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Let X be an algebraic variety equipped with a dominant rational map ϕ : X ⤏ X . A new quantity measuring the interaction of (X , ϕ) with trivial dynamical systems is introduced; the stabilised algebraic dimension of (X , ϕ) captures the maximum number of new algebraically independent invariant rational functions on (X × Y , ϕ × ψ) , as ψ : Y ⤏ Y ranges over all dominant rational maps on algebraic varieties. It is shown that this birational invariant agrees with the maximum dim X ′ where (X , ϕ) ⤏ (X ′ , ϕ ′) is a dominant rational equivariant map and ϕ ′ is part of an algebraic group action on X ′ . As a consequence, it is deduced that if some cartesian power of (X , ϕ) admits a nonconstant invariant rational function, then already the second cartesian power does. [ABSTRACT FROM AUTHOR]

A (noncommutative) Pólya series over a field K is a formal power series whose nonzero coefficients are contained in a finitely generated subgroup of K × . We show that rational Pólya series are unambiguous rational series, proving a 40 year old conjecture of Reutenauer. The proof combines methods from noncommutative algebra, automata theory, and number theory (specifically, unit equations). As a corollary, a rational series is a Pólya series if and only if it is Hadamard sub-invertible. Phrased differently, we show that every weighted finite automaton taking values in a finitely generated subgroup of a field (and zero) is equivalent to an unambiguous weighted finite automaton. [ABSTRACT FROM AUTHOR]

We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras. [ABSTRACT FROM AUTHOR]

A noncommutative analogue of the Zariski cancellation problem asks whether $$A[x]\cong B[x]$$ implies $$A\cong B$$ when A and B are noncommutative algebras. We resolve this affirmatively in the case when A is a noncommutative finitely generated domain over the complex field of Gelfand-Kirillov dimension two. In addition, we resolve the Zariski cancellation problem for several classes of Artin-Schelter regular algebras of higher Gelfand-Kirillov dimension. [ABSTRACT FROM AUTHOR]

Let $${\mathcal {A}}$$ be a finite set of $$d\times d$$ matrices with integer entries and let $$m_n({\mathcal {A}})$$ be the maximum norm of a product of $$n$$ elements of $${\mathcal {A}}$$ . In this paper, we classify gaps in the growth of $$m_n({\mathcal {A}})$$ ; specifically, we prove that $$\lim _{n\rightarrow \infty } \log m_n({\mathcal {A}})/\log n\in \mathbb {Z}_{\geqslant 0}\cup \{\infty \}.$$ This has applications to the growth of regular sequences as defined by Allouche and Shallit. [ABSTRACT FROM AUTHOR]

Escherichia coli RecA is the defining member of a ubiquitous class of DNA strand-exchange proteins that are essential for homologous recombination, a pathway that maintains genomic integrity by repairing broken DNA. To function, filaments of RecA must nucleate and grow on single-stranded DNA (ssDNA) in direct competition with ssDNA-binding protein (SSB), which rapidly binds and continuously sequesters ssDNA, kinetically blocking RecA assembly. This dynamic self-assembly on a DNA lattice, in competition with another protein, is unique for the RecA family compared to other filament-forming proteins such as actin and tubulin. The complexity of this process has hindered our understanding of RecA filament assembly because ensemble measurements cannot reliably distinguish between the nucleation and growth phases, despite extensive and diverse attempts. Previous single-molecule assays have measured the nucleation and growth of RecA-and its eukaryotic homologue RAD51-on naked double-stranded DNA and ssDNA; however, the template for RecA self-assembly in vivo is SSB-coated ssDNA. Using single-molecule microscopy, here we directly visualize RecA filament assembly on single molecules of SSB-coated ssDNA, simultaneously measuring nucleation and growth. We establish that a dimer of RecA is required for nucleation, followed by growth of the filament through monomer addition, consistent with the finding that nucleation, but not growth, is modulated by nucleotide and magnesium ion cofactors. Filament growth is bidirectional, albeit faster in the 5??3? direction. Both nucleation and growth are repressed at physiological conditions, highlighting the essential role of recombination mediators in potentiating assembly in vivo. We define a two-step kinetic mechanism in which RecA nucleates on transiently exposed ssDNA during SSB sliding and/or partial dissociation (DNA unwrapping) and then the RecA filament grows. We further demonstrate that the recombination mediator protein pair, RecOR (RecO and RecR), accelerates both RecA nucleation and filament growth, and that the introduction of RecF further stimulates RecA nucleation. [ABSTRACT FROM AUTHOR]

Let K be a field of characteristic p>0 and let f( t,..., t) be a power series in d variables with coefficients in K that is algebraic over the field of multivariate rational functions K( t,..., t). We prove a generalization of both Derksen's recent analogue of the Skolem-Mahler-Lech theorem in positive characteristic and a classical theorem of Christol, by showing that the set of indices ( n,..., n)∈ℕ for which the coefficient of $t_{1}^{n_{1}}\cdots t_{d}^{n_{d}}$ in f( t,..., t) is zero is a p-automatic set. Applying this result to multivariate rational functions leads to interesting effective results concerning some Diophantine equations related to S-unit equations and more generally to the Mordell-Lang Theorem over fields of positive characteristic. [ABSTRACT FROM AUTHOR]

We present a new method for proving non-holonomicity of sequences, which is based on results about the number of zeros of elementary and of analytic functions. Our approach is applicable to sequences that are defined as the values of an elementary function at positive integral arguments. We generalize several recent results, e.g., non-holonomicity of the logarithmic sequence is extended to rational functions involving log n. Moreover, we show that the sequence that arises from evaluating the Riemann zeta function at an increasing integer sequence with bounded gap lengths is not holonomic. [ABSTRACT FROM AUTHOR]

Face recognition difficulties are common in autism and could be a consequence of perceptual atypicalities that disrupt the ability to integrate current and prior information. We tested this theory by measuring the strength of serial dependence for faces (i.e. how likely is it that current perception of a face is biased towards a previously seen face) across the broader autism phenotype. Though serial dependence was not weaker in individuals with more autistic traits, more autistic traits were associated with greater integration of less similar faces. These results suggest that serial dependence is less specialised, and may not operate optimally, in individuals with more autistic traits and could therefore be a contributing factor to autism-linked face recognition difficulties. [ABSTRACT FROM AUTHOR]

Mitotic chromosome condensation has fascinated biologists since Flemming's early illustrations of mitosis in the late nineteenth century. Now - 130 years later - chromatid condensation is reconstituted in vitro with the minimum components. The results are remarkably and beautifully simple, requiring only core histones, three histone chaperones, topoisomerase II and condensin I. [ABSTRACT FROM AUTHOR]

It is important to understand the psychological factors that underlie heightened eating restraint, which represents a risk factor for various types of dysfunction, including eating disorders. This study tested the hypothesis that eating restraint will be predicted by fear of fatness in a manner that is moderated by avoidance of fatness, with such predictive capacity being most evident in those who exhibit elevated avoidance of fatness. Seventy nine participants varying in eating restraint took part in the study. Fear of fatness was measured using an Implicit Association Test, and avoidance of fatness was measured using an Approach-Avoidance Task. The data supported the hypothesis under test. The avoidance of fatness measure moderated the association between the fear of fatness measure and the measure of eating restraint. Specifically, fear of fatness was associated with increased eating restraint only when avoidance of fatness was elevated. It is suggested that these findings not only illuminate the psychological basis of individual differences in eating restraint, but also may inform the development of novel therapeutic interventions for dysfunctional eating restraint. [ABSTRACT FROM AUTHOR]

Serial dependence is a perceptual bias where current perception is biased towards prior visual input. This bias occurs when perceiving visual attributes, such as facial identity, and has been argued to play an important functional role in vision, stabilising the perception of objects through integration. In face identity recognition, this bias could assist in building stable representations of facial identity. If so, then individual variation in serial dependence could contribute to face recognition ability. To investigate this possibility, we measured both the strength of serial dependence and the range over which individuals showed this bias (the tuning) in 219 adults, using a new measure of serial dependence of facial identity. We found that better face recognition was associated with stronger serial dependence and narrower tuning, that is, showing serial dependence primarily when sequential faces were highly similar. Serial dependence tuning was further found to be a significant predictor of face recognition abilities independently of both object recognition and face identity aftereffects. These findings suggest that the extent to which serial dependence is used selectively for similar faces is important to face recognition. Our results are consistent with the view that serial dependence plays a functional role in face recognition. [ABSTRACT FROM AUTHOR]

Internalization of sociocultural attitudes regarding the so-called virtues of thinness and vices of fatness can lead to two motivational orientations: drive for thinness and fear of fat. The current study assessed drive for thinness and fear of fat, via approach and avoidance motivation towards thin-ideal and non-thin bodies respectively, and also the relation between these approach-avoidance tendencies and key eating disorder-related constructs. Participants were 95 female undergraduate students. Results revealed an approach bias for thin-ideal bodies and an avoidance bias for non-thin bodies. Furthermore, a greater approach bias towards thin-ideal bodies was associated with greater body dissatisfaction, thin-ideal internalization, and dietary restraint whilst controlling for body mass index. An avoidance bias away from non-thin bodies did not significantly correlate with any eating disorder-related constructs. These findings imply that drive for thinness may be more relevant than fear of fat as a risk factor for eating disorder symptoms in women. [ABSTRACT FROM AUTHOR]

Coupling of the Community Land Model (CLM3) to the ICTP Regional Climate Model (RegCM3) substantially improves the simulation of mean climate over West Africa relative to an older version of RegCM3 coupled to the Biosphere Atmosphere Transfer Scheme (BATS). Two 10-year simulations (1992–2001) show that the seasonal timing and magnitude of mean monsoon precipitation more closely match observations when the new land surface scheme is implemented. Specifically, RegCM3–CLM3 improves the timing of the monsoon advance and retreat across the Guinean Coast, and reduces a positive precipitation bias in the Sahel and Northern Africa. As a result, simulated temperatures are higher, thereby reducing the negative temperature bias found in the Guinean Coast and Sahel in RegCM3–BATS. In the RegCM3–BATS simulation, warmer temperatures in northern latitudes and wetter soils near the coast create excessively strong temperature and moist static energy gradients, which shifts the African Easterly Jet further north than observed. In the RegCM3–CLM3 simulation, the migration and position of the African Easterly Jet more closely match reanalysis winds. This improvement is triggered by drier soil conditions in the RegCM3–CLM3 simulation and an increase in evapotranspiration per unit precipitation. These results indicate that atmosphere–land surface coupling has the ability to impact regional-scale circulation and precipitation in regions exhibiting strong hydroclimatic gradients. [ABSTRACT FROM AUTHOR]