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Fast Deterministic Fully Dynamic Distance Approximation [article]

Jan van den Brand, Sebastian Forster, Yasamin Nazari
2022 arXiv   pre-print
In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees.  ...  We further give a deterministic algorithm for maintaining (1+ϵ)-approximate single-source distances with worst-case update time O(n^1.529), which also matches a conditional lower bound.  ...  Our main result is a deterministic, fully dynamic algorithm for maintaining a (1 + )-approximation of the distance between a fixed pair of nodes s, t ∈ V whose worst-case update time matches a conditional  ... 
arXiv:2111.03361v2 fatcat:qzxfmf2znzcjhlsfckrxispe5i

Probabilistic Inference for Fast Learning in Control [chapter]

Carl Edward Rasmussen, Marc Peter Deisenroth
2008 Lecture Notes in Computer Science  
We provide a novel framework for very fast model-based reinforcement learning in continuous state and action spaces.  ...  We implement policy iteration within the fast RL framework given by Algorithm 1 as follows. Initially, we assume fully unknown transition dynamics.  ...  Although we have not yet investigated this fully, we did assess whether it is possible to solve the problem using a deterministic model for the dynamics.  ... 
doi:10.1007/978-3-540-89722-4_18 fatcat:7xltrx7jjjev5pxgbos5noxdry

Testing for nonlinearity and low-dimensional dynamics in the slow solar wind

Wiesław M. Macek, Marek Strumik
2006 Advances in Space Research  
We focus on nonlinearity and possible deterministic behavior of the low-speed solar wind.  ...  The fraction of false-nearest-neighbors drops to zero at dimension equal to four for both the radial velocity and Alfvénic velocity, independent of the distance from the Sun.  ...  On the contrary, as it has recently been shown by Bruno et al. (2003) plasma dynamics in the case of the fast solar wind is much more variable with changing distance from the Sun.  ... 
doi:10.1016/j.asr.2005.07.038 fatcat:ckuxz4o6azhkbomkbpetnaf6gq

Acceleration of evolutionary spread by long-range dispersal

Oskar Hallatschek, Daniel S. Fisher
2014 Proceedings of the National Academy of Sciences of the United States of America  
In contrast to the exponential laws predicted by deterministic "mean-field" approximations, we show that the asymptotic growth is either according to a power-law or a stretched exponential, depending on  ...  We present a simple iterative scaling approximation supported by simulations and rigorous bounds that accurately predicts evolutionary spread for broad distributions of long distance dispersal.  ...  Breakdown of Deterministic Approximation.  ... 
doi:10.1073/pnas.1404663111 pmid:25368183 pmcid:PMC4246332 fatcat:3tprbpdmobcv3l7s3qvkzp6u5e

Chaos and multifractals in the solar wind

Wiesław M. Macek
2010 Advances in Space Research  
By employing the so-called false-nearest-neighbors method, we argue that the deterministic component of solar wind plasma dynamics should be low-dimensional.  ...  In fact, the results we have obtained using the method of topological embeddings indicate that the behavior of the solar wind can be approximately described by a low-dimensional chaotic attractor in the  ...  By employing the so-called false-nearest-neighbors method, we argue that the deterministic component of solar wind plasma dynamics should be low-dimensional.  ... 
doi:10.1016/j.asr.2008.12.026 fatcat:bba2n3wubjckbabm7nqjdwoe6e

A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics

Christian Kuehn
2011 Physica D : Non-linear phenomena  
We suggest that the mathematical theory of fast-slow systems provides a natural definition of critical transitions.  ...  Since noise often plays a crucial role near critical transitions the next step is to consider stochastic fast-slow systems.  ...  In particular, his ideas helped to significantly shape our definition of a critical transition point for deterministic fast-slow systems.  ... 
doi:10.1016/j.physd.2011.02.012 fatcat:g233lsz6vnfp5cbhxpyfvd5jse

New Stochastic Mode Reduction Strategy for Dissipative Systems

M. Schmuck, M. Pradas, S. Kalliadasis, G. A. Pavliotis
2013 Physical Review Letters  
Numerical computations for the generalized Kuramoto-Sivashinsky equation sup- port our method and reveal that the long-time underlying stochastic process of the fast (unresolved) modes obeys a universal  ...  The ERG provides the deterministic approximation [(7a) and (7b)] via Eq. (6) and PF NR ðs; UÞ ¼ 2i X jjj N e iðj=Þx X kþl¼j jkj N<jlj e À w l s w l  ...  the dynamics.  ... 
doi:10.1103/physrevlett.110.244101 pmid:25165926 fatcat:2mqot2apxzcrhowsngszmokh2u

Attractors in fully asymmetric neural networks

U Bastolla, G Parisi
1997 Journal of Physics A: Mathematical and General  
of the annealed approximation which we previously introduced for the study of Kauffman networks.  ...  Comparison with numerical results suggests that the approximation could become exact in the infinite size limit.  ...  of a deterministic map and the set of indices J labels the realization of the dynamic rules.  ... 
doi:10.1088/0305-4470/30/16/007 fatcat:p7g6dke3grellgwij7eg5nhgmu

Data Assimilation in Slow–Fast Systems Using Homogenized Climate Models

Lewis Mitchell, Georg A. Gottwald
2012 Journal of the Atmospheric Sciences  
A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes.  ...  The reliability of this reduced climate model in reproducing the statistics of the slow dynamics of the full deterministic model for finite values of the time scale separation is numerically established  ...  the fast chaotic Lorenz subsystem has almost fully decorrelated and that the rare transitions between the metastable states are approximately a Poisson process.  ... 
doi:10.1175/jas-d-11-0145.1 fatcat:k67ejsm5wveddaxte6y2q4mtzq

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

James C. Schaff, Fei Gao, Ye Li, Igor L. Novak, Boris M. Slepchenko, Martin Meier-Schellersheim
2016 PLoS Computational Biology  
Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity.  ...  Calcium 'sparks' in cardiomyocytes is one such example, in which dynamics of calcium ions, which are usually present in large numbers, can be described deterministically, whereas the channels open and  ...  Fully coupled systems in the limit of fast diffusion: validation against different solvers.  ... 
doi:10.1371/journal.pcbi.1005236 pmid:27959915 pmcid:PMC5154471 fatcat:o7uwrbkcajd4hnw3w4zlmnlvim

On the impact of discreteness and abstractions on modelling noise in gene regulatory networks

Chiara Bodei, Luca Bortolussi, Davide Chiarugi, Maria Luisa Guerriero, Alberto Policriti, Alessandro Romanel
2015 Computational biology and chemistry  
Then, we explore the effect of combining hybrid approaches and quasi-steady state approximations on model behaviour (and simulation time), to understand to what extent dynamics and quantitative features  ...  In this paper, we explore the impact of different forms of model abstraction and the role of discreteness on the dynamical behaviour of a simple model of gene regulation where a transcriptional repressor  ...  Continuous deterministic abstraction The most common approach for dynamics abstraction is to replace the stochastic model with a fully deterministic one based on ODEs.  ... 
doi:10.1016/j.compbiolchem.2015.04.004 pmid:25909953 fatcat:jahrhralyjhvpabxxhrughrg34

Algorithms and Hardness for Diameter in Dynamic Graphs

Bertie Ancona, Monika Henzinger, Liam Roditty, Virginia Vassilevska Williams, Nicole Wein, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
Some of the highlights include: Under popular hardness hypotheses, there can be no significantly better fully dynamic approximation algorithms than recomputing the answer after each update, or maintaining  ...  This is the situation for dynamic approximation algorithms as well, and even if only edge insertions or edge deletions need to be supported.  ...  The same limitation applies for fully dynamic (5/3 − )-approximation algorithms for Eccentricities with polynomial preprocessing time, and for fully dynamic (3/2 − )-approximation algorithms for Radius  ... 
doi:10.4230/lipics.icalp.2019.13 dblp:conf/icalp/AnconaHRWW19 fatcat:bg2j3huworg7jbf3lt2clk2clm

Algorithms and Hardness for Diameter in Dynamic Graphs [article]

Bertie Ancona, Monika Henzinger, Liam Roditty, Virginia Vassilevska Williams, Nicole Wein
2019 arXiv   pre-print
Some of the highlights include: - Under popular hardness hypotheses, there can be no significantly better fully dynamic approximation algorithms than recomputing the answer after each update, or maintaining  ...  This is the situation for dynamic approximation algorithms as well, and even if only edge insertions or edge deletions need to be supported.  ...  The same limitation applies for fully dynamic (5/3 − )-approximation algorithms for Eccentricities with polynomial preprocessing time, and for fully dynamic (3/2 − )-approximation algorithms for Radius  ... 
arXiv:1811.12527v3 fatcat:6unt2p5gf5hapmwbzwlsrobqni

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

Gabriele Vissio, Valerio Lucarini
2018 Nonlinear Processes in Geophysics  
We derive an expression for the deterministic and the stochastic component of the parametrization and we show that the approach allows for dealing seamlessly with the case of the Lorenz 63 being a fast  ...  By testing our methods on reduced-phase spaces obtained by projection, we find support for the idea that comparisons based on the Wasserstein distance might be of relevance in many applications despite  ...  Valerio Lucarini recalls several fond memories of very informal yet enlightening discussions with Anna Trevisan on nonlinear dynamics and data assimilation.  ... 
doi:10.5194/npg-25-413-2018 fatcat:tb4zjst5fbaire7q3bol4yubda

Fully Dynamic k-Center Clustering in Doubling Metrics [article]

Gramoz Goranci, Monika Henzinger, Dariusz Leniowski, Christian Schulz, Alexander Svozil
2020 arXiv   pre-print
We present a deterministic dynamic algorithm for the k-center clustering problem that provably achieves a (2+ϵ)-approximation in poly-logarithmic update and query time, if the underlying metric has bounded  ...  Driven by this, we study the metric k-center clustering problem in the fully dynamic setting, where the goal is to efficiently maintain a clustering while supporting an intermixed sequence of insertions  ...  Fully dynamic k-center clustering using navigating nets In this section, we present a fully-dynamic algorithm for the k-center clustering problem that achieves a (2 + ϵ)-approximation with a running time  ... 
arXiv:1908.03948v3 fatcat:4wf73hfl6nbhldu5paf4fvggsq
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