Number fields and function fields: coalescences, contrasts and emerging applications.

The similarity between the density of the primes and the density of irreducible polynomials defined over a finite field of q elements was first observed by Gauss. Since then, many other analogies have been uncovered between arithmetic in number fields and in function fields defined over a finite field. Although an active area of interaction for the past half century at least, the language and techniques used in analytic number theory and in the function field setting are quite different, and this has frustrated interchanges between the two areas. This situation is currently changing, and there has been substantial progress on a number of problems stimulated by bringing together ideas from each field. We here introduce the papers published in this Theo Murphy meeting issue, where some of the recent developments are explained.

Moments of Moments and Branching Random Walks.

We calculate, for a branching random walk X n ( l ) to a leaf l at depth n on a binary tree, the positive integer moments of the random variable 1 2 n ∑ l = 1 2 n e 2 ß X n ( l ) , for ß ∈ R . We obtain explicit formulae for the first few moments for finite n. In the limit n → ∞ , our expression coincides with recent conjectures and results concerning the moments of moments of characteristic polynomials of random unitary matrices, supporting the idea that these two problems, which both fall into the class of logarithmically correlated Gaussian random fields, are related to each other.

Hepatic fructose-1,6-diphosphatase deficiency. A cause of lactic acidosis and hypoglycemia in infancy.

An 8-month-old female, maintained on breast feeding for 6 months, experienced numerous attacks of hyperventilation when weaned to baby food and was admitted with severe lactic acidosis (20 mM) and hypoglycemia. Physical examination was negative except for hepatomegaly. Fasting (18 hr) after stabilization on a high carbohydrate diet resulted in hypoglycemia (plasma glucose 40 mg/100 ml), lactic acidosis (6-10 mM), and a rise in plasma alanine. Glucagon produced a glycemic response after 6 hr, but not after 18 hr fasting. Intravenous galactose increased plasma glucose (Delta 45 mg/100 ml) but intravenous fructose, glycerol, and alanine caused a 40-50% fall in plasma glucose and a significant rise in lactate (Delta 3-4 mM). Liver biopsy showed fatty infiltration. Liver slices incubated with galactose, lactate, fructose, alanine, or glycerol converted only galactose to glucose. Hepatic glycolytic intermediates were increased below the level of fructose-1,6-diphosphate and decreased above. Hepatic phosphorylase, glucose-6-phosphatase, amylo-1,6-glucosidase, phosphofructokinase, fructose-1-phosphate aldolase, and fructose-1,6-diphosphate aldolase levels were normal, but no fructose-1,6-diphosphatase (FDPase) activity was detected. Further studies on the liver homogenate of this patient revealed the presence of an acid-precipitable activator of FDPase. Normal plasma glucose and lactate levels were maintained on an 800 cal diet of 66% carbohydrate (sucrose and fructose excluded). 5% protein, and 20% fat. When carbohydrate was reduced to 35% and protein or fat increased to 23 and 53% respectively, lactic acidosis and hypoglycemia recurred. These studies show that a deficiency of FDPase produced infantile lactic acidosis and hypoglycemia and can be controlled by an appropriate diet.

Granulocyte colony-stimulating factor corrects the neutropenia associated with glycogen storage disease type Ib.

A young woman with glycogen storage disease, type Ib, and chronic neutropenia had severe recurrent infections. In a life-threatening situation, treatment with granulocyte colony-stimulating factor (G-CSF) resulted in the prompt correction of neutropenia. Subsequently, daily G-CSF therapy has allowed the maintenance of a normal neutrophil count and marked clinical improvement over a period of 18 months. The spectrum of neutropenic conditions which are responsive to G-CSF should include this inherited metabolic disorder.

Random matrix theory and critical phenomena in quantum spin chains.

We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups U(N),O(N), and Sp(2N). In particular we calculate critical exponents s,ν, and z, corresponding to the energy gap, correlation length, and dynamic exponent, respectively. We also compute the ground state correlators 〈σ_{i}^{x}σ_{i+n}^{x}〉_{g},〈σ_{i}^{y}σ_{i+n}^{y}〉_{g}, and 〈∏_{i=1}^{n}σ_{i}^{z}〉_{g}, all of which display quasi-long-range order with a critical exponent dependent upon system parameters. Our approach establishes universality of the exponents for the class of systems in question.

An experience with total parenteral nutrition in children.

Total parenteral nutrition has been used in the treatment of more than 100 children with gastrointestinal illnesses, including 90 under the age of 6 months. The incidence of complications has been reduced markedly as experience was acquired. Total parenteral nutrition has been especially valuable in patients with intractable diarrhea syndrome and it has been used successfully in the management of infants with overwhelming systemic infections.

Neoadjuvant chemotherapy for locally advanced transitional cell carcinoma of the bladder: do local findings suggest a potential for salvage of the bladder?

Sixteen patients with locally advanced transitional cell carcinoma of the bladder were given two to four cycles of combination chemotherapy with methotrexate, vinblastine, doxorubicin hydrochloride (Adriamycin), and cisplatin (M-VAC) in an effort to reduce tumor size and enhance the potential for surgical resection. All patients had initial clinical staging (based on cystoscopy and cystoscopic biopsy, urine cytology, computed tomographic scanning, and excretory urography). Before each cycle, all patients had repeat clinical staging tests. Ten patients underwent postchemotherapy bilateral pelvic lymphadenectomy and radical cystoprostatectomy, and their bladders were examined histopathologically by step-sectioning techniques. One patient underwent abdominal exploration, bilateral pelvic lymphadenectomy, and ipsilateral partial cystectomy. Five patients had repeat clinical staging only without removal of their bladders. Of the 16 patients, 5 (31%) had residual invasive tumor and no tumor response. Three patients (19%) had a partial response, two of whom had only carcinoma in situ (one with prostatic duct involvement) and one of whom had stage pT1, NO, MO disease. Five patients (31%) had normal findings on computed tomographic scans, cystoscopy, biopsy, and urine cytology and thus had complete responses. In addition, 3 of 11 patients who underwent pathologic staging had no residual tumor on clinical and surgical staging and were complete responders. The overall (partial + complete) response rate was 69%, and the overall complete remission rate (pathologic + clinical staging) was 50%. These results suggest that the concept of possible salvage of the bladder with the current treatment program might be premature and must be applied selectively.(ABSTRACT TRUNCATED AT 250 WORDS)

Acute acalculous cholecystitis. Complication of other illnesses in childhood.

Seventy-four cases of acalculous cholecystitis in infants and children (seven personal cases and 67 from the literature) were analyzed. In 45 cases the cholecystitis appeared as a complication of another illness. The primary illnesses in our patients were leptospirosis (four cases), diarrhea (two cases), and third-degree burns (one case). All seven children were critically ill. Abdominal pain and an abdominal mass were present in all. Fever was present in six of the seven patients, jaundice in four. Tube cholecystostomies were done in all cases. After recovery from their illness, the five surviving patients had normal bilary tracts when studied by cholangiography via the tube. Acute acalculous cholecystitis in infancey and childhood as a complication of injury or illness should be treated as an undrained abcess.

The clinical and radiological features of cholecystocolic fistulae.

The clinical and radiological features of seven patients presenting with cholecystocolic fistulae are reviewed. The majority of the patients were elderly (age range 43-85 years, mean 70.7 years) and there was a female preponderance (6:1). The condition usually has a benign clinical course. Diarrhoea was the most common presenting symptom and the typical clinical features of gallbladder disease were absent. Cholangitis occurred in only one patient. The time between onset of symptoms and diagnosis varied from 1 week to 2 years (mean 22 weeks). In only one patient was the diagnosis of biliary-intestinal fistula suspected on the basis of the plain abdominal radiograph (Case 5). A diagnosis of cholecystocolic fistula was established by barium enema (5 cases), endoscopic retrograde cholangiopancreatography (ERCP) (1 case) and diagnostic laparotomy (1 case). The only cause identified in this series was acute or chronic cholecystitis.

Congenital lip pits and Hirschsprung's disease.

A newborn infant with aganglionosis of the entire colon and terminal ileum also had congenital lip pits and a submucous cleft palate. These anomalies may be added to the growing list of conditions associated with Hirschsprung's disease.

Prepyloric gastric antral web: a puzzling epidemic.

Antral webs and diaphragms are considered a rare cause of gastric outlet obstruction in infants and children. A radiographic diagnosis of antral web was made in 28 children during a 26-mo period. Nonbilious, often projectile vomiting was the predominant presenting symptom in 24 infants who were less than 6 mo of age. The older children complained of pain, vomiting, fullness after eating, and eructation. The characteristic radiologic finging was a wirelike transverse septum 1--2 cm proximal to the pylorus. Poor antral filling was an important early clue in the radiographic search for the webs. Pyloroplasty was performed in 20 patients, frequently after failure of medical management of symptoms. Coexistent congenital abnormalities were present in 28% of patients. A search for environmental and familial factors has failed to elucidate any teratogenic influences in this population.

Perforated stress ulcers in infants.

During a 5-yr period, 10 infants less than 1 yr of age developed gastroduodenal perforation during treatment for severe underlying illness. Brisk gastrointestinal hemorrhage preceded perforation in most patients. In contrast to stress ulceration in adults, infants appear to have a higher frequency of single ulcers, perforation, and duodenal (rather than gastric) location. The mortality of 40% in this group, and in those patients reported in the literature who have been treated since 1960, implies that effective preventive and therapeutic measures are not yet available and also emphasizes the serious nature of the underlying disorder.

A multicentre retrospective audit of outcome of patients undergoing curative resection for rectal cancer.

AIM: This study describes the outcome of patients with rectal cancer treated in four New Zealand public hospitals before the advent of specialised colorectal units in order to provide a baseline against which any changes in management can be measured. METHODS: A retrospective review of case notes of patients who underwent resection of rectal cancer with curative intent over a period of 7-10 years up to 1995 in Christchurch, Wellington, Nelson, and Masterton Public Hospital's, was undertaken. Patients were identified from hospital records using a combination of methods (pathology data bases, clinical case mix data, operating logs and audit data). Metastatic disease was considered to be present if confirmed on histology or the clinical course of the patient was consistent with metastatic disease. Patients were excluded if there was perioperative evidence of metastatic disease or if they had transanal excision. Previously published results from Auckland and Dunedin Hospitals are compared. RESULTS: 524 patients with rectal cancer were identified who had undergone surgery with curative intent in the four hospitals. The overall permanent stoma rate was 37%. The overall 30-day mortality was 2.9%, five-year survival was 63% and local recurrence at five years was 26%. CONCLUSION: While low perioperative mortality and good long-term survival were achieved, there were high rates of local recurrence. These data are a baseline against which the impact of new approaches to curative resection for rectal cancer can be measured.

Sigmoid volvulus in late pregnancy.

Sigmoid volvulus in late pregnancy is an uncommon complication. We report a case of a 35 year old Caucasian woman who presented with symptoms and signs of intestinal obstruction when 34 weeks pregnant. Surgical management of the case is described and the literature reviewed.

[Cerebrovascular accidents. Case material based on hospital records]. / Acidentes vasculares cerebrais. Casuística segundo a base de dados hospitalar.

Perceiving that inaccuracy of clinical records is the rule rather than the exception, the author examines the data base of the Amarante Regional Hospital with particular relevance to the patients who were hospitalized with cerebral vascular accident (CVA) in the Department of Internal Medicine during 1990, 1991 and 1992. The objective is to view the existing computerised hospital database as a source of information for future studies within the clinical field and, at the same time, to be aware of the department's casuistry and to contribute to the epidemiological understanding of the population who lives in the area of influence of this hospital. In this department, 24% of all the hospitalised patients had either a recent CVA or had already had one previously. On the whole, the disease affected both sexes in an equal manner, but females later than males. The mortality rate was greater in patients with CVA (17%) than in those without CVA (9%) and was also greater in CVA-females (19%) than in CVA-males (15%). The intercurrences in the community were the cause of admission in 26% of the hospitalised patients with a CVA, and were mainly respiratory, metabolic and urinary diseases, and appeared to be more serious in males. The mortality rate in patients with intercurrences (19%) was only exceeded by that caused by hemorragic accidents (22%). The author examines and discusses the instances of error during the construction and data gathering of the database and draws his own conclusions.