The paper treats the issue of prediction in the economic (social) field, in a theoretical framework that replaces the truth with the reasonability. In this end, some already accepted parameters around the prediction need reconfiguration: causality to be replaced with explanatory protocol,...

Space-time manifold plays an important role to express the concepts of Relativity properly. Causality and space-time topology make easier the geometrical explanation of Minkowski space-time manifold. The Minkowski metric is the simplest empty space-time manifold in General Relativity, and is in...

We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out to have hidden strict convexity properties in many...

We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out to have hidden strict convexity properties in many...

We consider two Riemannian geometries for the manifold <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal{M }(p,m\times n)}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="script">M</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mo>×</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> of all <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$m\times n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>m</mi> <mo>×</mo> <mi>n</mi> </mrow> </math> </EquationSource> </InlineEquation> matrices of rank <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>p</mi> </math> </EquationSource> </InlineEquation>. The geometries are induced on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$${\mathcal{M }(p,m\times n)}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="script">M</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mo>×</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> by viewing it as the base...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

We formulate a Bohr-type rotating particle model for three light particles of rest mass mo each, forming a bound rotational state under the influence of their gravitational attraction, in the same way that electrostatic attraction leads to the formation of a bound proton–electron state in the...

The issue of the non-invariance of the Wald test under nonlinear reparametrisations of the restrictions under test is studied from a differential geometric viewpoint. Quantities that can be defined in purely geometrical terms are by construction invariant under reparametrisation, and various...