Binary Tree Approach to Scaling in Unimodal Maps

Ge, Rusjan, and Zweifel (J. Stat. Phys. 59, 1265 (1990)) introduced a binary tree which represents all the periodic windows in the chaotic regime of iterated one-dimensional unimodal maps. We consider the scaling behavior in a modified tree which takes into account the self-similarity of the window structure. A non-universal geometric convergence of the associated superstable parameter values towards a Misiurewicz point is observed for almost all binary sequences with periodic tails. There are an infinite number of exceptional sequences, however, which lead to superexponential scaling. The origin of such sequences is explained.Comment: 25 pages, plain Te

Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $N \times N$ matrices in $R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.Comment: 35 pages, 4 figures, LaTe

Evolutionary connectionism: algorithmic principles underlying the evolution of biological organisation in evo-devo, evo-eco and evolutionary transitions

The mechanisms of variation, selection and inheritance, on which evolution by natural selection depends, are not fixed over evolutionary time. Current evolutionary biology is increasingly focussed on understanding how the evolution of developmental organisations modifies the distribution of phenotypic variation, the evolution of ecological relationships modifies the selective environment, and the evolution of reproductive relationships modifies the heritability of the evolutionary unit. The major transitions in evolution, in particular, involve radical changes in developmental, ecological and reproductive organisations that instantiate variation, selection and inheritance at a higher level of biological organisation. However, current evolutionary theory is poorly equipped to describe how these organisations change over evolutionary time and especially how that results in adaptive complexes at successive scales of organisation (the key problem is that evolution is self-referential, i.e. the products of evolution change the parameters of the evolutionary process). Here we first reinterpret the central open questions in these domains from a perspective that emphasises the common underlying themes. We then synthesise the findings from a developing body of work that is building a new theoretical approach to these questions by converting well-understood theory and results from models of cognitive learning. Specifically, connectionist models of memory and learning demonstrate how simple incremental mechanisms, adjusting the relationships between individually-simple components, can produce organisations that exhibit complex system-level behaviours and improve the adaptive capabilities of the system. We use the term “evolutionary connectionism” to recognise that, by functionally equivalent processes, natural selection acting on the relationships within and between evolutionary entities can result in organisations that produce complex system-level behaviours in evolutionary systems and modify the adaptive capabilities of natural selection over time. We review the evidence supporting the functional equivalences between the domains of learning and of evolution, and discuss the potential for this to resolve conceptual problems in our understanding of the evolution of developmental, ecological and reproductive organisations and, in particular, the major evolutionary transitions

The tomato xylem sap protein XSP10 is required for full susceptibility to Fusarium wilt disease

XSP10 is an abundant 10 kDa protein found in the xylem sap of tomato. The protein displays structural similarity to plant lipid transfer proteins (LTPs). LTPs are involved in various physiological processes, including disease resistance, and some are able to bind and transfer diverse lipid molecules. XSP10 abundance in xylem sap declines upon infection with Fusarium oxysporum f. sp. lycopersici (Fol), implying involvement of XSP10 in the plant–pathogen interaction. Here, the biochemical characterization of XSP10 with respect to fatty acid-binding properties is reported; a weak but significant binding to saturated fatty acids was found. Furthermore, XSP10-silenced tomato plants were engineered and it was found that these plants exhibited reduced disease symptom development upon infection with a virulent strain of Fol. Interestingly, the reduced symptoms observed did not correlate with an altered expression profile for known reporter genes of plant defence (PR-1 and WIPI). This work demonstrates that XSP10 has lipid-binding properties and is required for full susceptibility of tomato to Fusarium wilt

Profiling of the BRCA1 transcriptome through microarray and ChIP-chip analysis

A role for BRCA1 in the direct and indirect regulation of transcription is well established. However, a comprehensive view of the degree to which BRCA1 impacts transcriptional regulation on a genome-wide level has not been defined. We performed genome-wide expression profiling and ChIP-chip analysis, comparison of which revealed that although BRCA1 depletion results in transcriptional changes in 1294 genes, only 44 of these are promoter bound by BRCA1. However, 27% of these transcripts were linked to transcriptional regulation possibly explaining the large number of indirect transcriptional changes observed by microarray analysis. We show that no specific consensus sequence exists for BRCA1 DNA binding but rather demonstrate the presence of a number of known and novel transcription factor (TF)- binding sites commonly found on BRCA1 bound promoters. Co-immunoprecipitations confirmed that BRCA1 interacts with a number of these TFs including AP2-α, PAX2 and ZF5. Finally, we show that BRCA1 is bound to a subset of promoters of genes that are not altered by BRCA1 loss, but are transcriptionally regulated in a BRCA1-dependent manner upon DNA damage. These data suggest a model, whereby BRCA1 is present on defined promoters as part of an inactive complex poised to respond to various genotoxic stimuli

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure

The Rice HGW Gene Encodes a Ubiquitin-Associated (UBA) Domain Protein That Regulates Heading Date and Grain Weight

Heading date and grain weight are two determining agronomic traits of crop yield. To date, molecular factors controlling both heading date and grain weight have not been identified. Here we report the isolation of a hemizygous mutation, heading and grain weight (hgw), which delays heading and reduces grain weight in rice. Analysis of hgw mutant phenotypes indicate that the hemizygous hgw mutation decreases latitudinal cell number in the lemma and palea, both composing the spikelet hull that is known to determine the size and shape of brown grain. Molecular cloning and characterization of the HGW gene showed that it encodes a novel plant-specific ubiquitin-associated (UBA) domain protein localized in the cytoplasm and nucleus, and functions as a key upstream regulator to promote expressions of heading date- and grain weight-related genes. Moreover, co-expression analysis in rice and Arabidopsis indicated that HGW and its Arabidopsis homolog are co-expressed with genes encoding various components of ubiquitination machinery, implying a fundamental role for the ubiquitination pathway in heading date and grain weight control

Aag DNA Glycosylase Promotes Alkylation-Induced Tissue Damage Mediated by Parp1

Alkylating agents comprise a major class of front-line cancer chemotherapeutic compounds, and while these agents effectively kill tumor cells, they also damage healthy tissues. Although base excision repair (BER) is essential in repairing DNA alkylation damage, under certain conditions, initiation of BER can be detrimental. Here we illustrate that the alkyladenine DNA glycosylase (AAG) mediates alkylation-induced tissue damage and whole-animal lethality following exposure to alkylating agents. Aag-dependent tissue damage, as observed in cerebellar granule cells, splenocytes, thymocytes, bone marrow cells, pancreatic β-cells, and retinal photoreceptor cells, was detected in wild-type mice, exacerbated in Aag transgenic mice, and completely suppressed in Aag−/− mice. Additional genetic experiments dissected the effects of modulating both BER and Parp1 on alkylation sensitivity in mice and determined that Aag acts upstream of Parp1 in alkylation-induced tissue damage; in fact, cytotoxicity in WT and Aag transgenic mice was abrogated in the absence of Parp1. These results provide in vivo evidence that Aag-initiated BER may play a critical role in determining the side-effects of alkylating agent chemotherapies and that Parp1 plays a crucial role in Aag-mediated tissue damage.National Institutes of Health (U.S.) (NIH grant R01-CA075576)National Institutes of Health (U.S.) (NIH grant R01-CA055042)National Institutes of Health (U.S.) (NIH grant R01-CA149261)National Institutes of Health (U.S.) (NIH grant P30-ES00002)National Institutes of Health (U.S.) (NIH grant P30-ES02109)National Center for Research Resources (U.S.) (grant number M01RR-01066)National Center for Research Resources (U.S.) (grant number UL1 RR025758, Harvard Clinical and Translational Science Center

A Novel RNAi Lethality Rescue Screen to Identify Regulators of Adipogenesis

Adipogenesis, the differentiation of fibroblast-like mesenchymal stem cells into mature adipocytes, is tightly regulated by a complex cascade of transcription factors, including the nuclear receptor Peroxisome proliferator activator receptor γ (PPARγ). RNAi-mediated knock down libraries may present an atractive method for the identification of additional adipogenic factors. However, using in vitro adipogenesis model systems for high-throughput screening with siRNA libraries is limited since (i) differentiation is not homogeneous, but results in mixed cell populations, and (ii) the expression levels (and activity) of adipogenic regulators is highly dynamic during differentiation, indicating that the timing of RNAi-mediated knock down during differentiation may be extremely critical. Here we report a proof-of-principle for a novel RNAi screening method to identify regulators of adipogenesis that is based on lethality rescue rather than differentiation, using microRNA expression driven by a PPARγ responsive RNA polymerase II promoter. We validated this novel method through screening of a dedicated deubiquitinase knock down library, resulting in the identification of UCHL3 as an essential deubiquitinase in adipogenesis. This system therefore enables the identification of novel genes regulating PPARγ-mediated adipogenesis in a high-throughput setting