11,147 research outputs found
Machine learning in solar physics
The application of machine learning in solar physics has the potential to
greatly enhance our understanding of the complex processes that take place in
the atmosphere of the Sun. By using techniques such as deep learning, we are
now in the position to analyze large amounts of data from solar observations
and identify patterns and trends that may not have been apparent using
traditional methods. This can help us improve our understanding of explosive
events like solar flares, which can have a strong effect on the Earth
environment. Predicting hazardous events on Earth becomes crucial for our
technological society. Machine learning can also improve our understanding of
the inner workings of the sun itself by allowing us to go deeper into the data
and to propose more complex models to explain them. Additionally, the use of
machine learning can help to automate the analysis of solar data, reducing the
need for manual labor and increasing the efficiency of research in this field.Comment: 100 pages, 13 figures, 286 references, accepted for publication as a
Living Review in Solar Physics (LRSP
Unobstructed Lagrangian cobordism groups of surfaces
We study Lagrangian cobordism groups of closed symplectic surfaces of genus
whose relations are given by unobstructed, immersed Lagrangian
cobordisms. Building upon work of Abouzaid and Perrier, we compute these
cobordism groups and show that they are isomorphic to the Grothendieck group of
the derived Fukaya category of the surface.Comment: 60 pages, 15 figure
Convex valuations, from Whitney to Nash
We consider the Whitney problem for valuations: does a smooth -homogeneous
translation-invariant valuation on exist that has given
restrictions to a fixed family of linear subspaces? A necessary condition
is compatibility: the given valuations must coincide on intersections. We show
that for , the grassmannian of -planes, this
condition becomes sufficient once . This complements the Klain and
Schneider uniqueness theorems with an existence statement, and provides a
recursive description of the image of the cosine transform. Informally
speaking, we show that the transition from densities to valuations is localized
to codimension .
We then look for conditions on when compatibility is also sufficient for
extensibility, in two distinct regimes: finite arrangements of subspaces, and
compact submanifolds of the grassmannian. In both regimes we find unexpected
flexibility. As a consequence of the submanifold regime, we prove a Nash-type
theorem for valuations on compact manifolds, from which in turn we deduce the
existence of Crofton formulas for all smooth valuations on manifolds. As an
intermediate step of independent interest, we construct Crofton formulas for
all odd translation-invariant valuations.Comment: 53 page
Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a -Poincar\'e inequality
We consider the question of whether a domain with uniformly thick boundary at
all locations and at all scales has a large portion of its boundary visible
from the interior; here, "visibility" indicates the existence of John curves
connecting the interior point to the points on the "visible boundary". In this
paper, we provide an affirmative answer in the setting of a doubling metric
measure space supporting a -Poincar\'e inequality for , thus
extending the results of [20,2,9] to non-Ahlfors regular spaces. We show that
-codimensional thickness of the boundary for implies
-codimensional thickness of the visible boundary. For such domains we prove
that traces of Sobolev functions on the domain belong to the Besov class of the
visible boundary
Nonnegative Ricci curvature, nilpotency, and Hausdorff dimension
Let be an open (complete and non-compact) manifold with and escape rate not . It is known that under these conditions, the
fundamental group has a finitely generated torsion-free nilpotent
subgroup of finite index, as long as is an infinite
group. We show that the nilpotency step of must be reflected in
the asymptotic geometry of the universal cover , in terms of the
Hausdorff dimension of an isometric -orbit: there exist an
asymptotic cone of and a closed -subgroup
of the isometry group of such that its orbit has Hausdorff
dimension at least the nilpotency step of . This resolves a
question raised by Wei and the author, and extends previous results on virtual
abelianness by the author
2023-2024 Boise State University Undergraduate Catalog
This catalog is primarily for and directed at students. However, it serves many audiences, such as high school counselors, academic advisors, and the public. In this catalog you will find an overview of Boise State University and information on admission, registration, grades, tuition and fees, financial aid, housing, student services, and other important policies and procedures. However, most of this catalog is devoted to describing the various programs and courses offered at Boise State
Short time existence for coupling of scaled mean curvature flow and diffusion
We prove a short time existence result for a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss a mean curvature flow scaled with a term that depends on a quantity defined on the surface coupled to a diffusion equation for that quantity. The proof is based on a splitting ansatz, solving both equations separately using linearization and a contraction argument. Our result is formulated for the case of immersed hypersurfaces and yields a uniform lower bound on the existence time that allows for small changes in the initial value of the height function
Derived -Geometry I: Foundations
This work is the first in a series laying the foundations of derived geometry
in the setting, and providing tools for the construction and study
of moduli spaces of solutions of Partial Differential Equations that arise in
differential geometry and mathematical physics. To advertise the advantages of
such a theory, we start with a detailed introduction to derived
-geometry in the context of symplectic topology and compare and
contrast with Kuranishi space theory. In the body of this work, we avail
ourselves of Lurie's extensive work on abstract structured spaces to define
-categories of derived -ring and -schemes and
derived -rings and -schemes with corners via a
universal property in a suitable -category of -categories
with respect to the ordinary categories of manifolds and manifolds with corners
(with morphisms the -maps of Melrose in the latter case), and prove many
basic structural features about them. Along the way, we establish some derived
flatness results for derived -rings of independent interest.Comment: 203 pages; comments welcom
Geometrical Interpretation of Multipoles and Moments on Differential Manifolds
In this thesis, the construction of a specific family of linear functionals with support on a closed embedding c : R ,→ M upon a manifold is discussed. The construction is performed in a purely coordinate free fashion, based on the De Rham push-forward approach and generalised to define "tensorial currents" called "multipoles". Several geometrical and algebraic properties are investigated and two main useful classes of non-trivial coordinate representations are compared and related to the choices of some extra structures on the manifold (i.e. affine connection, foliation, adapted atlas, adapted frames). It is shown that in general, the transformation rules are not given by the action of the linear group, unless some information upon the "transverse" directions with respect to the closed embedding is provided. It is shown how the multipoles are the geometrical objects naturally arising when some specific one parameter families of compact support tensor fields are expanded asymptotically around the closed embedding. In case a one parameter family satisfies also an extra condition (i.e. self similarity) it is shown how to recover the well known standard definition of "moments", opening the door to a new completely covariant and coordinate free meaning of the concept of "multipole expansion" of functions and tensor field upon the differential manifolds. It is shown how these linear functionals admit a coordinates representation coinciding with the moments commonly defined to perform the Pole-Dipole approximation of an Energy-Momentum Tensor field in General Relativity, and when a Levi Civita connection is assumed on a pseudo-Riemmanian manifold, the first two multipoles related to an Energy Momentum tensor field expansion can easily satisfy the well known Mathisson-Papapetrou-Dixon equation. Since the proposed method of construction of the multipoles does not rely on a specific metric or a specific affine connection, a generalisation of the Pole-Dipole approximation for a non metric connection is easily achieved, casting the Mathisson-Papapetrou-Dixon equation in presence of a non null torsion. Because of this, there is hence the possibility to interpret the test particles and test charges within the Relativistic Theories (possibly beyond General Relativity) just as the multipole approximation of the regular sources of the interaction fields, with a new clear geometrical background
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