On computational irreducibility and the predictability of complex physical systems

Using elementary cellular automata (CA) as an example, we show how to coarse-grain CA in all classes of Wolfram's classification. We find that computationally irreducible (CIR) physical processes can be predictable and even computationally reducible at a coarse-grained level of description. The resulting coarse-grained CA which we construct emulate the large-scale behavior of the original systems without accounting for small-scale details. At least one of the CA that can be coarse-grained is irreducible and known to be a universal Turing machine.Comment: 4 pages, 2 figures, to be published in PR

Cauchy-perturbative matching and outer boundary conditions: computational studies

We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to provide an accurate and numerically convergent description of the gravitational wave propagation and a stable numerical evolution.Comment: 20 pages, RevTe

Non-invertible transformations and spatiotemporal randomness

We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems can generate random dynamics. For instance, the chaotic Chua's circuit coupled to a circuit with a non-invertible I-V characteristic can generate unpredictable dynamics. In general, a nonperiodic time-series with truncated exponential behavior can be converted into unpredictable dynamics using non-invertible transformations. Using a new theoretical framework for chaos and randomness, we investigate some classes of coupled map lattices. We show that, in some cases, these systems can produce completely unpredictable dynamics. In a similar fashion, we explain why some wellknown spatiotemporal systems have been found to produce very complex dynamics in numerical simulations. We discuss real physical systems that can generate random dynamics.Comment: Accepted in International Journal of Bifurcation and Chao

Complementarity in classical dynamical systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.Comment: 18 pages, no figure

Evolution of the Schr\"odinger--Newton system for a self--gravitating scalar field

Using numerical techniques, we study the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein--Klein--Gordon (EKG) system, which results in the so called Schr\"odinger--Newton (SN) set of equations. We present the numerical code developed to evolve the SN system and topics related, like equilibrium configurations and boundary conditions. Also, we analyze the evolution of different initial configurations and the physical quantities associated to them. In particular, we readdress the issue of the gravitational cooling mechanism for Newtonian systems and find that all systems settle down onto a 0--node equilibrium configuration.Comment: RevTex file, 19 pages, 26 eps figures. Minor changes, matches version to appear in PR

Muslim Integration into Western Cultures: Between Origins and Destinations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91196/1/j.1467-9248.2012.00951.x.pd

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

Autophagy mediates degradation of nuclear lamina

Z.D. is supported by a fellow award from the Leukemia & Lymphoma Society. B.C.C. is supported by career development awards from the Dermatology Foundation, Melanoma Research Foundation, and American Skin Association. S.L.B., P.D.A. and R.M. are supported by NIA P01 grant (P01AG031862). S.L.B. is also supported by NIH R01 CA078831. R.D.G. is supported by R01 GM106023 and the Progeria Research Foundation

A large scale survey reveals that chromosomal copy-number alterations significantly affect gene modules involved in cancer initiation and progression

Background Recent observations point towards the existence of a large number of neighborhoods composed of functionally-related gene modules that lie together in the genome. This local component in the distribution of the functionality across chromosomes is probably affecting the own chromosomal architecture by limiting the possibilities in which genes can be arranged and distributed across the genome. As a direct consequence of this fact it is therefore presumable that diseases such as cancer, harboring DNA copy number alterations (CNAs), will have a symptomatology strongly dependent on modules of functionally-related genes rather than on a unique "important" gene. Methods We carried out a systematic analysis of more than 140,000 observations of CNAs in cancers and searched by enrichments in gene functional modules associated to high frequencies of loss or gains. Results The analysis of CNAs in cancers clearly demonstrates the existence of a significant pattern of loss of gene modules functionally related to cancer initiation and progression along with the amplification of modules of genes related to unspecific defense against xenobiotics (probably chemotherapeutical agents). With the extension of this analysis to an Array-CGH dataset (glioblastomas) from The Cancer Genome Atlas we demonstrate the validity of this approach to investigate the functional impact of CNAs. Conclusions The presented results indicate promising clinical and therapeutic implications. Our findings also directly point out to the necessity of adopting a function-centric, rather a gene-centric, view in the understanding of phenotypes or diseases harboring CNAs.Spanish Ministry of Science and Innovation (grant BIO2008-04212)Spanish Ministry of Science and Innovation (grant FIS PI 08/0440)GVA-FEDER (PROMETEO/2010/001)Red Temática de Investigación Cooperativa en Cáncer (RTICC) (grant RD06/0020/1019)Instituto de Salud Carlos III (ISCIII)Spanish Ministry of Science and InnovationSpanish Ministry of Health (FI06/00027