Fractional Calculus: Quo Vadimus? (Where Are We Going?)

Discussions under this title were held during a special session in frames of the International Conference “Fractional Differentiation and Applications” (ICFDA ’14) held in Catania (Italy), 23-25 June 2014, see details at http://www.icfda14.dieei.unict.it/. Along with the presentations made during this session, we include here some contributions by the participants sent afterwards and also by few colleagues planning but failed to attend. The intention of this special session was to continue the useful traditions from the first conferences on the Fractional Calculus (FC) topics, to pose open problems, challenging hypotheses and questions “where to go”, to discuss them and try to find ways to resolve.

A Multi–Agent Brokerage Platform for Media Content Recommendation

Near real time media content personalisation is nowadays a major challenge involving media content sources, distributors and viewers. This paper describes an approach to seamless recommendation, negotiation and transaction of personalised media content. It adopts an integrated view of the problem by proposing, on the business-to-business (B2B) side, a brokerage platform to negotiate the media items on behalf of the media content distributors and sources, providing viewers, on the business-to-consumer (B2C) side, with a personalised electronic programme guide (EPG) containing the set of recommended items after negotiation. In this setup, when a viewer connects, the distributor looks up and invites sources to negotiate the contents of the viewer personal EPG. The proposed multi-agent brokerage platform is structured in four layers, modelling the registration, service agreement, partner lookup, invitation as well as item recommendation, negotiation and transaction stages of the B2B processes. The recommendation service is a rule-based switch hybrid filter, including six collaborative and two content-based filters. The rule-based system selects, at runtime, the filter(s) to apply as well as the final set of recommendations to present. The filter selection is based on the data available, ranging from the history of items watched to the ratings and/or tags assigned to the items by the viewer. Additionally, this module implements (i) a novel item stereotype to represent newly arrived items, (ii) a standard user stereotype for new users, (iii) a novel passive user tag cloud stereotype for socially passive users, and (iv) a new content-based filter named the collinearity and proximity similarity (CPS). At the end of the paper, we present off-line results and a case study describing how the recommendation service works. The proposed system provides, to our knowledge, an excellent holistic solution to the problem of recommending multimedia contents.

Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

In this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

Reflexões sobre o adágio erasmista. "Il' dvlce bellvm inexpertis"*

De todos os Adágios de Erasmo (e escreveu sobre mais de quatro milhares), o comentário ao provérbio Dulce bellum inexpertis - ou "Adágio 3001" - é, sem dúvida, um dos mais conhecidos e mais actuais. Aparece pela primeira vez, em estado embrionário, na edição de 1508 e surge depois, muito aumentado e refundido, nas edições impressas por Froben, em Basiléia, em 1515, 1523 e 1526. O tema, particularmente grato ao espírito irenista de Erasmo, seduzia-o desde que, ao aproximar-se dos 40 anos, empreendera a sonhada viagem a Itália. Aqui, entre 1506 e 1509, assistira à entrada triunfal das tropas do papa Júlio II em Bolonha, facto que o levaria a compor o Antipolemus (texto infelizmente perdido), bem como o lulius Exclusus, panfleto que alguns autores também lhe atribuem e no qual o papa guerreiro é excluído sumariamente da entrada na corte celestial. À mesma linha ideológica do Adágio 3001 pertence ainda a Querela ou Querimonia Pacis, editada em 1517, pranto em louvor do pacifismo pontifício e da evangelização dos povos paganizados

Urticária ao Frio: Uma Realidade em Caracterização

Introdução: A urticária ao frio (UF), habitualmente considerada como benigna e autolimitada, é muitas vezes não diagnosticada nem devidamente valorizada. No entanto, pode ser causa de reacção sistémica grave, potencialmente fatal. Objectivos e Métodos: De forma a aprofundar o conhecimento sobre esta patologia, avaliámos 16 doentes com UF, caracterizando a clínica, etiologia e duração da doença. Resultados: A média etária foi de 18,3 anos (7-54 anos), com predomínio de crianças com menos de 18 anos (63%) e do sexo masculino (62,5%). O início dos sintomas ocorreu entre os 3 e os 46 anos. Em 5 doentes foi adquirida tolerância, variando a duração da doença entre 2 e 7 anos (média de 3,8 anos). Nos 11 doentes que mantinham sintomas, o tempo médio da doença foi de 4,3 anos (1-9 anos). As queixas eram do tipo imediato em todos os doentes, ocorrendo sobretudo no decurso de actividades aquáticas, mas também com exposição a ar frio, chuva, neve, ingestão de alimentos frios e manipulação de objectos frios. O padrão clínico foi do tipo I (urticária/angioedema localizado) em 4 doentes, do tipo II (urticária/angioedema generalizado, sem hipotensão) em 6, e do tipo III (reacção sistémica grave) em 6 (dos quais 5 eram crianças). O teste do cubo de gelo foi positivo em todos os casos, à excepção de 2 casos de UF atípica. Na maioria dos doentes com padrão clínico tipo III, o teste foi positivo com ≤ 3 minutos de estimulação. A maioria dos casos(81%) correspondeu a UF adquirida idiopática, destacando-se 3 casos de UF adquirida secundária: 1 criança com crioglobulinémia primária e 2 com uma forma secundária a infecção por vírus Epstein-Barr. Nenhum doente tinha história familiar de UF. Em 3 doentes a UF associava-se a outra urticária física: urticária colinérgica (2) e urticária aquagénica (1). A melhoria sintomática foi obtida em todos os doentes com anti histamínicos (isoladamente ou em associação). Foi prescrito kit de adrenalina nos casos com padrão clínico tipo III. Conclusões: A UF adquirida idiopática foi o tipo mais frequente, destacando-se 3 casos raros de UF secundária, um a crioglobulinémia primária e dois a mononucleose infecciosa. A quantificação do resultado do teste do cubo de gelo revelou-se importante para a avaliação da gravidade da doença e para o seguimento do doente. A UF manifestou-se, num elevado número de doentes, por reacção sistémica grave, particularmente em crianças e durante actividades aquáticas, realçando a importância do reconhecimento desta entidade clínica.

"Gente da nossa": uma construção mediática da ideia de "comunidade portuguesa".

O texto tem por base a investigação realizada no quadro do projecto ““Feeling the Pulse of the community" - Identity politics and narratives of a portuguese migrant community in Canada”, financiado pela Fundação para a Ciência e Tecnologia. O projecto centrou-se no estudo do programa de televisão “Gente da Nossa”, que integra as características dos “Ethnic minority media”. Colocando-se no interior do campo da Antropologia dos Media, a estratégia metodológica integrou uma etnografia da produção e da recepção. O texto coloca o programa “Gente da Nossa” no interior da problemática mais geral das relações complexas que se estabelecem entre a produção e a difusão dos conteúdos dos “media étnicos” e os processos de etnicização de comunidades migrantes: o programa é conceptualizado enquanto veículo estrategicamente usado nos processos de construção, difusão, objectificação e mercadorização de imagens da “comunidade portuguesa do Canadá”. Quando tomado no seu conjunto, o processo de etnicização surge como algo complexo: uma etnografia do detalhe permite ler e discutir as diferentes dimensões desse complexo trabalho de construção da ideia de “comunidade”.

Historic and recent occurrences of pinnipeds in the Archipelago of the Azores

The Archipelago of the Azores (Portugal) is located between 378 and 418N and 258 and 318W and crosses the Mid-Atlantic Ridge. It is the most isolated archipelago in the Atlantic, situated 1600 km west of mainland Portugal and 3500 km from the eastern coast of the United States of America. At present, the only population of seals occurring in the Portuguese territory is found on Desertas Islands, Archipelago of Madeira, where a colony of 24 Mediterranean monk seals, Monachus monachus (Hermann, 1779), still persists (Pires and Neves 2001). Nonetheless, historical accounts reported by Frutuoso (1983) dating from the early to late 1500s mention sightings of ‘‘sea wolves’’ (the old Portuguese folk term for the Mediterranean monk seal) at several sites along the Azorean Island of Santa Maria. Little is known about the occurrence of monk seals in this area over the past five centuries, but the species certainly did not escape deliberate killing by the first settlers. While the early monk seal reports by Frutuoso (1983) are the only reports referring to the presence of colonies of seals in the Azores, more recently several sightings and strandings of vagrant seals of other species have been noted.

Fractional pennes' bioheat equation: theoretical and numerical studies

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation

A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.

Modelling tyre-road noise with data mining techniques

The research aimed to establish tyre-road noise models by using a Data Mining approach that allowed to build a predictive model and assess the importance of the tested input variables. The data modelling took into account three learning algorithms and three metrics to define the best predictive model. The variables tested included basic properties of pavement surfaces, macrotexture, megatexture, and uneven- ness and, for the first time, damping. Also, the importance of those variables was measured by using a sensitivity analysis procedure. Two types of models were set: one with basic variables and another with complex variables, such as megatexture and damping, all as a function of vehicles speed. More detailed models were additionally set by the speed level. As a result, several models with very good tyre-road noise predictive capacity were achieved. The most relevant variables were Speed, Temperature, Aggregate size, Mean Profile Depth, and Damping, which had the highest importance, even though influenced by speed. Megatexture and IRI had the lowest importance. The applicability of the models developed in this work is relevant for trucks tyre-noise prediction, represented by the AVON V4 test tyre, at the early stage of road pavements use. Therefore, the obtained models are highly useful for the design of pavements and for noise prediction by road authorities and contractors.

Sex differences in the fetal heart rate variability indices of twins

Aims: To evaluate the differences in linear and complex heart rate dynamics in twin pairs according to fetal sex combination [male-female (MF), male-male (MM), and female-female (FF)]. Methods: Fourteen twin pairs (6 MF, 3 MM, and 5 FF) were monitored between 31 and 36.4 weeks of gestation. Twenty-six fetal heart rate (FHR) recordings of both twins were simultaneously acquired and analyzed with a system for computerized analysis of cardiotocograms. Linear and nonlinear FHR indices were calculated. Results: Overall, MM twins presented higher intrapair average in linear indices than the other pairs, whereas FF twins showed higher sympathetic-vagal balance. MF twins exhibited higher intrapair average in entropy indices and MM twins presented lower entropy values than FF twins considering the (automatically selected) threshold rLu. MM twin pairs showed higher intrapair differences in linear heart rate indices than MF and FF twins, whereas FF twins exhibited lower intrapair differences in entropy indices. Conclusions: The results of this exploratory study suggest that twins have sex-specific differences in linear and nonlinear indices of FHR. MM twins expressed signs of a more active autonomic nervous system and MF twins showed the most active complexity control system. These results suggest that fetal sex combination should be taken into consideration when performing detailed evaluation of the FHR in twins.

Protective role of peroxisome proliferator-activated receptor-β/δ in septic shock.

Rationale: Peroxisome proliferator activated receptor (PPAR)-beta/delta is a transcription factor that belongs to the PPAR nuclear hormone receptor family, but the role of PPAR-beta/delta in sepsis is unknown. Objectives: We investigated the role of PPAR-beta/delta in murine models of LPS-induced organ injury and dysfunction and cecal ligation and puncture (CLP)-induced polymicrobial sepsis. Methods: Wild-type (WT) and PPAR-beta/delta knockout (1(0) mice and C57BL/6 mice were subjected to LPS for 16 hours. C57BL/6 mice received the PPAR-beta/delta agonist GW0742 (0.03 mg/kg intravenously, 1 h after LPS) or GW0742 plus the PPAR-beta/delta antagonist GSK0660 (0.1 mg/kg intravenously, 30 min before LPS). CD-1 mice subjected to CLP received GW0742 or GW0742 plus GSK0660. Measurements and Main Results: In PPAR-beta/delta KO mice, endotoxemia exacerbated organ injury and dysfunction (cardiac, renal, and hepatic) and inflammation (lung) compared with WT mice. In C57BL/6 mice subjected to endotoxemia, GW0742 significantly (1) attenuated organ (cardiac and renal) dysfunction and inflammation (lung); (2) increased the phosphorylation of Akt and glycogen synthase kinase (GSK)-3 beta; (3) attenuated the increase in extracellular signal-regulated kinase (ERK)1/2 and signal transducer and activator of transcription (STAT)-3 phosphorylation; and (4) attenuated the activation of nuclear factor (NF)-kappa B and the expression of inducible nitric oxide synthase (iNOS). In CD-1 mice subjected to CLP, GW0742 improved 10-day survival. All the observed beneficial effects of GW0742 were attenuated by the PPAR-beta/delta antagonist GSK0660. Conclusions: PPAR-beta/delta protects against multiple organ injury and dysfunction, and inflammation caused by endotoxic shock and improves survival in polymicrobial sepsis by a mechanism that may involve activation of Akt and inhibition of GSK-3 beta and NF-kappa B.

Pore space analysis of beech wood: The vessel network

Water transport in wood is vital for the survival of trees. With synchrotron radiation X-ray tomographic microscopy (SRXTM), it has become possible to characterize and quantify the three-dimensional (3D) network formed by vessels that are responsible for longitudinal transport. In the present study, the spatial size dependence of vessels and the organization inside single growth rings in terms of vessel-induced porosity was studied by SRXTM. Network characteristics, such as connectivity, were deduced by digital image analysis from the processed tomographic data and related to known complex network topologies.