61,266 research outputs found
High accuracy semidefinite programming bounds for kissing numbers
The kissing number in n-dimensional Euclidean space is the maximal number of
non-overlapping unit spheres which simultaneously can touch a central unit
sphere. Bachoc and Vallentin developed a method to find upper bounds for the
kissing number based on semidefinite programming. This paper is a report on
high accuracy calculations of these upper bounds for n <= 24. The bound for n =
16 implies a conjecture of Conway and Sloane: There is no 16-dimensional
periodic point set with average theta series 1 + 7680q^3 + 4320q^4 + 276480q^5
+ 61440q^6 + ...Comment: 7 pages (v3) new numerical result in Section 4, to appear in
Experiment. Mat
Experimental study of energy-minimizing point configurations on spheres
In this paper we report on massive computer experiments aimed at finding
spherical point configurations that minimize potential energy. We present
experimental evidence for two new universal optima (consisting of 40 points in
10 dimensions and 64 points in 14 dimensions), as well as evidence that there
are no others with at most 64 points. We also describe several other new
polytopes, and we present new geometrical descriptions of some of the known
universal optima.Comment: 41 pages, 12 figures, to appear in Experimental Mathematic
Three-point bounds for energy minimization
Three-point semidefinite programming bounds are one of the most powerful
known tools for bounding the size of spherical codes. In this paper, we use
them to prove lower bounds for the potential energy of particles interacting
via a pair potential function. We show that our bounds are sharp for seven
points in RP^2. Specifically, we prove that the seven lines connecting opposite
vertices of a cube and of its dual octahedron are universally optimal. (In
other words, among all configurations of seven lines through the origin, this
one minimizes energy for all potential functions that are completely monotonic
functions of squared chordal distance.) This configuration is the only known
universal optimum that is not distance regular, and the last remaining
universal optimum in RP^2. We also give a new derivation of semidefinite
programming bounds and present several surprising conjectures about them.Comment: 30 page
Probabilistic modal {\mu}-calculus with independent product
The probabilistic modal {\mu}-calculus is a fixed-point logic designed for
expressing properties of probabilistic labeled transition systems (PLTS's). Two
equivalent semantics have been studied for this logic, both assigning to each
state a value in the interval [0,1] representing the probability that the
property expressed by the formula holds at the state. One semantics is
denotational and the other is a game semantics, specified in terms of
two-player stochastic parity games. A shortcoming of the probabilistic modal
{\mu}-calculus is the lack of expressiveness required to encode other important
temporal logics for PLTS's such as Probabilistic Computation Tree Logic (PCTL).
To address this limitation we extend the logic with a new pair of operators:
independent product and coproduct. The resulting logic, called probabilistic
modal {\mu}-calculus with independent product, can encode many properties of
interest and subsumes the qualitative fragment of PCTL. The main contribution
of this paper is the definition of an appropriate game semantics for this
extended probabilistic {\mu}-calculus. This relies on the definition of a new
class of games which generalize standard two-player stochastic (parity) games
by allowing a play to be split into concurrent subplays, each continuing their
evolution independently. Our main technical result is the equivalence of the
two semantics. The proof is carried out in ZFC set theory extended with
Martin's Axiom at an uncountable cardinal
Facilitating the driver detection of road surface type by selective manipulation of the steering-wheel acceleration signal
Copyright @ 2012 by Institution of Mechanical Engineers.Previous research has investigated the possibility of facilitating the driver detection of road surface type by means of selective manipulation of the steering-wheel acceleration signal. In previous studies a selective increase in acceleration amplitude has been found to facilitate road-surface-type detection, as has selective manipulation of the individual transient events which are present in the signal. The previous research results have been collected into a first guideline for the optimization of the steering-wheel acceleration signal, and the guideline has been tested in the current study. The test stimuli used in the current study were ten steering-wheel acceleration-time histories which were selected from an extensive database of road test measurements performed by the research group. The time histories, which were all from midsized European automobiles and European roads, were selected such that the widest possible operating envelope could be achieved in terms of the r.m.s. value of the steering acceleration, the kurtosis, the power spectral density function, and the number of transient events present in the signal. The time histories were manipulated by means of the mildly non-stationary mission synthesis algorithm in order to increase, by a factor of 2, both the number and the size of the transient events contained within the frequency interval from 20 Hz to 60Hz. The ensemble, composed of both the unmanipulated and the manipulated time histories, was used to perform a laboratory-based detection task with 15 participants, who were presented the individual stimuli in random order. The participants were asked to state, by answering 'yes' or 'no', whether each stimulus was considered to be from the road surface that was displayed in front of them by means of a large photograph on a board. The results suggest that the selectively manipulated steering-wheel acceleration stimuli produced improved detection for eight of the ten road surface types which were tested, with a maximum improvement of 14 per cent in the case of the broken road surface. The selective manipulation did lead, however, to some degradation in detection for the motorway road stimulus and for the noise road stimulus, thus suggesting that the current guideline is not universally optimal for all road surfaces
New multicategory boosting algorithms based on multicategory Fisher-consistent losses
Fisher-consistent loss functions play a fundamental role in the construction
of successful binary margin-based classifiers. In this paper we establish the
Fisher-consistency condition for multicategory classification problems. Our
approach uses the margin vector concept which can be regarded as a
multicategory generalization of the binary margin. We characterize a wide class
of smooth convex loss functions that are Fisher-consistent for multicategory
classification. We then consider using the margin-vector-based loss functions
to derive multicategory boosting algorithms. In particular, we derive two new
multicategory boosting algorithms by using the exponential and logistic
regression losses.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS198 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- …