7,949 research outputs found
Literature and the construction of reality
In this article I consider the idea that Glasersfeld’s “radical constructivism” offers an ideal framework for putting in place such a reality of the best fit for us. Along with this, I examine also the fundamental biological and epistemological limitations that we are faced with when trying to fathom objective reality and, secondly, the inescapable gap between language – which we use as a primary cognitive tool in our attempt to comprehend the world. The paper then show that literature – especially fiction – best meets the criteria for addressing these gaps and constructing such a model of reality in line with what radical constructivism proposes
What is Fair Pay for Executives? An Information Theoretic Analysis of Wage Distributions
The high pay packages of U.S. CEOs have raised serious concerns about what
would constitute a fair pay.Comment: 16 page
Jorge Luis Borges and the Nothingness of the Self
In this paper I discuss how Borges uses his ideas on selfhood to explore the “central problem of literature” that Andre Maurois highlighted and how in the process projects to the reader his idea of reality. I argue also that the self that Borges tries to present in his work may nevertheless not be always congruent with the self he may have wanted to convey. This is because his quest is influenced by a number of factors, not least the fact that the self-creation process is affected by our interplay with the external world
The densest subgraph problem in sparse random graphs
We determine the asymptotic behavior of the maximum subgraph density of large
random graphs with a prescribed degree sequence. The result applies in
particular to the Erd\H{o}s-R\'{e}nyi model, where it settles a conjecture of
Hajek [IEEE Trans. Inform. Theory 36 (1990) 1398-1414]. Our proof consists in
extending the notion of balanced loads from finite graphs to their local weak
limits, using unimodularity. This is a new illustration of the objective method
described by Aldous and Steele [In Probability on Discrete Structures (2004)
1-72 Springer].Comment: Published at http://dx.doi.org/10.1214/14-AAP1091 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Boolean Model in the Shannon Regime: Three Thresholds and Related Asymptotics
Consider a family of Boolean models, indexed by integers , where the
-th model features a Poisson point process in of intensity
with as , and balls of
independent and identically distributed radii distributed like , with satisfying a large deviations principle. It is shown
that there exist three deterministic thresholds: the degree threshold;
the percolation threshold; and the volume fraction threshold;
such that asymptotically as tends to infinity, in a sense made precise in
the paper: (i) for , almost every point is isolated, namely its
ball intersects no other ball; (ii) for , almost every
ball intersects an infinite number of balls and nevertheless there is no
percolation; (iii) for , the volume fraction is 0 and
nevertheless percolation occurs; (iv) for , almost every
ball intersects an infinite number of balls and nevertheless the volume
fraction is 0; (v) for , the whole space covered. The analysis
of this asymptotic regime is motivated by related problems in information
theory, and may be of interest in other applications of stochastic geometry
Information-Theoretic Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements
This paper studies the Shannon regime for the random displacement of
stationary point processes. Let each point of some initial stationary point
process in give rise to one daughter point, the location of which is
obtained by adding a random vector to the coordinates of the mother point, with
all displacement vectors independently and identically distributed for all
points. The decoding problem is then the following one: the whole mother point
process is known as well as the coordinates of some daughter point; the
displacements are only known through their law; can one find the mother of this
daughter point? The Shannon regime is that where the dimension tends to
infinity and where the logarithm of the intensity of the point process is
proportional to . We show that this problem exhibits a sharp threshold: if
the sum of the proportionality factor and of the differential entropy rate of
the noise is positive, then the probability of finding the right mother point
tends to 0 with for all point processes and decoding strategies. If this
sum is negative, there exist mother point processes, for instance Poisson, and
decoding strategies, for instance maximum likelihood, for which the probability
of finding the right mother tends to 1 with . We then use large deviations
theory to show that in the latter case, if the entropy spectrum of the noise
satisfies a large deviation principle, then the error probability goes
exponentially fast to 0 with an exponent that is given in closed form in terms
of the rate function of the noise entropy spectrum. This is done for two
classes of mother point processes: Poisson and Mat\'ern. The practical interest
to information theory comes from the explicit connection that we also establish
between this problem and the estimation of error exponents in Shannon's
additive noise channel with power constraints on the codewords
- …