The Role of the European Imperial Powers throughout the Armenian Schism in the 1870s

The Bull "Reversurus" (1867) and its dogmatic legitimization at the First Vatican Council in 1870 caused not only ecclesiastical controversy and Schism in the Armenian Catholic Church, but it had also wide political consequences for the Armenian Catholics in the Ottoman Empire. The conflict originally between the Armenian Catholics and Rome attracted very soon the attention of the European imperial Powers. France, the British Empire, the German Empire, Austria-Hungary and Russia were the main political powers who were involved in the Armenian affair. A full picture of the role of all these powers for the course of the Armenian Schism is missing. Mostly the role of France is foregrounded in the printed sources, as the main power, which supported the papacy to win during the Armenian affair. The role and the motives of the other imperial powers is almost missing. This article will try to describe as completely as possible the historical and political background, which brought to the escalation of the Armenian conflict beyond the national frontiers and led to number of conflicts at the international and transnational level. It will be shown that the imperial policy in Europe in the 19th century have played an enormous role throughout the Armenian Schism. It will be explained that several historical circumstances in Europe, especially the relation of the European imperial powers to each other as well as their expectations from the Ottoman Empire and its Armenian subjects were decisive for the duration and conclusion of the Armenian Schism.

Interaction of powers in the Philippine presidential system

The executive - legislative relations in the Philippines have been described in two contrasting stories, namely the "strong president" story, and the "strong congress" story. This paper tries to consolidate the existing arguments and propose a new perspective focusing on the "compromise exchange" between the president and the congress across the different policy areas. It considers that the policy outcome is not brought by unilateral power of the president or the congress, but formed as the product of such an exchange. Interaction of powers and their complementary function are addressed. Furthermore, aside from the constitutional power, the weak party discipline is pointed out as a key factor in making the exchange possible.

A geometric characterization of the upper bound for the span of the jones polynomial

Let D be a link diagram with n crossings, sA and sB be its extreme states and |sAD| (respectively, |sBD|) be the number of simple closed curves that appear when smoothing D according to sA (respectively, sB). We give a general formula for the sum |sAD| + |sBD| for a k-almost alternating diagram D, for any k, characterizing this sum as the number of faces in an appropriate triangulation of an appropriate surface with boundary. When D is dealternator connected, the triangulation is especially simple, yielding |sAD| + |sBD| = n + 2 - 2k. This gives a simple geometric proof of the upper bound of the span of the Jones polynomial for dealternator connected diagrams, a result first obtained by Zhu [On Kauffman brackets, J. Knot Theory Ramifications6(1) (1997) 125–148.]. Another upper bound of the span of the Jones polynomial for dealternator connected and dealternator reduced diagrams, discovered historically first by Adams et al. [Almost alternating links, Topology Appl.46(2) (1992) 151–165.], is obtained as a corollary. As a new application, we prove that the Turaev genus is equal to the number k of dealternator crossings for any dealternator connected diagram

Polynomial approximation using particle swarm optimization of lineal enhanced neural networks with no hidden layers.

This paper presents some ideas about a new neural network architecture that can be compared to a Taylor analysis when dealing with patterns. Such architecture is based on lineal activation functions with an axo-axonic architecture. A biological axo-axonic connection between two neurons is defined as the weight in a connection in given by the output of another third neuron. This idea can be implemented in the so called Enhanced Neural Networks in which two Multilayer Perceptrons are used; the first one will output the weights that the second MLP uses to computed the desired output. This kind of neural network has universal approximation properties even with lineal activation functions. There exists a clear difference between cooperative and competitive strategies. The former ones are based on the swarm colonies, in which all individuals share its knowledge about the goal in order to pass such information to other individuals to get optimum solution. The latter ones are based on genetic models, that is, individuals can die and new individuals are created combining information of alive one; or are based on molecular/celular behaviour passing information from one structure to another. A swarm-based model is applied to obtain the Neural Network, training the net with a Particle Swarm algorithm.

E-polynomial of the SL(3,C)-character variety of free groups.

We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3,C). Expanding upon techniques of Logares, Muñoz and Newstead (Rev. Mat. Complut. 26:2 (2013), 635-703), we stratify the space of representations and compute the E-polynomial of each geometrically described stratum using fibrations. Consequently, we also determine the E-polynomial of its smooth, singular, and abelian loci and the corresponding Euler characteristic in each case. Along the way, we give a new proof of results of Cavazos and Lawton (Int. J. Math. 25:6 (2014), 1450058).

Morphological classification of microtidal sand and gravel beaches

A new classification of microtidal sand and gravel beaches with very different morphologies is presented below. In 557 studied transects, 14 variables were used. Among the variables to be emphasized is the depth of the Posidonia oceanica. The classification was performed for 9 types of beaches: Type 1: Sand and gravel beaches, Type 2: Sand and gravel separated beaches, Type 3: Gravel and sand beaches, Type 4: Gravel and sand separated beaches, Type 5: Pure gravel beaches, Type 6: Open sand beaches, Type 7: Supported sand beaches, Type 8: Bisupported sand beaches and Type 9: Enclosed beaches. For the classification, several tools were used: discriminant analysis, neural networks and Support Vector Machines (SVM), the results were then compared. As there is no theory for deciding which is the most convenient neural network architecture to deal with a particular data set, an experimental study was performed with different numbers of neuron in the hidden layer. Finally, an architecture with 30 neurons was chosen. Different kernels were employed for SVM (Linear, Polynomial, Radial basis function and Sigmoid). The results obtained for the discriminant analysis were not as good as those obtained for the other two methods (ANN and SVM) which showed similar success.