Shilnikov Chaos, Low Interest Rates, and New Keynesian Macroeconomics

The paper shows that in a New Keynesian (NK) model, an active interest rate feedback monetary policy, when combined with a Ricardian passive fiscal policy, à la Leeper-Woodford, may induce the onset of a Shilnikov chaotic attractor in the region of the parameter space where uniqueness of the equilibrium prevails locally. Implications, ranging from long-term unpredictability to global indeterminacy, are discussed in the paper. We find that throughout the attractor, the economy lingers in particular regions, within which the emerging aperiodic dynamics tend to evolve for a long time around lower-than-targeted inflation and nominal interest rates. This can be interpreted as a liquidity trap phenomenon, produced by the existence of a chaotic attractor, and not by the influence of an unintended steady state or the Central Bank's intentional choice of a steady state nominal interest rate at its lower bound. In addition, our finding of Shilnikov chaos can provide an alternative explanation for the controversial “loanable funds” over-saving theory, which seeks to explain why interest rates and, to a lesser extent inflation rates, have declined to current low levels, such that the real rate of interest is below the marginal product of capital. Paradoxically, an active interest rate feedback policy can cause nominal interest rates, inflation rates, and real interest rates unintentionally to drift downwards within a Shilnikov attractor set. Policy options to eliminate or control the chaotic dynamics are developed

Shilnikov Chaos, Low Interest Rates, and New Keynesian Macroeconomics

The paper shows that in a New Keynesian (NK) model, an active interest rate feedback monetary policy, when combined with a Ricardian passive fiscal policy, à la Leeper-Woodford, may induce the onset of a Shilnikov chaotic attractor in the region of the parameter space where uniqueness of the equilibrium prevails locally. Implications, ranging from long-term unpredictability to global indeterminacy, are discussed in the paper. We find that throughout the attractor, the economy lingers in particular regions, within which the emerging aperiodic dynamics tend to evolve for a long time around lower-than-targeted inflation and nominal interest rates. This can be interpreted as a liquidity trap phenomenon, produced by the existence of a chaotic attractor, and not by the influence of an unintended steady state or the Central Bank's intentional choice of a steady state nominal interest rate at its lower bound. In addition, our finding of Shilnikov chaos can provide an alternative explanation for the controversial “loanable funds” over-saving theory, which seeks to explain why interest rates and, to a lesser extent inflation rates, have declined to current low levels, such that the real rate of interest is below the marginal product of capital. Paradoxically, an active interest rate feedback policy can cause nominal interest rates, inflation rates, and real interest rates unintentionally to drift downwards within a Shilnikov attractor set. Policy options to eliminate or control the chaotic dynamics are developed

Machining accuracy enhancement using machine tool error compensation and metrology

This dissertation aims to enhance machining accuracy by machine tool error reduction and workpiece metrology. The error characteristics are studied by building a quasi-static error model. Perturbed forward kinematic model is used for modeling a 5-axis Computer Numerical Control (CNC) machine with one redundant linear axis. It is found that the 1st order volumetric error model of the 5-axis machine is attributed to 32 error parameter groups. To identify the model by estimating these parameter groups using the least-squares fitting, errors at 290 quasi-randomly generated measurement points over the machine’s workspace are measured using a laser tracker. The identified error model explains 90% of the mean error of the training data sets. However, the measurements using the laser tracker take about 90 minutes, which may cause the identified error parameters to be inaccurate due to the slow varying and transient natures of thermal errors. To shorten the measurement time, an experimental design approach, which suggests the optimal observation locations such that the corresponding robustness of identification is maximized, is applied to design the optimal error observers. Since the observers must be uniformly distributed over the workspace for gaining redundancy, the constrained K-optimal designs are used to select 80 K-optimal observers for the 5-axis machine. Six measurement cycles using 80 observers are done at machine’s different thermal states within a 400-minute experiment. Six error models are trained with consistent performances and are found to be comparable to the one trained by 290 quasi-random observations. This shows the feasibility of using smaller but more strategical-chosen point-set in data-driven error models. More importantly, the growth on mean nominal (119.1 to 181.9 microns) and modeled error (26.3 to 33.9 microns) suggest the necessity of thermal error tracking for enhancing the machining accuracy. A point-set based metrology is also developed to compensate the inaccuracies introduced by workpiece and fixtures and enhance machining accuracy. The machinability of all planar features is examined by virtually comparing the scanned data with the nominal machining planes, which are also known as virtual gages. The virtual gaging problem is modeled as a constrained linear program. The optimal solution to the problem can compensate the displacement introduced by workpiece and fixtures and hence guarantee a conforming finished part. To transfer point-set data into mathematical constraints, algorithms that align, segment, downsize and filter the point-set data are exploited. The concept of virtual gage analysis is demonstrated using experimental data for a simple raw casting. However, for the case where the casting is defective, and some virtual gages are not feasible, the corresponding linear program was found to have no solution. By introducing slack variables to the original linear programming problem, the extended problem has been solved. The extended model is validated for the data obtained for another casting. Further, the analysis predicts the machining allowances on all functional features. Cylindrical surface and its tolerance verification play important role in machining process. Although there exist many approaches that can fit the maximum, minimum and minimum zone cylinders, the cylinder fitting problems can be even simplified. The proposed methodology seeks to reduce the number of parameters used in cylinder fitting model by using the projection model that considers the degenerated tolerance specifications of the projected 2-D point-set. Also, to avoid the problem of local optimum by introducing the optimal direction of projection such that the 2-D point projected onto this direction has optimal tolerance specifications (maximum, minimum and minimum zone circles), global optimum solver such as Particle Swarm Optimization (PSO) is used. The proposed simplified method shows consistent results compared with the results from literature

Analysis and Quality Assessment of LEO GPS Data for Geophysical and Ionospheric Applications

During the last few years, an ever-increasing fleet of Low Earth Orbiting (LEO) satellites for scientific purposes became operative. Most of these satellites carry dual-frequency Global Positioning System (GPS) receivers. The highly accurate dual-frequency observations allow mitigating the ionospheric signal contribution to estimate precise orbits and eventually the earth's gravity field. However, when comparing the obtained GPS only gravity fields derived from Swarm to gravity field solutions obtained by the dedicated gravity field mission GRACE, systematic band-shaped differences are visible in the vicinity of the geomagnetic equator. In this work, an empirical approach for the appropriate weighting of GPS observations is derived to mitigate these ionospheric artifacts. The cause of the artifacts is further analyzed by investigating the loop filter implementation. A tracking loop-specific transfer function is derived and used to invert the loop filter response to derive corrections for the GPS phase observations. Both methods are evaluated to achieve the best possible Swarm GPS only gravity field. Vice versa, the collected GPS observations from the LEO precise orbit determination antenna can also be used to gain insight into the topside ionosphere and plasmasphere. A three-dimensional model approach is developed using a fleet of LEO satellites to estimate a model of the electron density distribution between LEO and GPS satellites. Both aspects represent possibilities of using GPS/GNSS on-board of LEO satellites for geophysical applications

Aspects of emergent cyclicity in language and computation

This thesis has four parts, which correspond to the presentation and development of a theoretical framework for the study of cognitive capacities qua physical phenomena, and a case study of locality conditions over natural languages. Part I deals with computational considerations, setting the tone of the rest of the thesis, and introducing and defining critical concepts like ‘grammar’, ‘automaton’, and the relations between them . Fundamental questions concerning the place of formal language theory in linguistic inquiry, as well as the expressibility of linguistic and computational concepts in common terms, are raised in this part. Part II further explores the issues addressed in Part I with particular emphasis on how grammars are implemented by means of automata, and the properties of the formal languages that these automata generate. We will argue against the equation between effective computation and function-based computation, and introduce examples of computable procedures which are nevertheless impossible to capture using traditional function-based theories. The connection with cognition will be made in the light of dynamical frustrations: the irreconciliable tension between mutually incompatible tendencies that hold for a given dynamical system. We will provide arguments in favour of analyzing natural language as emerging from a tension between different systems (essentially, semantics and morpho-phonology) which impose orthogonal requirements over admissible outputs. The concept of level of organization or scale comes to the foreground here; and apparent contradictions and incommensurabilities between concepts and theories are revisited in a new light: that of dynamical nonlinear systems which are fundamentally frustrated. We will also characterize the computational system that emerges from such an architecture: the goal is to get a syntactic component which assigns the simplest possible structural description to sub-strings, in terms of its computational complexity. A system which can oscillate back and forth in the hierarchy of formal languages in assigning structural representations to local domains will be referred to as a computationally mixed system. Part III is where the really fun stuff starts. Field theory is introduced, and its applicability to neurocognitive phenomena is made explicit, with all due scale considerations. Physical and mathematical concepts are permanently interacting as we analyze phrase structure in terms of pseudo-fractals (in Mandelbrot’s sense) and define syntax as a (possibly unary) set of topological operations over completely Hausdorff (CH) ultrametric spaces. These operations, which makes field perturbations interfere, transform that initial completely Hausdorff ultrametric space into a metric, Hausdorff space with a weaker separation axiom. Syntax, in this proposal, is not ‘generative’ in any traditional sense –except the ‘fully explicit theory’ one-: rather, it partitions (technically, ‘parametrizes’) a topological space. Syntactic dependencies are defined as interferences between perturbations over a field, which reduce the total entropy of the system per cycles, at the cost of introducing further dimensions where attractors corresponding to interpretations for a phrase marker can be found. Part IV is a sample of what we can gain by further pursuing the physics of language approach, both in terms of empirical adequacy and theoretical elegance, not to mention the unlimited possibilities of interdisciplinary collaboration. In this section we set our focus on island phenomena as defined by Ross (1967), critically revisiting the most relevant literature on this topic, and establishing a typology of constructions that are strong islands, which cannot be violated. These constructions are particularly interesting because they limit the phase space of what is expressible via natural language, and thus reveal crucial aspects of its underlying dynamics. We will argue that a dynamically frustrated system which is characterized by displaying mixed computational dependencies can provide straightforward characterizations of cyclicity in terms of changes in dependencies in local domains

Proceedings of the fifth international workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information.The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations.Following the first edition of this workshop in 20061, the second edition in New-York in 20082, the third edition in Toronto in 20113, the forth edition in Nagoya Japan on September 22 20134, the fifth edition was held in Munich on October 9 20155.Contributions were solicited in Riemannian, sub-Riemannian and group theoretical methods, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, time-evolving geometric processes, stratified spaces, optimal transport, approximation methods in statistical learning and related subjects. Among the submitted papers, 14 were selected andorganized in 4 oral sessions

Forced vibrations of a cylinder

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe present thesis is examining the forced vibrations of a circular cylinder in the low Reynolds number flow of 200. A numerical study is performed that employs an already existing algorithm developed by (Breuer 1998) and enhanced with the characteristic of the cylinder’s motion by (MadaniKermani 2014) who employed the moving frame of reference method of (L. Li, Sherwin et al. 2002). The algorithm was extensively assessed for the benchmark studies of flow around a stationary circular cylinder. A new observation was made on the effect of the aspect ratio of the computational cells in the mid region of the wake. The studies so far are emphasizing on the characteristic of a dense mesh, with a small aspect ratio, in the high divergence areas in the near region of the cylinder surface, neglecting the effect of the regions away from the surface. The present study on a stationary circular cylinder flow, proved that the aspect ratio of the distant cells has a significant effect on the St number and the force coefficients. The main study of the thesis emphasizes on the lock-in region where the wake oscillates in unison with the harmonic motion of the cylinder. The study makes a new observation on the qualitative and quantitative description of the lock-in conditions. In particular, it reveals two regions of resonance and non-resonance lock-in. Despite the fact that the lock-in is achieved, when the frequency ratio is in the first part of the region away from the unity ratio, the forces are not greatly magnified. As the ratio approaches the unity the forces experience a resonance that reaches the highest value after the unity. Furthermore, the adaptation time of the flow to the motion of the cylinder is examined and extends the results of (Anagnostopoulos 2000) to the full extent of the lock-in and the non-lock-in regions. More precisely the flow strives to reach a steady state when it is in the lock-in region rather in the non-lock in cases it reaches the steady state faster. It is postulated that the adaptation time depends on both the numerical and the physical adaptation. Moreover, the force coefficients characteristic of sinusoidal behaviour in the lock-in region is attempted to be approximated by a Newton polynomial that is built by making use of the divided differences method. The amplitude of the forces is approximated by a third degree Netwon polynomial built from the results of the present thesis simulations. The use of an approximation is providing faster results ignoring the need for a full resolution of the Navier-Stokes equation

Lux junior 2023: 16. Internationales Forum für den lichttechnischen Nachwuchs, 23. – 25. Juni 2023, Ilmenau : Tagungsband

Während des 16. Internationales Forums für den lichttechnischen Nachwuchs präsentieren Studenten, Doktoranden und junge Absolventen ihre Forschungs- und Entwicklungsergebnisse aus allen Bereichen der Lichttechnik. Die Themen bewegen sich dabei von Beleuchtungsanwendungen in verschiedensten Bereichen über Lichtmesstechnik, Kraftfahrzeugbeleuchung, LED-Anwendung bis zu nichtvisuellen Lichtwirkungen. Das Forum ist speziell für Studierende und junge Absolventen des Lichtbereiches konzipiert. Es bietet neben den Vorträgen und Postern die Möglichkeit zu Diskussionen und individuellem Austausch. In den 30 Jahren ihres Bestehens entwickelte sich die zweijährig stattfindende Tagung zu eine Traditionsveranstaltung, die das Fachgebiet Lichttechnik der TU Ilmenau gemeinsam mit der Bezirksgruppe Thüringen-Nordhessen der Deutschen Lichttechnischen Gesellschaft LiTG e. V. durchführt