158,105 research outputs found
2-bit Flip Mutation Elementary Fitness Landscapes
Genetic Programming parity is not elementary.
GP parity cannot be represented as the sum of a small number
of elementary landscapes.
Statistics, including fitness distance correlation,
of Parity\u27s fitness landscape are calculated.
Using Walsh analysis the
eigen values and eigenvectors of the Laplacian of the two bit flip
fitness landscape are given
and a ruggedness measure for elementary landscapes is proposed.
An elementary needle in a haystack (NIH) landscape is given
Energy landscapes, ideal glasses, and their equation of state
Using the inherent structure formalism originally proposed by Stillinger and
Weber [Phys. Rev. A 25, 978 (1982)], we generalize the thermodynamics of an
energy landscape that has an ideal glass transition and derive the consequences
for its equation of state. In doing so, we identify a separation of
configurational and vibrational contributions to the pressure that corresponds
with simulation studies performed in the inherent structure formalism. We
develop an elementary model of landscapes appropriate to simple liquids which
is based on the scaling properties of the soft-sphere potential complemented
with a mean-field attraction. The resulting equation of state provides an
accurate representation of simulation data for the Lennard-Jones fluid,
suggesting the usefulness of a landscape-based formulation of supercooled
liquid thermodynamics. Finally, we consider the implications of both the
general theory and the model with respect to the so-called Sastry density and
the ideal glass transition. Our analysis shows that a quantitative connection
can be made between properties of the landscape and a simulation-determined
Sastry density, and it emphasizes the distinction between an ideal glass
transition and a Kauzmann equal-entropy condition.Comment: 11 pages, 3 figure
Pairs of SAT Assignment in Random Boolean Formulae
We investigate geometrical properties of the random K-satisfiability problem
using the notion of x-satisfiability: a formula is x-satisfiable if there exist
two SAT assignments differing in Nx variables. We show the existence of a sharp
threshold for this property as a function of the clause density. For large
enough K, we prove that there exists a region of clause density, below the
satisfiability threshold, where the landscape of Hamming distances between SAT
assignments experiences a gap: pairs of SAT-assignments exist at small x, and
around x=1/2, but they donot exist at intermediate values of x. This result is
consistent with the clustering scenario which is at the heart of the recent
heuristic analysis of satisfiability using statistical physics analysis (the
cavity method), and its algorithmic counterpart (the survey propagation
algorithm). The method uses elementary probabilistic arguments (first and
second moment methods), and might be useful in other problems of computational
and physical interest where similar phenomena appear
Problem Understanding through Landscape Theory
In order to understand the structure of a problem we need to measure some features of the problem. Some examples of measures suggested in the past are autocorrelation and fitness-distance correlation. Landscape theory, developed in the last years in the field of combinatorial optimization, provides mathematical expressions to efficiently compute statistics on optimization problems. In this paper we discuss how can we use optimización combinatoria in the context of problem understanding and present two software tools that can be used to efficiently compute the mentioned measures.Ministerio de EconomÃa y Competitividad (TIN2011-28194
Exact computation of the expectation curves of the bit-flip mutation using landscapes theory
Chicano, F., & Alba E. (2011). Exact computation of the expectation curves of the bit-flip mutation using landscapes theory. Proceedings of 13th Annual Genetic and Evolutionary Computation Conference, Dublin, Ireland, July 12-16, 2011. pp. 2027–2034.Bit-flip mutation is a common operation when a genetic algorithm is applied to solve a problem with binary representation. We use in this paper some results of landscapes theory and Krawtchouk polynomials to exactly compute the expected value of the fitness of a mutated solution. We prove that this expectation is a polynomial in p, the probability of flipping a single bit. We analyze these polynomials and propose some applications of the obtained theoretical results.Universidad de Málaga. Campus de Excelencia Internacional AndalucÃa Tech. This research has been partially funded by the Spanish Ministry of Science and Innovation and FEDER under contract TIN2008-06491-C04-01 (the M∗ project) and the Andalusian Government under contract P07-TIC-03044 (DIRICOM project)
Two Notions of Naturalness
My aim in this paper is twofold: (i) to distinguish two notions of
naturalness employed in BSM physics and (ii) to argue that recognizing this
distinction has methodological consequences. One notion of naturalness is an
"autonomy of scales" requirement: it prohibits sensitive dependence of an
effective field theory's low-energy observables on precise specification of the
theory's description of cutoff-scale physics. I will argue that considerations
from the general structure of effective field theory provide justification for
the role this notion of naturalness has played in BSM model construction. A
second, distinct notion construes naturalness as a statistical principle
requiring that the values of the parameters in an effective field theory be
"likely" given some appropriately chosen measure on some appropriately
circumscribed space of models. I argue that these two notions are historically
and conceptually related but are motivated by distinct theoretical
considerations and admit of distinct kinds of solution.Comment: 34 pages, 1 figur
The Landscape of US Elementary Mathematics Teacher Education: Course Requirements for Mathematics Content and Methods
The adequate preparation of future teachers of mathematics is critical, requiring sufficient opportunities to develop both pedagogical skill and content knowledge. Yet, despite new recommendations for mathematics teacher preparation, we know little about the landscape of course-based learning opportunities in US elementary teacher education programs. To what extent do US elementary teacher education programs meet the Standards for Preparing Teachers of Mathematics outlined by the Association of Mathematics Teacher Educators (AMTE) for mathematics content and methods courses? Based on an a priori power analysis, we gathered a random sample of 291 higher education institutions. Within these institutions, we analyzed 736 programs, including Bachelor’s, Master’s, and Credential programs. We found that overwhelmingly US elementary teacher education programs do not meet the aspirations outlined in the AMTE standards, with Master’s and Credential programs and those covering all elementary grades particularly falling short. Potential explanations for these challenges and implications for teacher education program design are discussed
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