Abstract:
The arrangement of nucleotides within a bacterial chromosome is influenced by numerous factors. The degeneracy of the third codon within each reading frame allows some flexibility of nucleotide selection; however, the third nucleotide in the triplet of each codon is at least partly determined by the preceding two. This is most evident in organisms with a strong G + C bias, as the degenerate codon must contribute disproportionately to maintaining that bias. Therefore, a correlation exists between the first two nucleotides and the third in all open reading frames. If the arrangement of nucleotides in a bacterial chromosome is represented as a Markov process, we would expect that the correlation would be completely captured by a second-order Markov model and an increase in the order of the model (e.g., third-, fourth-…order) would not capture any additional uncertainty in the process. In this manuscript, we present the results of a comprehensive study of the Markov property that exists in the DNA sequences of 906 bacterial chromosomes. All of the 906 bacterial chromosomes studied exhibit a statistically significant Markov property that extends beyond second-order, and therefore cannot be fully explained by codon usage. An unrooted tree containing all 906 bacterial chromosomes based on their transition probability matrices of third-order shares ～25% similarity to a tree based on sequence homologies of 16S rRNA sequences. This congruence to the 16S rRNA tree is greater than for trees based on lower-order models (e.g., second-order), and higher-order models result in diminishing improvements in congruence. A nucleotide correlation most likely exists within every bacterial chromosome that extends past three nucleotides. This correlation places significant limits on the number of nucleotide sequences that can represent probable bacterial chromosomes. Transition matrix usage is largely conserved by taxa, indicating that this property is likely inherited, however some important exceptions exist that may indicate the convergent evolution of some bacteria.

Abstract:
Automated DNA sequencing technology is so rapid that analysis has become the rate-limiting step. Hundreds of prokaryotic genome sequences are publicly available, with new genomes uploaded at the rate of approximately 20 per month. As a result, this growing body of genome sequences will include microorganisms not previously identified, isolated, or observed. We hypothesize that evolutionary pressure exerted by an ecological niche selects for a similar genetic repertoire in those prokaryotes that occupy the same niche, and that this is due to both vertical and horizontal transmission. To test this, we have developed a novel method to classify prokaryotes, by calculating their Pfam protein domain distributions and clustering them with all other sequenced prokaryotic species. Clusters of organisms are visualized in two dimensions as ‘mountains’ on a topological map. When compared to a phylogenetic map constructed using 16S rRNA, this map more accurately clusters prokaryotes according to functional and environmental attributes. We demonstrate the ability of this map, which we term a “niche map”, to cluster according to ecological niche both quantitatively and qualitatively, and propose that this method be used to associate uncharacterized prokaryotes with their ecological niche as a means of predicting their functional role directly from their genome sequence.

Abstract:
The advantages of a near-infrared variant of the Barnes-Evans method for estimating distances to Cepheid variables are described and quantified. A surface brightness-color relation for $K$ photometry and the $(V-K)_0$ color index is established using modern, high-precision angular diameters from optical interferometers. Applied to data for the galactic (cluster) Cepheid U Sgr, this method yields a distance of 0.660 $\pm$ 0.024 kpc and a true distance modulus of 9.10 $\pm$ 0.07 mag. This estimate compares with the true distance modulus of 9.37 $\pm$ 0.22 mag estimated by Gieren, Barnes, and Moffett (1993) using the classical Barnes-Evans technique. The possibility of estimating distances of LMC and SMC Cepheids directly -- without intermediate steps -- is discussed. The feasibility of determining the distance of M31 or M33 using this technique is examined and is probably within the reach of 8m-class telescopes.

Abstract:
The influence of new techniques on the discovery and characterization of pulsating variables has been enormous. In this paper, I will review the methods and results of a number of research programmes which have dramatically altered our ability to study variable stars and will likely bear fruit for many years into the future. Specifically, I will touch on results from the MACHO and EROS Projects, the HIPPARCOS mission, "flux difference" photometry and a handful of new algorithmic advances which I consider to be important.

Abstract:
We analyse the extent of possible computations following Hogarth in Malament-Hogarth (MH) spacetimes, and Etesi and N\'emeti in the special subclass containing rotating Kerr black holes. Hogarth had shown that any arithmetic statement could be resolved in a suitable MH spacetime. Etesi and Nemeti had shown that some \forall \exists relations on natural numbers which are neither universal nor co-universal, can be decided in Kerr spacetimes, and had asked specifically as to the extent of computational limits there. The purpose of this note is to address this question, and further show that MH spacetimes can compute far beyond the arithmetic: effectively Borel statements (so hyperarithmetic in second order number theory, or the structure of analysis) can likewise be resolved: Theorem A. If H is any hyperarithmetic predicate on integers, then there is an MH spacetime in which any query ? n \in H ? can be computed. In one sense this is best possible, as there is an upper bound to computational ability in any spacetime which is thus a universal constant of the space-time M. Theorem C. Assuming the (modest and standard) requirement that space-time manifolds be paracompact and Hausdorff, for any MH spacetime M there will be a countable ordinal upper bound, w(M), on the complexity of questions in the Borel hierarchy resolvable in it.

Abstract:
We show the equivalence between the existence of winning strategies for $G_{\delta \sigma}$ (also called $\Sigma^{0}_{3}$) games in Cantor or Baire space, and the existence of functions generalized-recursive in a higher type-2 functional. (Such recursions are associated with certain transfinite computational models.) We show, inter alia, that the set of indices of convergent recursions in this sense is a complete $\Game \Sigma_{3}^{0}$ set: as paraphrase, the listing of those games at this level that are won by player I, essentially has the same information as the `halting problem' for this notion of recursion. Moreover the strategies for the first player in such games are recursive in this sense. We thereby establish the ordinal length of monotone $\Game \Sigma^{0}_{3}$-inductive operators, and characterise the first ordinal where such strategies are to be found in the constructible hierarchy. In summary: Theorem (a) The following sets are recursively isomorphic. (i) The complete ittm-semi-recursive-in-${eJ}$ set, $H^{eJ}$; (ii) the $\Sigma_{1}$-theory of $( L_{\eta_{0}} , \in ) $, where $\eta_{0}$ is the closure ordinal of $\Game \Sigma_{3}^{0}$-monotone induction; (iii) the complete $\Game \Sigma_{3}^{0}$ set of integers. (b) The ittm-recursive-in-${eJ}$ sets of integers are precisely those of $L_{\eta_{0}}$.

Abstract:
We locate winning strategies for various Sigma^0_3-games in the L-hierarchy in order to prove that Sigma^0_3 Determinacy is intermediate between Pi^1_3-CA_0 (even Pi^1_2-CA_0 (lightface) with Pi^1_3-lightface definable parameters allowed) and Delta^1_3-CA_0 + AQI. (Here "AQI" is the statement in second order number theory that every arithmeical quasi-inductive definition on any input stabilizes).

Abstract:
Balance control must be rapidly modified to provide stability in the face of environmental challenges. Although changes in reactive balance over repeated perturbations have been observed previously, only anticipatory postural adjustments preceding voluntary movements have been studied in the framework of motor adaptation and learning theory. Here, we hypothesized that adaptation occurs in task-level balance control during responses to perturbations due to central changes in the control of both anticipatory and reactive components of balance. Our adaptation paradigm consisted of a Training set of forward support-surface perturbations, a Reversal set of novel countermanding perturbations that reversed direction, and a Washout set identical to the Training set. Adaptation was characterized by a change in a motor variable from the beginning to the end of each set, the presence of aftereffects at the beginning of the Washout set when the novel perturbations were removed, and a return of the variable at the end of the Washout to a level comparable to the end of the Training set. Task-level balance performance was characterized by peak center of mass (CoM) excursion and velocity, which showed adaptive changes with repetitive trials. Only small changes in anticipatory postural control, characterized by body lean and background muscle activity were observed. Adaptation was found in the evoked long-latency muscular response, and also in the sensorimotor transformation mediating that response. Finally, in each set, temporal patterns of muscle activity converged towards an optimum predicted by a trade-off between maximizing motor performance and minimizing muscle activity. Our results suggest that adaptation in balance, as well as other motor tasks, is mediated by altering central sensitivity to perturbations and may be driven by energetic considerations.

Abstract:
The discovery of a large number of beat Cepheids in the Large Magellanic Cloud in the MACHO survey, provides an opportunity to compare the characteristics of such Cepheids over a range of metallicities. We produced a large grid of linear nonadiabatic pulsation models using the OPAL opacity tables and with compositions corresponding to those of the Milky Way, and the Large and Small Magellanic Clouds. Using the relationship between the period ratio and the main pulsation period, we are able to define a range of models which correspond to the observed beat Cepheids, and thereby constrain the physical characteristics of the LMC beat Cepheids. We are also able to make some predictions about the nature of the yet-to-be-discovered SMC beat Cepheids.

Abstract:
In this paper we have examined the age and internal dynamics of the young binary LMC cluster NGC 1850 using BV CCD images and echelle spectra of 52 supergiants. Isochrone fits to a BV color-magnitude diagram revealed that the primary cluster has an age of $\tau = 90 \pm 30$ Myr while the secondary member has $\tau = 6 \pm 5$ Myr. BV surface brightness profiles were constructed out to R $>$ 40 pc, and single-component King-Michie (KM) models were applied. The total cluster luminosity varied from L$_B$ = 2.60 - 2.65 $\times 10^6$ L$_B$\sol\ and L$_V$ = 1.25 - 1.35 $\times 10^6$ as the anisotropy radius varied from infinity to three times the scale radius with the isotropic models providing the best agreement with the data. Of the 52 stars with echelle spectra, a subset of 36 were used to study the cluster dynamics. The KM radial velocity distributions were fitted to these velocities yielding total cluster masses of 5.4 - 5.9 $\pm 2.4 \times 10^4$ M\sol\ corresponding to M/L$_B$ = 0.02 $\pm 0.01$ M\sol/L$_B$\sol\ or M/L$_V$ = 0.05 $\pm 0.02$ M\sol/L$_V$\sol. A rotational signal in the radial velocities has been detected at the 93\% confidence level implying a rotation axis at a position angle of 100\deg. A variety of rotating models were fit to the velocity data assuming cluster ellipticities of $\epsilon = 0.1 - 0.3$. These models provided slightly better agreement with the radial velocity data than the KM models and had masses that were systematically lower by a few percent. The preferred value for the slope of a power-law IMF is a relatively shallow, $x = 0.29 \pmm{+0.3}{-0.8}$ assuming the B-band M/L or $x = 0.71 \pmm{+0.2}{-0.4}$ for the V-band.