scholarly journals Consistency Analysis of Spectral Regularization Algorithms

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yukui Zhu ◽  
Hongwei Sun
Keyword(s):  
Error Bounds ◽  
Operator Norm ◽  
Consistency Analysis ◽  
Usual Definition ◽  
Spectral Regularization ◽  
Learning Rates ◽  
Definition Of

We investigate the consistency of spectral regularization algorithms. We generalize the usual definition of regularization function to enrich the content of spectral regularization algorithms. Under a more general prior condition, using refined error decompositions and techniques of operator norm estimation, satisfactory error bounds and learning rates are proved.

scholarly journals THE QUARK CONDENSATE IN THE GELL-MANN-OAKES-RENNER RELATION

1996 ◽  
Vol 11 (16) ◽  
pp. 1331-1337 ◽  
Author(s):  
K. LANGFELD ◽  
C. KETTNER
Keyword(s):  
Quark Propagator ◽  
Quark Condensate ◽  
Usual Definition ◽  
Gluon Exchange ◽  
Current Mass ◽  
Definition Of

The quark condensate which enters the Gell-Mann-Oakes-Renner (GMOR) relation, is investigated in the framework of one-gluon-exchange models. The usual definition of the quark condensate via the trace of the quark propagator produces a logarithmic divergent condensate. In the product of current mass and condensate, this divergence is precisely compensated by the bare current mass. The finite value of the product in fact does not contradict the relation recently obtained by Cahill and Gunner. Therefore the GMOR relation is still satisfied.

Some Features in the Spectra of Extragalactic Radio Sources

1981 ◽  
Vol 4 (2) ◽  
pp. 184-187 ◽  
Author(s):  
O. B. Slee
Keyword(s):  
Spectral Index ◽  
Recent Analysis ◽  
Radio Sources ◽  
Usual Definition ◽  
Extragalactic Radio Sources ◽  
Flux Data ◽  
Straight Line ◽  
Consistent Manner ◽  
Definition Of ◽  
Second Degree

A recent analysis of the spectra of about 2000 sources in the Culgoora-3 list (Slee 1977) of radio sources (Slee et al. 1981) has revealed some interesting features which may be the result of source evolution. The Culgoora-3 spectra were obtained by combining the 80 and 160 MHz flux densities from the Culgoora radioheliograph with other published flux data between 10 and 10,000 MHz; this is probably the most accurate set of spectra yet derived for a large number of sources selected for observation in a reasonably consistent manner. In addition to fitting the log S-log v data for each source with a straight line (its slope is the usual definition of spectral index) Slee et al. also fitted second-degree and third-degree polynomials to search for curvature in the spectra.

Panurgus platymerus Pérez, 1895 (Hymenoptera: Andrenidae) synonymy, status of the Warncke lectotype

Zootaxa ◽  
2003 ◽  
Vol 136 (1) ◽  
pp. 1
Author(s):  
SEBASTIEN PATINY
Keyword(s):  
North African ◽  
African Species ◽  
Usual Definition ◽  
Definition Of

The usual definition of Panurgus platymerus Pérez, 1895 does not fit the lectotype designated by Warncke in the Pérez collection. We propose here to place the specimens previously determined as Panurgus platymerus under the name Panurgus pyropygus Friese, 1901. Panurgus platymerus will be reserved for specimens of a large North-African species close to Panurgus cephalotes Latreille, 1811.

Stochastic comparisons of random processes, with applications in reliability

1973 ◽  
Vol 10 (03) ◽  
pp. 572-585 ◽  
Author(s):  
Gordon Pledger ◽  
Frank Proschan
Keyword(s):  
Practical Importance ◽  
Random Processes ◽  
Stochastic Comparison ◽  
Random Vectors ◽  
Stochastic Comparisons ◽  
Usual Definition ◽  
Definition Of ◽  
First Time

The usual definition of stochastic comparison of random vectors is extended to stochastic comparison of random processes. Conditions are stated under which {X (t), t ≧ 0} stochastically larger than {Y (t), t ≧ 0} implies that for increasing functionals f. Applications are made to reliability problems, yielding stochastic comparisons for systems of independently operating machines assuming exponential failure and exponential repair. From these stochastic comparisons we may then deduce similar stochastic comparisons for functionals of practical importance in reliability applications, such as the total machine up-time, the first time that the number of functioning machines drops below a specified number, the total time during which at least a specified number of machines are functioning, etc.

The effect of failure in extended and intermittent photoperiodic lighting on the growth of white spruce container seedlings

1985 ◽  
Vol 15 (4) ◽  
pp. 734-737 ◽  
Author(s):  
J. T. Arnott ◽  
C. S. Simmons
Keyword(s):  
Dark Period ◽  
Dry Weight ◽  
White Spruce ◽  
Shoot Length ◽  
Day Length ◽  
Lighting System ◽  
Usual Definition ◽  
Short Day ◽  
Lighting Systems ◽  
Definition Of

White spruce seedlings (seed source, 58°50′ N) were grown in a container nursery at Victoria, B.C. (48°28′ N) under the following two photoperiod regimes: (i) natural day length artifically extended to 18 h (120 lx from an incandescent source); (ii) natural day length with dark period interruption for 2.5 min every 30 min (120 lx from an incandescent source). Beginning on July 17, 12 weeks after sowing, batches of seedlings experienced a simulated failure of the lighting systems of from 0 to 9 nights. Although the reduced photoperiod did not fit the usual definition of a short day, failure of the lighting system in (i) and (ii) caused significant reductions in seedling shoot length and dry weight and a significant increase in root dry weight.

THERMO FIELD DYNAMICS IN TIME REPRESENTATION

1994 ◽  
Vol 09 (07) ◽  
pp. 1153-1180 ◽  
Author(s):  
Y. YAMANAKA ◽  
H. UMEZAWA ◽  
K. NAKAMURA ◽  
T. ARIMITSU
Keyword(s):  
Kinetic Equation ◽  
Time Dependent ◽  
Nonequilibrium Systems ◽  
Renormalization Condition ◽  
Usual Definition ◽  
Time Representation ◽  
Self Energy ◽  
Thermo Field Dynamics ◽  
Self Consistent ◽  
Definition Of

Making use of the thermo field dynamics (TFD) we formulate a calculable method for time-dependent nonequilibrium systems in a time representation (t-representation) rather than in the k0-Fourier representation. The corrected one-body propagator in the t-representation has the form of B−1 (diagonal matrix) B (B being a thermal Bogoliubov matrix). The number parameter in B here is the observed number (the Heisenberg number) with a fluctuation. With the usual definition of the on-shell self-energy a self-consistent renormalization condition leads to a kinetic equation for the number parameter. This equation turns out to be the Boltzmann equation, from which the entropy law follows.

The complexity of ascendant sequences in locally nilpotent groups

2014 ◽  
Vol 24 (02) ◽  
pp. 189-205 ◽  
Author(s):  
Chris J. Conidis ◽  
Richard A. Shore
Keyword(s):  
Nilpotent Groups ◽  
Low Complexity ◽  
Order Type ◽  
Usual Definition ◽  
Locally Nilpotent Groups ◽  
Locally Nilpotent ◽  
Normal Form Theorem ◽  
Algebraic Normal Form ◽  
Definition Of ◽  
Transfinite Recursion

We analyze the complexity of ascendant sequences in locally nilpotent groups, showing that if G is a computable locally nilpotent group and x0, x1, …, xN ∈ G, N ∈ ℕ, then one can always find a uniformly computably enumerable (i.e. uniformly [Formula: see text]) ascendant sequence of order type ω + 1 of subgroups in G beginning with 〈x0, x1, …, xN〉G, the subgroup generated by x0, x1, …, xN in G. This complexity is surprisingly low in light of the fact that the usual definition of ascendant sequence involves arbitrarily large ordinals that index sequences of subgroups defined via a transfinite recursion in which each step is incomputable. We produce this surprisingly low complexity sequence via the effective algebraic commutator collection process of P. Hall, and a related purely algebraic Normal Form Theorem of M. Hall for nilpotent groups.

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