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The Wreath Process: A totally generative model of geometric shape based on nested symmetries [article]

Diana Borsa, Thore Graepel, Andrew Gordon
2015 arXiv   pre-print
To this end, we propose the stochastic wreath process, a fully generative probabilistic model of drawings.  ...  The proposed stochastic wreath process extends Leyton's theory by defining a probability distribution over geometric shapes in terms of noise processes that are aligned with the generative group structure  ...  model-generated as well as hand-drawn images of geometric shapes.  ... 
arXiv:1506.03041v1 fatcat:sregnjraq5gzjhrvwnl6ekcd5i

Geometry as Transfer

Michael Leyton
2008 Theoria et Historia Scientiarum  
Thus, the transfer of the fiber-group copy G(F)g to the fiber-group copy G(F)hg is given algebraically by conjugation of G(F)g by h. That is:  ...  This automorphic action corresponds algebraically to conjugation of the fiber-group product by h.  ...  The total energy of the system is given by a smooth function H on this space, and is called the Hamiltonian. The "gradient" of this function generates a flow on phase space.  ... 
doi:10.12775/ths.2008.012 fatcat:rk77yxe2sna6dffr3zttbovdoq

Interoperability and objects

Michael Leyton
2006 International Journal of Product Lifecycle Management  
His new foundations for geometry are elaborated in his books, Symmetry, Causality, Mind (MIT Press, 630 pages) and A Generative Theory of Shape (Springer-Verlag, 550 pages).  ...  The book A Generative Theory of Shape (Michael Leyton, Springer-Verlag, 2001) develops new foundations for geometry specifically designed to give a single mathematical language for the enormous range of  ...  As a consequence: New theory of invariants: In our generative theory, the invariant is the symmetry ground-state of a generative process.  ... 
doi:10.1504/ijplm.2006.008672 fatcat:2rtdhioevfaj5gsrsahu77vykm

Unified Functorial Signal Representation II: Category action, Base Hierarchy, Geometries as Base structured categories [article]

Salil Samant, Shiv Dutt Joshi
2017 arXiv   pre-print
Then using permutation action on a finite set, we introduce the notion of a hierarchy of base structured categories [(X_2a_F_2aB_2a) (X_2b_F_2bB_2b) ...]  ...  Further utilizing the existing notion of transformation double category (X_1_F_1B_1) // 2G, we demonstrate that a hierarchy of bases naturally leads one from 2-groups to n-category theory.  ...  The model using hierarchy of groups leading to wreath groups is utilized by Leyton in proposing the generative theory of shape; see [19] and references therein.  ... 
arXiv:1611.02437v2 fatcat:6repvq4s2bbx7m3fkirzqn4x6i

Subject Index to Volumes 1–75

2001 Information Processing Letters  
, 1971 , 2317 the type free λ-calculus, 125 model theoretically, 700 model theory, 95, 2046, 2077, 3392 for program schemas, 95 of the predicate calculus, 95 modeling, 919, 1964, 2562, 2733, 2737, 2923  ...  a longest path, 1828 shortest path, 505, 815, 816, 3985 length of the longest cycle, 3048 edge, 1254 string, 112 length of the word chain, 1959 word chains, 1462, 1959 length preserving rule  ...  a matrix, 3196 order n matrices, 623 tensors, 719 the adjacency matrix of a line graph, 252 rank one matrices, 1164 matrix, 472 rank queries, 1761 r decision trees, 2406 rankable set, 3245 ranked, 1610  ... 
doi:10.1016/s0020-0190(01)00175-2 fatcat:5y67tfm6yfbblakrus5nnhs73e

Self-organization of hexagonal agglomeration patterns in new economic geography models

Kiyohiro Ikeda, Kazuo Murota, Takashi Akamatsu, Tatsuhito Kono, Yuki Takayama
2014 Journal of Economic Behavior and Organization  
These distributions are the ones envisaged by central place theory and also inferred to emerge by Krugman (1996) for a core-periphery model in two dimensions. (K.  ...  The existence of hexagonal distributions as stable equilibria is demonstrated by a comparative static analysis with respect to transport costs for specific core-periphery models.  ...  equilibria in general core-periphery models on the regular triangular lattice.  ... 
doi:10.1016/j.jebo.2013.12.008 fatcat:popcoq4hbfbshbexidtnpcazwe

Exploring Bistability in the Cycles of the Solar Dynamo through Global Simulations [article]

Loren Matilsky, Juri Toomre
2020 arXiv   pre-print
We discuss this new family of dynamo models in the context of the extensive observations of the Sun's surface magnetic field with the Solar and Heliospheric Observatory (SOHO) and the Solar Dynamics Observatory  ...  However, a number of more complicated time-dependent behaviors have also been identified.  ...  Thus, it is possible that the pairs are associated with nests of Hale and anti-Hale active regions on opposite sides of the Sun, although a systematic study of the MDI/HMI magnetograms would be needed  ... 
arXiv:1912.08158v2 fatcat:w7cxmdvvf5gyxhgy2itpcjtqe4

Computational Enumeration of Colorings of Hyperplanes of Hypercubes for all Irreducible Representations and Applications

Krishnan Balasubramanian
2018 Journal of Mathematical Sciences and Modelling  
We obtain the generating functions for the combinatorial enumeration of colorings of all hyperplanes of hypercubes for all irreducible representations of the hyperoctahedral groups.  ...  The computational group theoretical techniques involve the construction of generalized character cycle indices of all irreducible representations for all hyperplanes of the hypercube using the Möbius function  ...  For a cube these operations are assigned to the various matrix conjugacy classes in Table 1 based on the permutation's orbits it generates upon its action on the vertices or edges or faces of the 3D  ... 
doi:10.33187/jmsm.471940 fatcat:nls5gm4f2ffb7am5lojz3x5xh4

Spectral Functional-Digraph Theory, Stability, and Entropy for Gene Regulatory Networks

Devin Akman, Füsun Akman
2018 Frontiers in Applied Mathematics and Statistics  
in terms of their symmetries.  ...  Finally, we will redefine the stability of a GRN and assert that it is closely related to the entropy of its phase space.  ...  The algebraic multiplicity of 0 is the total number of transient vertices in G, whereas the geometric multiplicity is the total number of the leaves (and the number of the zero columns) of A.  ... 
doi:10.3389/fams.2018.00028 fatcat:vrypcpuvhbf6jb7zzmuwdeufb4

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
60Jxx Markov processes 60J05 Discrete-time Markov processes on general state spaces 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60J20 Applications of Markov chains  ...  n-manifolds (4 < n < ∞) 57N16 Geometric structures on manifolds [See also 57M50] 57N17 Topology of topological vector spaces 57N20 Topology of infinite-dimensional manifolds [See also 58Bxx] 57N25 Shapes  ...  in this section 83Cxx General relativity 83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems) 83C10 Equations of motion 83C15 Exact solutions 83C20 Classes of solutions  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue

Classical and quantum discrete dynamical systems

V. V. Kornyak
2013 Physics of particles and nuclei  
For a consistent description of the symmetries of dynamical systems at different times and the symmetries of the various parts of such systems, we introduce discrete analogs of the gauge connections.  ...  We show that quantum behavior is the result of a fundamental inability to trace the identity of indistinguishable objects in the process of evolution.  ...  The group F loc describes the symmetries of the neighborhood of a vertex of the graph. It is an analog of infinitesimal symmetries in physical models based on differential equations.  ... 
doi:10.1134/s106377961301005x fatcat:odk5uf3libaujoavq2nouvfnoq

Quantification of environmental and economic impacts for main categories of building labeling schemes

Erkki Seinre, Jarek Kurnitski, Hendrik Voll
2014 Energy and Buildings  
FaculTy oF civil enGineerinG chair oF heaTinG and venTilaTion chair of heating and ventilation mainly focuses on the research in hvac systems, indoor climate of the buildings, energy efficient and sustainable  ...  disorders and the effect of external physical stressor.  ...  Brain research Group The research activity is continuously aimed to development of algorithms for detection of characteristic changes in the brain electroencephalographyc (eeG) signal related to the mental  ... 
doi:10.1016/j.enbuild.2013.11.048 fatcat:ckgxbn7mtrh47gf4xsdaaio5jm

Bayesian large-scale structure inference and cosmic web analysis [article]

Florent Leclercq
2015 arXiv   pre-print
The method, based on Bayesian probability theory, provides accurate means of uncertainty quantification.  ...  We present detailed probabilistic maps of the dynamic cosmic web, and offer a general solution to the problem of classifying structures in the presence of uncertainty.  ...  This allows to make a connection between a static (based on the density profiles) and a dynamic (based on the velocity profiles) characterization of voids.  ... 
arXiv:1512.04985v1 fatcat:kmvpzxbt5jgjxpmzdgd5jslzn4

A look at the importance of the economic valuation of the regulation services of natural wetlands [chapter]

Christian Alejandra Vidal Sierra, Ciro Alfonso Serna Mendoza, Coral Jazvel Pacheco Figueroa
2021 Conflicts over use of urban and regional spaces in the time of climate changes. Good management and planning practices  
It is a very broad topic and causes several controversies about the forms of urbanization processes and the adaptation of urban space to these changes. Governance also plays an important role here.  ...  INTRODUCTORY WORDS Katarzyna Dembicz presents a very important text on education for development and the mistaken western visions applied to the local Latin American world.  ...  key ecosystem processes for the maintenance of the economy based on agricultural production, especially coffee.  ... 
doi:10.31338/uw.9788323548546.pp.196-205 fatcat:hc6y3kotn5avja4oyh6hj5537q

Material Image. Affordances as a New Approach to Visual Culture Studies

Martina Sauer, Elisabeth Günther, Sven Günther, Nikolaus Dietrich, Yael Young, Hans-Dieter Huber, Sarah Ullrich, Kathraina Geis, Fabiana Senkpiel, Stefanie Bräuer, Klaus Schwarzfischer, Petra Leutner
2021 Zenodo  
In general, questions concerning the meaning of art are frequently linked to the process of perception and imagination. This process can b [...]  ...  However, the significance of art and all kinds of aesthetic experiences represent a transformation for our nature as human beings.  ...  Already the recognition of a regularity (a rotational symmetry) is put in by the observer as a cognition (based on unconscious conclusions). [2.]  ... 
doi:10.5281/zenodo.6371577 fatcat:5636fykjdzhe5jwcnrgvrspqxy
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