981 research outputs found
Tensor Galileons and Gravity
The particular structure of Galileon interactions allows for
higher-derivative terms while retaining second order field equations for scalar
fields and Abelian -forms. In this work we introduce an index-free
formulation of these interactions in terms of two sets of Grassmannian
variables. We employ this to construct Galileon interactions for mixed-symmetry
tensor fields and coupled systems thereof. We argue that these tensors are the
natural generalization of scalars with Galileon symmetry, similar to -forms
and scalars with a shift-symmetry. The simplest case corresponds to linearised
gravity with Lovelock invariants, relating the Galileon symmetry to
diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to
gravity, and demonstrate in an explicit example that the inclusion of
appropriate counterterms retains second order field equations.Comment: 24 pages; v2: references added, minor clarification
Towards expert-inspired automatic criterion to cut a dendrogram for real-industrial applications
Hierarchical clustering is one of the most preferred choices to understand the underlying structure of a dataset and defining typologies, with multiple applications in real life. Among the existing clustering algorithms, the hierarchical family is one of the most popular, as it permits to understand the inner structure of the dataset and find the number of clusters as an output, unlike popular methods, like k-means. One can adjust the granularity of final clustering to the goals of the analysis themselves. The number of clusters in a hierarchical method relies on the analysis of the resulting dendrogram itself. Experts have criteria to visually inspect the dendrogram and determine the number of clusters. Finding automatic criteria to imitate experts in this task is still an open problem. But, dependence on the expert to cut the tree represents a limitation in real applications like the fields industry 4.0 and
additive manufacturing. This paper analyses several cluster validity indexes in the context of determining the suitable number of clusters in hierarchical clustering. A new Cluster Validity Index (CVI) is proposed such that it properly catches the implicit criteria used by experts when analyzing dendrograms. The proposal has been applied on a range of datasets and validated against experts ground-truth overcoming the results obtained by the State of the Art and also significantly reduces the computational cost .Peer ReviewedPostprint (published version
Construction of Evidently Positive Series and An Alternative Construction for a Family of Partition Generating Functions due to Kanade and Russell
We give an alternative construction for a family of partition generating
functions due to Kanade and Russell. In our alternative construction, we use
ordinary partitions instead of jagged partitions. We also present new
generating functions which are evidently positive series for partitions due to
Kanade and Russell. To obtain those generating functions, we first construct an
evidently positive series for a key infinite product. In that construction, a
series of combinatorial moves is used to decompose an arbitrary partition into
a base partition together with some auxiliary partitions that bijectively
record the moves
Glossary
We present the analysis of the binary gravitational microlensing event
MOA-2015-BLG-020. The event has a fairly long timescale (about 63 days) and
thus the light curve deviates significantly from the lensing model that is
based on the rectilinear lens-source relative motion. This enables us to
measure the microlensing parallax through the annual parallax effect. The
microlensing parallax parameters constrained by the ground-based data are
confirmed by the Spitzer observations through the satellite parallax method. By
additionally measuring the angular Einstein radius from the analysis of the
resolved caustic crossing, the physical parameters of the lens are determined.
It is found that the binary lens is composed of two dwarf stars with masses
and in the
Galactic disk. Assuming the source star is at the same distance as the bulge
red clump stars, we find the lens is at a distance .
In the end, we provide a summary and short discussion of all published
microlensing events in which the annual parallax effect is confirmed by other
independent observations.Comment: 16 pages, 5 figure
Glossary
Modular necks were introduced in total hip arthroplasty (THA) to improve restoration of hip-geometry and reduce dislocation-rates. This presumed advantage was evaluated retrospectively for patients with arthritis in otherwise anatomically normal hips. Restoration of hip-geometry was assessed on preoperative and postoperative calibrated radiographs in 95 consecutive primary THAs with a modular neck design and compared with 95 match controlled THAs with a similar monoblock stem. No significant differences were seen in restoration of body moment arm, leg length and cupangle. Offset restoration revealed a borderline significant difference (P = 0.48) with higher values for the monoblock stem. In both groups 4 dislocations within one year were encountered. In this study modular necks did not reveal a clear benefit in restoring hip geometry and dislocation rate after straightforward THA
- …