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The broad concept of emergence is instrumental in various of the most challenging open scientific questions -- yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory…

In real-world systems, phase transitions often materialize abruptly, making it difficult to design appropriate controls that help uncover underlying processes. Some agent-based computational models display transformations similar to phase…

Actual causation is concerned with the question "what caused what?" Consider a transition between two states within a system of interacting elements, such as an artificial neural network, or a biological brain circuit. Which combination of…

Concrete computing machines, either sequential or concurrent, rely on an intimate relation between computation and time. We recall the general characteristic properties of physical time and of present realizations of computing systems. We…

Computing according to laymens procedures is changed to contain a paradigm of inoptimality in the high level and assembled code. The code is changed to maximize the flow of information contained in the electrons so that they function more…

In distributed systems where strong consistency is costly when not impossible, causal consistency provides a valuable abstraction to represent program executions as partial orders. In addition to the sequential program order of each…

Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a…

Consciousness spans macroscopic experience and microscopic neuronal activity, yet linking these scales remains challenging. Prevailing theories, such as Integrated Information Theory, focus on a single scale, overlooking how causal power…

Causal emergence is the theory that macroscales can reduce the noise in causal relationships, leading to stronger causes at the macroscale. First identified using the effective information and later the integrated information in model…

Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…

Causality is the relationship where one event contributes to the production of another, with the cause being partly responsible for the effect and the effect partly dependent on the cause. In this paper, we propose a novel and effective…

Neural networks often have identifiable computational structures - components of the network which perform an interpretable algorithm or task - but the mechanisms by which these emerge and the best methods for detecting these structures are…

Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that…

Although it has been notoriously difficult to pin down precisely what it is that makes life so distinctive and remarkable, there is general agreement that its informational aspect is one key property, perhaps the key property. The unique…

We describe a new form of retrocausality, which is found in the behaviour of a class of causal set theories, called energetic causal sets (ECS). These are discrete sets of events, connected by causal relations. They have three orders: (1) a…

Emergence is a pregnant property in various fields. It is the fact for a phenomenon to appear surprisingly and to be such that it seems at first sight that it is not possible to predict its apparition. That is the reason why it has often…

The problem of emergence in physical theories makes necessary to build a general theory of the relationships between the observed system and the observing system. It can be shown that there exists a correspondence between classical systems…

Beneficial to advanced computing devices, models with massive parameters are increasingly employed to extract more information to enhance the precision in describing and predicting the patterns of objective systems. This phenomenon is…

Theories for reasoning about programs with effects initially focused on basic manipulation of lists and other mutable data. The next challenge was to consider higher-order programming, adding functions as first class objects to mutable…

There has been much controversy over weak and strong emergence in physics and biology. As pointed out by Phil Anderson in many papers, the existence of broken symmetries is the key to emergence of properties in much of solid state physics.…