407,446 research outputs found
Equivariant Universal Coefficient and Kunneth Spectral Sequences
We construct hyper-homology spectral sequences of Z-graded and ROG-graded
Mackey functors for Ext and Tor over G-equivariant S-algebras (A-infty ring
spectra) for finite groups G. These specialize to universal coefficient and
Kunneth spectral sequences
On Generalized Computable Universal Priors and their Convergence
Solomonoff unified Occam's razor and Epicurus' principle of multiple
explanations to one elegant, formal, universal theory of inductive inference,
which initiated the field of algorithmic information theory. His central result
is that the posterior of the universal semimeasure M converges rapidly to the
true sequence generating posterior mu, if the latter is computable. Hence, M is
eligible as a universal predictor in case of unknown mu. The first part of the
paper investigates the existence and convergence of computable universal
(semi)measures for a hierarchy of computability classes: recursive, estimable,
enumerable, and approximable. For instance, M is known to be enumerable, but
not estimable, and to dominate all enumerable semimeasures. We present proofs
for discrete and continuous semimeasures. The second part investigates more
closely the types of convergence, possibly implied by universality: in
difference and in ratio, with probability 1, in mean sum, and for Martin-Loef
random sequences. We introduce a generalized concept of randomness for
individual sequences and use it to exhibit difficulties regarding these issues.
In particular, we show that convergence fails (holds) on generalized-random
sequences in gappy (dense) Bernoulli classes.Comment: 22 page
Universal bifurcation property of two- or higher-dimensional dissipative systems in parameter space: Why does 1D symbolic dynamics work so well?
The universal bifurcation property of the H\'enon map in parameter space is
studied with symbolic dynamics. The universal- region is defined to
characterize the bifurcation universality. It is found that the universal-
region for relative small is not restricted to very small values. These
results show that it is also a universal phenomenon that universal sequences
with short period can be found in many nonlinear dissipative systems.Comment: 10 pages, figures can be obtained from the author, will appeared in
J. Phys.
Universal Sequential Outlier Hypothesis Testing
Universal outlier hypothesis testing is studied in a sequential setting.
Multiple observation sequences are collected, a small subset of which are
outliers. A sequence is considered an outlier if the observations in that
sequence are generated by an "outlier" distribution, distinct from a common
"typical" distribution governing the majority of the sequences. Apart from
being distinct, the outlier and typical distributions can be arbitrarily close.
The goal is to design a universal test to best discern all the outlier
sequences. A universal test with the flavor of the repeated significance test
is proposed and its asymptotic performance is characterized under various
universal settings. The proposed test is shown to be universally consistent.
For the model with identical outliers, the test is shown to be asymptotically
optimal universally when the number of outliers is the largest possible and
with the typical distribution being known, and its asymptotic performance
otherwise is also characterized. An extension of the findings to the model with
multiple distinct outliers is also discussed. In all cases, it is shown that
the asymptotic performance guarantees for the proposed test when neither the
outlier nor typical distribution is known converge to those when the typical
distribution is known.Comment: Proc. of the Asilomar Conference on Signals, Systems, and Computers,
2014. To appea
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