Arithmetical problems in number fields, abelian varieties and modular forms

Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research.

Hyperhomocysteinaemia in young patients with non-arteritic anterior ischaemic optic neuropathy.

BACKGROUND/AIM: Elevated plasma homocysteine is a newly identified vascular risk factor among patients under age 55 years with cerebrovascular, cardiovascular, or peripheral vascular disease. This study sought to evaluate retrospectively the plasma homocysteine status among healthy younger patients with ischaemic optic disc disease. METHODS: 12 non-diabetic patients who had been diagnosed with non-arteritic anterior ischaemic optic neuropathy (NAION) before the age of 50 years were identified from chart review. None had experienced previous ischaemic cerebrovascular, cardiovascular, or peripheral vascular events. Plasma homocysteine, CBC, renal function, vitamin B6, vitamin B12, and folate levels were sampled in the fasting state. RESULTS: Two of 12 patients (17%) had hyperhomocysteinaemia. Both had experienced NAION in both eyes with recurrent episodes. Neither patient was hypertensive nor had a smoking history. One of these two patients had mild hypercholesterolaemia which did not warrant medication. CONCLUSIONS: Elevated plasma homocysteine may be associated with NAION. An evaluation for hyperhomocysteinaemia should be considered in patients with NAION who do not have the typical risk factor such as older age, diabetes, hypertension, or tobacco use. It should also be considered in young patients with bilateral or recurrent attacks of NAION.

Transformation kernel density estimation of actuarial loss functions

[cat] Es presenta un estimador nucli transformat que és adequat per a distribucions de cua pesada. Utilitzant una transformació basada en la distribució de probabilitat Beta l’elecció del paràmetre de finestra és molt directa. Es presenta una aplicació a dades d’assegurances i es mostra com calcular el Valor en Risc.

The induced generalized OWA operator

[spa] Se presenta el operador OWA generalizado inducido (IGOWA). Es un nuevo operador de agregación que generaliza al operador OWA a través de utilizar las principales características de dos operadores muy conocidos como son el operador OWA generalizado y el operador OWA inducido. Entonces, este operador utiliza medias generalizadas y variables de ordenación inducidas en el proceso de reordenación. Con esta formulación, se obtiene una amplia gama de operadores de agregación que incluye a todos los casos particulares de los operadores IOWA y GOWA, y otros casos particulares. A continuación, se realiza una generalización mayor al operador IGOWA a través de utilizar medias cuasi-aritméticas. Finalmente, también se desarrolla un ejemplo numérico del nuevo modelo en un problema de toma de decisiones financieras.

The induced generalized OWA operator

[spa] Se presenta el operador OWA generalizado inducido (IGOWA). Es un nuevo operador de agregación que generaliza al operador OWA a través de utilizar las principales características de dos operadores muy conocidos como son el operador OWA generalizado y el operador OWA inducido. Entonces, este operador utiliza medias generalizadas y variables de ordenación inducidas en el proceso de reordenación. Con esta formulación, se obtiene una amplia gama de operadores de agregación que incluye a todos los casos particulares de los operadores IOWA y GOWA, y otros casos particulares. A continuación, se realiza una generalización mayor al operador IGOWA a través de utilizar medias cuasi-aritméticas. Finalmente, también se desarrolla un ejemplo numérico del nuevo modelo en un problema de toma de decisiones financieras.

How to assign a likelihood ratio in a footwear mark case: an analysis and discussion in the light of R v T

This article analyses and discusses issues that pertain to the choice of relevant databases for assigning values to the components of evaluative likelihood ratio procedures at source level. Although several formal likelihood ratio developments currently exist, both case practitioners and recipients of expert information (such as judiciary) may be reluctant to consider them as a framework for evaluating scientific evidence in context. The recent ruling R v T and ensuing discussions in many forums provide illustrative examples for this. In particular, it is often felt that likelihood ratio-based reasoning amounts to an application that requires extensive quantitative information along with means for dealing with technicalities related to the algebraic formulation of these approaches. With regard to this objection, this article proposes two distinct discussions. In a first part, it is argued that, from a methodological point of view, there are additional levels of qualitative evaluation that are worth considering prior to focusing on particular numerical probability assignments. Analyses will be proposed that intend to show that, under certain assumptions, relative numerical values, as opposed to absolute values, may be sufficient to characterize a likelihood ratio for practical and pragmatic purposes. The feasibility of such qualitative considerations points out that the availability of hard numerical data is not a necessary requirement for implementing a likelihood ratio approach in practice. It is further argued that, even if numerical evaluations can be made, qualitative considerations may be valuable because they can further the understanding of the logical underpinnings of an assessment. In a second part, the article will draw a parallel to R v T by concentrating on a practical footwear mark case received at the authors' institute. This case will serve the purpose of exemplifying the possible usage of data from various sources in casework and help to discuss the difficulty associated with reconciling the depth of theoretical likelihood ratio developments and limitations in the degree to which these developments can actually be applied in practice.

Transformation kernel density estimation of actuarial loss functions

[cat] Es presenta un estimador nucli transformat que és adequat per a distribucions de cua pesada. Utilitzant una transformació basada en la distribució de probabilitat Beta l’elecció del paràmetre de finestra és molt directa. Es presenta una aplicació a dades d’assegurances i es mostra com calcular el Valor en Risc.

Successive treatment with cyclosporine and infliximab in steroid-refractory ulcerative colitis.

OBJECTIVES: Rescue therapy with either cyclosporine (CYS) or infliximab (IFX) is an effective option in patients with intravenous steroid-refractory attacks of ulcerative colitis (UC). In patients who fail, colectomy is usually recommended, but a second-line rescue therapy with IFX or CYS is an alternative. The aims of this study were to investigate the efficacy and tolerance of IFX and CYS as a second-line rescue therapy in steroid-refractory UC or indeterminate colitis (IC) unsuccessfully treated with CYS or IFX.METHODS: This was a retrospective survey of patients seen during the period 2000-2008 in the GETAID centers. Inclusion criteria included a delay of <1 month between CYS withdrawal (when used first) and IFX, or a delay of <2 months between IFX (when used first) and CYS, and a follow-up of at least 3 months after inclusion. Time-to-colectomy, clinical response, and occurrence of serious adverse events were analyzed.RESULTS: A total of 86 patients (median age 34 years; 49 males; 71 UC and 15 IC) were successively treated with CYS and IFX. The median (+/-s.e.) follow-up time was 22.6 (7.0) months. During the study period, 49 patients failed to respond to the second-line rescue therapy and underwent a colectomy. The probability of colectomy-free survival (+/-s.e.) was 61.3 +/- 5.3% at 3 months and 41.3 +/- 5.6% at 12 months. A case of fatal pulmonary embolism occurred at 1 day after surgery in a 45-year-old man. Also, nine infectious complications were observed during the second-line rescue therapy.CONCLUSIONS: In patients with intravenous steroid-refractory UC and who fail to respond to CYS or IFX, a second-line rescue therapy may be effective in carefully selected patients, avoiding colectomy within 2 months in two-thirds of them. The risk/benefit ratio should still be considered individually.

History of biological warfare and bioterrorism.

Bioterrorism literally means using microorganisms or infected samples to cause terror and panic in populations. Bioterrorism had already started 14 centuries before Christ, when the Hittites sent infected rams to their enemies. However, apart from some rare well-documented events, it is often very difficult for historians and microbiologists to differentiate natural epidemics from alleged biological attacks, because: (i) little information is available for times before the advent of modern microbiology; (ii) truth may be manipulated for political reasons, especially for a hot topic such as a biological attack; and (iii) the passage of time may also have distorted the reality of the past. Nevertheless, we have tried to provide to clinical microbiologists an overview of some likely biological warfare that occurred before the 18th century and that included the intentional spread of epidemic diseases such as tularaemia, plague, malaria, smallpox, yellow fever, and leprosy. We also summarize the main events that occurred during the modern microbiology era, from World War I to the recent 'anthrax letters' that followed the World Trade Center attack of September 2001. Again, the political polemic surrounding the use of infectious agents as a weapon may distort the truth. This is nicely exemplified by the Sverdlovsk accident, which was initially attributed by the authorities to a natural foodborne outbreak, and was officially recognized as having a military cause only 13 years later.

Gout: why is this curable disease so seldom cured?

Gout is the most common inflammatory arthritis and one in which pathogenesis and risk factors are best understood. One of the treatment objectives in current guidelines is 'cure'. However, audits show that only a minority of patients with gout receive adequate advice and treatment. Suboptimal care and outcomes reflect inappropriately negative perceptions of the disease, both in patients and providers. Historically, gout has been portrayed as a benign and even comical condition that is self-inflicted through overeating and alcohol excess. Doctors often focus on managing acute attacks rather than viewing gout as a chronic progressive crystal deposition disease. Urate-lowering treatment is underprescribed and often underdosed. Appropriate education of patients and doctors, catalysed by recent introduction of new urate-lowering treatments after many years with no drug development in the field, may help to overcome these barriers and improve management of this easily diagnosed and curable form of potentially severe arthritis.

Invariant decomposition of the retarded electromagnetic field.

The integral representation of the electromagnetic two-form, defined on Minkowski space-time, is studied from a new point of view. The aim of the paper is to obtain an invariant criteria in order to define the radiative field. This criteria generalizes the well-known structureless charge case. We begin with the curvature two-form, because its field equations incorporate the motion of the sources. The gauge theory methods (connection one-forms) are not suited because their field equations do not incorporate the motion of the sources. We obtain an integral solution of the Maxwell equations in the case of a flow of charges in irrotational motion. This solution induces us to propose a new method of solving the problem of the nature of the retarded radiative field. This method is based on a projection tensor operator which, being local, is suited to being implemented on general relativity. We propose the field equations for the pair {electromagnetic field, projection tensor J. These field equations are an algebraic differential first-order system of oneforms, which verifies automatically the integrability conditions.

Acute intussusception: a classic clinical picture?

57 patients with acute intussusception were admitted to the Children's Hospital Zurich between 1972 and 1979. All were treated surgically. One died, 7 needed a bowel resection, 9 intussusceptions were difficult and 32 easy to reduce. The retrospectively reviewed data show that the classic symptomatology, beginning suddenly in a healthy male (60%) under 3 years of age (91%) with attacks of colicky pain (81%), vomiting (93%), a palpable abdominal mass (72%) and rectal bleeding (72%), appears during the course of illness or may not be present at all. This leads to misdiagnosis, wrong treatment and worsening of the pathology. Blood per rectum, the most typical symptom, was present in the first hours of illness in only 5%, vomiting in 44% and colicky pain in 33% of the patients. A high degree of awareness is therefore necessary to diagnose intussusception during the first hours of illness, and particular stress must be laid on the accuracy of the diagnosis because reducibility and resection rate depend directly on the duration of the symptoms.