Nilpotent orbits of a generalization of Hodge structures

We study a generalization of Hodge structures which first appeared in the work of Cecotti and Vafa. It consists of twistors, that is, holomorphic vector bundles on P^1, with additional structure, a flat connection on C^*, a real subbundle and a pairing. We call these objects TERP-structures. We generalize to TERP-structures a correspondence of Cattani, Kaplan and Schmid between nilpotent orbits of Hodge structures and polarized mixed Hodge structures. The proofs use work of Simpson and Mochizuki on variations of twistor structures and a control of the Stokes structures of the poles at zero and infinity. The results are applied to TERP-structures which arise via oscillating integrals from holomorphic functions with isolated singularities.Comment: 43 pages, some very minor modifications, misprints correcte

Moment-based Estimation of Mixtures of Regression Models

Finite mixtures of regression models provide a flexible modeling framework for many phenomena. Using moment-based estimation of the regression parameters, we develop unbiased estimators with a minimum of assumptions on the mixture components. In particular, only the average regression model for one of the components in the mixture model is needed and no requirements on the distributions. The consistency and asymptotic distribution of the estimators is derived and the proposed method is validated through a series of simulation studies and is shown to be highly accurate. We illustrate the use of the moment-based mixture of regression models with an application to wine quality data.Comment: 17 pages, 3 figure

Hydrodynamics of an oscillating articulated eel-like structure

This study examines the hydrodynamic performance of a highly simplified eel-like structure consisting of three articulated segments with the two aft segments oscillating. A physical model was built and tested to determine the forces developed with the model stationary, to find the self-propulsion speed, and to explore the effect on hydrodynamic performance of different swimming patterns. It was found that hydrodynamic performance increases with increasing oscillation frequency; the highest forces when stationary, and the highest self-propulsion speeds were produced by swimming patterns in which the amplitude in the aft segment is larger than that in the forward segment, and in which the motion of the aft segment lags the forward segment. A simple semi-empirical model based on Morison’s equation was implemented to predict the hydrodynamic forces. This was shown to predict mean thrust well in cases in which the aft segment oscillates in phase with the forward segment, but less reliably when the phase difference between the segments increases. Force time histories are generally not well-predicted using this approach. Nonetheless, self-propulsion speeds are predicted within 30% in all cases examined

Quantum cosmological consistency condition for inflation

We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consistency condition for inflationary models that guarantees compatibility with a tunneling origin and can lead to a testable quantum cosmological prediction. The general method is demonstrated explicitly for the model of natural inflation.Comment: 1+16 pages, 3 figures. v2: typos corrected, minor improvement of the discussio

What can quantum cosmology say about the inflationary universe?

We propose a method to extract predictions from quantum cosmology for inflation that can be confronted with observations. Employing the tunneling boundary condition in quantum geometrodynamics, we derive a probability distribution for the inflaton field. A sharp peak in this distribution can be interpreted as setting the initial conditions for the subsequent phase of inflation. In this way, the peak sets the energy scale at which the inflationary phase has started. This energy scale must be consistent with the energy scale found from the inflationary potential and with the scale found from a potential observation of primordial gravitational waves. Demanding a consistent history of the universe from its quantum origin to its present state, which includes decoherence, we derive a condition that allows one to constrain the parameter space of the underlying model of inflation. We demonstrate our method by applying it to two models: Higgs inflation and natural inflation.Comment: 13 pages, 2 figures. Contribution to the Proceedings of the DICE14 meeting, Castiglioncello, September 201

"I like how it looks but it is not beautiful" -- Sensory appeal beyond beauty

Statements such as “X is beautiful but I don’t like how it looks” or “I like how X looks but it is not beautiful” sound contradictory. How contradictory they sound might however depend on the object X and on the aesthetic adjective being used (“beautiful”, “elegant”, “dynamic”, etc.). In our study, the first sentence was estimated to be more contradictory than the latter: If we describe something as beautiful, we often intend to evaluate its appearance, whereas it is less counterintuitive to appreciate an appearance without finding it beautiful. Furthermore, statements including “beautiful” appeared more contradictory than those including “elegant” and “dynamic”, pointing to its greater evaluative component. When related to artworks, sentences could appear less contradictory due to readers’ consideration of the divergence between conventional beauty and art-related sensory pleasures that can even include negative valence. Such ambivalence might be more frequent in art-objects than in other artefacts. Indeed, in our study, sentences referring to artworks were estimated to be less contradictory compared to sentences referring to other artefacts. Meanwhile, an additional small group of graphic design students showed a less clear difference between art-related and non-art-related sentences. We discuss the potential influence of art experience and interest as well as theoretical and methodological challenges like the conceptualization of beauty

An inventory control project in a major Danish company using compound renewal demand models

We describe the development of a framework to compute the optimal inventory policy for a large spare-parts’ distribution centre operation in the RA division of the Danfoss Group in Denmark. The RA division distributes spare parts worldwide for cooling and A/C systems. The warehouse logistics operation is highly automated. However, the procedures for estimating demands and the policies for the inventory control system that were in use at the beginning of the project did not fully match the sophisticated technological standard of the physical system. During the initial phase of the project development we focused on the fitting of suitable demand distributions for spare parts and on the estimation of demand parameters. Demand distributions were chosen from a class of compound renewal distributions. In the next phase, we designed models and algorithmic procedures for determining suitable inventory control variables based on the fitted demand distributions and a service level requirement stated in terms of an order fill rate. Finally, we validated the results of our models against the procedures that had been in use in the company. It was concluded that the new procedures were considerably more consistent with the actual demand processes and with the stated objectives for the distribution centre. We also initiated the implementation and integration of the new procedures into the company’s inventory management systemBase-stock policy; compound distribution; fill rate; inventory control; logistics; stochastic processes

Identification of Musical Instruments by means of the Hough-Transformation

In order to distinguish between the sounds of different musical instruments, certain instrument-specific sound features have to be extracted from the time series representing a given recorded sound. The Hough Transform is a pattern recognition procedure that is usually applied to detect specific curves or shapes in digital pictures (Shapiro, 1978). Due to some similarity between pattern recognition and statistical curve fitting problems, it may as well be applied to sound data (as a special case of time series data). The transformation is parameterized to detect sinusoidal curve sections in a digitized sound, the motivation being that certain sounds might be identified by certain oscillation patterns. The returned (transformed) data is the timepoints and amplitudes of detected sinusoids, so the result of the transformation is another ?condensed? time series. This specific Hough Transform is then applied to sounds played by different musical instruments. The generated data is investigated for features that are specific for the musical instrument that played the sound. Several classification methods are tried out to distinguish between the instruments and it turns out that RDA (a hybrid method combining LDA and QDA) (Friedman, 1989) performs best. The resulting error rate is better than those achieved by humans (Bruderer, 2003). --