Exact solutions and superposition rules for Hamiltonian systems generalizing stochastic SIS epidemic models with variable infection rates

Using the theory of Lie-Hamilton systems, formal generalized stochastic Hamiltonian systems that enlarge a recently proposed stochastic SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the particular interpretation of the time-dependent coefficients, these systems generally admit an exact solution, up to the case of the maximal extension within the classification of Lie-Hamilton systems, for which a superposition rule is constructed. The method provides the algebraic frame to which any SIS epidemic model that preserves the above mentioned properties is subjected. In particular, we obtain exact solutions for generalized SIS Hamitonian models based on the book and oscillator algebras, denoted respectively by $\mathfrak{b}_2$ and $\mathfrak{h}_4$. The last generalization corresponds to a SIS system possessing the so-called two-photon algebra symmetry $\mathfrak{h}_6$, according to the embedding chain $\mathfrak{b}_2\subset \mathfrak{h}_4\subset \mathfrak{h}_6$, for which an exact solution cannot generally be found, but a nonlinear superposition rule is explicitly given.Comment: 24 page

Computer-Aided Analysis of Solvable Rigid Lie Algebras with a Given Eigenvalue Spectrum

With the help of symbolic computer packages, the study of the cohomological rigidity of real solvable Lie algebras of rank one with a maximal torus of derivations t and the eigenvalue spectrum spec(t)=(1,k,k+1,⋯,n+k−2) initiated in a previous work is continued for arbitrary values k≥2, obtaining new hierarchies of solvable rigid Lie algebras

Some features of rank one real solvable cohomologically rigid lie algebras with a nilradical contracting onto the model filiform lie algebra Qn

The generic structure and some peculiarities of real rank one solvable Lie algebras possessing a maximal torus of derivations with the eigenvalue spectrum spec(t) = (1, k, k +1, ..., n + k-3, n +2k -3) for k [mayor o igual] 2 are analyzed, with special emphasis on the resulting Lie algebras for which the second Chevalley cohomology space vanishes. From the detailed inspection of the values k [menor o igual] 5, some series of cohomologically rigid algebras for arbitrary values of k are determined

Drug Prescribing in Patients with Impaired Renal Function: are Interventions Still Needed to Improve Patient Safety?

An intervention study of 3 months was performed at a third-level university hospital to investigate if drug adjustment interventions towards chronic kidney disease (CKD) patients are still needed. Patients with a glomerular filtration rate < 60 mL/min/1.73 m2 and a prescribed medication that needed an adjustment for CKD were selected. Demographic and clinical data, prescription information, non-adjusted medication, interventions, and acceptance of recommendation were registered. A total of 706 patients were included (77.5 % stage 3 of CKD, 13.2 % stage 4 and 7.2 % stage 5), 281 (8.5 %) of 3,315 prescriptions were considered non-adjusted (52.3 % stage 3, 28.8 % stage 4 and 18.9 % stage 5) and were intervened: 220 (78.3 %) dose reduction, 32 (11.4 %) contraindicated, 21 (7.5 %) follow up, and 8 (2.8 %) dose increment. Fifty per cent of the interventions were accepted. Antibiotics became in 45 % of the interventions. Intervention and education about the important of drug adjustment in CKD is still needed to improve safety on these patients.Colegio de Farmacéuticos de la Provincia de Buenos Aire

Modernity, representation, and personality in Antonio Flores's Ayer, hoy, y mañana (1863-64)

This article explores a highly important but little known text of 19c Spain, Ayer, Hoy, y Mañana by Antonio Flores. The text explores the contradictory and tense relationship between modernity and personality. It suggests that the primacy of representation within modernity undermines and contradicts modernity's concern with individual personality. The article analyses Flores' vast work within the context of the political thought of the time, showing how Flores engages with but seeks to undermine leftist thought

Comparative efficacy of two primary care interventions to assist withdrawal from long term benzodiazepine use: A protocol for a clustered, randomized clinical trial

<p>Abstract</p> <p>Background</p> <p>Although benzodiazepines are effective, long-term use is not recommended because of potential adverse effects; the risks of tolerance and dependence; and an increased risk of hip fractures, motor vehicle accidents, and memory impairment. The estimated prevalence of long-term benzodiazepine use in the general population is about 2,2 to 2,6%, is higher in women and increases steadily with age. Interventions performed by General Practitioners may help patients to discontinue long-term benzodiazepine use. We have designed a trial to evaluate the effectiveness and safety of two brief general practitioner-provided interventions, based on gradual dose reduction, and will compare the effectiveness of these interventions with that of routine clinical practice.</p> <p>Methods/Design</p> <p>In a three-arm cluster randomized controlled trial, general practitioners will be randomly allocated to: a) a group in which the first patient visit will feature a structured interview, followed by visits every 2-3 weeks to the end of dose reduction; b) a group in which the first patient visit will feature a structured interview plus delivery of written instructions to self-reduce benzodiazepine dose, or c) routine care. Using a computerized pharmaceutical prescription database, 495 patients, aged 18-80 years, taking benzodiazepine for at least 6 months, will be recruited in primary care health districts of three regions of Spain (the Balearic Islands, Catalonia, and Valencia). The primary outcome will be benzodiazepine use at 12 months. The secondary outcomes will include measurements of anxiety and depression symptoms, benzodiazepine dependence, quality of sleep, and alcohol consumption.</p> <p>Discussion</p> <p>Although some interventions have been shown to be effective in reducing benzodiazepine consumption by long-term users, the clinical relevance of such interventions is limited by their complexity. This randomized trial will compare the effectiveness and safety of two complex stepped care interventions with that of routine care in a study with sufficient statistical power to detect clinically relevant differences.</p> <p>Trial Registration</p> <p>Current Controlled Trials: <a href="http://www.controlled-trials.com/ISRCTN13024375">ISRCTN13024375</a></p

Construction of Rank-One Solvable Rigid Lie Algebras with Nilradicals of a Decreasing Nilpotence Index

It is shown that for any integers k≥2, q≥2k and N≥k+q+2, there exists a real solvable Lie algebra of the first rank with a maximal torus of derivations t possessing the eigenvalue spectrum spec(t)=1,2,⋯,k,q,q+1⋯,N, a nilradical of the nilpotence index N−k and a characteristic sequence (N−k,1k)

Construction of rank-one solvable rigid Lie algebras with nilradicals of a decreasing nilpotence index

It is shown that for any integers ≥2 , ≥2 and ≥++2 , there exists a real solvable Lie algebra of the first rank with a maximal torus of derivations possessing the eigenvalue spectrum spec()=(1,2,⋯,,,+1⋯,), a nilradical of the nilpotence index − and a characteristic sequence (−,1). .Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu