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Moments of Uniform Random Multigraphs with Fixed Degree Sequences

Philip S. Chodrow
2020 SIAM Journal on Mathematics of Data Science  
We study the expected adjacency matrix of a uniformly random multigraph with fixed degree sequence \bfd \in \BbbZ n + .  ...  We test the estimator on synthetic and empirical degree sequences, finding that it enjoys relative error against ground truth a full order of magnitude smaller than the standard approximation.  ...  (f) As in (e), for the Zipf degree sequence. Figure 2 ( 2 b) shows the clumping of edges between pairs of nodes. On Figure 2 . 2 Figure 2.  ... 
doi:10.1137/19m1288772 fatcat:sqpg5kntafgbpk6berbeb6qls4

How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions? [article]

Andris Ambainis and Ronald de Wolf (CWI and U of Amsterdam)
2013 arXiv   pre-print
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions  ...  We show that for these measures the correct lower bound is Omega(log n / loglog n), and we exhibit quantum algorithms for two functions where this bound is achieved.  ...  We thank Artūrs Bačkurs, Oded Regev, Mario Szegedy, and the anonymous CCC referees for useful comments and references.  ... 
arXiv:1206.0717v2 fatcat:65tbomget5gzpfcgqq7dqyhrfe

Wadge Degrees of Infinitary Rational Relations

Olivier Finkel
2008 Mathematics in Computer Science  
The Borel and the Wadge hierarchies of the class RAT_omega of infinitary rational relations accepted by 2-tape Büchi automata are equal to the Borel and the Wadge hierarchies of omega-languages accepted  ...  In particular, for every non-null recursive ordinal α, there exist some Σ^0_α-complete and some Π^0_α-complete infinitary rational relations.  ...  Acknowledgements Thanks to the anonymous referees for useful comments on a preliminary version of this paper.  ... 
doi:10.1007/s11786-008-0045-7 fatcat:mljqvuczaba53jgyswxz6mxgae

SoS and Planted Clique: Tight Analysis of MPW Moments at all Degrees and an Optimal Lower Bound at Degree Four [article]

Samuel B. Hopkins and Pravesh K. Kothari and Aaron Potechin
2015 arXiv   pre-print
For $2 < d = o(\sqrt{\log{(n)}})$, degree $2d$ SoS does not recover the planted clique unless $\omega \gg n^{1/(d + 1)} /(2^d poly \log n)$, improving upon the bound due to MPW.  ...  Degree four SoS does not recover the planted clique unless $\omega \gg \sqrt n poly \log n$, improving upon the bound $\omega \gg n^{1/3}$ due to DM.  ...  We especially thank Boaz Barak for introducing the problem to us, for numerous conversations which led to many of the proofs in this paper, and for invaluable help and advice in writing it.  ... 
arXiv:1507.05230v1 fatcat:ilfntzjljbdo3cdu6xetaox3v4

Codimension two nonsingular subvarieties of quadrics: scrolls and classification in degree $d\leq 10$

Mark Andrea A. de CATALDO
1998 Journal of the Mathematical Society of Japan  
First the sectional genus $g$ is exhibited as a function of the degree $d$ of the scroll. The degree $d$ is then bounded from above by the use of Castelnuovo-type bounds for $g$ .  ...  AS a by-pass result of this classification in low degree we are able to construct all scrolls, except for one case: when the degree $d=12$ and the base is a minimal $K3$ surface.  ...  As for Type F), seeProposition 3.4.8. PROOF OF THEOREM 2.1.1. The degree $d$ is always an even integer by Remark 1.1.1.  ... 
doi:10.2969/jmsj/05040879 fatcat:qeuxd7hxbredhnwvcwhsydebge

A Regularity Lemma, and Low-Weight Approximators, for Low-Degree Polynomial Threshold Functions

Ilias Diakonikolas, Rocco A. Servedio, Li-Yang Tan, Andrew Wan
2010 2010 IEEE 25th Annual Conference on Computational Complexity  
We give a "regularity lemma" for degree-d polynomial threshold functions (PTFs) over the Boolean cube {−1, 1} n .  ...  As an application of this regularity lemma, we prove that for any constants d ≥ 1, > 0, every degree-d PTF over n variables can be approximated to accuracy by a constantdegree PTF that has integer weights  ...  (We use the notation Ω d () below to indicate that the hidden constant of the big-Omega depends on d.) Theorem 3.  ... 
doi:10.1109/ccc.2010.28 dblp:conf/coco/DiakonikolasSTW10 fatcat:2bbdzaxqkzcl3e2fqsczurscay

Molecular Friction in Dilute Gases. II. Thermal Relaxation of Translational and Rotational Degrees of Freedom

Norman F. Sather, John S. Dahler
1961 Journal of Chemical Physics  
This means that the equipartition theorem can not be ap- plied to this degree of freedom even though the mass distribution be nonsingular.  ...  Therefore, numerical estimates of the relaxa- tion times can be obtained very easily from the exten- sive tables of omega integrals which have been con- structed for a wide variety of pair potential functions  ... 
doi:10.1063/1.1732206 fatcat:y3jb2gpwjvbwtlluzsiuvyspbi

Exact side effects for interprocedural dependence analysis

Peiyi Tang
1993 Proceedings of the 7th international conference on Supercomputing - ICS '93  
The representation of the exact side e ects proposed in this paper can be used by the Omega test to support the exact interprocedural dependence analysis in parallelizing compilers.  ...  Exact side e ects of array references in subroutines are essential for exact interprocedural dependence analysis.  ...  Pugh for making the Omega System freely available for anonymous ftp.  ... 
doi:10.1145/165939.165964 dblp:conf/ics/Tang93 fatcat:ygbhg47uvbahjpcnvrejaeqixa

Deformations of transversely symplectic and transversely contact foliations

J. Girbau, G. Guasp
1991 Tsukuba Journal of Mathematics  
a strong versality theorem for deformations of transversely holomorphic foliations.  ...  , moreover, $H^{i}(CP^{2n+1}, \Omega^{1}(E))=0$ for $i>0$ we deduce from the second exact sequence the vanishing of $H^{1}(CP^{2n+1}, \Theta_{\omega})$ and $H^{2}(CP^{2n+1}, \Theta_{\omega})$ .  ... 
doi:10.21099/tkbjm/1496161671 fatcat:klhj2qsk45ctvg6xwk3qz3md4i

A construction of an automorphic sheaf for GLr on the moduli space of parabolic structures

Syu Kato
1999 Proceedings of the Symposium on Representation Theory  
Finally, we give an estimate for the characteristic variety of our sheaf and see it contains Nilp for sufficiently high degree case.  ...  Here the diagram above is exact for all lines, $\bullet$ $\phi_{i}$ is uniquely determined via the composition $0arrow\omega-r+i+1^{\phi i+1\rho i+1}arrow B_{i+1}arrow B_{i+1}^{1}\otimes\omegaarrow B_{  ... 
doi:10.34508/repsympo.1999.0_15 fatcat:2wl6wpufzfft3mgyo6ngvgjrhm

Homologically Trivial Self-Maps

Akira SASAO
1996 Tokyo Journal of Mathematics  
also homotopically trivial. (2) $IfSq^{2}(e^{n})=0andSq^{2}(e^{n+2})\neq 0(n\geqq 4)$ , then the same conclusion as (1) holds with an exceptional case in which there exists only one homotopically non-trivial  ...  The author would like to express his deep appreciation $t\langle$ the referee for his kind advice.  ...  $\alpha=\eta_{n}$ ) and consider a part of the homotopy exact sequence of the pair $(A, S^{n})$ : $\pi_{n+5}(A, S^{n})\rightarrow\pi_{n+4}(S^{n})d_{1}\rightarrow\pi_{n+4}(A)i\rightarrow\pi_{n+4}(A, S^{  ... 
doi:10.3836/tjm/1270043220 fatcat:uupmf5x5rngl5d2cpkte5tjeue

Lifting Theorems and Smooth Profinite Groups [article]

C. De Clercq, M. Florence
2017 arXiv   pre-print
If moreover the field k is finite, Omega powers are endowed with a striking extra operation: the Transfer, to shifted Omega powers of finite-codimensional linear subspaces.  ...  We then define the notion of exact sequences of G-modules of Kummer type. To finish, we give applications of this formalism.  ...  Acknowledgements We are grateful to Patrick Brosnan for his support, and for spotting a mistake in the last part of the previous version of this paper, one year ago.  ... 
arXiv:1710.10631v1 fatcat:qpzybudmofbzbpdjl6xjn3ocpq

Page 3624 of Mathematical Reviews Vol. , Issue 89G [page]

1989 Mathematical Reviews  
Just as in the proof of the finite developments theorem in an earlier paper of ours [J.  ...  To facilitate comparison with existing proofs 03 MATHEMATICAL LOGIC AND FOUNDATIONS 3624 (i.e. for systems without surjective pairing), we work with the sys- tem N-HA?  ... 

Clebsch parameterization: Basic properties and remarks on its applications

Z. Yoshida
2009 Journal of Mathematical Physics  
The Clebsch parameterization $(u=\nabla\varphi+\alpha\nabla\beta)$ has advantages in elucidating structural properties of vector fields; for example, it helps formulating the Hamiltonian form of ideal  ...  fluid mechanics, representing topological constraints (Casimir invariants), integrating the Cauchy characteristics of vortex fields, etc.  ...  Thus the claim that $\omega\in$ $\mathcal{W}^{(1)}(\Omega)$ implies that every exact contravariant vector (2-form) can be cast in a Clebsch 2-form, contradicting Theorem 1.  ... 
doi:10.1063/1.3256125 fatcat:envcwr34hbgddfovt37fet77gy

On group theoretical Hopf algebras and exact factorization of finite groups [article]

Sonia Natale
2002 arXiv   pre-print
We also describe their Drinfeld double as a twisting of D^omega(Sigma), for an appropriate 3-cocycle omega coming from the Kac exact sequence.  ...  We show that a semisimple Hopf algebra A is group theoretical if and only if its Drinfeld double is a twisting of the Dijkgraaf-Pasquier-Roche quasi-Hopf algebra D^omega(Sigma), for some finite group Sigma  ...  We follow the lines of the method in [2] . for all x, y ∈ F , and for all homogeneous v ∈ V , where |v| denotes the degree of homogeneity of v ∈ V .  ... 
arXiv:math/0208054v1 fatcat:4ngjyp63lvcm5c2ne3yjlvh5am
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