A neural network-based trajectory planner for redundant systems using direct inverse modeling

Redundant (i.e., under-determined) systems can not be trained effectively using direct inverse modeling with supervised learning, for reasons well out-lined by Michael Jordan at MIT. There is a loop-hole , however, in Jordan\u27s preconditions, which seems to allow just such an architecture. A robot path planner implementing a cerebellar inspired habituation paradigm with such an architecture will be introduced. The system, called ARTFORMS, for Adaptive Redundant Trajectory Formation System uses on-line training of multiple CMACS. CMACs are locally generalizing networks, and have an a priori deterministic geometric input space mapping. These properties together with on-line learning and rapid convergence satisfy the loop-hole conditions. Issues of stability/plasticity, presentation order and generalization, computational complexity, and subsumptive fusion of multiple networks are discussed. Two implementations are described. The first is shown not to be goal directed enough for ultimate success. The second, which is highly successful, is made more goal directed by the addition of secondary training, which reduces the dimensionality of the problem by using a set of constraint equations. Running open loop with respect to posture (the system metric which reduces dimensionality) is seen to be the root cause of the first system\u27s failure, not the use of the direct inverse method. In fact, several nice properties of direct inverse modeling contribute to the system\u27s convergence speed, robustness and compliance. The central problem used to demonstrate this method is the control of trajectory formation for a planar kinematic chain with a variable number of joints. Finally, this method is extended to implement adaptive obstacle avoidance

Signal processing based method for solving inverse scattering problems

The problem of reconstructing an image of the permittivity distribution inside a penetrable and strongly scattering object from a finite number of noisy scattered field measurements has always been very challenging because it is ill-posed in nature. Several techniques have been developed which are either computationally very expensive or typically require the object to be weakly scattering. I have developed here a non-linear signal processing method, which will recover images for both strong scatterers and weak scatterers. This nonlinear or cepstral filtering method requires that the scattered field data is first preprocessed to generate a minimum phase function in the object domain. In 2-D or higher dimensional problems, I describe the conditions for minimum phase and demonstrate how an artificial reference wave can be numerically combined with measured complex scattering data in order to enforce this condition, by satisfying Rouche‘s theorem. In the cepstral domain one can filter the frequencies associated with an object from those of the scattered field. After filtering, the next step is to inverse Fourier transform these data and exponentiate to recover the image of the object under test. In addition I also investigate the scattered field sampling requirements for the inverse scattering problem. The proposed inversion technique is applied to the measured experimental data to recover both shape and relative permittivity of unknown objects. The obtained results confirm the effectiveness of this algorithm and show that one can identify optimal parameters for the reference wave and an optimal procedure that results in good reconstructions of a penetrable, strongly scattering permittivity distribution

Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference

We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. In this spirit, we provide a complete English translation of the original proceedings (lectures and discussions), and give background essays on the three main interpretations presented: de Broglie's pilot-wave theory, Born and Heisenberg's quantum mechanics, and Schroedinger's wave mechanics. We provide an extensive analysis of the lectures and discussions that took place, in the light of current debates about the meaning of quantum theory. The proceedings contain much unexpected material, including extensive discussions of de Broglie's pilot-wave theory (which de Broglie presented for a many-body system), and a "quantum mechanics" apparently lacking in wave function collapse or fundamental time evolution. We hope that the book will contribute to the ongoing revival of research in quantum foundations, as well as stimulate a reconsideration of the historical development of quantum physics. A more detailed description of the book may be found in the Preface. (Copyright by Cambridge University Press (ISBN: 9780521814218).)Comment: 553 pages, 33 figures. Draft of a book (as of Sept. 2006, same as v1). Published in Oct. 2009, with corrections and an appendix, by Cambridge University Press (available at http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521814218

Teleseismic study of rupture processes with long duration

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 1994.Includes bibliographical references (p. 229-238).by Pierre Frédéric Ihmle.Ph.D

Detecting a stochastic background of gravitational waves with non-standard polarizations

In this thesis work I consider the detection of a stochastic background of gravitational waves (SGWB) produced in the context of a generic theory of gravity. I will show in the second chapter that most theories admit solutions in terms of gravitational waves(GWs); these may differ in their propagation speed or, most relevant for the present work, in their polarization modes. For example, it is well-known that many theories of gravity, obtained for example as low-energy limits of string theories, predict a propagating scalar mode of polarization in addition to the usual tensor ones of General Relativity (GR). I will present a thorough discussion of the classification of GWs polarizations according to the E(2) scheme, which comprises the analysis of the non-vanishing components of the Riemann tensor as measured by a locally inertial observer, and thereafter the interaction of GWs with a detector. In the third chapter I present a comprehensive characterization of an SGWB with non-standard polarizations in terms of the detector response to it. Some considerations are made on the most general form that the corresponding signal may have according to alternative theories of gravity and the production mechanisms described before. It follows then the discussion about some “first order approximations” that will be useful for its study in these preliminary phases. The aim of the present work is to relax some of the usual constraints adopted in standard literature to include also the possibility of non-standard polarizations, and open up to a new more general class of possible SGWBs. In the second part of this chapter I construct and study an optimal detection algorithm for a generic SGWB. In particular, I will give importance to a procedure that is as less dependent as possible on the details of the model; for example, I begin without introducing any assumptions about the shape of the power spectrum densities of the stochastic signal. Only later they will be considered cases where it becomes necessary to include further assumptions, for example, in order to obtain some estimates on the parameters characterizing a certain model. This choice is motivated by the desire of understanding how much sensitivity is lost when a not well defined model is available, which is even more true when we extend the framework to include also alternative theories. In this sense, the present work is meant as an upgrade to those already present in literature and commonly adopted in the standard data analysis for the research of an SGWB. I will recover the known results from the literature adding only later some further assumptions. This treatment has some advantages over the standard one, in particular from a theoretical point of view. Finally, in Chapter 4, I make use of the proposed algorithm to study real data from Virgo and LIGO. The current upper limit on the intensity of the (standard) SGWB, published in 2009, is reconsidered. As it was reasonable to expect, it is not possible to improve this limit or, even more so, to perform a detection of a non-standard SGWB. Anyway, the upper limits on the non-standard polarization modes are computed and compared with the standard one. Also, several related quantities are computed and analysed from the point of view of the detection. The important news comes from the study of the predicted sensitivities that will be achieved by the advanced detectors with the scheduled upgrades (2015-2021). I will show that these sensitivities will become good enough to test several mechanisms of production of an SGWB, both of cosmological and of astrophysical origin, or at least to determine further upper limits on them. Therefore, we can expect that the tools provided by the study of GWs within an SGWB will become worth for testing alternative theories of gravity, as well as early Universe cosmological models and astrophysical ones

Examining mathematical reasoning through enacted visualisation

This study sets out to analyse the co-emergence of visualisation and reasoning processes when selected learners engaged in solving word problems. The study argues that visualisation processes and mathematical reasoning processes are closely interlinked in the process of engaging in any mathematical activity. This qualitative research project adopted a case study methodology embedded within a broader interpretative orientation. The research participants were a cohort of 17 mixedgender and mixed-ability Grade 11 learners from a private school in southern Namibia. Data was collected in three phases and comprised of one-on-one task-based interviews in the first phase, focus group task-based interviews in the second, and semi-structured reflective interviews in the third. The analytical framework was informed by elements of enactivism and consisted of a hybrid of observable visualisation and mathematical reasoning indicators. The study was framed by an enactivist perspective that served as a linking mediator to bring visualisation and reasoning processes together, and as a lens through which the coemergence of these processes was observed and analysed. The key enactivist concepts of structural coupling and co-emergence were the two mediating ideas that enabled me to discuss the links between visualisation and reasoning that emerged whilst my participants solved the set word problems. The study argues that the visualisation processes enacted by the participants when solving these problems are inseparable from the reasoning processes that the participants brought to bear; that is, they co-emerged

Detecting a stochastic background of gravitational waves with non-standard polarizations

In this thesis work I consider the detection of a stochastic background of gravitational waves (SGWB) produced in the context of a generic theory of gravity. I will show in the second chapter that most theories admit solutions in terms of gravitational waves(GWs); these may differ in their propagation speed or, most relevant for the present work, in their polarization modes. For example, it is well-known that many theories of gravity, obtained for example as low-energy limits of string theories, predict a propagating scalar mode of polarization in addition to the usual tensor ones of General Relativity (GR). I will present a thorough discussion of the classification of GWs polarizations according to the E(2) scheme, which comprises the analysis of the non-vanishing components of the Riemann tensor as measured by a locally inertial observer, and thereafter the interaction of GWs with a detector. In the third chapter I present a comprehensive characterization of an SGWB with non-standard polarizations in terms of the detector response to it. Some considerations are made on the most general form that the corresponding signal may have according to alternative theories of gravity and the production mechanisms described before. It follows then the discussion about some “first order approximations” that will be useful for its study in these preliminary phases. The aim of the present work is to relax some of the usual constraints adopted in standard literature to include also the possibility of non-standard polarizations, and open up to a new more general class of possible SGWBs. In the second part of this chapter I construct and study an optimal detection algorithm for a generic SGWB. In particular, I will give importance to a procedure that is as less dependent as possible on the details of the model; for example, I begin without introducing any assumptions about the shape of the power spectrum densities of the stochastic signal. Only later they will be considered cases where it becomes necessary to include further assumptions, for example, in order to obtain some estimates on the parameters characterizing a certain model. This choice is motivated by the desire of understanding how much sensitivity is lost when a not well defined model is available, which is even more true when we extend the framework to include also alternative theories. In this sense, the present work is meant as an upgrade to those already present in literature and commonly adopted in the standard data analysis for the research of an SGWB. I will recover the known results from the literature adding only later some further assumptions. This treatment has some advantages over the standard one, in particular from a theoretical point of view. Finally, in Chapter 4, I make use of the proposed algorithm to study real data from Virgo and LIGO. The current upper limit on the intensity of the (standard) SGWB, published in 2009, is reconsidered. As it was reasonable to expect, it is not possible to improve this limit or, even more so, to perform a detection of a non-standard SGWB. Anyway, the upper limits on the non-standard polarization modes are computed and compared with the standard one. Also, several related quantities are computed and analysed from the point of view of the detection. The important news comes from the study of the predicted sensitivities that will be achieved by the advanced detectors with the scheduled upgrades (2015-2021). I will show that these sensitivities will become good enough to test several mechanisms of production of an SGWB, both of cosmological and of astrophysical origin, or at least to determine further upper limits on them. Therefore, we can expect that the tools provided by the study of GWs within an SGWB will become worth for testing alternative theories of gravity, as well as early Universe cosmological models and astrophysical ones