12,536 research outputs found
On the existence of accessible paths in various models of fitness landscapes
We present rigorous mathematical analyses of a number of well-known
mathematical models for genetic mutations. In these models, the genome is
represented by a vertex of the -dimensional binary hypercube, for some ,
a mutation involves the flipping of a single bit, and each vertex is assigned a
real number, called its fitness, according to some rules. Our main concern is
with the issue of existence of (selectively) accessible paths; that is,
monotonic paths in the hypercube along which fitness is always increasing. Our
main results resolve open questions about three such models, which in the
biophysics literature are known as house of cards (HoC), constrained house of
cards (CHoC) and rough Mount Fuji (RMF). We prove that the probability of there
being at least one accessible path from the all-zeroes node to
the all-ones node tends respectively to 0, 1 and 1, as
tends to infinity. A crucial idea is the introduction of a generalization of
the CHoC model, in which the fitness of is set to some
. We prove that there is a very sharp threshold at
for the existence of accessible paths from to . As a corollary we prove significant concentration,
for below the threshold, of the number of accessible paths about the
expected value (the precise statement is technical; see Corollary 1.4). In the
case of RMF, we prove that the probability of accessible paths from to existing tends to provided the drift parameter
satisfies , and for any fitness
distribution which is continuous on its support and whose support is connected.Comment: Published in at http://dx.doi.org/10.1214/13-AAP949 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Permutations destroying arithmetic progressions in finite cyclic groups
A permutation \pi of an abelian group G is said to destroy arithmetic
progressions (APs) if, whenever (a,b,c) is a non-trivial 3-term AP in G, that
is c-b=b-a and a,b,c are not all equal, then (\pi(a),\pi(b),\pi(c)) is not an
AP. In a paper from 2004, the first author conjectured that such a permutation
exists of Z/nZ, for all n except 2,3,5 and 7. Here we prove, as a special case
of a more general result, that such a permutation exists for all n >= n_0, for
some explcitly constructed number n_0 \approx 1.4 x 10^{14}. We also construct
such a permutation of Z/pZ for all primes p > 3 such that p = 3 (mod 8).Comment: 11 pages, no figure
How well do we know the age and mass distributions of the star cluster system in the Large Magellanic Cloud?
[ABRIDGED] The LMC star cluster system offers the unique opportunity to
independently check the accuracy of age and mass determinations based on a
number of complementary techniques, including isochrone analysis. Using our
sophisticated tool for star cluster analysis based on broad-band spectral
energy distributions (SEDs), we reanalyse the Hunter et al. (2003) LMC cluster
photometry. Our main aim is to set the tightest limits yet on the accuracy of
ABSOLUTE age determinations based on broad-band SEDs, and therefore on the
usefulness of such an approach. Our broad-band SED fits yield reliable ages,
with statistical absolute uncertainties within Delta[log(Age/yr)] = 0.4
overall. The systematic differences we find with respect to previous age
determinations are caused by conversions of the observational photometry to a
different filter system. The LMC's cluster formation rate (CFR) has been
roughly constant outside of the well-known age gap between ~3 and 13 Gyr, when
the CFR was a factor of ~5 lower. We derive the characteristic cluster
disruption time-scale, log(t_4^dis/yr) = 9.9 +- 0.1, where t_dis = t_4^dis
(M_cl/10^4 Msun)^0.62. This long characteristic disruption time-scale implies
that we are observing the INITIAL cluster mass function (CMF). We conclude that
the youngest mass and luminosity-limited LMC cluster subsets show shallower
slopes than the slope of alpha = -2 expected (at least below masses of a few x
10^3 Msun), which is contrary to dynamical expectations. This may imply that
the initial CMF slope of the LMC cluster system as a whole is NOT well
represented by a power-law, although we cannot disentangle the unbound from the
bound clusters at the youngest ages.Comment: 14 pages, 8 figures, resubmitted to MNRAS after responding to referee
repor
Income support systems, labour supply incentives and employment â some cross-country evidence
This paper summarizes a set of expert reports commissioned by the IFAU. The expert reports cover Estonia, Germany, Italy, the Netherlands, Sweden, and the United Kingdom. These countries represent range of welfare states, both in terms of scope and design. And in each country there are interesting experiences from which other countries may learn. The overall objective is to identify policy tools that help generate sustained increases in employment in the long run. Therefore, we focus on policies that improve the incentives for labour force participation and reduce the barriers to participation.Labour force participation; employment; income support; long-run sustainability
The "No Justice in the Universe" phenomenon: why honesty of effort may not be rewarded in tournaments
In 2000 Allen Schwenk, using a well-known mathematical model of matchplay
tournaments in which the probability of one player beating another in a single
match is fixed for each pair of players, showed that the classical
single-elimination, seeded format can be "unfair" in the sense that situations
can arise where an indisputibly better (and thus higher seeded) player may have
a smaller probability of winning the tournament than a worse one. This in turn
implies that, if the players are able to influence their seeding in some
preliminary competition, situations can arise where it is in a player's
interest to behave "dishonestly", by deliberately trying to lose a match. This
motivated us to ask whether it is possible for a tournament to be both honest,
meaning that it is impossible for a situation to arise where a rational player
throws a match, and "symmetric" - meaning basically that the rules treat
everyone the same - yet unfair, in the sense that an objectively better player
has a smaller probability of winning than a worse one. After rigorously
defining our terms, our main result is that such tournaments exist and we
construct explicit examples for any number n >= 3 of players. For n=3, we show
(Theorem 3.6) that the collection of win-probability vectors for such
tournaments form a 5-vertex convex polygon in R^3, minus some boundary points.
We conjecture a similar result for any n >= 4 and prove some partial results
towards it.Comment: 26 pages, 2 figure
A Unified Analysis of Stochastic Optimization Methods Using Jump System Theory and Quadratic Constraints
We develop a simple routine unifying the analysis of several important
recently-developed stochastic optimization methods including SAGA, Finito, and
stochastic dual coordinate ascent (SDCA). First, we show an intrinsic
connection between stochastic optimization methods and dynamic jump systems,
and propose a general jump system model for stochastic optimization methods.
Our proposed model recovers SAGA, SDCA, Finito, and SAG as special cases. Then
we combine jump system theory with several simple quadratic inequalities to
derive sufficient conditions for convergence rate certifications of the
proposed jump system model under various assumptions (with or without
individual convexity, etc). The derived conditions are linear matrix
inequalities (LMIs) whose sizes roughly scale with the size of the training
set. We make use of the symmetry in the stochastic optimization methods and
reduce these LMIs to some equivalent small LMIs whose sizes are at most 3 by 3.
We solve these small LMIs to provide analytical proofs of new convergence rates
for SAGA, Finito and SDCA (with or without individual convexity). We also
explain why our proposed LMI fails in analyzing SAG. We reveal a key difference
between SAG and other methods, and briefly discuss how to extend our LMI
analysis for SAG. An advantage of our approach is that the proposed analysis
can be automated for a large class of stochastic methods under various
assumptions (with or without individual convexity, etc).Comment: To Appear in Proceedings of the Annual Conference on Learning Theory
(COLT) 201
A variant of the multi-agent rendezvous problem
The classical multi-agent rendezvous problem asks for a deterministic
algorithm by which points scattered in a plane can move about at constant
speed and merge at a single point, assuming each point can use only the
locations of the others it sees when making decisions and that the visibility
graph as a whole is connected. In time complexity analyses of such algorithms,
only the number of rounds of computation required are usually considered, not
the amount of computation done per round. In this paper, we consider
points distributed independently and uniformly at random
in a disc of radius and, assuming each point can not only see but also, in
principle, communicate with others within unit distance, seek a randomised
merging algorithm which asymptotically almost surely (a.a.s.) runs in time
O(n), in other words in time linear in the radius of the disc rather than in
the number of points. Under a precise set of assumptions concerning the
communication capabilities of neighboring points, we describe an algorithm
which a.a.s. runs in time O(n) provided the number of points is .
Several questions are posed for future work.Comment: 18 pages, 3 figures. None of the authors has any previous experience
in this area of research (multi-agent systems), hence we welcome any feedback
from specialist
The Hegselmann-Krause dynamics on the circle converge
We consider the Hegselmann-Krause dynamics on a one-dimensional torus and
provide the first proof of convergence of this system. The proof requires only
fairly minor modifications of existing methods for proving convergence in
Euclidean space.Comment: 9 pages, 2 figures. Version 2: A small error in the proof of Theorem
1.1 is corrected and an acknowledgement added. Bibliography update
N-body simulations of star clusters
Two aspects of our recent N-body studies of star clusters are presented: (1)
What impact does mass segregation and selective mass loss have on integrated
photometry? (2) How well compare results from N-body simulations using NBODY4
and STARLAB/KIRA?Comment: 2 pages, 1 figure with 4 panels (in colour, not well visible in
black-and-white; figures screwed in PDF version, ok in postscript; to see
further details get the paper source). Conference proceedings for IAUS246
'Dynamical Evolution of Dense Stellar Systems', ed. E. Vesperini (Chief
Editor), M. Giersz, A. Sills, Capri, Sept. 2007; v2: references correcte
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