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Regularity properties for dominating projective sets

1995
*
Annals of Pure and Applied Logic
*

This improves a theorem of Spinas [15] saying that every

doi:10.1016/0168-0072(94)00027-z
fatcat:as7pvykzqbd4ji53clhjhdzxtq
*dominating*analytic*set*contains the branches of a uniform tree, i.e. a superperfect tree with the*property*that*for*every splitnode all the successor ... Since the proof of analytic u-*regularity*uses a game argument it was clear that (*projective*) determinacy implies u-*regularity*of all (*projective*)*sets*. ... Then in V [G] every*projective**set*is strongly u-*regular*. Proof. By Theorem 1.1 it is enough to prove that in V [G] every*dominating**projective**set*contains a*dominating*closed*set*. ...##
###
Page 626 of Mathematical Reviews Vol. , Issue 96b
[page]

1996
*
Mathematical Reviews
*

*projective*

*sets*. ... The proof of u-

*regularity*of analytic

*sets*uses a game argument and so (

*projective*) determinacy implies u-

*regularity*of all (projec- tive)

*sets*. ...

##
###
Page 2116 of Mathematical Reviews Vol. , Issue 97D
[page]

1997
*
Mathematical Reviews
*

The minimum car- dinality of an n-

*dominating**set*is called the n-*domination*number and is denoted by y,(G). ... A*set*D of vertices of G is an n-*dominating**set*if every vertex in V(G) — D is within distance n from some vertex of D. ...##
###
Noetherian intersections of regular local rings of dimension two
[article]

2017
*
arXiv
*
pre-print

Let D be a 2-dimensional

arXiv:1709.00486v1
fatcat:jmztryv4kncuhmsruuzs4lb7xq
*regular*local ring and let Q(D) denote the quadratic tree of 2-dimensional*regular*local overrings of D. ... To do so, we describe the desingularization of*projective*models over D both algebraically in terms of the saturation of complete ideals and order-theoretically in terms of the quadratic tree Q(D). ... This paper is an outgrowth of a*project*the authors are working on with Alan Loper in [11] . We thank Alan*for*helpful conversations and*for*motivating us to consider the topics in this paper. ...##
###
Dominating projective sets in the Baire space

1994
*
Annals of Pure and Applied Logic
*

We construct a

doi:10.1016/0168-0072(94)90025-6
fatcat:5p6ynswpmjfedjmev5x7b6ugzi
*dominating*closed*set*with the*property*that*for*no uniform tree whose branches are contained in the closed*set*, the*set*of these branches is*dominating*. We also show that from a Z.' ... We call this*property*of analytic*sets*u-*regularity*. However, we show that the concept of uniform tree does not suffice to characterize*dominating*analytic*sets*in general. ... as u-*regularity*of all (*projective*)*sets*. ...##
###
Regularity of projections revisited
[article]

2000
*
arXiv
*
pre-print

The concept of

arXiv:math/0006132v1
fatcat:wzdf2xnz65ccpgvqfeijis5uti
*regularity*in the meta-topological*setting*of*projections*in the double dual of a C*-algebra addresses the interrelations of a*projection*p with its closure,*for*instance in the form that ... Although automatic in the commutative case, it has been known since the late sixties that*regularity*fails*for*many*projections*. ... If it did, then by functional calculus, it would also*dominate*an element b with the*property*that b(ω) was a*projection*on a nonempty open*set*U of Ω. ...##
###
On the Origins of the Block Structure Phenomenon in Neural Network Representations
[article]

2022
*
arXiv
*
pre-print

However, the

arXiv:2202.07184v1
fatcat:6wopk6pk6jatpeog73nbwbtq3q
*set*of*dominant*datapoints, and the precise shared image statistic, can vary across random seeds. ... By analyzing*properties*of the*dominant*PCs, we find that the block structure arises from*dominant*datapoints - a small group of examples that share similar image statistics (e.g. background color). ... We further discover a small*set*of*dominant*datapoints (with large activation norms) that are responsible*for*the block structure. ...##
###
Algebraic subellipticity and dominability of blow-ups of affine spaces
[article]

2016
*
arXiv
*
pre-print

*For*algebraic manifolds in general, we prove that strong algebraic

*dominability*, a weakening of algebraic subellipticity, is preserved by an arbitrary blow-up with a smooth centre. ... Little is known about the behaviour of the Oka

*property*of a complex manifold with respect to blowing up a submanifold. ... A challenging open question in basic Oka theory is whether the Oka

*property*

*for*, say,

*projective*manifolds is a birational invariant. ...

##
###
Page 182 of Mathematical Reviews Vol. , Issue 2002A
[page]

2002
*
Mathematical Reviews
*

A

*set*E is said to be*regular*if there is a constant C } such that f Le trinie ir _ } i the triple integral r[/C< H\ENB(x,r))<Cr’*for*x » O<r<alE where B(x,r) is the closed ball with centre x and radius ... Furthermore, the author shows that the well-known connection between the pack- i exceptional*sets*of*projections*ing and box counting dimension is also valid*for*the packing and box counting profiles ( ...##
###
Projective dimension of (hyper)graphs and the Castelnuovo-Mumford regularity of bipartite graphs
[article]

2016
*
arXiv
*
pre-print

We prove that the

arXiv:1605.02956v1
fatcat:u3itxelouzeujbw6xqqardrdfm
*projective*dimension of any (hyper)graph can be bounded from above by the (Castelnuovo-Mumford)*regularity*of its Levi graph (or incidence bipartite graph). ... Moreover, we show that known upper bounds on prod-dim(G) involving*domination*parameters are in fact upper bounds to reg(S(G)). ... Proof of Claim 3: Suppose that A is a vertex-wise*dominating**set*with ΥpSpGqq " |A| satisfying the following*properties*: piq A e is an edge-wise*dominating**set**for*G of minimum possible size among any ...##
###
An unexpected discovery

2014
*
Involve. A Journal of Mathematics
*

We were looking

doi:10.2140/involve.2014.7.373
fatcat:qq76cyvg55cqlc2bau5gzafpoa
*for*a new approach because the proof I had written is too long*for*publication, but the result itself is interesting. ... One summer, I chose two undergraduate students to work with me on a research*project*. Our goal was specifically to find a new approach to proving a theorem I had already proved several years before. ... The result in question classifies a*set*of graphs with certain*properties*. I gave Trevor and Yixiao the statement of the theorem. Theorem 1. ...##
###
Statistical analysis of nonlinearly reconstructed near-infrared tomographic images. I. Theory and simulations

2002
*
IEEE Transactions on Medical Imaging
*

It was observed that the bias error

doi:10.1109/tmi.2002.801155
pmid:12374313
fatcat:7gg5nc7kcjdiricgfospe43nee
*dominates*at high*regularization*parameter values while variance*dominates*as the algorithm is allowed to approach the optimal solution. ... This optimum does not necessarily correspond to the minimum*projection*error solution, but typically requires further iteration with a decreasing*regularization*parameter to reach the lowest image error ... Further, if*regularization*gets too low, images become*dominated*by random*property*value variations. ...##
###
Approximation and interpolation of regular maps from affine varieties to algebraic manifolds
[article]

2019
*
arXiv
*
pre-print

*projective*manifolds. ... We consider the analogue

*for*

*regular*maps from affine varieties to suitable algebraic manifolds of Oka theory

*for*holomorphic maps from Stein spaces to suitable complex manifolds. ... By aEll 1 , Y is strongly algebraically

*dominable*, meaning that

*for*every y ∈ Y , there is a

*regular*map g : C n → Y with 0 → y that is nondegenerate at 0. ...

##
###
A NEW APPROACH FOR AUDIO CLASSIFICATION AND SEGMENTATION USING GABOR WAVELETS AND FISHER LINEAR DISCRIMINATOR

2005
*
International journal of pattern recognition and artificial intelligence
*

*For*

*regular*textures, the texture primitives are assumed to be parallelograms, the two

*dominant*directions are extracted by Hough transform. ... To get more discriminative features

*for*

*regularity*computation, the Fourier spectrum is treated as an image and the Fourier transform is performed again to produce an enhanced Fourier spectrum. ... To compute the scale and

*regularity*, the filtered images are

*projected*along the two

*dominant*directions to form two

*sets*of

*projections*. ...

##
###
An efficient computation method for the texture browsing descriptor of MPEG-7

2005
*
Image and Vision Computing
*

*For*

*regular*textures, the texture primitives are assumed to be parallelograms, the two

*dominant*directions are extracted by Hough transform. ... To get more discriminative features

*for*

*regularity*computation, the Fourier spectrum is treated as an image and the Fourier transform is performed again to produce an enhanced Fourier spectrum. ... To compute the scale and

*regularity*, the filtered images are

*projected*along the two

*dominant*directions to form two

*sets*of

*projections*. ...

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