Hyperconnected Research Articles

Degenerating Hermitian metrics and spectral geometry of the canonical bundle

Let (X,h) be a compact and irreducible Hermitian complex space of complex dimension m. In this paper we are interested in the Dolbeault operator acting on the space of L2 sections of the canonical bundle of reg(X), the regular part of X. More precisely let d‾m,0:L2Ωm,0(reg(X),h)→L2Ωm,1(reg(X),h) be an arbitrarily fixed closed extension of ∂‾m,0:L2Ωm,0(reg(X),h)→L2Ωm,1(reg(X),h) where the domain of the latter operator is Ωcm,0(reg(X)). We establish various properties such as closed range of d‾m,0, compactness of the inclusion D(d‾m,0)↪L2Ωm,0(reg(X),h) where D(d‾m,0), the domain of d‾m,0, is endowed with the corresponding graph norm, and discreteness of the spectrum of the associated Hodge–Kodaira Laplacian d‾m,0⁎∘d‾m,0 with an estimate for the growth of its eigenvalues. Several corollaries such as trace class property for the heat operator associated to d‾m,0⁎∘d‾m,0, with an estimate for its trace, are derived. Finally in the last part we provide several applications to the Hodge–Kodaira Laplacian in the setting of both compact irreducible Hermitian complex spaces with isolated singularities and complex projective surfaces.

The Origin and Nature of the Hyper-Connected Society in the light of Political Economy

The Origin and Nature of the Hyper-Connected Society in the light of Political Economy

Development of User-customized Device Intelligent Character using IoT-based Lifelog data in Hyper-Connected Society

Development of User-customized Device Intelligent Character using IoT-based Lifelog data in Hyper-Connected Society

Distributed Intelligence Core Technology of Hyper-Connected Space

Distributed Intelligence Core Technology of Hyper-Connected Space

A new convergence inducing the SI-topology

In their attempt to develop domain theory in situ T0 spaces, Zhao and Ho introduced a new topology defined by irreducible sets of a resident topological space, called the SI-topology. Notably, the SI-topology of the Alexandroff topology of posets is exactly the Scott topology, and so the SI-topology can be seen as a generalisation of the Scott topology in the context of general T0 spaces. It is well known that the convergence structure that induces the Scott topology is the Scott-convergence - also known as lim-inf convergence by some authors. Till now, it is not known which convergence structure induces the SI-topology of a given T0 space. In this paper, we fill in this gap in the literature by providing a convergence structure, called the SI-convergence structure, that induces the SI-topology. Additionally, we introduce the notion of I-continuity that is closely related to the SI-convergence structure, but distinct from the existing notion of SI-continuity (introduced by Zhao and Ho earlier). For SI-continuity, we obtain here some equivalent conditions for it. Finally, we give some examples of non-Alexandroff SI-continuous spaces.

Deletion Presolve for Accelerating Infeasibility Diagnosis in Optimization Models

Whereas much research in the area of optimization is directed toward developing algorithms for optimization of feasible models, the diagnosis of infeasible models has not received as much attention. Identification of irreducible infeasible sets (IISs) can facilitate the process of correcting infeasible models. Several filtering algorithms have been proposed for IIS identification but efficient implementations are available only for linear programs. We propose a novel approach for IIS identification that is applicable to linear programs (LPs), nonlinear programs (NLPs), mixed-integer linear programs (MIPs), and mixed-integer nonlinear programs (MINLPs). The approach makes use of a deletion presolve procedure that exploits bounds tightening techniques to reduce the model to an infeasible set (IS) in a computationally efficient manner. The IS is subsequently reduced to an IIS by applying one of the currently available exact filtering algorithms for IIS identification. We implement the proposed deletion presolve along with four filtering algorithms for IIS identification within the global solver BARON. The effectiveness and usefulness of the proposed approach is demonstrated through computational experiments on a test set of 790 infeasible LPs, NLPs, MIPs, and MINLPs. Deletion presolve rapidly eliminates a large fraction of the problem constraints and speeds up the filtering algorithms by over forty times on average. Speedups of as high as 1,000 times are observed for some problems, while, for 40% of the test problems, the deletion presolve itself reduces the original model to an IIS.

The classification problem for operator algebraic varieties and their multiplier algebras

We study from the perspective of Borel complexity theory the classification problem for multiplier algebras associated with operator algebraic varieties. These algebras are precisely the multiplier algebras of irreducible complete Nevanlinna-Pick spaces. We prove that these algebras are not classifiable up to algebraic isomorphism using countable structures as invariants. In order to prove such a result, we develop the theory of turbulence for Polish groupoids, which generalizes Hjorth’s turbulence theory for Polish group actions. We also prove that the classification problem for multiplier algebras associated with varieties in a finite-dimensional ball up to isometric isomorphism has maximum complexity among the essentially countable classification problems. In particular, this shows that Blaschke sequences are not smoothly classifiable up to conformal equivalence via automorphisms of the disc.

How right is the right to education in México?

This article approaches the meaning and the reaches of education as a human right. For this purpose we will be touching central principles such as human rights and the right to educationon. From this paradigm we will present a brief panorama of obligatory education in Mexico, focusing on elementary school conditions as stated in the 2014 Report on Education Evaluation by the National Institute for the Evaluation of Education. We propose as conclusion the need to enforce all Mexican schools have an irreducible set of conditions that guarantee a minimum of learning opportunities for all students.

Sufficiently collapsed irreducible Alexandrov 3-spaces are geometric

We prove that sufficiently collapsed, closed and irreducible three-dimensional Alexandrov spaces are modeled on one of the eight three-dimensional Thurston geometries. This extends a result of Shioya and Yamaguchi, originally formulated for Riemannian manifolds, to the Alexandrov setting.

Equilibrium Spline Interface ( ESI) for magnetic confinement codes

A compact and comprehensive interface between magneto-hydrodynamic (MHD) equilibrium codes and gyro-kinetic, particle orbit, MHD stability, and transport codes is presented. Its irreducible set of equilibrium data consists of three (in the 2-D case with occasionally one extra in the 3-D case) functions of coordinates and four 1-D radial profiles together with their first and mixed derivatives. The C reconstruction routines, accessible also from FORTRAN, allow the calculation of basis functions and their first derivatives at any position inside the plasma and in its vicinity. After this all vector fields and geometric coefficients, required for the above mentioned types of codes, can be calculated using only algebraic operations with no further interpolation or differentiation. Program summaryProgram Title: ESIProgram Files doi:http://dx.doi.org/10.17632/w6z58s6ntv.1Licensing provisions: GNU General Public License 3 (GPL)Programming language: CSupplementary material:C2esi.c, F2esi.f, demoC.c, demoF.c RZdemoC.c, RZdemoF.f programs for generation the ESI data and demonstration of their use.Nature of problem: In plasma simulations, the equilibrium codes play a fundamental role in supplying the information about magnetic configuration for different more sophisticated plasma problems: stability, transport, particle orbit or gyro-kinetics. At present, there are two extreme approaches to make a choice of output data from numerical equilibria. One of them requires all functions, necessary for the client code, at all necessary positions to be supplied by the equilibrium codes. This approach works only for closely related pairs of codes, making them highly dependent on each other. It requires excessive storage capacities because the required data may not be very smooth. This approach is not-suitable also for the situation when the client codes need physics variables at unpredictable positions inside the plasma.The other approach uses only primitive information from the equilibrium codes, such as coordinates of grid points and a few radial profiles. Then, the client codes generate all the necessary functions from equilibrium data with their own mappers, which use interpolation and numerical differentiation of original data, both causing convergence problems in the client codes.Solution method: The Equilibrium Spline Interface ( ESI), is proposed as a universal buffer between the equilibrium codes and the other plasma physics codes. ESI possesses comprehensive information about magnetic configuration and is able to provide it to magnetic confinement codes in the ready to use form.Additional comments: The main file esiXZ.c with ESI routines is described in the main text. Two (C and FORTRAN) programs C2esi.c, F2esi.f demonstrate the generation of ESI data files. Four other demo programs, linked with esiXZ.c demonstrate the use of the interface in magnetic flux coordinates ( demoC.c, demoF.f) and in laboratory cylindrical coordinates r,z ( RZdemoC.c, RZdemoF.f).

Fuzzy soft hyperconnected spaces

Fuzzy soft hyperconnected spaces

Decent Living Standards: Material Prerequisites for Human Wellbeing

We define a set of universal, irreducible and essential set of material conditions for achieving basic human wellbeing, along with indicators and quantitative thresholds, which can be operationalized for societies based on local customs and preferences. We draw support for this decent living standard (DLS) from different accounts of basic justice, including the capability approach and basic needs. The DLS goes beyond existing multidimensional poverty indicators by comprehensively addressing living conditions and the means of social participation. The DLS offers a normative basis to develop minimum wage and reference budgets, and to assess the environmental impacts, such as climate change, of eradicating poverty.

Wieler solenoids, Cuntz–Pimsner algebras and -theory

We study irreducible Smale spaces with totally disconnected stable sets and their associated$K$-theoretic invariants. Such Smale spaces arise as Wieler solenoids, and we restrict to those arising from open surjections. The paper follows three converging tracks: one dynamical, one operator algebraic and one$K$-theoretic. Using Wieler’s theorem, we characterize the unstable set of a finite set of periodic points as a locally trivial fibre bundle with discrete fibres over a compact space. This characterization gives us the tools to analyse an explicit groupoid Morita equivalence between the groupoids of Deaconu–Renault and Putnam–Spielberg, extending results of Thomsen. The Deaconu–Renault groupoid and the explicit Morita equivalence lead to a Cuntz–Pimsner model for the stable Ruelle algebra. The$K$-theoretic invariants of Cuntz–Pimsner algebras are then studied using the Cuntz–Pimsner extension, for which we construct an unbounded representative. To elucidate the power of these constructions, we characterize the Kubo–Martin–Schwinger (KMS) weights on the stable Ruelle algebra of a Wieler solenoid. We conclude with several examples of Wieler solenoids, their associated algebras and spectral triples.

Ergodic properties of matrix equilibrium states

Given a finite irreducible set of real$d\times d$matrices$A_{1},\ldots ,A_{M}$and a real parameter$s>0$, there exists a unique shift-invariant equilibrium state on$\{1,\ldots ,M\}^{\mathbb{N}}$associated to$(A_{1},\ldots ,A_{M},s)$. In this paper we characterize the ergodic properties of such equilibrium states in terms of the algebraic properties of the semigroup generated by the associated matrices. We completely characterize when the equilibrium state has zero entropy, when it gives distinct Lyapunov exponents to the natural cocycle generated by$A_{1},\ldots ,A_{M}$, and when it is a Bernoulli measure. We also give a general sufficient condition for the equilibrium state to be mixing, and give an example where the equilibrium state is ergodic but not totally ergodic. Connections with a class of measures investigated by Kusuoka are explored in an appendix.

On the Period Map for Polarized Hyperkähler Fourfolds

Abstract We study smooth projective hyperkähler fourfolds that are deformations of Hilbert squares of K3 surfaces and are equipped with a polarization of fixed degree and divisibility. They are parametrized by a quasi-projective irreducible 20-dimensional moduli space and Verbitksy’s Torelli theorem implies that their period map is an open embedding. Our main result is that the complement of the image of the period map is a finite union of explicit Heegner divisors that we describe. We also prove that infinitely many Heegner divisors in a given period space have the property that their general points correspond to fourfolds which are isomorphic to Hilbert squares of a K3 surfaces, or to double EPW (Eisenbud–Popescu–Walter) sextics. In two appendices, we determine the groups of biregular or birational automorphisms of various projective hyperkähler fourfolds with Picard number 1 or 2.

Covering Maps and Ideal Embeddings of Compact Homogeneous Spaces

The notion of ideal embeddings was introduced by the author at the Third Pacific Rim Geometry Conference held at Seoul in 1996. Roughly speaking, an ideal embedding is an isometrical embedding which receives the least possible amount of tension from the surrounding space at each point. In this article, we study ideal embeddings of irreducible compact homogenous spaces in Euclidean spaces. Our main result states that if $\pi: M\to N$ is a covering map between two irreducible compact homogeneous spaces with $\lambda_1(M)\ne \lambda_1(N)$, then $N$ does not admit an ideal embedding in a Euclidean space, although $M$ could.

Investigating the Fractal Characteristics of Pore-Fractures in Bituminous Coals and Anthracites through Fluid Flow Behavior

The characteristics of pore-fractures are the key petrophysical properties used to assess and evaluate coalbed methane (CBM) reservoirs and include pore types, structure types, porosity/percentage, and pore-fracture space properties. To study the storage and seepage capability of a CBM reservoir, based on 18 coal samples with the maximum vitrinite reflectance (Ro,max) in the range of 1.06–3.04%, we used the nuclear magnetic resonance (NMR) method and fractal analysis to investigate the effect of coalification on the characteristics of pore-fractures. First, the pore-fracture space in a coal reservoir includes irreducible fluid space and moveable fluid space. We built up the moveable fluid NMR fractal based on the saturated/irreducible fluid NMR fractals. Saturated fluid fractal (Dw), irreducible fluid fractal (Dir), and moveable fluid fractal (DM) have the following relationship: DM > Dir > DW. Additionally, Dir has a huge fluctuating value area with the maximum vitrinite reflectance (Ro,max) varying between 1.93% and 2.06%. The curve lg(T2) and lg(V) for a moveable fluid fractal has four typical types. The shapes “C”, “Z”, “S”, and “T” correspond to four structure types (A, B, C, and D), which provide significant guidance for CBM exploitation. Moreover, the saturated-irreducible T2 distribution has a special shape, known as the pendular ring, which affects the seepage ability and permeability. Second, we classify the pore-fracture types based on the saturated fluid NMR fractal and the T2 distribution as follows: adsorbed pore (T2 < 0.4 ms, < 10 nm), transition pore (T2 = 0.4–2.5 ms, 10–100 nm), seepage pore (T2 > 2.5 ms, > 100 nm). At Ro,max = 1.06–3.04%, the percentages of pore-fracture types show that coalification have three coalification jumps at Ro,max = 1.3%, 2.0%, and 2.8%. The porosities of pore-fracture types show that the thermal volatilization of fillers in pore-fractures begins at Ro,max = 1.5% and disappears at Ro,max = 2.5%. Different fluid space fractals demonstrate that when Ro,max < 2.0%, the coal reservoir tends to be compressed and consolidated, whereas when Ro,max > 2.0% the coal reservoir tends to be orderly and uniform. BVM/BVI is the ratio of the irreducible fluid space (BVI) and the movable fluid space (BVM). Finally, the permeability indicates a positive exponential function with BVM/BVI for seepage pores, and it exhibits a negative exponential function with BVM/BVI for adsorbed pores and transition pores. The NMR method combining fractal analysis with coalification enables us to characterize pore-fractures and the effects of coalification on pore-fractures quantitatively, which contributes to guiding CBM exploitation. Moreover, the relationship between permeability and BVM/BVI is beneficial for predicting the favorable areas for CBM exploitation.

Partially Divisible Completions of Rigid Metabelian Pro-p-groups

Previously, the author defined the concept of a rigid (abstract) group. By analogy, a metabelian pro-p-group G is said to be rigid if it contains a normal series of the form G = G1 ≥ G2 ≥ G3 = 1 such that the factor group A = G/G2 is torsion-free Abelian, and G2 being a ZpA-module is torsion-free. An abstract rigid group can be completed and made divisible. Here we do something similar for finitely generated rigid metabelian pro-p-groups. In so doing, we need to exit the class of pro-p-groups, since even the completion of a torsion-free nontrivial Abelian pro-p-group is not a pro-p-group. In order to not complicate the situation, we do not complete a first factor, i.e., the group A. Indeed, A is simply structured: it is isomorphic to a direct sum of copies of Zp. A second factor, i.e., the group G2, is completed to a vector space over a field of fractions of a ring ZpA, in which case the field and the space are endowed with suitable topologies. The main result is giving a description of coordinate groups of irreducible algebraic sets over such a partially divisible topological group.

Empathic Cyberactivism: The Potential of Hyperconnected Social Media Networks and Empathic Virtual Reality for Feminism

Empathic Cyberactivism: The Potential of Hyperconnected Social Media Networks and Empathic Virtual Reality for Feminism

Unification and extension of intersection algorithms in numerical algebraic geometry

The solution set of a system of polynomial equations, called an algebraic set, can be decomposed into finitely many irreducible components. In numerical algebraic geometry, irreducible algebraic sets are represented by witness sets, whereas general algebraic sets allow a numerical irreducible decomposition comprising a collection of witness sets, one for each irreducible component. We denote the solution set of any system of polynomials f:CN→Cn as V(f)⊂CN. Given a witness set for some algebraic set Z⊂CN and a system of polynomials f:CN→Cn, the algorithms of this paper compute a numerical irreducible decomposition of the set Z∩V(f). While extending the types of intersection problems that can be solved via numerical algebraic geometry, this approach is also a unification of two existing algorithms: the diagonal intersection algorithm and the homotopy membership test. The new approach includes as a special case the “extension problem” where one wishes to intersect an irreducible component A of V(g(x)) with V(f(x,y)), where f introduces new variables, y. For example, this problem arises in computing the singularities of A when the singularity conditions are expressed in terms of new variables associated to the tangent space of A. Several examples are included to demonstrate the effectiveness of our approach applied in a variety of scenarios.