How far can Nim in disguise be stretched?

A move in the game of nim consists of taking any positive number of tokens from a single pile. Suppose we add the class of moves of taking a nonnegative number of tokens jointly from all the piles. We give a complete answer to the question which moves in the class can be adjoined without changing the winning strategy of nim. The results apply to other combinatorial games with unbounded Sprague-Grundy function values. We formulate two weakened conditions of the notion of nim-sum 0 for proving the results.Comment: To appear in J. Combinatorial Theory (A

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

In this paper an optimisation algorithm based on Differential Dynamic Programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution

Income-Related Minimum Taxation Concepts and Their Impact on Corporate Investment Decisions

In this paper we analyze the impact of various minimum taxation concepts on corporate investment decisions. These investments can be realized in the form of either a real or a financial investment. In a quantitative analysis we refer to the future values of the investments as an indicator of tax-favored and tax-discriminated projects. Varying the concept-specific loss-offset parameters and cash flow time structure and performing a Monte Carlo simulation reveals the impact of the particular minimum taxation concept. For the first time a comprehensive set of equations has been deduced to integrate different minimum tax concepts in a unique model. The resulting equations can be used as a basis for further analyses of group taxation, wealth taxation and asymmetric taxation and allows us to gain first insights into the direction and magnitude of tax distortions of possible competing concepts. Depending on the set of parameters, complex and ambiguous tax effects can be identified. The effect of minimum taxation depends on the existence and magnitude of a depreciation effect. Both effects run contrary to each other, and the depreciation effect is always greater. We find that all concepts distort in the same direction and that real investments with increasing cash flows are more likely to be discriminated by minimum taxation than financial investments or real investments with constant cash flows. However, in comparison to real investments with decreasing cash flows financial investments suffer more from income-related minimum taxation concepts. These results provide interesting information for corporate investors having to decide on the location of an investment, and for tax reform discussions

The PPCD1 Mouse: Characterization of a Mouse Model for Posterior Polymorphous Corneal Dystrophy and Identification of a Candidate Gene

The PPCD1 mouse, a spontaneous mutant that arose in our mouse colony, is characterized by an enlarged anterior chamber resulting from metaplasia of the corneal endothelium and blockage of the iridocorneal angle by epithelialized corneal endothelial cells. The presence of stratified multilayered corneal endothelial cells with abnormal patterns of cytokeratin expression are remarkably similar to those observed in human posterior polymorphous corneal dystrophy (PPCD) and the sporadic condition, iridocorneal endothelial syndrome. Affected eyes exhibit epithelialized corneal endothelial cells, with inappropriate cytokeratin expression and proliferation over the iridocorneal angle and posterior cornea. We have termed this the “mouse PPCD1” phenotype and mapped the mouse locus for this phenotype, designated “Ppcd1”, to a 6.1 Mbp interval on Chromosome 2, which is syntenic to the human Chromosome 20 PPCD1 interval. Inheritance of the mouse PPCD1 phenotype is autosomal dominant, with complete penetrance on the sensitive DBA/2J background and decreased penetrance on the C57BL/6J background. Comparative genome hybridization has identified a hemizygous 78 Kbp duplication in the mapped interval. The endpoints of the duplication are located in positions that disrupt the genes Csrp2bp and 6330439K17Rik and lead to duplication of the pseudogene LOC100043552. Quantitative reverse transcriptase-PCR indicates that expression levels of Csrp2bp and 6330439K17Rik are decreased in eyes of PPCD1 mice. Based on the observations of decreased gene expression levels, association with ZEB1-related pathways, and the report of corneal opacities in Csrp2bptm1a(KOMP)Wtsi heterozygotes and embryonic lethality in nulls, we postulate that duplication of the 78 Kbp segment leading to haploinsufficiency of Csrp2bp is responsible for the mouse PPCD1 phenotype. Similarly, CSRP2BP haploinsufficiency may lead to human PPCD

Epigenetic Regulation of Histone H3 Serine 10 Phosphorylation Status by HCF-1 Proteins in C. elegans and Mammalian Cells

BACKGROUND: The human herpes simplex virus (HSV) host cell factor HCF-1 is a transcriptional coregulator that associates with both histone methyl- and acetyltransferases, and a histone deacetylase and regulates cell proliferation and division. In HSV-infected cells, HCF-1 associates with the viral protein VP16 to promote formation of a multiprotein-DNA transcriptional activator complex. The ability of HCF proteins to stabilize this VP16-induced complex has been conserved in diverse animal species including Drosophila melanogaster and Caenorhabditis elegans suggesting that VP16 targets a conserved cellular function of HCF-1. METHODOLOGY/PRINCIPAL FINDINGS: To investigate the role of HCF proteins in animal development, we have characterized the effects of loss of the HCF-1 homolog in C. elegans, called Ce HCF-1. Two large hcf-1 deletion mutants (pk924 and ok559) are viable but display reduced fertility. Loss of Ce HCF-1 protein at reduced temperatures (e.g., 12 degrees C), however, leads to a high incidence of embryonic lethality and early embryonic mitotic and cytokinetic defects reminiscent of mammalian cell-division defects upon loss of HCF-1 function. Even when viable, however, at normal temperature, mutant embryos display reduced levels of phospho-histone H3 serine 10 (H3S10P), a modification implicated in both transcriptional and mitotic regulation. Mammalian cells with defective HCF-1 also display defects in mitotic H3S10P status. CONCLUSIONS/SIGNIFICANCE: These results suggest that HCF-1 proteins possess conserved roles in the regulation of cell division and mitotic histone phosphorylation

Cross-Border Group-Taxation and Loss-Offset in the EU - An Analysis for CCCTB (Common Consolidated Corporate Tax Base) and Etas (European Tax Allocation System)

The European Commission proposed to replace the currently existing Separate Accounting by an EU-wide tax system based on a Common Consolidated Corporate Tax Base (CCCTB). Besides the CCCTB, there is an alternative tax reform proposal, the European Tax Allocation System (ETAS). In a dynamic capital budgeting model we analyze the impacts of selected loss-offset limitations currently existing in the EU under both concepts on corporate crossborder real investments of MNE. The analyses show that replacing Separate Accounting by either concept can lead to increasing profitability due to cross-border loss compensation. However, if the profitability increases, the study indicates that the main criteria of decisions on location are the tax rate divergences within the EU Member States. High tax rate differentials in the Member States imply significant redistribution of tax payments under CCCTB and ETAS. The results clarify that in both reform proposals tax payment reallocations occur in favor of the holding. National loss-offset limitations and minimum taxation concepts in tendency lose their impact on the profitability under both proposals. However, we found scenarios in which national minimum taxation can encroach upon the group level, although in our model the minimum taxation's impacts seem to be slight. Moreover, we identify harmful paradoxes in ETAS due to the tax credit mechanism. Our results can contribute to the current discussion on corporate group tax harmonization within the EU and other economic zones, e.g. the US, and help to anticipate the tax effects of lossoffset restrictions under the respective tax systems

NatF Contributes to an Evolutionary Shift in Protein N-Terminal Acetylation and Is Important for Normal Chromosome Segregation

N-terminal acetylation (N-Ac) is a highly abundant eukaryotic protein modification. Proteomics revealed a significant increase in the occurrence of N-Ac from lower to higher eukaryotes, but evidence explaining the underlying molecular mechanism(s) is currently lacking. We first analysed protein N-termini and their acetylation degrees, suggesting that evolution of substrates is not a major cause for the evolutionary shift in N-Ac. Further, we investigated the presence of putative N-terminal acetyltransferases (NATs) in higher eukaryotes. The purified recombinant human and Drosophila homologues of a novel NAT candidate was subjected to in vitro peptide library acetylation assays. This provided evidence for its NAT activity targeting Met-Lys- and other Met-starting protein N-termini, and the enzyme was termed Naa60p and its activity NatF. Its in vivo activity was investigated by ectopically expressing human Naa60p in yeast followed by N-terminal COFRADIC analyses. hNaa60p acetylated distinct Met-starting yeast protein N-termini and increased general acetylation levels, thereby altering yeast in vivo acetylation patterns towards those of higher eukaryotes. Further, its activity in human cells was verified by overexpression and knockdown of hNAA60 followed by N-terminal COFRADIC. NatF's cellular impact was demonstrated in Drosophila cells where NAA60 knockdown induced chromosomal segregation defects. In summary, our study revealed a novel major protein modifier contributing to the evolution of N-Ac, redundancy among NATs, and an essential regulator of normal chromosome segregation. With the characterization of NatF, the co-translational N-Ac machinery appears complete since all the major substrate groups in eukaryotes are accounted for

Experimental concepts for toxicity prevention and tissue restoration after central nervous system irradiation

Several experimental strategies of radiation-induced central nervous system toxicity prevention have recently resulted in encouraging data. The present review summarizes the background for this research and the treatment results. It extends to the perspectives of tissue regeneration strategies, based for example on stem and progenitor cells. Preliminary data suggest a scenario with individually tailored strategies where patients with certain types of comorbidity, resulting in impaired regeneration reserve capacity, might be considered for toxicity prevention, while others might be "salvaged" by delayed interventions that circumvent the problem of normal tissue specificity. Given the complexity of radiation-induced changes, single target interventions might not suffice. Future interventions might vary with patient age, elapsed time from radiotherapy and toxicity type. Potential components include several drugs that interact with neurodegeneration, cell transplantation (into the CNS itself, the blood stream, or both) and creation of reparative signals and a permissive microenvironment, e.g., for cell homing. Without manipulation of the stem cell niche either by cell transfection or addition of appropriate chemokines and growth factors and by providing normal perfusion of the affected region, durable success of such cell-based approaches is hard to imagine

Multiple Histone Methyl and Acetyltransferase Complex Components Bind the HLA-DRA Gene

Major histocompatibility complex class II (MHC-II) genes are fundamental components that contribute to adaptive immune responses. While characterization of the chromatin features at the core promoter region of these genes has been studied, the scope of histone modifications and the modifying factors responsible for activation of these genes are less well defined. Using the MHC-II gene HLA-DRA as a model, the extent and distribution of major histone modifications associated with active expression were defined in interferon-γ induced epithelial cells, B cells, and B-cell mutants for MHC-II expression. With active transcription, nucleosome density around the proximal regulatory region was diminished and histone acetylation and methylation modifications were distributed throughout the gene in distinct patterns that were dependent on the modification examined. Irrespective of the location, the majority of these modifications were dependent on the binding of either the X-box binding factor RFX or the class II transactivator (CIITA) to the proximal regulatory region. Importantly, once established, the modifications were stable through multiple cell divisions after the activating stimulus was removed, suggesting that activation of this system resulted in an epigenetic state. A dual crosslinking chromatin immunoprecipitation method was used to detect histone modifying protein components that interacted across the gene. Components of the MLL methyltransferase and GCN5 acetyltransferase complexes were identified. Some MLL complex components were found to be CIITA independent, including MLL1, ASH2L and RbBP5. Likewise, GCN5 containing acetyltransferase complex components belonging to the ATAC and STAGA complexes were also identified. These results suggest that multiple complexes are either used or are assembled as the gene is activated for expression. Together the results define and illustrate a complex network of histone modifying proteins and multisubunit complexes participating in MHC-II transcription