Spatial patterns for a predator-prey system with Beddington-DeAngelis functional response and fractional cross-diffusion

In this paper, we investigate a predator-prey system with fractional type cross-diffusion incorporating the Beddington-DeAngelis functional response subjected to the homogeneous Neumann boundary condition. First, by using the maximum principle and the Harnack inequality, we establish a priori estimate for the positive stationary solution. Second, we study the non-existence of non-constant positive solutions mainly by employing the energy integral method and the Poincaré inequality. Finally, we discuss the existence of non-constant positive steady states for suitable large self-diffusion $d_2$ or cross-diffusion $d_4$ by using the Leray-Schauder degree theory, and the results reveal that the diffusion $d_2$ and the fractional type cross-diffusion $d_4$ can create spatial patterns

Exploring the developing preterm brain with diffusion tensor magnetic resonance imaging

Imperial Users onl

Inferring ecosystem states and quantifying their resilience : linking theories to ecological data

The core of my thesis concerns addressing the ecosystem resilience in a data-driven manner. In this direction, I have tried to make a bridge between advanced mathematical models and existing ecological data. I could come up with some quantitative measures of resilience and applied them to some ecological field and experimental data. These measures are more exact compared with the classical measures mentioned by Holling. I show that Holling measures are just two extremes of the measure I introduced and they do not necessarily capture the notion of resilience in its real sense of the word. Furthermore, I could also address the resilience of low-resolution tropical satellite data across the tropics (South America, Africa, south east Asia and, Australia). Besides, my thesis also sheds more light on the concept of ‘alternative stable states’ which is an important concept in ecology. I argue that advanced ‘system reconstruction’ approaches should be applied first, from where one can better justify weather or not an ecosystem has alternative stable states. </p

Nonlinear dynamics of plankton ecosystem with impulsive control and environmental fluctuations

It is well known that the density of plankton populations always increases and decreases or keeps invariant for a long time, and the variation of plankton density is an important factor influencing the real aquatic environments, why do these situations occur? It is an interesting topic which has become the common interest for many researchers. As the basis of the food webs in oceans, lakes, and reservoirs, plankton plays a significant role in the material circulation and energy flow for real aquatic ecosystems that have a great effect on the economic and social values. Planktonic blooms can occur in some environments, however, and the direct or indirect adverse effects of planktonic blooms on real aquatic ecosystems, such as water quality, water landscape, aquaculture development, are sometimes catastrophic, and thus planktonic blooms have become a challenging and intractable problem worldwide in recent years. Therefore, to understand these effects so that some necessary measures can be taken, it is important and meaningful to investigate the dynamic growth mechanism of plankton and reveal the dynamics mechanisms of formation and disappearance of planktonic blooms. To this end, based on the background of the ecological environments in the subtropical lakes and reservoirs, this dissertation research takes mainly the planktonic algae as the research objective to model the mechanisms of plankton growth and evolution. In this dissertation, some theories related to population dynamics, impulsive control dynamics, stochastic dynamics, as well as the methods of dynamic modeling, dynamic analysis and experimental simulation, are applied to reveal the effects of some key biological factors on the dynamics mechanisms of the spatial-temporal distribution of plankton and the termination of planktonic blooms, and to predict the dynamics evolutionary processes of plankton growth. The main results are as follows: Firstly, to discuss the prevention and control strategies on planktonic blooms, an impulsive reaction-diffusion hybrid system was developed. On the one hand, the dynamic analysis showed that impulsive control can significantly influence the dynamics of the system, including the ultimate boundedness, extinction, permanence, and the existence and uniqueness of positive periodic solution of the system. On the other hand, some experimental simulations were preformed to reveal that impulsive control can lead to the extinction and permanence of population directly. More precisely, the prey and intermediate predator populations can coexist at any time and location of their inhabited domain, while the top predator population undergoes extinction when the impulsive control parameter exceeds some a critical value, which can provide some key arguments to control population survival by means of some reaction-diffusion impulsive hybrid systems in the real life. Additionally, a heterogeneous environment can affect the spatial distribution of plankton and change the temporal-spatial oscillation of plankton distribution. All results are expected to be helpful in the study of dynamic complex of ecosystems. Secondly, a stochastic phytoplankton-zooplankton system with toxic phytoplankton was proposed and the effects of environmental stochasticity and toxin-producing phytoplankton (TPP) on the dynamics mechanisms of the termination of planktonic blooms were discussed. The research illustrated that white noise can aggravate the stochastic oscillation of plankton density and a high-level intensity of white noise can accelerate the extinction of plankton and may be advantageous for the disappearance of harmful phytoplankton, which imply that the white noise can help control the biomass of plankton and provide a guide for the termination of planktonic blooms. Additionally, some experimental simulations were carried out to reveal that the increasing toxin liberation rate released by TPP can increase the survival chance of phytoplankton population and reduce the biomass of zooplankton population, but the combined effects of those two toxin liberation rates on the changes in plankton are stronger than that of controlling any one of the two TPP. All results suggest that both white noise and TPP can play an important role in controlling planktonic blooms. Thirdly, we established a stochastic phytoplankton-toxic producing phytoplankton-zooplankton system under regime switching and investigated how the white noise, regime switching and TPP affect the dynamics mechanisms of planktonic blooms. The dynamical analysis indicated that both white noise and toxins released by TPP are disadvantageous to the development of plankton and may increase the risk of plankton extinction. Also, a series of experimental simulations were carried out to verify the correctness of the dynamical analysis and further reveal the effects of the white noise, regime switching and TPP on the dynamics mechanisms of the termination of planktonic blooms. On the one hand, the numerical study revealed that the system can switch from one state to another due to regime shift, and further indicated that the regime switching can balance the different survival states of plankton density and decrease the risk of plankton extinction when the density of white noise are particularly weak. On the other hand, an increase in the toxin liberation rate can increase the survival chance of phytoplankton but reduce the biomass of zooplankton, which implies that the presence of toxic phytoplankton may have a positive effect on the termination of planktonic blooms. These results may provide some insightful understanding on the dynamics of phytoplankton-zooplankton systems in randomly disturbed aquatic environments. Finally, a stochastic non-autonomous phytoplankton-zooplankton system involving TPP and impulsive perturbations was studied, where the white noise, impulsive perturbations and TPP are incorporated into the system to simulate the natural aquatic ecological phenomena. The dynamical analysis revealed some key threshold conditions that ensure the existence and uniqueness of a global positive solution, plankton extinction and persistence in the mean. In particular, we determined if there is a positive periodic solution for the system when the toxin liberation rate reaches a critical value. Some experimental simulations also revealed that both white noise and impulsive control parameter can directly influence the plankton extinction and persistence in the mean. Significantly, enhancing the toxin liberation rate released by TPP increases the possibility of phytoplankton survival but reduces the zooplankton biomass. All these results can improve our understanding of the dynamics of complex of aquatic ecosystems in a fluctuating environment

Essays in Applied Economics

This work includes the results of a broad research carried out during the PhD course in Economics at the University of Genova. The first part of this work consists of two articles that can be ascribed to the literature on the long and short run economic impact of infrastructure. In particular, the first article is devoted to investigate the long-term impact of the Roman road network on today\u2019s propensity to export following a micro funded model by Duranton et al. (2014) that links roads to trade. The paper main result is that, controlling for possible determinants of propensity to trade and for the lenght and the location of Roman road system dating back to 117 A.D., the latter still influences today\u2019s propensity to export of the Italian NUTS-2 regions. Moreover, we investigate two potential channels underlying this result that have been highlighted in the previous literature. In particular, results in this paper confirm the well supported hypothesis in the literature that Roman roads are correlated with today\u2019s roads even though they were not established on the same route. However our paper does not lend support to the idea that Roman roads foster current trade by influencing social capital. The second article deals on the literature on the economic impact of transport infrastructure, and in particular on the role that road infrastructure can have on innovative regional capacity. We follow the seminal contribution by Agrawal et al. (2017) and we estimate a model of "roads and innovation" where the innovative activity in 1988 is linked to the length of motorways system in 1983, in order to investigate the impact of motorways endowment on the innovative capacity in each Italian NUTS-3 region. The main challenging issue about the estimation of our model arises from the possible endogeneity of highways stock. To deal with this problem, we follow the "historical instrumental variable" approach by using the length of the ancient Roman roads system dating back to 117 A.D. as an instrument for the length of current motorways. Overall, our Instrumental Variable estimates indicate that 1983 highways network has a positive and significant impact on 1988 innovative capacity. Moreover, we find a declining role for highways over time. Furthermore, results suggest a spatial reorganization of economic activity rather than a pure net economic effect. The second part of this work contains an article that belongs to the literature on the multidimensional indexes of well-being. In particular, following the growing interest in new and better measures of development, we elaborate an index of development for the Republics that gained independence after the Soviet Union broke up. We base our analysis on a set of variables from the World Development Indicators database released by theWorld Bank. We select the variables through principal component analysis and we calculate the index using factorial analysis. Therefore, following the well supported hypothesis in the literature that good governance has a key positive influence on development, we compare this index with a proposed index of governance, elaborating data from the Worldwide Governance Indicators database of the World Bank. As expected, the correlation between our index of development and our index of governance is high. Finally we perform a cluster analysis to group country according to the two indices

Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation: Special Report of the Intergovernmental Panel on Climate Change

This Special Report on Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation (SREX) has been jointly coordinated by Working Groups I (WGI) and II (WGII) of the Intergovernmental Panel on Climate Change (IPCC). The report focuses on the relationship between climate change and extreme weather and climate events, the impacts of such events, and the strategies to manage the associated risks. The IPCC was jointly established in 1988 by the World Meteorological Organization (WMO) and the United Nations Environment Programme (UNEP), in particular to assess in a comprehensive, objective, and transparent manner all the relevant scientific, technical, and socioeconomic information to contribute in understanding the scientific basis of risk of human-induced climate change, the potential impacts, and the adaptation and mitigation options. Beginning in 1990, the IPCC has produced a series of Assessment Reports, Special Reports, Technical Papers, methodologies, and other key documents which have since become the standard references for policymakers and scientists.This Special Report, in particular, contributes to frame the challenge of dealing with extreme weather and climate events as an issue in decisionmaking under uncertainty, analyzing response in the context of risk management. The report consists of nine chapters, covering risk management; observed and projected changes in extreme weather and climate events; exposure and vulnerability to as well as losses resulting from such events; adaptation options from the local to the international scale; the role of sustainable development in modulating risks; and insights from specific case studies

Effects of increasing temperatures and CO2 on phytoplankton and marine biogeochemical cycles - Combining experimental work and numerical modeling

The ongoing increase in atmospheric carbon dioxide (CO2) leads to a global increase in temperatures and its subsequent uptake by the ocean considerably alters the carbonate chemistry of seawater, a phenomenon generally referred to as “ocean acidification”. Both ocean warming and acidification occur at a pace unprecedented in recent geological history and are expected to significantly affect marine biota. In the present thesis, the sensitivity of marine ecosystems and biogeochemical cycling to increasing temperatures and CO2 was investigated in a combined approach of numerical modeling and experimental work. In a first step, the role of direct temperature effects in the response of marine ecosystems to ocean warming was investigated by simulating climate change in a global earth system model, based on emission scenarios for the 21st century. The study revealed fundamental uncertainties in our knowledge about temperature sensitivities of marine ecosystems and biogeochemical cycling. Depending on whether biological processes were assumed temperature sensitive or not, simulated marine NPP increased or decreased under projected climate change. Motivated by the outcome of this modeling study, a mesocosm experiment was carried out to specifically investigate the temperature sensitivity of biogeochemically important processes in diatom-dominated plankton communities.The results from this mesocosm study suggested a pronounced increase in carbon uptake and production of organic matter in response to elevated temperatures, which was contrary to results from similar experiments. A major difference to previous mesocosm studies was the dominant phytoplankton species, suggesting that the physiological response of this species determined the biogeochemical response of the entire plankton community. In order to test this hypothesis, culture experiments were conducted to compare the sensitivities of two globally important diatom species (Thalassiosira weissflogii and Dactyliosolen fragilissimus)to temperature and CO2.The results of these experiments revealed a pronounced effect of temperature and CO2 on carbon uptake and partitioning into particulate and dissolved organic matter, and especially the phenomenon of carbon overconsumption and the associated decoupling of carbon and nitrogen cycling. Furthermore, the experiments could show that the sensitivity of these processes to temperature and CO2 varies substantially between species, thereby confirming the hypothesis derived from the preceding mesocosm study. The findings from these various laboratory experiments were the basis for the development of a novel biogeochemical ecosystem model. Most models do not account for carbon overconsumption and dynamic stoichiometry, and sensitivities of associated processes to temperature and pCO2, as observed in these experimental studies. Consequently, a model was constructed that simulates carbon overconsumption and its sensitivity to temperature and pCO2. Application of this model may help to understand how carbon overconsumption and associated processes affect marine biogeochemical cycling. Further work investigated how the warming-induced decrease seawater viscosity under global warming might affect sinking velocity of marine particles and the carbon flux to the deep ocean. Application of a global earth system model demonstrated that this previously overlooked 'viscosity effect' could have profound impacts on marine biogeochemical cycling and oceanic carbon uptake over the next centuries to millennia. In the model experiment, the viscosity effect significantly accelerated particle sinking, thereby effectively reducing the portion of organic matter that is respired in the surface ocean and enhancing the long-term sequestration of atmospheric CO2 in the ocean. The representation of particle sinking in biogeochemical models was investigated in more detail in an additional sensitivity analysis. Results of this study demonstrated that the inherent structure of commonly used ecosystem models sets an upper limit to the flux of organic matter from the euphotic zone to the deep ocean, even under light-saturated and nutrient-replete conditions. This upper limit is determined by the functional form of the various process descriptions in the simulated ecosystem, as well as their respective parameter settings. These findings indicate that, even though such relatively simple ecosystem models may show good skill in reproducing observed current distributions of biogeochemical tracers, it is questionable whether such models can realistically simulate the sensitivity of biogeochemical cycles to environmental change. Altogether, this doctoral thesis revealed substantial sensitivities of marine carbon fluxes to increases in temperature and CO2, which should be considered when assessing the impact of climate change on marine ecosystems and feedbacks on the global carbon cycle

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described