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

Phantom cosmology as a simple model with dynamical complexity

We study the Friedmann-Robertson-Walker model with phantom fields modelled in terms of scalar fields. We apply the Ziglin theory of integrability and find that the flat model is nonintegrable. Then we cannot expect to determine simple analytical solutions of the Einstein equations. We demonstrate that there is only a discrete set of parameters where this model is integrable. For comparison we describe the phantoms fields in terms of the barotropic equation of state. It is shown that in the contrast to the phantoms modelled as scalar fields, the dynamics is always integrable and phase portraits are constructed. In this case we find the duality relation.Comment: RevTeX4, 11 pages, 2 figures; rewritten (v.2); new section on complex dynamics in cases with and without spontaneous symmetry breaking (v.3); this new section on numerical analysis of complex dynamics was dropped, upload to match version in PRE (v.4

Modified Friedmann Cosmologies - theory & observations

We investigate a class of Cardassian scenarios of the universe evolution in notions of the qualitative theory of dynamical systems. This theory allows us to analyze all solutions for all possible initial conditions on the phase plane. In the Cardassian models we find that big-rip singularities are present as a typical behavior in the future if $n<0$. Some exact solutions for the flat Cardassian models as well as a duality relation were found. In turn from the statistical analysis of Knop's SNIa data, without any priors on matter content in the model, we obtain that at the 99% confidence level this big-rip scenario will reach. The potential function for the Hamiltonian description of dynamics is reconstructed from the SNIa data (inverse dynamical problem). We also pointed out the statistical analysis results depend oversensitively on the choice of the model parameter $\mathcal{M}$.Comment: RevTeX4, 30 pages, 11 figure

Środowisko - tak, Zieloni - nie. Problematyka ochrony środowiska naturalnego w badaniach empirycznych

This article presents the perception of environmental issue by Polish society - attaching importance to these issues and the assessment of political activities in solving environmental problems. The first part of the article describes environmentalism and the green parties which gained relevant position in Western European party system in the 70s of the twentieth century. Then the activities of the Greens in Poland and other Central European countries are described that took place after the collapse of the communist system in 1989. The article also illustrates the results of research on social perception of the environmental issues. The vast majority of Poles consider these issues important and claim that politicians should increase their activities in this area. Nevertheless, this doesn’t affect the position o f the Greens in the Polish party system. This is due to the history after World War II when Central Europe was in the Soviet sphere of influence and the weakness o f the green parties that have never been able to present their offer efficiently to public opinion

Oppenheimer and Bondi limits : the case of the singular conformal curvature

Spherically symmetric, gravitating configurations built of the regularly distributed gas in equilibrium still admit a singular Weyl curvature. In contrast to the Black Holes, the singularity located in the center of the gas cloud is naked – forms the repulsive point-like gravity source. Configurations of this kind can exceed both the Oppenheimer limit and the Bondi limit

Molecular spectroscopic markers of abnormal protein aggregation

Abnormal protein aggregation has been intensively studied for over 40 years and broadly discussed in the literature due to its significant role in neurodegenerative diseases etiology. Structural reorganization and conformational changes of the secondary structure upon the aggregation determine aggregation pathways and cytotoxicity of the aggregates, and therefore, numerous analytical techniques are employed for a deep investigation into the secondary structure of abnormal protein aggregates. Molecular spectroscopies, including Raman and infrared ones, are routinely applied in such studies. Recently, the nanoscale spatial resolution of tip-enhanced Raman and infrared nanospectroscopies, as well as the high sensitivity of the surface-enhanced Raman spectroscopy, have brought new insights into our knowledge of abnormal protein aggregation. In this review, we order and summarize all nano- and micro-spectroscopic marker bands related to abnormal aggregation. Each part presents the physical principles of each particular spectroscopic technique listed above and a concise description of all spectral markers detected with these techniques in the spectra of neurodegenerative proteins and their model systems. Finally, a section concerning the application of multivariate data analysis for extraction of the spectral marker bands is included

Variabilities in global DNA methylation and β\beta-sheet richness establish spectroscopic landscapes among subtypes of pancreatic cancer

Purpose: Knowledge about pancreatic cancer (PC) biology has been growing rapidly in recent decades. Nevertheless, the survival of PC patients has not greatly improved. The development of a novel methodology suitable for deep investigation of the nature of PC tumors is of great importance. Molecular imaging techniques, such as Fourier transform infrared (FTIR) spectroscopy and Raman hyperspectral mapping (RHM) combined with advanced multivariate data analysis, were useful in studying the biochemical composition of PC tissue. Methods: Here, we evaluated the potential of molecular imaging in differentiating three groups of PC tumors, which originate from different precursor lesions. Specifically, we comprehensively investigated adenocarcinomas (ACs): conventional ductal AC, intraductal papillary mucinous carcinoma, and ampulla of Vater AC. FTIR microspectroscopy and RHM maps of 24 PC tissue slides were obtained, and comprehensive advanced statistical analyses, such as hierarchical clustering and nonnegative matrix factorization, were performed on a total of 211,355 Raman spectra. Additionally, we employed deep learning technology for the same task of PC subtyping to enable automation. The so-called convolutional neural network (CNN) was trained to recognize spectra specific to each PC group and then employed to generate CNN-prediction-based tissue maps. To identify the DNA methylation spectral markers, we used differently methylated, isolated DNA and compared the observed spectral differences with the results obtained from cellular nuclei regions of PC tissues. Results: The results showed significant differences among cancer tissues of the studied PC groups. The main findings are the varying content of β-sheet-rich proteins within the PC cells and alterations in the relative DNA methylation level. Our CNN model efficiently differentiated PC groups with 94% accuracy. The usage of CNN in the classification task did not require Raman spectral data preprocessing and eliminated the need for extensive knowledge of statistical methodologies. Conclusions: Molecular spectroscopy combined with CNN technology is a powerful tool for PC detection and subtyping. The molecular fingerprint of DNA methylation and β-sheet cytoplasmic proteins established by our results is different for the main PC groups and allowed the subtyping of pancreatic tumors, which can improve patient management and increase their survival. Our observations are of key importance in understanding the variability of PC and allow translation of the methodology into clinical practice by utilizing liquid biopsy testing

Particle-Like Description in Quintessential Cosmology

Assuming equation of state for quintessential matter: $p=w(z)\rho$, we analyse dynamical behaviour of the scale factor in FRW cosmologies. It is shown that its dynamics is formally equivalent to that of a classical particle under the action of 1D potential $V(a)$. It is shown that Hamiltonian method can be easily implemented to obtain a classification of all cosmological solutions in the phase space as well as in the configurational space. Examples taken from modern cosmology illustrate the effectiveness of the presented approach. Advantages of representing dynamics as a 1D Hamiltonian flow, in the analysis of acceleration and horizon problems, are presented. The inverse problem of reconstructing the Hamiltonian dynamics (i.e. potential function) from the luminosity distance function $d_{L}(z)$ for supernovae is also considered.Comment: 35 pages, 26 figures, RevTeX4, some applications of our treatment to investigation of quintessence models were adde