Avances recientes en algebras conmutativas, teoría de las clausuras justas (tight closure)

RESUMEN     En [5] Hochster y Huneke introdujeron la noción de clausura justa para anillos Noetherianos de característica prima, y para álgebras finitamante generadas sobre un campo de característica cero. La teoría generada a raíz de esta noción ha producido nuevas pruebas de algunos teoremas clásicos del álgebra conmutativa y de la teoría de anillos de invariantes, así como de algunas de las conjeturas homológicas. El objetivo de este artículo es mostrar a grandes rasgos los aspectos esenciales de esta teoría y sus aplicaciones más importantes. Se mostrarán algunos avances recientes y se discutirán algunos de los problemas centrales de la teoría que aún permanecen abiertos

Avances recientes en algebras conmutativas, teoría de las clausuras justas (tight closure)

RESUMEN     En [5] Hochster y Huneke introdujeron la noción de clausura justa para anillos Noetherianos de característica prima, y para álgebras finitamante generadas sobre un campo de característica cero. La teoría generada a raíz de esta noción ha producido nuevas pruebas de algunos teoremas clásicos del álgebra conmutativa y de la teoría de anillos de invariantes, así como de algunas de las conjeturas homológicas. El objetivo de este artículo es mostrar a grandes rasgos los aspectos esenciales de esta teoría y sus aplicaciones más importantes. Se mostrarán algunos avances recientes y se discutirán algunos de los problemas centrales de la teoría que aún permanecen abiertos

El problema de π-geografía y el problema de Hurwitz

Let d > 2 be an integer and let π be a partition of d. This article aims to determine for which pairs of integers (a, b) there exists a branched cover F : Σ → D  2 = {z ∈ C : |z| 6 1} with χ(Σ) = −b and having a critical values, such that the monodromy obtained when traversing the boundary of D 2 once and positively belongs to the conjugacy class in the symmetric group Sd determined by π. Four variants of this question are studied: i) without requiring the connectedness of the domain, ii) requiring the connectedness of the domain, iii) without requiring the connectedness of the domain but requiring the semistability of the map, iv) requiring the connectedness of the domain and the semistability of the map. Complete solutions are obtained of the first two variants, and partial solutions are obtained of the remaining variants. The article also explains how these questions arise when analogous questions for maps whose domain is four dimensional are studied.MSC: 11M35Sea d ≥ 2 un entero y  una partición de d. En este artículo se estudia el problema de para qué pares de enteros (a, b) existe un recubrimiento ramificado F : ∑ → D2 = {z ∈ C : |z| 6 ≤ 1} que tenga a valores críticos, x(∑) = −b, y tal que la monodromía que se obtiene cuando se recorre la frontera de D2 en sentido positivo pertenece a la clase de conjugancia en el grupo simétrico Sd determinada por la partición π. Se estudian cuatro variantes de este problema: i) sin requerir conexidad del dominio, ii) requiriendo conexidad del dominio, iii) sin requerir conexidad del dominio, pero exigiendo que el recubrimiento sea semiestable, iv) requiriendo que el dominio sea conexo y que el recubrimiento sea semiestable. Se obtienen soluciones completas de las primeras dos variantes, y se obtiene una solución parcial de las variantes restantes. Además se explica cómo el interés por estos problemas surge del estudio de una pregunta análoga para funciones cuyo dominio es 4-dimensional.MSC: 11M3

An integer factorization algorithm which uses diffusion as a computational engine

In this article we develop an algorithm which computes a divisor of an integer $N$, which is assumed to be neither prime nor the power of a prime. The algorithm uses discrete time heat diffusion on a finite graph. If $N$ has $m$ distinct prime factors, then the probability that our algorithm runs successfully is at least $p(m) = 1-(m+1)/2^{m}$. We compute the computational complexity of the algorithm in terms of classical, or digital, steps and in terms of diffusion steps, which is a concept that we define here. As we will discuss below, we assert that a diffusion step can and should be considered as being comparable to a quantum step for an algorithm which runs on a quantum computer. With this, we prove that our factorization algorithm uses at most $O((\log N)^{2})$ deterministic steps and at most $O((\log N)^{2})$ diffusion steps with an implied constant which is effective. By comparison, Shor's algorithm is known to use at most $O((\log N)^{2}\log (\log N) \log (\log \log N))$ quantum steps on a quantum computer. As an example of our algorithm, we simulate the diffusion computer algorithm on a desktop computer and obtain factorizations of $N=33$ and $N=1363$.Comment: 30 pages, 2 figure

El problema de π-geografía y el problema de Hurwitz

Let d ≥ 2 be an integer and a partition of d. In this article we study the problem of for which pairs of integers (a, b) there is a branched coating F: ∑ → D2 = {z ∈ C: | z | 6 ≤ 1} that has critical values, x (∑) = −b, and such that the monodromy that is obtained when crossing the border of D2 in a positive sense belongs to the conjugation class in the symmetric group Sd determined by the π partition. Four variants of this problem are studied: i) without requiring domain connection, ii) requiring domain connection, iii) without requiring domain connection, but requiring that the coating be semi-stable, iv) requiring that the domain be related and that the coating is semi-stable. Complete solutions of the first two variants are obtained, and a partial solution of the remaining variants is obtained. It also explains how the interest in these problems arises from the study of an analogous question for functions whose domain is 4-dimensional.Sea d ≥ 2 un entero y una partición de d. En este artículo se estudia el problema de para qué pares de enteros (a, b) existe un recubrimiento ramificado F : ∑ → D2 = {z ∈ C : |z| 6 ≤ 1} que tenga a valores críticos, x(∑) = −b, y tal que la monodromía que se obtiene cuando se recorre la frontera de D2 en sentido positivo pertenece a la clase de conjugancia en el grupo simétrico Sd determinada por la partición π. Se estudian cuatro variantes de este problema: i) sin requerir conexidad del dominio, ii) requiriendo conexidad del dominio, iii) sin requerir conexidad del dominio, pero exigiendo que el recubrimiento sea semiestable, iv) requiriendo que el dominio sea conexo y que el recubrimiento sea semiestable. Se obtienen soluciones completas de las primeras dos variantes, y se obtiene una solución parcial de las variantes restantes. Además se explica cómo el interés por estos problemas surge del estudio de una pregunta análoga para funciones cuyo dominio es 4-dimensional

Technical and clinical evaluation of a closed loop TIVA system with SEDLineTM spectral density monitoring: Multicentric prospective cohort study

Introduction: Closed loop total intravenous anesthesia is a technique in which the patient’s hemodynamic and anesthetic depth variables are monitored, and based on this information, a computer controls the infusion rate of drugs to keep them within pre-established clinical parameters. Objective: To describe the technical and clinical performance of a closed loop system for total intravenous anesthesia with propofol and remifentanil, using the SEDLineTM monitor Design: Multicentric prospective cohort study Setting: Surgery room Patients: ASA I-II undergoing elective surgery Measurements: The authors designed a closed loop system that implements a control algorithm based on anesthetic depth monitoring and the Patient State Index (PSITM) of the SEDLine monitor for propofol, and on hemodynamic variables for remifentanil. The measurement of clinical performance was made based on the percentage of PSITM maintenance time in the range 20–50. Precision analysis was evaluated by measuring median performance error (MDPE) can be defined as the median difference between actual and desired values, which refers to the degree of precision in which the controller is able to maintain the control variable within the objective set by the anesthesiologist; it represents the direction (over-prediction or underprediction) of performance error (PE) rather than size of errors, which is represented by MDAPE, median absolute percentage error, Wobble index, which is used for measuring the intrasubject variability in performance error. Results: Data were obtained from 93 patients in three healthcare centers. The percentage of PSITM maintenance time in the 20–50 range was 92% (80.7–97.0). MDPE was 10.7 (− 11.0–18.0), MDAPE 21.0 (14.2– 26.8) and wobble 10.7 (7.0–16.9). No adverse surgical or anesthetic events were found

Synthesis, leishmanicidal, trypanocidal and cytotoxic activities of quinoline-chalcone and quinoline-chromone hybrids

We report herein the synthesis and biological activities (cytotoxicity, leishmanicidal and trypanocidal) of six quinoline-chalcone and five quinoline-chromone hybrids. The synthesized compounds were evaluated against amastigotes forms of Leishmania (V) panamensis, which is the most prevalent Leishmania species in Colombia and Trypanosoma cruzi, which is the major pathogenic species to humans. Cytotoxicity was evaluated against human U-937 macrophages. Compounds 8–12, 20, 23 and 24 showed activity against Leishmania (V) panamensis, while compounds 9, 10, 12, 20 and 23 had activity against Trypanosoma cruzi with EC50 values lower than 18 mg mL−1. 20 was the most active compound for both Leishmania (V) panamensis and Trypanosoma cruzi with EC50 of 6.11 ± 0.26 μg mL−1 (16.91 μM) and 4.09 ± 0.24 (11.32 μM), respectively. All hybrids compounds showed better activity than the anti-leishmanial drug meglumine antimoniate. Compounds 20 and 23 showed higher activity than benznidazole, the current anti-trypanosomal drug. Although these compounds showed toxicity for mammalian U-937 cells,they still have the potential to be considered as candidates to antileishmanial or trypanocydal drug development

Especies de flebotomíneos (Diptera: Psychodidae) recolectados en reservas naturales de las regiones del Darién y del Pacífico en Colombia

Introduction: The departments of Chocó and Antioquia in Colombia show climatic and vegetation conditions favoring the establishment of vector species of the genus Lutzomyia and the transmission of Leishmania spp. to human populations entering conserved forest environments.Objective: To report the species of Phlebotomine sandflies present in three natural reserves in the Darien and Pacific regions of Colombia.Materials and methods: Sand flies were collected specifically in the natural reserves El Aguacate (Acandí, Chocó), Nabugá (Bahía Solano, Chocó) and Tulenapa (Carepa, Antioquia). Sand flies were collected with CDC light traps, active search in resting places and Shannon traps. The taxonomic determination of species was based on taxonomic keys. For some species of taxonomic interest, we evaluated the partial sequences of the 5’ region of COI gene.Results: A total of 611 adult sand flies were collected: 531 in Acandí, 45 in Carepa and 35 in Bahía Solano. Seventeen species of the genus Lutzomyia, three of the genus Brumptomyia and one of the genus Warileya were identified. The genetic distances (K2P) and grouping supported (>99%) in the neighbor joining dendrogram were consistent for most established molecular operational taxonomic units (MOTU) of the Aragaoi group and clearly confirmed the identity of Lu. coutinhoi.Conclusion: Species that have importance in the transmission of leishmaniasis in Acandí, Bahía Solano and Carepa were identified. The presence of Lu. coutinhoi was confirmed and consolidated in Colombia.Introducción. Los departamentos de Chocó y Antioquia en Colombia presentan condiciones climáticas y de vegetación que favorecen el establecimiento de especies de vectores del género Lutzomyia y la transmisión de Leishmania spp. a poblaciones humanas que ingresan a ambientes selváticos conservados.Objetivo. Reportar las especies de flebotomíneos presentes en tres reservas naturales de las regiones del Darién y del Pacífico en Colombia.Materiales y métodos. Los flebotomíneos se recolectaron en las reservas naturales El Aguacate (Acandí, Chocó), Nabugá (Bahía Solano, Chocó) y Tulenapa (Carepa, Antioquia). La recolección se hizo con trampas de luz CDC, mediante búsqueda activa en sitios de reposo y con trampas Shannon. La determinación taxonómica de especies se basó en las claves taxonómicas. En algunas especies de interés taxonómico, se evaluó el uso de secuencias parciales de la región 5’ del gen COI. Resultados. Se recolectaron 611 flebotomíneos adultos: 531 en Acandí, 45 en Carepa y 35 en Bahía Solano. Se identificaron 17 especies del género Lutzomyia, tres del género Brumptomyia y una del género Warileya. Las distancias genéticas (K2P) y los soportes de agrupación (>99 %) en el dendrograma de neighbor joining correspondieron a la mayoría de unidades taxonómicas operacionales moleculares (Molecular Operational Taxonomic Units, MOTU) establecidas para el grupo Aragaoi y confirmaron claramente la identidad de Lu. coutinhoi.Conclusión. Se identificaron especies que tienen importancia en la transmisión de la leishmaniasis en Acandí, Bahía Solano y Carepa. Se confirmó la presencia de Lu. coutinhoi en Colombia