A New Approach to Detect Spurious Regressions using Wavelets

In this paper, we propose the use of wavelet covariance and correlation to detect spurious regression. Based on Monte Carlo simulation results and experiments with real exchange rate data, it is shown that the wavelet approach is able to detect spurious relationship in a bivariate time series more directly. Using the wavelet approach, it is sufficient to detect a spurious regression between bivariate time series if the wavelet covariance and correlation for the two series are significantly equal to zero. The wavelet approach does not rely on restrictive assumptions which are critical to the Durbin Watson test. Another distinct advantage of the graphical wavelet analysis of wavelet covariance and correlation to detect spurious regression is the simplicity and efficiency of the decision rule compared to the complicated Durbin-Watson decision rules.Wavelet analysis, spurious regression

Refined BPS invariants of 6d SCFTs from anomalies and modularity

F-theory compactifications on appropriate local elliptic Calabi-Yau manifolds engineer six dimensional superconformal field theories and their mass deformations. The partition function $Z_{top}$ of the refined topological string on these geometries captures the particle BPS spectrum of this class of theories compactified on a circle. Organizing $Z_{top}$ in terms of contributions $Z_\beta$ at base degree $\beta$ of the elliptic fibration, we find that these, up to a multiplier system, are meromorphic Jacobi forms of weight zero with modular parameter the Kaehler class of the elliptic fiber and elliptic parameters the couplings and mass parameters. The indices with regard to the multiple elliptic parameters are fixed by the refined holomorphic anomaly equations, which we show to be completely determined from knowledge of the chiral anomaly of the corresponding SCFT. We express $Z_\beta$ as a quotient of weak Jacobi forms, with a universal denominator inspired by its pole structure as suggested by the form of $Z_{top}$ in terms of 5d BPS numbers. The numerator is determined by modularity up to a finite number of coefficients, which we prove to be fixed uniquely by imposing vanishing conditions on 5d BPS numbers as boundary conditions. We demonstrate the feasibility of our approach with many examples, in particular solving the E-string and M-string theories including mass deformations, as well as theories constructed as chains of these. We make contact with previous work by showing that spurious singularities are cancelled when the partition function is written in the form advocated here. Finally, we use the BPS invariants of the E-string thus obtained to test a generalization of the Goettsche-Nakajima-Yoshioka $K$-theoretic blowup equation, as inspired by the Grassi-Hatsuda-Marino conjecture, to generic local Calabi-Yau threefolds.Comment: 64 pages; v2: typos correcte

Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs

We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the partition function at given base degree, exact in all fiber classes to arbitrary order and to all genus, in terms of a rational function of weak Jacobi forms. Our results yield, at given base degree, the elliptic genus of the corresponding non-critical 6d string, and thus the associated BPS invariants of the 6d theory. The required elliptic indices are determined from the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the corresponding 6d theories, and completely fix the holomorphic anomaly equation constraining the partition function. We introduce subrings of the known rings of Weyl invariant Jacobi forms which are adapted to the additional symmetries of the partition function, making its computation feasible to low base wrapping number. In contradistinction to the case of simpler singularities, generic vanishing conditions on BPS numbers are no longer sufficient to fix the modular ansatz at arbitrary base wrapping degree. We show that to low degree, imposing exact vanishing conditions does suffice, and conjecture this to be the case generally.Comment: 67 pages; v2 typos corrected, references adde

The Omega deformed B-model for rigid N=2 theories

We give an interpretation of the Omega deformed B-model that leads naturally to the generalized holomorphic anomaly equations. Direct integration of the latter calculates topological amplitudes of four dimensional rigid N=2 theories explicitly in general Omega-backgrounds in terms of modular forms. These amplitudes encode the refined BPS spectrum as well as new gravitational couplings in the effective action of N=2 supersymmetric theories. The rigid N=2 field theories we focus on are the conformal rank one N=2 Seiberg-Witten theories. The failure of holomorphicity is milder in the conformal cases, but fixing the holomorphic ambiguity is only possible upon mass deformation. Our formalism applies irrespectively of whether a Lagrangian formulation exists. In the class of rigid N=2 theories arising from compactifications on local Calabi-Yau manifolds, we consider the theory of local P2. We calculate motivic Donaldson-Thomas invariants for this geometry and make predictions for generalized Gromov-Witten invariants at the orbifold point.Comment: 73 pages, no figures, references added and typos correcte

Gender stereotypes about intellectual ability emergy early and influence children's interests: extension and replication

Negative gender stereotypes targeting women’s intellectual ability are a deterrent to women’spursuit of prestigious careers in fields whose members believe brilliance is required for success.Previous research has documented that children start to develop gender stereotypes aboutbrilliance at the age of six. This can have lifelong effects as people are drawn towards genderedactivities, careers, etc. Statistical replication with preexisting data from Bian et al. (2017)supports this claim. To further examine the validity and sufficiency of the measures in theoriginal study, we develop an extension by implementing two new statistical models. Lastly, wepropose future work to address the possible role of masculine appearances in the perception ofbrilliance

One-pot preparation of three-component oil-in-water high internal phase emulsions stabilized by palm-based laureth surfactants and their moisturizing properties

In the present study, olive and olein oils had been used for the preparation of three-component high internal phase emulsions with oil volume fraction of more than 0.77 stabilized by palm-based laureth surfactants for the first time, respectively. These emulsions were easily prepared by one-pot homogenization. The critical micelle concentration and Gibbs energy of the as-synthesized surfactants were determined and discussed. Likewise, the morphology, structural properties, stability and hydration efficacy of the as-prepared emulsions were investigated. Droplet size distribution observed from the optical micrographs was in agreement with the light scattering results which suggested that droplet size increased with increasing ethylene oxide chain length. The rheological measurements of the emulsions at room (25°C) and elevated (40°C) temperatures were interpreted to give clear and direct explanation on the structure and stability of the emulsions. The hydration efficacy of the emulsions was examined in vivo using a corneometer. Both the emulsions containing olive and olein oils, respectively exhibited high stability as indicated by the rheological measurements and the structural properties did not differ from one another. However, olein oil’s hydration efficacy was higher than olive oil’s, suggesting that olein oil could well be a potential moisturizing lipid which might interest the dermatologists

γ-ray assisted synthesis of Ni3Se2 nanoparticles stabilized by natural polymer

Nickel selenide nanoparticles were synthesized using γ-ray irradiation in the presence of natural polymer, chitosan as capping agent. Chitosan is the deacetylated product of chitin, the second most abundant organic resources after cellulose. The nanoparticles were produced using nickel acetate and selenium dioxide and the as-prepared chitosan stabilized nanoparticles were soluble and stable in aqueous solution. The morphology and structure of the nickel selenide nanoparticles were characterized using transmission electron microscope (TEM) and X-ray diffraction (XRD). Optical properties of the nanoparticles were characterized by UV–Visible spectrophotometer and photoluminescent spectroscopy. The XRD result shows that the nickel selenide conformed to Ni3Se2 with crystal structure of rhombohedral. The absorption spectrum of the Ni3Se2 nanoparticles covered from around 300–600 nm which makes it a potential photovoltaic and optoelectronic device material. In this report, γ-ray irradiation provided a “green”, simple and clean route for the synthesis of chitosan stabilized Ni3Se2 nanoparticles. The size and size distribution of the nickel selenide nanoparticles were influenced by the concentration of chitosan and absorbed dose of γ-ray irradiation