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[en] Various controversial aspects of the ''hierachical clustering'' and ''pancake'' theories for galaxy formation are reviewed. Recent numerical simulations show that both theories are capable of providing an explanation for the observed galaxy correlation function, though it is necessary to adopt a variant of the hierachical model that takes account of galaxy mergers. A critical problem for the pancake theory is the fate of fluctuations during the recombination period. The new technique of Jones and Wyse (1982) for handling this reduces the problem to solving two linear ordinary differential equations for the velocity and radiation field fluctuation amplitudes. Finally, the question of the initial conditions for these theories, and the evolution of energy density perturbations is discussed
[en] The last 25 years have seen functional magnetic resonance imaging (fMRI) grow from an interesting experimental imaging technique in the hands of some to a primary investigation of choice in the localization and lateralization of brain function prior to surgery. Developments in the field of computational neurosciences have transformed fMRI analysis from classical subtractive type analysis to dynamic casual modeling, and now to graph theory analysis. This has widened the scope of fMRI, and is therefore finding applications in understanding neural correlates of diseases like autism and Alzheimer's disease, prognostication of diseases like traumatic brain injury, and has the potential to direct therapy. It is unfortunately true that this widened ambit has not received the clinical attention it deserves, probably because fMRI is susceptible to artifacts from skull base and blood products and has reduced sensitivity in patients with vascular malformations, or because a change in medical practice usually lags behind the technological and scientific developments that make it possible. This review focuses on the developmental chronology of fMRI image analysis in the last 25 years with highlights on major milestones like developments in the field of paradigms, analysis methods, resting state fMRI, and functional connectivity. To make the statistical images of brain at work more colorful, the article starts with genesis of fMRI and ends with the hope of a promising bright future. Many inputs for this article are obtained from a series of 103 review articles edited by Bandettini et al., compiling personal experiences of pioneers in this field. Interested readers are encouraged to refer to these for a more complete overview.
[en] We present two new discrete Painlevé equations the coefficients of which are expressed in terms of the seventh root of unity and have, thus, a periodicity of 7. We describe the procedure for the derivation of equations with maximal periodicity and explain the origin of these systems in geometrical terms. (fast track communications)
[en] Here, physics can be a weighty subject, full of substance and gravitas. It is therefore perhaps entirely reasonable that a central topic of the discipline is mass. But what is mass, really? What is the origin and nature of this most essential feature of the world around us? And are there any surprises to be had as we dig deeper into that question? In this article, I hope to surprise every reader at least once.
[en] The outcomes of asteroidal catastrophic collisions are strongly affected by the target asteroid's gravity, since only the fragments escaping with initial velocities higher than the target's escape velocity are not reaccumulated into 'rubble pile' remnants. This idea can be compared with the observational evidence on the properties of family asteroids in several ways: (1) the shape and spin period of the 'reaccumulated' family asteroids will roughly fit the relationships valid for self-gravitating fluid bodies; (2) the relative velocities of the few escaping fragments arising from a breakup event marginally overcoming self-gravity will often have an anisotropic distribution, affecting the final distribution of orbital elements; (3) the amount of mass which in a given family escaped to 'infinity' will be correlated with the target's size, since only for objects larger than approx. 100 km self-gravity plays an important role. These predictions are discussed and compared with the available data. (Auth.)