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.

Polynomial regression using a perceptron with axo-axonic connections

Social behavior is mainly based on swarm colonies, in which each individual shares its knowledge about the environment with other individuals to get optimal solutions. Such co-operative model differs from competitive models in the way that individuals die and are born by combining information of alive ones. This paper presents the particle swarm optimization with differential evolution algorithm in order to train a neural network instead the classic back propagation algorithm. The performance of a neural network for particular problems is critically dependant on the choice of the processing elements, the net architecture and the learning algorithm. This work is focused in the development of methods for the evolutionary design of artificial neural networks. This paper focuses in optimizing the topology and structure of connectivity for these networks

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).

Mean-value identities as an opportunity for Monte Carlo error reduction

In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.

High-speed polynomial basis multipliers over GF(2(m)) for special pentanomial.

Efficient hardware implementations of arithmetic operations in the Galois field are highly desirable for several applications, such as coding theory, computer algebra and cryptography. Among these operations, multiplication is of special interest because it is considered the most important building block. Therefore, high-speed algorithms and hardware architectures for computing multiplication are highly required. In this paper, bit-parallel polynomial basis multipliers over the binary field GF(2(m)) generated using type II irreducible pentanomials are considered. The multiplier here presented has the lowest time complexity known to date for similar multipliers based on this type of irreducible pentanomials.

Performing the personal within the organizational: Communicating professional identities through Taiwanese commercial airline pilots' personal narratives

This dissertation project explored professionalism and the performance of identities by examining Taiwanese commercial airline pilots' discursive practices in everyday life. The intentions for this project were to not only expand current knowledge of organizational communication from a critical rhetorical perspective, but to further explore the under-appreciated concept of professionalism of organizational members. Theoretically, I traced theoretical analysis in the sociology of professions and further investigated scholarship from identity research in organizational communication studies. This research agenda helped to advance communication-based understandings of the meanings and practices of professional identity as a complement to the sociological conception. I further merged a performance paradigm and critical rhetorical perspective to examine the discursive practices of organizational members and to challenge the bias of traditional textual approaches. Methodologically, I conducted ethnographic interviews with Taiwanese commercial airline pilots in order to understand how they construct their personal, social, and professional identities. Five narrative themes were identified and demonstrated in this project: (1) It takes a lot to become a commercial airline pilot, (2) Being a professional commercial airline pilot is to build up sufficient knowledge, beyond average skill, and correct attitude, (3) Pilots' resistance and dissent toward company management, (4) Popular (re)presentation influences professionalism, (5) Power and fear affect professionalism. Pilots' personal narratives were presented in performative writing and in poetic transcription to make word alive with sounds featuring their meanings. Their personal storytelling created a dialogic space to not only let pilots' voice to be heard but also revealed how identities are created within and against a larger organizational identity. Overall, this project demonstrated the interdisciplinary examination of the meanings, functions, and consequence of discursive practices in everyday professional life. It also critiqued relationships between power, domination, and resistance while reintroducing the roles of the body and materiality in the domain of professionalism, and provides ethical readings of larger and complex organizational cultures. Applying communication-oriented analysis to study professionalism indeed challenged the long time neglected phenomena regarding the power of the symbolic in sociological approaches and raised the awareness of structural, material, and bodily condition of work.

Visions of the Spanish Revolution: identities and conflicts in post-welfare societies

This is a case study that analyzes photographic documents of the social protest in Spain between 2011 and 2013. The analysis is qualitative and considers the use of space, the visual expression of the messages and the orientation toward the causes or effects of political, economic and social changes. Visual sociology allows us to appreciate, in the case of the Spanish Revolution, a dynamic of “reflexivity” unrecognizable from other research approaches. Two successive waves of social mobilization in response to two different shocks can be appreciated. The first is given by political corruption, unemployment and the threat to consumer society. The second shock is caused by the savage cuts in the Welfare State. Social mobilization is expressed differently in each phase, and the forms taken by the protests show how the class structure in post industrial society shapes the reactions to the crisis of the Welfare State.

New Europeans, New Identities; Reflections on Europe’s Dilemma. IES WORKING PAPER 1/2008

This paper examines issues relating to the integration of immigrants, particularly Muslim immigrants, into European societies. It first contemplates whether a true European identity really exists. Building on the different conceptions of (European) identity, the paper claims that a sense of belonging is crucial in helping immigrants integrate into Europe. The paper also argues that identity is, actually, most relevant when it is under threat. The paper therefore looks at the nature of Muslim society in Europe and some of the reasons for disaffection in that population. While doing this, the paper compares the various models of integration in, for example, the United States, Canada and Israel with the attempt by a number of EU Member States to find satisfactory integration strategies. Also, the efforts of the European Commission to forge an acceptable integration framework through the principles elaborated following the Hague declaration in November 2004 are discussed. The paper concludes that integration is best approached by creating cohesive communities and loyalties at the local level.

SPORRT; simplified polynomial root finding at a remote terminal.

"Supported in part by ... Grant no. US NSF GP-9665."

A method for solving polynomial equations by continued fractions.

Bibliography: p. 16.

On the use of finite field based modeling in polynomial manipulation,

Vita: p. 105.

Identities: Of light and heat, of caloric and electricity ...

Mode of access: Internet.