Renormalizable two-parameter piecewise isometries.

We exhibit two distinct renormalization scenarios for two-parameter piecewise isometries, based on 2π/5 rotations of a rhombus and parameter-dependent translations. Both scenarios rely on the recently established renormalizability of a one-parameter triangle map, which takes place if and only if the parameter belongs to the algebraic number field K=Q(5) associated with the rotation matrix. With two parameters, features emerge which have no counterpart in the single-parameter model. In the first scenario, we show that renormalizability is no longer rigid: whereas one of the two parameters is restricted to K, the second parameter can vary continuously over a real interval without destroying self-similarity. The mechanism involves neighbouring atoms which recombine after traversing distinct return paths. We show that this phenomenon also occurs in the simpler context of Rauzy-Veech renormalization of interval exchange transformations, here regarded as parametric piecewise isometries on a real interval. We explore this analogy in some detail. In the second scenario, which involves two-parameter deformations of a three-parameter rhombus map, we exhibit a weak form of rigidity. The phase space splits into several (non-convex) invariant components, on each of which the renormalization still has a free parameter. However, the foliations of the different components are transversal in parameter space; as a result, simultaneous self-similarity of the component maps requires that both of the original parameters belong to the field K

ILAE Genetic Literacy Series: Postmorterm Genetic Testing in Sudden Unexpected Death in Epilepsy

A 24-year-old man with non-lesional bitemporal lobe epilepsy since age 16 years was found dead in bed around midday. He was last seen the previous night when he was witnessed to have a tonic–clonic seizure. Before his death, he was experiencing weekly focal impaired awareness seizures and up to two focal-to-bilateral tonic–clonic seizures each year. He had trialed several antiseizure medications and was on levetiracetam 1500 mg/day, lamotrigine 400 mg/day, and clobazam 10 mg/day at the time of death. Other than epilepsy, his medical history was unremarkable. Of note, he had an older brother with a history of febrile seizures and a paternal first cousin with epilepsy. No cause of death was identified following a comprehensive postmortem investigation. The coroner classified the death as “sudden unexpected death in epilepsy” (SUDEP), and it would qualify as “definite SUDEP” using the current definitions.1 This left the family with many questions unanswered; in particular, they wish to know what caused the death and whether it could happen to other family members. Could postmortem genetic testing identify a cause of death, provide closure to the family, and facilitate cascade genetic testing of first-degree family members who may be at risk of sudden death? While grieving family members struggle with uncertainty about the cause of death, we as clinicians also face similar uncertainties about genetic contributions to SUDEP, especially when the literature is sparse, and the utility of genetic testing is still being worked out. We aim to shed some light on this topic, highlighting areas where data is emerging but also areas where uncertainty remains, keeping our case in mind as we examine this clinically important area

Links between traumatic brain injury and ballistic pressure waves originating in the thoracic cavity and extremities

Identifying patients at risk of traumatic brain injury (TBI) is important because research suggests prophylactic treatments to reduce risk of long-term sequelae. Blast pressure waves can cause TBI without penetrating wounds or blunt force trauma. Similarly, bullet impacts distant from the brain can produce pressure waves sufficient to cause mild to moderate TBI. The fluid percussion model of TBI shows that pressure impulses of 15-30 psi cause mild to moderate TBI in laboratory animals. In pigs and dogs, bullet impacts to the thigh produce pressure waves in the brain of 18-45 psi and measurable injury to neurons and neuroglia. Analyses of research in goats and epidemiological data from shooting events involving humans show high correlations (r > 0.9) between rapid incapacitation and pressure wave magnitude in the thoracic cavity. A case study has documented epilepsy resulting from a pressure wave without the bullet directly hitting the brain. Taken together, these results support the hypothesis that bullet impacts distant from the brain produce pressure waves that travel to the brain and can retain sufficient magnitude to induce brain injury. The link to long-term sequelae could be investigated via epidemiological studies of patients who were gunshot in the chest to determine whether they experience elevated rates of epilepsy and other neurological sequelae

On the Trace Anomaly and the Anomaly Puzzle in N=1 Pure Yang-Mills

The trace anomaly of the energy-momentum tensor is usually quoted in the form which is proportional to the beta function of the theory. However, there are in general many definitions of gauge couplings depending on renormalization schemes, and hence many beta functions. In particular, N=1 supersymmetric pure Yang-Mills has the holomorphic gauge coupling whose beta function is one-loop exact, and the canonical gauge coupling whose beta function is given by the Novikov-Shifman-Vainshtein-Zakharov beta function. In this paper, we study which beta function should appear in the trace anomaly in N=1 pure Yang-Mills. We calculate the trace anomaly by employing the N=4 regularization of N=1 pure Yang-Mills. It is shown that the trace anomaly is given by one-loop exact form if the composite operator appearing in the trace anomaly is renormalized in a preferred way. This result gives the simplest resolution to the anomaly puzzle in N=1 pure Yang-Mills. The most important point is to examine in which scheme the quantum action principle is valid, which is crucial in the derivation of the trace anomaly.Comment: 25 pages, 1 figure; v2:slight correction in sec.5, minor addition in appendi

ILAE Genetic Literacy Series: Self-limited familial epilepsy syndromes with onset in neonatal age and infancy

The self-limited (familial) epilepsies with onset in neonates or infants, formerly called benign familial neonatal and/or infantile epilepsies, are autosomal dominant disorders characterized by neonatal- or infantile-onset focal motor seizures and the absence of neurodevelopmental complications. Seizures tend to remit during infancy or early childhood and are therefore called “self-limited”. A positive family history for epilepsy usually suggests the genetic etiology, but incomplete penetrance and de novo inheritance occur. Here, we review the phenotypic spectrum and the genetic architecture of self-limited (familial) epilepsies with onset in neonates or infants. Using an illustrative case study, we describe important clues in recognition of these syndromes, diagnostic steps including genetic testing, management, and genetic counseling

Light-Induced Responses of Slow Oscillatory Neurons of the Rat Olivary Pretectal Nucleus

Background: The olivary pretectal nucleus (OPN) is a small midbrain structure responsible for pupil constriction in response to eye illumination. Previous electrophysiological studies have shown that OPN neurons code light intensity levels and therefore are called luminance detectors. Recently, we described an additional population of OPN neurons, characterized by a slow rhythmic pattern of action potentials in light-on conditions. Rhythmic patterns generated by these cells last for a period of approximately 2 minutes. Methodology: To answer whether oscillatory OPN cells are light responsive and whether oscillatory activity depends on retinal afferents, we performed in vivo electrophysiology experiments on urethane anaesthetized Wistar rats. Extracellular recordings were combined with changes in light conditions (light-dark-light transitions), brief light stimulations of the contralateral eye (diverse illuminances) or intraocular injections of tetrodotoxin (TTX). Conclusions: We found that oscillatory neurons were able to fire rhythmically in darkness and were responsive to eye illumination in a manner resembling that of luminance detectors. Their firing rate increased together with the strength of the light stimulation. In addition, during the train of light pulses, we observed two profiles of responses: oscillationpreserving and oscillation-disrupting, which occurred during low- and high-illuminance stimuli presentation respectively. Moreover, we have shown that contralateral retina inactivation eliminated oscillation and significantly reduced the firin

The risk of angiosarcoma following primary breast cancer

Lymphangiosarcoma of the upper extremity is a rare and aggressive tumour reported to occur following post-mastectomy lymphoedema (Stewart–Treves syndrome). Haemangiosarcoma, a related rare tumour, has occasionally been reported to occur in the breast following irradiation. We conducted a case-control study using the University of Southern California-Cancer Surveillance Program, the population-based cancer registry for Los Angeles County, to evaluate the relationship between invasive female breast cancer and subsequent upper extremity or chest lymphangiosarcoma and haemangiosarcoma together referred to as angiosarcoma. Cases were females diagnosed between 1972 and 1995 with angiosarcoma of the upper extremity (n = 20) or chest (n = 48) who were 25 years of age or older and residing in Los Angeles County when diagnosed. Other sarcomas at the same anatomic sites were also studied. Controls were females diagnosed with cancers other than sarcoma during the same time period (n = 266 444). Cases and controls were then compared with respect to history of a prior invasive epithelial breast cancer. A history of breast cancer increased the risk of upper extremity angiosarcoma by more than 59-fold (odds ratio [OR] = 59.3, 95% confidence interval [95% CI] = 21.9–152.8). A strong increase in risk after breast cancer was also observed for angiosarcoma of the chest and breast (OR = 11.6, 95% CI = 4.3–26.1) and for other sarcomas of the chest and breast (OR = 3.3, 95% CI = 1.1–1.7). © 1999 Cancer Research Campaig

Diversity and abundance of solitary and primitively eusocial bees in an urban centre: a case study from Northampton (England)

The apparent reduction of solitary and primitively eusocial bees populations has remained a huge concern over the past few decades and urbanisation is considered as one of the factors affecting bees at different scales depending on bee guild. As urbanisation is increasing globally it necessitates more research to understand the complex community dynamics of solitary and primitively eusocial bees in urban settings. We investigated the urban core of a British town for diversity and abundance of solitary bees using standardized methods, and compared the results with nearby meadows and nature reserves. The study recorded 48 species within the town, about 22 % of the total species and 58 % of the genera of solitary bees in the United Kingdom. Furthermore we found the urban core to be more diverse and abundant in solitary and primitively eusocial bees compared to the meadows and nature re-serves. Of particular note was an urban record of the nationally rare Red Data Book species Coelioxys quadridentata and its host Anthophora quadrimaculata. This research demonstrates that urban settings can contribute significantly to the conservation of solitary and primitively eusocial bees in Britain