Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

Synchronization and Basins of Synchronized in Two-Dimensional Piecewise Maps Via Coupling Three Pieces of One-Dimensional Maps

This paper is devoted to the synchronization of a dynamical system defined by two different coupling versions of two identical piecewise linear bimodal maps. We consider both local and global studies, using different tools as natural transversal Lyapunov exponent, Lyapunov functions, eigenvalues and eigenvectors and numerical simulations. We obtain theoretical results for the existence of synchronization on coupling parameter range. We characterize the synchronization manifold as an attractor and measure the synchronization speed. In one coupling version, we give a necessary and sufficient condition for the synchronization. We study the basins of synchronization and show that, depending upon the type of coupling, they can have very different shapes and are not necessarily constituted by the whole phase space; in some cases, they can be riddled.

Big Bang bifurcations and allee effect in Blumberg’s dynamics

This paper concerns dynamics and bifurcations properties of a class of continuous-defined one-dimensional maps, in a three-dimensional parameter space: Blumberg's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon, associated with the stability of a fixed point. A central point of our investigation is the study of bifurcations structure for this class of functions. We verified that under some sufficient conditions, Blumberg's functions have a particular bifurcations structure: the big bang bifurcations of the so-called "box-within-a-box" type, but for different kinds of boxes. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct attractors. This work contributes to clarify the big bang bifurcation analysis for continuous maps. To support our results, we present fold and flip bifurcations curves and surfaces, and numerical simulations of several bifurcation diagrams.

From weak Allee effect to no Allee effect in Richards’ growth models

Population dynamics have been attracting interest since many years. Among the considered models, the Richards’ equations remain one of the most popular to describe biological growth processes. On the other hand, Allee effect is currently a major focus of ecological research, which occurs when positive density dependence dominates at low densities. In this chapter, we propose the dynamical study of classes of functions based on Richards’ models describing the existence or not of Allee effect. We investigate bifurcation structures in generalized Richards’ functions and we look for the conditions in the (β, r) parameter plane for the existence of a weak Allee effect region. We show that the existence of this region is related with the existence of a dovetail structure. When the Allee limit varies, the weak Allee effect region disappears when the dovetail structure also disappears. Consequently, we deduce the transition from the weak Allee effect to no Allee effect to this family of functions. To support our analysis, we present fold and flip bifurcation curves and numerical simulations of several bifurcation diagrams.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

Explosion birth and extinction: Double big bang bifurcations and Allee effect in Tsoularis-Wallace's growth models

This work concerns dynamics and bifurcations properties of a new class of continuous-defined one-dimensional maps: Tsoularis-Wallace's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon of extinction. To establish this result we introduce the notions of Allee's functions, Allee's effect region and Allee's bifurcation curve. Another central point of our investigation is the study of bifurcation structures for this class of functions, in a three-dimensional parameter space. We verified that under some sufficient conditions, Tsoularis-Wallace's functions have particular bifurcation structures: the big bang and the double big bang bifurcations of the so-called "box-within-a-box" type. The double big bang bifurcations are related to the existence of flip codimension-2 points. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct kinds of boxes. This work contributes to clarify the big bang bifurcation analysis for continuous maps and understand their relationship with explosion birth and extinction phenomena.

Economias de escala em centros hospitalares

RESUMO - Perante o actual contexto de contenção de gastos no sector da saúde e consequente preocupação com a eficiência do sistema, tem‐se assistido a mudanças várias no modelo de gestão e organizacional do sistema de saúde. Destaca‐se a alteração da estrutura hospitalar, com vista à racionalização dos seus recursos internos, onde as fusões hospitalares têm assumido um papel determinante. Em Portugal, nos últimos 10 anos, assistiu‐se a uma significativa redução do número de hospitais (de sensivelmente 90 para 50 unidades), exclusivamente através das fusões e sem quaisquer alterações no número de estruturas físicas existentes. Não obstante os argumentos justificativos desta reforma, a avaliação dos objectivos implícitos é insuficiente. Neste âmbito, pretendeu‐se com este estudo contribuir para a análise do impacte da criação de centros hospitalares na redução de gastos, isto é, verificar se a consolidação e consequente reengenharia dos processos produtivos teve consequencias ao nível da obtenção de economias de escala. Para esta análise usou‐se uma base de dados em painel, onde se consideraram 75 hospitais durante 7 anos (2003‐2009), número que foi reduzindo ao longo do período em análise devido às inúmeras fusões já referidas. Para avaliar os ganhos relativos às fusões hospitalares, ao nível da eficiência técnica e das economias de escala, recorreu‐se à fronteira estocástica especificada função custo translog. Estimada a fronteira, foi possível analisar três centros hospitalares específicos, onde se comparou o período pré‐fusão (2005‐2006) com o período após a fusão (2008‐2009). Como variáveis explicativas, relativas à produção hospitalar, considerou‐se o número de casos tratados e os dias de internamento (Vita, 1990; Schuffham et al., 1996), o número de consultas e o número de urgências, sendo estas variáveis as mais comuns na literatura (Vita, 1990; Fournier e Mitchell, 1992; Carreira, 1999). Quanto à variável dependente usou‐se o custo variável total, que compreende o total de custos anuais dos hospitais excepto de imobilizado. Como principais conclusões da investigação, em consequência da criação dos centros hospitalares, são de referir os ganhos de escala na fusão de hospitais de reduzida dimensão e com mais serviços complementares. --------ABSTRACT - Driven by the current pressure on resources induced by budgetary cuts, the Portuguese Ministry of Health is imposing changes in the management model and organization of NHS hospitals. The most recent change is based on the creation of Hospital Centres that are a result of administrative mergers of existing hospitals. In less than 10 years the number of hospitals passed from around 90 to around 50, only due to the mergers and without any change in the existing number of physical institutions. According to the political discourse, one of the main goals expected from this measure is the creation of synergies and more efficiency in the use of available resources. However, the merger of the hospitals has been a political decision without support or evaluation of the first experiments. The aim of this study is to measure the results of this policy by looking at economies of scale namely through reductions in the expenditures, as expected and sought by the MoH. Data used covers 7 years (2003‐2009) and 75 hospitals, number that has been reduced my the enoumerous mergers during the last decade. This work uses a stochastic frontier analysis through the translog cost function to examine the gains from mergers, which were decomposed into technical efficiency and economies of scale. It was analised these effects by the creation of three specific hospital centers, using a longitudinal approach to compare the period pre‐merger (2003‐2006) with the post‐merger period (2007‐09). To measure changes in inpatient hospital production volume and length of stay are going to be considered as done by Vita (1990) and Schuffham et al. (1996). For outpatient services the number of consultations and emergencies are going to be considered (Vita, 1990; Fournier e Mitchell, 1992; Carreira, 1999). Total variable cost is considered as the dependent variable explained the aforementioned ones. After a review of the literature results expected point to benefits from the mergers, namely a reduction in total expenditures and in the number of duplicated services. Results extracted from our data point in the same direction, and thus for the existence of some economies of scale only for small hospitals.

Mutilations Due to Medical Disorders in Children

Soft-tissue and bone necrosis, although rare in childhood, occasionally occur in the course of infectious diseases, either viral or bacterial, and seem to be the result of hypoperfusion on a background of disseminated intravascular coagulation. Treatment consists in correction of septic shock and control of necrosis. Necrosis, once started, shows extraordinarily rapid evolution, leading to soft-tissue and bone destruction and resulting in anatomic, functional, psychological, and social handicaps. Ten mutilated children were treated from January 1986 to January 1999 in Hospital de Dona Estefaˆ nia, Lisbon, Portugal. One was recovering from hemolytic-uremic syndrome with a severe combined immunodeficiency, another malnourished, anemic child had malaria, and three had chicken pox (in one case complicated by meningococcal septicemia). There were three cases of meningococcal and two of pyocyanic septicemia (one in a burned child and one in a patient with infectious mononucleosis). The lower limbs (knee,leg, foot) were involved in five cases, the face (ear, nose, lip) in four, the perineum in three, the pelvis (inguinal region, iliac crest) in two, the axilla in one, and the upper limb (radius, hand) in two. Primary prevention is based on early recognition of risk factors and timely correction. Secondary prevention consists of immediate etiologic and thrombolytic treatment to restrict the area of necrosis. Tertiary prevention relies on adequate rehabilitation with physiotherapy and secondary operations to obtain the best possible functional and esthetic result.

The new mobility paradigm: transformation of value chain and business models

We would like to thank Philipp Schwarz and Julia Gückel for their dedicated support in preparing this paper and our colleagues and students of the School of Engineering and the Business School for our fruitful discussions.

Aspectos epidemiológicos e clínicos dos acidentes ofídicos ocorridos nos municípios do Estado do Amazonas

No Amazonas, o acidente ofídico é um problema de saúde pública pouco conhecido. Por este motivo, foi realizado um estudo descritivo dos acidentes ofídicos atendidos nas Unidades de Saúde de 34 municípios, um distrito e dois pelotões de fronteira do Estado do Amazonas. As características mais comuns encontradas dentre os pacientes foram: agricultor (50,4%), do sexo masculino (81,3%), em idade produtiva (72,1%), picado no membro inferior (88,5%), por jararaca (48,6%) ou surucucu (46,8%), na zona rural de seu município (70,2%) e que só recebeu atendimento médico em tempo superior a seis horas, após acidente (57,3%). As manifestações locais mais freqüentes foram: edema (76,9%), dor (68,7%), eritema (10,2%) e hemorragia (9,3%). Hemorragia (18,8%) foi a manifestação sistêmica mais freqüente. O antiveneno foi administrado em apenas 65,9% dos pacientes. A via mais utilizada foi a endovenosa (52,3%), sendo relevante o uso de vias não mais recomendadas (47,7%). O antiveneno administrado, na maioria dos pacientes, foi o antibotrópico (66,7%). As complicações mais freqüentes foram abcesso (13,7%), necrose (12,3%), infecção secundária (8,3%), insuficiência renal (2,5%) e gangrena (2,5%). Os procedimentos médicos mais usados para o tratamento das complicações foram: drenagem (52,6%), debridamento (28,9%), amputação (10,5%), limpeza cirúrgica (5,3%) e diálise peritoneal (2,6%). A letalidade foi de 1%.

Prevalence and clinical importance of mesenteric venous thrombosis in the swiss inflammatory bowel disease cohort.

OBJECTIVE. The purpose of this study was to evaluate the prevalence of mesenteric venous thrombosis (MVT) in the Swiss Inflammatory Bowel Disease Cohort Study and to correlate MVT with clinical outcome. MATERIALS AND METHODS. Abdominal portal phase CT was used to examine patients with inflammatory bowel disease (IBD). Two experienced abdominal radiologists retrospectively analyzed the images, focusing on the superior and inferior mesenteric vein branches and looking for signs of acute or chronic thrombosis. The location of abnormalities was registered. The presence of MVT was correlated with IBD-related radiologic signs and complications. RESULTS. The cases of 160 patients with IBD (89 women, 71 men; Crohn disease [CD], 121 patients; ulcerative colitis [UC], 39 patients; median age at diagnosis, 27 years for patients with CD, 32 years for patients with UC) were analyzed. MVT was detected in 43 patients with IBD (26.8%). One of these patients had acute MVT; 38, chronic MVT; and four, both. The prevalence of MVT did not differ between CD (35/121 [28.9%]) and UC (8/39 [20.5%]) (p = 0.303). The location of thrombosis was different between CD and UC (CD, jejunal or ileal veins only [p = 0.005]; UC, rectocolic veins only [p = 0.001]). Almost all (41/43) cases of thrombosis were peripheral. MVT in CD patients was more frequently associated with bowel wall thickening (p = 0.013), mesenteric fat hypertrophy (p = 0.005), ascites (p = 0.002), and mesenteric lymph node enlargement (p = 0.036) and was associated with higher rate of bowel stenosis (p < 0.001) and more intestinal IBD-related surgery (p = 0.016) in the outcome. Statistical analyses for patients with UC were not relevant because of the limited population (n = 8). CONCLUSION. MVT is frequently found in patients with IBD. Among patients with CD, MVT is associated with bowel stenosis and CD-related intestinal surgery.

Morphologie et reproduction des plantes le long de gradients altitudinaux.

Les communautés végétales sont connues pour changer avec l'altitude. Certains traits morphologiques présents chez les végétaux qui les composent sont adaptés à un type de milieux et y sont représentés préférentiellement. Dans cette étude, nous nous sommes intéressés à la variation des traits présents chez les plantes le long du gradient altitudinal. Nous avons ainsi étudié dix transects altitudinaux en milieux ouverts et en forêts dans les Alpes valaisannes, vaudoises et dans le Jura. Par ce biais, nous avons pu mettre en évidence une variation importance de la dominance de certains traits le long de l'altitude. Nous discutons les mécanismes évolutifs ayant modelés les motifs observés.

An alteration in the levels of populations of CD4+ Treg is in part responsible for altered cytokine production by cells of aged mice which follows injection with a fetal liver extract.

We have shown previously that a fetal sheep liver extract (FSLE) containing significant quantities of fetal ovine gamma globin chain (Hbgamma) and LPS injected into aged (>20 months) mice could reverse the altered polarization (increased IL-4 and IL-10 with decreased IL-2 and IFNgamma) in cytokine production seen from ConA stimulated lymphoid cells of those mice. The mechanism(s) behind this change in cytokine production were not previously investigated. We report below that aged mice show a >60% decline in numbers and suppressive function of both CD4(+)CD25(+)Foxp3(+) Treg and so-called Tr3 (CD4(+)TGFbeta(+)), and that their number/function is restored to levels seen in control (8-week-old) mice by FSLE. In addition, on a per cell basis, CD4(+)CD25(-)Treg from aged mice were >4-fold more effective in suppression of proliferation and IL-2 production from ConA-activated lymphoid cells of a pool of CD4(+)CD25(-)T cells from 8-week-old mice than similar cells from young animals, and this suppression by CD25(-)T cells was also ameliorated following FSLE treatment. Infusion of anti-TGFbeta and anti-IL-10 antibodies in vivo altered Treg development following FSLE treatment, and attenuated FSLE-induced alterations in cytokine production profiles.