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Point-plane incidences and some applications in positive characteristic [article]

Misha Rudnev
2018 arXiv   pre-print
These are the problem of the minimum number of distinct nonzero values of a non-degenerate bilinear form on a point set in d=2, the analogue of the Erdős distinct distance problem in d=2,3 and additive  ...  The point-plane incidence theorem states that the number of incidences between n points and m≥ n planes in the projective three-space over a field F, is O(m√(n)+ m k), where k is the maximum number of  ...  This accounts for the role of the parameter k in Theorem 1 versus Theorem 2.  ... 
arXiv:1806.03534v1 fatcat:2lkpl6rdw5e47iq2okkvumu4my

Some Fundamental Theorems in Mathematics [article]

Oliver Knill
2022 arXiv   pre-print
An expository hitchhikers guide to some theorems in mathematics.  ...  Liouville: every prime p=4k+1 is the sum of two squares.  ...  Let π(x) be the prime-counting function which gives the number of primes smaller or equal to x.  ... 
arXiv:1807.08416v4 fatcat:lw7lbsxyznfrnaozilxapihmdy

The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg [article]

Jesus A. De Loera, Xavier Goaoc, Frédéric Meunier, Nabil Mustafa
2018 arXiv   pre-print
We discuss five discrete results: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carath\'eodory, Helly, and Tverberg from combinatorial geometry.  ...  We explore their connections and emphasize their broad impact in application areas such as game theory, graph theory, mathematical optimization, computational geometry, etc.  ...  He is grateful to the labex BEZOUT and the CERMICS research center atÉcole National des Ponts et Chaussées for the support received, and the enjoyable and welcoming environment in which the topics in this  ... 
arXiv:1706.05975v3 fatcat:rtwl6jd77zbtbklqco4wxym5ly

The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg

Jesús A. De Loera, Xavier Goaoc, Frédéric Meunier, Nabil H. Mustafa
2019 Bulletin of the American Mathematical Society  
of dimension i in |K|; for example, the rank of H 0 (K, Z 2 ) counts the number of connected components of |K|.  ...  In particular, if K is a single vertex, then all its homology groups are trivial except the 0th one.  ...  Acknowledgments The authors are truly grateful to the two anonymous referees who provided a very large and very detailed set of comments, insights, and corrections.  ... 
doi:10.1090/bull/1653 fatcat:vby5jazp2zd6lc2ev3qqgxm2cq

Relevance of accurate Monte Carlo modeling in nuclear medical imaging

Habib Zaidi
1999 Medical Physics (Lancaster)  
Current and future trends in the field are also discussed.  ...  Factors which have contributed to the wider use include improved models of radiation transport processes, the practicality of application with the development of acceleration schemes and the improved speed  ...  Von Neumann, Ulam and Fermi applied the method towards neutron diffusion problems in the Manhattan Project at Los Alamos during World War II.  ... 
doi:10.1118/1.598559 pmid:10227362 fatcat:ea6pbismqbccpn2qdnbatigg2e

Cycle Expansions for Intermittent Maps

Roberto Artuso, Predrag Cvitanović, Gregor Tanner
2003 Progress of Theoretical Physics Supplement  
In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space.  ...  Marginality leads to long-time dynamical correlations, in contrast to the exponentially fast decorrelations of purely chaotic dynamics.  ...  A. was partially supported by the PRIN-2000 project "Chaos and localization in classical and quantum systems", by INFM PA "Weak chaos: theory and applications", and by EU contract QTRANS Network ("Quantum  ... 
doi:10.1143/ptps.150.1 fatcat:zjevxui46ncannqivc34eifchy

Quantization of classical maps with tunable Ruelle-Pollicott resonances

Andrzej Ostruszka, Christopher Manderfeld, Karol Życzkowski, Fritz Haake
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We investigate the correspondence between the decay of correlation in classical system, governed by Ruelle--Pollicott resonances, and the properties of the corresponding quantum system.  ...  As an application of such tailormade resonances we reveal the role of Ruelle--Pollicott resonances for the localization properties of quantum energy eigenstates.  ...  In both cases ⌬ϭ1/8. side, where ͐d⍀ Q kk Ј ϭ0. ͑The prime will be dropped in the following.͒ For nϭ0 the integral on the left-hand side of Eq. ͑27͒ gives the dimension N.  ... 
doi:10.1103/physreve.68.056201 pmid:14682865 fatcat:lyegfz7lyjbodefmy4j7uj7trm

Brain–Computer Interfaces for Human Augmentation

Davide Valeriani, Caterina Cinel, Riccardo Poli
2019 Brain Sciences  
The field of brain–computer interfaces (BCIs) has grown rapidly in the last few decades, allowing the development of ever faster and more reliable assistive technologies for converting brain activity into  ...  are listed in reference [71].  ...  Acknowledgments: This research was supported by the European Fund for Regional Development (EFRD-or EFRE in German) under Grants GE-1-1-047 and IT-1-2-001.  ... 
doi:10.3390/brainsci9020022 pmid:30682766 pmcid:PMC6406539 fatcat:4kjekrytqrcd7h4egrqlxsdbpq

Computational universes

Karl Svozil
2005 Chaos, Solitons & Fractals  
Suspicions that the world might be some sort of a machine or algorithm existing "in the mind" of some symbolic number cruncher have lingered from antiquity.  ...  Modern developments in physics and computer science have lent support to the thesis, but empirical evidence is needed before it can begin to replace our contemporary world view.  ...  Tee from the University of Auckland has provided reference [4] , and Peter Mittelstaedt referred to the beautiful quotation of Kant.  ... 
doi:10.1016/j.chaos.2004.11.055 fatcat:cwzhp45zujeefavfv3kebucafq

Frontiers of chaotic advection

Hassan Aref, John R. Blake, Marko Budišić, Silvana S. S. Cardoso, Julyan H. E. Cartwright, Herman J. H. Clercx, Kamal El Omari, Ulrike Feudel, Ramin Golestanian, Emmanuelle Gouillart, GertJan F. van Heijst, Tatyana S. Krasnopolskaya (+11 others)
2017 Reviews of Modern Physics  
This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear  ...  We thank the Lorentz Center for its financial support and the Lorentz Center staff for making the workshop a great success.  ...  We acknowledge the three who are no longer with us, Hassan Aref, John Blake, and Slava (Viatcheslav) Meleshko, with whom we planned and worked on the paper.  ... 
doi:10.1103/revmodphys.89.025007 fatcat:r4qm33uup5bobhnijyofvnq4ue

An Introduction to Cellular Automata [chapter]

M. Delorme
1999 Cellular Automata  
The c.a will have output 1, that is be in accepting state, at each prime time t.  ...  Fischer uses a similar but less efficient method : he crosses out the multiples of every integer, (thereby loosing his time in vain for integers not prime), starting from their square, which is the first  ...  An illustration for the square diagonal grouper is given in Figures 14 and 15.  ... 
doi:10.1007/978-94-015-9153-9_1 fatcat:vi4d6bwvrnhkdl6vg7oaey6fea

Analyzing the environment structure of higher-order languages using frame strings

Matthew Might, Olin Shivers
2007 Theoretical Computer Science  
Reasoning about program behaviour in programming languages based on the λ calculus requires reasoning in a unified way about control, data and environment structure.  ...  We state the critical theorems needed to establish correctness of the entire technology suite, with their proofs.  ...  We developed the core of our frame-string model while visiting the University of Aarhus in the Fall of 2004.  ... 
doi:10.1016/j.tcs.2006.12.031 fatcat:ariqc6ukl5eprlfidptb3uhddi

Floating Bodies of Equilibrium in 2D, the Tire Track Problem and Electrons in a Parabolic Magnetic Field [article]

Franz J. Wegner
2007 arXiv   pre-print
Starting point is the differential equation given by the author in archive physics/0205059 and Studies in Appl. Math. 111 (2003) 167-183.  ...  The curves are also trajectories of charges in a perpendicular magnetic field.  ...  Introduction In this paper we consider a class of curves, which are solution to three problems: (i) the two-dimensional version of the floating body problem asked by Stanislaw Ulam in the Scottish Book  ... 
arXiv:physics/0701241v3 fatcat:tm5zbhyuc5f7rfg3eyt6kc6aly

Editors: Nils Anders Danielsson, Bengt Nordström

Aloïs Brunel
Aloïs Brunel; licensed under Creative Commons License BY-ND 18th International Workshop on Types for Proofs and Programs (TYPES 2011)   unpublished
Borsuk-Ulam theorem.  ...  The winding number around a point z ∈ C of a closed curve γ basically counts how many time γ turns counterclockwise around z.  ...  proof of the prime number theorem.  ... 
fatcat:qwyvcyvuobei3fuir2wqll22pq

Heuristic Algorithm for Efficient Data Retrieval Scheduling in the Multichannel Wireless Broadcast Environments

A. Porselvi, S.Brindha Devi
2015 International Journal of Computer Applications Technology and Research  
In this paper, we investigate the multi-item data retrieval scheduling in the push-based multichannel broadcast environments.  ...  When there is no replicated item in a broadcast cycle, we show that an optimal retrieval schedule can be obtained in polynomial time. 337 investigate the approximability of MCDR in push-based broadcast  ...  along the corresponding ring segment.  ... 
doi:10.7753/ijcatr0405.1001 fatcat:7xpnnpep5vd7hcrmcjr4fvpnq4
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