105,012 research outputs found
Weak n-categories: opetopic and multitopic foundations
We generalise the concepts introduced by Baez and Dolan to define opetopes
constructed from symmetric operads with a category, rather than a set, of
objects. We describe the category of 1-level generalised multicategories, a
special case of the concept introduced by Hermida, Makkai and Power, and
exhibit a full embedding of this category in the category of symmetric operads
with a category of objects. As an analogy to the Baez-Dolan slice construction,
we exhibit a certain multicategory of function replacement as a slice
construction in the multitopic setting, and use it to construct multitopes. We
give an explicit description of the relationship between opetopes and
multitopes.Comment: 41 page
Rumor processes in random environment on N and on Galton-Watson trees
The aim of this paper is to study rumor processes in random environment. In a
rumor process a signal starts from the stations of a fixed vertex (the root)
and travels on a graph from vertex to vertex. We consider two rumor processes.
In the firework process each station, when reached by the signal, transmits it
up to a random distance. In the reverse firework process, on the other hand,
stations do not send any signal but they "listen" for it up to a random
distance. The first random environment that we consider is the deterministic
1-dimensional tree N with a random number of stations on each vertex; in this
case the root is the origin of N. We give conditions for the
survival/extinction on almost every realization of the sequence of stations.
Later on, we study the processes on Galton-Watson trees with random number of
stations on each vertex. We show that if the probability of survival is
positive, then there is survival on almost every realization of the infinite
tree such that there is at least one station at the root. We characterize the
survival of the process in some cases and we give sufficient conditions for
survival/extinction.Comment: 28 page
Domain and range for angelic and demonic compositions
We give finite axiomatizations for the varieties generated by representable
domain--range algebras when the semigroup operation is interpreted as angelic
or demonic composition, respectively
On the multistationarity of chemical reaction networks
We present a new conjecture about a necessary condition that a (bio)chemical
network has to satisfy for it to exhibit multistationarity. According to a
Theorem of Feliu and Wiuf [27, 12], the conjecture is known for strictly
monotonic kinetics. We give several examples illustrating our conjecture
A discrete, unitary, causal theory of quantum gravity
A discrete model of Lorentzian quantum gravity is proposed. The theory is
completely background free, containing no reference to absolute space, time, or
simultaneity. The states at one slice of time are networks in which each vertex
is labelled with two arrows, which point along an adjacent edge, or to the
vertex itself. The dynamics is specified by a set of unitary replacement rules,
which causally propagate the local degrees of freedom. The inner product
between any two states is given by a sum over histories. Assuming it converges
(or can be Abel resummed), this inner product is proven to be hermitian and
fully gauge-degenerate under spacetime diffeomorphisms. At least for states
with a finite past, the inner product is also positive. This allows a Hilbert
space of physical states to be constructed.Comment: 38 pages, 9 figures, v3 added to exposition and references, v4
expanded prospects sectio
Evolution of the Scale Factor with a Variable Cosmological Term
Evolution of the scale factor a(t) in Friedmann models (those with zero
pressure and a constant cosmological term Lambda) is well understood, and
elegantly summarized in the review of Felten and Isaacman [Rev. Mod. Phys. 58,
689 (1986)]. Developments in particle physics and inflationary theory, however,
increasingly indicate that Lambda ought to be treated as a dynamical quantity.
We revisit the evolution of the scale factor with a variable Lambda-term, and
also generalize the treatment to include nonzero pressure. New solutions are
obtained and evaluated using a variety of observational criteria. Existing
arguments for the inevitability of a big bang (ie., an initial state with a=0)
are substantially weakened, and can be evaded in some cases with Lambda_0 (the
present value of Lambda) well below current experimental limits.Comment: 29 pages, 12 figures (not included), LaTeX, uses Phys Rev D style
files (revtex.cls, revtex.sty, aps.sty, aps10.sty, prabib.sty). To appear in
Phys Rev
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