相关论文: An Explicit and Simple Relationship Between Two Mo…
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
Collective Adaptive Systems often consist of many heterogeneous components typically organised in groups. These entities interact with each other by adapting their behaviour to pursue individual or collective goals. In these systems, the…
The Schwinger oscillator operator representation of SU(3) is analysed with particular reference to the problem of multiplicity of irreducible representations. It is shown that with the use of an $Sp(2,R)$ unitary representation commuting…
Here we briefly describe some topics along the lines of projective spaces and related geometric constructions connected to linear algebra, which provide fundamental examples in classical geometry and analysis.
Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…
Two classifications of second order ODE's cubic with respect to the first order derivative are compared in the case of general position, which is common for both classifications. The correspondence of vectorial, pseudovectorial, scalar, and…
We study relations between reflections in (positive or negative) points in the complex hyperbolic plane. It is easy to see that the reflections in the points q_1,q_2 obtained from p_1,p_2 by moving p_1,p_2 along the geodesic generated by…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
We derive a perturbative formula for the direct interaction between two four-dimensional geometries. Based on the spectral action principle we give an explicit potential up to the third order perturbation around the flat vacua. We present…
We present a simple visual description of the topology of the space of three-dimensional rotations, requiring just intuition, imagination and no advanced math.
A noncommutative space is considered the position operators of which satisfy the commutativity relations of a Lie algebra. The basic tools for calculation on this space, including the product of the fields, inner product and the proper…
A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…
Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…
A simple model for the formation of a complex organism is introduced. Individuals can communicate and specialize, leading to an increase in productivity. If there are limits to the capacity of individuals to communicate with other…
The irreducible representations of the Lie algebra ${\frak su}$(3) describe rotational bands in the context of the nuclear shell and interacting boson models. The density matrices associated with ${\frak su}$(3) provide an alternative…
We prove many new results about interacting Fock spaces. We pose many open problems; for most of them we prove that their solutions have no choice but being nontrivial. We ask the kind reader to consult the extended abstract in the paper.
In this work we try to clarify the fundamental relationship between bits and qubits, starting from very simple George Boole equation. We derive a generic and compact expression for basis vectors of qubit which can be useful in further…
Considered two linear regression models of a given response variable with some predictor set and its subset. It is shown that there is a linear relationship between coefficients of these models. Some corollaries of the proved theorem is…
The Schwinger oscillator operator representation of SU(3), studied in a previous paper from the representation theory point of view, is analysed to discuss the intimate relationships between standard oscillator coherent state systems and…
Spatial understanding is a fundamental problem with wide-reaching real-world applications. The representation of spatial knowledge is often modeled with spatial templates, i.e., regions of acceptability of two objects under an explicit…