3,348 research outputs found
Categories, norms and weights
The well-known Lawvere category R of extended real positive numbers comes
with a monoidal closed structure where the tensor product is the sum. But R has
another such structure, given by multiplication, which is *-autonomous.
Normed sets, with a norm in R, inherit thus two symmetric monoidal closed
structures, and categories enriched on one of them have a 'subadditive' or
'submultiplicative' norm, respectively. Typically, the first case occurs when
the norm expresses a cost, the second with Lipschitz norms.
This paper is a preparation for a sequel, devoted to 'weighted algebraic
topology', an enrichment of directed algebraic topology. The structure of R,
and its extension to the complex projective line, might be a first step in
abstracting a notion of algebra of weights, linked with physical measures.Comment: Revised version, 16 pages. Some minor correction
The Return of Quarantinism and How to Keep It in Check: From Wishful Regulations to Political Accountability
Concerns about emerging and re-emerging infectious diseases have given a new lease of life to quarantinist measures: a series of time-honoured techniques for controlling the spread of infectious diseases through breaking the chain of human contagion. Since such measures typically infringe individual rights or privacy their use is subject to legal regulations and gives rise to ethical and political worries and suspicions. Yet in some circumstances they can be very effective. After considering some case studies that show how epidemics are unique, fluid and affected by a multitude of contingent factors, it is argued that the legal and ethical guidelines may not always be the best approach to discipline the use of quarantinist measures. An alternative model based on ex-post political accountability for reasonableness is proposed. This model restores the centrality of political decision and expert judgement in situations characterized by high risk, uncertainty and contingency. It is argued that such alternative model affords quicker and more flexible responses to serious outbreaks of infections, while providing adequate protection against abuses
Computer simulation of the phase diagram for a fluid confined in a fractal and disordered porous material
We present a grand canonical Monte Carlo simulation study of the phase
diagram of a Lennard-Jones fluid adsorbed in a fractal and highly porous
aerogel. The gel environment is generated from an off-lattice diffusion limited
cluster-cluster aggregation process. Simulations have been performed with the
multicanonical ensemble sampling technique. The biased sampling function has
been obtained by histogram reweighting calculations. Comparing the confined and
the bulk system liquid-vapor coexistence curves we observe a decrease of both
the critical temperature and density in qualitative agreement with experiments
and other Monte Carlo studies on Lennard-Jones fluids confined in random
matrices of spheres. At variance with these numerical studies we do not observe
upon confinement a peak on the liquid side of the coexistence curve associated
with a liquid-liquid phase coexistence. In our case only a shouldering of the
coexistence curve appears upon confinement. This shoulder can be associated
with high density fluctuations in the liquid phase. The coexisting vapor and
liquid phases in our system show a high degree of spatial disorder and
inhomogeneity.Comment: 8 pages, 8 figures, to be published in Phys. Rev.
A convenient category of locally preordered spaces
As a practical foundation for a homotopy theory of abstract spacetime, we
extend a category of certain compact partially ordered spaces to a convenient
category of locally preordered spaces. In particular, we show that our new
category is Cartesian closed and that the forgetful functor to the category of
compactly generated spaces creates all limits and colimits.Comment: 26 pages, 0 figures, partially presented at GETCO 2005; changes:
claim of Prop. 5.11 weakened to finite case and proof changed due to problems
with proof of Lemma 3.26, now removed; Eg. 2.7, statement before Lem. 2.11,
typos, and other minor problems corrected throughout; extensive rewording;
proof of Lem. 3.31, now 3.30, adde
Finite Sets And Symmetric Simplicial Sets
The category of finite cardinals (or, equivalently, of finite sets) is the symmetric analogue of the category of finite ordinals, and the ground category of a relevant category of presheaves, the augmented symmetric simplicial sets. We prove here that this ground category has characterisations similar to the classical ones for the category of finite ordinals, by the existence of a universal symmetric monoid, or by generators and relations. The latter provides a definition of symmetric simplicial sets by faces, degeneracies and transpositions, under suitable relations
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