157 research outputs found
Cellular Structures for Computation in the Quantum Regime
We present a new cellular data processing scheme, a hybrid of existing
cellular automata (CA) and gate array architectures, which is optimized for
realization at the quantum scale. For conventional computing, the CA-like
external clocking avoids the time-scale problems associated with ground-state
relaxation schemes. For quantum computing, the architecture constitutes a novel
paradigm whereby the algorithm is embedded in spatial, as opposed to temporal,
structure. The architecture can be exploited to produce highly efficient
algorithms: for example, a list of length N can be searched in time of order
cube root N.Comment: 11 pages (LaTeX), 3 figure
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A Combinatorial Parametric Engineering Model for Solid Freeform Fabrication
Fabricated parts are often represented as compact connected smooth 3-manifolds with
boundary, where the boundaries consist of compact smooth 2-manifolds. This class of mathematical
structures includes topological spaces with enclosed voids and tunnels. Useful information about these
structures are coded into level functions (Morse functions) which map points in the 3-manifold onto their
height above a fixed plane. By definition, Morse functions are smooth functions, all of whose critical
points are nondegenerate. This information is presented by the Reeb graph construction that develops a
topologically informative skeleton of the manifold whose nodes are the critical points of the Morse function
and whose edges are associated with the connected components between critical slices. This approach
accurately captures the SFF process: using a solid geometric model of the part, defining surface
boundaries; selecting a part orientation; forming planar slices, decomposing the solid into a sequence of
thin cross-sectional polyhedral layers; and then fabricating the part by producing the polyhedra by additive
manufacturing. This note will define a qualitative and combinatorial parametric engineering model of the
SFF part design process. The objects under study will be abstract simplicial complexes K with boundary
∂K. Systems of labeled 2-surfaces in K, called slices, will be associated with the cross-sectional polyhedral
layers. The labeled slices are mapped into a family of digraph automata, which, unlike cellular automata,
are defined not on regular lattices with simple connectivities (cells usually have either 4 or 8 cell
neighborhoods) but on unrestricted digraphs whose connectivities are irregular and more complicated.Mechanical Engineerin
Sensitivity to noise and ergodicity of an assembly line of cellular automata that classifies density
We investigate the sensitivity of the composite cellular automaton of H.
Fuk\'{s} [Phys. Rev. E 55, R2081 (1997)] to noise and assess the density
classification performance of the resulting probabilistic cellular automaton
(PCA) numerically. We conclude that the composite PCA performs the density
classification task reliably only up to very small levels of noise. In
particular, it cannot outperform the noisy Gacs-Kurdyumov-Levin automaton, an
imperfect classifier, for any level of noise. While the original composite CA
is nonergodic, analyses of relaxation times indicate that its noisy version is
an ergodic automaton, with the relaxation times decaying algebraically over an
extended range of parameters with an exponent very close (possibly equal) to
the mean-field value.Comment: Typeset in REVTeX 4.1, 5 pages, 5 figures, 2 tables, 1 appendix.
Version v2 corresponds to the published version of the manuscrip
The solution of the Sixth Hilbert Problem: the Ultimate Galilean Revolution
I argue for a full mathematisation of the physical theory, including its
axioms, which must contain no physical primitives. In provocative words:
"physics from no physics". Although this may seem an oxymoron, it is the royal
road to keep complete logical coherence, hence falsifiability of the theory.
For such a purely mathematical theory the physical connotation must pertain
only the interpretation of the mathematics, ranging from the axioms to the
final theorems. On the contrary, the postulates of the two current major
physical theories either don't have physical interpretation (as for von
Neumann's axioms for quantum theory), or contain physical primitives as
"clock", "rigid rod ", "force", "inertial mass" (as for special relativity and
mechanics). A purely mathematical theory as proposed here, though with limited
(but relentlessly growing) domain of applicability, will have the eternal
validity of mathematical truth. It will be a theory on which natural sciences
can firmly rely. Such kind of theory is what I consider to be the solution of
the Sixth Hilbert's Problem. I argue that a prototype example of such a
mathematical theory is provided by the novel algorithmic paradigm for physics,
as in the recent information-theoretical derivation of quantum theory and free
quantum field theory.Comment: Opinion paper. Special issue of Philosophical Transaction A, devoted
to the VI Hilbert problem, after the Workshop "Hilbert's Sixth Problem",
University of Leicester, May 02-04 201
Cellular Automata as a Means Complex Systems Modelling
Стаття присвячена характеристиці кліткових автоматів як методу моделювання складних систем. Багато складних явищ та процесів, таких як самовідтворення, ріст, розвиток тощо складно описати за допомогою диференціальних рівнянь та їх систем. Проте це вдається легко змоделювати за допомогою кліткових автоматів. Відповідно зростає популярність моделей, побудованих на їх основі. Клітковий автомат характеризується дискретним простором і часом. Така структура є зручною для моделювання різноманітних фізичних, біологічних та інформаційних процесів. Застосування кліткових автоматів дозволяє змоделювати складну поведінку об’єктів чи явищ без використання складного і громіздкого математичного опису. Популярність кліткових автоматів пояснюється їх відносною простотою у поєднанні з великими можливостями використання для моделювання сукупності однорідних взаємозв’язаних об’єктів. Поряд з цим відзначають і слабкий загальний теоретичний фундамент кліткових автоматів, недостатнє вивчення питань збіжності обчислювальних експериментів та стійкості отриманих результатів.
Для дослідження використовувались такі методи як системний науково-методологічний аналіз підручників і навчальних посібників, монографій, статей і матеріалів науково-методичних конференцій; спостереження навчального процесу; аналіз результатів навчання студентів у відповідності до проблеми дослідження; синтез, порівняння та узагальнення теоретичних положень, розкритих у науковій та навчальній літературі; узагальнення власного педагогічного досвіду та досвіду колег з інших закладів вищої освіти.
У статті наводиться історична довідка з розвитку теорії кліткових автоматів. Пропонується схема реалізації кліткових автоматів. Детальніше описується гра «Життя».
Подальші дослідження будуть зосереджені на аналізі можливостей використання кліткових автоматів для моделювання складних систем та методиці навчання моделювання на основі кліткових автоматів для студентів другого (магістерського) рівня вищої освіти педагогічного університету у межах дисципліни «Основи штучного інтелекту».The article is devoted to the characterization of cellular automata as a method for modeling complex systems. Many complex phenomena and processes, such as self-reproduction, growth, development, etc. are difficult to describe by using differential equations and their systems. However, this can be easily modeled by using cellular automata. Accordingly, models have become more popular built up from them. The cellular automata is characterized by discrete space and time. This structure is convenient for modeling a variety physical, biological and information processes. The use of cellular automata allows you to simulate the complex behavior of objects or phenomena without the use of complicated and cumbersome mathematical descriptions. Cellular automata is popular because of its relative simplicity in combination with the great possibilities of using for modeling a set of homogeneous interconnected objects. Along with this, we note the weak general theoretical foundation of cellular automata, the insufficient study of the problems of convergence of computational experiments and the stability of the results.
We used methods such as systematic review of textbooks and manuals, monographs, articles and materials of scientific and methodical conferences; analysis of student learning outcomes in accordance with the research problem; synthesis, comparison and synthesis of theoretical positions described in scientific and educational literature; generalization of our own pedagogical experience and experience of colleagues from other higher educational institutions.
In the article we present a historical background on the development of the cellular automata theory. We propose the implementation scheme of cellular automata and describe the Conway’s Game of life in more detail.
We will focus further research on the analysis of the possibilities of using cellular automata for the modeling of complex systems and teaching methodology of modeling based on cellular automata for students of the second (master's) level of higher education at a pedagogical university within the discipline "Fundamentals of Artificial Intelligence"
The ideal energy of classical lattice dynamics
We define, as local quantities, the least energy and momentum allowed by
quantum mechanics and special relativity for physical realizations of some
classical lattice dynamics. These definitions depend on local rates of
finite-state change. In two example dynamics, we see that these rates evolve
like classical mechanical energy and momentum.Comment: 12 pages, 4 figures, includes revised portion of arXiv:0805.335
Finite size scaling in three-dimensional bootstrap percolation
We consider the problem of bootstrap percolation on a three dimensional
lattice and we study its finite size scaling behavior. Bootstrap percolation is
an example of Cellular Automata defined on the -dimensional lattice
in which each site can be empty or occupied by a single
particle; in the starting configuration each site is occupied with probability
, occupied sites remain occupied for ever, while empty sites are occupied by
a particle if at least among their nearest neighbor sites are
occupied. When is fixed, the most interesting case is the one :
this is a sort of threshold, in the sense that the critical probability
for the dynamics on the infinite lattice switches from zero to one
when this limit is crossed. Finite size effects in the three-dimensional case
are already known in the cases : in this paper we discuss the case
and we show that the finite size scaling function for this problem is
of the form . We prove a conjecture proposed by
A.C.D. van Enter.Comment: 18 pages, LaTeX file, no figur
Energy Transport in an Ising Disordered Model
We introduce a new microcanonical dynamics for a large class of Ising systems
isolated or maintained out of equilibrium by contact with thermostats at
different temperatures. Such a dynamics is very general and can be used in a
wide range of situations, including disordered and topologically inhomogenous
systems. Focusing on the two-dimensional ferromagnetic case, we show that the
equilibrium temperature is naturally defined, and it can be consistently
extended as a local temperature when far from equilibrium. This holds for
homogeneous as well as for disordered systems. In particular, we will consider
a system characterized by ferromagnetic random couplings . We show that the dynamics relaxes to steady states,
and that heat transport can be described on the average by means of a Fourier
equation. The presence of disorder reduces the conductivity, the effect being
especially appreciable for low temperatures. We finally discuss a possible
singular behaviour arising for small disorder, i.e. in the limit .Comment: 14 pages, 8 figure
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