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Journal articles on the topic 'Simplicial map'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Po�naru, V. "nondegenerate simplicial map." Duke Mathematical Journal 63, no. 2 (1991): 421–29. http://dx.doi.org/10.1215/s0012-7094-91-06318-0.

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Paluzo-Hidalgo, Eduardo, Rocio Gonzalez-Diaz, Miguel A. Gutiérrez-Naranjo, and Jónathan Heras. "Optimizing the Simplicial-Map Neural Network Architecture." Journal of Imaging 7, no. 9 (2021): 173. http://dx.doi.org/10.3390/jimaging7090173.

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Simplicial-map neural networks are a recent neural network architecture induced by simplicial maps defined between simplicial complexes. It has been proved that simplicial-map neural networks are universal approximators and that they can be refined to be robust to adversarial attacks. In this paper, the refinement toward robustness is optimized by reducing the number of simplices (i.e., nodes) needed. We have shown experimentally that such a refined neural network is equivalent to the original network as a classification tool but requires much less storage.

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Paluzo-Hidalgo, Eduardo, Rocio Gonzalez-Diaz, Miguel A. Gutiérrez-Naranjo, and Jónathan Heras. "Simplicial-Map Neural Networks Robust to Adversarial Examples." Mathematics 9, no. 2 (2021): 169. http://dx.doi.org/10.3390/math9020169.

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Broadly speaking, an adversarial example against a classification model occurs when a small perturbation on an input data point produces a change on the output label assigned by the model. Such adversarial examples represent a weakness for the safety of neural network applications, and many different solutions have been proposed for minimizing their effects. In this paper, we propose a new approach by means of a family of neural networks called simplicial-map neural networks constructed from an Algebraic Topology perspective. Our proposal is based on three main ideas. Firstly, given a classifi

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Dupont, Johan L., and Rune Ljungmann. "Integration of simplicial forms and Deligne cohomology." MATHEMATICA SCANDINAVICA 97, no. 1 (2005): 11. http://dx.doi.org/10.7146/math.scand.a-14961.

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We present two approaches to constructing an integration map along the fiber for smooth Deligne cohomology. The first is defined in the simplicial model, where a class in Deligne cohomology is represented by a simplicial form, and the second in a related but more combinatorial model .

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Jardine, J. F. "Model structures for pro-simplicial presheaves." Journal of K-theory 7, no. 3 (2011): 499–525. http://dx.doi.org/10.1017/is011003012jkt149.

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AbstractThis paper displays model structures for the category of pro-objects in simplicial presheaves on an arbitrary small Grothendieck site. The first of these is an analogue of the Edwards-Hastings model structure for pro-simplicial sets, in which the cofibrations are monomorphisms and the weak equivalences are specified by comparisons of function complexes. Other model structures are built from the Edwards-Hastings structure by using Bousfield-Friedlander localization techniques. There is, in particular, an n-type structure for pro-simplicial presheaves, and also a model structure in which

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Scoville, Nicholas A., and Willie Swei. "On the Lusternik–Schnirelmann category of a simplicial map." Topology and its Applications 216 (February 2017): 116–28. http://dx.doi.org/10.1016/j.topol.2016.11.015.

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7

Robbin, Joel W., and Dietmar A. Salamon. "Lyapunov maps, simplicial complexes and the Stone functor." Ergodic Theory and Dynamical Systems 12, no. 1 (1992): 153–83. http://dx.doi.org/10.1017/s0143385700006647.

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AbstractLet be an attractor network for a dynamical system ft: M → M, indexed by the lower sets of a partially ordered set P. Our main theorem asserts the existence of a Lyapunov map ψ:M → K(P) which defines the attractor network. This result is used to prove the existence of connection matrices for discrete-time dynamical systems.

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Saneblidze, Samson. "On the construction of a covering map." Georgian Mathematical Journal 26, no. 2 (2019): 303–9. http://dx.doi.org/10.1515/gmj-2019-2016.

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Abstract Let {Y=\lvert X\rvert} be the geometric realization of a path-connected simplicial set X, and let {G=\pi_{1}(X)} be the fundamental group. Given a subgroup {H\subset G} , let {G/H} be the set of cosets. Using the combinatorial model {\boldsymbol{\Omega}X\to\mathbf{P}X\to X} of the path fibration {{\Omega}Y\to{P}Y\to Y} and a canonical action {\mu\colon\boldsymbol{\Omega}X\times G/H\to G/H} , we construct a covering map {G/H\to Y_{H}\to Y} as the geometric realization of the associated short sequence {G/H\to\mathbf{P}X\times_{\mu}G/H\to X} . This construction, in particular, does not u

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Saliieva, Olha, and Yurii Yaremchuk. "INVESTIGATION OF CHANGES IN THE LEVEL OF NETWORK SECURITY BASED ON A COGNITIVE APPROACH." Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska 14, no. 4 (2024): 82–85. https://doi.org/10.35784/iapgos.6719.

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A study was conducted on the impact of the most significant threats on the level of network security based on the examination of impulse processes on a fuzzy cognitive map. A topological analysis of the structure of the cognitive map was performed, simplicial complexes were constructed, and their structural vectors were determined. Based on the obtained data, a set of control and target concepts of the fuzzy cognitive map was formed, and the relationships between these concepts within the simplicial complexes were established. Taking this information into account, a study was conducted on the

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10

Batko, Bogdan, Tomasz Kaczynski, Marian Mrozek, and Thomas Wanner. "Linking Combinatorial and Classical Dynamics: Conley Index and Morse Decompositions." Foundations of Computational Mathematics 20, no. 5 (2020): 967–1012. http://dx.doi.org/10.1007/s10208-020-09444-1.

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Abstract We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a multivalued dynamical system F on the geometric realization of the simplicial complex. Moreover, F may be chosen in such a way that the isolated invariant sets, Conley indices, Morse decompositions and Conley–Morse graphs of the combinatorial vector field give rise to isomorphic objects in the multivalued map case.

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11

Wagner, Uli, and Pascal Wild. "Coboundary expansion, equivariant overlap, and crossing numbers of simplicial complexes." Israel Journal of Mathematics 256, no. 2 (2023): 675–717. http://dx.doi.org/10.1007/s11856-023-2521-9.

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AbstractWe prove the following quantitative Borsuk–Ulam-type result (an equivariant analogue of Gromov’s Topological Overlap Theorem): Let X be a free ℤ/2-complex of dimension d with coboundary expansion at least ηk in dimension 0 ≤ k < d. Then for every equivariant map F: X →ℤ/2 ℝd, the fraction of d-simplices σ of X with 0 ∈ F (σ) is at least 2−d Π k=0 d−1 ηk.As an application, we show that for every sufficiently thick d-dimensional spherical building Y and every map f: Y → ℝ2d, we have f(σ) ∩ f(τ) ≠ ∅ for a constant fraction μd > 0 of pairs {σ, τ} of d-simplices of Y. In particular, s

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Glass, Cheyne, Micah Miller, Thomas Tradler, and Mahmoud Zeinalian. "The Hodge Chern character of holomorphic connections as a map of simplicial presheaves." Algebraic & Geometric Topology 22, no. 3 (2022): 1057–112. http://dx.doi.org/10.2140/agt.2022.22.1057.

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Cardim, Nancy de Souza, and Mário Olivero Marques da Silva. "AN ISOTOPY EXTENSION ON OPEN MANIFOLDS." JP Journal of Geometry and Topology 32, no. 2 (2024): 131–41. https://doi.org/10.17654/0972415x24009.

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Let be a compact topological manifold of , with connected boundary . Let be the simplicial group of homeomorphisms and denote the interior of by Int . Let Int be the restriction map and let be the homotopy fiber of over the . We proved that is isomorphic to , where is the concordance space of .

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14

Elvira-Donazar, Carmen, and Luis-Javier Hernandez-Paricio. "Closed model categories for the n-type of spaces and simplicial sets." Mathematical Proceedings of the Cambridge Philosophical Society 118, no. 1 (1995): 93–103. http://dx.doi.org/10.1017/s0305004100073485.

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AbstractFor each integer n ≥ 0, we give a distinct closed model category structure to the categories of spaces and of simplicial sets. Recall that a non-empty map is said to be a weak equivalence if it induces isomorphisms on the homotopy groups for any choice of base point. Putting the condition on dimensions ≥ n, we have the notion of a weak n-equivalence which is at the base of the nth closed model category structure given here.

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Akyar, B., and J. L. Dupont. "Lattice gauge field theory and prismatic sets." MATHEMATICA SCANDINAVICA 108, no. 1 (2011): 26. http://dx.doi.org/10.7146/math.scand.a-15159.

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We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set $S$ and the prismatic star of $S$. Both have the same homotopy type as $S$ and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group $G$ and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the

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16

Lyzzaik, Abdallah. "The geometry of open continuous mappings having two valences between Riemann surfaces." Mathematical Proceedings of the Cambridge Philosophical Society 120, no. 2 (1996): 309–29. http://dx.doi.org/10.1017/s0305004100074879.

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AbstractAn open continuous function from an open Riemann surface with finite genus and finite number of boundary components into a closed Riemann surface is termed a (p, q)-map, 0 < q < p, if it has a finite number of branch points and assumes every point in the image surface either p or q times, counting multiplicity, with possibly a finite number of exceptions.The object of this paper is to prove that the geometry of any (p, q)-map resembles that of a (p, q)-map whose q-set (the set of image points of f that are taken on exactly q times, counting multiplicity), constitutes a finite set

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17

Bura, Andrei, Qijun He, and Christian Reidys. "Weighted Homology of Bi-Structures over Certain Discrete Valuation Rings." Mathematics 9, no. 7 (2021): 744. http://dx.doi.org/10.3390/math9070744.

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An RNA bi-structure is a pair of RNA secondary structures that are considered as arc-diagrams. We present a novel weighted homology theory for RNA bi-structures, which was obtained through the intersections of loops. The weighted homology of the intersection complex X features a new boundary operator and is formulated over a discrete valuation ring, R. We establish basic properties of the weighted complex and show how to deform it in order to eliminate any 3-simplices. We connect the simplicial homology, Hi(X), and weighted homology, Hi,R(X), in two ways: first, via chain maps, and second, via

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Pavutnitskiy, Fedor, and Jie Wu. "A simplicial James–Hopf map and decompositions of the unstable Adams spectral sequence for suspensions." Algebraic & Geometric Topology 19, no. 1 (2019): 77–108. http://dx.doi.org/10.2140/agt.2019.19.77.

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19

Forssell, Henrik, Håkon Robbestad Gylterud, and David I. Spivak. "Type theoretical databases." Journal of Logic and Computation 30, no. 1 (2020): 217–38. http://dx.doi.org/10.1093/logcom/exaa009.

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Abstract We show how the display-map category of finite (symmetric) simplicial complexes can be seen as representing the totality of database schemas and instances in a single mathematical structure. We give a sound interpretation of a certain dependent type theory in this model and show how it allows for the syntactic specification of schemas and instances and the manipulation of the same with the usual type-theoretic operations.

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AGISHTEIN, M. E., and A. A. MIGDAL. "SIMULATIONS OF FOUR-DIMENSIONAL SIMPLICIAL QUANTUM GRAVITY AS DYNAMICAL TRIANGULATION." Modern Physics Letters A 07, no. 12 (1992): 1039–61. http://dx.doi.org/10.1142/s0217732392000938.

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Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. We studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: we reached about 5×104 simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model sh

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Otera, Daniele. "Double points and universal covers." Filomat 36, no. 4 (2022): 1171–77. http://dx.doi.org/10.2298/fil2204171o.

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In this note we study the double points set of a particular covering map of an open manifold, and we present a new procedure for building universal covering spaces of such manifolds. This is done by means of an arborescent construction, starting from a presentation of the manifold as a non-compact simplicial complex with pairwise identified faces. The proof uses the so-called ?zipping theory? of Po?naru which helps the understanding of the topology of the quotient manifold resulted from the combinatorial presentation.

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22

del Hoyo, Matias, and Rui Loja Fernandes. "Riemannian metrics on Lie groupoids." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 735 (2018): 143–73. http://dx.doi.org/10.1515/crelle-2015-0018.

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AbstractWe introduce a notion of metric on a Lie groupoid, compatible with multiplication, and we study its properties. We show that many families of Lie groupoids admit such metrics, including the important class of proper Lie groupoids. The exponential map of these metrics allows us to establish a linearization theorem for Riemannian groupoids, obtaining both a simpler proof and a stronger version of the Weinstein–Zung linearization theorem for proper Lie groupoids. This new notion of metric has a simplicial nature which will be explored in future papers of this series.

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ARAMAYONA, JAVIER, and CHRISTOPHER J. LEININGER. "FINITE RIGID SETS IN CURVE COMPLEXES." Journal of Topology and Analysis 05, no. 02 (2013): 183–203. http://dx.doi.org/10.1142/s1793525313500076.

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We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex 𝔛 of the curve complex [Formula: see text] such that every locally injective simplicial map [Formula: see text] is the restriction of an element of [Formula: see text], unique up to the (finite) pointwise stabilizer of 𝔛 in [Formula: see text]. Furthermore, if S is not a twice-punctured torus, then we can replace [Formula: see text] in this statement with the extended mapping class group Mod ±(S).

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24

Hinderink, Steffen, and Marcel Campen. "Galaxy Maps: Localized Foliations for Bijective Volumetric Mapping." ACM Transactions on Graphics 42, no. 4 (2023): 1–16. http://dx.doi.org/10.1145/3592410.

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A method is presented to compute volumetric maps and parametrizations of objects over 3D domains. As a key feature, continuity and bijectivity are ensured by construction. Arbitrary objects of ball topology, represented as tetrahedral meshes, are supported. Arbitrary convex as well as star-shaped domains are supported. Full control over the boundary mapping is provided. The method is based on the technique of simplicial foliations, generalized to a broader class of domain shapes and applied adaptively in a novel localized manner. This increases flexibility as well as efficiency over the state

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Daverman, R. J., and D. Repovš. "General Position Properties That Characterize 3-Manifolds." Canadian Journal of Mathematics 44, no. 2 (1992): 234–51. http://dx.doi.org/10.4153/cjm-1992-016-x.

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AbstractThis paper defines three simplicial approximation properties for maps of 2-cells and 2-spheres into spaces, each providing homotopical tameness conditions on the approximating images. These are the general position properties used in the two main results. The first shows that a resolvable generalized 3-manifold is a genuine 3- manifold if and only if it has the weakest of these approximation properties as well as a mild 3-dimensional disjoint disks condition known as the Light Map Separation Property. The second shows a resolvable generalized 3-manifold to be a 3-manifold if and only i

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Kewat, Pramod Kumar, and Nilay Kumar Mondal. "Two classes of few-Lee weight Z2[u]-linear codes using simplicial complexes and minimal codes via Gray map." Discrete Mathematics 346, no. 12 (2023): 113650. http://dx.doi.org/10.1016/j.disc.2023.113650.

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Stammeier, Nicolai. "The nature of generalized scales." International Journal of Algebra and Computation 29, no. 06 (2019): 1035–62. http://dx.doi.org/10.1142/s0218196719500401.

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The notion of a generalized scale emerged in recent joint work with Afsar–Brownlowe–Larsen on equilibrium states on [Formula: see text]-algebras of right Least Common Multiple (LCM) monoids, where it features as the key datum for the dynamics under investigation. This work provides the structure theory for such monoidal homomorphisms. We establish the uniqueness of the generalized scale and characterize its existence in terms of a simplicial graph arising from a new notion of irreducibility inside right LCM monoids. In addition, the method yields an explicit construction of the generalized sca

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Mahadevan, Sridhar. "Universal Causality." Entropy 25, no. 4 (2023): 574. http://dx.doi.org/10.3390/e25040574.

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Universal Causality is a mathematical framework based on higher-order category theory, which generalizes previous approaches based on directed graphs and regular categories. We present a hierarchical framework called UCLA (Universal Causality Layered Architecture), where at the top-most level, causal interventions are modeled as a higher-order category over simplicial sets and objects. Simplicial sets are contravariant functors from the category of ordinal numbers Δ into sets, and whose morphisms are order-preserving injections and surjections over finite ordered sets. Non-random interventions

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Arai, Mamiko, Vicky Brandt, and Yuri Dabaghian. "The Effects of Theta Precession on Spatial Learning and Simplicial Complex Dynamics in a Topological Model of the Hippocampal Spatial Map." PLoS Computational Biology 10, no. 6 (2014): e1003651. http://dx.doi.org/10.1371/journal.pcbi.1003651.

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Manon, Christopher. "Toric Geometry ofSL2(ℂ) Free Group Character Varieties from Outer Space". Canadian Journal of Mathematics 70, № 2 (2018): 354–99. http://dx.doi.org/10.4153/cjm-2016-042-0.

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AbstractCuller and Vogtmann defined a simplicial spaceO(g), calledouter space, to study the outer automorphism group of the free groupFg. Using representation theoretic methods, we give an embedding ofO(g) into the analytification of X(Fg,SL2(ℂ)), theSL2(ℂ) character variety ofFg, reproving a result of Morgan and Shalen. Then we show that every pointvcontained in a maximal cell ofO(g) defines a flat degeneration of X(Fg,SL2(ℂ)) to a toric varietyX(PΓ). We relate X(Fg,SL2(ℂ)) andX(v) topologically by showing that there is a surjective, continuous, proper map Ξv:X(Fg,SL2(ℂ)) →X(v). We then show

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31

Blanc, Anthony. "Topological K-theory of complex noncommutative spaces." Compositio Mathematica 152, no. 3 (2015): 489–555. http://dx.doi.org/10.1112/s0010437x15007617.

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The purpose of this work is to give a definition of a topological K-theory for dg-categories over$\mathbb{C}$and to prove that the Chern character map from algebraic K-theory to periodic cyclic homology descends naturally to this new invariant. This topological Chern map provides a natural candidate for the existence of a rational structure on the periodic cyclic homology of a smooth proper dg-algebra, within the theory of noncommutative Hodge structures. The definition of topological K-theory consists in two steps: taking the topological realization of algebraic K-theory and inverting the Bot

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Yue, Yunguang, Xingwu Liu, Fengchun Lei, and Jie Wu. "A Topological Characterization to Arbitrary Resilient Asynchronous Complexity." Mathematics 10, no. 15 (2022): 2720. http://dx.doi.org/10.3390/math10152720.

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In this work, we extend the topology-based framework and method for the quantification and classification of general resilient asynchronous complexity. We presentthe arbitrary resilient asynchronous complexity theorem, applied to decision tasks in an iterated delayed model which is based on a series of communicating objects, each of which mainly consists of the delayed algorithm. In order to do this, we first introduce two topological structures, delayed complex and reduced delayed complex, and build the topological computability model, and then investigate some properties of those structures

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Miranda Jr., Gastão F., Gilson Giraldi, Carlos E. Thomaz, and Daniel Millàn. "Composition of Local Normal Coordinates and Polyhedral Geometry in Riemannian Manifold Learning." International Journal of Natural Computing Research 5, no. 2 (2015): 37–68. http://dx.doi.org/10.4018/ijncr.2015040103.

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The Local Riemannian Manifold Learning (LRML) recovers the manifold topology and geometry behind database samples through normal coordinate neighborhoods computed by the exponential map. Besides, LRML uses barycentric coordinates to go from the parameter space to the Riemannian manifold in order to perform the manifold synthesis. Despite of the advantages of LRML, the obtained parameterization cannot be used as a representational space without ambiguities. Besides, the synthesis process needs a simplicial decomposition of the lower dimensional domain to be efficiently performed, which is not c

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Grange, Pascal. "Topology of the mesoscale connectome of the mouse brain." Computational and Mathematical Biophysics 8, no. 1 (2020): 126–40. http://dx.doi.org/10.1515/cmb-2020-0106.

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AbstractThe wiring diagram of the mouse brain has recently been mapped at a mesoscopic scale in the Allen Mouse Brain Connectivity Atlas. Axonal projections from brain regions were traced using green fluoresent proteins. The resulting data were registered to a common three-dimensional reference space. They yielded a matrix of connection strengths between 213 brain regions. Global features such as closed loops formed by connections of similar intensity can be inferred using tools from persistent homology. We map the wiring diagram of the mouse brain to a simplicial complex (filtered by connecti

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Mehrabbeik, Mahtab, Atefeh Ahmadi, Fatemeh Bakouie, Amir Homayoun Jafari, Sajad Jafari, and Dibakar Ghosh. "The Impact of Higher-Order Interactions on the Synchronization of Hindmarsh–Rose Neuron Maps under Different Coupling Functions." Mathematics 11, no. 13 (2023): 2811. http://dx.doi.org/10.3390/math11132811.

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In network analysis, links depict the connections between each pair of network nodes. However, such pairwise connections fail to consider the interactions among more agents, which may be indirectly connected. Such non-pairwise or higher-order connections can be signified by involving simplicial complexes. The higher-order connections become even more noteworthy when it comes to neuronal network synchronization, an emerging phenomenon responsible for the many biological processes in real-world phenomena. However, involving higher-order interactions may considerably increase the computational co

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BARGE, MARCY, and CARL OLIMB. "Asymptotic structure in substitution tiling spaces." Ergodic Theory and Dynamical Systems 34, no. 1 (2012): 55–94. http://dx.doi.org/10.1017/etds.2012.118.

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AbstractEvery sufficiently regular non-periodic space of tilings of $\mathbb {R}^d$ has at least one pair of distinct tilings that are asymptotic under translation in all the directions of some open $(d-1)$-dimensional hemisphere. If the tiling space comes from a substitution, there is a way of defining a location on such tilings at which asymptoticity ‘starts’. This leads to the definition of the branch locus of the tiling space: this is a subspace of the tiling space, of dimension at most $d-1$, that summarizes the ‘asymptotic in at least a half-space’ behavior in the tiling space. We prove

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CHIASELOTTI, G., T. GENTILE, and F. INFUSINO. "SYMMETRY GEOMETRY BY PAIRINGS." Journal of the Australian Mathematical Society 106, no. 03 (2018): 342–60. http://dx.doi.org/10.1017/s1446788718000137.

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In this paper, we introduce asymmetry geometryfor all those mathematical structures which can be characterized by means of a generalization (which we call pairing) of a finite rectangular table. In more detail, let$\unicode[STIX]{x1D6FA}$be a given set. Apairing$\mathfrak{P}$on$\unicode[STIX]{x1D6FA}$is a triple$\mathfrak{P}:=(U,F,\unicode[STIX]{x1D6EC})$, where$U$and$\unicode[STIX]{x1D6EC}$are nonempty sets and$F:U\times \unicode[STIX]{x1D6FA}\rightarrow \unicode[STIX]{x1D6EC}$is a map having domain$U\times \unicode[STIX]{x1D6FA}$and codomain$\unicode[STIX]{x1D6EC}$. Through this notion, we i

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Dingle, Kamal, Mohammad Alaskandarani, Boumediene Hamzi, and Ard A. Louis. "Exploring Simplicity Bias in 1D Dynamical Systems." Entropy 26, no. 5 (2024): 426. http://dx.doi.org/10.3390/e26050426.

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Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input–output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and te

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Brown, Ray, and Leon O. Chua. "Chaos: Generating Complexity from Simplicity." International Journal of Bifurcation and Chaos 07, no. 11 (1997): 2427–36. http://dx.doi.org/10.1142/s021812749700162x.

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The most commonly used mapping to illustrate the phenomenon of chaos is the map x → 2x mod (1). This map is known as the 'unilateral shift' because, in the binary number system this map shifts all digits to the left by one decimal place, and truncates the integer. The second most commonly used paradigm of chaos is the Smale horseshoe whose complexity is essentially the bilateral shift obtained when we simply shift without truncation in some symbol system. Neither of these paradigms fully explains chaos since shifts cannot generate complex orbits from simple (rational) initial conditions. How c

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40

Haimes, Paul, Stuart Medley, and Barnard Clarkson. "Geo Spatial Simplicity: Designing Map Interfaces for Bushfire Planning." International Journal of Visual Design 7, no. 2 (2014): 37–45. http://dx.doi.org/10.18848/2325-1581/cgp/v07i02/38737.

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41

Cools, Kees, and Mirjam Van Praag. "On the Virtues of Transparency and Simplicity." Maandblad Voor Accountancy en Bedrijfseconomie 74, no. 11 (2000): 24–37. http://dx.doi.org/10.5117/mab.74.12720.

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Cools, Kees, and Praag Mirjam Van. "On the Virtues of Transparency and Simplicity." Maandblad Voor Accountancy en Bedrijfseconomie 74, no. (11) (2000): 24–37. https://doi.org/10.5117/mab.74.12720.

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Brugarolas, Miguel. "Divine Simplicity and Creation of Man." American Catholic Philosophical Quarterly 91, no. 1 (2017): 29–51. http://dx.doi.org/10.5840/acpq2016127102.

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Troung, Tuyen Trung. "The simplicity of the first spectral radius of a meromorphic map." Michigan Mathematical Journal 63, no. 3 (2014): 623–33. http://dx.doi.org/10.1307/mmj/1409932635.

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Keeports, David. "A Map-coloring Algorithm." Mathematics Teacher 84, no. 9 (1991): 759–63. http://dx.doi.org/10.5951/mt.84.9.0759.

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Among the most tantalizing propositions of mathematics are those generalizations that are easily and concisely stated and are readily shown to be true for specific cases yet, despite their apparent simplicity, defy concise proof. Outstanding examples of such propositions include Fermat's last theorem (see Vanden Eynden [1989]), the Goldbach conjecture, and the four-color theorem. Because such propositions can be understood by students with almost no previous background in mathematics, they are easily introduced in mathematics courses intended for the liberal arts student.

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Greenwood, Michael T. "Non-Duality, Simplicity and the Chong Mai." Medical Acupuncture 30, no. 1 (2018): 8–14. http://dx.doi.org/10.1089/acu.2017.1263.

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Krulikovskyi, Oleh, Serhii Haliuk, Ihor Safronov, and Valentyn Lesinskyi. "TWO-DIMENSIONAL HYPERCHAOTIC MAP FOR CHAOTIC OSCILLATIONS." Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska 14, no. 3 (2024): 29–34. http://dx.doi.org/10.35784/iapgos.6165.

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This manuscript explores a two-dimensional hyperchaotic map for generating chaotic oscillations. Hyperchaotic maps are finding increasing applications in various scientific and technological fields due to the unique properties of their generated oscillations. The studied map, based on two interconnected piecewise-linear functions, is one of the simplest for generating oscillations with a predetermined distribution of values across a continuous parameter space. This simplicity allows for wide applicability in various contexts. The paper presents simulation results demonstrating control over the

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Korycka-Skorupa, Jolanta, and Izabela Gołębiowska. "Numbers on Thematic Maps: Helpful Simplicity or Too Raw to Be Useful for Map Reading?" ISPRS International Journal of Geo-Information 9, no. 7 (2020): 415. http://dx.doi.org/10.3390/ijgi9070415.

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As the development of small-scale thematic cartography continues, there is a growing interest in simple graphic solutions, e.g., in the form of numerical values presented on maps to replace or complement well-established quantitative cartographic methods of presentation. Numbers on maps are used as an independent form of data presentation or function as a supplement to the cartographic presentation, becoming a legend placed directly on the map. Despite the frequent use of numbers on maps, this relatively simple form of presentation has not been extensively empirically evaluated. This article p

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Wang, Jun Qiang, and Jing Wu. "An Improved Frequency Agility Mechanism for SimpliciTI Protocol." Applied Mechanics and Materials 543-547 (March 2014): 3486–89. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.3486.

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The rapid growth of application for low-cost, low power sensor nodes based on WSN brings its own challenges. SimpliciTI is a simple low-power RF network protocol that with open Source, flexibility, and low-cost, short development cycle and so on. Aiming at the blindness problem of channel migration when this specific frequency is noisy, We presented PSCP-FA(periodic synchronism and channel prediction Frequency agility) which accomplish the channel agility predictable. Furthermore, we evaluated the impact of energy of efficiency compared with S-MAC and FA. Our simulation results show that PSCP-

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de, Lange Peter, Rob D. Smissen, Jeremy R. Rolfe, and Colin C. Ogle. "Systematics of Simplicia Kirk (Poaceae, Agrostidinae) – an endemic, threatened New Zealand grass genus." PhytoKeys 75 (December 9, 2016): 119–44. https://doi.org/10.3897/phytokeys.75.10328.

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A new species of the New Zealand endemic grass Simplicia, S. felix is described. The new species is segregated from and compared with S. buchananii and S. laxa. Simplicia felix occurs mostly in lightly shaded areas of seasonally dry alluvial forest. A distribution map and an assessment of the conservation status of the new species are presented. Genetic variation in the genus was examined, building on previously published work but including additional sampling. Analysis of nrDNA ITS and ETS and plastid trnL intron and trnL–F intergenic spacer sequences show S. felix to be more closely related

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