Finding Multiple Solutions in Nonlinear Integer Programming with Algebraic Test-Sets

We explain how to compute all the solutions of a nonlinear integer problem using the algebraic test-sets associated to a suitable linear subproblem. These test-sets are obtained using Gröbner bases. The main advantage of this method, compared to other available alternatives, is its exactness within a quite good efficiency.Ministerio de Economía y Competitividad MTM2016-75024-PMinisterio de Economía y Competitividad MTM2016-74983-C2- 1-RJunta de Andalucía P12-FQM-269

On the computation of Bernstein–Sato ideals

AbstractIn this paper we compare the approach of Briançon and Maisonobe for computing Bernstein–Sato ideals—based on computations in a Poincaré–Birkhoff–Witt algebra—with the readily available method of Oaku and Takayama. We show that it can deal with interesting examples that have proved intractable so far

Localization at hyperplane arrangements: Combinatorics and D-modules

AbstractWe describe an algorithm deciding if the annihilating ideal of the meromorphic function 1f, where f=0 defines an arrangement of hyperplanes, is generated by linear differential operators of order 1. The algorithm is based on the comparison of two characteristic cycles and uses a combinatorial description of the characteristic cycle of the D-module of meromorphic functions with respect to f, due to Àlvarez Montaner, García López and Zarzuela

Comparison of theoretical complexities of two methods for computing annihilating ideals of polynomials

AbstractLet f1,…,fp be polynomials in C[x1,…,xn] and let D=Dn be the n-th Weyl algebra. We provide upper bounds for the complexity of computing the annihilating ideal of fs=f1s1⋯fpsp in D[s]=D[s1,…,sp]. These bounds provide an initial explanation of the differences between the running times of the two methods known to obtain the so-called Bernstein–Sato ideals

An algebraic approach to integer portfolio problems

Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model. We propose an algebraic approach to maximize the expected return under a given admissible level of risk measured by the covariance matrix. To reach an optimal portfolio it is an essential ingredient the computation of different test sets (via Gröbner basis) of linear subproblems that are used in a dual search strategy.Finance Portfolio Non-linear integer programming Grobner bases

Adherencia a las terapias biologicas en pacientes con artropatias inflamatorias cronicas.

INTRODUCTION: The aims of the study were to quantify adherence, determine the factors that can predict adherence and identify the consequences of poorer adherence in patients with chronic inflammatory arthropathies treated with biological therapies in daily clinical practice. METHOD: A descriptive, observational and retrospective study was carried out. Patients with rheumatoid arthritis, ankylosing spondylitis and psoriatic arthritis who started a biologic therapy between 1 January 2009 and 31 December 2016 were included. Variables related to socioeconomic status, the disease, the biological therapy and hospital resources were included. Adherence was calculated by using the medication possession ratio. RESULTS: Three hundred and sixty-two patients and 423 lines of biological therapy were included. Mean age +/- standard deviation was 50.3 +/- 13.9 years, and 228 (53.9%) were women. The percentage of adherent patients was 187 out of 216 (87%) in rheumatoid arthritis, 91 out of 107 (85%) in ankylosing spondylitis and 84 out of 100 (84%) in psoriatic arthritis. Greater adherence was associated with more frequent visits to the pharmacy service (odds ratio 1.2, 95% confidence interval: 1.1-1.3 [p = 0.001]) and poorer adherence with a failure to attend scheduled appointments at the rheumatology clinic (odds ratio 0.2, 95% confidence interval: 0.1-0.9 [p = 0.030]). There were no differences between adherent and non-adherent patients in terms of the number of hospital resources used. CONCLUSIONS: There are no differences in adherence to biological therapies among patients with chronic inflammatory arthropathies. Adherence correlates with attendance at outpatient appointments, but this does not imply an increase in the use of hospital resources