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Coding cells of digital spaces: a framework to write generic digital topology algorithms

Lachaud Jacques-Olivier
2003 Electronic Notes in Discrete Mathematics  
It induces a simple, generic and efficient framework for implementing classical digital topology data structures and algorithms.  ...  This paper proposes a concise coding of the cells of n-dimensional finite regular grids.  ...  Due to limited space, the reader is referred to [12] for more details. 2 Coding cells of digital spaces C n 2.1 Cellular decomposition C n ; binary coding of unoriented cells We denote by C n the set  ... 
doi:10.1016/s1571-0653(04)00497-4 fatcat:wcnleshl2jhplhq67jra6cjyre

Computations in Space and Space in Computations [chapter]

Jean-Louis Giavitto, Olivier Michel, Julien Cohen, Antoine Spicher
2005 Lecture Notes in Computer Science  
Prusinkiewicz at the University of Calgary (who coined the term "computation in space") and the members of the Epigenomic group at GENOPOLE-Évry, for stimulating discussions, thoughtful remarks and warm  ...  Acknowledgments The authors would like to thanks Franck Delaplace at LaMI, Frédéric Gruau at University of Paris-Sud, Florent Jacquemard at INRIA/LSV-Cachan, C. Godin and P.  ...  So, it is always possible to code (at the price of explicit coding the topological relation into some value inspected at run-time) any specific topology on top of the multiset topology.  ... 
doi:10.1007/11527800_11 fatcat:oyoyp6k6dvgtfeqg3k7yy55bva

Design Space Exploration of hardware spiking neurons for embedded Artificial Intelligence

Nassim Abderrahmane, Edgar Lemaire, Benoît Miramond
2019 Neural Networks  
In this context, we propose a framework for neuromorphic hardware design space exploration, which allows to define a suitable architecture based on application-specific constraints and starting from a  ...  These architectures are derived from a novel funnel-like Design Space Exploration framework for neuromorphic hardware.  ...  Acknowledgement We would like to thank Olivier Bichler and CEA LIST for providing us the N2D2 framework licence.  ... 
doi:10.1016/j.neunet.2019.09.024 pmid:31593842 fatcat:so2fuhlod5aldlofmpbgf5yagi

The Future of Search and Discovery in Big Data Analytics: Ultrametric Information Spaces [article]

Fionn Murtagh, Pedro Contreras
2012 arXiv   pre-print
Consider observation data, comprised of n observation vectors with values on a set of attributes. This gives us n points in attribute space.  ...  Having data structured as a tree, implied by having our observations embedded in an ultrametric topology, offers great advantage for proximity searching.  ...  Creating a grid structure, i.e. partitioning the data space into a finite number of non-overlapping cells. 2. Calculating the cell density for each cell.  ... 
arXiv:1202.3451v1 fatcat:55il2iqgtjasbklitdwrughy5y

Geodesics in fibered latent spaces: A geometric approach to learning correspondences between conditions [article]

Tariq Daouda, Reda Chhaibi, Prudencio Tossou, Alexandra-Chloé Villani
2020 arXiv   pre-print
This work introduces a geometric framework and a novel network architecture for creating correspondences between samples of different conditions.  ...  Under this formalism, the latent space is a fiber bundle stratified into a base space encoding conditions, and a fiber space encoding the variations within conditions.  ...  Morally, a fiber bundle M is a topological space locally stratified along two directions (see Fig. 2 .1): • The horizontal direction is tangent to a topological space called the base manifold B (in our  ... 
arXiv:2005.07852v3 fatcat:rwppuk53jfcq3eexn4cbjib3ha

Efficient Neighbor-Finding on Space-Filling Curves [article]

David Holzmüller
2019 arXiv   pre-print
However, it appears that a generalization of the algorithm to suitable adaptive grids is possible.  ...  Many algorithms, for example grid-based numerical PDE solvers, have to access all neighbor cells of each grid cell during a grid traversal.  ...  To store all squares of a given level sequentially in memory, we take the order generated by the space-filling curve, see The base-4 digits of a square in the tree consist of the base-4 digits of its  ... 
arXiv:1710.06384v3 fatcat:bze5qifgyjerxm44by5oupot3y

STATS: A framework for microprocessor and system-level design space exploration

David H. Albonesi, Israel Koren
1999 Journal of systems architecture  
As microprocessor-based systems grow in complexity, and the processor-memory speed gap widens further, more emphasis needs to be placed on early design space exploration in order to produce the highest  ...  We discuss the critical issues associated with architectural evaluation of complex microprocessor-based systems, and present a methodology for the comprehensive and semi-automatic evaluation of processor  ...  Acknowledgements The authors thank Tryggve Fossum, Michael Adler, Joel Emer, Geo Lowney, Bob Nix, and David Webb of Digital Equipment Corporation for developing and licensing the compilation and simulation  ... 
doi:10.1016/s1383-7621(98)00052-6 fatcat:7ikxbpyvrfaqph2aiq7god74ci

Geometric Model Checking of Continuous Space [article]

Nick Bezhanishvili and Vincenzo Ciancia and David Gabelaia and Gianluca Grilletti and Diego Latella and Mieke Massink
2022 arXiv   pre-print
SLCS constitutes the kernel of a solid logical framework for reasoning about discrete space, such as graphs and digital images, interpreted as quasi discrete closure spaces.  ...  Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic.  ...  Finally, for X ⊆ X, the topological sub-space of (X, C) generated by X is the pair (X , C ), where C (A) = C(A) ∩ X for all A ⊆ X .  ... 
arXiv:2105.06194v2 fatcat:w6sqisekjndgrnhrsydoaokftq

Bio-Inspired Evolutionary Model of Spiking Neural Networks in Ionic Liquid Space

Ensieh Iranmehr, Saeed Bagheri Shouraki, Mohammad Mahdi Faraji, Nasim Bagheri, Bernabe Linares-Barranco
2019 Frontiers in Neuroscience  
In order to study the effect of the applied stimulus in an ionic liquid space through time, a diffusion operator is used which somehow compensates for the separation between spatial and temporal coding  ...  High plasticity of this model makes learning possible with a fewer number of neurons.  ...  In this algorithm, in order to generate a new population of individuals, the best individual of the current generation has to be chosen.  ... 
doi:10.3389/fnins.2019.01085 pmid:31787863 pmcid:PMC6856051 fatcat:kcc32j4eivgipjdfsoa34hv3q4

Landscapes on spaces of trees

Oliver Bastert, Dan Rockmore, Peter F. Stadler, Gottfried Tinhofer
2002 Applied Mathematics and Computation  
the cost functions onto the eigenspaces of the underlying graph and the topology of local minima and their connecting saddle points.  ...  The collection of possible phylogenetic trees is arranged as a so-called Robinson graph by means of the nearest neighborhood interchange move.  ...  Thanks to Christoph Flamm for the source code of barriers.  ... 
doi:10.1016/s0096-3003(01)00164-3 fatcat:jyh27s6mlfgmbcghgk2wlq5pti

Computer-Assisted Interactive Documentary and Performance Arts in Illimitable Space [article]

Miao Song
2012 arXiv   pre-print
The journey of this research has been unusual because it requires a researcher with solid knowledge and background in multiple disciplines; who also has to be creative and sensitive in order to combine  ...  documentary footage on film, video, or images, and text via a variety of devices [....] and programming, and installing all the needed interfaces such that it all works in real-time.  ...  The general principle is having to load and compile a source code shader file and dynamically link it from within OpenGL.  ... 
arXiv:1212.6250v1 fatcat:2bulqbnpsbc3daw5s6xeqvk26y

A Proposal for Modeling Indoor–Outdoor Spaces through IndoorGML, Open Location Code and OpenStreetMap

Rubén Cantarero Navarro, Ana Rubio Ruiz, Javier Dorado Chaparro, Felix J. Villanueva Molina, Maria J. Santofimia Romero, David Villa Alises, Juan C. Lopez Lopez
2020 ISPRS International Journal of Geo-Information  
This adds an additional challenge to the representation of this information due to the need to represent characteristic information of the space from different points of view in a model, such as WiFi coverage  ...  Traditionally, the standards of spatial modeling are oriented to represent the quantitative information of space.  ...  When a cell represents a plus code area, the state of that area is determined by the geometric center of the plus code area to which it is associated.  ... 
doi:10.3390/ijgi9030169 fatcat:ro4ov5yyvngqppiofilnttsiaa

Space and High Energy Experiments Advanced Electronic Systems 2012

Ryszard S. Romaniuk
2012 International Journal of Electronics and Telecommunications  
It is also a great occasion for SPIE, IEEE, OSA and PSP students to meet together in a large group spanning the whole country with guests from this part of Europe.  ...  A digest of Wilga references is presented [1]-[60]. This paper is the first part of the digest focused on astronomy, space, astroparticle physics, accelerators, and high energy physics experiments.  ...  Such approach may expose some problems related to the hardware design. These issues appear during attempts to write the code, when a skilful programmer detects obvious inefficiencies.  ... 
doi:10.2478/v10177-012-0060-0 fatcat:2nrsjwpharcuva4642wi3zmbim

Dynamical Systems as Temporal Feature Spaces [article]

Peter Tino
2020 arXiv   pre-print
We propose a framework for rigorous analysis of such state representations in vanishing memory state space models such as echo state networks (ESN).  ...  We show that: (1) The usual ESN strategy of randomly generating input-to-state, as well as state coupling leads to shallow memory time series representations, corresponding to cross-correlation operator  ...  topology 7 and a constant weight v > 0 of the input-to-state coupling.  ... 
arXiv:1907.06382v3 fatcat:qfhwcvdf3fh3raqkm2t2qr7w7i

Advanced architectures for real-time Delay-Doppler Map GNSS-reflectometers: The GPS reflectometer instrument for PAU (griPAU)

E. Valencia, A. Camps, J.F. Marchan-Hernandez, X. Bosch-Lluis, N. Rodriguez-Alvarez, I. Ramos-Perez
2010 Advances in Space Research  
at the GPS L1 frequency with the C/A codes.  ...  This has brought out the need of designing and implementing appropriate receivers in order to track and process this kind of signals in real-time to avoid the storage of huge volumes of raw data.  ...  Acknowledgements This work, conducted as part of a EURYI (European Young Investigator) Award, 2004, was supported by funds from the Participating Organizations of EURYI and the EC Sixth Framework Program  ... 
doi:10.1016/j.asr.2010.02.002 fatcat:qbl5l6mj2nctzjcoabznop4rzi
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