Acoustic wave response to groove arrays in model ears

Many mammals and some owls have parallel grooved structures associated with auditory structures that may be exploiting acoustic products generated by groove arrays. To test the hypothesis that morphological structures in the ear can manipulate acoustic information, we expose a series of similar-sized models with and without groove arrays to different sounds in identical conditions and compare their amplitude and frequency responses. We demonstrate how two different acoustic signals are uniquely influenced by the models. Depending on multiple factors (i.e., array characteristics, acoustic signal used, and distance from source) the presence of an array can increase the signal strength of select spectral components when compared to a model with no array. With few exceptions, the models with arrays increased the total amplitude of acoustic signals over that of the smooth model at all distances we tested up to 160 centimeters. We conclude that the ability to uniquely alter the signal based on an array’s characteristics is evolutionarily beneficial and supports the concept that different species have different array configurations associated with their biological needs.

Heat transfer and skin-friction in channel with flow behind a cylinder

The paper presents the results of an experimental study of the parameters of the boundary layer, distribution of static pressure, heat transfer and friction coefficients of smooth surface located in the wake behind the cylinder in the channel. Cylinders of various diameters were placed in a slotted channel with a height of 30 mm on its axis. In all experiments, the flow velocity at the inlet was 50 m/s. The cylinder was made unheated. The friction coefficients of the smooth model were determined both from the velocity profile in the boundary layer and by direct weighing of the model on a one-component strain-gage balance. The local values of the heat transfer coefficients were determined by transient heat-transfer method using a thermal imager. The values of the heat transfer and friction coefficients in the wake behind the cylinder, referred to the values on the smooth wall in the undisturbed flow, varied in the range 1.15–1.65 and 1.3–1.75, respectively. The value of the Reynolds analogy factor for all cylinder diameters turned out to be less than unity.

Foreground Estimation in Neuronal Images With a Sparse-Smooth Model for Robust Quantification

3D volume imaging has been regarded as a basic tool to explore the organization and function of the neuronal system. Foreground estimation from neuronal image is essential in the quantification and analysis of neuronal image such as soma counting, neurite tracing and neuron reconstruction. However, the complexity of neuronal structure itself and differences in the imaging procedure, including different optical systems and biological labeling methods, result in various and complex neuronal images, which greatly challenge foreground estimation from neuronal image. In this study, we propose a robust sparse-smooth model (RSSM) to separate the foreground and the background of neuronal image. The model combines the different smoothness levels of the foreground and the background, and the sparsity of the foreground. These prior constraints together contribute to the robustness of foreground estimation from a variety of neuronal images. We demonstrate the proposed RSSM method could promote some best available tools to trace neurites or locate somas from neuronal images with their default parameters, and the quantified results are similar or superior to the results that generated from the original images. The proposed method is proved to be robust in the foreground estimation from different neuronal images, and helps to improve the usability of current quantitative tools on various neuronal images with several applications.

Mathematical Modeling of the Origami Navel Shell

The well-known Nautilus shell has been modeled extensively both by mathematicians and origamists. However, there is wide disagreement on the best-fitting mathematical model — partly because there is significant variability across different Nautilus Shells found in nature, and no single model can describe all of them well. Origami structures, however, have precise repeatable folding instructions, and do not exhibit such variability. Ironically, no known mathematical models exist for these structures. In this research, we mathematically model a prominent origami design, the Navel Shell by Tomoko Fuse, believed to be based on the Nautilus. We use first-principles geometric and trigonometric constructs for developing a non-smooth Geometric Model of the ideal origami spiral. We then search for the best-fitting parametric smooth spiral approximation, by formulating the fitting problem as a minimization problem over four unknowns. We write a Python computer program for searching the space numerically. Our evaluations show that: (i) the Smooth spiral is an excellent fit for the Geometric Model; (ii) our models for Origami Navel Shell are different from prior mathematical models for the Nautilus shell, but they come close to a recent model for a rare species of Nautilus; (iii) the Geometric Model explains the outer edges of origami images quite well and helps identify construction errors in the inner edges; and (iv) the Smooth Model helps understand how well the ideal Navel Shell matches different variants of the Nautilus species. We hope our research lays the foundation for further mathematical modeling of origami structures.

Towards a reproducible snow load map – an example for Austria

The European Committee for Standardization defines zonings and calculation criteria for different European regions to assign snow loads for structural design. In the Alpine region these defaults are quite coarse; countries therefore use their own products, and inconsistencies at national borders are a common problem. A new methodology to derive a snow load map for Austria is presented, which is reproducible and could be used across borders. It is based on (i) modeling snow loads with the specially developed Δsnow model at 897 sophistically quality controlled snow depth series in Austria and neighboring countries and (ii) a generalized additive model where covariates and their combinations are represented by penalized regression splines, fitted to series of yearly snow load maxima derived in the first step. This results in spatially modeled snow load extremes. The new approach outperforms a standard smooth model and is much more accurate than the currently used Austrian snow load map when compared to the RMSE of the 50-year snow load return values through a cross-validation procedure. No zoning is necessary, and the new map's RMSE of station-wise estimated 50-year generalized extreme value (GEV) return levels gradually rises to 2.2 kN m−2 at an elevation of 2000 m. The bias is 0.18 kN m−2 and positive across all elevations. When restricting the range of validity of the new map to 2000 m elevation, negative bias values that significantly underestimate 50-year snow loads at a very small number of stations are the only objective problem that has to be solved before the new map can be proposed as a successor of the current Austrian snow load map.

The Disposition Effect under the Reference Dependent Smooth Model of Ambiguity

The disposition effect is a commonly observed puzzle in financial markets. Several theoretical explanations for the disposition effect have been provided; however, it remains unresolved. We attempt to explain the effect by incorporating ambiguity attitudes that vary depending on the reference point. We extend the smooth model of ambiguity by Klibanoff, P., M. Marinacci, and S. Mukerji. 2005. “A Smooth Model of Decision Making under Ambiguity.” Econometrica 73: 1849–92 to depend on the reference point. Numerical examples show that the disposition effect is more pronounced under our reference-dependent smooth model of ambiguity if the investor gets her/his utility from the realized gains and losses.

High-resolution imaging follow-up of doubly imaged quasars

ABSTRACT We report upon 3 years of follow-up and confirmation of doubly imaged quasar lenses through imaging campaigns from 2016 to 2018 with the Near-Infrared Camera2 (NIRC2) on the W. M. Keck Observatory. A sample of 57 quasar lens candidates are imaged in adaptive-optics-assisted or seeing-limited K′-band observations. Out of these 57 candidates, 15 are confirmed as lenses. We form a sample of 20 lenses adding in a number of previously known lenses that were imaged with NIRC2 in 2013–14 as part of a pilot study. By modelling these 20 lenses, we obtain K′-band relative photometry and astrometry of the quasar images and the lens galaxy. We also provide the lens properties and predicted time delays to aid planning of follow-up observations necessary for various astrophysical applications, e.g. spectroscopic follow-up to obtain the deflector redshifts for the newly confirmed systems. We compare the departure of the observed flux ratios from the smooth-model predictions between doubly and quadruply imaged quasar systems. We find that the departure is consistent between these two types of lenses if the modelling uncertainty is comparable.

Elliptic Fibrations and Kodaira Dimensions of Schreieder’s Varieties

We discuss the birational geometry and the Kodaira dimension of certain varieties previously constructed by Schreieder, proving that in any dimension they admit an elliptic fibration and they are not of general type. The $l$-dimensional variety $Y_{(n)}^{(l)}$, which is the quotient of the product of a certain curve $C_{(n)}$ by itself $l$ times by a group $G\simeq \left ({\mathbb{Z}}/n{\mathbb{Z}}\right )^{l-1}$ of automorphisms, was constructed by Schreieder to obtain varieties with prescribed Hodge numbers. If $n=3^c$ Schreieder constructed an explicit smooth birational model of it, and Flapan proved that the Kodaira dimension of this smooth model is 1, if $c>1$; if $l=2$ it is a modular elliptic surface; if $l=3$ it admits a fibration in K3 surfaces. In this paper we generalize these results: without any assumption on $n$ and $l$ we prove that $Y_{(n)}^{(l)}$ admits many elliptic fibrations and its Kodaira dimension is at most 1. Moreover, if $l=2$, its minimal resolution is a modular elliptic surface, obtained by a base change of order $n$ on a specific extremal rational elliptic surface; if $l\geq 3$ it has a birational model that admits a fibration in K3 surfaces and a fibration in $(l-1)$-dimensional varieties of Kodaira dimension at most 0.