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Moments of Uniform Random Multigraphs with Fixed Degree Sequences

2020
*
SIAM Journal on Mathematics of Data Science
*

We study

doi:10.1137/19m1288772
fatcat:sqpg5kntafgbpk6berbeb6qls4
*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. ...##
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How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?
[article]

2013
*
arXiv
*
pre-print

It has long been known that any Boolean function that depends on n input variables has both

arXiv:1206.0717v2
fatcat:65tbomget5gzpfcgqq7dqyhrfe
*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. ...##
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Wadge Degrees of Infinitary Rational Relations

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. ...

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

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. ...

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

1998
*
Journal of the Mathematical Society of Japan
*

First

doi:10.2969/jmsj/05040879
fatcat:qeuxd7hxbredhnwvcwhsydebge
*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. ...##
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A Regularity Lemma, and Low-Weight Approximators, for Low-Degree Polynomial Threshold Functions

2010
*
2010 IEEE 25th Annual Conference on Computational Complexity
*

We give a "regularity lemma"

doi:10.1109/ccc.2010.28
dblp:conf/coco/DiakonikolasSTW10
fatcat:2bbdzaxqkzcl3e2fqsczurscay
*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. ...##
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Molecular Friction in Dilute Gases. II. Thermal Relaxation of Translational and Rotational Degrees of Freedom

1961
*
Journal of Chemical Physics
*

This means that

doi:10.1063/1.1732206
fatcat:y3jb2gpwjvbwtlluzsiuvyspbi
*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 ...##
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Exact side effects for interprocedural dependence analysis

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. ...

##
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Deformations of transversely symplectic and transversely contact foliations

1991
*
Tsukuba Journal of Mathematics
*

a strong versality

doi:10.21099/tkbjm/1496161671
fatcat:klhj2qsk45ctvg6xwk3qz3md4i
*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 $H^{2}(CP^{2n+1}, \Theta_{\*omega*})$ . ...##
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A construction of an automorphic sheaf for GLr on the moduli space of parabolic structures

1999
*
Proceedings of the Symposium on Representation Theory
*

Finally, we give an estimate

doi:10.34508/repsympo.1999.0_15
fatcat:2wl6wpufzfft3mgyo6ngvgjrhm
*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_{ ...##
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Homologically Trivial Self-Maps

1996
*
Tokyo Journal of Mathematics
*

also homotopically trivial. (2) $IfSq^{2}(e^{n})=0andSq^{2}(e^{n+2})\neq 0(n\geqq 4)$ , then

doi:10.3836/tjm/1270043220
fatcat:uupmf5x5rngl5d2cpkte5tjeue
*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^{ ...##
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Lifting Theorems and Smooth Profinite Groups
[article]

2017
*
arXiv
*
pre-print

If moreover

arXiv:1710.10631v1
fatcat:qpzybudmofbzbpdjl6xjn3ocpq
*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. ...##
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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? ...##
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Clebsch parameterization: Basic properties and remarks on its applications

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. ...

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

2002
*
arXiv
*
pre-print

We also describe their Drinfeld double as a twisting of D^

arXiv:math/0208054v1
fatcat:4ngjyp63lvcm5c2ne3yjlvh5am
*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 . ...
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