The Dynamics of Growth and Distribution in a Spatially Heterogeneous World

This paper tries to reconcile growth and geographical economics by dealing directly with capital accumulation through time and space and by seeing growth convergence and spatial agglomeration as jointly generated by dynamic processes displaying pattern formation. It presents a centralized economy in which a Bergson-Samuelson- Millian central planner finds a flow of optimal distributions of consumption, subject to a spatial-temporal capital accumulation budget constraint. The main conclusions are: first, if the behavioral parameters are symmetric, but there is an asymmetric distribution of the capital stock, then the long run asymptotic distribution will be spatially homogeneous; second, if there is homogeneous distribution of the capital stock, but there is an asymmetric shock in any parameter, then the economy will converge towards a spatially heterogeneous asymptotic state; third, spatially heterogeneous asymptotic states will only emerge exogenously, not endogenously; fourth, the spatial propagation mechanism can give birth, when the production function is close to linear, to a Turing instability, which implies that for some parameter values, a conditionally stable spacetime distribution should display spatial pattern formation.Optimal growth and distribution; Spatial growth; Optimal control of partial differential equations; Traveling waves; Fourier transforms; Turing instability.

Equilibrium asset prices and bubbles in a continuous time OLG model

In a Yaari-Blanchard overlapping generations endowment economy, and drawing on the equivalence between Radner (R) and Arrow-Debreu (AD) equi- libria, we prove that equilibrium AD prices have an explicit representation as a double integral equation. This allows for an analytic characterization of the relationship between life-cycle and cohort heterogeneity and asset prices. For a simple distribution, we prove that bubbles may exist, and derive conditions for ruling them out.overlapping generations, asset pricing, bubbles, integral equations, LambertW function

Using data visualization to deduce faces expressions

Conferência Internacional, realizada na Turquia, de 6-8 de setembro de 2018.Collect and examine in real time multi modal sensor data of a human face, is an important problem in computer vision, with applications in medical and monitoring analysis, entertainment and security. Although its advances, there are still many open issues in terms of the identification of the facial expression. Different algorithms and approaches have been developed to find out patterns and characteristics that can help the automatic expression identification. One way to study data is through data visualizations. Data visualization turns numbers and letters into aesthetically pleasing visuals, making it easy to recognize patterns and find exceptions. In this article, we use information visualization as a tool to analyse data points and find out possible existing patterns in four different facial expressions.info:eu-repo/semantics/publishedVersio

Local and global indeterminacy in two-sector models of endogenous growth

In this paper we consider a two-sector endogenous growth model where the productions of the final good and human capital require economy-wide external effects. Assuming constant returns to scale at the private and social levels, we show that local and global indeterminacy of equilibrium paths are compatible with any values for the elasticity of intertemporal substitution in consumption and any sign for the capital intensity difference across the two sectors.Two-sector model, endogenous growth, economy-wide externalities, local and global indeterminacy

Business Cycles with Endogenous Mark-ups

Endogenous mark-ups have been a matter of interest in macroeconomics, especially from the middle 1990’s onwards. However, the complexity of this class of models, does not allow general ualitative conclusions in most cases, and there is plenty of room for investigation, especially in the reasons driving the emergence of multiple equilibria and non-saddle-point dynamics. In this article we extend a simple dynamic general equilibrium model to include the possibility of strategic interaction between producers in each industry, and entry affects the level of macroeconomic efficiency through an endogenous mark-up. We demonstrate multiple equilibria is a likely outcome even in an exogenous labour-supply framework. A pair of equilibria exists (a stable and an unstable one) and they are connected through a heteroclinic orbit. When we allow labour supply to vary, a third equilibrium may emerge if the government is present in the economy, and local indeterminacy may existEndogenous mark-ups, Multiple equilibria, Local dynamics

Economic growth theory, fifty years after

Fifty year have passed since Solow’s [21] paper on economic growth theory has been published. With a non-specialized reader in mind, we present the main ensuing phases of the theory and the way our own research relates to it. The history of growth theory is conventionally divided into two phases: until early 1970’s, the research is labeled exogenous growth theory, and, starting in late 1980’s until the present, the new growth or endogenous growth theory is being developed. We present the main models of both theories, the stylized facts of growth and a broad view on their compliance of theory with them. At last, we report some avenues that we have been exploring, as well as their motivation and results. This research addresses the topics: existence of multiple BGP’s, indeterminacy, non-monotonous transitions and an exploration on the integration of spatial and growth theories using PDE’s.info:eu-repo/semantics/publishedVersio

Local dynamics for optimal control problems of three-dimensional ODE systems

This paper presents a complete characterization of the local dynamics for optimal control problems in three-dimensional systems of ordinary differential equations by using geometrical methods. The particular structure of the Jacobian implies that the sixth-order characteristic polynomial is equivalent to a composition of two lower-order polynomials, which are solvable by radicals. The classification problem for local dynamics is addressed by finding partitions, over an intermediate three-dimensional space, which are homomorphic to the subspaces tangent to the complex, center and stable sub-manifolds. The main results are: a local stability theorem and necessary conditions for the existence of fold, Hopf, double-fold and fold-Hopf bifurcations.info:eu-repo/semantics/publishedVersio

Facial analysis with depth maps and deep learning

Tese de Doutoramento em Ciência e Tecnologia Web em associação com a Universidade de Trás-os-Montes e Alto Douro, apresentada à Universidade AbertaA recolha e análise sequencial de dados multimodais do rosto humano é um problema importante em visão por computador, com aplicações variadas na análise e monitorização médica, entretenimento e segurança. No entanto, devido à natureza do problema, há uma falta de sistemas acessíveis e fáceis de usar, em tempo real, com capacidade de anotações, análise 3d, capacidade de reanalisar e com uma velocidade capaz de detetar padrões faciais em ambientes de trabalho. No âmbito de um esforço contínuo, para desenvolver ferramentas de apoio à monitorização e avaliação de emoções/sinais em ambiente de trabalho, será realizada uma investigação relativa à aplicabilidade de uma abordagem de análise facial para mapear e avaliar os padrões faciais humanos. O objetivo consiste em investigar um conjunto de sistemas e técnicas que possibilitem responder à questão de como usar dados de sensores multimodais para obter um sistema de classificação para identificar padrões faciais. Com isso em mente, foi planeado desenvolver ferramentas para implementar um sistema em tempo real de forma a reconhecer padrões faciais. O desafio é interpretar esses dados de sensores multimodais para classificá-los com algoritmos de aprendizagem profunda e cumprir os seguintes requisitos: capacidade de anotações, análise 3d e capacidade de reanalisar. Além disso, o sistema tem que ser capaze de melhorar continuamente o resultado do modelo de classificação para melhorar e avaliar diferentes padrões do rosto humano. A FACE ANALYSYS, uma ferramenta desenvolvida no contexto desta tese de doutoramento, será complementada por várias aplicações para investigar as relações de vários dados de sensores com estados emocionais/sinais. Este trabalho é útil para desenvolver um sistema de análise adequado para a perceção de grandes quantidades de dados comportamentais.Collecting and analyzing in real time multimodal sensor data of a human face is an important problem in computer vision, with applications in medical and monitoring analysis, entertainment, and security. However, due to the exigent nature of the problem, there is a lack of affordable and easy to use systems, with real time annotations capability, 3d analysis, replay capability and with a frame speed capable of detecting facial patterns in working behavior environments. In the context of an ongoing effort to develop tools to support the monitoring and evaluation of human affective state in working environments, this research will investigate the applicability of a facial analysis approach to map and evaluate human facial patterns. Our objective consists in investigating a set of systems and techniques that make it possible to answer the question regarding how to use multimodal sensor data to obtain a classification system in order to identify facial patterns. With that in mind, it will be developed tools to implement a real-time system in a way that it will be able to recognize facial patterns from 3d data. The challenge is to interpret this multi-modal sensor data to classify it with deep learning algorithms and fulfill the follow requirements: annotations capability, 3d analysis and replay capability. In addition, the system will be able to enhance continuously the output result of the system with a training process in order to improve and evaluate different patterns of the human face. FACE ANALYSYS is a tool developed in the context of this doctoral thesis, in order to research the relations of various sensor data with human facial affective state. This work is useful to develop an appropriate visualization system for better insight of a large amount of behavioral data.N/

The dynamics of growth and distribution in a spatially heterogeneous world

This paper tries to reconcile growth and geographical economics by dealing di¬rectly with capital accumulation through time and space and by seeing growth convergence and spatial agglomeration as jointly generated by dynamic processes displaying pattern formation. It presents a centralized economy in which a Bergson-Samuelson-Millian central planner finds a flow of optimal distributions of consumption, subject to a spatial-temporal capital accumulation budget constraint. The main conclusions are: first, if the behavioral parameters are symmetric, but there is an asymmetric distribution of the capital stock, then the long run asymptotic distribution will be spatially homogeneous; second, if there is homogeneous distribution of the capital stock, but there is an asymmetric shock in any parameter, then the economy will converge towards a spatially heterogeneous asymptotic state; third, spatially heterogeneous asymptotic states will only emerge exogenously, not endogenously; fourth, the spatial propagation mechanism can give birth, when the production function is close to linear, to a Turing instability, which implies that for some parameter values, a conditionally stable spacetime distribution should display spatial pattern formation