Neural fields with sigmoidal firing rates: approximate solutions

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of even approximate solutions to such models is of interest to the broad mathematical neuroscience community. Here we develop one such scheme, for stationary and travelling wave solutions, that can deal with a certain class of smoothed Heaviside functions. The distribution that smoothes the Heaviside is viewed as a fundamental object, and all expressions describing the scheme are constructed in terms of integrals over this distribution. The comparison of our scheme and results from direct numerical simulations is used to highlight the very good levels of approximation that can be achieved by iterating the process only a small number of times.

Exploration of the dendritic cell algorithm with the duration calculus

As one of the newest members in Articial Immune Systems (AIS), the Dendritic Cell Algorithm (DCA) has been applied to a range of problems. These applications mainly belong to the eld of anomaly detection. However, real-time detection, a new challenge to anomaly detection, requires improvement on the real-time capability of the DCA. To assess such capability, formal methods in the research of real-time systems can be employed. The ndings of the assessment can provide guideline for the future development of the algorithm. Therefore, in this paper we use an interval logic based method, named the Duration Calcu- lus (DC), to specify a simplied single-cell model of the DCA. Based on the DC specications with further induction, we nd that each individual cell in the DCA can perform its function as a detector in real-time. Since the DCA can be seen as many such cells operating in parallel, it is potentially capable of performing real-time detection. However, the analysis process of the standard DCA constricts its real-time capability. As a result, we conclude that the analysis process of the standard DCA should be replaced by a real-time analysis component, which can perform periodic analysis for the purpose of real-time detection.

Del videojuego a la realidad : sistema interactivo para la seguridad vial

El vertiginoso crecimiento de los centros urbanos, las tecnologías emergentes y la demanda de nuevos servicios por parte de la población plantea encaminar esfuerzos hacia el desarrollo de las ciudades inteligentes. Éste concepto ha tomado fuerza entre los sectores político, económico, social, académico, ambiental y civil; de forma paralela, se han generado iniciativas que conducen hacia la integración de la infraestructura, la tecnología y los servicios para los ciudadanos. En éste contexto, una de las problemáticas con mayor impacto en la sociedad es la seguridad vial. Es necesario contar con mecanismos que disminuyan la accidentalidad, mejoren la atención a incidentes, optimicen la movilidad urbana y planeación municipal, ayuden a reducir el consumo de combustible y la emisión de gases de efecto de invernadero, así como ofrecer información dinámica y efectiva a los viajeros. En este artículo se describen dos (2) enfoques que contribuyen de manera eficiente dicho problema: los videojuegos como juegos serios y los sistemas de transporte inteligente. Ambos enfoques están encaminados a evitar colisiones y su diseño e implementación requieren componentes altamente tecnológicos (e.g. sistemas telemáticos e informáticos, inteligencia artificial, procesamiento de imágenes y modelado 3D).

Lot production size problem and simulation of urban transport

OBJECTIVES AND STUDY METHOD: There are two subjects in this thesis: “Lot production size for a parallel machine scheduling problem with auxiliary equipment” and “Bus holding for a simulated traffic network”. Although these two themes seem unrelated, the main idea is the optimization of complex systems. The “Lot production size for a parallel machine scheduling problem with auxiliary equipment” deals with a manufacturing setting where sets of pieces form finished products. The aim is to maximize the profit of the finished products. Each piece may be processed in more than one mold. Molds must be mounted on machines with their corresponding installation setup times. The key point of our methodology is to solve the single period lot-sizing decisions for the finished products together with the piece-mold and the mold-machine assignments, relaxing the constraint that a single mold may not be used in two machines at the same time. For the “Bus holding for a simulated traffic network” we deal with One of the most annoying problems in urban bus operations is bus bunching, which happens when two or more buses arrive at a stop nose to tail. Bus bunching reflects an unreliable service that affects transit operations by increasing passenger-waiting times. This work proposes a linear mathematical programming model that establishes bus holding times at certain stops along a transit corridor to avoid bus bunching. Our approach needs real-time input, so we simulate a transit corridor and apply our mathematical model to the data generated. Thus, the inherent variability of a transit system is considered by the simulation, while the optimization model takes into account the key variables and constraints of the bus operation. CONTRIBUTIONS AND CONCLUSIONS: For the “Lot production size for a parallel machine scheduling problem with auxiliary equipment” the relaxation we propose able to find solutions more efficiently, moreover our experimental results show that most of the solutions verify that molds are non-overlapping even if they are installed on several machines. We propose an exact integer linear programming, a Relax&Fix heuristic, and a multistart greedy algorithm to solve this problem. Experimental results on instances based on real-world data show the efficiency of our approaches. The mathematical model and the algorithm for the lot production size problem, showed in this research, can be used for production planners to help in the scheduling of the manufacturing. For the “Bus holding for a simulated traffic network” most of the literature considers quadratic models that minimize passenger-waiting times, but they are harder to solve and therefore difficult to operate by real-time systems. On the other hand, our methodology reduces passenger-waiting times efficiently given our linear programming model, with the characteristic of applying control intervals just every 5 minutes.

On the duration of negative surplus

Doutoramento em Matemática

Changes in the storage and sink of carbon dioxide in subsurface atmospheres controlled by climate-driven processes: the case of the Ojo Guareña karst system

A comprehensive environmental monitoring program was conducted in the Ojo Guareña cave system (Spain), one of the longest cave systems in Europe, to assess the magnitude of the spatiotemporal changes in carbon dioxide gas (CO2) in the cave–soil–atmosphere profile. The key climate-driven processes involved in gas exchange, primarily gas diffusion and cave ventilation due to advective forces, were characterized. The spatial distributions of both processes were described through measurements of CO2 and its carbon isotopic signal (δ13C[CO2]) from exterior, soil and cave air samples analyzed by cavity ring-down spectroscopy (CRDS). The trigger mechanisms of air advection (temperature or air density differences or barometric imbalances) were controlled by continuous logging systems. Radon monitoring was also used to characterize the changing airflow that results in a predictable seasonal or daily pattern of CO2 concentrations and its carbon isotopic signal. Large daily oscillations of CO2 levels, ranging from 680 to 1900 ppm day−1 on average, were registered during the daily oscillations of the exterior air temperature around the cave air temperature. These daily variations in CO2 concentration were unobservable once the outside air temperature was continuously below the cave temperature and a prevailing advective-renewal of cave air was established, such that the daily-averaged concentrations of CO2 reached minimum values close to atmospheric background. The daily pulses of CO2 and other tracer gases such as radon (222Rn) were smoothed in the inner cave locations, where fluctuation of both gases was primarily correlated with medium-term changes in air pressure. A pooled analysis of these data provided evidence that atmospheric air that is inhaled into dynamically ventilated caves can then return to the lower troposphere as CO2-rich cave air.

The average mixing matrix signature

Laplacian-based descriptors, such as the Heat Kernel Signature and the Wave Kernel Signature, allow one to embed the vertices of a graph onto a vectorial space, and have been successfully used to find the optimal matching between a pair of input graphs. While the HKS uses a heat di↵usion process to probe the local structure of a graph, the WKS attempts to do the same through wave propagation. In this paper, we propose an alternative structural descriptor that is based on continuoustime quantum walks. More specifically, we characterise the structure of a graph using its average mixing matrix. The average mixing matrix is a doubly-stochastic matrix that encodes the time-averaged behaviour of a continuous-time quantum walk on the graph. We propose to use the rows of the average mixing matrix for increasing stopping times to develop a novel signature, the Average Mixing Matrix Signature (AMMS). We perform an extensive range of experiments and we show that the proposed signature is robust under structural perturbations of the original graphs and it outperforms both the HKS and WKS when used as a node descriptor in a graph matching task.

Keeping Variables within Bounds: Using Information between Observations

This research develops an econometric framework to analyze time series processes with bounds. The framework is general enough that it can incorporate several different kinds of bounding information that constrain continuous-time stochastic processes between discretely-sampled observations. It applies to situations in which the process is known to remain within an interval between observations, by way of either a known constraint or through the observation of extreme realizations of the process. The main statistical technique employs the theory of maximum likelihood estimation. This approach leads to the development of the asymptotic distribution theory for the estimation of the parameters in bounded diffusion models. The results of this analysis present several implications for empirical research. The advantages are realized in the form of efficiency gains, bias reduction and in the flexibility of model specification. A bias arises in the presence of bounding information that is ignored, while it is mitigated within this framework. An efficiency gain arises, in the sense that the statistical methods make use of conditioning information, as revealed by the bounds. Further, the specification of an econometric model can be uncoupled from the restriction to the bounds, leaving the researcher free to model the process near the bound in a way that avoids bias from misspecification. One byproduct of the improvements in model specification is that the more precise model estimation exposes other sources of misspecification. Some processes reveal themselves to be unlikely candidates for a given diffusion model, once the observations are analyzed in combination with the bounding information. A closer inspection of the theoretical foundation behind diffusion models leads to a more general specification of the model. This approach is used to produce a set of algorithms to make the model computationally feasible and more widely applicable. Finally, the modeling framework is applied to a series of interest rates, which, for several years, have been constrained by the lower bound of zero. The estimates from a series of diffusion models suggest a substantial difference in estimation results between models that ignore bounds and the framework that takes bounding information into consideration.

Product/Brand co-creation methodology crossing marketing, design thinking, creativity and management: ideas(r)evolution

This thesis introduce a new innovation methodology called IDEAS(R)EVOLUTION that was developed according to an on-going experimental research project started in 2007. This new approach to innovation has initial based on Design thinking for innovation theory and practice. The concept of design thinking for innovation has received much attention in recent years. This innovation approach has climbed from the design and designers knowledge field towards other knowledge areas, mainly business management and marketing. Human centered approach, radical collaboration, creativity and breakthrough thinking are the main founding principles of Design thinking that were adapted by those knowledge areas due to their assertively and fitness to the business context and market complexity evolution. Also Open innovation, User-centered innovation and later on Living Labs models emerge as answers to the market and consumers pressure and desire for new products, new services or new business models. Innovation became the principal business management focus and strategic orientation. All this changes had an impact also in the marketing theory. It is possible now to have better strategies, communications plans and continuous dialogue systems with the target audience, incorporating their insights and promoting them to the main dissemination ambassadors of our innovations in the market. Drawing upon data from five case studies, the empirical findings in this dissertation suggest that companies need to shift from Design thinking for innovation approach to an holistic, multidimensional and integrated innovation system. The innovation context it is complex, companies need deeper systems then the success formulas that “commercial “Design thinking for innovation “preaches”. They need to learn how to change their organization culture, how to empower their workforce and collaborators, how to incorporate external stakeholders in their innovation processes, hoe to measure and create key performance indicators throughout the innovation process to give them better decision making data, how to integrate meaning and purpose in their innovation philosophy. Finally they need to understand that the strategic innovation effort it is not a “one shot” story it is about creating a continuous flow of interaction and dialogue with their clients within a “value creation chain“ mindset; RESUMO: Metodologia de co-criação de um produto/marca cruzando Marketing, Design Thinking, Criativity and Management - IDEAS(R)EVOLUTION. Esta dissertação apresenta uma nova metodologia de inovação chamada IDEAS(R)EVOLUTION, que foi desenvolvida segundo um projecto de investigação experimental contínuo que teve o seu início em 2007. Esta nova abordagem baseou-se, inicialmente, na teoria e na práctica do Design thinking para a inovação. Actualmente o conceito do Design Thinking para a inovação “saiu” do dominio da area de conhecimento do Design e dos Designers, tendo despertado muito interesse noutras áreas como a Gestão e o Marketing. Uma abordagem centrada na Pessoa, a colaboração radical, a criatividade e o pensamento disruptivo são principios fundadores do movimento do Design thinking que têm sido adaptados por essas novas áreas de conhecimento devido assertividade e adaptabilidade ao contexto dos negócios e à evolução e complexidade do Mercado. Também os modelos de Inovação Aberta, a inovação centrada no utilizador e mais tarde os Living Labs, emergem como possiveis soluções para o Mercado e para a pressão e desejo dos consumidores para novos productos, serviços ou modelos de negócio. A inovação passou a ser o principal foco e orientação estratégica na Gestão. Todas estas mudanças também tiveram impacto na teoria do Marketing. Hoje é possivel criar melhores estratégias, planos de comunicação e sistemas continuos de diálogo com o público alvo, incorporando os seus insights e promovendo os consumidores como embaixadores na disseminação da inovação das empresas no Mercado Os resultados empiricos desta tese, construídos com a informação obtida nos cinco casos realizados, sugerem que as empresas precisam de se re-orientar do paradigma do Design thinking para a inovação, para um sistema de inovação mais holistico, multidimensional e integrado. O contexto da Inovação é complexo, por isso as empresas precisam de sistemas mais profundos e não apenas de “fórmulas comerciais” como o Design thinking para a inovação advoga. As Empresas precisam de aprender como mudar a sua cultura organizacional, como capacitar sua força de trabalho e colaboradores, como incorporar os públicos externos no processo de inovação, como medir o processo de inovação criando indicadores chave de performance e obter dados para um tomada de decisão mais informada, como integrar significado e propósito na sua filosofia de inovação. Por fim, precisam de perceber que uma estratégia de inovação não passa por ter “sucesso uma vez”, mas sim por criar um fluxo contínuo de interação e diálogo com os seus clientes com uma mentalidade de “cadeia de criação de valor”

Energy balance model applied to pasture experimental areas in São Paulo State, Brazil.

The Simple Algorithm for Evapotranspiration Retrieving (SAFER) was used to estimate biophysical parameters and theenergy balance components in two different pasture experimental areas, in the São Paulo state, Brazil. The experimentalpastures consist in six rotational (RGS) and three continuous grazing systems (CGS) paddocks. Landsat-8 images from2013 and 2015 dry and rainy seasons were used, as these presented similar hydrological cycle, with 1,600 mm and 1,613mm of annual precipitation, resulting in 19 cloud-free images. Bands 1 to 7 and thermal bands 10 and 11 were used withweather data from a station located nearthe experimental area. NDVI, biomass, evapotranspiration and latent heat flux(λE) temporal values statistically differ CGS from RGS areas. Grazing systems influences the energy partition and theseresults indicate that RGS benefits biomass production, evapotranspiration and the microclimate, due higher LE values.SAFER is a feasible tool to estimate biophysical parameters and energy balance components in pasture and has potentialto discriminate continuous and rotation grazing systems in a temporal analysis.

Transition from time-continuous systems to discrete mappings

Detailed transport studies in plasmas require the solution of the time evolution of many different initial positions of test particles in the phase space of the systems to be investigated. To reduce this amount of numerical work, one would like to replace the integration of the time-continues system with a mapping.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov's transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov's transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov’s transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

Rigorous finite-time guarantees for optimization on continuous domains by simulated annealing

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

Random response of nonlinear continuous systems

This thesis presents a technique for obtaining the stochastic response of a nonlinear continuous system. First, the general method of nonstationary continuous equivalent linearization is developed. This technique allows replacement of the original nonlinear system with a time-varying linear continuous system. Next, a numerical implementation is described which allows solution of complex problems on a digital computer. In this procedure, the linear replacement system is discretized by the finite element method. Application of this method to systems satisfying the one-dimensional wave equation with two different types of constitutive nonlinearities is described. Results are discussed for nonlinear stress-strain laws of both hardening and softening types.