Topological Prismatoids and Small Simplicial Spheres of Large Diameter

We introduce topological prismatoids, a combinatorial abstraction of the (geometric) prismatoids recently introduced by the second author to construct counter-examples to the Hirsch conjecture. We show that the `strong $d$-step Theorem' that allows to construct such large-diameter polytopes from `non-$d$-step' prismatoids still works at this combinatorial level. Then, using metaheuristic methods on the flip graph, we construct four combinatorially different non-$d$-step $4$-dimensional topological prismatoids with $14$ vertices. This implies the existence of $8$-dimensional spheres with $18$ vertices whose combinatorial diameter exceeds the Hirsch bound. These examples are smaller that the previously known examples by Mani and Walkup in 1980 ($24$ vertices, dimension $11$). Our non-Hirsch spheres are shellable but we do not know whether they are realizable as polytopes.Comment: 20 pages. Changes from v1 and v2: Reduced the part on shellability and general improvement to accesibilit

Some critics to the contagion correlation test

The term contagion is generally used to refer to the spread3 of market shocks from one country to another. However, identifying what is meant by contagion and its consequences has become in recent years a literature in itself4, given the importance of such consequences on economies all over the world. Despite the lack of theoretical consensus, some authors try to measure contagion through the use of correlation tests. The aim of my work is to raise a technical and conceptual critique concerning these models. To support my concerns I provide a broad vision and background of contagion literature and an insight in the particular field of contagion correlation test. The work is organized in four parts. Firstly, an overview of definitional issues concerning contagion, as presented in the literature, is explained together with the different crisis transmission channels that authors have identified. Secondly, a detailed description of the contagion correlation test –as the most common means to search for contagion—is presented, giving a full overview of the models used in the literature. Thirdly, I will express my concerns about the test and the models of the previous section. Finally, some conclusions are stated.

Norm Monitoring under Partial Action Observability

In the context of using norms for controlling multi-agent systems, a vitally important question that has not yet been addressed in the literature is the development of mechanisms for monitoring norm compliance under partial action observability. This paper proposes the reconstruction of unobserved actions to tackle this problem. In particular, we formalise the problem of reconstructing unobserved actions, and propose an information model and algorithms for monitoring norms under partial action observability using two different processes for reconstructing unobserved actions. Our evaluation shows that reconstructing unobserved actions increases significantly the number of norm violations and fulfilments detected.Comment: Accepted at the IEEE Transaction on Cybernetic

Temporal and spatial homogeneity in air pollutants panel EKC estimations: Two nonparametric tests applied to Spanish provinces

Although panel data have been used intensively by a wealth of studies investigating the GDP-pollution relationship, the poolability assumption used to model these data is almost never addressed. This paper applies a strategy to test the poolability assumption with methods robust to functional misspecification. Nonparametric poolability tests are performed to check the temporal and spatial homogeneity of the panel and their results are compared with the conventional F-tests for a balanced panel of 48 Spanish provinces on four air pollutant emissions (CH4, CO, CO2 and NMVOC) over the 1990-2002 period. We show that temporal homogeneity may allow the pooling of the data and drive to well-defined nonparametric and parametric cross-sectional U-inverted shapes for all air pollutants. However, the presence of spatial heterogeneity makes this shape compatible with different timeseries patterns in every province - mainly increasing or decreasing depending on the pollutant. These results highlight the extreme sensitivity of the income-pollution relationship to region- or country-specific factors.Environmental Kuznets Curve; Air pollutants; Non/Semiparametric estimations; Poolability tests