On chaos, transient chaos and ghosts in single populations models with allee effects

Density-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.

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.

Behavioral and synaptic circuit analysis in models of neuropsychiatric disorders: Dissecting the in vivo role of the postsynaptic density proteins nArgBP2 and Shank3 using genetic engineered mice

Dissertation presented to obtain the Ph.D degree in Biology

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

Discrete and continuous compositions

This paper examines a dataset which is modeled well by thePoisson-Log Normal process and by this process mixed with LogNormal data, which are both turned into compositions. Thisgenerates compositional data that has zeros without any need forconditional models or assuming that there is missing or censoreddata that needs adjustment. It also enables us to model dependenceon covariates and within the composition

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, the geometric marginals conform with the traditional (arithmetic) marginals.These decompositions can be compared with standard log-linear models.Key words: balance, compositional data, simplex, Aitchison geometry, composition,orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure,contingency table

Using 3D surface datasets to understand landslide evolution: From analogue models to real case study

Early detection of landslide surface deformation with 3D remote sensing techniques, as TLS, has become a great challenge during last decade. To improve our understanding of landslide deformation, a series of analogue simulation have been carried out on non-rigid bodies coupled with 3D digitizer. All these experiments have been carried out under controlled conditions, as water level and slope angle inclination. We were able to follow 3D surface deformation suffered by complex landslide bodies from precursory deformation still larger failures. These experiments were the basis for the development of a new algorithm for the quantification of surface deformation using automatic tracking method on discrete points of the slope surface. To validate the algorithm, comparisons were made between manually obtained results and algorithm surface displacement results. Outputs will help in understanding 3D deformation during pre-failure stages and failure mechanisms, which are fundamental aspects for future implementation of 3D remote sensing techniques in early warning systems.

A note on discrete claims problems

In this note, we consider claims problems with indivisible goods. Specifically, by applying recursively the P-rights lower bound (Jiménez-Gómez and Marco-Gil (2008)), we ensure the fulfillment of Weak Order Preservation, considered by many authors as a minimal requirement of fairness. Moreover, we retrieve the Discrete Constrained Equal Losses and the Discrete Constrained Equal Awards rules (Herrero and Martíınez (2008)). Finally, by the recursive double imposition of a lower and an upper bound, we obtain the average between them. Keywords: Claims problems, Indivisibilities, Order Preservation, Constrained Egalitarian rules, Midpoint. JEL classification: C71, D63, D71.

The Limits of Discrete Time Repeated Games:Some Notes and Comments

This paper studies the limits of discrete time repeated games with public monitoring. We solve and characterize the Abreu, Milgrom and Pearce (1991) problem. We found that for the "bad" ("good") news model the lower (higher) magnitude events suggest cooperation, i.e., zero punishment probability, while the highrt (lower) magnitude events suggest defection, i.e., punishment with probability one. Public correlation is used to connect these two sets of signals and to make the enforceability to bind. The dynamic and limit behavior of the punishment probabilities for variations in ... (the discount rate) and ... (the time interval) are characterized, as well as the limit payo¤s for all these scenarios (We also introduce uncertainty in the time domain). The obtained ... limits are to the best of my knowledge, new. The obtained ... limits coincide with Fudenberg and Levine (2007) and Fudenberg and Olszewski (2011), with the exception that we clearly state the precise informational conditions that cause the limit to converge from above, to converge from below or to degenerate. JEL: C73, D82, D86. KEYWORDS: Repeated Games, Frequent Monitoring, Random Pub- lic Monitoring, Moral Hazard, Stochastic Processes.

Patients' and physicians' preferences for type 2 diabetes mellitus treatments in Spain and Portugal: a discrete choice experiment.

OBJECTIVE To assess Spanish and Portuguese patients' and physicians' preferences regarding type 2 diabetes mellitus (T2DM) treatments and the monthly willingness to pay (WTP) to gain benefits or avoid side effects. METHODS An observational, multicenter, exploratory study focused on routine clinical practice in Spain and Portugal. Physicians were recruited from multiple hospitals and outpatient clinics, while patients were recruited from eleven centers operating in the public health care system in different autonomous communities in Spain and Portugal. Preferences were measured via a discrete choice experiment by rating multiple T2DM medication attributes. Data were analyzed using the conditional logit model. RESULTS Three-hundred and thirty (n=330) patients (49.7% female; mean age 62.4 [SD: 10.3] years, mean T2DM duration 13.9 [8.2] years, mean body mass index 32.5 [6.8] kg/m(2), 41.8% received oral + injected medication, 40.3% received oral, and 17.6% injected treatments) and 221 physicians from Spain and Portugal (62% female; mean age 41.9 [SD: 10.5] years, 33.5% endocrinologists, 66.5% primary-care doctors) participated. Patients valued avoiding a gain in bodyweight of 3 kg/6 months (WTP: €68.14 [95% confidence interval: 54.55-85.08]) the most, followed by avoiding one hypoglycemic event/month (WTP: €54.80 [23.29-82.26]). Physicians valued avoiding one hypoglycemia/week (WTP: €287.18 [95% confidence interval: 160.31-1,387.21]) the most, followed by avoiding a 3 kg/6 months gain in bodyweight and decreasing cardiovascular risk (WTP: €166.87 [88.63-843.09] and €154.30 [98.13-434.19], respectively). Physicians and patients were willing to pay €125.92 (73.30-622.75) and €24.28 (18.41-30.31), respectively, to avoid a 1% increase in glycated hemoglobin, and €143.30 (73.39-543.62) and €42.74 (23.89-61.77) to avoid nausea. CONCLUSION Both patients and physicians in Spain and Portugal are willing to pay for the health benefits associated with improved diabetes treatment, the most important being to avoid hypoglycemia and gaining weight. Decreased cardiovascular risk and weight reduction became the third most valued attributes for physicians and patients, respectively.

Bilinear models for spatio-temporal point distribution analysis: application to extrapolation of left ventricular, biventricular and whole heart cardiac dynamics

In this work we describe the usage of bilinear statistical models as a means of factoring the shape variability into two components attributed to inter-subject variation and to the intrinsic dynamics of the human heart. We show that it is feasible to reconstruct the shape of the heart at discrete points in the cardiac cycle. Provided we are given a small number of shape instances representing the same heart atdifferent points in the same cycle, we can use the bilinearmodel to establish this. Using a temporal and a spatial alignment step in the preprocessing of the shapes, around half of the reconstruction errors were on the order of the axial image resolution of 2 mm, and over 90% was within 3.5 mm. From this, weconclude that the dynamics were indeed separated from theinter-subject variability in our dataset.

Discrete devaluations and multiple equilibria in a first generation model of currency crises

The first generation models of currency crises have often been criticized because they predict that, in the absence of very large triggering shocks, currency attacks should be predictable and lead to small devaluations. This paper shows that these features of first generation models are not robust to the inclusion of private information. In particular, this paper analyzes a generalization of the Krugman-Flood-Garber (KFG) model, which relaxes the assumption that all consumers are perfectly informed about the level of fundamentals. In this environment, the KFG equilibrium of zero devaluation is only one of many possible equilibria. In all the other equilibria, the lack of perfect information delays the attack on the currency past the point at which the shadow exchange rate equals the peg, giving rise to unpredictable and discrete devaluations.

Revenue management under general discrete choice model of consumer behavior

Customer choice behavior, such as 'buy-up' and 'buy-down', is an importantphe-nomenon in a wide range of industries. Yet there are few models ormethodologies available to exploit this phenomenon within yield managementsystems. We make some progress on filling this void. Specifically, wedevelop a model of yield management in which the buyers' behavior ismodeled explicitly using a multi-nomial logit model of demand. Thecontrol problem is to decide which subset of fare classes to offer ateach point in time. The set of open fare classes then affects the purchaseprobabilities for each class. We formulate a dynamic program todetermine the optimal control policy and show that it reduces to a dynamicnested allocation policy. Thus, the optimal choice-based policy caneasily be implemented in reservation systems that use nested allocationcontrols. We also develop an estimation procedure for our model based onthe expectation-maximization (EM) method that jointly estimates arrivalrates and choice model parameters when no-purchase outcomes areunobservable. Numerical results show that this combined optimization-estimation approach may significantly improve revenue performancerelative to traditional leg-based models that do not account for choicebehavior.

Probabilistic maximal covering location-allocation models with constrained waiting time or queue length for congested systems

When dealing with the design of service networks, such as healthand EMS services, banking or distributed ticket selling services, thelocation of service centers has a strong influence on the congestion ateach of them, and consequently, on the quality of service. In this paper,several models are presented to consider service congestion. The firstmodel addresses the issue of the location of the least number of single--servercenters such that all the population is served within a standard distance,and nobody stands in line for a time longer than a given time--limit, or withmore than a predetermined number of other clients. We then formulateseveral maximal coverage models, with one or more servers per service center.A new heuristic is developed to solve the models and tested in a 30--nodesnetwork.

Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facilitylocation modeling. This is not at all surprising since location policy is one of the mostprofitable areas of applied systems analysis in regional science and ample theoretical andapplied challenges are offered. Location-allocation models seek the location of facilitiesand/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or severalobjectives generally related to the efficiency of the system or to the allocation of resources.This paper concerns the location of facilities or services in discrete space or networks, thatare related to the public sector, such as emergency services (ambulances, fire stations, andpolice units), school systems and postal facilities. The paper is structured as follows: first,we will focus on public facility location models that use some type of coverage criterion,with special emphasis in emergency services. The second section will examine models based onthe P-Median problem and some of the issues faced by planners when implementing thisformulation in real world locational decisions. Finally, the last section will examine newtrends in public sector facility location modeling.