13,481 research outputs found
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 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)
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