Likelihood Geometry

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likelihood degree. We present an introduction to this theory and its statistical motivations. Many favorite objects from combinatorial algebraic geometry are featured: toric varieties, A-discriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. These notes were written for the second author's lectures at the CIME-CIRM summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.Comment: 45 pages; minor changes and addition

Chemokine receptor CXCR4 oligomerization is disrupted selectively by the antagonist ligand IT1t

CXCR4, a member of the family of chemokine-activated G protein-coupled receptors, is widely expressed in immune response cells. It is involved in both cancer development and progression as well as viral infection, notably by HIV-1. A variety of methods, including structural information, have suggested the receptor may exist as a dimer or oligomer. However, the mechanistic details surrounding receptor oligomerization and its potential dynamic regulation remain unclear. Using both biochemical and biophysical means we confirm that CXCR4 can exist as a mixture of monomers, dimers and higher-order oligomers in cell membranes and show that oligomeric structure becomes more complex as receptor expression levels increase. Mutations of CXCR4 residues located at a putative dimerization interface result in monomerization of the receptor. Additionally, binding of the CXCR4 antagonist IT1t— a small, drug-like isothiourea derivative — rapidly destabilizes the oligomeric structure, while AMD3100, another well-characterized CXCR4 antagonist, does not. Although a mutation that regulates constitutive activity of CXCR4 also results in monomerization of the receptor, binding of IT1t to this variant promotes receptor dimerization. These results provide novel insights into the basal organization of CXCR4 and how antagonist ligands of different chemotypes differentially regulate its oligomerization state

Four lectures on secant varieties

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhause

DNA Methylation Profiling Enables Accurate Classification of Nonductal Primary Pancreatic Neoplasms

Background & Aims: Cytologic and histopathologic diagnosis of non-ductal pancreatic neoplasms can be challenging in daily clinical practice, whereas it is crucial for therapy and prognosis. The cancer methylome is successfully used as a diagnostic tool in other cancer entities. Here, we investigate if methylation profiling can improve the diagnostic work-up of pancreatic neoplasms. Methods: DNA methylation data were obtained for 301 primary tumors spanning 6 primary pancreatic neoplasms and 20 normal pancreas controls. Neural Network, Random Forest, and extreme gradient boosting machine learning models were trained to distinguish between tumor types. Methylation data of 29 nonpancreatic neoplasms (n = 3708) were used to develop an algorithm capable of detecting neoplasms of non-pancreatic origin. Results: After benchmarking 3 state-of-the-art machine learning models, the random forest model emerged as the best classifier with 96.9% accuracy. All classifications received a probability score reflecting the confidence of the prediction. Increasing the score threshold improved the random forest classifier performance up to 100% with 87% of samples with scores surpassing the cutoff. Using a logistic regression model, detection of nonpancreatic neoplasms achieved an area under the curve of >0.99. Analysis of biopsy specimens showed concordant classification with their paired resection sample. Conclusions: Pancreatic neoplasms can be classified with high accuracy based on DNA methylation signatures. Additionally, non-pancreatic neoplasms are identified with near perfect precision. In summary, methylation profiling can serve as a valuable adjunct in the diagnosis of pancreatic neoplasms with minimal risk for misdiagnosis, even in the pre-operative setting

Wpływ serwisu linii towarowych kolei transnarodowych na harmonogramowanie pociągów w głównych korytarzach

In this paper we discuss several consequences of the freight transnational rail liner service on the rail corridor capacity. The Northern part of the IVth TEN-T corridor on Romanian territory has specific feature related to the passenger flows connecting important Romanian demographic and economic clusters, on one side, and on the other side, to its diagonal crossing aspect, from the Western border to the Constanta port, connecting the Central Europe countries to the Black Sea regions, which means that there are a lot of expectation in terms of this corridor rail capacity: this corridor will, be for a long time further, the single and first completed continuous upgraded and modernised rail corridor. Its utilization will necessarily be heterogeneously planned (meaning for passengers rapid trains and freight rapid trains, from domestic/internal market, but especially for external market of Romania). In this paper, we consider a simple mathematical model for the calculus of capacity in two different cases: for a homogeneous utilization, meaning that all trains have the same running speeds and for heterogeneous utilization, when the passenger trains have the higher speed and hence, the higher priority over the freight trains, even if some of them are freight transnational liner service. Special feature of liner rail service has to be considered (fixed schedule, no stops for passenger train advance). We draw several useful possible solutions to be considered in order to preserve the active corridor capacity, and to assure a smooth flow for the transnational liner services, which ultimately will enhance the rail attractiveness.W artykule przedyskutujemy wpływ serwisu międzynarodowego, kolejowego transportu towarów na przepustowość korytarzy. Północna część IV-tego korytarza TEN-T na terytorium Rumunii posiada specyficzne cechy oparte o przepływy pasażerów łącząc ważne demograficznie i ekonomicznie ośrodki Rumunii, z jednej strony, a z drugiej strony o diagonalny aspekt skrzyżowań ze wschodniej granicy do portu Konstanca, łącząc centralne kraje Europy z regionami Morza Czarnego, co oznacza wielkie oczekiwania związane z przepustowością korytarzy kolejowych. Rozważamy prosty matematyczny model obliczania przepływu w dwóch różnych przypadkach - dla jednorodnego wykorzystania, co oznacza, że wszystkie pociągi mają taka samą prędkość przebiegu oraz niejednorodne wykorzystanie, kiedy pociągi pasażerskie maja większą prędkość i stąd wyższy priorytet niż pociągi towarowe, nawet jeśli niektóre z nich są międzynarodowymi liniami towarowymi. Dla tej ostatniej sytuacji zostało narysowanych kilka użytecznych, możliwych rozwiązań rozpatrywanych w szczególności by chronić aktywny przepływ korytarzy, oraz by zabezpieczyć płynny przepływ dla serwisu linii transnarodowych, które w końcu uwydatnią atrakcyjność kolei

Modèle d'estimation des accidents de la route dans les zones urbaines

Urban areas are significantly different in terms of traffic risk. In a decisive manner, they are the result of urban development policies. The shape, size and configuration of an entire urban area, the facilities to satisfy people and the need for mobility of goods, as well as behavioural attitudes of the population, are essential for a traffic pattern and its associated risks. In this framework, the purpose of this paper is to identify the effects of urban area characteristics on road accidents. Using specific spatial analysis, a model of accident estimation in the urban areas of Bucharest is developed. The study aims to provide useful tools for urban decision makers for a-priori analysis of the consequences of urban outline changes on traffic risks.Les zones urbaines sont très différentes en termes de risque associé à la circulation. En manière décisive, ils sont le résultat des stratégies du développement urbain. La forme, la dimension et la configuration de l'ensemble de la région urbaine, l'offre pour satisfaire les besoins de mobilité des personnes et des marchandises, ainsi que les attitudes comportementales de la population sont essentielles pour le modèle de la circulation et le risque routier. Dans ce contexte, l'objectif de cet article est d'identifier les effets des caractéristiques des zones urbaines sur les accidents de la route. L'étude vise à fournir des décideurs dans la planification urbaine des instruments nécessaires pour analyser apriori les conséquences des changements de la structure urbaine sur le risque routier