Strictly positive definite functions on compact abelian groups

We study the Fourier characterisation of strictly positive definite functions on compact abelian groups. Our main result settles the case $G = F \times \mathbb{T}^r$, with $r \in \mathbb{N}$ and $F$ finite. The characterisation obtained for these groups does not extend to arbitrary compact abelian groups; it fails in particular for all torsion-free groups.Comment: 9 pages; submitted to Proc. AM

How much should we Distribute Morphology?

Studies of morphology, as carried out in practice, focus on a proper subset of bound morphemes which satisfy two properties: their inherent "meanings" are those of general grammatical categories, and they don\u27t receive stress like members of compounds. A question then arises, are there any morphology-specific principles, those of a "Morphological Component," that apply only to such forms? A number of candidates are examined in turn: "Non-maximality," Head Placement, Merger, Alternative Realization, and two Phonological Boundary Conditions. It is argued that the only principles specific to morphology are the last ones, i.e. that properly formulated principles of boundary erasure permit morphology to be completely "distributed" to the syntactic and phonological components

Q : the only Functional Head above N and A

Current versions of Chomskyan syntax take for granted that maximal or "extended" projections of the fundamental lexical categories N, A, V and P contain elaborate systems of functional heads and projections, which also differ in nature for each of these systems. This paper begins an argument, to be continued elsewhere, that this approach is currently more than "taken to extremes"; rather it is fundamentally misguided. All functional modifiers truly independent of a lexical category are types of quantifying or counting. Several unexplained properties then fall into place, among other those of subject phrases and measure phrases, and many differences between English and Japanese, both in counting and regarding subject NPs

θ-Role Assignment in Derived Nominals

Chomsky and Stowell attribute an asymmetry in noun and verb complement systems to how these categories assign Case. Here, Case assignment is dependent on structural configurations that θ-role theory determines; it is the latter which explains asymmetries in the noun and verb complement systems.Several predicate attribute and Vk (clausal) complement types are examined, and all confirm the θ-role theory in which V can assign θ-roles directly to sisters of any phrasal type, while N and A can assign θ-roles only "indirectly," to Ymax appearing in PP structures. This predicts the new patterns examined here, as well as the asymmetry in how objects of verbs and derived nominals are syntactically realized.Chomsky et Stowell attribuent l’asymétrie entre les compléments des noms et ceux des verbes aux propriétés respectives d’assignation de Cas de ces deux catégories. Ici, l’assignation du Cas dépend des configurations structurales déterminées par la théorie des rôles thématiques; c’est cette dernière qui explique les asymétries entre le système de complémentation du nom et celui du verbe.Plusieurs types d’attributs prédicatifs et de compléments Vk (phrastiques) sont examinés, et tous confirment la théorie Thêta selon laquelle V peut assigner des rôles thématiques directement aux soeurs de n’importe quel noeud phrastique, alors que N et A ne peuvent assigner qu’indirectement des rôles thématiques aux Ymax apparaissant dans des structures de PP. Ceci prédit les nouveaux patrons examinés ici, ainsi que l’asymétrie relative à la réalisation des objets des verbes et des nominaux dérivés

Correlates of substitution rate variation in mammalian protein-coding sequences

BACKGROUND: Rates of molecular evolution in different lineages can vary widely, and some of this variation might be predictable from aspects of species' biology. Investigating such predictable rate variation can help us to understand the causes of molecular evolution, and could also help to improve molecular dating methods. Here we present a comprehensive study of the life history correlates of substitution rate variation across the mammals, comparing results for mitochondrial and nuclear loci, and for synonymous and non-synonymous sites. We use phylogenetic comparative methods, refined to take into account the special nature of substitution rate data. Particular attention is paid to the widespread correlations between the components of mammalian life history, which can complicate the interpretation of results. RESULTS: We find that mitochondrial synonymous substitution rates, estimated from the 9 longest mitochondrial genes, show strong negative correlations with body mass and with maximum recorded lifespan. But lifespan is the sole variable to remain after multiple regression and model simplification. Nuclear synonymous substitution rates, estimated from 6 genes, show strong negative correlations with body mass and generation time, and a strong positive correlation with fecundity. In contrast to the mitochondrial results, the same trends are evident in rates of nonsynonymous substitution. CONCLUSION: A substantial proportion of variation in mammalian substitution rates can be explained by aspects of their life history, implying that molecular and life history evolution are closely interlinked in this group. The strength and consistency of the nuclear body mass effect suggests that molecular dating studies may have been systematically misled, but also that methods could be improved by incorporating the finding as a priori information. Mitochondrial synonymous rates also show the body mass effect, but for apparently quite different reasons, and the strength of the relationship with maximum lifespan provides support for the hypothesis that mtDNA damage is causally linked to aging

Towards a Simulator Tool for Predicting Sprinting and Long Jump Motions with and without Running-Specific Prostheses: An Optimization-Based Approach

The performances of sprinters and long jumpers with below the knee amputation (BKA) have improved continuously since the development of prostheses specifically for athletic movements. In the last years, a number of athletes with BKA have attempted to compete in non-amputee competitions. Due to the specific shape and material properties of the running-specific prosthesis (RSP), concerns exist that it may give athletes an advantage over non-amputee athletes. In this work, we investigate and compare sprinting and long jump movements of athletes with and without unilateral BKA using accurate computer models. In this context, the aim of the work is to describe similarities and differences between the athletes’ movements and to show that the employed model- and optimization-based computations are useful for this purpose. We created subject-specific multi-body models for five different athletes (four non-amputee athletes, one athlete with unilateral BKA) in order to be able to investigate the different movements. Depending on the research question, the models vary in the number of degrees of freedom (DOFs), from 16 DOFs for a two-dimensional model in the sagittal plane to 31 DOFs for a three-dimensional model. For the athlete with BKA, we created a three-segment model of the RSP with one rotational DOF in the sagittal plane. The respective motion is described by a sequence of several phases, which differ by the type of ground contact. Each of these phases is described by its own set of ordinary differential equations (ODEs) or differential algebraic equations (DAEs). We use multi-phase optimal control problems (OCPs) with discontinuities to generate sprint and long jump motions. Three different formulations of OCPs are adopted in this work. (1) We formulate a least squares OCP to reconstruct the dynamics of sprint and long jump motion capture recordings of the individual athletes. (2) For the generation of realistic motions, which can be used for prediction, we formulate a synthesis OCP; this optimizes an objective function consisting of a weighted combination of chosen optimization criteria. (3) Last, in the study of sprint movements, we use an inverse optimal control problem (IOCP): this consists of an inner loop, in which a synthesis OCP is solved, and an outer loop, which adjusts the weights of the individual optimization criteria such that the distance between the inner loop solution and a reference movement becomes minimal. We have successfully applied these three optimization problem formulations to the computation of two sprint steps of three athletes without and one athlete with unilateral transtibial amputation. Here, the movements of the non-amputee athletes differ from that of the amputee athlete in a large number of variables. In particular, the athletes use different actuation strategies for running with and without a RSP. We have observed lower torques in the amputee athlete in the leg affected by the amputation than in the non-amputee control group. In contrast, significantly larger torques occurred in the joints of the upper extremity in the amputee athlete. Furthermore, the comparison has shown that the asymmetry created by the RSP is reflected throughout the body and affects the entire movement. Using the OCPs for motion reconstruction (1) and synthesis (2), we have successfully computed the last three steps of the approach and the jump of a long jump for an athlete without and an athlete with unilateral amputation. In the reconstructed solutions, the amputee athlete achieves a greater jump distance compared to the non-amputee athlete, despite a slower approach velocity, because his take-off is more efficient. In the synthesis solutions, on the other hand, the non-amputee athlete achieves the greater jump distance because he generates a greater vertical force during the take-off and achieves a better ratio of gain of vertical to loss of horizontal velocity. Finally, we have presented our idea of a simulator tool to compare the amputee athlete with himself without amputation and have demonstrated it using the sprint and long jump movements. For this purpose, we have kept the model of the athlete with unilateral transtibial amputation from the previous studies and have created a non-amputee version of the same model by mirroring the biological leg. We have selected one objective function each for sprinting and for long jump and have solved the OCP for motion synthesis (2) for both model versions. Using the differences to the solutions based on the models of two real athletes, we have highlighted the importance of the simulator tool in the evaluation of advantages and disadvantages due to the use of the RSP