Topological structures of complex belief systems

The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join-semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology.

Topological structures of complex belief systems (II): Textual materialization

Mythical and religious belief systems in a social context can be regarded as a conglomeration of sacrosanct rites, which revolve around substantive values that involve an element of faith. Moreover, we can conclude that ideologies, myths and beliefs can all be analyzed in terms of systems within a cultural context. The significance of being able to define ideologies, myths and beliefs as systems is that they can figure in cultural explanations. This, in turn, means that such systems can figure in logic-mathematical analyses.

Gibbs Energy of Mixing Function: Topological Analysis in Azeotropic Systems

ESAT 2014. 27th European Symposium on Applied Thermodynamics, Eindhoven University of Technology, July 6-9, 2014.

New glimpses on convex infinite optimization duality

Given a convex optimization problem (P) in a locally convex topological vector space X with an arbitrary number of constraints, we consider three possible dual problems of (P), namely, the usual Lagrangian dual (D), the perturbational dual (Q), and the surrogate dual (Δ), the last one recently introduced in a previous paper of the authors (Goberna et al., J Convex Anal 21(4), 2014). As shown by simple examples, these dual problems may be all different. This paper provides conditions ensuring that inf(P)=max(D), inf(P)=max(Q), and inf(P)=max(Δ) (dual equality and existence of dual optimal solutions) in terms of the so-called closedness regarding to a set. Sufficient conditions guaranteeing min(P)=sup(Q) (dual equality and existence of primal optimal solutions) are also provided, for the nominal problems and also for their perturbational relatives. The particular cases of convex semi-infinite optimization problems (in which either the number of constraints or the dimension of X, but not both, is finite) and linear infinite optimization problems are analyzed. Finally, some applications to the feasibility of convex inequality systems are described.

Stability in Linear Optimization Under Perturbations of the Left-Hand Side Coefficients

This paper studies stability properties of linear optimization problems with finitely many variables and an arbitrary number of constraints, when only left hand side coefficients can be perturbed. The coefficients of the constraints are assumed to be continuous functions with respect to an index which ranges on certain compact Hausdorff topological space, and these properties are preserved by the admissible perturbations. More in detail, the paper analyzes the continuity properties of the feasible set, the optimal set and the optimal value, as well as the preservation of desirable properties (boundedness, uniqueness) of the feasible and of the optimal sets, under sufficiently small perturbations.

Topological spin waves in the atomic-scale magnetic skyrmion crystal

We study the spin waves of the triangular skyrmion crystal that emerges in a two-dimensional spin lattice model as a result of the competition between Heisenberg exchange, Dzyalonshinkii–Moriya interactions, Zeeman coupling and uniaxial anisotropy. The calculated spin wave bands have a finite Berry curvature that, in some cases, leads to non-zero Chern numbers, making this system topologically distinct from conventional magnonic systems. We compute the edge spin-waves, expected from the bulk-boundary correspondence principle, and show that they are chiral, which makes them immune to elastic backscattering. Our results illustrate how topological phases can occur in self-generated emergent superlattices at the mesoscale.

The European Citizens‘ Initiative – Chances, Constraints and Limits. IHS Political Science Series No. 134, April 2013

In order to celebrate the 20th anniversary of the establishment of European Union citizenship under the Maastricht Treaty in 1993, the year 2013 has been designated by the European Commission as the ‘European Year of Citizens’. The European Citizen’s Initiative (ECI) – labelled by the Commission as a ‘direct gateway through which citizens can make their voices heard in Brussels’ - may emerge in the European awareness as a new appealing platform for policy-shaping and communication. The ECI, through its transnational vox civilis character, figures among the most important novelties in the Lisbon Treaty and in the long run may facilitate and accelerate the bottom-up building of a European demos. The question is, however, whether the mechanism of pan-European signature collection is strong enough to face the democratic challenges present in the EU, especially during the ongoing financial crisis.

Exports and Capacity Constraints: A smooth transition regression model for six euro-area countries. CEPS Working Document No. 395/May 2014

The significant gains in export market shares made in a number of vulnerable euro-area crisis countries have not been accompanied by an appropriate improvement in price competitiveness. This paper argues that, under certain conditions, firms consider export activity as a substitute for serving domestic demand. The strength of the link between domestic demand and exports is dependent on capacity constraints. Our econometric model for six euro-area countries suggests domestic demand pressure and capacity-constraint restrictions as additional variables of a properly specified export equation. As an innovation to the literature, we assess the empirical significance through the logistic and the exponential variant of the non-linear smooth transition regression model. We find that domestic demand developments are relevant for the short-run dynamics of exports in particular during more extreme stages of the business cycle. A strong substitutive relationship between domestic and foreign sales can most clearly be found for Spain, Portugal and Italy, providing evidence of the importance of sunk costs and hysteresis in international trade.

Productivity and Credit Constraints: Firm-Level Evidence from Propensity Score Matching. Factor Markets Working Paper No. 3, September 2011

Drawing on a unique, farm-level panel dataset with 37,409 observations and employing a matching estimator, this paper analyses how farm access to credit affects farm input allocation and farm efficiency in the Central and Eastern European transition countries. We find that farms are asymmetrically credit constrained with respect to inputs. Farm use of variable inputs and capital investment increases up to 2.3% and 29%, respectively, per €1,000 of additional credit. Our estimates also suggest that farm access to credit increases total factor productivity up to 1.9% per €1,000 of additional credit, indicating that an improvement in access to credit results in an adjustment in the relative input intensities on farms. This finding is further supported by a negative effect of better access to credit on labour, suggesting that these two are substitutes. Interestingly, farms are found not to be credit constrained with respect to land.

Commonalities and Differences in Labour Market Developments and Constraints in Different EU Regions. Factor Markets Working Paper No. 22, February 2012

This paper provides a detailed overview of the differences across EU member states’ labour markets, through the extensive use of descriptive statistics. The objective is two-fold: firstly, it identifies the commonalities and differences in rural labour markets across EU regions and their developments, with special regard to agriculture, and secondly it emphasises the constraints that may hinder the efficient functioning of labour markets. Therefore, the paper starts with a description of the main indicators in the general labour market theory, such as the structure of the population in terms of age and gender distribution, unemployment and activity rates, employment levels, quality of human capital, migration patterns, and so forth. Secondly, we focus on the differences among rural and urban areas to then look closely at the agricultural sector. The institutional framework in which labour market institutions operate is also included. Lastly, as an attempt to summarise the analysis and to classify the EU member states according to certain rural and specific agricultural indicators, cluster analysis is also employed. Policy implications include investment in human capital and vocational training, support to young farmers, promoting economic diversification and upgrading infrastructure, with special regard to the new member states and to the Southern parts of Europe.

Primary sex determination of placental mammals: a modelling study uncovers dynamical developmental constraints in the formation of Sertoli and granulosa cells

Primary sex determination in placental mammals is a very well studied developmental process. Here, we aim to investigate the currently established scenario and to assess its adequacy to fully recover the observed phenotypes, in the wild type and perturbed situations. Computational modelling allows clarifying network dynamics, elucidating crucial temporal constrains as well as interplay between core regulatory modules.