints required as compared to the existing lower bound linear programming method used in literature. With reference to the second objective, a few important planar stability problems in geomechanics associated with interference of footings and vertical anchors have been solved in the present thesis. Footings are essentially used to transfer the compressive loads of the super structures to underlying soil media. On the other hand, vertical anchors are used for generating passive supports to retaining walls, sheet piles and bulkheads. A large number of research investigations have been reported in literature to compute the collapse load for a single isolated strip footing and a single vertical anchor. It is a common practice to estimate the bearing capacity of footings or pullout capacity of anchors without considering the effect of interference. There are, however, clear evidences from the available literature that (i) the ultimate bearing capacity of footings, and (ii) the ultimate pullout capacity of anchors, are significantly affected by their interference effect. Based on different available methods, the interference of footings, in a group of two footings as well as an infinite number of multiple footings, has been examined by different researchers in order to compute the ultimate bearing capacity considering the group effect. However, there is no research study to find the ultimate bearing capacity of interfering footings with the usage of the lower bound limit analysis. In the present thesis, the ultimate bearing capacity of two and an infinite number of multiple strip footings placed on sandy soil with horizontal ground surface, has been determined. The analysis has been performed for smooth as well as rough footings. The failure loads for interfering footings are found to be always greater than the single isolated footing. The effect of the footings' interference is expressed in terms of an efficiency factor ( ξγ); where, ξγ is defined as the ratio of the magnitude of failure load for a footing of width B in presence of the other footing to the magnitude of failure load of an isolated strip footing having the same width. The effect of the interference on the failure load (i) for rough footings becomes always greater than smooth footings, (ii) increases with an increase in soil frictional angle φ, and (iii) becomes almost negligible beyond the spacing, S > 3B. It is observed that the failure load for a footing in a group of an infinite number of multiple strip footings becomes always greater than that for two interfering footings. Attempts have been made in this thesis to investigate the group effect of two vertical anchors on their horizontal pullout resistance (PuT). The anchors are considered to be embedded at a certain clear spacing (S) along the same vertical plane. The group effect has been studied separately for anchors embedded in (i) sandy soil, and (ii) undrained clay, respectively. For anchors embedded in clays, an increase of soil cohesion with depth, in a linear fashion, has also been taken into consideration. The magnitude of PuT has been obtained in terms of a group efficiency factor, ηγ for sand and ηc for clay, with respect to the failure load for a single isolated vertical plate with the same H/B. The pullout capacity of a group of two anchors either in sand or in undrained clay becomes quite extensive as compared to a single isolated anchor. The magnitudes of ηγ and ηc become maximum corresponding to a certain critical value of S/B, which has been found to lie generally between 0.5 and 1. The value of ηγ for a given S/B has been found to become larger for greater values of H/B, φ, and δ. For greater values of H/B, the group effect becomes more significant in contributing the pullout resistance. The horizontal pullout capacity of a single isolated vertical anchor embedded in sand in the presence of pseudo static horizontal earthquake body forces has also been determined by using the lower bound finite element limit analysis. The variation of the pullout factor Fγ with changes in the embedment ratio of the smooth and rough anchor plates for different values of horizontal earthquake acceleration coefficient ( αh) has been investigated. The analysis clearly reveals that the pullout resistance decreases quite significantly with an increase in the magnitude of the earthquake acceleration coefficient. For the various problems selected in the present thesis, the failure patterns have also been exclusively drawn in order to understand the development of the plastic zones within the chosen domain for solving a given problem. The results obtained from the analysis, for the various problems taken up in this thesis, have been thoroughly compared with those reported in literature.

abstract: Signal compressed using classical compression methods can be acquired using brute force (i.e. searching for non-zero entries in component-wise). However, sparse solutions require combinatorial searches of high computations. In this thesis, instead, two Bayesian approaches are considered to recover a sparse vector from underdetermined noisy measurements. The first is constructed using a Bernoulli-Gaussian (BG) prior distribution and is assumed to be the true generative model. The second is constructed using a Gamma-Normal (GN) prior distribution and is, therefore, a different (i.e. misspecified) model. To estimate the posterior distribution for the correctly specified scenario, an algorithm based on generalized approximated message passing (GAMP) is constructed, while an algorithm based on sparse Bayesian learning (SBL) is used for the misspecified scenario. Recovering sparse signal using Bayesian framework is one class of algorithms to solve the sparse problem. All classes of algorithms aim to get around the high computations associated with the combinatorial searches. Compressive sensing (CS) is a widely-used terminology attributed to optimize the sparse problem and its applications. Applications such as magnetic resonance imaging (MRI), image acquisition in radar imaging, and facial recognition. In CS literature, the target vector can be recovered either by optimizing an objective function using point estimation, or recovering a distribution of the sparse vector using Bayesian estimation. Although Bayesian framework provides an extra degree of freedom to assume a distribution that is directly applicable to the problem of interest, it is hard to find a theoretical guarantee of convergence. This limitation has shifted some of researches to use a non-Bayesian framework. This thesis tries to close this gab by proposing a Bayesian framework with a suggested theoretical bound for the assumed, not necessarily correct, distribution. In the simulation study, a general lower Bayesian Cram\'er-Rao bound (BCRB) bound is extracted along with misspecified Bayesian Cram\'er-Rao bound (MBCRB) for GN model. Both bounds are validated using mean square error (MSE) performances of the aforementioned algorithms. Also, a quantification of the performance in terms of gains versus losses is introduced as one main finding of this report. / Dissertation/Thesis / Masters Thesis Computer Engineering 2019

Within such disciplines as Management Science, Information and Computer Science, Engineering, Mathematics and Operations Research, problems of cutting and packing (C&P) of concrete and abstract objects appear under various specifications (cutting problems, knapsack problems, container and vehicle loading problems, pallet loading, bin packing, assembly line balancing, capital budgeting, changing coins, etc.), although they all have essentially the same logical structure. In cutting problems, a large object must be divided into smaller pieces; in packing problems, small items must be combined to large objects. Most of these problems are NP-hard. Since the pioneer work of L.V. Kantorovich in 1939, which first appeared in the West in 1960, there has been a steadily growing number of contributions in this research area. In 1961, P. Gilmore and R. Gomory presented a linear programming relaxation of the one-dimensional cutting stock problem. The best-performing algorithms today are based on their relaxation. It was, however, more than three decades before the first `optimum? algorithms appeared in the literature and they even proved to perform better than heuristics. They were of two main kinds: enumerative algorithms working by separation of the feasible set and cutting plane algorithms which cut off infeasible solutions. For many other combinatorial problems, these two approaches have been successfully combined. In this thesis we do it for one-dimensional stock cutting and two-dimensional two-stage constrained cutting. For the two-dimensional problem, the combined scheme provides mostly better solutions than other methods, especially on large-scale instances, in little time. For the one-dimensional problem, the integration of cuts into the enumerative scheme improves the results of the latter only in exceptional cases. While the main optimization goal is to minimize material input or trim loss (waste), in a real-life cutting process there are some further criteria, e.g., the number of different cutting patterns (setups) and open stacks. Some new methods and models are proposed. Then, an approach combining both objectives will be presented, to our knowledge, for the first time. We believe this approach will be highly relevant for industry.

A new branch of machine and deep learning models has evolved in constrained optimization, specifically in mixed integer programming problems (MIP). These models draw inspiration from earlier solver methods, primarily the heuristic, branch and bound. While utilizing the branch and bound framework, machine and deep learning models enhance either the computational efficiency or performance of the model. This thesis examines how imitating different variable selection strategies of classical MIP solvers behave on a state-of-the-art deep learning model. A recently developed deep learning algorithm is used in this thesis, which represents the branch and bound state as a bipartite graph. This graph serves as the input to a graph network model, which determines the variable in the MIP on which branching occurs. This thesis compares how imitating different classical branching strategies behaves on different algorithm outputs and, most importantly, time span. More specifically, this thesis conducts an empirical study on a MIP known as the facility location problem (FLP) and compares the different methods for imitation. This thesis shows that the deep learning algorithm can outperform the classical methods in terms of time span. More specifically, imitating the branching strategies resulting in small branch and bound trees give rise to a more rapid performance in finding the global optimum. Lastly, it is shown that a smaller embedding size in the network model is preferred for these instances when looking at the trade-off between variable selection and time cost. / En ny typ av maskin och djupinlärningsmodeller har utvecklats inom villkors optimering, specifikt för så kallade blandade heltalsproblem (MIP). Dessa modeller hämtar inspiration från tidigare lösningsmetoder, främst en heuristisk som kallas “branch and bound”. Genom att använda “branch and bound” ramverket förbättrar maskin och djupinlärningsmodeller antingen beräkningshastigheten eller prestandan hos modellen. Denna uppsats undersöker hur imitation av olika strategier för val av variabler från klassiska MIP-algoritmer beter sig på en modern djupinlärningsmodell. I denna uppsats används en nyligen utvecklad djupinlärningsalgoritm som representerar “branch and bound” tillståndet som en bipartit graf. Denna graf används som indata till en “graph network” modell som avgör vilken variabel i MIP-problemet som tas hänsyn till. Uppsatsen jämför hur imitation av olika klassiska “branching” strategier påverkar olika algoritmutgångar, framför allt, tidslängd. Mer specifikt utför denna uppsats en empirisk studie på ett MIP-problem som kallas för “facility location problem” (FLP) och jämför imitationen av de olika metoderna. I denna uppsats visas det att denna djupinlärningsalgoritm kan överträffa de klassiska metoderna när det gäller tidslängd. Mer specifikt ger imitation av “branching” strategier som resulterar i små “branch and bound” träd upphov till en snabbare prestation vid sökning av den globala optimala lösningen. Slutligen visas det att en mindre inbäddningsstorlek i nätverksmodellen föredras i dessa fall när man ser på avvägningen mellan val av variabler och tidskostnad.

Upward Bound (UB) projects provide educational support services to high school students in order to address inequalities in college access for low-income (LI) and first-generation students (FGS). However, access alone does not eradicate systemic barriers to positive collegiate experiences and degree attainment. As a federally funded program, UB regularly collects mandated outcome data; however, little is known about the specific academic, social, and emotional supports these programs provide. Especially lacking are in-depth qualitative studies that follow students into college and focus on students’ own stories. To address this gap in research, this study used in-depth interviews to capture the stories of LI, FGS first-year college experiences. Thematic analysis was used to identify challenges, successes, and commonalities in how participants described impacts of their UB participation. The research questions included: 1) What are the academic and social experiences of Upward Bound alumni in their first year at a four-year postsecondary institution, and 2) What is the perceived relationship between Upward Bound participation and the first-year college experience of Program alumni? This research leveraged Yosso’s (2005) Community Cultural Wealth framework to elevate diverse forms of capital involved in students’ UB participation and college experiences. Analysis revealed significant themes related to expectations, belonging, the pressure to succeed, mental health, the impact of the UB experience, and the power of voice, concluding that, through UB participation, students’ existing capital/cultural wealth is honored, leveraged, and ultimately multiplied. Recommendations for addressing pervasive obstacles to success in college are provided for Upward Bound projects and higher education.

In this paper we propose a time-varying parameter VAR model for the housing market in the United States, the United Kingdom, Japan and the Euro Area. For these four economies, we answer the following research questions: (i) How can we evaluate the stance of monetary policy when the policy rate hits the zero lower bound? (ii) Can developments in the housing market still be explained by policy measures adopted by central banks? (iii) Did central banks succeed in mitigating the detrimental impact of the financial crisis on selected housing variables? We analyze the relationship between unconventional monetary policy and the housing markets by using the shadow interest rate estimated by Krippner (2013b). Our findings suggest that the monetary policy transmission mechanism to the housing market has not changed with the implementation of quantitative easing or forward guidance, and central banks can affect the composition of an investors portfolio through investment in housing. A counterfactual exercise provides some evidence that unconventional monetary policy has been particularly successful in dampening the consequences of the financial crisis on housing markets in the United States, while the effects are more muted in the other countries considered in this study. (authors' abstract) / Series: Department of Economics Working Paper Series

Thesis (PhD)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Please refer to full text for abstract. / AFRIKAANSE OPSOMMING: Sien asb volteks vir opsomming.

Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: The goal of this thesis is to investigate the effects of distorting a graphene lattice and connect- ing this distorted graphene sheet to a superconductor. At low energies the possible excitation states in graphene are restricted to two distinct regions in momentum space called valleys. Many electronic applications are possible if one can design a graphene system where excitations can be forced to occupy a single valley in a controllable way. Investigating the spectrum of the distorted graphene sheet reveals that, if the chemical potential is chosen to coincide with a bulk Landau level, the normal-superconductor interface always supports propagating modes in both directions. Excitations from opposite valleys travel in opposite directions along the interface. The spectrum of a distorted graphene sheet terminated by an armchair edge, in contrast, is dis- persionless. We verify this insulating nature of the armchair edge for finite samples by numerical means. Furthermore, we verify previous analytical results pertaining to a graphene sheet with NS interface and an applied perpendicular real magnetic field numerically. In the process, it is shown that considering graphene sheets of perfect width is not necessary, as long as the width a few magnetic lengths away from the interface is well-defined. By then considering a finite graphene sheet, terminated by armchair edges, that is distorted and connected to a superconductor, we find bound states near the NS interface that can be changed by distorting the graphene lattice further. / AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om die uitwerking van die vervorming van ’n grafeenrooster te ondersoek wanneer die met ’n supergeleier verbind word. By lae energieë word die moontlike opwekkings in grafeen beperk tot twee aparte gebiede van momentumruimte — die sogenaamde valleie. Verskeie elektroniese toepassings is moontlik indien ’n grafeenstelsel ontwerp kan word waar opwekkings slegs ’n enkele vallei beset en die besetting beheer kan word. Deur die spektrum van die vervormde grafeenrooster te ondersoek word daar gevind dat, indien die chemiese potensiaal gekies word om saam te val met ’n Landauvlak, die NS-tussenvlak geleiding in beide rigtings ondersteun. Opwekkings van verskillende valleie beweeg in teenoorgestelde rigtings langs die tussenvlak. Daarteenoor is die spektrum van ’n vervormde grafeenroster met ’n leunstoelrand dispersieloos. Ons bevestig hierdie insulerende gedrag van ’n leunstoelrand vir eindige grafeen- roosters deur middel van ’n numeriese berekening. Verder word vorige analitiese resultate wat verband hou met ’n grafeenrooster met normaal-supergeleiertussenvlakstelsel en loodregte mag- neetveld op die vlak bevestig deur middel van numeriese berekeninge. In die proses word dit ook aangedui dat die grafeenrooster nie ’n perfekte wydte hoef te hˆe nie, solank die wydte goed gedefinieer is vir ’n paar magnetiese lengtes in die omgewing van die tussenvlak. Deur dan die eindige grafeenrooster met leunstoelrande te koppel aan ’n supergeleier word gebonde toe- stande naby aan die NS tussenvalk gevind. Hierdie toestande kan gemanipuleer word deur die grafeenrooster verder te vervorm.

No description available.

This paper develops a Bayesian Global VAR (GVAR) model to track the international transmission dynamics of two stylized shocks, namely a supply and demand shock to US-based safe assets. Our main findings can be summarized as follows. First, we find that (positive) supply-sided shocks lead to pronounced increases in economic activity which spills over to foreign countries. The impact of supply-sided shocks can also be seen for other quantities of interest, most notably equity prices and exchange rates in Europe. Second, a demand-sided shock leads to an appreciation of the US dollar and generally lower yields on US securities, forcing investors to shift their portfolios towards foreign fixed income securities. This yields sizable positive effects on US output, equity prices and a general decrease in financial market volatility. / Series: Department of Economics Working Paper Series