322 research outputs found
Hold your horses : temporal multiplexity and conflict moderation in the “Palio di Siena” (1743-2010)
The paper elaborates the concept of temporal multiplexity, defined as the overlaying of ties of different duration, such as transient employment and enduring organizational ties. This concept is instrumental in resolving long-standing challenges in network research, such as capturing the interplay between different levels of analysis or time horizons. This is made possible by longitudinal network and mobility data (1743–2010) from the Palio di Siena—the famous horse race in Siena, Italy. The outcome of interest is Palio-related collective violence. The analysis shows that relationally loaded organizational ties of rivalry or friendship increase the likelihood of incidents, whereas mobility along the same lines reduces it. The results support sociological arguments that symmetrical social space of friendship or rivalry is conducive to conflict. Mobility is a factor of moderation—by connecting employers within the actor and transferring relational content between them, it creates misalignment between the assumption of a role and fulfillment of its expectations. Mobility relaxes the relational constraints of jockeys, reducing their compliance with bellicose demands. The uncertainty resulting from mobility may have a collective benefit that is ignored by employers: the moderation of conflict
Packing of concave polyhedra with continuous rotations using nonlinear optimisation
We study the problem of packing a given collection of arbitrary, in general concave, polyhedra into a cuboid of minimal volume. Continuous rotations and translations of polyhedra are allowed. In addition, minimal allowable distances between polyhedra are taken into account. We derive an exact mathematical model using adjusted radical free quasi phi-functions for concave polyhedra to describe non-overlapping and distance constraints. The model is a nonlinear programming formulation. We develop an efficient solution algorithm, which employs a fast starting point algorithm and a new compaction procedure. The procedure reduces our problem to a sequence of nonlinear programming subproblems of considerably smaller dimension and a smaller number of nonlinear inequalities. The benefit of this approach is borne out by the computational results, which include a comparison with previously published instances and new instances
Optimal clustering of a pair of irregular objects
Cutting and packing problems arise in many fields of applications and theory. When dealing with irregular objects, an important subproblem is the identification of the optimal clustering of two objects. Within this paper we consider a container (rectangle, circle, convex polygon) of variable sizes and two irregular objects bounded by circular arcs and/or line segments, that can be continuously translated and rotated. In addition minimal allowable distances between objects and between each object and the frontier of a container, may be imposed. The objects should be arranged within a container such that a given objective will reach its minimal value. We consider a polynomial function as the objective, which depends on the variable parameters associated with the objects and the container. The paper presents a universal mathematical model and a solution strategy which are based on the concept of phi-functions and provide new benchmark instances of finding the containing region that has either minimal area, perimeter or homothetic coefficient of a given container, as well as finding the convex polygonal hull (or its approximation) of a pair of objects
Mark correlations: relating physical properties to spatial distributions
Mark correlations provide a systematic approach to look at objects both
distributed in space and bearing intrinsic information, for instance on
physical properties. The interplay of the objects' properties (marks) with the
spatial clustering is of vivid interest for many applications; are, e.g.,
galaxies with high luminosities more strongly clustered than dim ones? Do
neighbored pores in a sandstone have similar sizes? How does the shape of
impact craters on a planet depend on the geological surface properties? In this
article, we give an introduction into the appropriate mathematical framework to
deal with such questions, i.e. the theory of marked point processes. After
having clarified the notion of segregation effects, we define universal test
quantities applicable to realizations of a marked point processes. We show
their power using concrete data sets in analyzing the luminosity-dependence of
the galaxy clustering, the alignment of dark matter halos in gravitational
-body simulations, the morphology- and diameter-dependence of the Martian
crater distribution and the size correlations of pores in sandstone. In order
to understand our data in more detail, we discuss the Boolean depletion model,
the random field model and the Cox random field model. The first model
describes depletion effects in the distribution of Martian craters and pores in
sandstone, whereas the last one accounts at least qualitatively for the
observed luminosity-dependence of the galaxy clustering.Comment: 35 pages, 12 figures. to be published in Lecture Notes of Physics,
second Wuppertal conference "Spatial statistics and statistical physics
Modeling Heterogeneous Materials via Two-Point Correlation Functions: I. Basic Principles
Heterogeneous materials abound in nature and man-made situations. Examples
include porous media, biological materials, and composite materials. Diverse
and interesting properties exhibited by these materials result from their
complex microstructures, which also make it difficult to model the materials.
In this first part of a series of two papers, we collect the known necessary
conditions on the standard two-point correlation function S2(r) and formulate a
new conjecture. In particular, we argue that given a complete two-point
correlation function space, S2(r) of any statistically homogeneous material can
be expressed through a map on a selected set of bases of the function space. We
provide new examples of realizable two-point correlation functions and suggest
a set of analytical basis functions. Moreover, we devise an efficient and
isotropy- preserving construction algorithm, namely, the Lattice-Point
algorithm to generate realizations of materials from their two- point
correlation functions based on the Yeong-Torquato technique. Subsequent
analysis can be performed on the generated images to obtain desired macroscopic
properties. These developments are integrated here into a general scheme that
enables one to model and categorize heterogeneous materials via two-point
correlation functions.Comment: 37 pages, 26 figure
Stochastic reconstruction of sandstones
A simulated annealing algorithm is employed to generate a stochastic model
for a Berea and a Fontainebleau sandstone with prescribed two-point probability
function, lineal path function, and ``pore size'' distribution function,
respectively. We find that the temperature decrease of the annealing has to be
rather quick to yield isotropic and percolating configurations. A comparison of
simple morphological quantities indicates good agreement between the
reconstructions and the original sandstones. Also, the mean survival time of a
random walker in the pore space is reproduced with good accuracy. However, a
more detailed investigation by means of local porosity theory shows that there
may be significant differences of the geometrical connectivity between the
reconstructed and the experimental samples.Comment: 12 pages, 5 figure
Optimal spatial transportation networks where link-costs are sublinear in link-capacity
Consider designing a transportation network on vertices in the plane,
with traffic demand uniform over all source-destination pairs. Suppose the cost
of a link of length and capacity scales as for fixed
. Under appropriate standardization, the cost of the minimum cost
Gilbert network grows essentially as , where on and on . This quantity is an upper bound in
the worst case (of vertex positions), and a lower bound under mild regularity
assumptions. Essentially the same bounds hold if we constrain the network to be
efficient in the sense that average route-length is only times
average straight line length. The transition at corresponds to
the dominant cost contribution changing from short links to long links. The
upper bounds arise in the following type of hierarchical networks, which are
therefore optimal in an order of magnitude sense. On the large scale, use a
sparse Poisson line process to provide long-range links. On the medium scale,
use hierachical routing on the square lattice. On the small scale, link
vertices directly to medium-grid points. We discuss one of many possible
variant models, in which links also have a designed maximum speed and the
cost becomes .Comment: 13 page
Sampling-based Algorithms for Optimal Motion Planning
During the last decade, sampling-based path planning algorithms, such as
Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have
been shown to work well in practice and possess theoretical guarantees such as
probabilistic completeness. However, little effort has been devoted to the
formal analysis of the quality of the solution returned by such algorithms,
e.g., as a function of the number of samples. The purpose of this paper is to
fill this gap, by rigorously analyzing the asymptotic behavior of the cost of
the solution returned by stochastic sampling-based algorithms as the number of
samples increases. A number of negative results are provided, characterizing
existing algorithms, e.g., showing that, under mild technical conditions, the
cost of the solution returned by broadly used sampling-based algorithms
converges almost surely to a non-optimal value. The main contribution of the
paper is the introduction of new algorithms, namely, PRM* and RRT*, which are
provably asymptotically optimal, i.e., such that the cost of the returned
solution converges almost surely to the optimum. Moreover, it is shown that the
computational complexity of the new algorithms is within a constant factor of
that of their probabilistically complete (but not asymptotically optimal)
counterparts. The analysis in this paper hinges on novel connections between
stochastic sampling-based path planning algorithms and the theory of random
geometric graphs.Comment: 76 pages, 26 figures, to appear in International Journal of Robotics
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