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Oriented two-dimensional circuits

A.K. Dewdney, Frank Harary
1981 Discrete Mathematics  
%oato@&rath~r than top@@cal lines; when an n-circuit is defined for oriented ~~plex&s *as a. %ruc@re achieved .by a certain minimization process?  ...  The natural generalization of a direted graph is an oriented cxxnp& a fuildamental concept in algebraic topology. Our..study of such qmiplms foIlq*s comt.  ...  A complex K is constructed from two complexes 1ik.e I.+ and the required oriented 't-circuit is then defined.  ... 
doi:10.1016/0012-365x(81)90162-x fatcat:5p5mfs7tqjdyhp27m4uxvgph5u

Design-Oriented Two-Stage Surrogate Modeling of Miniaturized Microstrip Circuits with Dimensionality Reduction

Slawomir Koziel, Anna Pietrenko-Dabrowska, Muath Al-Hasan
2020 IEEE Access  
INDEX TERMS Microwave design, compact circuits, surrogate modeling, domain confinement, principal component analysis, dimensionality reduction.  ...  Notwithstanding, a construction of approximation models for microwave components is hindered by the dimensionality issues as well as high nonlinearity of system characteristics.  ...  The visualization is provided assuming three-dimensional parameter space and two-dimensional objective space (cf.  ... 
doi:10.1109/access.2020.3006708 fatcat:mut5vvrzobc4hcnnlbydps2pda

Geometric Structure behind Duality and Manifestation of Self-Duality from Electrical Circuits to Metamaterials

Nakata, Urade, Nakanishi
2019 Symmetry  
In electromagnetic systems, duality is manifested in various forms: circuit, Keller–Dykhne, electromagnetic, and Babinet dualities.  ...  Figure 12 . 12 Outer-oriented components of an inner-oriented edge in a two-dimensional plane.  ...  Figure 7 . 7 Two types of orientation: (a) inner and (b) outer orientation of a surface in a three-dimensional space.  ... 
doi:10.3390/sym11111336 fatcat:mpuwegonxrafbdxozbzwonumvu

Page 540 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 25, Issue 4 [page]

1923 American Mathematical Society. Transactions of the American Mathematical Society  
7,-; when both are immersed in an n-dimensional oriented manifold.  ...  With certain conventions as to sign this number represents the excess of the number of positive over the number of negative intersections of a k-dimensional circuit 7, with an (n—)-dimensional circuit  ... 

Nearly tight bounds on the number of Hamiltonian circuits of the hypercube and generalizations

Tomás Feder, Carlos Subi
2009 Information Processing Letters  
As a consequence, if M d is the number of perfect matchings and H d is the number of Hamiltonian circuits of the d-dimensional hypercube, then M 4 d−2 ≤ H d ≤ M 2 d /4.  ...  We conjecture that for every perfect matching M of the d-dimensional n-vertex hypercube, d ≥ 2, there exists a second perfect matching M such that the union of M and M forms a Hamiltonian circuit of the  ...  For Hamiltonian circuits, the bound follows by choosing M 1 and M 2 forming the circuit in the two possible orders and dividing by two.  ... 
doi:10.1016/j.ipl.2008.10.015 fatcat:nswhoqrmcffknfaetcsjonc2ge

The Intersection Numbers

Oswald Veblen
1923 Transactions of the American Mathematical Society  
r"_fc when both are immersed in an n-dimensional oriented manifold.  ...  following two conventions will be followed: (1) if Ao Ax • • • Ak denotes a given oriented Zc-cell (k = 1,2, ..., n) any even permutation of A9 Ax ••• Ak denotes the same oriented ft-cell and any odd  ...  ¿=i It should be observed that these formulas cannot be obtained by reducing the formulas of § 10, modulo 2, because the formulas of the present section take account of non-orientable circuits which do  ... 
doi:10.2307/1989306 fatcat:ayzeirmqcbesziuiv24naomfwu

The intersection numbers

Oswald Veblen
1923 Transactions of the American Mathematical Society  
r"_fc when both are immersed in an n-dimensional oriented manifold.  ...  following two conventions will be followed: (1) if Ao Ax • • • Ak denotes a given oriented Zc-cell (k = 1,2, ..., n) any even permutation of A9 Ax ••• Ak denotes the same oriented ft-cell and any odd  ...  ¿=i It should be observed that these formulas cannot be obtained by reducing the formulas of § 10, modulo 2, because the formulas of the present section take account of non-orientable circuits which do  ... 
doi:10.1090/s0002-9947-1923-1501259-6 fatcat:sc6r23iu3na2bda5bd23wopexe

Evaluation of Hardware Oriented MRCoHOG using Logic Simulation

Yuta Yamasaki, Shiryu Ooe, Akihiro Suzuki, Kazuhiro Kuno, Hideo Yamada, Shuichi Enokida, Hakaru Tamukoh
2017 Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications  
In this paper, a hardware oriented MRCoHOG is proposed.  ...  Moreover, MRCoHOG is implemented in a digital circuit with the proposed method.  ...  Figure 2 : 2 Two-dimensional histogram on CoHOG. Figure 3 : 3 Two-dimensional histogram on MRCoHOG.  ... 
doi:10.5220/0006165803410345 dblp:conf/visapp/YamasakiOSKYET17 fatcat:zsnctyy5wfgabdxrych3oftrka

Partitions of Points into Simplices withk-dimensional Intersection. Part II: Proof of Reay's Conjecture in Dimensions 4 and 5

Jean-Pierre Roudneff
2001 European journal of combinatorics (Print)  
. , X m such that m i=1 conv X i is at least k-dimensional. Using the tools developed in [13] and oriented matroid theory, we prove this conjecture for d = 4 and d = 5.  ...  How about, to that end, we introduce the notion of a k-lopsided oriented matroid and we characterize these combinatorial objects for certain values of k.  ...  Case 3. k = 3. 4-positive independence and two-dimensional intersection now imply |S i | + |S j | ≥ 8 for all i = j, hence |S i | = 4 for all i.  ... 
doi:10.1006/eujc.2000.0494 fatcat:emh2rufztvg5jcgahfdbefltby

On Embedding a Qualitative Representation in a Two-Dimensional Plane

Kazuko Takahashi, Takao Sumitomo, Izumi Takeuti
2008 Spatial Cognition and Computation  
This paper discusses embedding in a two-dimensional plane a symbolic representation for spatial data using the simple objects, points(P ), lines(L), circuits(C) and areas(A).  ...  We also give an algorithm for drawing the figure of the PLCA expression that satisfies this condition in a two-dimensional plane and prove its correctness.  ...  = {c 0 } a 1 .circuits = {c 1 } a 2 .circuits = {c 2 , c 3 } Orientation of a Circuit Each circuit of a planar PLCA expression e has an orientation of inner or outer.  ... 
doi:10.1080/13875860801944887 fatcat:w26ux7dxqvcx7b3wh34urwmbne

Design and Application of a NEW Seven-Dimensional Hyperchaotic System

Duanzeng Liu, Jianliang Zhu, Hao Sun
2014 International Journal of Control and Automation  
Because the chaotic characteristics of the hyperchaotic system is more complex, so design a higher dimensional hyperchaotic system has become a new orientation of the chaos theory research.  ...  This article also design the realizing hardware circuit and do its simulation with Multisim.  ...  MATLAB simulation results System (1) has two-dimensional and three-dimensional attractors.  ... 
doi:10.14257/ijca.2014.7.4.35 fatcat:xymlz5tn3zflpgddt5xbzw5pdq

Analysis of self-equilibrated networks through cellular modeling [article]

Omar Aloui, David Orden, Nizar Bel Hadj Ali, Landolf Rhode-Barbarigos
2020 arXiv   pre-print
For instance, in DC electrical circuits (which correspond to one-dimensional networks), flow orientation is set by convention from higher voltage to lower voltage (negative potential difference).  ...  They showed that the flow densities of the cells in two dimensions and three dimensions can be obtained through the product of the signed volume of two specific oriented two-simplices and three-simplices  ...  The flow associated to the circuit is defined by: Elementary circuits represent cycles in graph theory: closed paths where every vertex has exactly two neighbors.  ... 
arXiv:2008.04570v1 fatcat:g4xyd4n7kjb75dcp6qorjr26l4

Page 156 of Annals of Mathematics Vol. 23, Issue [page]

1921 Annals of Mathematics  
It is easily seen that in a homology the right and left sides together constitute the boundary of an oriented two- dimensional manifold though not in general a 2-cell.  ...  It is easily seen that in a homology (mod 2 the right and left sides constitute the boundary of a two-dimensional manifold which need not be oriented. (See Veblen, loc. cit., Chap. II, § 37.  ... 

On the existence of electrical networks

C. E. Clark
1941 Bulletin of the American Mathematical Society  
A circuit of a network is a topological circle of the network together with an orientation of this circle. Let two circuits d and Cy have the branches fry, p -\, 2, • • • , in common.  ...  We break Ci at one of its vertices A and insert two branches bi and b between the two ends A\ and -4 2 of the broken circuit.  ...  A circuit of a network is a topological circle of the network together with an orientation of this circle. Let two circuits d and Cy have the branches fry, p -\, 2, • • • , in common.  ... 
doi:10.1090/s0002-9904-1941-07563-4 fatcat:yi7vev5gqvfkhnvbow5u2cxr6u

A Naive-Bayes-based fault diagnosis approach for analog circuit by using image-oriented feature extraction and selection technique

Wei He, Yigang He, Bing Li, Chaolong Zhang
2019 IEEE Access  
Second, the local optimal-oriented pattern is applied to all the XWT spectrum images to generate the original high-dimensional feature set.  ...  The simulation results on two typical circuits have demonstrated that the proposed method is a promising means to detect and classify most analog circuit faults, achieving a better diagnosis accuracy than  ...  Various projection approaches are commonly utilized in obtaining features of matrices such as two direction two dimensional linear discriminative analysis (TD2DLDA) [18] , two-dimensional non-negative  ... 
doi:10.1109/access.2018.2888950 fatcat:fxpe5ltnbjhf7lp4c2icof3diq
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