Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces

As in the case of the associahedron and cyclohedron, the permutohedron can also be defined as an appropriate compactification of a configuration space of points on an interval or on a circle. The construction of the compactification endows the permutohedron with a projection to the cyclohedron, and the cyclohedron with a projection to the associahedron. We show that the preimages of any point via these projections might not be homeomorphic to (a cell decomposition of) a disk, but are still contractible. We briefly explain an application of this result to the study of knot spaces from the point of view of the Goodwillie-Weiss manifold calculus.Comment: 27 pages The new version gives a more detailed exposition for the projection from the cyclohedron to the associahedron as maps of compactifications of configuration spaces. We also develop a similar picture for the projection from the permutohedron to the cyclohedron/associahedro

Nontrivial classes in H∗(Imb(S1,Rn))H^*(Imb(S^1,\R^n)) from nontrivalent graph cocycles

We construct nontrivial cohomology classes of the space $Imb(S^1,\R^n)$ of imbeddings of the circle into $\R^n$, by means of Feynman diagrams. More precisely, starting from a suitable linear combination of nontrivalent diagrams, we construct, for every even number $n\geq 4$, a de Rham cohomology class on $Imb(S^1,\R^n)$. We prove nontriviality of these classes by evaluation on the dual cycles.Comment: 10 pages, 11 figures. V2: minor changes, typos correcte

Algebraic structures on graph cohomology

We define algebraic structures on graph cohomology and prove that they correspond to algebraic structures on the cohomology of the spaces of imbeddings of S^1 or R into R^n. As a corollary, we deduce the existence of an infinite number of nontrivial cohomology classes in Imb(S^1,R^n) when n is even and greater than 3. Finally, we give a new interpretation of the anomaly term for the Vassiliev invariants in R^3.Comment: Typos corrected, exposition improved. 14 pages, 2 figures. To appear in J. Knot Theory Ramification

Complex-valued forecasting of the global solar irradiation

In this paper, a forecasting of the global solar irradiation in the complex-valued domain is proposed. A method to transform the meteorological data into complex values is developed and the Complex Valued Neural Network (CVNN) is used to model and forecast the daily and the hourly solar irradiation. The measured data of Tamanrasset city, Algeria (altitude: 1362 m; latitude: 22°48 N; longitude: 05°26 E) is used to validate the developed model. In the hourly solar irradiation case, the 24 h ahead will be forecasted using the combination of the past daily meteorological dataset. Several models are presented to test the feasibility and the performance of the CVNN for forecasting either daily or hourly solar irradiation for both multi input single output and multi input multi output strategies. Results obtained throughout this paper show that the CVNN technique is suitable for modeling and forecasting daily and hourly solar irradiatio