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

Counterexamples to some pointwise estimates of the maximal Cauchy transform in terms of the Cauchy transform

Motivated by the work of Mateu, Orobitg, Pérez and Verdera, who proved inequalities of the form $T_*f\lesssim M(Tf)$ or $T_*f\lesssim M^2(Tf)$ for certain singular integral operators $T$, such as the Hilbert or the Beurling transforms, we study the possibility of establishing this type of control for the Cauchy transform along a Lipschitz graph. We show that this is not possible in general, and we give a partial positive result when the graph is substituted by a Jordan curve.

Bernstein's problem on weighted polynomial approximation

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure [lletra "mu" minúscula de l'alfabet grec] on the real line we give a criterion for density of polynomials in Lp[lletra "mu" minúscula de l'alfabet grec entre parèntesis].

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.

Adaptively weighted maximum likelihood estimation of discrete distributions

SummaryDiscrete data arise in various research fields, typically when the observations are count data.I propose a robust and efficient parametric procedure for estimation of discrete distributions. The estimation is done in two phases. First, a very robust, but possibly inefficient, estimate of the model parameters is computed and used to indentify outliers. Then the outliers are either removed from the sample or given low weights, and a weighted maximum likelihood estimate (WML) is computed.The weights are determined via an adaptive process such that if the data follow the model, then asymptotically no observation is downweighted.I prove that the final estimator inherits the breakdown point of the initial one, and that its influence function at the model is the same as the influence function of the maximum likelihood estimator, which strongly suggests that it is asymptotically fully efficient.The initial estimator is a minimum disparity estimator (MDE). MDEs can be shown to have full asymptotic efficiency, and some MDEs have very high breakdown points and very low bias under contamination. Several initial estimators are considered, and the performances of the WMLs based on each of them are studied.It results that in a great variety of situations the WML substantially improves the initial estimator, both in terms of finite sample mean square error and in terms of bias under contamination. Besides, the performances of the WML are rather stable under a change of the MDE even if the MDEs have very different behaviors.Two examples of application of the WML to real data are considered. In both of them, the necessity for a robust estimator is clear: the maximum likelihood estimator is badly corrupted by the presence of a few outliers.This procedure is particularly natural in the discrete distribution setting, but could be extended to the continuous case, for which a possible procedure is sketched.RésuméLes données discrètes sont présentes dans différents domaines de recherche, en particulier lorsque les observations sont des comptages.Je propose une méthode paramétrique robuste et efficace pour l'estimation de distributions discrètes. L'estimation est faite en deux phases. Tout d'abord, un estimateur très robuste des paramètres du modèle est calculé, et utilisé pour la détection des données aberrantes (outliers). Cet estimateur n'est pas nécessairement efficace. Ensuite, soit les outliers sont retirés de l'échantillon, soit des faibles poids leur sont attribués, et un estimateur du maximum de vraisemblance pondéré (WML) est calculé.Les poids sont déterminés via un processus adaptif, tel qu'asymptotiquement, si les données suivent le modèle, aucune observation n'est dépondérée.Je prouve que le point de rupture de l'estimateur final est au moins aussi élevé que celui de l'estimateur initial, et que sa fonction d'influence au modèle est la même que celle du maximum de vraisemblance, ce qui suggère que cet estimateur est pleinement efficace asymptotiquement.L'estimateur initial est un estimateur de disparité minimale (MDE). Les MDE sont asymptotiquement pleinement efficaces, et certains d'entre eux ont un point de rupture très élevé et un très faible biais sous contamination. J'étudie les performances du WML basé sur différents MDEs.Le résultat est que dans une grande variété de situations le WML améliore largement les performances de l'estimateur initial, autant en terme du carré moyen de l'erreur que du biais sous contamination. De plus, les performances du WML restent assez stables lorsqu'on change l'estimateur initial, même si les différents MDEs ont des comportements très différents.Je considère deux exemples d'application du WML à des données réelles, où la nécessité d'un estimateur robuste est manifeste : l'estimateur du maximum de vraisemblance est fortement corrompu par la présence de quelques outliers.La méthode proposée est particulièrement naturelle dans le cadre des distributions discrètes, mais pourrait être étendue au cas continu.

Ab initio absorption spectrum of NiO combining molecular dynamics with the embedded cluster approach in a discrete reaction field

We developed a procedure that combines three complementary computational methodologies to improve the theoretical description of the electronic structure of nickel oxide. The starting point is a Car-Parrinello molecular dynamics simulation to incorporate vibrorotational degrees of freedom into the material model. By means ofcomplete active space self-consistent field second-order perturbation theory (CASPT2) calculations on embedded clusters extracted from the resulting trajectory, we describe localized spectroscopic phenomena on NiO with an efficient treatment of electron correlation. The inclusion of thermal motion into the theoretical description allowsus to study electronic transitions that, otherwise, would be dipole forbidden in the ideal structure and results in a natural reproduction of the band broadening. Moreover, we improved the embedded cluster model by incorporating self-consistently at the complete active space self-consistent field (CASSCF) level a discrete (or direct) reaction field (DRF) in the cluster surroundings. The DRF approach offers an efficient treatment ofelectric response effects of the crystalline embedding to the electronic transitions localized in the cluster. We offer accurate theoretical estimates of the absorption spectrum and the density of states around the Fermi level of NiO, and a comprehensive explanation of the source of the broadening and the relaxation of the charge transferstates due to the adaptation of the environment

On codes, matroids, and secure multiparty computation from linear secret-sharing schemes

Error-correcting codes and matroids have been widely used in the study of ordinary secret sharing schemes. In this paper, the connections between codes, matroids, and a special class of secret sharing schemes, namely, multiplicative linear secret sharing schemes (LSSSs), are studied. Such schemes are known to enable multiparty computation protocols secure against general (nonthreshold) adversaries.Two open problems related to the complexity of multiplicative LSSSs are considered in this paper. The first one deals with strongly multiplicative LSSSs. As opposed to the case of multiplicative LSSSs, it is not known whether there is an efficient method to transform an LSSS into a strongly multiplicative LSSS for the same access structure with a polynomial increase of the complexity. A property of strongly multiplicative LSSSs that could be useful in solving this problem is proved. Namely, using a suitable generalization of the well-known Berlekamp–Welch decoder, it is shown that all strongly multiplicative LSSSs enable efficient reconstruction of a shared secret in the presence of malicious faults. The second one is to characterize the access structures of ideal multiplicative LSSSs. Specifically, the considered open problem is to determine whether all self-dual vector space access structures are in this situation. By the aforementioned connection, this in fact constitutes an open problem about matroid theory, since it can be restated in terms of representability of identically self-dual matroids by self-dual codes. A new concept is introduced, the flat-partition, that provides a useful classification of identically self-dual matroids. Uniform identically self-dual matroids, which are known to be representable by self-dual codes, form one of the classes. It is proved that this property also holds for the family of matroids that, in a natural way, is the next class in the above classification: the identically self-dual bipartite matroids.

Transmission Fourier transform infrared microspectroscopy allows simultaneous assessment of cutin and cell-wall polysaccharides of Arabidopsis petals.

A procedure for the simultaneous analysis of cell-wall polysaccharides, amides and aliphatic polyesters by transmission Fourier transform infrared microspectroscopy (FTIR) has been established for Arabidopsis petals. The combination of FTIR imaging with spectra derivatization revealed that petals, in contrast to other organs, have a characteristic chemical zoning with high amount of aliphatic compounds and esters in the lamina and of polysaccharides in the stalk of the petal. The hinge region of petals was particular rich in amides as well as in vibrations potentially associated with hemicellulose. In addition, a number of other distribution patterns have been identified. Analyses of mutants in cutin deposition confirmed that vibrations of aliphatic compounds and esters present in the lamina were largely associated with the cuticular polyester. Calculation of spectrotypes, including the standard deviation of intensities, allowed detailed comparison of the spectral features of various mutants. The spectrotypes not only revealed differences in the amount of polyesters in cutin mutants, but also changes in other compound classes. For example, in addition to the expected strong deficiencies in polyester content, the long-chain acyl CoA synthase 2 mutant showed increased intensities of vibrations in a wavelength range that is typical for polysaccharides. Identical spectral features were observed in quasimodo2, a cell-wall mutant of Arabidopsis with a defect in pectin formation that exhibits increased cellulose synthase activity. FTIR thus proved to be a convenient method for the identification and characterization of mutants affected in the deposition of cutin in petals.

A polynomial algorithm for special case of the one-machine scheduling problem with time-lags

The standard one-machine scheduling problem consists in schedulinga set of jobs in one machine which can handle only one job at atime, minimizing the maximum lateness. Each job is available forprocessing at its release date, requires a known processing timeand after finishing the processing, it is delivery after a certaintime. There also can exists precedence constraints between pairsof jobs, requiring that the first jobs must be completed beforethe second job can start. An extension of this problem consistsin assigning a time interval between the processing of the jobsassociated with the precedence constrains, known by finish-starttime-lags. In presence of this constraints, the problem is NP-hardeven if preemption is allowed. In this work, we consider a specialcase of the one-machine preemption scheduling problem with time-lags, where the time-lags have a chain form, and propose apolynomial algorithm to solve it. The algorithm consist in apolynomial number of calls of the preemption version of the LongestTail Heuristic. One of the applicability of the method is to obtainlower bounds for NP-hard one-machine and job-shop schedulingproblems. We present some computational results of thisapplication, followed by some conclusions.

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.