Toward reconstruction of dynamics of the Universe from distant supernovae type Ia

We demonstrate a model-independent method of estimating qualitative dynamics of an accelerating universe from observations of distant type Ia supernovae. Our method is based on the luminosity-distance function, optimized to fit observed distances of supernovae, and the Hamiltonian representation of dynamics for the quintessential universe with a general form of equation of state $p=w(a(z))\rho$. Because of the Hamiltonian structure of FRW dynamics with the equation of state $p = w(a(z)) \rho$, the dynamics is uniquelly determined by the potential function $V(a)$ of the system. The effectiveness of this method in discrimination of model parameters of Cardassian evolution scenario is also given. Our main result is the following, restricting to the flat model with the current value of $\Omega_{m,0}=0.3$, the constraints at $2\sigma$ confidence level to the presence of $\rho^{n}$ modification of the FRW models are $-0.50 \lesssim n \lesssim 0.36$.Comment: 15 pages, 12 figures, RevTeX

Analysis of time-frequency scattering transforms

In this paper we address the problem of constructing a feature extractor which combines Mallat's scattering transform framework with time-frequency (Gabor) representations. To do this, we introduce a class of frames, called uniform covering frames, which includes a variety of semi-discrete Gabor systems. Incorporating a uniform covering frame with a neural network structure yields the Fourier scattering transform $\mathcal{S}_\mathcal{F}$ and the truncated Fourier scattering transform. We prove that $\mathcal{S}_\mathcal{F}$ propagates energy along frequency decreasing paths and its energy decays exponentially as a function of the depth. These quantitative estimates are fundamental in showing that $\mathcal{S}_\mathcal{F}$ satisfies the typical scattering transform properties, and in controlling the information loss due to width and depth truncation. We introduce the fast Fourier scattering transform algorithm, and illustrate the algorithm's performance. The time-frequency covering techniques developed in this paper are flexible and give insight into the analysis of scattering transforms

Symbolic Tensor Calculus -- Functional and Dynamic Approach

In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached

In Search of Traces of the Past: Comics as a Medium for History Great and Small

In Search of Traces of the Past: Comics as a Medium for History Great and SmallThe analysis of the article’s author focuses on the graphic novels The Property by Rutu Modan and We Won’t See Auschwitz by Jérémy Dres. Th e comics discussed deal with similar issues. Both refer to the wartime and postwar fate of Polish Jews, show military history as a factor shaping the family history of multiple generations, and touch upon issues concerning identity, Polish-Jewish relations, and national stereotypes. Through the use of comics, both authors try to preserve pieces of family history while touching upon many far more general and universal issues. Comics prove in this case to be a handy tool in the telling of intertwining histories great and small.In Search of Traces of the Past: Comics as a Medium for History Great and SmallThe analysis of the article’s author focuses on the graphic novels The Property by Rutu Modan and We Won’t See Auschwitz by Jérémy Dres. Th e comics discussed deal with similar issues. Both refer to the wartime and postwar fate of Polish Jews, show military history as a factor shaping the family history of multiple generations, and touch upon issues concerning identity, Polish-Jewish relations, and national stereotypes. Through the use of comics, both authors try to preserve pieces of family history while touching upon many far more general and universal issues. Comics prove in this case to be a handy tool in the telling of intertwining histories great and small