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In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
The origin of the anomalies is analyzed. It is shown that they are due to the fact that the generators of the symmetry do not leave invariant the domain of definition of the Hamiltonian and then a term, normally forgotten in the Heisenberg…
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the irrational rotations on the unit circle $\beta \mapsto \set{\alpha+\beta}$, $\alpha \in \R\setminus \Q$. In…
A quandle is an algebraic system originating in knot theory, which can be regarded as a generalization of the conjugation of groups. This structure naturally defines two subgroups of its automorphism group, which are called the inner…
A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…
We consider Clifford algebras with nonsymmetric bilinear forms, which are isomorphic to the standard symmetric ones, but not equal. Observing, that the content of physical theories is dependent on the injection $\oplus^n\bigwedge…
The regularity theory for pluriclosed flow hinges on obtaining $C^{\alpha}$ regularity for the metric assuming uniform equivalence to a background metric. This estimate was established in \cite{StreetsPCFBI} by an adaptation of ideas from…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
Normalization is ubiquitous in economics, and a growing literature shows that ``normalizations'' can matter for interpretation, counterfactual analysis, misspecification, and inference. This paper provides a general framework for these…
Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically,…
Inverse problems, where in broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
We explore the origins of parameters in adimensional theories -- fundamental theories with no classical massive scales. If the parameters originate as draws from a distribution, it should be possible to write a distribution for them that…
We develop here a concept of deformed algebras through three examples and an application. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through formal series. We show how the example of…
We study some new invariant measures arising from local inverse iterates. Examples are also given.
We introduce a new method for studying murmurations, based on random matrix theory. With this method, we exhibit murmurations or similar phenomena: assuming ratios conjectures, for elliptic curves ordered by height, quadratic twists of a…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
We find and describe unexpected isomorphisms between two very different objects associated to hypersurface singularities. One object is the Milnor algebra of a function, while the other object associated to a singularity is the local ring…
We discuss the following proposition: Renormalization Group flow of quantum theory with a biased symmetry exhibits a fixed hypersurface at which the symmetry is exact. Such emergent symmetries may have important phenomenological…