112,968 research outputs found
Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: explicit time-stepping and efficient mass matrix inversion
Full text linkWe present a class of spline finite element methods for time-domain wave
propagation which are particularly amenable to explicit time-stepping. The
proposed methods utilize a discontinuous Galerkin discretization to enforce
continuity of the solution field across geometric patches in a multi-patch
setting, which yields a mass matrix with convenient block diagonal structure.
Over each patch, we show how to accurately and efficiently invert mass matrices
in the presence of curved geometries by using a weight-adjusted approximation
of the mass matrix inverse. This approximation restores a tensor product
structure while retaining provable high order accuracy and semi-discrete energy
stability. We also estimate the maximum stable timestep for spline-based finite
elements and show that the use of spline spaces result in less stringent CFL
restrictions than equivalent piecewise continuous or discontinuous finite
element spaces. Finally, we explore the use of optimal knot vectors based on L2
n-widths. We show how the use of optimal knot vectors can improve both
approximation properties and the maximum stable timestep, and present a simple
heuristic method for approximating optimal knot positions. Numerical
experiments confirm the accuracy and stability of the proposed methods
The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple
Full text linkIn this paper, we introduce a definition of BV functions in a Gelfand triple
which is an extension of the definition of BV functions in [2] by using
Dirichlet form theory. By this definition, we can consider the stochastic
reflection problem associated with a self-adjoint operator and a
cylindrical Wiener process on a convex set in a Hilbert space . We
prove the existence and uniqueness of a strong solution of this problem when
is a regular convex set. The result is also extended to the
non-symmetric case. Finally, we extend our results to the case when
, where
Dynamic Set Intersection
Full text linkConsider the problem of maintaining a family of dynamic sets subject to
insertions, deletions, and set-intersection reporting queries: given , report every member of in any order. We show that in the word
RAM model, where is the word size, given a cap on the maximum size of
any set, we can support set intersection queries in
expected time, and updates in expected time. Using this algorithm
we can list all triangles of a graph in
expected time, where and
is the arboricity of . This improves a 30-year old triangle enumeration
algorithm of Chiba and Nishizeki running in time.
We provide an incremental data structure on that supports intersection
{\em witness} queries, where we only need to find {\em one} .
Both queries and insertions take O\paren{\sqrt \frac{N}{w/\log^2 w}} expected
time, where . Finally, we provide time/space tradeoffs for
the fully dynamic set intersection reporting problem. Using words of space,
each update costs expected time, each reporting query
costs expected time where
is the size of the output, and each witness query costs expected time.Comment: Accepted to WADS 201
Spatial learning and memory in the tortoise (Geochelone carbonaria)
Get PDFA single tortoise (Geochelone carbonaria) was trained in an eight-arm radial maze, with the apparatus and general procedures modeled on those used to demonstrate spatial learning in rats. The tortoise learned to perform reliably above chance, preferentially choosing baited arms, rather than returning to arms previously visited on a trial. Test sessions that examined control by olfactory cues revealed that they did not affect performance. No systematic, stereotyped response patterns were evident. In spite of differences in brain structure, the tortoise showed spatial learning abilities comparable to those observed in mammals
Complementation between mouse Mfn1 and Mfn2 protects mitochondrial fusion defects caused by CMT2A disease mutations
Get PDFMfn2, an oligomeric mitochondrial protein important for mitochondrial fusion, is mutated in Charcot-Marie-Tooth disease (CMT) type 2A, a peripheral neuropathy characterized by axonal degeneration. In addition to homooligomeric complexes, Mfn2 also associates with Mfn1, but the functional significance of such heterooligomeric complexes is unknown. Also unknown is why Mfn2 mutations in CMT2A lead to cell type–specific defects given the widespread expression of Mfn2. In this study, we show that homooligomeric complexes formed by many Mfn2 disease mutants are nonfunctional for mitochondrial fusion. However, wild-type Mfn1 complements mutant Mfn2 through the formation of heterooligomeric complexes, including complexes that form in trans between mitochondria. Wild-type Mfn2 cannot complement the disease alleles. Our results highlight the functional importance of Mfn1–Mfn2 heterooligomeric complexes and the close interplay between the two mitofusins in the control of mitochondrial fusion. Furthermore, they suggest that tissues with low Mfn1 expression are vulnerable in CMT2A and that methods to increase Mfn1 expression in the peripheral nervous system would benefit CMT2A patients
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