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Regularity properties for dominating projective sets

Jörg Brendle, Greg Hjorth, Otmar Spinas
1995 Annals of Pure and Applied Logic  
This improves a theorem of Spinas [15] saying that every 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.  ... 
doi:10.1016/0168-0072(94)00027-z fatcat:as7pvykzqbd4ji53clhjhdzxtq

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]

William Heinzer, Bruce Olberding
2017 arXiv   pre-print
Let D be a 2-dimensional 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.  ... 
arXiv:1709.00486v1 fatcat:jmztryv4kncuhmsruuzs4lb7xq

Dominating projective sets in the Baire space

Otmar Spinas
1994 Annals of Pure and Applied Logic  
We construct a 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.  ... 
doi:10.1016/0168-0072(94)90025-6 fatcat:5p6ynswpmjfedjmev5x7b6ugzi

Regularity of projections revisited [article]

Charles A. Akemann, Soren Eilers
2000 arXiv   pre-print
The concept of 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.  ... 
arXiv:math/0006132v1 fatcat:wzdf2xnz65ccpgvqfeijis5uti

On the Origins of the Block Structure Phenomenon in Neural Network Representations [article]

Thao Nguyen, Maithra Raghu, Simon Kornblith
2022 arXiv   pre-print
However, the 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.  ... 
arXiv:2202.07184v1 fatcat:6wopk6pk6jatpeog73nbwbtq3q

Algebraic subellipticity and dominability of blow-ups of affine spaces [article]

Finnur Larusson, Tuyen Trung Truong
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.  ... 
arXiv:1606.08115v4 fatcat:ftt7jnbbfreylhpe7j3kgxqwjq

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]

Türker Bıyıkoğlu, Yusuf Civan
2016 arXiv   pre-print
We prove that the 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  ... 
arXiv:1605.02956v1 fatcat:u3itxelouzeujbw6xqqardrdfm

An unexpected discovery

Erika King
2014 Involve. A Journal of Mathematics  
We were looking 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.  ... 
doi:10.2140/involve.2014.7.373 fatcat:qq76cyvg55cqlc2bau5gzafpoa

Statistical analysis of nonlinearly reconstructed near-infrared tomographic images. I. Theory and simulations

B.W. Pogue, Xiaomei Song, T.D. Tosteson, T.O. McBride, Shudong Jiang, K.D. Paulsen
2002 IEEE Transactions on Medical Imaging  
It was observed that the bias error 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.  ... 
doi:10.1109/tmi.2002.801155 pmid:12374313 fatcat:7gg5nc7kcjdiricgfospe43nee

Approximation and interpolation of regular maps from affine varieties to algebraic manifolds [article]

Finnur Larusson, Tuyen Trung Truong
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.  ... 
arXiv:1706.00519v3 fatcat:sgcnpsrzqrc2hh7f43ck2g6hey

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

RUEI-SHIANG LIN, LING-HWEI CHEN
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.  ... 
doi:10.1142/s0218001405004289 fatcat:asmrcdvu45fb5bhwwldejvh5sy

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

Kuen-Long Lee, Ling-Hwei Chen
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.  ... 
doi:10.1016/j.imavis.2004.12.002 fatcat:cykokrwczrgddmyxgmzwyui34y
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