7,252 research outputs found
Some relational structures with polynomial growth and their associated algebras II: Finite generation
The profile of a relational structure is the function which
counts for every integer the number, possibly infinite, of
substructures of induced on the -element subsets, isomorphic
substructures being identified. If takes only finite values, this
is the Hilbert function of a graded algebra associated with , the age
algebra , introduced by P.~J.~Cameron.
In a previous paper, we studied the relationship between the properties of a
relational structure and those of their algebra, particularly when the
relational structure admits a finite monomorphic decomposition. This
setting still encompasses well-studied graded commutative algebras like
invariant rings of finite permutation groups, or the rings of quasi-symmetric
polynomials.
In this paper, we investigate how far the well know algebraic properties of
those rings extend to age algebras. The main result is a combinatorial
characterization of when the age algebra is finitely generated. In the special
case of tournaments, we show that the age algebra is finitely generated if and
only if the profile is bounded. We explore the Cohen-Macaulay property in the
special case of invariants of permutation groupoids. Finally, we exhibit
sufficient conditions on the relational structure that make naturally the age
algebra into a Hopf algebra.Comment: 27 pages; submitte
Chaos and Order in Nature/Creation: A Reading of Genesis l-2:4a in Dialogue with Science and Philosophy
With inspiration from post-modern scientific theories (complexity theory, chaos theory, relativity theory, uncertainty theory, no-singularity/boundary theory), and from philosophical understandings of nature (ecstatic naturalism and Taoism), the author offers an innovative reading of the Genesis creation stories, focusing on the concepts of order and chaos. While criticizing the
dichotomous dualism that underpins the human ordering system, she connects these rich meanings and wisdom signified by nature with theological discourse through a discussion of the infinity of God, the abjection of origin, the autonomy of creatures, and nature's complex and fluid manifestations.ye
Highly versatile atomic micro traps generated by multifrequency magnetic field modulation
We propose the realization of custom-designed adiabatic potentials for cold
atoms based on multimode radio frequency radiation in combination with static
inhomogeneous magnetic fields. For example, the use of radio frequency combs
gives rise to periodic potentials acting as gratings for cold atoms. In strong
magnetic field gradients the lattice constant can be well below 1 micrometer.
By changing the frequencies of the comb in time the gratings can easily be
propagated in space, which may prove useful for Bragg scattering atomic matter
waves. Furthermore, almost arbitrarily shaped potential are possible such as
disordered potentials on a scale of several 100 nm or lattices with a spatially
varying lattice constant. The potentials can be made state selective and, in
the case of atomic mixtures, also species selective. This opens new
perspectives for generating tailored quantum systems based on ultra cold single
atoms or degenerate atomic and molecular quantum gases.Comment: 12 pages, 6 figure
Ab Initio Modeling of Ecosystems with Artificial Life
Artificial Life provides the opportunity to study the emergence and evolution
of simple ecosystems in real time. We give an overview of the advantages and
limitations of such an approach, as well as its relation to individual-based
modeling techniques. The Digital Life system Avida is introduced and prospects
for experiments with ab initio evolution (evolution "from scratch"),
maintenance, as well as stability of ecosystems are discussed.Comment: 13 pages, 2 figure
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