Related papers: Higher rank Brill-Noether theory and coherent syst…
This note considers fairly general quasi-homogeneous systems of first-order nonlinear ODEs and homogeneous systems of second-order nonlinear ODEs that contain arbitrary functions of several arguments. It presents several exact solutions to…
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…
These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of $N$-differential modules and $N$-complexes. Several applications and examples coming…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
A new class of higher-spin gauge theories associated with various Coxeter groups is proposed. The emphasize is on the $B_p$--models. The cases of $B_1$ and its infinite graded-symmetric product $sym\,(\times B_1)^\infty$ correspond to the…
This chapter revisits the concept of excitability, a basic system property of neurons. The focus is on excitable systems regarded as behaviors rather than dynamical systems. By this we mean open systems modulated by specific interconnection…
We introduce and axiomatize the notion of a reflective cardinal, use it to give semantics to higher order set theory, and explore connections between the notion of reflective cardinals and large cardinal axioms.
In this paper we develop a blow up theory for the parabolic-elliptic Keller-Segel system, which can be viewed as a parabolic counterpart to the Liouville equation. This theory is applied to the study of first time singularities, ancient…
The Noether procedure represents a perturbative scheme to construct all possible consistent interactions starting from a given free theory. In this note we describe how cubic interactions involving higher spins in any constant-curvature…
This paper surveys the theory of compactness of the d-bar-Neumann problem. It also contains several results which improve upon what was previously known.
Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…
In this letter, we propose high order layered complex networks. The synchronization is discussed in detail. The relations of synchronization, individual coupling matrices and the intrinsic function of the uncoupled system are given. As…
We analyze the relation of the notion of pluri-Lagrangian systems, which recently emerged in the theory of integrable systems, to the classical notion of variational symmetry, due to E. Noether.
Even if a ring A is coherent, the polynomial ring A[X] in one variable could fail to be coherent. In this note we show that A[X] is graded coherent with the standard grading deg X=1. More generally, we give a criterion of graded…
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…
This article presents an overview of neutrino physics research, with highlights on the physics goals, results and interpretations of the current neutrino experiments and future directions and program. It is not meant to be a comprehensive…
Several stimulating open questions in high energy spin physics will be described together with the striking progress recently achieved in this field. In view of the new experimental facilities and the new tools, soon available, I will try…
Chemical reaction networks (CRNs) are prototypical complex systems because reactions are nonlinear and connected in intricate ways, and they are also essential to understand living systems. Here, I discuss how recent developments in…
Generalized uncertainty relations may depend not only on the commutator relation of two observables considered, but also on mutual correlations, in particular, on entanglement. The equivalence between the uncertainty relation and Bohr's…
A Brill-Noether degeneracy locus is closure in $\Pic^d(C)$ of the locus of line bundles with a specified rank function $r(a,b) = h^0(C,L(-ap-bq))$. These loci generalize the classical Brill-Noether loci $W^r_d(C)$ as well as Brill-Noether…