463 research outputs found
Paraconsistent vagueness: a positive argument
Paraconsistent approaches have received little attention in the literature
on vagueness (at least compared to other proposals). The reason seems to be that
many philosophers have found the idea that a contradiction might be true (or that
a sentence and its negation might both be true) hard to swallow. Even advocates of
paraconsistency on vagueness do not look very convinced when they consider this
fact; since they seem to have spent more time arguing that paraconsistent theories
are at least as good as their paracomplete counterparts, than giving positive reasons
to believe on a particular paraconsistent proposal. But it sometimes happens that the
weakness of a theory turns out to be its mayor ally, and this is what (I claim) hap-
pens in a particular paraconsistent proposal known as subvaluationism. In order to
make room for truth-value gluts subvaluationism needs to endorse a notion of logical
consequence that is, in some sense, weaker than standard notions of consequence. But
this weakness allows the subvaluationist theory to accommodate higher-order vague-
ness in a way that it is not available to other theories of vagueness (such as, for example,
its paracomplete counterpart, supervaluationism)
KEEFE, ROSANNA, Theories of Vagueness, Cambridge University Press, Cambridge, 2000, 220 pĂĄgs. [RECENSIĂN]
Supervaluationism and the timeless solution to the foreknowledge problem
If God knew I were going to write this paper, was I able to refrain from writing it this morning? One possible response to this question is that God's knowledge does not take place in time and therefore He does not properly fore-know. According to this response, God knows absolutely everything, it's just that He knows everything outside of time. The so-called timeless solution was one of the influential responses to the foreknowledge problem in classical Christian Theology. This solution, however, seemed to lose support in the recent debate. For example, Pike claims that "the doctrine of God's timelessness entered Christian Theology (only) because Platonic thought was stylish at the time" (Pike, 1970, 190) and Hasker (2001) catalogues this as one of the minor solutions to the problem. One possible source for this general attitude towards timelessness is the thought that the very idea of timelessness is incoherent. In this paper I argue that that the timeless solution to the foreknowledge problem is congenial with the supervaluationist theory of branching time and that this formal framework provides, in fact, a precise characterization of the timeless solution to the foreknowledge problem. The views presented in this paper are in line with those of Kretzmann and Stump (1981), Leftow (1991) and De Florio and Frigerio (2015)
CUTOFF AT THE " ENTROPIC TIME " FOR SPARSE MARKOV CHAINS
International audienceWe study convergence to equilibrium for a large class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix P the mass is essentially concentrated on few entries. Moreover, the random environment is such that rows of P are independent and such that the entries are exchangeable within each row. This includes various models of random walks on sparse random directed graphs. The models are generally non reversible and the equilibrium distribution is itself unknown. In this general setting we establish the cutoff phenomenon for the total variation distance to equilibrium, with mixing time given by the logarithm of the number of states times the inverse of the average row entropy of P. As an application, we consider the case where the rows of P are i.i.d. random vectors in the domain of attraction of a Poisson-Dirichlet law with index α â (0, 1). Our main results are based on a detailed analysis of the weight of the trajectory followed by the walker. This approach offers an interpretation of cutoff as an instance of the concentration of measure phenomenon
Trebouxia lynnae sp. nov. (former Trebouxia sp. TR9): biology and biogeography of an epitome lichen symbiotic microalga
Two microalgal species, Trebouxia jamesii and Trebouxia sp. TR9, were detected as the main photobionts coexisting in the thalli of the lichen Ramalina farinacea. Trebouxia sp. TR9 emerged as anew taxon in lichen symbioses and was successfully isolated and propagated in in vitro culture andthoroughly investigated. Several years of research have confirmed the taxon Trebouxia sp. TR9 tobe a model/reference organism for studying mycobiontâphotobiont association patterns in lichensymbioses. Trebouxia sp. TR9 is the first symbiotic, lichen-forming microalga for which an exhaustivecharacterization of cellular ultrastructure, physiological traits, genetic and genomic diversity is available.The cellular ultrastructure was studied by light, electron and confocal microscopy; physiologicaltraits were studied as responses to different abiotic stresses. The genetic diversity was previouslyanalyzed at both the nuclear and organelle levels by using chloroplast, mitochondrial, and nucleargenome data, and a multiplicity of phylogenetic analyses were carried out to study its intraspecificdiversity at a biogeographical level and its specificity association patterns with the mycobiont.Here, Trebouxia sp. TR9 is formally described by applying an integrative taxonomic approach and ispresented to science as Trebouxia lynnae, in honor of Lynn Margulis, who was the primary modernproponent for the significance of symbiosis in evolution. The complete set of analyses that werecarried out for its characterization is provided
Spectral density of random graphs with topological constraints
The spectral density of random graphs with topological constraints is
analysed using the replica method. We consider graph ensembles featuring
generalised degree-degree correlations, as well as those with a community
structure. In each case an exact solution is found for the spectral density in
the form of consistency equations depending on the statistical properties of
the graph ensemble in question. We highlight the effect of these topological
constraints on the resulting spectral density.Comment: 24 pages, 6 figure
Spectral Theory of Sparse Non-Hermitian Random Matrices
Sparse non-Hermitian random matrices arise in the study of disordered
physical systems with asymmetric local interactions, and have applications
ranging from neural networks to ecosystem dynamics. The spectral
characteristics of these matrices provide crucial information on system
stability and susceptibility, however, their study is greatly complicated by
the twin challenges of a lack of symmetry and a sparse interaction structure.
In this review we provide a concise and systematic introduction to the main
tools and results in this field. We show how the spectra of sparse
non-Hermitian matrices can be computed via an analogy with infinite dimensional
operators obeying certain recursion relations. With reference to three
illustrative examples --- adjacency matrices of regular oriented graphs,
adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency
matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the
use of these methods to obtain both analytic and numerical results for the
spectrum, the spectral distribution, the location of outlier eigenvalues, and
the statistical properties of eigenvectors.Comment: 60 pages, 10 figure
Small ball probability, Inverse theorems, and applications
Let be a real random variable with mean zero and variance one and
be a multi-set in . The random sum
where are iid copies of
is of fundamental importance in probability and its applications.
We discuss the small ball problem, the aim of which is to estimate the
maximum probability that belongs to a ball with given small radius,
following the discovery made by Littlewood-Offord and Erdos almost 70 years
ago. We will mainly focus on recent developments that characterize the
structure of those sets where the small ball probability is relatively
large. Applications of these results include full solutions or significant
progresses of many open problems in different areas.Comment: 47 page
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