Related papers: A model of the cubic connectedness locus

We address the problem of topology of quadrature domains, namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in the quadrature identity.

We consider the extension of the Jackson calculus into higher dimensions and specifically into Clifford analysis.

We settle the existence of certain "anti-magic" cubes using combinatorial block designs and graph decompositions to align a handful of small examples.

The idea that data lies on a non-linear space has brought up the concept of manifold learning as a part of machine learning.

Starting from a cubic form, we give a general construction of a quasi-complete homogeneous manifold endowed with a natural contact structure. We show that it can be compactified into a projective contact manifold if and only if the cubic…

We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.

We define a relation that describes the ternary commutator for congruence modular varieties. Properties of this relation are used to investigate the theory of the higher commutator for congruence modular varieties.

We describe topologically the discriminant locus of a smooth cubic surface in the complex projective space ${\mathbb{CP}}^3$ that contains 5 fibres of the projection ${\mathbb{CP}}^3 \longrightarrow S^4$.

We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of…

We generalize the Cooper problem to the case of many interacting particles in the vicinity of the Fermi level in the presence of disorder. On the basis of this approach we study numerically the variation of the pair coupling energy in small…

Inspired by the works in linkage theory of modules, we define the concept of linkage of sheaves of modules as a generalization of linkage of modules. Thus, we expressed it in geometry algebraic language. We show that the linkedness of…

In this paper we study the conjugate locus in convex manifolds. Our main tool is Jacobi fields, which we use to define a special coordinate system on the unit sphere of the tangent space; this provides a natural coordinate system to study…

In this paper we provide theoretical results that relate steady states of continuous and discrete models arising from biology.

We show that quantum computation circuits with coherent states as the logical qubits can be constructed using very simple linear networks, conditional measurements and coherent superposition resource states.

We exhibit a percolating ergodic and isotropic lattice model in all but at least two dimensions that has zero effective conductivity in all spatial directions and for all non-trivial choices of the connectivity parameter. The model is based…

Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.

We provide a survey on relational models. Relational models describe complete networked {domains by taking into account global dependencies in the data}. Relational models can lead to more accurate predictions if compared to non-relational…

Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…

In an array of coupled cavities where the cavities are doped with an atomic V-system, and the two excited levels couple to cavity photons of different polarizations, we show how to construct various spin models employed in characterizing…

Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side. We introduce "network models" to encode these ways of combining networks. Different network models describe different kinds of…