相关论文: Algorithmic Theories of Everything

I am presenting a first-ever scientific collection of short sayings on probability and statistics expressed by most various men of science, many classics included, from antiquity to Kepler to our time. Quite understandably, the reader will…

We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are…

Contemporary global optimization algorithms are based on local measures of utility, rather than a probability measure over location and value of the optimum. They thus attempt to collect low function values, not to learn about the optimum.…

Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…

In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…

Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…

Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…

Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…

Probability theory as a physical theory is, in a sense, the most general physics theory available, more encompassing than relativity theory and quantum mechanics, which comply with probability theory. Taking this simple fact seriously, I…

We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…

We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…

In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…

We develop a theory of estimation when in addition to a sample of $n$ observed outcomes the underlying probabilities of the observed outcomes are known, as is typically the case in the context of numerical simulation modeling, e.g. in…

We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…

A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…

Quantum theory combines density matrices, Born probabilities, tensor-product composites, positive-operator-valued measures (POVMs), and quantum channels. In a finite-dimensional causal operational theory, we prove that two postulates…

Special relativity is most naturally formulated as a theory of space-time geometry, but within the space-time framework probability apears to be at best an epistemic notion - a matter of what can be known, not of the status of events in…

For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of the universe as a sample point of an accumulative stochastic process. The model give predictions that are nearly identical…

Suppose that we are given an infinite binary sequence which is random for a Bernoulli measure of parameter $p$. By the law of large numbers, the frequency of zeros in the sequence tends to~$p$, and thus we can get better and better…

Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities…