Description Of Facets Research Articles

Combinatorics of essential sets for positroids

Positroids are a family of matroids introduced by Postnikov in the study of non-negative Grassmannians. Postnikov identified several combinatorial objects in bijections with positroids, among which are bounded affine permutations. On the other hand, the notion of essential sets, introduced for permutations by Fulton, was used by Knutson in the study of the special family of interval rank positroids. We generalize Fulton's essential sets to bounded affine permutations. The bijection of the latter with positroids, allows the study of the relationship between them. From the point of view of positroids, essential sets are maximally dependent cyclic intervals. We define connected essential sets and prove that they give a facet description of the positroid polytope, as well as equations defining the positroid variety. We define a subset of essential sets, called core, which contains minimal rank conditions to uniquely recover a positroid. We provide an algorithm to retrieve the positroid satisfying the rank conditions in the core or any compatible rank condition on cyclic intervals.

Deformation cones of graph associahedra and nestohedra

We give the facet description of the deformation cones of graph associahedra and nestohedra, generalizing the classical parametrization of the family of deformed permutahedra by the cone of submodular functions. When the underlying building set is made of intervals, this leads in particular to the construction of kinematic nestohedra generalizing the kinematic associahedra that recently appeared in the theory of scattering amplitudes.

Removahedral Congruences versus Permutree Congruences

The associahedron is classically constructed as a removahedron, i.e. by deleting inequalities in the facet description of the permutahedron. This removahedral construction extends to all permutreehedra (which interpolate between the permutahedron, the associahedron and the cube). Here, we investigate removahedra constructions for all quotientopes (which realize the lattice quotients of the weak order). On the one hand, we observe that the permutree fans are the only quotient fans realized by a removahedron. On the other hand, we show that any permutree fan can be realized by a removahedron constructed from any realization of the braid fan. Our results finally lead to a complete description of the type cones of the permutree fans.

Towards a Taxonomy of Trustworthy Digital Repository Impacts

AbstractMeasuring the societal impact of digital repositories is a wicked problem. To capture information about the impacts of digital repositories that become certified as Trustworthy Digital Repositories (TDRs), a taxonomy describing activities cited as evidence of compliance with TDR standards is needed to relate those activities to socially beneficial outcomes. This paper presents a Minimum Viable Prototype (MVP) for a TDR Impacts taxonomy to enable the expression of their activities in a structured way. Our MVP provides a proof‐of‐concept that by formalizing concepts about TDRs in a taxonomy, we can investigate ways to measure whether the impacts associated with becoming and remaining a certified TDR are also impacts that generate societal value. Implications of the work described include potential strategies to identify, extract, and/or author machine‐readable descriptions of measurable facets of TDR activities and the resulting impacts on communities.

Studying autocratization in Turkey: political institutions, populism, and neoliberalism

AbstractIn this review article I classify the literature on the Turkish political regime during Justice and Development Party rule as two waves of studies, and a potential third wave. The first wave was prevalent at least until the Gezi uprisings in 2013. I argue that, in this wave, the main debate was between two rival and largely culturalist perspectives with conceptual toolkits that tended to interpret regime change through the lens of social transformations. I also maintain that scholarly works written from the hegemonic perspective of this wave, utilizing center–periphery and state–society dichotomies, and a narrow range of concepts from the democratization literature (from defective democracy to democratic consolidation), have misidentified/misinterpreted burgeoning autocratization in Turkey as democratization, albeit with problems. The Gezi uprisings brought to the fore already existing authoritarian features of the Turkish political regime and led to the second wave of studies. In the second wave, the focus was on naming Turkey’s new political regime as a diminished subtype of authoritarianism, and thick descriptions of different facets of Turkey’s new authoritarianism. Finally, I suggest that there is a need for a third wave that builds on recent studies and focuses on explaining Turkey’s autocratization process and democratic breakdown, as well as the impact of autocratization on other aspects of Turkish politics and society.

Effects of decimetre-scale surface roughness on L-band brightness temperature of sea ice

Abstract. Sea ice thickness is an essential climate variable. Current L-Band sea ice thickness retrieval methods do not account for sea ice surface roughness that is hypothesised to be not relevant to the process. This study attempts to validate this hypothesis that has not been tested yet. To test this hypothesis, we created a physical model of sea ice roughness based on geometrical optics and merged it into the L-band emissivity model of sea ice that is similar to the one used in the operational sea ice thickness retrieval algorithm. The facet description of sea ice surface used in geometrical optics is derived from 2-D surface elevation measurements. Subsequently the new model was tested with TB measurements performed during the SMOSice 2014 field campaign. Our simulation results corroborate the hypothesis that sea ice surface roughness has a marginal impact on near-nadir TB (used in the current operational retrieval). We demonstrate that the probability distribution function of surface slopes can be approximated with a parametric function whose single parameter can be used to characterise the degree of roughness. Facet azimuth orientation is isotropic at scales greater than 4.3 km. The simulation results indicate that surface roughness is a minor factor in modelling the sea ice brightness temperature. The change in TB is most pronounced at incidence angles greater than 40∘ and can reach up to 8 K for vertical polarisation at 60∘. Therefore current and future L-band missions (SMOS, SMAP, CIMR, SMOS-HR) measuring at such angles can be affected. Comparison of the brightness temperature simulations with the SMOSice 2014 radiometer data does not yield definite results.

Faces of 2-Dimensional Simplex of Order and Chain Polytopes

Each of the descriptions of vertices, edges, and facets of the order and chain polytope of a finite partially ordered set are well known. In this paper, we give an explicit description of faces of 2-dimensional simplex in terms of vertices. Namely, it will be proved that an arbitrary triangle in 1-skeleton of the order or chain polytope forms the face of 2-dimensional simplex of each polytope. These results mean a generalization in the case of 2-faces of the characterization known in the case of edges.

The cone of supermodular games on finite distributive lattices

In this article we study supermodular functions on finite distributive lattices. Relaxing the assumption that the domain is a powerset of a finite set, we focus on geometrical properties of the polyhedral cone of such functions. Specifically, we generalize the criterion for extremality and study the face lattice of the supermodular cone. An explicit description of facets by the corresponding tight linear inequalities is provided.

Еssential properties of national interests; classification

National interests are multifaceted and multi-aspect phenomenon requiring a structured uniform understanding. According to the most important features, classification contributes to the systematization and refinement of knowledge about national interests, describing them as a holistic category. This allows identifying problems in their implementation, to identify and evaluate threats to national security. In scientific literature, classification of national interests is carried out by using various approaches for various reasons, as well as from the perspective of various branches of science. Above-mentioned makes it difficult to form a unified view of national interests in all their manifestations, taking into account existing interconnections and interdependencies. It often takes place when formal and meaningful description of individual facets and aspects of national interests are mixed. As a result of the study, it is presented that the key properties of national interests allow to be described as a system, that includes structural elements. These essential properties, serve for grouping and structuring the classification of approaches, presented in the theory of national security.

Approaches and typology to be applied for building information models verification

Experts from different countries are engaged in the study and development of verification systems of information models of construction projects. Nevertheless a problem of systematization and structuring of information on the types of inspections that the information model of the construction object can be subjected to still exist. In this article the author proposes a possible version of the classification of information model verification types using the faceted method, which determines the potential extensibility of this classification. The facet classification method involves the parallel division of a set of objects into independent classification groupings. It does not assume a rigid classification structure and preconstructed finite groupings. Classification groupings are formed by combining values taken from the corresponding facets. The article gives a detailed description of facets that may be applied.

Permutrees

We introduce permutrees, a unified model for permutations, binary trees, Cambrian trees and binary sequences. On the combinatorial side, we study the rotation lattices on permutrees and their lattice homomorphisms, unifying the weak order, Tamari, Cambrian and boolean lattices and the classical maps between them. On the geometric side, we provide both the vertex and facet descriptions of a polytope realizing the rotation lattice, specializing to the permutahedron, the associahedra, and certain graphical zonotopes. On the algebraic side, we construct a Hopf algebra on permutrees containing the known Hopf algebraic structures on permutations, binary trees, Cambrian trees, and binary sequences.

On facet-inducing inequalities for combinatorial polytopes

One of the central questions of polyhedral combinatorics is the question of the algorithmic relationship between the vertex and facet descriptions of convex polytopes. From the standpoint of combinatorial optimization, the main reason for the actuality of this question is the possibility of applying the methods of convex analysis to solving the extremal combinatorial problems. In this paper, we consider the combinatorial polytopes of a sufficiently general form. We obtain a few of necessary conditions and a sufficient condition for a supporting inequality of a polytope to be a facet inequality and give an illustration of the use of the developed technology to the polytope of some graph approximation problem.

О ДИНАМИЧЕСКОЙ ЗАДАЧЕ ПОСТРОЕНИЯ ОСТОВА ПОЛИЭДРАЛЬНОГО КОНУСА

This paper considers a dynamic problem of computing generators of a polyhedral cone. The problem is to sequentially perform operations of adding and removing inequalities from a facet description of the polyhedral cone with a corresponding re-computation of generators. The application of a double description method for both operations is discussed and complexity estimation is given in the paper. Adding a new inequality corresponds to a single step of the double description method. It can be performed with time complexity being quadratic or cubic of the input size for the current step, depending on the modification of the method and adjacency tests chosen. We give complexity bounds for adding a single inequality with widely used algebraic and combinatorial adjacency tests. The problem of removing inequalities is intrinsically much harder, compared to adding inequalities. We briefly describe the naive and incremental algorithms and show an example with output size being superpolynomial of the input size in case of removing a single inequality. A subclass of problems with certain adjacency properties is investigated, for this subclass we prove that the output size is bounded by a quadratic function of the input size. Finally, we prove that for the distinguished subclass any finite sequence of adding and removing inequalities can be performed in polynomial time of the input size.

Qué anidaedra son quitaedra?

Un quitaedro es un politopo obtenido quitando desigualdades en la descripción de las facetas de un permutaedro clásico. Ejemplos pertinentes van del asociaedro al permutaedro, lo cual levanta la pregunta de caracterizar cuales anidaedra se pueden realizar como quitaedra. En este artículo, demostramos que el complejo anidado de cualquier conjunto de construcción cerrado por intersección se puede realizar como quitaedron. Presentamos dos construcciones complementarias: una basada en los árboles de construcción y el albanico anidado, y la otra basada en sumas de Minkowski de dilatación de caras del simplejo estándar. En general, este condición de clausura es suficiente pero no necesaria para obtener quitaedra. En contraste, demostramos que el abanico anidado de un conjunto de construcción gráfico es el abanico normal de un quitaedro si y solo si el conjunto de construcción gráfico es cerrado por intersección, lo cual es equivalente a que el grafo correspondiente sea plena de cuerdas (i.e., que cada ciclo induce un grafo completo).

From overexcitabilities to openness: Informing gifted education with psychological science

ABSTRACTIn the theory of positive disintegration (TPD), Dabrowski described overexcitabilities (OEs), manifestations of inner energy with a developmental purpose that appear more common in gifted individuals. Unfortunately, most studies present OEs outside of the context of the original theory as if they were standalone traits applicable to gifted students. In this atheoretical conceptualization, OEs seem to define the personality trait of openness to experience described in the five-factor model of personality (FFM) as each OE can be matched with a specific facet of openness. Descriptions of facets of openness and corresponding OEs are strongly similar. In this article we argue that they are conceptually equivalent and that current research on openness and OE supports this assertion. The FFM has robust empirical support, and TPD lacks empirical support; additionally, OEs as currently presented in gifted education deviate from TPD’s original tenets. Therefore, gifted education should shift its way of explaining these tendencies by framing them as the personality trait of openness to experience rather than OEs.

A Definition of Type Domain of a Parallelotope

Each convex polytope P = P(α) can be described by a set of linear inequalities determined by vectors p and right hand sides α(p). For a fixed set of vectors p, a type domain D(P ₀ ) of a polytope P ₀ and, in particular, of a parallelotope P ₀ is defined as a set of parameters α(p) such that polytopes P(α) have the same combinatorial type as P ₀ for all α ∈ D(P ₀ ). In the second part of the paper, a facet description of zonotopes and zonotopal parallelotopes are given. The article is published in the author’s wording.

Key Problem of Component-Based Software Development

In order to improve the component dynamic test efficiency, this paper proposes a keating component built-in test case generation method of genetic algorithm and designs the chromosome coding method. The test point and keating component facet description of dynamic test data generation method. Mass in order to improve the generation of test cases and add Yang the convergence speed of genetic algorithm. We improve the algorithm of the method for calculating the fitness function and fitness function not only consider the case of path coverage, but also considers the path coverage rate of increase, thus effectively improved the path coverage and reduce the Yang cases produce cost.

Comparing faceted and smoothed tool surface descriptions in sheet metal forming simulation

This study deals with different tool surface description methods used in the finite element analysis of sheet metal forming processes. The description of arbitrarily-shaped tool surfaces using the traditional linear finite elements is compared with two distinct smooth surface description approaches: (i) Bézier patches obtained from the Computer-Aided Design model and (ii) smoothing the finite element mesh using Nagata patches. The contact search algorithm is presented for each approach, exploiting its special features in order to ensure an accurate and efficient contact detection. The influence of the tool modelling accuracy on the numerical results is analysed using two sheet forming examples, the unconstrained cylindrical bending and the reverse deep drawing of a cylindrical cup. Smoothing the contact surfaces with Nagata patches allows creating more accurate tool models, both in terms of shape and normal vectors, when compared with the conventional linear finite element mesh. The computational efficiency is evaluated in this study through the total number of increments and the required CPU time. The mesh refinement in the faceted description approach is not effective in terms of computational efficiency due to large discontinuities in the normal vector field across facets, even when adopting fine meshes.

A Maximum Entropy Approach to the Realizability of Spin Correlation Matrices

Deriving the form of the optimal solution of a maximum entropy problem, we obtain an infinite family of linear inequalities characterizing the polytope of spin correlation matrices. For n ≤ 6, the facet description of such a polytope is provided through a minimal system of Bell-type inequalities.

Polytopes associated to dihedral groups

In this note we investigate the convex hull of those n × n permutation matrices that correspond to symmetries of a regular n -gon. We give the complete facet description. As an application, we show that this yields a Gorenstein polytope, and we determine the Ehrhart h * -vector.