118,287 research outputs found
A Criterion for Comparing Measurement Results and Determining Conformity with Specifications
In this paper a new criterion for comparing measurement results and determining conformity with specifications is proposed, which essentially is a strategy of estimating the empirical relationships of objects. Comparing with traditional methods given in GUM: 2008 and ISO 14253-1, this criterion improves the resolution of comparison by reducing the sizes of the coverage intervals to be compared. Interval order (a binary relation) is used for comparing the coverage intervals of the measurand and represents the empirical relations. The systematic effects of measurement are classified into two types: monotonic and non-monotonic effects, so that, without correcting the monotonic effects, a biased measurand can be specified to represent the empirical relations. Thereby the uncertainty components arising from the monotonic effects can be removed from the combined uncertainty. A strategy is given for determining the relationships among measurement results and specification limits. An example is given to demonstrate the application of the criterion
A criterion for comparing measurement results and determining conformity with specifications
In this paper a new criterion for comparing measurement results and determining conformity with specifications is proposed, which essentially is a strategy of estimating the empirical relationships of objects. Comparing with traditional methods given in GUM:2008 and ISO 14253-1, this criterion improves the resolution of comparison by reducing the sizes of the coverage intervals to be compared. Interval order (a binary relation) is used for comparing the coverage intervals of the measurand and represents the empirical relations. The systematic effects of measurement are classified into two types: monotonic and non-monotonic effects, so that, without correcting the monotonic effects, a biased measurand can be specified to represent the empirical relations. Thereby the uncertainty components arising from the monotonic effects can be removed from the combined uncertainty. A strategy is given for determining the relationships among measurement results and specification limits. An example is given to demonstrate the application of the criterion
Homoclinic Bifurcations for the Henon Map
Chaotic dynamics can be effectively studied by continuation from an
anti-integrable limit. We use this limit to assign global symbols to orbits and
use continuation from the limit to study their bifurcations. We find a bound on
the parameter range for which the Henon map exhibits a complete binary
horseshoe as well as a subshift of finite type. We classify homoclinic
bifurcations, and study those for the area preserving case in detail. Simple
forcing relations between homoclinic orbits are established. We show that a
symmetry of the map gives rise to constraints on certain sequences of
homoclinic bifurcations. Our numerical studies also identify the bifurcations
that bound intervals on which the topological entropy is apparently constant.Comment: To appear in PhysicaD: 43 Pages, 14 figure
Systematic investigation of the expected gravitational wave signal from supermassive black hole binaries in the pulsar timing band
In this letter we carry out the first systematic investigation of the
expected gravitational wave (GW) background generated by supermassive black
hole (SMBH) binaries in the nHz frequency band accessible to pulsar timing
arrays (PTAs). We take from the literature several estimates of the redshift
dependent galaxy mass function and of the fraction of close galaxy pairs to
derive a wide range of galaxy merger rates. We then exploit empirical black
hole-host relations to populate merging galaxies with SMBHs. The result of our
procedure is a collection of a large number of phenomenological SMBH binary
merger rates consistent with current observational constraints on the galaxy
assembly at z<1.5. For each merger rate we compute the associated GW signal,
eventually producing a large set of estimates of the nHz GW background that we
use to infer confidence intervals of its expected amplitude. When considering
the most recent SMBH-host relations, accounting for ultra-massive black holes
in brightest cluster galaxies, we find that the nominal interval of
the expected GW signal is only a factor of 3-to-10 below current PTA limits,
implying a non negligible chance of detection in the next few years.Comment: 6 pages, 3 figures, submitted to MNRAS lette
A mixed effects model for longitudinal relational and network data, with applications to international trade and conflict
The focus of this paper is an approach to the modeling of longitudinal social
network or relational data. Such data arise from measurements on pairs of
objects or actors made at regular temporal intervals, resulting in a social
network for each point in time. In this article we represent the network and
temporal dependencies with a random effects model, resulting in a stochastic
process defined by a set of stationary covariance matrices. Our approach builds
upon the social relations models of Warner, Kenny and Stoto [Journal of
Personality and Social Psychology 37 (1979) 1742--1757] and Gill and Swartz
[Canad. J. Statist. 29 (2001) 321--331] and allows for an intra- and
inter-temporal representation of network structures. We apply the methodology
to two longitudinal data sets: international trade (continuous response) and
militarized interstate disputes (binary response).Comment: Published in at http://dx.doi.org/10.1214/10-AOAS403 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Concepts for Decision Making under Severe Uncertainty with Partial Ordinal and Partial Cardinal Preferences
We introduce three different approaches for decision making under uncertainty if (I) there is only partial (both cardinally and ordinally scaled) information on an agent’s preferences and (II) the uncertainty about the states of nature is described by a credal set (or some other imprecise probabilistic model). Particularly, situation (I) is modeled by a pair of binary relations, one specifying the partial rank order of the alternatives and the other modeling partial information on the strength of preference. Our first approach relies on decision criteria constructing complete rankings of the available acts that are based on generalized expectation intervals. Subsequently, we introduce different concepts of global admissibility that construct partial orders between the available acts by comparing them all simultaneously. Finally, we define criteria induced by suitable binary relations on the set of acts and, therefore, can be understood as concepts of local admissibility. For certain criteria, we provide linear programming based algorithms for checking optimality/admissibility of acts. Additionally, the paper includes a discussion of a prototypical situation by means of a toy example
Two bijections on Tamari intervals
We use a recently introduced combinatorial object, the interval-poset, to
describe two bijections on intervals of the Tamari lattice. Both bijections
give a combinatorial proof of some previously known results. The first one is
an inner bijection between Tamari intervals that exchanges the initial rise and
lower contacts statistics. Those were introduced by Bousquet-M\'elou, Fusy, and
Pr\'eville-Ratelle who proved they were symmetrically distributed but had no
combinatorial explanation. The second bijection sends a Tamari interval to a
closed flow of an ordered forest. These combinatorial objects were studied by
Chapoton in the context of the Pre-Lie operad and the connection with the
Tamari order was still unclear.Comment: 12 pages, 10 figure
Counting smaller elements in the Tamari and m-Tamari lattices
We introduce new combinatorial objects, the interval- posets, that encode
intervals of the Tamari lattice. We then find a combinatorial interpretation of
the bilinear operator that appears in the functional equation of Tamari
intervals described by Chapoton. Thus, we retrieve this functional equation and
prove that the polynomial recursively computed from the bilinear operator on
each tree T counts the number of trees smaller than T in the Tamari order. Then
we show that a similar m + 1-linear operator is also used in the functionnal
equation of m-Tamari intervals. We explain how the m-Tamari lattices can be
interpreted in terms of m+1-ary trees or a certain class of binary trees. We
then use the interval-posets to recover the functional equation of m-Tamari
intervals and to prove a generalized formula that counts the number of elements
smaller than or equal to a given tree in the m-Tamari lattice.Comment: 46 pages + 3 pages of code appendix, 27 figures. Long version of
arXiv:1212.0751. To appear in Journal of Combinatorial Theory, Series
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