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In quantum mechanics, not everything that can be observed can be observed simultaneously. Observational data exhibits \emph{contextuality} -- a generalisation of nonlocality -- if the result of an observation is necessarily dependent on…
The Principle of Relativity has so far been understood as the {\it covariance} of laws of Physics with respect to a general class of reference frame transformations. That relativity, however, has only been expressed with the help of {\it…
Certain causal models involving unmeasured variables induce no independence constraints among the observed variables but imply, nevertheless, inequality contraints on the observed distribution. This paper derives a general formula for such…
In this paper we analyse scalar-tensor theories-specific instances of which include mainstream inflation and dark energy models-in light of the spacetime-matter dichotomy. We argue that it is difficult to categorise the scalar fields as…
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…
We suggest a new cosmological scenario which naturally guarantees the smallness of scalar masses and VEVs, without invoking supersymmetry or any other (non-gravitationaly coupled) new physics at low energies. In our framework, the scalar…
We study a modification of the Plebanski action, which generically corresponds to a bi-metric theory of gravity, and identify a subclass which is equivalent to the Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories. In this manner,…
In this paper I shall consider various possible scalar-vector-tensor field theories which might be used to describe the Universe. After imposing numerous constraints of a physical and mathematical nature on the theories under consideration,…
Spontaneous scalarization phenomenon in scalar-tensor gravity is known to be a form of phase transition, and it was recently shown that the order of this transition changes depending on the parameters of the theory. There exists a…
We collect in this note some observations on the role of symmetries in Bayesian inference problems, that can be useful or detrimental depending on the way they act on the signal and on the observations. We emphasize in particular the need…
The Sobol' indices are a recognized tool in global sensitivity analysis. When the uncertain variables in a model are statistically independent, the Sobol' indices may be easily interpreted and utilized. However, their interpretation and…
The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective…
The scalar-tensor theory of gravitation has been and still is one of the most widely discussed "alternative theories" to General Relativity (GR). Despite nearly half a century of its age, it continues to attract renewed interests of not…
The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with…
Recently, it was shown that most popular IR measures are not interval-scaled, implying that decades of experimental IR research used potentially improper methods, which may have produced questionable results. However, it was unclear if and…
In the era of "big data", it is becoming more of a challenge to not only build state-of-the-art predictive models, but also gain an understanding of what's really going on in the data. For example, it is often of interest to know which, if…
The work is based on two premises: local availability of mathematics to an observer at any space time location, and the observation that number systems, as structures satisfying axioms for the number type being considered, can be scaled by…
Modellers of complex biological or social systems are often faced with an invidious choice: to use simple models with few mechanisms that can be fully analysed, or to construct complicated models that include all the features which are…
We discuss some of the issues which we encounter when we try to invoke the scalar-tensor theories of gravitation as a theoretical basis of quintessence. One of the advantages of appealing to these theories is that they allow us to implement…
Forced advection of passive tracer, $\theta $, in nonlinear relaxational medium by large scale (Batchelor problem) incompressible velocity field at scales less than the correlation length of the flow and larger than the diffusion scale is…