scholarly journals Asymptotics of polygons in restricted geometries subject to a force

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Nicholas Beaton ◽  
Jeremy Eng ◽  
Christine Soteros
Keyword(s):  
Free Energy ◽  
Asymptotic Form ◽  
Restricted Geometry ◽  
International Audience

International audience We consider self-avoiding polygons in a restricted geometry, namely an infinite L × M tube in Z3. These polygons are subjected to a force f, parallel to the infinite axis of the tube. When f > 0 the force stretches the polygons, while when f < 0 the force is compressive. In this extended abstract we obtain and prove the asymptotic form of the free energy in the limit f → −∞. We conjecture that the f → −∞ asymptote is the same as the free energy of Hamiltonian polygons, which visit every vertex in a L × M × N box.

scholarly journals Digital Trees and Memoryless Sources: from Arithmetics to Analysis

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Philippe Flajolet ◽  
Mathieu Roux ◽  
Brigitte Vallée
Keyword(s):  
Probabilistic Models ◽  
Asymptotic Form ◽  
Leader Election ◽  
Text Compression ◽  
Digital Trees ◽  
Arithmetic Properties ◽  
International Audience ◽  
Error Terms ◽  
Dynamic Hashing

International audience Digital trees, also known as $\textit{"tries''}$, are fundamental to a number of algorithmic schemes, including radix-based searching and sorting, lossless text compression, dynamic hashing algorithms, communication protocols of the tree or stack type, distributed leader election, and so on. This extended abstract develops the asymptotic form of expectations of the main parameters of interest, such as tree size and path length. The analysis is conducted under the simplest of all probabilistic models; namely, the $\textit{memoryless source}$, under which letters that data items are comprised of are drawn independently from a fixed (finite) probability distribution. The precise asymptotic structure of the parameters' expectations is shown to depend on fine singular properties in the complex plane of a ubiquitous $\textit{Dirichlet series}$. Consequences include the characterization of a broad range of asymptotic regimes for error terms associated with trie parameters, as well as a classification that depends on specific $\textit{arithmetic properties}$, especially irrationality measures, of the sources under consideration.

scholarly journals Continued Classification of 3D Lattice Models in the Positive Octant

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Axel Bacher ◽  
Manuel Kauers ◽  
Rika Yatchak
Keyword(s):  
Asymptotic Behaviour ◽  
Generating Function ◽  
Asymptotic Form ◽  
Three Dimensional ◽  
Lattice Models ◽  
Dimensional Lattice ◽  
Lattice Walks ◽  
Small Set ◽  
International Audience

International audience We continue the investigations of lattice walks in the three-dimensional lattice restricted to the positive octant. We separate models which clearly have a D-finite generating function from models for which there is no reason to expect that their generating function is D-finite, and we isolate a small set of models whose nature remains unclear and requires further investigation. For these, we give some experimental results about their asymptotic behaviour, based on the inspection of a large number of initial terms. At least for some of them, the guessed asymptotic form seems to tip the balance towards non-D-finiteness.

Encultured minds, not error reduction minds

2020 ◽  
Vol 43 ◽  
Author(s):  
Robert Mirski ◽  
Mark H. Bickhard ◽  
David Eck ◽  
Arkadiusz Gut
Keyword(s):  
Free Energy ◽  
Error Reduction ◽  
Energy Principle ◽  
Free Energy Principle ◽  
Current Article

Abstract There are serious theoretical problems with the free-energy principle model, which are shown in the current article. We discuss the proposed model's inability to account for culturally emergent normativities, and point out the foundational issues that we claim this inability stems from.

On the free energy of a ferromagnet : anisotropy and rotation

1987 ◽  
Vol 48 (2) ◽  
pp. 169-171 ◽  
Author(s):  
G. Aubert ◽  
E. du Tremolet de Lacheisserie
Keyword(s):  
Free Energy

Smectic A-Smectic B interface : faceting and surface free energy measurement

1989 ◽  
Vol 50 (24) ◽  
pp. 3527-3534 ◽  
Author(s):  
P. Oswald ◽  
F. Melo ◽  
C. Germain
Keyword(s):  
Free Energy ◽  
Surface Free Energy ◽  
Energy Measurement ◽  
Smectic A

ON THE FREE ENERGY OF VORTICES IN ROTATING He II

1978 ◽  
Vol 39 (C6) ◽  
pp. C6-222-C6-223
Author(s):  
L. J. Campbell ◽  
R. Ziff
Keyword(s):  
Free Energy
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