Search results for "Centroid"
showing 10 items of 37 documents
A Vector Approach to Euler's Line of a Triangle
1992
Among the many interesting properties that triangles possess there is one that quickly attracts our curiosity and stays easily in our mind: The centroid, circumcentre and orthocentre all lie in a common line (Euler's Line). An elementary simple proof can be obtained using metric and affine properties of the points involved, [1]. Our aim here is to illustrate a proof using vectors. We identify points in the plane with their position vectors. It is easy to see that the centroid G of the triangle ABC is given by the identity
Non-Contact Measurement of River Surface Velocity and Discharge Estimation with a Low-Cost Doppler Radar Sensor
2020
River discharge is an important variable to measure in order to predict droughts and flood occurrences. Once the cross-sectional geometry of the river is known, discharge can be inferred from water level and surface flow velocity measurements. Since river discharges are of particular interest during extreme weather events, when river sites cannot be safely accessed, noncontact sensing technologies are particularly appealing. To this purpose, this work proposes a prototype of a low-cost continuous wave (CW) Doppler radar sensor, which is able to monitor the surface flow velocity of rivers. The prototype is tested at two gauged sites in central Italy, along the Tiber River. The surface flow v…
Distributed and proximity-constrained C-means for discrete coverage control
2018
In this paper we present a novel distributed coverage control framework for a network of mobile agents, in charge of covering a finite set of points of interest (PoI), such as people in danger, geographically dispersed equipment or environmental landmarks. The proposed algorithm is inspired by C-Means, an unsupervised learning algorithm originally proposed for non-exclusive clustering and for identification of cluster centroids from a set of observations. To cope with the agents' limited sensing range and avoid infeasible coverage solutions, traditional C-Means needs to be enhanced with proximity constraints, ensuring that each agent takes into account only neighboring PoIs. The proposed co…
Adaptive learning of compressible strings
2020
Suppose an oracle knows a string $S$ that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is $s$ a substring of $S$?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm needs to ask the oracle $\sigma n/4 -O(n)$ queries in order to be able to reconstruct the hidden string, where $\sigma$ is the size of the alphabet of $S$ and $n$ its length, and gave an algorithm that spends $(\sigma-1)n+O(\sigma \sqrt{n})$ queries to reconstruct $S$. The main contribution of our paper is to improve the above upper-bound in the context where the string is compressible. We first present a universal algorithm that, given a (computable) compre…
Statistical power of disease cluster and clustering tests for rare diseases: A simulation study of point sources
2012
Abstract Two recent epidemiological studies on clustering of childhood leukemia showed different results on the statistical power of disease cluster and clustering tests, possibly an effect of spatial data aggregation. Eight different leukemia cluster scenarios were simulated using individual addresses of all 1,009,332 children living in Denmark in 2006. For each scenario, a number of point sources were defined with an increased risk ratio at centroid, decreasing linearly to 1.0 at the edge; aggregation levels were administrative units of Danish municipalities and squares of 5, 12.5 and 25 km 2 . Six statistical methods were compared. Generally, statistical power decreased with increasing s…
Weakly supervised alignment of multisensor images
2015
Manifold alignment has become very popular in recent literature. Aligning data distributions prior to product generation is an appealing strategy, since it allows to provide data spaces that are more similar to each other, regardless of the subsequent use of the transformed data. We propose a methodology that finds a common representation among data spaces from different sensors using geographic image correspondences, or semantic ties. To cope with the strong deformations between the data spaces considered, we propose to add nonlineari-ties by expanding the input space with Gaussian Radial Basis Function (RBF) features with respect to the centroids of a partitioning of the data. Such featur…
Non-parametric spectrum cartography using adaptive radial basis functions
2017
This paper presents a framework for spectrum cartography based on the use of adaptive Gaussian radial basis functions (RBF) centered around a specific number of centroid locations, which are determined, jointly with the other RBF parameters, by the available measurement values at given sensor locations in a specific geographical area. The spectrum map is constructed non-parametrically as no prior knowledge about the transmitters is assumed. The received signal power at each location (over a given bandwidth and time period) is estimated as a weighted contribution from different RBF, in such a way that the both RBF parameters and the weights are jointly optimized using an alternating minimiza…
A time-of-flight correction procedure for fast-timing data of recoils with varying implantation positions at a spectrometer focal plane
2019
Abstract Fast-timing measurements at the focal plane of a separator can suffer from poor timing resolution. This is due to the variations in time-of-flight (ToF) for photons travelling to a given detector, which arise from the changes in the implantation positions of the recoil nuclei emitting the γ rays of interest. In order to minimise these effects on timing measurements, a procedure is presented that improves fast-timing data by performing ToF corrections on an event-by-event basis. This method was used to correct data collected with an array of eight LaBr 3 detectors, which detected γ rays from spatially distributed 138Gd recoil-implants at the focal plane of the Recoil-Ion-Transport-U…
Analyzing and organizing the sonic space of vocal imitations
2015
The sonic space that can be spanned with the voice is vast and complex and, therefore, it is difficult to organize and explore. In order to devise tools that facilitate sound design by vocal sketching we attempt at organizing a database of short excerpts of vocal imitations. By clustering the sound samples on a space whose dimensionality has been reduced to the two principal components, it is experimentally checked how meaningful the resulting clusters are for humans. Eventually, a representative of each cluster, chosen to be close to its centroid, may serve as a landmark in the exploration of the sound space, and vocal imitations may serve as proxies for synthetic sounds.
Maximum likelihood positioning for gamma-ray imaging detectors with depth of interaction measurement
2009
Abstract The center of gravity algorithm leads to strong artifacts for gamma-ray imaging detectors that are based on monolithic scintillation crystals and position sensitive photo-detectors. This is a consequence of using the centroids as position estimates. The fact that charge division circuits can also be used to compute the standard deviation of the scintillation light distribution opens a way out of this drawback. We studied the feasibility of maximum likelihood estimation for computing the true gamma-ray photo-conversion position from the centroids and the standard deviation of the light distribution. The method was evaluated on a test detector that consists of the position sensitive …