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Zero-Parity Stabbing Information

Joseph O'Rourke, Irena Pashchenko
1999 arXiv   pre-print
In the same spirit, we define the "zero-parity (ZP) stabbing information" to be a natural weakening of their "weak stabbing information," retaining only the distinction among zero, odd, even>0 in the number  ...  Whereas the weak stabbing information's relation to visibility remains an open problem, we completely settle the analogous questions for zero-parity information, with three results: (1) ZP information  ...  And it remains unclear what additional information is gained by having the absolute stabbing numbers rather than only their zero-parity information. ied, but the relationship between this graph and the  ... 
arXiv:cs/9906022v1 fatcat:gldpby4ugvb5bkhex75cubliqm

Stabbing information of a simple polygon

Hazel Everett, Ferran Hurtado, Marc Noy
1999 Discrete Applied Mathematics  
In fact, we define three variations of the stabbing information. strong. weak and labelled, and explore the relationships among them.  ...  We also show that the labelled stabbing information is equivalent to the order type. We give algorithms for computing each of these new structures. 0  ...  Fig. 6 shows that strong stabbing information is not determined by weak stabbing information. Fig. 7 shows that labelled stabbing information is not determined by strong stabbing information.  ... 
doi:10.1016/s0166-218x(98)00144-9 fatcat:wlfblwu2qrbazkzy32sv257jwa

Avoiding coherent errors with rotated concatenated stabilizer codes

Yingkai Ouyang
2021 npj Quantum Information  
The ultimate goal in QEC is to protect quantum information under realistic noise models.  ...  When b a = 1 and the other syndrome bits are zero, an AD error must have occurred on either the (2a − 1)th or the (2a)th qubit.  ...  ADDITIONAL INFORMATION Correspondence and requests for materials should be addressed to Y.O.  ... 
doi:10.1038/s41534-021-00429-8 fatcat:vykagyn2qze2ncvq2owjkgc4ry

Avoiding coherent errors with rotated concatenated stabilizer codes [article]

Yingkai Ouyang
2020 arXiv   pre-print
The ultimate goal in QEC is to protect quantum information under realistic noise models.  ...  When λ approaches zero, the advantage of CE codes becomes most pronounced. V.  ...  If the parity of the first and second qubit is odd, while the parity of the remaining blocks is even, then we can ascertain that either K 1 or K 2 has occured. 3.  ... 
arXiv:2010.00538v1 fatcat:cr6q6dsrwfh2vhxg5erexwwraq

Multipartite Nonlocality in Clifford Networks [article]

Amanda Gatto Lamas, Eric Chitambar
2022 arXiv   pre-print
It is interesting to investigate whether Clifford quantum information processing has similar limitations for other quantum information tasks and phenomena, such as the emergence of quantum nonlocality.  ...  Observe that the parity check on any marginal of P is also in the set of parity checks of P.  ... 
arXiv:2208.04731v4 fatcat:irgnmzkuefgshgyddr24h7ahqi

Simplification and repair of polygonal models using volumetric techniques

F.S. Nooruddin, G. Turk
2003 IEEE Transactions on Visualization and Computer Graphics  
TABLE 1 This 1 Table Summarizes the Types of Degeneracies that the Ray-Stabbing and Parity-Count Methods Are Able to Fix TABLE 2 This 2 Table Shows the Timing Information for Each Stage of Our Simplification  ...  In this section, we present two new methods of voxelization, the parity-count and the ray-stabbing methods.  ... 
doi:10.1109/tvcg.2003.1196006 fatcat:ul2z4uuet5fknpyqv4tn7ynlse

Constraining Saturn's interior with ring seismology: effects of differential rotation and stable stratification [article]

Janosz W. Dewberry, Christopher R. Mankovich, Jim Fuller, Dong Lai, Wenrui Xu
2021 arXiv   pre-print
Finally, we find that including realistic equatorial antisymmetry in Saturn's differential rotation profile couples modes with even and odd equatorial parity, producing oscillations that could in principle  ...  Our model with r stab = 0.72R S does exhibit parity-mixing between the sectoral m = 3 f mode and an odd-parity, ∼ 18 g mode (along with a simultaneous coupling with an even-parity, ∼ 11 g mode).  ...  Figure 10 , but for our fiducial model with r stab = 0.70RS, for which the frequency of the m = 3, ∼ 4, n = 2 g mode (with odd equatorial parity) falls close to that of the sectoral m = 3 f mode.  ... 
arXiv:2106.07659v3 fatcat:7dre4svw4rhkzgyuocp6n6cu3m

Parities on 2-knots and 2-links [article]

Denis A. Fedoseev, Vassily O. Manturov
2016 arXiv   pre-print
By using parity new invariants are constructed and known invariants are refined.  ...  The notion of parity is introduced via techniques similar to the ones used by the second named author in 1-dimensional case.  ...  is zero in the group G.  ... 
arXiv:1606.06947v1 fatcat:tygkv7xxbzgxbjls22mh3wfjh4

Choiceless Polynomial Time, Symmetric Circuits and Cai-Fürer-Immerman Graphs [article]

Benedikt Pago
2021 arXiv   pre-print
Instead, the second entry of each triple in every τ -object now contains the relevant parity information.  ...  The kernel of χ({e}) T is the set of all vectors in F E 2 which are zero at index e. This is precisely Stab E (e 0 ) = Stab E (e 1 ), as desired.  ...  . • Else, if WaitingForReturn is true, then: from the output of gate h (which is possible by storing auxiliary information in the implementation).  ... 
arXiv:2107.03778v1 fatcat:5wuqyd46yrfv5d64ko3jvadsze

A Class of Quantum LDPC Codes Constructed From Finite Geometries

Salah A. Aly
2008 IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference  
Low-density parity check (LDPC) codes are a significant class of classical codes with many applications.  ...  The parity check matrices of these codes are adapted to be self-orthogonal with containing only one cycle of length four.  ...  Furthermore, S stab is constructed from a binary selforthogonal parity check matrix H orth EG,ℓ of size k × n.  ... 
doi:10.1109/glocom.2008.ecp.217 dblp:conf/globecom/Aly08 fatcat:aqmr45qmkzhhvfr42mdmuwg6qy

Generating the spin mapping class group by Dehn twists [article]

Ursula Hamenstädt
2021 arXiv   pre-print
Structure of the spin mapping class group of odd parity The goal of this section is to prove the first part of Theorem 3. We begin with some additional information on the spin mapping class group.  ...  If r is even then this spin structure has a parity, and this parity is odd.  ... 
arXiv:2002.08213v3 fatcat:5pytatz7hzf6jcofqwxvf7x5ye

Generating the spin mapping class group by Dehn twists

Ursula Hamenstädt
2021 Annales Henri Lebesgue  
-The Z/2Z-spin structure φ on S induces a Z/2Z-spin structure φ c on Σ whose parity coincides with the parity of φ. If Π : Stab(c)/Z → Mod(Σ) TOME 4 (2021) Proposition 3.4.  ...  If r is even then this spin structure has a parity, and this parity is odd.  ... 
doi:10.5802/ahl.112 fatcat:z3jppji6vbconktr4mybwdhtbm

Some topics in analysis of boolean functions

Ryan O'Donnell
2008 Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08  
Parity is the next easiest function to consider: using Fact 3.10 and the fact that Parity has all its weight on the set [n], we get that Stab 1−2 (Parity) = (1 − 2 ) n .  ...  Having zero bias is probably a necessary (but not sufficient) condition for a voting rule f to seem "fair".  ... 
doi:10.1145/1374376.1374458 dblp:conf/stoc/ODonnell08 fatcat:xhmjfdb5czbs5kew5obgpkxpnm

Dimensions of Some Binary Codes Arising From A Conic in PG(2,q) [article]

Peter Sin, Junhua Wu, Qing Xiang
2009 arXiv   pre-print
The incidence matrices between the secant/passant lines and the external/internal points were used in keith1 to produce several classes of structured low-density parity-check binary codes.  ...  In the following lemmas, we investigate the parity of |H P,Q ∩ C| for any two external points P and Q. This information will be used in the proof of Lemma 7.1. Proof: Part (i) is obvious.  ...  Let B be a 2-block of defect zero of H.  ... 
arXiv:0911.2018v1 fatcat:qissstvervbvzgshmrxcd4sxmm

Shellability, Ehrhart Theory, and r-stable Hypersimplices [article]

Benjamin Braun, Liam Solus
2016 arXiv   pre-print
This vector encodes useful information about the polytope P. For example, vol(P) = i h * i d!  ...  Hence, the h * -polynomial of the relative interior of ∆ stab(r) n,2 stab(r) • n,2 ; x +x n , where ∆ stab(r) • n,2 stab(r) n,2 stab(r) n,2 Notice that the result given by this subtractive  ... 
arXiv:1408.4713v3 fatcat:ocz3z5llnnfpznm4lqteaban6m
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