27,065 research outputs found
Packing symplectic manifolds by hand
We construct explicit maximal symplectic packings of minimal rational and
ruled symplectic 4-manifolds by few balls in a very simple way.Comment: 31 pages, 18 figure
Ultrametric pseudodifferential operators and wavelets for the case of non homogeneous measure
A family of orthonormal bases of ultrametric wavelets in the space of
quadratically integrable with respect to arbitrary measure functions on general
(up to some topological restrictions) ultrametric space is introduced.
Pseudodifferential operators (PDO) on the ultrametric space are investigated.
We prove that these operators are diagonal in the introduced bases of
ultrametric wavelets and compute the corresponding eigenvalues.
Duality between ultrametric spaces and directed trees is discussed. In
particular, a new way of construction of ultrametric spaces by completion of
directed trees is proposed.Comment: 16 pages, LaTeX, some corrections and generalization
Are Lock-Free Concurrent Algorithms Practically Wait-Free?
Lock-free concurrent algorithms guarantee that some concurrent operation will
always make progress in a finite number of steps. Yet programmers prefer to
treat concurrent code as if it were wait-free, guaranteeing that all operations
always make progress. Unfortunately, designing wait-free algorithms is
generally a very complex task, and the resulting algorithms are not always
efficient. While obtaining efficient wait-free algorithms has been a long-time
goal for the theory community, most non-blocking commercial code is only
lock-free.
This paper suggests a simple solution to this problem. We show that, for a
large class of lock- free algorithms, under scheduling conditions which
approximate those found in commercial hardware architectures, lock-free
algorithms behave as if they are wait-free. In other words, programmers can
keep on designing simple lock-free algorithms instead of complex wait-free
ones, and in practice, they will get wait-free progress.
Our main contribution is a new way of analyzing a general class of lock-free
algorithms under a stochastic scheduler. Our analysis relates the individual
performance of processes with the global performance of the system using Markov
chain lifting between a complex per-process chain and a simpler system progress
chain. We show that lock-free algorithms are not only wait-free with
probability 1, but that in fact a general subset of lock-free algorithms can be
closely bounded in terms of the average number of steps required until an
operation completes.
To the best of our knowledge, this is the first attempt to analyze progress
conditions, typically stated in relation to a worst case adversary, in a
stochastic model capturing their expected asymptotic behavior.Comment: 25 page
Friction, Free Axes of Rotation and Entropy
Friction forces acting on rotators may promote their alignment and therefore
eliminate degrees of freedom in their movement. The alignment of rotators by
friction force was demonstrated by experiments performed with different
spinners, demonstrating how friction generates negentropy in a system of
rotators. A gas of rigid rotators influenced by friction force is considered.
The orientational negentropy generated by a friction force was estimated with
the Sackur-Tetrode equation. The minimal change in total entropy of a system of
rotators, corresponding to their eventual alignment, decreases with
temperature. The reported effect may be of the primary importance for a phase
equilibrium and motion of ubiquitous colloidal and granular systems.Comment: 10 pages, 7 image
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