Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem ��� to decide whether a word is an element of some basis of the free group ��� and the free factor problem can also be solved in polynomial time.

Rational design of an organometallic glutathione transferase inhibitor.

Double trouble: A hybrid organic-inorganic (organometallic) inhibitor was designed to target glutathione transferases. The metal center is used to direct protein binding, while the organic moiety acts as the active-site inhibitor (see picture). The mechanism of inhibition was studied using a range of biophysical and biochemical methods.

Rational first integrals in the Darboux theory of integrability in Cn

"Vegeu el resum a l'inici del document del fitxer adjunt."

Functional sphere profiling reveals the complexity of neuroblastoma tumor-initiating cell model.

Neuroblastoma (NB) is a neural crest-derived childhood tumor characterized by a remarkable phenotypic diversity, ranging from spontaneous regression to fatal metastatic disease. Although the cancer stem cell (CSC) model provides a trail to characterize the cells responsible for tumor onset, the NB tumor-initiating cell (TIC) has not been identified. In this study, the relevance of the CSC model in NB was investigated by taking advantage of typical functional stem cell characteristics. A predictive association was established between self-renewal, as assessed by serial sphere formation, and clinical aggressiveness in primary tumors. Moreover, cell subsets gradually selected during serial sphere culture harbored increased in vivo tumorigenicity, only highlighted in an orthotopic microenvironment. A microarray time course analysis of serial spheres passages from metastatic cells allowed us to specifically "profile" the NB stem cell-like phenotype and to identify CD133, ABC transporter, and WNT and NOTCH genes as spheres markers. On the basis of combined sphere markers expression, at least two distinct tumorigenic cell subpopulations were identified, also shown to preexist in primary NB. However, sphere markers-mediated cell sorting of parental tumor failed to recapitulate the TIC phenotype in the orthotopic model, highlighting the complexity of the CSC model. Our data support the NB stem-like cells as a dynamic and heterogeneous cell population strongly dependent on microenvironmental signals and add novel candidate genes as potential therapeutic targets in the control of high-risk NB.

Electronic compliance monitoring in resistant hypertension: the basis for rational therapeutic decisions.

OBJECTIVE: Incomplete compliance is one of several possible causes of uncontrolled hypertension. Yet, non-compliance remains largely unrecognized and is falsely interpreted as treatment resistance, because it is difficult to confirm or exclude objectively. The goal of this study was to evaluate the potential benefits of electronic monitoring of drug compliance in the management of patients with resistant hypertension. METHODS: Forty-one hypertensive patients resistant to a three-drug regimen (average blood pressure 156/ 106 +/- 23/11 mmHg, mean +/- SD) were studied prospectively. They were informed that for the next 2 months, their presently prescribed drugs would be provided in electronic monitors, without any change in treatment, so as to provide the treating physician with a measure of their compliance. Thereafter, patients were offered the possibility of prolonging the monitoring of compliance for another 2 month period, during which treatment was adapted if necessary. RESULTS: Monitoring of compliance alone was associated with a significant improvement of blood pressure at 2 months (145/97 +/- 20/15 mmHg, P < 0.01). During monitoring, blood pressure was normalized (systolic < 140 mmHg or diastolic < 90 mmHg) in one-third of the patients and insufficient compliance was unmasked in another 20%. When analysed according to tertiles of compliance, patients with the lowest compliance exhibited significantly higher achieved diastolic blood pressures (P = 0.04). In 30 patients, compliance was monitored up to 4 months and drug therapy was adapted whenever necessary. In these patients, a further significant decrease in blood pressure was obtained (from 150/100 +/- 18/15 to 143/94 +/- 22/11 mmHg, P = 0.04/0.02). CONCLUSIONS: These results suggest that objective monitoring of compliance using electronic devices may be a useful step in the management of patients with refractory hypertension, as it enables physicians to take rational decisions based on reliable and objective data of drug compliance and hence to improve blood pressure control.

Systematic identification of genomic markers of drug sensitivity in cancer cells.

Clinical responses to anticancer therapies are often restricted to a subset of patients. In some cases, mutated cancer genes are potent biomarkers for responses to targeted agents. Here, to uncover new biomarkers of sensitivity and resistance to cancer therapeutics, we screened a panel of several hundred cancer cell lines--which represent much of the tissue-type and genetic diversity of human cancers--with 130 drugs under clinical and preclinical investigation. In aggregate, we found that mutated cancer genes were associated with cellular response to most currently available cancer drugs. Classic oncogene addiction paradigms were modified by additional tissue-specific or expression biomarkers, and some frequently mutated genes were associated with sensitivity to a broad range of therapeutic agents. Unexpected relationships were revealed, including the marked sensitivity of Ewing's sarcoma cells harbouring the EWS (also known as EWSR1)-FLI1 gene translocation to poly(ADP-ribose) polymerase (PARP) inhibitors. By linking drug activity to the functional complexity of cancer genomes, systematic pharmacogenomic profiling in cancer cell lines provides a powerful biomarker discovery platform to guide rational cancer therapeutic strategies.

A Model of Near-Rational Exuberance

We study how the use of judgement or ���add-factors��� in forecasting may disturb the set of equilibrium outcomes when agents learn using recursive methods. We isolate conditions under which new phenomena, which we call exuberance equilibria, can exist in a standard self-referential environment. Local indeterminacy is not a requirement for existence. We construct a simple asset pricing example and find that exuberance equilibria, when they exist, can be extremely volatile relative to fundamental equilibria.

Does Ricardian Equivalence Hold When Expectations are not Rational?

This paper considers the Ricardian Equivalence proposition when expectations are not rational and are instead formed using adaptive learning rules. We show that Ricardian Equivalence continues to hold provided suitable additional conditions on learning dynamics are satisfied. However, new cases of failure can also emerge under learning. In particular, for Ricardian Equivalence to obtain, agents��� expectations must not depend on government���s financial variables under deficit financing.

Rational Expectations Dynamics: A Methodological Critique

This paper analyses RE macromodels from the methodological perspective. It proposes a particular property, robustness, which should be considered a necessary feature of scienti cally valid models in economics, but which is absent from many RE macromodels. To restore this property many macroeconomists resort to detailed and implausible assumptions, which take their models a long way from simple Rational Expectations. The paper draws attention to the problems inherent in the technique of local linearisation and concludes by proposing the use of nonlinear models, analysed globally.

Measuring Tax Complexity

This paper critically examines a number of issues relating to the measurement of tax complexity. It starts with an analysis of the concept of tax complexity, distinguishing tax design complexity and operational complexity. It considers the consequences/costs of complexity, and then examines the rationale for measuring complexity. Finally it applies the analysis to an examination of an index of complexity developed by the UK Office of Tax Simplification (OTS).

Identification of case complexity and increased health care utilization in patients with rheumatoid arthritis.

OBJECTIVES: To document biopsychosocial profiles of patients with rheumatoid arthritis (RA) by means of the INTERMED and to correlate the results with conventional methods of disease assessment and health care utilization. METHODS: Patients with RA (n = 75) were evaluated with the INTERMED, an instrument for assessing case complexity and care needs. Based on their INTERMED scores, patients were compared with regard to severity of illness, functional status, and health care utilization. RESULTS: In cluster analysis, a 2-cluster solution emerged, with about half of the patients characterized as complex. Complex patients scoring especially high in the psychosocial domain of the INTERMED were disabled significantly more often and took more psychotropic drugs. Although the 2 patient groups did not differ in severity of illness and functional status, complex patients rated their illness as more severe on subjective measures and on most items of the Medical Outcomes Study Short Form 36. Complex patients showed increased health care utilization despite a similar biologic profile. CONCLUSIONS: The INTERMED identified complex patients with increased health care utilization, provided meaningful and comprehensive patient information, and proved to be easy to implement and advantageous compared with conventional methods of disease assessment. Intervention studies will have to demonstrate whether management strategies based on INTERMED profiles can improve treatment response and outcome of complex patients.

The rational search for natural neolignans

A rational method of search for natural neolignans of desired structures is outlined. This involves consultation of a collection of chemical profiles of plant families. The profiles are assembled considering the biosynthetic class (in the present case lignoids), subclass (neolignans), structural types (neolignan skeleta) and relative frequency of substitutional derivatives belonging to each type (known compounds). The method is of course applicable to ani class of natural products. Its use in the case of neolignans is here selected as an exemple in view of the recently discovered antagonism towards PAF of kadsurenone, a representative of this subclass of phytochemicals. Application of the chemical profiles to phylogenetic studies is illustrated.