Abstract:
In this paper, we investigate super robust estimation approaches, which generate a reliable estimation even when the noise observations are more than half in an experiment. The following preliminary research results on super robustness are presented: (1) It is proved that statistically, the maximum likelihood location estimator of exponential power distribution (or L^p location estimator, for short) is strict super robust, for a given p<1. (2) For a given experiment and a super robust estimator family, there is an estimator that generates an estimation that is close enough to a perfect estimation, for general transformation groups. (3)L^p estimator family is a super robust estimator family. (4) For a given experiment, L^p estimator on translation, scaling and rotation generates perfect estimation when p is small enough, even for very noisy experiments.

Abstract:
The paper reports on the comparison of the wetting properties of super-hydrophobic silicon nanowires (NWs), using drop impact impalement and electrowetting (EW) experiments. A correlation between the resistance to impalement on both EW and drop impact is shown. From the results, it is evident that when increasing the length and density of NWs: (i) the thresholds for drop impact and EW irreversibility increase (ii) the contact-angle hysteresis after impalement decreases. This suggests that the structure of the NWs network could allow for partial impalement, hence preserving the reversibility, and that EW acts the same way as an external pressure. The most robust of our surfaces show a threshold to impalement higher than 35 kPa, while most of the super-hydrophobic surfaces tested so far have impalement threshold smaller than 10 kPa.

Abstract:
Phenotypic robustness, or canalization, has been extensively investigated both experimentally and theoretically. However, it remains unknown to what extent robustness varies between individuals, and whether factors buffering environmental variation also buffer genetic variation. Here we introduce a quantitative genetic approach to these issues, and apply this approach to data from three species. In mice, we find suggestive evidence that for hundreds of gene expression traits, robustness is polymorphic and can be genetically mapped to discrete genomic loci. Moreover, we find that the polymorphisms buffering genetic variation are distinct from those buffering environmental variation. In fact, these two classes have quite distinct mechanistic bases: environmental buffers of gene expression are predominantly sex-specific and trans-acting, whereas genetic buffers are not sex-specific and often cis-acting. Data from studies of morphological and life-history traits in plants and yeast support the distinction between polymorphisms buffering genetic and environmental variation, and further suggest that loci buffering different types of environmental variation do overlap with one another. These preliminary results suggest that naturally occurring polymorphisms affecting phenotypic robustness could be abundant, and that these polymorphisms may generally buffer either genetic or environmental variation, but not both.

Abstract:
In robust statistics, the breakdown point of an estimator is the percentage of outliers with which an estimator still generates reliable estimation. The upper bound of breakdown point is 50%, which means it is not possible to generate reliable estimation with more than half outliers. In this paper, it is shown that for majority of experiences, when the outliers exceed 50%, but if they are distributed randomly enough, it is still possible to generate a reliable estimation from minority good observations. The phenomenal of that the breakdown point is larger than 50% is named as super robustness. And, in this paper, a robust estimator is called strict robust if it generates a perfect estimation when all the good observations are perfect. More specifically, the super robustness of the maximum likelihood estimator of the exponential power distribution, or L^p estimation, where p<1, is investigated. This paper starts with proving that L^p (p<1) is a strict robust location estimator. Further, it is proved that L^p (p < 1)has the property of strict super-robustness on translation, rotation, scaling transformation and robustness on Euclidean transform.

Abstract:
Most current studies estimate the invulnerability of complex networks using a qualitative method that analyzes the inaccurate decay rate of network efficiency. This method results in confusion over the invulnerability of various types of complex networks. By normalizing network efficiency and defining a baseline, this paper defines the invulnerability index as the integral of the difference between the normalized network efficiency curve and the baseline. This quantitative method seeks to establish a benchmark for the robustness and fragility of networks and to measure network invulnerability under both edge and node attacks. To validate the reliability of the proposed method, three small-world networks were selected as test beds. The simulation results indicate that the proposed invulnerability index can effectively and accurately quantify network resilience. The index should provide a valuable reference for determining network invulnerability in future research.

Abstract:
We calculate the spectrum of density fluctuations in models of inflation based on a weakly self-coupled scalar matter field minimally coupled to gravity, and specifically investigate the dependence of the predictions on modifications of the physics on length scales smaller than the Planck length. These modifications are encoded in terms of modified dispersion relations. Whereas for some classes of dispersion relations the predictions are unchanged compared to the usual ones which are based on a linear dispersion relation, for other classes important differences are obtained, involving tilted spectra, spectra with exponential factors and with oscillations. We conclude that the predictions of inflationary cosmology in these models are not robust against changes in the super-Planck-scale physics.

Abstract:
Previous studies on the invulnerability of scale-free networks under edge attacks supported the conclusion that scale-free networks would be fragile under selective attacks. However, these studies are based on qualitative methods with obscure definitions on the robustness. This paper therefore employs a quantitative method to analyze the invulnerability of the scale-free networks, and uses four scale-free networks as the experimental group and four random networks as the control group. The experimental results show that some scale-free networks are robust under selective edge attacks, different to previous studies. Thus, this paper analyzes the difference between the experimental results and previous studies, and suggests reasonable explanations.

Abstract:
Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an analogue of Riemann surfaces in the world of super geometry. After a short introduction to super differential geometry we will compare Riemann surfaces and super Riemann surfaces. We will see that super Riemann surfaces can be viewed as Riemann surfaces with an additional field, the gravitino. An extension of the harmonic action functional to super Riemann surfaces is presented and applications to the moduli space of super Riemann surfaces are considered.

Abstract:
The predictive accuracy of the generalized liquid drop model (GLDM) formula for alpha decay half-lives has been investigated in a detailed manner and a variant of the formula with improved coefficients is proposed. The method employs the experimental alpha half-lives of the well-known alpha standards (REFERENCE) to obtain the coefficients of the analytical formula using the experimental Qalpha values (the DSR-E formula), as well as the finite range droplet model (FRDM) derived Qalpha values (the FRDMFRDM formula). The predictive accuracy of these formulae were checked against the experimental alpha half-lives of an independent set of nuclei (TEST) that span approximately the same Z,A region as the standards and possess reliable alpha spectroscopic data, and were found to yield good results for the DSR-E formula but not for the FRDM-FRDM formula. The two formulae were used to obtain the alpha half-lives of super-heavy (SHE) and heavy nuclides where the relative accuracy was found to markedly improve for the FRDM-FRDM, which corroborates the appropriateness of the FRDM masses and the GLDM prescription for high Z,A nuclides. Further improvement resulted, especially for the FRDM-FRDM formula, after a simple linear optimization over the calculated and experimental half-lives of TEST was used to re-calculate the half-lives of the SHE and heavy nuclides. The advantage of this optimization was that it required no recalculation of the coefficients of the basic DSR-E or FRDM-FRDM formulae. The halflives for 324 medium-mass to super-heavy alpha decaying nuclides, calculated using these formulae and the comparison with experimental half-lives, are presented.

Abstract:
This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.