scholarly journals Causal influence in operational probabilistic theories

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 515
Author(s):  
Paolo Perinotti
Keyword(s):  
Quantum Theory ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Classical Theory ◽  
The Other ◽  
Causal Influence ◽  
Causal Networks ◽  
A Cell ◽  
Reversible Evolution ◽  
Probabilistic Theories

We study the relation of causal influence between input systems of a reversible evolution and its output systems, in the context of operational probabilistic theories. We analyse two different definitions that are borrowed from the literature on quantum theory—where they are equivalent. One is the notion based on signalling, and the other one is the notion used to define the neighbourhood of a cell in a quantum cellular automaton. The latter definition, that we adopt in the general scenario, turns out to be strictly weaker than the former: it is possible for a system to have causal influence on another one without signalling to it. Remarkably, the counterexample comes from classical theory, where the proposed notion of causal influence determines a redefinition of the neighbourhood of a cell in cellular automata. We stress that, according to our definition, it is impossible anyway to have causal influence in the absence of an interaction, e.g. in a Bell-like scenario. We study various conditions for causal influence, and introduce the feature that we call no interaction without disturbance, under which we prove that signalling and causal influence coincide. The proposed definition has interesting consequences on the analysis of causal networks, and leads to a revision of the notion of neighbourhood for classical cellular automata, clarifying a puzzle regarding their quantisation that apparently makes the neighbourhood larger than the original one.

Pseudorandom Number Generators Based on Asynchronous Cellular Automata and Cellular Automata With Inhomogeneous Cells

2017 ◽  
pp. 127-138
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Local State ◽  
Active Cell ◽  
State Function ◽  
Local Function ◽  
Time Step ◽  
Random Number Generators ◽  
Asynchronous Cellular Automata ◽  
A Cell

The sixth chapter deals with the construction of pseudo-random number generators based on a combination of two cellular automata, which were considered in the previous chapters. The generator is constructed based on two cellular automata. The first cellular automaton controls the location of the active cell on the second cellular automaton, which realizes the local state function for each cell. The active cell on the second cellular automaton is the main cell and from its output bits of the bit sequence are formed at the output of the generator. As the first cellular automaton, an asynchronous cellular automaton is used in this chapter, and a synchronous cellular automaton is used as the second cellular automaton. In this case, the active cell of the second cellular automaton realizes another local function at each time step and is inhomogeneous. The algorithm for the work of a cell of a combined cellular automaton for implementing a generator and its hardware implementation are presented.

scholarly journals Cellular automata in operational probabilistic theories

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 294 ◽  
Author(s):  
Paolo Perinotti
Keyword(s):  
Cellular Automata ◽  
Cayley Graph ◽  
Small Scale ◽  
General Version ◽  
Causal Influence ◽  
Small Scale Structure ◽  
Composite Systems ◽  
Usual Property ◽  
Update Rules ◽  
Probabilistic Theories

The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite systems. The notion of causal influence is introduced, and its relation with the usual property of signalling is discussed. We then introduce homogeneity, namely the property of an update rule to evolve every system in the same way, and prove that systems evolving by a homogeneous rule always correspond to vertices of a Cayley graph. Next, we define the notion of locality for update rules. Cellular automata are then defined as homogeneous and local update rules. Finally, we prove a general version of the wrapping lemma, that connects CA on different Cayley graphs sharing some small-scale structure of neighbourhoods.

scholarly journals Causality re-established

2018 ◽  
Vol 376 (2123) ◽  
pp. 20170313 ◽  
Author(s):  
Giacomo Mauro D’Ariano
Keyword(s):  
Quantum Theory ◽  
Classical Theory ◽  
Recent Literature ◽  
Foundations Of Quantum Mechanics ◽  
Classical Case ◽  
The Status ◽  
Interpretation Of Quantum Theory ◽  
False Idea ◽  
Block Universe ◽  
Probabilistic Theories

Causality has never gained the status of a ‘law’ or ‘principle’ in physics. Some recent literature has even popularized the false idea that causality is a notion that should be banned from theory. Such misconception relies on an alleged universality of the reversibility of the laws of physics, based either on the determinism of classical theory, or on the multiverse interpretation of quantum theory, in both cases motivated by mere interpretational requirements for realism of the theory. Here, I will show that a properly defined unambiguous notion of causality is a theorem of quantum theory, which is also a falsifiable proposition of the theory. Such a notion of causality appeared in the literature within the framework of operational probabilistic theories. It is a genuinely theoretical notion, corresponding to establishing a definite partial order among events, in the same way as we do by using the future causal cone on Minkowski space. The notion of causality is logically completely independent of the misidentified concept of ‘determinism’, and, being a consequence of quantum theory, is ubiquitous in physics. In addition, as classical theory can be regarded as a restriction of quantum theory, causality holds also in the classical case, although the determinism of the theory trivializes it. I then conclude by arguing that causality naturally establishes an arrow of time. This implies that the scenario of the ‘block Universe’ and the connected ‘past hypothesis’ are incompatible with causality, and thus with quantum theory: they are both doomed to remain mere interpretations and, as such, are not falsifiable, similar to the hypothesis of ‘super-determinism’. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

TrueLife – Evolving the Game of Life

2017 ◽  
Author(s):  
Kent Fenwick
Keyword(s):  
Quantum Theory ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Model System ◽  
Game Of Life ◽  
Current State ◽  
Emergence Theory ◽  
Unique Aspect ◽  
Conway’S Game Of Life ◽  
Scientific American

John Conway’s Game of Life, published in Scientific American in 1970 is an attempt to model the behavior  of life using a 2D cellular automaton. Although a breakthrough discovery for cellular automata and  emergence theory, the game is restricted and incomplete due to its static, simplified rules. We will show that the game does not model life accurately and propose an alternative: TrueLife. TrueLife is a non­  deterministic, non­local, evolving Game of Life variant that we believe is more complete than Life for  several key reasons. TrueLife is unique since at each generation a rule is chosen randomly from a list and  applied to the current state. This allows the game to be inherently non­deterministic since it is impossible to know which rule is being applied at a given iteration. TrueLife will also be a learning simulation where rules that produce better results will be applied more frequently. Another unique aspect of TrueLife is the motivation behind the rules. The original Life rules are Darwinian and selfish acting only on local inputs that lead to local outputs. TrueLife’s rules will be non­local and act globally across the entire grid. TrueLife’s rules were formalized by drawing on much broader areas of science such as ecology, psychology and quantum theory. We are currently in the process of finding a model system to which  TrueLife would be best suited.

scholarly journals Mean equicontinuity and mean sensitivity on cellular automata

2020 ◽  
pp. 1-18
Author(s):  
LUGUIS DE LOS SANTOS BAÑOS ◽  
FELIPE GARCíA-RAMOS
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
The Other ◽  
Other Hand ◽  
Full Shift ◽  
Mean Sensitivity

Abstract We show that a cellular automaton (or shift-endomorphism) on a transitive subshift is either almost equicontinuous or sensitive. On the other hand, we construct a cellular automaton on a full shift (hence a transitive subshift) that is neither almost mean equicontinuous nor mean sensitive.

Simulating Self-Regeneration and Self-Replication Processes Using Movable Cellular Automata with a Mutual Equilibrium Neighborhood

2020 ◽  
Vol 29 (4) ◽  
pp. 741-757
Author(s):  
Kateryna Hazdiuk ◽  
◽  
Volodymyr Zhikharevich ◽  
Serhiy Ostapov ◽  
◽  
...  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Three Dimensional ◽  
Computer Models ◽  
The Self ◽  
Model Construction ◽  
Natural Phenomena ◽  
Different Types ◽  
Movable Cellular Automata ◽  
Self Replication

This paper deals with the issue of model construction of the self-regeneration and self-replication processes using movable cellular automata (MCAs). The rules of cellular automaton (CA) interactions are found according to the concept of equilibrium neighborhood. The method is implemented by establishing these rules between different types of cellular automata (CAs). Several models for two- and three-dimensional cases are described, which depict both stable and unstable structures. As a result, computer models imitating such natural phenomena as self-replication and self-regeneration are obtained and graphically presented.

scholarly journals Comparison between instrumental variable and mediation-based approaches for reconstructing causal gene networks in yeast

2021 ◽  
Author(s):  
Adriaan-Alexander Ludl ◽  
Tom Michoel
Keyword(s):  
Instrumental Variable ◽  
Gene Networks ◽  
Omics Data ◽  
Causal Gene ◽  
Causal Networks ◽  
Transcriptomics Data ◽  
A Cell ◽  
Flow Of Information

Causal gene networks model the flow of information within a cell. Reconstructing causal networks from omics data is challenging because correlation does not imply causation. When genomics and transcriptomics data...

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

A new classical theory of electrons

1951 ◽  
Vol 209 (1098) ◽  
pp. 291-296 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Classical Theory ◽  
Physical Significance ◽  
Gauge Transformations

In the theory of the electromagnetic field without charges, the potentials are not fixed by the field, but are subject to gauge transformations. The theory thus involves more dynamical variables than are physically needed. It is possible by destroying the gauge transformations to make the superfluous variables acquire a physical significance and describe electric charges. One gets in this way a simplified classical theory of electrons, which appears to be more suitable than the usual one as a basis for a passage to the quantum theory.

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