A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.

Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs

Most research on single machine scheduling has assumedthe linearity of job holding costs, which is arguablynot appropriate in some applications. This motivates ourstudy of a model for scheduling $n$ classes of stochasticjobs on a single machine, with the objective of minimizingthe total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable,nondecreasing and convex on the number of jobs in eachclass. We formulate the problem as a linear program overa certain greedoid polytope, and establish that it issolved optimally by a dynamic (priority) index rule,whichextends the classical Smith's rule (1956) for the linearcase. Unlike Smith's indices, defined for each class, ournew indices are defined for each extended class, consistingof a class and a number of jobs in that class, and yieldan optimal dynamic index rule: work at each time on a jobwhose current extended class has larger index. We furthershow that the indices possess a decomposition property,as they are computed separately for each class, andinterpret them in economic terms as marginal expected cost rate reductions per unit of expected processing time.We establish the results by deploying a methodology recentlyintroduced by us [J. Niño-Mora (1999). "Restless bandits,partial conservation laws, and indexability. "Forthcomingin Advances in Applied Probability Vol. 33 No. 1, 2001],based on the satisfaction by performance measures of partialconservation laws (PCL) (which extend the generalizedconservation laws of Bertsimas and Niño-Mora (1996)):PCL provide a polyhedral framework for establishing theoptimality of index policies with special structure inscheduling problems under admissible objectives, which weapply to the model of concern.

Mapping of Environmental Data Using Kernel-Based Methods

Recently, kernel-based Machine Learning methods have gained great popularity in many data analysis and data mining fields: pattern recognition, biocomputing, speech and vision, engineering, remote sensing etc. The paper describes the use of kernel methods to approach the processing of large datasets from environmental monitoring networks. Several typical problems of the environmental sciences and their solutions provided by kernel-based methods are considered: classification of categorical data (soil type classification), mapping of environmental and pollution continuous information (pollution of soil by radionuclides), mapping with auxiliary information (climatic data from Aral Sea region). The promising developments, such as automatic emergency hot spot detection and monitoring network optimization are discussed as well.

Follicular Peripheral T-cell Lymphoma Expands the Spectrum of Classical Hodgkin Lymphoma Mimics.

Epstein-Barr virus (EBV)-infected B cells with Reed-Sternberg-like cell (RS) features may occur in peripheral T-cell lymphomas (PTCLs), especially in angioimmunoblastic T-cell lymphoma. Here, we report 5 patients presenting with lymphadenopathy whose first biopsies demonstrated nodular lymphoid proliferations containing scattered CD30, CD15, EBV Hodgkin and Reed-Sternberg-like cells, which led to an initial diagnosis of lymphocyte-rich classical Hodgkin lymphoma. However, the uncommon clinical features and/or the occurrence of relapse as PTCL prompted review of the biopsies with expanded immunohistologic and molecular studies and revision of the diagnoses to follicular variant of PTCL (F-PTCL). All cases had atypical small to medium-sized CD3 T cells that expressed CD10 (4/5) and the follicular helper T-cell (TFH) antigens BCL6, PD1, CXCL13, and ICOS. All demonstrated clonal T cells with a similar pattern in multiple samples from 4 patients. In 2 cases, flow cytometry demonstrated circulating lymphocytes with an abnormal sCD3, CD4, ICOS immunophenotype. Two patients had a skin rash at presentation, and 1 had B symptoms. Two of the 4 patients treated with polychemotherapy are alive at 3 and 6 years after first diagnosis. These cases highlight how some F-PTCLs may closely mimic lymphocyte-rich classical Hodgkin lymphoma requiring careful assessment of the T cells before rendering the latter diagnosis. The functional properties of TFH cells might lead to the presence of EBV-positive B blasts with RS-like features in TFH-derived PTCL such as angioimmunoblastic T-cell lymphoma and F-PTCL.

Comparison of Energy Minimization Methods for 3-D Brain Tissue Classification

This paper presents 3-D brain tissue classificationschemes using three recent promising energy minimizationmethods for Markov random fields: graph cuts, loopybelief propagation and tree-reweighted message passing.The classification is performed using the well knownfinite Gaussian mixture Markov Random Field model.Results from the above methods are compared with widelyused iterative conditional modes algorithm. Theevaluation is performed on a dataset containing simulatedT1-weighted MR brain volumes with varying noise andintensity non-uniformities. The comparisons are performedin terms of energies as well as based on ground truthsegmentations, using various quantitative metrics.

Median problems in networks

The P-median problem is a classical location model par excellence . In this paper we, firstexamine the early origins of the problem, formulated independently by Louis Hakimi andCharles ReVelle, two of the fathers of the burgeoning multidisciplinary field of researchknown today as Facility Location Theory and Modelling. We then examine some of thetraditional heuristic and exact methods developed to solve the problem. In the third sectionwe analyze the impact of the model in the field. We end the paper by proposing new lines ofresearch related to such a classical problem.

Perfusion and diffusion MRI of glioblastoma progression in a four-year prospective temozolomide clinical trial.

PURPOSE: This study was performed to determine the impact of perfusion and diffusion magnetic resonance imaging (MRI) sequences on patients during treatment of newly diagnosed glioblastoma. Special emphasis has been given to these imaging technologies as tools to potentially anticipate disease progression, as progression-free survival is frequently used as a surrogate endpoint. METHODS AND MATERIALS: Forty-one patients from a phase II temolozomide clinical trial were included. During follow-up, images were integrated 21 to 28 days after radiochemotherapy and every 2 months thereafter. Assessment of scans included measurement of size of lesion on T1 contrast-enhanced, T2, diffusion, and perfusion images, as well as mass effect. Classical criteria on tumor size variation and clinical parameters were used to set disease progression date. RESULTS: A total of 311 MRI examinations were reviewed. At disease progression (32 patients), a multivariate Cox regression determined 2 significant survival parameters: T1 largest diameter (p < 0.02) and T2 size variation (p < 0.05), whereas perfusion and diffusion were not significant. CONCLUSION: Perfusion and diffusion techniques cannot be used to anticipate tumor progression. Decision making at disease progression is critical, and classical T1 and T2 imaging remain the gold standard. Specifically, a T1 contrast enhancement over 3 cm in largest diameter together with an increased T2 hypersignal is a marker of inferior prognosis.

Value and depreciation of mineral resources over the very long run: An empirical contrast of different methods

The paper contrasts empirically the results of alternative methods for estimating thevalue and the depreciation of mineral resources. The historical data of Mexico andVenezuela, covering the period 1920s-1980s, is used to contrast the results of severalmethods. These are the present value, the net price method, the user cost method andthe imputed income method. The paper establishes that the net price and the user costare not competing methods as such, but alternative adjustments to different scenariosof closed and open economies. The results prove that the biases of the methods, ascommonly described in the theoretical literature, only hold under the most restrictedscenario of constant rents over time. It is argued that the difference between what isexpected to happen and what actually did happen is for the most part due to a missingvariable, namely technological change. This is an important caveat to therecommendations made based on these models.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

Exact and approximate stepdown methods for multiple hypothesis testing

Consider the problem of testing k hypotheses simultaneously. In this paper,we discuss finite and large sample theory of stepdown methods that providecontrol of the familywise error rate (FWE). In order to improve upon theBonferroni method or Holm's (1979) stepdown method, Westfall and Young(1993) make eective use of resampling to construct stepdown methods thatimplicitly estimate the dependence structure of the test statistics. However,their methods depend on an assumption called subset pivotality. The goalof this paper is to construct general stepdown methods that do not requiresuch an assumption. In order to accomplish this, we take a close look atwhat makes stepdown procedures work, and a key component is a monotonicityrequirement of critical values. By imposing such monotonicity on estimatedcritical values (which is not an assumption on the model but an assumptionon the method), it is demonstrated that the problem of constructing a validmultiple test procedure which controls the FWE can be reduced to the problemof contructing a single test which controls the usual probability of a Type 1error. This reduction allows us to draw upon an enormous resamplingliterature as a general means of test contruction.

How much structure in empirical models?

This chapter highlights the problems that structural methods and SVAR approaches have when estimating DSGE models and examining their ability to capture important features of the data. We show that structural methods are subject to severe identification problems due, in large part, to the nature of DSGE models. The problems can be patched up in a number of ways but solved only if DSGEs are completely reparametrized or respecified. The potential misspecification of the structural relationships give Bayesian methods an hedge over classical ones in structural estimation. SVAR approaches may face invertibility problems but simple diagnostics can help to detect and remedy these problems. A pragmatic empirical approach ought to use the flexibility of SVARs against potential misspecificationof the structural relationships but must firmly tie SVARs to the class of DSGE models which could have have generated the data.

Comparison of different methods for thin section EM analysis of Mycobacterium smegmatis.

Bacteria are generally difficult specimens to prepare for conventional resin section electron microscopy and mycobacteria, with their thick and complex cell envelope layers being especially prone to artefacts. Here we made a systematic comparison of different methods for preparing Mycobacterium smegmatis for thin section electron microscopy analysis. These methods were: (1) conventional preparation by fixatives and epoxy resins at ambient temperature. (2) Tokuyasu cryo-section of chemically fixed bacteria. (3) rapid freezing followed by freeze substitution and embedding in epoxy resin at room temperature or (4) combined with Lowicryl HM20 embedding and ultraviolet (UV) polymerization at low temperature and (5) CEMOVIS, or cryo electron microscopy of vitreous sections. The best preservation of bacteria was obtained with the cryo electron microscopy of vitreous sections method, as expected, especially with respect to the preservation of the cell envelope and lipid bodies. By comparison with cryo electron microscopy of vitreous sections both the conventional and Tokuyasu methods produced different, undesirable artefacts. The two different types of freeze-substitution protocols showed variable preservation of the cell envelope but gave acceptable preservation of the cytoplasm, but not lipid bodies, and bacterial DNA. In conclusion although cryo electron microscopy of vitreous sections must be considered the 'gold standard' among sectioning methods for electron microscopy, because it avoids solvents and stains, the use of optimally prepared freeze substitution also offers some advantages for ultrastructural analysis of bacteria.