Singularities of nn-fold integrals of the Ising class and the theory of elliptic curves

We introduce some multiple integrals that are expected to have the same singularities as the singularities of the $n$-particle contributions $\chi^{(n)}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals for $n=1, 2, 3, 4$ and only modulo some primes for $n=5$ and $6$, thus providing a large set of (possible) new singularities of the $\chi^{(n)}$. We discuss the singularity structure for these multiple integrals by solving the Landau conditions. We find that the singularities of the associated ODEs identify (up to $n= 6$) with the leading pinch Landau singularities. The second remarkable obtained feature is that the singularities of the ODEs associated with the multiple integrals reduce to the singularities of the ODEs associated with a {\em finite number of one dimensional integrals}. Among the singularities found, we underline the fact that the quadratic polynomial condition $1+3 w +4 w^2 = 0$, that occurs in the linear differential equation of $\chi^{(3)}$, actually corresponds to a remarkable property of selected elliptic curves, namely the occurrence of complex multiplication. The interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group, namely isogenies of elliptic curves, is sketched. Most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting an interpretation in terms of (motivic) mathematical structures beyond the theory of elliptic curves.Comment: 39 pages, 7 figure

Anaphylaxis

Anaphylaxis is an acute, potentially fatal systemic reaction with varied mechanisms and clinical presentations. Although prompt recognition and treatment of anaphylaxis are imperative, both patients and healthcare professionals often fail to recognize and diagnose early signs and symptoms of the condition. Clinical manifestations vary widely, however, the most common signs are cutaneous symptoms, including angioedema, urticaria, erythema and pruritus. Immediate intramuscular administration of epinephrine into the lateral thigh is first-line therapy, even if the diagnosis is uncertain. The mainstays of long-term management include specialist assessment, avoidance measures, and the provision of an epinephrine auto-injector and an individualized anaphylaxis action plan. This article provides an overview of the causes, clinical features, diagnosis and acute and long-term management of this serious allergic reaction

Protecting children from their families and themselves: State laws and the constitution

State laws provide a variety of means to protect children from self-inflicted or parentally-inflicted harm. In recent years, the Supreme Court has imposed stringent procedural requirements on juvenile delinquency laws. In the past year, however, the Court has refused to extend these procedural stringencies to analogous child-protective state laws. This article explores generally the rationale for court application, by constitutional mandate, of procedural safeguards to a broad range of child-protective legislation. The article suggests that some criminal-procedure rights are vitally important to protect children and their parents from inappropriate state interventions, but that wholesale application of all criminal rights, as if these laws were no different from criminal laws, unduly restricts proper application of these laws. Guidelines for determining what criminal rights should and should not be applied to child-protective legislation generally are suggested .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45257/1/10964_2005_Article_BF01537066.pd

Psychiatric diagnoses, trauma, and suicidiality

BACKGROUND: This study aimed to examine the associations between psychiatric diagnoses, trauma and suicidiality in psychiatric patients at intake. METHODS: During two months, all consecutive patients (n = 139) in a psychiatric hospital in Western Norway were interviewed (response rate 72%). RESULTS: Ninety-one percent had been exposed to at least one trauma; 69 percent had been repeatedly exposed to trauma for longer periods of time. Only 7% acquired a PTSD diagnosis. The comorbidity of PTSD and other psychiatric diagnoses were 78%. A number of diagnoses were associated with specific traumas. Sixty-seven percent of the patients reported suicidal thoughts in the month prior to intake; thirty-one percent had attempted suicide in the preceding week. Suicidal ideation, self-harming behaviour, and suicide attempts were associated with specific traumas. CONCLUSION: Traumatised patients appear to be under- or misdiagnosed which could have an impact on the efficiency of treatment