A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

High-resolution numerical modelling of flow-vegetation interactions

In this paper, we present and apply a new three-dimensional model for the prediction of canopy-flow and turbulence dynamics in open-channel flow. The approach uses a dynamic immersed boundary technique that is coupled in a sequentially staggered manner to a large eddy simulation. Two different biomechanical models are developed depending on whether the vegetation is dominated by bending or tensile forces. For bending plants, a model structured on the Euler-Bernoulli beam equation has been developed, whilst for tensile plants, an N-pendula model has been developed. Validation against flume data shows good agreement and demonstrates that for a given stem density, the models are able to simulate the extraction of energy from the mean flow at the stem-scale which leads to the drag discontinuity and associated mixing layer.

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

Numerical Taxonomy of Old World Phlebotominae (Diptera: Psychodidae): 1. Considerations of Morphological Characters in the Genus Phlebotomus Rondani & Berté 1840

Numerical analyses (correspondence analysis, ascending hierarchical classification, cladistic approach) were applied to the morphological characters of the adults of the genus Phlebotomus Rondani & Berté 1840. They confirm the reliability of the classic classifications, and also redefine the taxonomic and phylogenetic position of certain taxa. Thus, Spelaeophlebotomus Theodor 1948, Idiophlebotomus Quate & Fairchild 1961 and Australophlebotomus Theodor 1948 deserve generic rank. Among the vectors of leishmaniasis, the subgenus Phlebotomus Rondani & Berté 1840 is probably ancient. The results attribute an intermediate taxonomic and phylogenetic position to the taxa Euphlebotomus Theodor 1948 and Anaphlebotomus Theodor 1948, and reveal the probable artificial nature of the latter. The comparatively large numbers of species of subgenera Paraphlebotomus Theodor 1948, Synphlebotomus Theodor 1948 and, above all, Larroussius Nitzulescu 1931 and Adlerius Nitzulescu 1931, suggest that they are relatively recent. The development of adult morphological characters, the validity of their use in taxonomy and proposals for further studies are discussed.

Numerical Taxonomy of Old World Phlebotominae (Diptera: Psychodidae): 2. Restatement of Classification upon Subgeneric Morphological Characters

Numerical analyses (correspondence analysis, ascending hierarchical classification, and cladistics) were done with morphological characters of adult phlebotomine sand flies. The resulting classification largely confirms that of classical taxonomy for supra-specific groups from the Old World, though the positions of some groups are adjusted. The taxa Spelaeophlebotomus Theodor 1948, Idiophlebotomus Quate & Fairchild 1961, Australophlebotomus Theodor 1948 and Chinius Leng 1987 are notably distinct from other Old World groups, particularly from the genus Phlebotomus Rondani & Berté 1840. Spelaeomyia Theodor 1948 and, in particular, Parvidens Theodor & Mesghali 1964 are clearly separate from Sergentomyia França & Parrot 1920.

Application of a roughness-length representation to parameterize energy loss in 3-D numerical simulations of large rivers

Recent technological advances in remote sensing have enabled investigation of the morphodynamics and hydrodynamics of large rivers. However, measuring topography and flow in these very large rivers is time consuming and thus often constrains the spatial resolution and reach-length scales that can be monitored. Similar constraints exist for computational fluid dynamics (CFD) studies of large rivers, requiring maximization of mesh-or grid-cell dimensions and implying a reduction in the representation of bedform-roughness elements that are of the order of a model grid cell or less, even if they are represented in available topographic data. These ``subgrid'' elements must be parameterized, and this paper applies and considers the impact of roughness-length treatments that include the effect of bed roughness due to ``unmeasured'' topography. CFD predictions were found to be sensitive to the roughness-length specification. Model optimization was based on acoustic Doppler current profiler measurements and estimates of the water surface slope for a variety of roughness lengths. This proved difficult as the metrics used to assess optimal model performance diverged due to the effects of large bedforms that are not well parameterized in roughness-length treatments. However, the general spatial flow patterns are effectively predicted by the model. Changes in roughness length were shown to have a major impact upon flow routing at the channel scale. The results also indicate an absence of secondary flow circulation cells in the reached studied, and suggest simpler two-dimensional models may have great utility in the investigation of flow within large rivers. Citation: Sandbach, S. D. et al. (2012), Application of a roughness-length representation to parameterize energy loss in 3-D numerical simulations of large rivers, Water Resour. Res., 48, W12501, doi: 10.1029/2011WR011284.

Nonclassical measurement error with applications to labor and development issues

Zero correlation between measurement error and model error has been assumed in existing panel data models dealing specifically with measurement error. We extend this literature and propose a simple model where one regressor is mismeasured, allowing the measurement error to correlate with model error. Zero correlation between measurement error and model error is a special case in our model where correlated measurement error equals zero. We ask two research questions. First, we wonder if the correlated measurement error can be identified in the context of panel data. Second, we wonder if classical instrumental variables in panel data need to be adjusted when correlation between measurement error and model error cannot be ignored. Under some regularity conditions the answer is yes to both questions. We then propose a two-step estimation corresponding to the two questions. The first step estimates correlated measurement error from a reverse regression; and the second step estimates usual coefficients of interest using adjusted instruments.

Multi-stage oligopoly models with nested logit demand structures: A simplifying approach

Solving multi-stage oligopoly models by backward induction can easily become a com- plex task when rms are multi-product and demands are derived from a nested logit frame- work. This paper shows that under the assumption that within-segment rm shares are equal across segments, the analytical expression for equilibrium pro ts can be substantially simpli ed. The size of the error arising when this condition does not hold perfectly is also computed. Through numerical examples, it is shown that the error is rather small in general. Therefore, using this assumption allows to gain analytical tractability in a class of models that has been used to approach relevant policy questions, such as for example rm entry in an industry or the relation between competition and location. The simplifying approach proposed in this paper is aimed at helping improving these type of models for reaching more accurate recommendations.

Quantificació de l'error comès pels models de níxol ecològic al predir la distribució d'especies generalistes

Report for the scientific sojourn carried out at the University of California at Berkeley, from September to December 2007. Environmental niche modelling (ENM) techniques are powerful tools to predict species potential distributions. In the last ten years, a plethora of novel methodological approaches and modelling techniques have been developed. During three months, I stayed at the University of California, Berkeley, working under the supervision of Dr. David R. Vieites. The aim of our work was to quantify the error committed by these techniques, but also to test how an increase in the sample size affects the resultant predictions. Using MaxEnt software we generated distribution predictive maps, from different sample sizes, of the Eurasian quail (Coturnix coturnix) in the Iberian Peninsula. The quail is a generalist species from a climatic point of view, but an habitat specialist. The resultant distribution maps were compared with the real distribution of the species. This distribution was obtained from recent bird atlases from Spain and Portugal. Results show that ENM techniques can have important errors when predicting the species distribution of generalist species. Moreover, an increase of sample size is not necessary related with a better performance of the models. We conclude that a deep knowledge of the species’ biology and the variables affecting their distribution is crucial for an optimal modelling. The lack of this knowledge can induce to wrong conclusions.

Analyzing complex rock slope deformation at Stampa, western Norway, by integrating geomorphology, kinematics and numerical modeling

The unstable rock slope, Stampa, above the village of Flåm, Norway, shows signs of both active and postglacial gravitational deformation over an area of 11 km2. Detailed structural field mapping, annual differential Global Navigation Satellite System (GNSS) surveys, as well as geomorphic analysis of high-resolution digital elevation models based on airborne and terrestrial laser scanning indicate that slope deformation is complex and spatially variable. Numerical modeling was used to investigate the influence of former rockslide activity and to better understand the failure mechanism. Field observations, kinematic analysis and numerical modeling indicate a strong structural control of the unstable area. Based on the integration of the above analyses, we propose that the failure mechanism is dominated by (1) a toppling component, (2) subsiding bilinear wedge failure and (3) planar sliding along the foliation at the toe of the unstable slope. Using differential GNSS, 18 points were measured annually over a period of up to 6 years. Two of these points have an average yearly movement of around 10 mm/year. They are located at the frontal cliff on almost completely detached blocks with volumes smaller than 300,000 m3. Large fractures indicate deep-seated gravitational deformation of volumes reaching several 100 million m3, but the movement rates in these areas are below 2 mm/year. Two different lobes of prehistoric rock slope failures were dated with terrestrial cosmogenic nuclides. While the northern lobe gave an average age of 4,300 years BP, the southern one resulted in two different ages (2,400 and 12,000 years BP), which represent most likely multiple rockfall events. This reflects the currently observable deformation style with unstable blocks in the northern part in between Joasete and Furekamben and no distinct blocks but a high rockfall activity around Ramnanosi in the south. With a relative susceptibility analysis it is concluded that small collapses of blocks along the frontal cliff will be more frequent. Larger collapses of free-standing blocks along the cliff with volumes > 100,000 m3, thus large enough to reach the fjord, cannot be ruled out. A larger collapse involving several million m3 is presently considered of very low likelihood.

Numerical simulation of left ventricular assist device implantations: comparing the ascending and the descending aorta cannulations.

In this work we present numerical simulations of continuous flow left ventricle assist device implantation with the aim of comparing difference in flow rates and pressure patterns depending on the location of the anastomosis and the rotational speed of the device. Despite the fact that the descending aorta anastomosis approach is less invasive, since it does not require a sternotomy and a cardiopulmonary bypass, its benefits are still controversial. Moreover, the device rotational speed should be correctly chosen to avoid anomalous flow rates and pressure distribution in specific location of the cardiovascular tree. With the aim of assessing the differences between these two approaches and device rotational speed in terms of flow rate and pressure waveforms, we set up numerical simulations of network of one-dimensional models where we account for the presence of an outflow cannula anastomosed to different locations of the aorta. Then, we use the resulting network to compare the results of the two different cannulations for several stages of heart failure and different rotational speed of the device. The inflow boundary data for the heart and the cannulas are obtained from a lumped parameters model of the entire circulatory system with an assist device, which is validated with clinical data. The results show that ascending and descending aorta cannulations lead to similar waveforms and mean flow rate in all the considered cases. Moreover, regardless of the anastomosis region, the rotational speed of the device has an important impact on wave profiles; this effect is more pronounced at high RPM.

The relationship between forensic science and judicial error: a study covering error sources, bias, and remedies

Summary : Forensic science - both as a source of and as a remedy for error potentially leading to judicial error - has been studied empirically in this research. A comprehensive literature review, experimental tests on the influence of observational biases in fingermark comparison, and semistructured interviews with heads of forensic science laboratories/units in Switzerland and abroad were the tools used. For the literature review, some of the areas studied are: the quality of forensic science work in general, the complex interaction between science and law, and specific propositions as to error sources not directly related to the interaction between law and science. A list of potential error sources all the way from the crime scene to the writing of the report has been established as well. For the empirical tests, the ACE-V (Analysis, Comparison, Evaluation, and Verification) process of fingermark comparison was selected as an area of special interest for the study of observational biases, due to its heavy reliance on visual observation and recent cases of misidentifications. Results of the tests performed with forensic science students tend to show that decision-making stages are the most vulnerable to stimuli inducing observational biases. For the semi-structured interviews, eleven senior forensic scientists answered questions on several subjects, for example on potential and existing error sources in their work, of the limitations of what can be done with forensic science, and of the possibilities and tools to minimise errors. Training and education to augment the quality of forensic science have been discussed together with possible solutions to minimise the risk of errors in forensic science. In addition, the time that samples of physical evidence are kept has been determined as well. Results tend to show considerable agreement on most subjects among the international participants. Their opinions on possible explanations for the occurrence of such problems and the relative weight of such errors in the three stages of crime scene, laboratory, and report writing, disagree, however, with opinions widely represented in existing literature. Through the present research it was therefore possible to obtain a better view of the interaction of forensic science and judicial error to propose practical recommendations to minimise their occurrence. Résumé : Les sciences forensiques - considérés aussi bien comme source de que comme remède à l'erreur judiciaire - ont été étudiées empiriquement dans cette recherche. Une revue complète de littérature, des tests expérimentaux sur l'influence du biais de l'observation dans l'individualisation de traces digitales et des entretiens semi-directifs avec des responsables de laboratoires et unités de sciences forensiques en Suisse et à l'étranger étaient les outils utilisés. Pour la revue de littérature, quelques éléments étudies comprennent: la qualité du travail en sciences forensiques en général, l'interaction complexe entre la science et le droit, et des propositions spécifiques quant aux sources d'erreur pas directement liées à l'interaction entre droit et science. Une liste des sources potentielles d'erreur tout le long du processus de la scène de crime à la rédaction du rapport a également été établie. Pour les tests empiriques, le processus d'ACE-V (analyse, comparaison, évaluation et vérification) de l'individualisation de traces digitales a été choisi comme un sujet d'intérêt spécial pour l'étude des effets d'observation, due à son fort recours à l'observation visuelle et dû à des cas récents d'identification erronée. Les résultats des tests avec des étudiants tendent à prouver que les étapes de prise de décision sont les plus vulnérables aux stimuli induisant des biais d'observation. Pour les entretiens semi-structurés, onze forensiciens ont répondu à des questions sur des sujets variés, par exemple sur des sources potentielles et existantes d'erreur dans leur travail, des limitations de ce qui peut être fait en sciences forensiques, et des possibilités et des outils pour réduire au minimum ses erreurs. La formation et l'éducation pour augmenter la qualité des sciences forensiques ont été discutées ainsi que les solutions possibles pour réduire au minimum le risque d'erreurs en sciences forensiques. Le temps que des échantillons sont gardés a été également déterminé. En général, les résultats tendent à montrer un grand accord sur la plupart des sujets abordés pour les divers participants internationaux. Leur avis sur des explications possibles pour l'occurrence de tels problèmes et sur le poids relatif de telles erreurs dans les trois étapes scène de crime;', laboratoire et rédaction de rapports est cependant en désaccord avec les avis largement représentés dans la littérature existante. Par cette recherche il était donc possible d'obtenir une meilleure vue de l'interaction des sciences forensiques et de l'erreur judiciaire afin de proposer des recommandations pratiques pour réduire au minimum leur occurrence. Zusammenfassung : Forensische Wissenschaften - als Ursache und als Hilfsmittel gegen Fehler, die möglicherweise zu Justizirrtümern führen könnten - sind hier empirisch erforscht worden. Die eingestzten Methoden waren eine Literaturübersicht, experimentelle Tests über den Einfluss von Beobachtungseffekten (observer bias) in der Individualisierung von Fingerabdrücken und halbstandardisierte Interviews mit Verantwortlichen von kriminalistischen Labors/Diensten in der Schweiz und im Ausland. Der Literaturüberblick umfasst unter anderem: die Qualität der kriminalistischen Arbeit im Allgemeinen, die komplizierte Interaktion zwischen Wissenschaft und Recht und spezifische Fehlerquellen, welche nicht direkt auf der Interaktion von Recht und Wissenschaft beruhen. Eine Liste möglicher Fehlerquellen vom Tatort zum Rapportschreiben ist zudem erstellt worden. Für die empirischen Tests wurde der ACE-V (Analyse, Vergleich, Auswertung und Überprüfung) Prozess in der Fingerabdruck-Individualisierung als speziell interessantes Fachgebiet für die Studie von Beobachtungseffekten gewählt. Gründe sind die Wichtigkeit von visuellen Beobachtungen und kürzliche Fälle von Fehlidentifizierungen. Resultate der Tests, die mit Studenten durchgeführt wurden, neigen dazu Entscheidungsphasen als die anfälligsten für Stimuli aufzuzeigen, die Beobachtungseffekte anregen könnten. Für die halbstandardisierten Interviews beantworteten elf Forensiker Fragen über Themen wie zum Beispiel mögliche und vorhandene Fehlerquellen in ihrer Arbeit, Grenzen der forensischen Wissenschaften und Möglichkeiten und Mittel um Fehler zu verringern. Wie Training und Ausbildung die Qualität der forensischen Wissenschaften verbessern können ist zusammen mit möglichen Lösungen zur Fehlervermeidung im selben Bereich diskutiert worden. Wie lange Beweismitten aufbewahrt werden wurde auch festgehalten. Resultate neigen dazu, für die meisten Themen eine grosse Übereinstimmung zwischen den verschiedenen internationalen Teilnehmern zu zeigen. Ihre Meinungen über mögliche Erklärungen für das Auftreten solcher Probleme und des relativen Gewichts solcher Fehler in den drei Phasen Tatort, Labor und Rapportschreiben gehen jedoch mit den Meinungen, welche in der Literatur vertreten werden auseinander. Durch diese Forschungsarbeit war es folglich möglich, ein besseres Verständnis der Interaktion von forensischen Wissenschaften und Justizirrtümer zu erhalten, um somit praktische Empfehlungen vorzuschlagen, welche diese verringern. Resumen : Esta investigación ha analizado de manera empírica el rol de las ciencias forenses como fuente y como remedio de potenciales errores judiciales. La metodología empleada consistió en una revisión integral de la literatura, en una serie de experimentos sobre la influencia de los sesgos de observación en la individualización de huellas dactilares y en una serie de entrevistas semiestructuradas con jefes de laboratorios o unidades de ciencias forenses en Suiza y en el extranjero. En la revisión de la literatura, algunas de las áreas estudiadas fueron: la calidad del trabajo en ciencias forenses en general, la interacción compleja entre la ciencia y el derecho, así como otras fuentes de error no relacionadas directamente con la interacción entre derecho y ciencia. También se ha establecido una lista exhaustiva de las fuentes potenciales de error desde la llegada a la escena del crimen a la redacción del informe. En el marco de los tests empíricos, al analizar los sesgos de observación dedicamos especial interés al proceso de ACE-V (análisis, comparación, evaluación y verificación) para la individualización de huellas dactilares puesto que este reposa sobre la observación visual y ha originado varios casos recientes de identificaciones erróneas. Los resultados de las experimentaciones realizadas con estudiantes sugieren que las etapas en las que deben tornarse decisiones son las más vulnerables a lös factores que pueden generar sesgos de observación. En el contexto de las entrevistas semi-estructuradas, once científicos forenses de diversos países contestaron preguntas sobre varios temas, incluyendo las fuentes potenciales y existehtes de error en su trabajo, las limitaciones propias a las ciencias forenses, las posibilidades de reducir al mínimo los errores y las herramientas que podrían ser utilizadas para ello. Se han sugerido diversas soluciones para alcanzar este objetivo, incluyendo el entrenamiento y la educación para aumentar la calidad de las ciencias forenses. Además, se ha establecido el periodo de conservación de las muestras judiciales. Los resultados apuntan a un elevado grado de consenso entre los entrevistados en la mayoría de los temas. Sin embargo, sus opiniones sobre las posibles causas de estos errores y su importancia relativa en las tres etapas de la investigación -la escena del crimen, el laboratorio y la redacción de informe- discrepan con las que predominan ampliamente en la literatura actual. De este modo, esta investigación nos ha permitido obtener una mejor imagen de la interacción entre ciencias forenses y errores judiciales, y comenzar a formular una serie de recomendaciones prácticas para reducirlos al minimo.