487 research outputs found
Palmated Antlers of Moose May Serve as A Parabolic Reflector of Sounds
It has been postulated that the excellent sense of hearing in moose is mostly due to: (1) the large surface of the external ear, (2) better stereophony due to the large distance between ears, (3) independently movable, extremely adjustable pinna, and (4) the amplification of sounds reflected by the palms of the antlers. The last factor, possible reflection of sounds into pinna by the palm of the antlers, was tested in this study on a large antler trophy of Alaskan moose. The reception of a standard tone, broadcast from the frontally placed speaker, was recorded by a sound level meter located in an artificial moose ear. Three locations of the ear, as positioned relative to the speaker, e.g., frontward, sideward, and backward, were tested. The weakest reception was recorded in the backward position of the ear. If the sound pressure measured in the frontward position was set as 100%, the sound pressure in the backward position was 79%. The strongest reception was recorded when the artificial ear was positioned toward the center of the antler palm. In this position, the sound pressure was 119% relative to the frontward position. These findings strongly indicate that the palm of moose antlers may serve as an effective, parabolic reflector which increases the acoustic pressure of the incoming sound
Morphological investigations of the winter coat in white-tailed deer: Differences in skin, glands and hair structure of various body regions
The persistence landscape and some of its properties
Persistence landscapes map persistence diagrams into a function space, which
may often be taken to be a Banach space or even a Hilbert space. In the latter
case, it is a feature map and there is an associated kernel. The main advantage
of this summary is that it allows one to apply tools from statistics and
machine learning. Furthermore, the mapping from persistence diagrams to
persistence landscapes is stable and invertible. We introduce a weighted
version of the persistence landscape and define a one-parameter family of
Poisson-weighted persistence landscape kernels that may be useful for learning.
We also demonstrate some additional properties of the persistence landscape.
First, the persistence landscape may be viewed as a tropical rational function.
Second, in many cases it is possible to exactly reconstruct all of the
component persistence diagrams from an average persistence landscape. It
follows that the persistence landscape kernel is characteristic for certain
generic empirical measures. Finally, the persistence landscape distance may be
arbitrarily small compared to the interleaving distance.Comment: 18 pages, to appear in the Proceedings of the 2018 Abel Symposiu
Random geometric complexes
We study the expected topological properties of Cech and Vietoris-Rips
complexes built on i.i.d. random points in R^d. We find higher dimensional
analogues of known results for connectivity and component counts for random
geometric graphs. However, higher homology H_k is not monotone when k > 0. In
particular for every k > 0 we exhibit two thresholds, one where homology passes
from vanishing to nonvanishing, and another where it passes back to vanishing.
We give asymptotic formulas for the expectation of the Betti numbers in the
sparser regimes, and bounds in the denser regimes. The main technical
contribution of the article is in the application of discrete Morse theory in
geometric probability.Comment: 26 pages, 3 figures, final revisions, to appear in Discrete &
Computational Geometr
Velvet antlers as medicinal preparation and nutritional supplement
Farmski uzgoj jelenske divljači karakteriziran je proizvodnjom kvalitetne divljačine i rogova u bastu te pored toga predstavlja osnovu za napučivanje prirodnih staništa jelenskom divljači. Ova je činjenica od posebna značaja za ugrožene vrste jelena. Rogovi u bastu predstavljaju rastuće, nepotpuno mineralizirano tkivo prekriveno specifičnom kožnom tvorbom zvanom bast. Odstranjivanje rogova u bastu je složen kirurški zahvat koji zahtijeva primjenu neke od postojećih metoda anestezije. Nakon odstranjivanja, rogovi u bastu prolaze postupak pripreme, u pravilu kroz dehidraciju, otapanje u alkoholu ili vodenu ekstrakciju. Sastav rastućih rogova pokazuje izrazitu dijetetsku komponentu te prisutnost velikog broja različitih biološki aktivnih molekula. Ovakav je sastav razlogom njihove izrazite primjene u sklopu tradicijske medicine Dalekog Istoka. Unatoč svemu, njihova primjena na zapadnom tržištu je neznatna, prvenstveno uslijed brojnih predrasuda i nedostatka znanstvenih potvrda o njihovom djelovanju. Konačno, u proizvodnji rogova u bastu neophodno je zadovoljiti sve aspekte dobrobiti mužjaka, pravilne pripreme i dodatnih mogućnosti zaštite produkta te veterinarsko sanitarnog nadzora u proizvodnji.Deer farming is characterized by production of quality venison and velvet antlers. It may also serve as a base for reintroducing threatened deer species into their natural habitats. Velvet antlers are growing, premineralized tissues that are covered by special type of skin, called the velvet. Velvet antler removal is a complex surgical procedure that demands the application of one of the available methods of anaesthesia. After the procedure, velvet antlers have to be treated, mainly through dehydration procedure, water extraction procedure or as alcohol solution. The composition of the velvet antlers reveals various dietetic components and a presence of large number of different biologically active molecules. This is the reason why velvet antlers are traditionally used as a part of Oriental traditional medicine. Despite these facts their use on the western market is still minor, mainly due to some prejudices and the lack of rigorous scientific proofs of effectiveness. Finally, in order to protect the quality of the final product and to satisfy all aspects of animal welfare, additional measures such as veterinary monitoring of velvet antler production should be taken
Categorification of persistent homology
We redevelop persistent homology (topological persistence) from a categorical
point of view. The main objects of study are diagrams, indexed by the poset of
real numbers, in some target category. The set of such diagrams has an
interleaving distance, which we show generalizes the previously-studied
bottleneck distance. To illustrate the utility of this approach, we greatly
generalize previous stability results for persistence, extended persistence,
and kernel, image and cokernel persistence. We give a natural construction of a
category of interleavings of these diagrams, and show that if the target
category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational
Geometr
The Theory of the Interleaving Distance on Multidimensional Persistence Modules
In 2009, Chazal et al. introduced -interleavings of persistence
modules. -interleavings induce a pseudometric on (isomorphism
classes of) persistence modules, the interleaving distance. The definitions of
-interleavings and generalize readily to multidimensional
persistence modules. In this paper, we develop the theory of multidimensional
interleavings, with a view towards applications to topological data analysis.
We present four main results. First, we show that on 1-D persistence modules,
is equal to the bottleneck distance . This result, which first
appeared in an earlier preprint of this paper, has since appeared in several
other places, and is now known as the isometry theorem. Second, we present a
characterization of the -interleaving relation on multidimensional
persistence modules. This expresses transparently the sense in which two
-interleaved modules are algebraically similar. Third, using this
characterization, we show that when we define our persistence modules over a
prime field, satisfies a universality property. This universality result
is the central result of the paper. It says that satisfies a stability
property generalizing one which is known to satisfy, and that in
addition, if is any other pseudometric on multidimensional persistence
modules satisfying the same stability property, then . We also show
that a variant of this universality result holds for , over arbitrary
fields. Finally, we show that restricts to a metric on isomorphism
classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in
Foundations of Computational Mathematics. 36 page
A convenient category of locally preordered spaces
As a practical foundation for a homotopy theory of abstract spacetime, we
extend a category of certain compact partially ordered spaces to a convenient
category of locally preordered spaces. In particular, we show that our new
category is Cartesian closed and that the forgetful functor to the category of
compactly generated spaces creates all limits and colimits.Comment: 26 pages, 0 figures, partially presented at GETCO 2005; changes:
claim of Prop. 5.11 weakened to finite case and proof changed due to problems
with proof of Lemma 3.26, now removed; Eg. 2.7, statement before Lem. 2.11,
typos, and other minor problems corrected throughout; extensive rewording;
proof of Lem. 3.31, now 3.30, adde
Persistent topology for natural data analysis - A survey
Natural data offer a hard challenge to data analysis. One set of tools is
being developed by several teams to face this difficult task: Persistent
topology. After a brief introduction to this theory, some applications to the
analysis and classification of cells, lesions, music pieces, gait, oil and gas
reservoirs, cyclones, galaxies, bones, brain connections, languages,
handwritten and gestured letters are shown
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