On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Self-Organising Maps and Correlation Analysis as a Tool to Explore Patterns in Excitation-Emission Matrix Data Sets and to Discriminate Dissolved Organic Matter Fluorescence Components

Dissolved organic matter (DOM) is a complex mixture of organic compounds, ubiquitous in marine and freshwater systems. Fluorescence spectroscopy, by means of Excitation-Emission Matrices (EEM), has become an indispensable tool to study DOM sources, transport and fate in aquatic ecosystems. However the statistical treatment of large and heterogeneous EEM data sets still represents an important challenge for biogeochemists. Recently, Self-Organising Maps (SOM) has been proposed as a tool to explore patterns in large EEM data sets. SOM is a pattern recognition method which clusterizes and reduces the dimensionality of input EEMs without relying on any assumption about the data structure. In this paper, we show how SOM, coupled with a correlation analysis of the component planes, can be used both to explore patterns among samples, as well as to identify individual fluorescence components. We analysed a large and heterogeneous EEM data set, including samples from a river catchment collected under a range of hydrological conditions, along a 60-km downstream gradient, and under the influence of different degrees of anthropogenic impact. According to our results, chemical industry effluents appeared to have unique and distinctive spectral characteristics. On the other hand, river samples collected under flash flood conditions showed homogeneous EEM shapes. The correlation analysis of the component planes suggested the presence of four fluorescence components, consistent with DOM components previously described in the literature. A remarkable strength of this methodology was that outlier samples appeared naturally integrated in the analysis. We conclude that SOM coupled with a correlation analysis procedure is a promising tool for studying large and heterogeneous EEM data sets.

A priori parameterisation of the CERES soil-crop models and tests against several European data sets

Mechanistic soil-crop models have become indispensable tools to investigate the effect of management practices on the productivity or environmental impacts of arable crops. Ideally these models may claim to be universally applicable because they simulate the major processes governing the fate of inputs such as fertiliser nitrogen or pesticides. However, because they deal with complex systems and uncertain phenomena, site-specific calibration is usually a prerequisite to ensure their predictions are realistic. This statement implies that some experimental knowledge on the system to be simulated should be available prior to any modelling attempt, and raises a tremendous limitation to practical applications of models. Because the demand for more general simulation results is high, modellers have nevertheless taken the bold step of extrapolating a model tested within a limited sample of real conditions to a much larger domain. While methodological questions are often disregarded in this extrapolation process, they are specifically addressed in this paper, and in particular the issue of models a priori parameterisation. We thus implemented and tested a standard procedure to parameterize the soil components of a modified version of the CERES models. The procedure converts routinely-available soil properties into functional characteristics by means of pedo-transfer functions. The resulting predictions of soil water and nitrogen dynamics, as well as crop biomass, nitrogen content and leaf area index were compared to observations from trials conducted in five locations across Europe (southern Italy, northern Spain, northern France and northern Germany). In three cases, the model’s performance was judged acceptable when compared to experimental errors on the measurements, based on a test of the model’s root mean squared error (RMSE). Significant deviations between observations and model outputs were however noted in all sites, and could be ascribed to various model routines. In decreasing importance, these were: water balance, the turnover of soil organic matter, and crop N uptake. A better match to field observations could therefore be achieved by visually adjusting related parameters, such as field-capacity water content or the size of soil microbial biomass. As a result, model predictions fell within the measurement errors in all sites for most variables, and the model’s RMSE was within the range of published values for similar tests. We conclude that the proposed a priori method yields acceptable simulations with only a 50% probability, a figure which may be greatly increased through a posteriori calibration. Modellers should thus exercise caution when extrapolating their models to a large sample of pedo-climatic conditions for which they have only limited information.

Development of an epidermal growth factor derivative with EGFR blocking activity.

The members of the epidermal growth factor (EGF)/ErbB family are prime targets for cancer therapy. However, the therapeutic efficiency of the existing anti-ErbB agents is limited. Thus, identifying new molecules that inactivate the ErbB receptors through novel strategies is an important goal on cancer research. In this study we have developed a shorter form of human EGF (EGFt) with a truncated C-terminal as a novel EGFR inhibitor. EGFt was designed based on the superimposition of the three-dimensional structures of EGF and the Potato Carboxypeptidase Inhibitor (PCI), an EGFR blocker previously described by our group. The peptide was produced in E. coli with a high yield of the correctly folded peptide. EGFt showed specificity and high affinity for EGFR but induced poor EGFR homodimerization and phosphorylation. Interestingly, EGFt promoted EGFR internalization and translocation to the cell nucleus although it did not stimulate the cell growth. In addition, EGFt competed with EGFR native ligands, inhibiting the proliferation of cancer cells. These data indicate that EGFt may be a potential EGFR blocker for cancer therapy. In addition, the lack of EGFR-mediated growth-stimulatory activity makes EGFt an excellent delivery agent to target toxins to tumours over-expressing EGFR.

Self-Organising Maps and Correlation Analysis as a Tool to Explore Patterns in Excitation-Emission Matrix Data Sets and to Discriminate Dissolved Organic Matter Fluorescence Components

Dissolved organic matter (DOM) is a complex mixture of organic compounds, ubiquitous in marine and freshwater systems. Fluorescence spectroscopy, by means of Excitation-Emission Matrices (EEM), has become an indispensable tool to study DOM sources, transport and fate in aquatic ecosystems. However the statistical treatment of large and heterogeneous EEM data sets still represents an important challenge for biogeochemists. Recently, Self-Organising Maps (SOM) has been proposed as a tool to explore patterns in large EEM data sets. SOM is a pattern recognition method which clusterizes and reduces the dimensionality of input EEMs without relying on any assumption about the data structure. In this paper, we show how SOM, coupled with a correlation analysis of the component planes, can be used both to explore patterns among samples, as well as to identify individual fluorescence components. We analysed a large and heterogeneous EEM data set, including samples from a river catchment collected under a range of hydrological conditions, along a 60-km downstream gradient, and under the influence of different degrees of anthropogenic impact. According to our results, chemical industry effluents appeared to have unique and distinctive spectral characteristics. On the other hand, river samples collected under flash flood conditions showed homogeneous EEM shapes. The correlation analysis of the component planes suggested the presence of four fluorescence components, consistent with DOM components previously described in the literature. A remarkable strength of this methodology was that outlier samples appeared naturally integrated in the analysis. We conclude that SOM coupled with a correlation analysis procedure is a promising tool for studying large and heterogeneous EEM data sets.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

Let $Q$ be a suitable real function on $C$. An $n$-Fekete set corresponding to $Q$ is a subset ${Z_{n1}},\dotsb, Z_{nn}}$ of $C$ which maximizes the expression $\Pi^n_i_{sets are, in a sense, maximally spread out with respect to the equilibrium measure. In general, our results apply only to a part of the Fekete set, which is at a certain distance away from the boundary of the droplet. However, for the potential $Q=|Z|^2$ we obtain results which hold globally, and we conjecture that such global results are true for a wide range of potentials.

On the Connectivity of the Julia sets of meromorphic functions

We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.

Splat-based surface reconstruction from defect-laden point sets

We introduce a method for surface reconstruction from point sets that is able to cope with noise and outliers. First, a splat-based representation is computed from the point set. A robust local 3D RANSAC-based procedure is used to filter the point set for outliers, then a local jet surface - a low-degree surface approximation - is fitted to the inliers. Second, we extract the reconstructed surface in the form of a surface triangle mesh through Delaunay refinement. The Delaunay refinement meshing approach requires computing intersections between line segment queries and the surface to be meshed. In the present case, intersection queries are solved from the set of splats through a 1D RANSAC procedure

Gp120/CD4 blocking antibodies are frequently elicited in ART-naïve chronically HIV-1 infected individuals

Antibodies with the ability to block the interaction of HIV-1 envelope glycoprotein (Env) gp120 with CD4, including those overlapping the CD4 binding site (CD4bs antibodies), can protect from infection by HIV-1, and their elicitation may be an interesting goal for any vaccination strategy. To identify gp120/CD4 blocking antibodies in plasma samples from HIV-1 infected individuals we have developed a competitive flow cytometry-based functional assay. In a cohort of treatment-naïve chronically infected patients, we showed that gp120/ CD4 blocking antibodies were frequently elicited (detected in 97% plasma samples) and correlated with binding to trimeric HIV-1 envelope glycoproteins. However, no correlation was observed between functional CD4 binding blockade data and titer of CD4bs antibodies determined by ELISA using resurfaced gp120 proteins. Consistently, plasma samples lacking CD4bs antibodies were able to block the interaction between gp120 and its receptor, indicating that antibodies recognizing other epitopes, such as PGT126 and PG16, can also play the same role. Antibodies blocking CD4 binding increased over time and correlated positively with the capacity of plasma samples to neutralize the laboratory-adapted NL4.3 and BaL virus isolates, suggesting their potential contribution to the neutralizing workforce of plasma in vivo. Determining whether this response can be boosted to achieve broadly neutralizing antibodies may provide valuable information for the design of new strategies aimed to improve the anti-HIV-1 humoral response and to develop a successful HIV- 1 vaccine.

A Comparative Study of Desktop, Fishtank, and Cave Systems for the Exploration of Volume Rendered Confocal Data Sets

We present a participant study that compares biological data exploration tasks using volume renderings of laser confocal microscopy data across three environments that vary in level of immersion: a desktop, fishtank, and cave system. For the tasks, data, and visualization approach used in our study, we found that subjects qualitatively preferred and quantitatively performed better in the cave compared with the fishtank and desktop. Subjects performed real-world biological data analysis tasks that emphasized understanding spatial relationships including characterizing the general features in a volume, identifying colocated features, and reporting geometric relationships such as whether clusters of cells were coplanar. After analyzing data in each environment, subjects were asked to choose which environment they wanted to analyze additional data sets in - subjects uniformly selected the cave environment.

Blocking and unblocking in a navigation task

Rodrigo, Chamizo, McLaren, & Mackintosh (1997) demonstrated the blocking effect in a navigational task using a swimming pool: rats initially trained to use three landmarks (ABC) to find an invisible platform learned less about a fourth landmark (X) added later than did rats trained from the outset with these four landmarks (ABCX). The aim of the experiment reported here was to demonstrate unblocking using a similar procedure as in the previous work. Three groups of rats were initially trained to find an invisible platfom in the presence of three landmarks: ABC for the Blocking and Unblocking groups and LMN for the Control group. Then, all animals were trained to find the platform in the presence of four landmarks, ABCX. In this second training, unlike animals in the Blocking group to which only a new landmark (X) was added in comparison to the first training, the animals in the Unblocking group also had a change in the platform position. In the Control group, both the four landmarks and the platform position were totally new at the beginning of this second training. As in Rodrigo et al. (1997) a blocking effect was found: rats in the Blocking group learned less with respect to the added landmark (X) than did animals in the Control group. However, rats in the Unblocking group learned about the added landmark (X) as well as did animals in the Control group. The results are interpreted as an unblocking effect due to a change in the platform position between the two phases of training, similarly to what is normal in classical conditioning experiments, in which a change in the conditions of reinforcement between the two training phases of a blocking design produce an attenuation or elimination of this effect. These results are explained within an error-correcting connectionist account of spatial navigation (McLaren, 2002).