117 research outputs found
Solar Radiation Pressure Binning for the Geosynchronous Orbit
Orbital maintenance parameters for individual satellites or groups of satellites have traditionally been set by examining orbital parameters alone, such as through apogee and perigee height binning; this approach ignored the other factors that governed an individual satellite's susceptibility to non-conservative forces. In the atmospheric drag regime, this problem has been addressed by the introduction of the "energy dissipation rate," a quantity that represents the amount of energy being removed from the orbit; such an approach is able to consider both atmospheric density and satellite frontal area characteristics and thus serve as a mechanism for binning satellites of similar behavior. The geo-synchronous orbit (of broader definition than the geostationary orbit -- here taken to be from 1300 to 1800 minutes in orbital period) is not affected by drag; rather, its principal non-conservative force is that of solar radiation pressure -- the momentum imparted to the satellite by solar radiometric energy. While this perturbation is solved for as part of the orbit determination update, no binning or division scheme, analogous to the drag regime, has been developed for the geo-synchronous orbit. The present analysis has begun such an effort by examining the behavior of geosynchronous rocket bodies and non-stabilized payloads as a function of solar radiation pressure susceptibility. A preliminary examination of binning techniques used in the drag regime gives initial guidance regarding the criteria for useful bin divisions. Applying these criteria to the object type, solar radiation pressure, and resultant state vector accuracy for the analyzed dataset, a single division of "large" satellites into two bins for the purposes of setting related sensor tasking and orbit determination (OD) controls is suggested. When an accompanying analysis of high area-to-mass objects is complete, a full set of binning recommendations for the geosynchronous orbit will be available
Euler-Bessel and Euler-Fourier Transforms
We consider a topological integral transform of Bessel (concentric
isospectral sets) type and Fourier (hyperplane isospectral sets) type, using
the Euler characteristic as a measure. These transforms convert constructible
\zed-valued functions to continuous -valued functions over a vector
space. Core contributions include: the definition of the topological Bessel
transform; a relationship in terms of the logarithmic blowup of the topological
Fourier transform; and a novel Morse index formula for the transforms. We then
apply the theory to problems of target reconstruction from enumerative sensor
data, including localization and shape discrimination. This last application
utilizes an extension of spatially variant apodization (SVA) to mitigate
sidelobe phenomena
Discrete Morse functions for graph configuration spaces
We present an alternative application of discrete Morse theory for
two-particle graph configuration spaces. In contrast to previous constructions,
which are based on discrete Morse vector fields, our approach is through Morse
functions, which have a nice physical interpretation as two-body potentials
constructed from one-body potentials. We also give a brief introduction to
discrete Morse theory. Our motivation comes from the problem of quantum
statistics for particles on networks, for which generalized versions of anyon
statistics can appear.Comment: 26 page
Computational Topology Techniques for Characterizing Time-Series Data
Topological data analysis (TDA), while abstract, allows a characterization of
time-series data obtained from nonlinear and complex dynamical systems. Though
it is surprising that such an abstract measure of structure - counting pieces
and holes - could be useful for real-world data, TDA lets us compare different
systems, and even do membership testing or change-point detection. However, TDA
is computationally expensive and involves a number of free parameters. This
complexity can be obviated by coarse-graining, using a construct called the
witness complex. The parametric dependence gives rise to the concept of
persistent homology: how shape changes with scale. Its results allow us to
distinguish time-series data from different systems - e.g., the same note
played on different musical instruments.Comment: 12 pages, 6 Figures, 1 Table, The Sixteenth International Symposium
on Intelligent Data Analysis (IDA 2017
Persistent Homology Over Directed Acyclic Graphs
We define persistent homology groups over any set of spaces which have
inclusions defined so that the corresponding directed graph between the spaces
is acyclic, as well as along any subgraph of this directed graph. This method
simultaneously generalizes standard persistent homology, zigzag persistence and
multidimensional persistence to arbitrary directed acyclic graphs, and it also
allows the study of more general families of topological spaces or point-cloud
data. We give an algorithm to compute the persistent homology groups
simultaneously for all subgraphs which contain a single source and a single
sink in arithmetic operations, where is the number of vertices in
the graph. We then demonstrate as an application of these tools a method to
overlay two distinct filtrations of the same underlying space, which allows us
to detect the most significant barcodes using considerably fewer points than
standard persistence.Comment: Revised versio
Parallel Mapper
The construction of Mapper has emerged in the last decade as a powerful and
effective topological data analysis tool that approximates and generalizes
other topological summaries, such as the Reeb graph, the contour tree, split,
and joint trees. In this paper, we study the parallel analysis of the
construction of Mapper. We give a provably correct parallel algorithm to
execute Mapper on multiple processors and discuss the performance results that
compare our approach to a reference sequential Mapper implementation. We report
the performance experiments that demonstrate the efficiency of our method
The Iowa Homemaker vol.10, no.3
Iowa State “Mans” the Kitchen by Helen Melton, page 1
At Home in Nippon by Sarah Field, page 2
And Rush That Order, Please! by Bessie Hammer, page 3
Luncheon – Mile High by Mildred Ghrist Day, page 3
Gotta Job? by Julia Bourne, page 4
“P’s” and “Q’s” in China Selection by Ida M. Shilling, page 5
4-H Club by Helen Melton, page 6
State Association by Marcia E. Turner, page 8
Child Health May Day by Anafred Stephenson, page 10
Editorial, page 11
Alumnae News by Dorothy B. Anderson, page 1
Path homology and temporal networks
We present an algorithm to compute path homology for simple digraphs, and use
it to topologically analyze various small digraphs en route to an analysis of
complex temporal networks which exhibit such digraphs as underlying motifs. The
digraphs analyzed include all digraphs, directed acyclic graphs, and undirected
graphs up to certain numbers of vertices, as well as some specially constructed
cases. Using information from this analysis, we identify small digraphs
contributing to path homology in dimension for three temporal networks, and
relate these digraphs to network behavior. We conclude that path homology can
provide insight into temporal network structure and vice versa
Towards Minimal Barcodes
In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs of birth and death times of homology classes are encoded in the form of intervals. Starting from a polyhedral complex K (an object subdivided into cells which are polytopes) and an initial order of the set of vertices, we are concerned with the general problem of searching for filters (an order of the rest of the cells) that provide a minimal barcode representation in the sense of having minimal number of “k-significant” intervals, which correspond to homology classes with life-times longer than a fixed number k. As a first step, in this paper we provide an algorithm for computing such a filter for k = 1 on the Hasse diagram of the poset of faces of K
Topological features for monitoring human activities at distance
In this paper, a topological approach for monitoring human activities is presented. This approach makes possible to protect the person’s privacy hiding details that are not essential for processing a security alarm. First, a stack of human silhouettes, extracted by background subtraction and thresholding, are glued through their gravity centers, forming a 3D digital binary image I. Secondly, different orders of the simplices are applied on a simplicial complex obtained from I, which capture relations among the parts of the human body when walking. Finally, a topological signature is extracted from the persistence diagrams according to each order. The measure cosine is used to give a similarity value between topological signatures. In this way, the powerful topological tool known as persistent homology is novelty adapted to deal with gender classification, person identification, carrying bag detection and simple action recognition. Four experiments show the strength of the topological feature used; three of they use the CASIA-B database, and the fourth use the KTH database to present the results in the case of simple actions recognition. In the first experiment the named topological signature is evaluated, obtaining 98.8% (lateral view) of correct classification rates for gender identification. In the second one are shown results for person identification, obtaining an average of 98.5%. In the third one the result obtained is 93.8% for carrying bag detection. And in the last experiment the results were 97.7% walking and 97.5% running, which were the actions took from the KTH database
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