Measuring motion with kinematically redundant accelerometer arrays: theory, simulation and implementation

This work presents two schemes of measuring the linear and angular kinematics of a rigid body using a kinematically redundant array of triple-axis accelerometers with potential applications in biomechanics. A novel angular velocity estimation algorithm is proposed and evaluated that can compensate for angular velocity errors using measurements of the direction of gravity. Analysis and discussion of optimal sensor array characteristics are provided. A damped 2 axis pendulum was used to excite all 6 DoF of the a suspended accelerometer array through determined complex motion and is the basis of both simulation and experimental studies. The relationship between accuracy and sensor redundancy is investigated for arrays of up to 100 triple axis (300 accelerometer axes) accelerometers in simulation and 10 equivalent sensors (30 accelerometer axes) in the laboratory test rig. The paper also reports on the sensor calibration techniques and hardware implementation.

The economic theory of the firm as a foundation for international business theory

The economic theory of the firm is central to the theory of the multinational enterprise. Recent literature on multinationals, however, makes only limited reference to the economic theory of the firm. Multinationals play an important role in coordinating the international division of labour through internal markets. The paper reviews the economic principles that underlie this view. Optimal internalisation equates marginal benefits and costs. The benefits of internalisation stem mainly from the difficulties of licensing proprietary knowledge, reflecting the view that MNEs possess an ‘ownership’ or ‘firm-specific’ advantage. The costs of internalisation, it is argued, reflect managerial capability, and in particular the capability to manage a large firm. The paper argues that management capability is a complement to ownership advantage. Ownership advantage determines the potential of the firm, and management capability governs the fulfilment of this potential through overcoming barriers to growth. The analysis is applied to a variety of issues, including out-sourcing, geographical dispersion of production, and regional specialisation in marketing.

The determinants of a cross market arbitrage opportunity: theory and evidence for the European bond market

This paper examines the determinants of cross-platform arbitrage profits. We develop a structural model that enables us to decompose the likelihood of an arbitrage opportunity into three distinct factors: the fixed cost to trade the opportunity, the level at which one of the platforms delays a price update and the impact of the order flow on the quoted prices (inventory and asymmetric information effects). We then investigate the predictions from the theoretical model for the European Bond market with the estimation of a probit model. Our main finding is that the results found in the empirical part corroborate strongly the predictions from the structural model. The event of a cross market arbitrage opportunity has a certain degree of predictability where an optimal ex ante scenario is represented by a low level of spreads on both platforms, a time of the day close to the end of trading hours and a high volume of trade.

Fundamental insights into ontogenetic growth from theory and fish

The fundamental features of growth may be universal, because growth trajectories of most animals are very similar, but a unified mechanistic theory of growth remains elusive. Still needed is a synthetic explanation for how and why growth rates vary as body size changes, both within individuals over their ontogeny and between populations and species over their evolution. Here we use Bertalanffy growth equations to characterize growth of ray-finned fishes in terms of two parameters, the growth rate coefficient, K, and final body mass, m∞. We derive two alternative empirically testable hypotheses and test them by analyzing data from FishBase. Across 576 species, which vary in size at maturity by almost nine orders of magnitude, K scaled as m_∞^(-0.23). This supports our first hypothesis that growth rate scales as m_∞^(-0.25) as predicted by metabolic scaling theory; it implies that species which grow to larger mature sizes grow faster as juveniles. Within fish species, however, K scaled as m_∞^(-0.35). This supports our second hypothesis which predicts that growth rate scales as m_∞^(-0.33) when all juveniles grow at the same rate. The unexpected disparity between across- and within-species scaling challenges existing theoretical interpretations. We suggest that the similar ontogenetic programs of closely related populations constrain growth to m_∞^(-0.33) scaling, but as species diverge over evolutionary time they evolve the near-optimal m_∞^(-0.25) scaling predicted by metabolic scaling theory. Our findings have important practical implications because fish supply essential protein in human diets, and sustainable yields from wild harvests and aquaculture depend on growth rates.

Optimal infinity-quasiconformal immersions

For a Hamiltonian K ∈ C2(RN × n) and a map u:Ω ⊆ Rn − → RN, we consider the supremal functional (1) The “Euler−Lagrange” PDE associated to (1)is the quasilinear system (2) Here KP is the derivative and [ KP ] ⊥ is the projection on its nullspace. (1)and (2)are the fundamental objects of vector-valued Calculus of Variations in L∞ and first arose in recent work of the author [N. Katzourakis, J. Differ. Eqs. 253 (2012) 2123–2139; Commun. Partial Differ. Eqs. 39 (2014) 2091–2124]. Herein we apply our results to Geometric Analysis by choosing as K the dilation function which measures the deviation of u from being conformal. Our main result is that appropriately defined minimisers of (1)solve (2). Hence, PDE methods can be used to study optimised quasiconformal maps. Nonconvexity of K and appearance of interfaces where [ KP ] ⊥ is discontinuous cause extra difficulties. When n = N, this approach has previously been followed by Capogna−Raich ? and relates to Teichmüller’s theory. In particular, we disprove a conjecture appearing therein.

Lie algebra methods for the applications to the statistical theory of turbulence

Approximate Lie symmetries of the Navier-Stokes equations are used for the applications to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to involve the Reynolds number dependence into scaling laws. Moreover, the optimal systems of all finite-dimensional Lie subalgebras of the approximate symmetry transformations of the Navier-Stokes are constructed. We show how the scaling groups obtained can be used to introduce the Reynolds number dependence into scaling laws explicitly for stationary parallel turbulent shear flows. This is demonstrated in the framework of a new approach to derive scaling laws based on symmetry analysis [11]-[13].

A stopping rule while searching for optimal solution of facility-location

Solutions to combinatorial optimization, such as p-median problems of locating facilities, frequently rely on heuristics to minimize the objective function. The minimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. However, pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small branch of the literature suggests using statistical principles to estimate the minimum and use the estimate for either stopping or evaluating the quality of the solution. In this paper we use test-problems taken from Baesley's OR-library and apply Simulated Annealing on these p-median problems. We do this for the purpose of comparing suggested methods of minimum estimation and, eventually, provide a recommendation for practioners. An illustration ends the paper being a problem of locating some 70 distribution centers of the Swedish Post in a region.

How does the use of different road networks effect the optimal location of facilities in rural areas?

The p-median problem is often used to locate P service facilities in a geographically distributed population. Important for the performance of such a model is the distance measure. Distance measure can vary if the accuracy of the road network varies. The rst aim in this study is to analyze how the optimal location solutions vary, using the p-median model, when the road network is alternated. It is hard to nd an exact optimal solution for p-median problems. Therefore, in this study two heuristic solutions are applied, simulating annealing and a classic heuristic. The secondary aim is to compare the optimal location solutions using dierent algorithms for large p-median problem. The investigation is conducted by the means of a case study in a rural region with an asymmetrically distributed population, Dalecarlia. The study shows that the use of more accurate road networks gives better solutions for optimal location, regardless what algorithm that is used and regardless how many service facilities that is optimized for. It is also shown that the simulated annealing algorithm not just is much faster than the classic heuristic used here, but also in most cases gives better location solutions.

Hybrid Auctions I: Theory

In this paper we examine the properties of a hybrid auction that combines a sealed bid and an ascending auction. In this auction, each bidder submits a sealed bid. Once the highest bid is known, the bidder who submitted it is declared the winner if her bid is higher than the second highest by more than a predetermined amount or percentage. If at least one more bidder submitted a bid su¢ciently close to the highest bid (that is, if the di¤erence between this bid and the highest bid is smaller than the predetermined amount or percentage) the quali…ed buyers compete in an open ascending auction that has the highest bid of the …rst stage as the reserve price. Quali…ed bidders include not only the highest bidder in the …rst stage but also those who bid close enough to her. We show that this auction generates more revenue than a standard auction. Although this hybrid auction does not generate as much revenue as the optimal auction, it is ex-post e¢cient.

Private or public? a taxonomy of optimal ownership and management regimes

We develop a theory of public versus private ownership based on value diversion by managers. Government is assumed to face stronger institutional constraints than has been assumed in previous literature. The model which emerges from these assumptions is fexible and has wide application. We provide amapping between the qualitative characteristics of an asset, its main use - including public goods characteristics, and spillovers toother assets values - and the optimal ownership and management regime. The model is applied to single and multiple related assets. We address questions such as; when is it optimal to have one of a pair ofr elated assets public and the other private; when is joint management desirable; and when should a public asset be managed by the owner of a related private asset? We show that while private ownership can be judged optimal in some cases solely on the basis of qualitative information, the optimality of any other ownership and management regimes relies on quantitative analysis. Our results reveal the situations in which policy makers will have difficulty in determining the opimal regime.

Essays on monetary and banking theory

Esta tese de Doutorado é dedicada ao estudo de instabilidade financeira e dinâmica em Teoria Monet ária. E demonstrado que corridas banc árias são eliminadas sem custos no modelo padrão de teoria banc ária quando a popula ção não é pequena. É proposta uma extensão em que incerteza agregada é mais severa e o custo da estabilidade financeira é relevante. Finalmente, estabelece-se otimalidade de transições na distribui ção de moeda em economias em que oportunidades de trocas são escassas e heterogêneas. Em particular, otimalidade da inflação depende dos incentivos dinâmicos proporcionados por tais transi ções. O capí tulo 1 estabelece o resultado de estabilidade sem custos para economias grandes ao estudar os efeitos do tamanho populacional na an álise de corridas banc árias de Peck & Shell. No capí tulo 2, otimalidade de dinâmica é estudada no modelo de monet ário de Kiyotaki & Wright quando a sociedade é capaz de implementar uma polí tica inflacion ária. Apesar de adotar a abordagem de desenho de mecanismos, este capí tulo faz um paralelo com a an álise de Sargent & Wallace (1981) ao destacar efeitos de incentivos dinâmicos sobre a interação entre as polí ticas monet ária e fiscal. O cap ítulo 3 retoma o tema de estabilidade fi nanceira ao quanti car os custos envolvidos no desenho ótimo de um setor bancário à prova de corridas e ao propor uma estrutura informacional alternativa que possibilita bancos insolventes. A primeira an álise mostra que o esquema de estabilidade ótima exibe altas taxas de juros de longo prazo e a segunda que monitoramento imperfeito pode levar a corridas bancárias com insolvência.

Essays on banking theory and history of financial arrangements

Esta tese contém dois capítulos, cada um lidando com a teoria e a história dos bancos e arranjos financeiros. No capítulo 1, busca-se extender uma economia Diamond-Dybvig com monitoramento imperfeito dos saques antecipados e realizar uma comparação do bem estar social em cada uma das alocações possíveis, como proposto em Presscott and Weinberg(2003). Esse monitoramento imperfeito é implementado a partir da comunicação indireta ( através de um meio de pagamento) entre os agentes e a máquina de depósitos e saques que é um agregado do setor produtivo e financeiro. A extensão consiste em estudar alocações onde uma fração dos agentes pode explorar o monitoramento imperfeito e fraudar a alocação contratada ao consumirem mais cedo além do limite, usando múltiplos meios de pagamento. Com a punição limitada no período de consumo tardio, essa nova alocação pode ser chamada de uma alocação separadora em contraste com as alocações agregadoras onde o agente com habilidade de fraudar é bloqueado por um meio de pagamento imune a fraude, mas custoso, ou por receber consumo futuro suficiente para tornar a fraude desinteressante. A comparação de bem estar na gama de parâmetros escolhida mostra que as alocações separadoras são ótimas para as economias com menor dotação e as agregadoras para as de nível intermediário e as ricas. O capítulo termina com um possível contexto histórico para o modelo, o qual se conecta com a narrativa histórica encontrada no capítulo 2. No capítulo 2 são exploradas as propriedade quantitativas de um sistema de previsão antecedente para crises financeiras, com as váriaveis sendo escolhidas a partir de um arcabouço de ``boom and bust'' descrito mais detalhadamente no apêndice 1. As principais variáveis são: o crescimento real nos preços de imóveis e ações, o diferencial entre os juros dos títulos governamentais de 10 anos e a taxa de 3 meses no mercado inter-bancário e o crescimento nos ativos totais do setor bancário. Essas variáveis produzem uma taxa mais elevada de sinais corretos para as crises bancárias recentes (1984-2008) do que os sistemas de indicadores antecedentes comparáveis. Levar em conta um risco de base crescente ( devido à tendência de acumulação de distorções no sistema de preços relativos em expansões anteriores) também provê informação e eleva o número de sinais corretos em países que não passaram por uma expansão creditícia e nos preços de ativos tão vigorosa.

Optimal growth in a two-sector model without discounting: a geometric investigation

We characterize optimal policy in a two-sector growth model with xed coeÆcients and with no discounting. The model is a specialization to a single type of machine of a general vintage capital model originally formulated by Robinson, Solow and Srinivasan, and its simplicity is not mirrored in its rich dynamics, and which seem to have been missed in earlier work. Our results are obtained by viewing the model as a specific instance of the general theory of resource allocation as initiated originally by Ramsey and von Neumann and brought to completion by McKenzie. In addition to the more recent literature on chaotic dynamics, we relate our results to the older literature on optimal growth with one state variable: speci cally, to the one-sector setting of Ramsey, Cass and Koopmans, as well as to the two-sector setting of Srinivasan and Uzawa. The analysis is purely geometric, and from a methodological point of view, our work can be seen as an argument, at least in part, for the rehabilitation of geometric methods as an engine of analysis.

Portfolio choice with a correlated background risk : theory and evidence

We extend the static portfolio choice problem with a small background risk to the case of small partially correlated background risks. We show that respecting the theories under which risk substitution appears, except for the independence of background risk, it is perfectly rational for the individual to increase his optimal exposure to portfolio risk when risks are partially negatively correlated. Then, we test empirically the hypothesis of risk substitutability using INSEE data on French households. We find that households respond by increasing their stockholdings in response to the increase in future earnings uncertainty. This conclusion is in contradiction with results obtained in other countries. So, in light of these results, our model provides an explanation to account for the lack of empirical consensus on cross-country tests of risk substitution theory that encompasses and criticises all of them.