Papers by Diego Maldonado
Differential and Integral Equations, Nov 18, 2013
This note introduces bilinear estimates intended as a step towards an L ∞-endpoint Kato-Ponce ine... more This note introduces bilinear estimates intended as a step towards an L ∞-endpoint Kato-Ponce inequality. In particular, a bilinear version of the classical Gagliardo-Nirenberg interpolation inequalities for a product of functions is proved.
Boundedness properties for bilinear paraproducts on several function spaces are presented. The me... more Boundedness properties for bilinear paraproducts on several function spaces are presented. The methods are based on the realization of paraproducts as bilinear Calderón-Zygmund operators and the molecular characterization of function spaces. This provides a unified approach for the study of paraproducts, recovering some know results and establishing several new.
We build upon the techniques introduced by De Philippis and Figalli in [7], regarding W 2,1+ε bou... more We build upon the techniques introduced by De Philippis and Figalli in [7], regarding W 2,1+ε bounds for the Monge-Ampère operator, to improve the recent A∞ estimates for D 2 ϕ to A2 ones. Also, we prove a (1, 2)−Poincaré inequality and weak (q, p)−Poincaré inequalities associated to the Monge-Ampère quasi-metric structure. In turn, these Poincaré inequalities are used to prove Harnack's inequality for non-negative solutions to the linearized Monge-Ampère under minimal geometric assumptions. 1 1+ε 0 ≤ C|S| S w(x) −1 dx , (1.4) for every section S = S ϕ (x 0 , t). Here w denotes either W ϕ or w ϕ. As an application of the underlying real analysis associated to the Monge-Ampère equation, in Section 5 we prove a (1, 2)−Poincaré inequality and weak (q, p)−Poincaré inequalities associated to the Monge-Ampère quasi-metric structure. These inequalities complement the recent results on Sobolev-type inequalities associated to the Monge-Ampère structure introduced by G. Tian and X.-J. Wang in [20] and further carried out in [17]. To the best of our knowledge, Theorem 1.3 below contains the first Poincaré-type inequalities for the Monge-Ampère structure (see Section 2 for the appropriate definitions). Theorem 1.3. Assume that µ ϕ ∈ (DC) ϕ. Then there exists a constant C > 0, depending only on the (DC) ϕ constants for µ ϕ and dimension n, such that given any section S := S ϕ (x 0 , t) and u ∈ C 1 (S) we have
Journal of Mathematical Analysis and Applications, 2021
Abstract Morrey-type inequalities within the Monge-Ampere quasi-metric structure are proved under... more Abstract Morrey-type inequalities within the Monge-Ampere quasi-metric structure are proved under various conditions on the underlying Monge-Ampere measure. A number of examples of convex functions satisfying the required assumptions are described. Applications include interior C 1 - and C 2 -estimates for solutions to Monge-Ampere equations as well as Morrey-type inequalities with respect to monomial weights.
Information and Computation, 2020
In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defin... more In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the active cells remain unchanged, and the new value of an inactive cell depends only on the sum of its active neighbors. We classify all the Cellular Automata in the class of TFCA, grouping them in five different classes: the Trivial rules, Turing Universal rules, Algebraic rules, Topological rules and Fractal Growing rules. At the same time, we study in this family the Stability problem, consisting in deciding whether an inactive cell becomes active, given an initial configuration. We exploit the properties of the automata in each group to show that: • For Algebraic and Topological Rules the Stability problem is in NC.
Journal of Differential Equations, 2019
By means of the Monge-Ampère real-analysis and PDE techniques associated to certain convex functi... more By means of the Monge-Ampère real-analysis and PDE techniques associated to certain convex functions, an approach towards Harnack inequalities is developed that simultaneously extends the one for uniformly elliptic operators from the De Giorgi-Nash-Moser theory and the one for the linearized Monge-Ampère operator from the Caffarelli-Gutiérrez theory. Applications include regularity properties for solutions to divergence-form elliptic equations with power-like singularities and C 2-estimates for solutions to the Monge-Ampère equation.
Association for Women in Mathematics Series, 2016
A study on the preservation of eccentricities of Monge-Ampère sections under an integral Dini-typ... more A study on the preservation of eccentricities of Monge-Ampère sections under an integral Dini-type condition on the Monge-Ampère measure is presented. The approach is based solely on C 2,α-estimates for solutions to the Monge-Ampère equation. The main results are then related to the local quasi-conformal Jacobian problem and to a priori estimates for solutions to the linearized Monge-Ampère equation.
Proceedings of the American Mathematical Society, Dec 1, 2006
We study the engulfing property for convex functions in Carnot groups. As an application we show ... more We study the engulfing property for convex functions in Carnot groups. As an application we show that the horizontal gradient of functions with this property is Hölder continuous.
Lecture Notes in Computer Science, 2015
We show the existence of Turing-universal and intrinsically universal cellular automata exhibitin... more We show the existence of Turing-universal and intrinsically universal cellular automata exhibiting both time symmetry and number conservation; this is achieved by providing a way to simulate reversible CA with time-symmetric CA, which preserves the number-conserving property. We also provide some additional results and observations concerning the simulation relations between reversible, time-symmetric and number-conserving CA in the context of partitioned CA.
Proceedings of the American Mathematical Society, 2015
In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling pr... more In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure.
A42. MONITORING IN THE ICU, 2009
In the present document it is exposed in an abstract way the models of credit portfolioes CreditM... more In the present document it is exposed in an abstract way the models of credit portfolioes CreditMetricsTM, KMV, CreditRisk+, Credit Portfolio View in such a way that they could be calibrated and implemented in financial institutions where the quality and quantity of credit information is scanty, giving place to which they have capable tools for monitoring the risk and the
The American Journal of Gastroenterology, 2002
This study evaluated the prevalence of intestinal metaplasia (IM) in patients with varying length... more This study evaluated the prevalence of intestinal metaplasia (IM) in patients with varying lengths of columnar-lined esophagus (CLE) during long-term endoscopic and histopathologic surveillance. A total of 177 patients were followed for a median surveillance period of 5.1 yr and a median four endoscopies per patient. Fifty-two percent of the patients had IM at first surveillance endoscopy. The prevalence of IM increased with increasing number of endoscopies, and after six endoscopies the IM prevalence had increased from 30% to 64% in patients with a 1–2 cm CLE length, and from 45% to 89% in those with a 3–4 cm length. IM was found in longer CLE segments early in the surveillance period, whereas detection of IM was evenly spread out over the surveillance period in the short segment patients. A second aim of this study was to compare the effectiveness of antireflux surgery with acid suppressant therapy in preventing the development of IM. Studying patients without IM at the first two endoscopies, the investigators found that IM developed significantly less frequently among the 20 surgically treated patients compared with the 49 medically treated patients (PPI therapy in 45 out of 49). The time to development of IM was shorter in the medically treated group (p 0.001, log-rank test) and in a multivariable logistic analysis, prior antireflux surgery was the only significant factor associated with a reduced risk of intestinalization (10.3-fold decreased risk). (Am J Gastroenterol 2002;97:2136–2137. © 2002 by Am. Coll. of Gastroenter-
Geospatial health, 2010
Time-series of coarse-resolution greenness values derived through remote sensing have been used a... more Time-series of coarse-resolution greenness values derived through remote sensing have been used as a surrogate environmental variable to help monitor and predict occurrences of a number of vector-borne and zoonotic diseases, including malaria. Often, relationships between a remotely-sensed index of greenness, e.g. the normalized difference vegetation index (NDVI), and disease occurrence are established using temporal correlation analysis. However, the strength of these correlations can vary depending on type and change of land cover during the period of record as well as inter-annual variations in the climate drivers (precipitation, temperature) that control the NDVI values. In this paper, the correlation between a long (260 months) time-series of monthly disease case rates and NDVI values derived from the Global Inventory Modeling and Mapping Studies (GIMMS) data set were analysed for two departments (administrative units) located in the Atlantic Forest biome of eastern Paraguay. Each of these departments has undergone extensive deforestation during the period of record and our analysis considers the effect on correlation of active versus quiescent periods of case occurrence against a background of changing land cover. Our results show that time-series data, smoothed using the Fourier Transform tool, showed the best correlation. A moving window analysis suggests that four years is the optimum time frame for correlating these values, and the strength of correlation depends on whether it is an active or a quiescent period. Finally, a spatial analysis of our data shows that areas where land cover has changed, particularly from forest to non-forest, are well correlated with malaria case rates.
Pensamiento y Cultura, 2002
... Page 4. Pensamiento y Cultura 144 Número 5 ● 2002 Diego Maldonado ... Las dos casas que enmar... more ... Page 4. Pensamiento y Cultura 144 Número 5 ● 2002 Diego Maldonado ... Las dos casas que enmarcan la entrada a este parque sir-vieron de portería al conjunto y parecen dos casas de Hansel y Gretel por su graciosa forma, que encanta a niños y adultos. ...
Potential Analysis, 2009
We prove a mean value inequality for non-negative solutions to L ϕ u = 0 in any domain ⊂ R n , wh... more We prove a mean value inequality for non-negative solutions to L ϕ u = 0 in any domain ⊂ R n , where L ϕ is the Monge-Ampère operator linearized at a convex function ϕ, under minimal assumptions on the Monge-Ampère measure of ϕ. An application to the Harnack inequality for affine maximal hypersurfaces is included.
Mathematische Zeitschrift, 2007
We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel... more We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition. We prove that this isotropic doubling condition is satisfied by the distance functions of certain fractal sets. Finally, we construct an isotropic doubling measure that is not absolutely continuous with respect to the Lebesgue measure.
Journal of Mathematical Analysis and Applications, 2009
We prove mapping properties of the form T :Ḃ α 1 ,q 1 p 1 × L p 2 →Ḃ α 2 ,q 2 p 3 and T :Ḃ α 1 ,q... more We prove mapping properties of the form T :Ḃ α 1 ,q 1 p 1 × L p 2 →Ḃ α 2 ,q 2 p 3 and T :Ḃ α 1 ,q 1 p 1 ×Ḃ α 2 ,q 2 p 2 → L p 3 , for certain related indices p1, p2, p3, q1, q2, α1, α2 ∈ R, where T is a bilinear Hörmander-Mihlin multiplier or a molecular paraproduct. Applications to bilinear Littlewood-Paley theory are discussed.
This document exposes a EWS that is based on two models, the …rst corresponds to a full econometr... more This document exposes a EWS that is based on two models, the …rst corresponds to a full econometric model such as the Logistics and the second is a …nancial model based on OVT for the KMV model. Both models are based on …nancial indicators CAMEL evaluation methodology for the Cooperative System of Ecuador, so that they become an easy tool for interpretation by the entities that comprise this system as well as the regulator and supervisor, giving rise to easily identify …nancial crisis phenomena. The models exposed are considered inside the MPT where CAMEL is a traditional …nance valuation model and Logit & KMV are new tools like a EWS. Hence, the three models CAMEL, KMV and Logit, are placed to the Ecuadorian cooperative reality in order to establish a rating of each entity that labors in the Cooperative System headed for analyze its current …nancial situation and identify possible vulnerability of the system.
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Papers by Diego Maldonado