Related papers: Studies on the Lorenz model
An overview is given of basic models combining discreteness in their linear parts (i.e. the models are built as dynamical lattices) and nonlinearity acting at sites of the lattices or between the sites. The considered systems include the…
We develop the relative Morse index theory for linear self-adjoint operator equation without compactness assumption and give the relationship between the index defined in [44] and [45]. Then we generalize the method of saddle point…
The modular reduction of the Steinberg lattice of the general linear group is studied
This is an overview of various aspects of the 6-vertex model in statistical mechanics and related models.
We generalize a recent result of Clausen: For a number field with integers O, we compute the K-theory of locally compact O-modules. For the rational integers this recovers Clausen's result as a special case. Our method of proof is quite…
We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution $W(x)=w(r)e^{i\theta}$. Using explicit representation formulae for the Fourier modes in $\theta$, we obtain sharp estimates for…
Rural-urban classifications are essential for analyzing geographic, demographic, environmental, or socioeconomic processes across the rural-urban continuum. However, existing county-level classifications may ignore the within-county…
By homotopy linear algebra we mean the study of linear functors between slices of the $\infty$-category of $\infty$-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices…
We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.
This paper studies the sensitivity to the observations of the block/group Lasso solution to an overdetermined linear regression model. Such a regularization is known to promote sparsity patterns structured as nonoverlapping groups of…
We study the properties of marginal distributions-projections of the phase space representation of a physical system-under relativistic transforms. We consider the Galileo case as well as the Lorentz transforms exploiting the relativistic…
Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.
In this work we consider an unfolding of a normal form of the Lorenz system near a triple-zero singularity. We are interested in the analysis of double-zero bifurcations emerging from that singularity. Their local study provide partial…
Model theoretic internality provides conditions under which the group of automorphisms of a model over a reduct is itself a definable group. In this paper we formulate a categorical analogue of the condition of internality, and prove an…
We discuss to what extent the local techniques of resolution of singularities over fields of characteristic zero can be applied to improve singularities in general. For certain interesting classes of singularities, this leads to an embedded…
We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.
This letter deals with the controllability issue of complex networks. An index is chosen to quantitatively measure the extent of controllability of given network. The effect of this index is analyzed based on empirical studies on various…
Field equations for generalized principle models with nonconstant metric are derived and ansatz for their Lax pairs is given. Equations that define the Lax pairs are solved for the simplest solvable group. The solution is dependent on one…
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…
We establish local characterizations of matrix monotonicity and convexity of fixed order by giving integral representations connecting the Loewner and Kraus matrices, previously known to characterize these properties, to respective Hankel…