Fibrational induction rules for initial algebras

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, an induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of particular syntactic forms. We establish the correctness of our generic induction rule by reducing induction to iteration. We show how our rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The former lies outside the scope of Hermida and Jacobs’ work because it is not polynomial; as far as we are aware, no induction rules have been known to exist for the latter two in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set

Social change in kinship and marriage among the Yoruba of western Nigeria

The material has shown that in traditional Yoruba society the lineage is the unit of social action. Jchwab ( 1955, pp.355 -6), speaking of the Yoruba town of Oshogbo, states explicitly, "Apart from the usual differentials of sex and age, membership in an idile (lineage) is the primary determinant of an individual's social, economic and political role. The idile forms the basis for association in the residential unit, the compound.'The new trend towards autonomy of the domestic group is well documented. The Sofers (1956) comment on the decline of the importance of the clan in Jinja, the trend towards monogamy and the emerging tendency to regard marriage as a relationship between two individuals rather than as an inter-group affair. Similar information is provided by Busia (1950) on Sekondi -Takoradi, Hellmann (1956) on South Africa, Doucy and Feldheim (1956) on two districts in the Belgian Congo, Banton (1957) on Freetown, Crabtree (1950) on the urban areas of Ghana, and Lombard (1954) on Cotonou. The last describes the general trend (op.cit. p. 356), "De tous temps, la famille a ete en Afrique la cellule sociale fondamentale. Autrefois, le menage n'etait qu'une fraction de la famille, sans personnalite ni autonomie. Aujourd'hui, sans avoir rompu totalement avec la grande collectivite, il tend a representer principalement dans les villes, l'element essentiel de la vie familiale ".To conclude, the following quotation sums up the position among the Yoruba, as among other African societies in transition to -day."What in fact has happened under the impact of industrialisation and technical change is that life has become very much more specialised. In the towns, the kin group is no longer economically self -sufficient, and in the rural areas its solidarity for the multiple tasks performed under the traditional system is seriously impaired by migration. The result is that a new social organisation has arisen which has taken over many of the activities previously carried on by the extended family and the lineage. There is now specialisation not only of economic activities but of all the principal activities of community life, including the care and training of children, religion, recreation, government, and mutual aid." (Little, 1955, pp. 283 -4)

Fluid Elasticity Can Enable Propulsion at Low Reynolds Number

Conventionally, a microscopic particle that performs a reciprocal stroke cannot move through its environment. This is because at small scales, the response of simple Newtonian fluids is purely viscous and flows are time-reversible. We show that by contrast, fluid elasticity enables propulsion by reciprocal forcing that is otherwise impossible. We present experiments on rigid objects actuated reciprocally in viscous fluids, demonstrating for the first time a purely elastic propulsion set by the object's shape and boundary conditions. We describe two different artificial "swimmers" that experimentally realize this principle.Comment: 5 pages, 4 figure

Cosmology with velocity dispersion counts: an alternative to measuring cluster halo masses

The evolution of galaxy cluster counts is a powerful probe of several fundamental cosmological parameters. A number of recent studies using this probe have claimed tension with the cosmology preferred by the analysis of the Planck primary CMB data, in the sense that there are fewer clusters observed than predicted based on the primary CMB cosmology. One possible resolution to this problem is systematic errors in the absolute halo mass calibration in cluster studies, which is required to convert the standard theoretical prediction (the halo mass function) into counts as a function of the observable (e.g., X-ray luminosity, Sunyaev-Zel'dovich flux, optical richness). Here we propose an alternative strategy, which is to directly compare predicted and observed cluster counts as a function of the one-dimensional velocity dispersion of the cluster galaxies. We argue that the velocity dispersion of groups/clusters can be theoretically predicted as robustly as mass but, unlike mass, it can also be directly observed, thus circumventing the main systematic bias in traditional cluster counts studies. With the aid of the BAHAMAS suite of cosmological hydrodynamical simulations, we demonstrate the potential of the velocity dispersion counts for discriminating even similar $\Lambda$CDM models. These predictions can be compared with the results from existing redshift surveys such as the highly-complete Galaxy And Mass Assembly (GAMA) survey, and upcoming wide-field spectroscopic surveys such as the Wide Area Vista Extragalactic Survey (WAVES) and the Dark Energy Survey Instrument (DESI).Comment: 15 pages, 13 figures. Accepted for publication in MNRAS. New section on cosmological forecasts adde

Photomechanical Investigation of Structural Behavior of Gyroscope Components. Task IV - Analysis of Initial Redesign of AB5-K8 GYROSCOPE

Photomechanics of structure and materials in redesigned AB5-K8 gyroscope component

Rouse Chains with Excluded Volume Interactions: Linear Viscoelasticity

Linear viscoelastic properties for a dilute polymer solution are predicted by modeling the solution as a suspension of non-interacting bead-spring chains. The present model, unlike the Rouse model, can describe the solution's rheological behavior even when the solvent quality is good, since excluded volume effects are explicitly taken into account through a narrow Gaussian repulsive potential between pairs of beads in a bead-spring chain. The use of the narrow Gaussian potential, which tends to the more commonly used delta-function repulsive potential in the limit of a width parameter "d" going to zero, enables the performance of Brownian dynamics simulations. The simulations results, which describe the exact behavior of the model, indicate that for chains of arbitrary but finite length, a delta-function potential leads to equilibrium and zero shear rate properties which are identical to the predictions of the Rouse model. On the other hand, a non-zero value of "d" gives rise to a prediction of swelling at equilibrium, and an increase in zero shear rate properties relative to their Rouse model values. The use of a delta-function potential appears to be justified in the limit of infinite chain length. The exact simulation results are compared with those obtained with an approximate solution which is based on the assumption that the non-equilibrium configurational distribution function is Gaussian. The Gaussian approximation is shown to be exact to first order in the strength of excluded volume interaction, and is found to be accurate above a threshold value of "d", for given values of chain length and strength of excluded volume interaction.Comment: Revised version. Long chain limit analysis has been deleted. An improved and corrected examination of the long chain limit will appear as a separate posting. 32 pages, 9 postscript figures, LaTe

The evolution of pebble size and shape in space and time

We propose a mathematical model which suggests that the two main geological observations about shingle beaches, i.e. the emergence of predominant pebble size ratios and strong segregation by size are interrelated. Our model is a based on a system of ODEs called the box equations, describing the evolution of pebble ratios. We derive these ODEs as a heuristic approximation of Bloore's PDE describing collisional abrasion. While representing a radical simplification of the latter, our system admits the inclusion of additional terms related to frictional abrasion. We show that nontrivial attractors (corresponding to predominant pebble size ratios) only exist in the presence of friction. By interpreting our equations as a Markov process, we illustrate by direct simulation that these attractors may only stabilized by the ongoing segregation process.Comment: 22 pages, 8 figure

The preparation of a Non-Desiccated Sodium Caseinate Sol and its use in ice cream

1. The body and texture of ice cream are improved by the replacement of dry skimmilk by sodium caseinate sols. This improvement was shown up to 2.5 to 5.0 percent replacement, depending on the composition of the mix. 2. The flavor of ice cream was progressively improved by the replacement of dry skimmilk by sodium caseinate sols up to 3 to 4 percent replacement, depending on the composition of the mix. 3. This flavor improvement was due to the careful pH control used in the preparation of the sodium caseinate sols. 4. The type of melting of the ice cream was altered by the replacement of dry skimmilk by sodium caseinate sols. 5. The use of sodium caseinate sols increased the initial and maximum overrun and decreased the whipping time of the ice creams produced. 6. The curves for whipping time show that from 1.5 to 3.0 percent replacement of dry skimmilk by the sodium caseinate sols is necessary to effect sufficient improvement in whip to warrant their use. A 3 percent replacement would be necessary with a mix containing 14 percent fat and 10 percent serum solids. 7. The use of sodium caseinate preparations as additional solids, i.e., in addition to the amounts of serum solids (8 to 10 percent) commonly used by the trade, has been suggested. The amounts of milk protein that would be required to yield sufficient improvement in whip and in body and texture score would, in the light of the figures presented, be large enough to make their use questionable

Moving time: The influence of action on duration perception

Perceiving the sensory consequences of action accurately is essential for appropriate interaction with our physical and social environments. Prediction mechanisms are considered necessary for fine-tuned sensory control of action, yet paradoxically may distort perception. Here, we examine this paradox by addressing how movement influences the perceived duration of sensory outcomes congruent with action. Experiment 1 required participants to make judgments about the duration of vibrations applied to a moving or stationary finger. In Experiments 2 and 3, participants judged observed finger movements that were congruent or incongruent with their own actions. In all experiments, target events were perceived to be longer when congruent with movement. Interestingly, this temporal dilation did not differ as a function of stimulus perspective (1st or 3rd person) or spatial location. We propose that this bias may reflect the operation of an adaptive mechanism for sensorimotor selection and control that preactivates anticipated outcomes of action. The bias itself may have surprising implications for both action control and perception of others: we may be in contact with grasped objects for less time than we realize, and others' reactions to us may be briefer than we believe. (PsycINFO Database Record (c) 2014 APA, all rights reserved)