Will the digital computer transform classical mathematics?

Mathematics and machines have influenced each other for millennia. The advent of the digital computer introduced a powerfully new element that promises to transform the relation between them. This paper outlines the thesis that the effect of the digital computer on mathematics, already widespread, is likely to be radical and far-reaching. To articulate this claim, an abstract model of doing mathematics is introduced based on a triad of actors of which one, the 'agent', corresponds to the function performed by the computer. The model is used to frame two sorts of transformation. The first is pragmatic and involves the alterations and progressive colonization of the content and methods of enquiry of various mathematical fields brought about by digital methods. The second is conceptual and concerns a fundamental antagonism between the infinity enshrined in classical mathematics and physics (continuity, real numbers, asymptotic definitions) and the inherently real and material limit of processes associated with digital computation. An example which lies in the intersection of classical mathematics and computer science, the P=NP problem, is analysed in the light of this latter issue.     

Muscle glycogen recovery after exercise measured by 13C-magnetic resonance spectroscopy in humans: effect of nutritional solutions

The rate of glycogen resynthesis in human skeletal muscle after glycogen-depleting exercise is known to depend on carbohydrate intake and is reported to reach a plateau after an adequate amount of carbohydrate (CHO) consumption. Efforts to maximize the rate of glycogen storage by changing the type and form of CHO, as well as by adding proteins or lipids have yielded inconsistent results. The objective of this study was to assess whether isocaloric addition of proteins and arginine to a CHO diet in the first 4 h after an endurance exercise would increase the rate of glycogen synthesis. The CHO solution, given twice at a 2 h interval according to earlier optimized protocols, contained 1.7 g CHO/kg(body weieght) The effects of this solution were compared to those of an isocaloric solution containing 1.2 g CHO/kg(body weight) plus 0.5 g protein/kg(body weight) (including 5 g arginine). Glycogen was measured in quadriceps muscle in vivo with natural abundance 13C-magnetic resonance spectroscopy before exercise and twice after exercise, before and at the end of a 4-h period following the intake of one of the solutions. Eight subjects took part in a randomized cross-over trial separated by at least 1 week. Glycogen synthesis was found to be significantly increased with both regimes compared to a zero-caloric placebo diet, but no significant difference in glycogen resynthesis was found between the CHO-only diet and the one supplemented by proteins and arginine. It is estimated that significance would have been reached for an increase of 34%, while the effectively measured synthesis rates only differed by 5%.     

Muscle glycogen recovery after exercise measured by13C-magnetic resonance spectroscopy in humans: effect of nutritional solutions

The rate of glycogen resynthesis in human skeletal muscle after glycogen-depleting exercise is known to depend on carbohydrate intake and is reported to reach a platean after an adequate amount of carbohydrate (CHO) consumption. Efforts to maximize the rate of glycogen storage by changing the type and form of CHO, as well as by adding proteins or lipids have yielded inconsistent results. The objective of this study was to assess whether isocaloric addition of proteins and arginine to a CHO diet in the first 4 h after an endurance exercise would increase the rate of glycogen synthesis. The CHO solution, given twice at a 2 h interval according to earlier optimized protocols, contained 1.7 g CHO kg^{body weight}. The effects of this solution were compared to those of an isocaloric solution containing 1.2 g CHO/kg^{body weight} plus 0.5 g protein/kg^{body weight} (including 5 g arginine). Glycogen was measured in quadriceps muscle in vivo with natural abundance¹³C-magnetic resonance spectroscopy before exercise and twice after exercise, before and at the end of a 4-h period following the intake of one of the solutions. Eight subjects took part in a randomized cross-over trial separated by at least 1 week. Glycogen synthesis was found to be significantly increased with both regimes compared to a zero-caloric placebo diet, but no significant difference in glycogen resynthesis was found between the CHO-only diet and the one supplemented by proteins and arginine. It is estimated that significance would have been reached for an increase of 34%, while the effectively measured synthesis rates only differed by 5%.     

The recipient splenic artery for arterialization in orthotopic liver transplantation

Adequate hepatic arterial reconstruction is essential for successful liver transplantation. In the case of insufficient recipient hepatic arterial flow, most surgeons recommend the use of the aorta for arterialization of the graft. We report here on a technique in which the recipient splenic artery is used in such a setting. The splenic artery is dissected from its origin on a 3-to-4 cm segment and divided. The proximal segment is flipped to the right and anastomosed to the graft's celiac axis in an end-to-end fashion. This technique was used in 7 of 79 orthotopic liver transplantations (9%) because the native hepatic artery was deemed to be inadequate for anastomosis. There were no complications related to the use of this technique and no arterial thromboses. Arterialization of hepatic grafts using the recipient proximal splenic artery is a simple, safe, and efficient technique that can be recommended in the presence of an inadequate recipient hepatic arterial flow.     

Requirement for both the amino-terminal catalytic domain and a noncatalytic domain for in vivo activity of ADP-ribosylation factor GTPase-activating protein

The small GTP-binding protein ADP-ribosylation factor-1 (ARF1) regulates intracellular transport by modulating the interaction of coat proteins with the Golgi complex. Coat protein association with Golgi membranes requires activated, GTP-bound ARF1, whereas GTP hydrolysis catalyzed by an ARF1-directed GTPase-activating protein (GAP) deactivates ARF1 and results in coat protein dissociation. We have recently cloned a Golgi-associated ARF GAP. Overexpression of GAP was found to result in a phenotype that reflects ARF1 deactivation (Aoe, T., Cukierman, E., Lee, A., Cassel, D., Peters, P. J., and Hsu, V. W. (1997) EMBO J. 16, 7305-7316). In this study, we used this phenotype to define domains in GAP that are required for its function in vivo. As expected, mutations in the amino-terminal part of GAP that were previously found to abolish ARF GAP catalytic activity in vitro abrogated ARF1 deactivation in vivo. Significantly, truncations at the carboxyl-terminal part of GAP that did not affect GAP catalytic activity in vitro also diminished ARF1 deactivation. Thus, a noncatalytic domain is required for GAP activity in vivo. This domain may be involved in the targeting of GAP to the Golgi membrane.     

Concomitant infusion cisplatin and hyperfractionated radiotherapy for locally advanced nasopharyngeal and paranasal sinus tumors

PURPOSE: This is a prospective study to improve the therapeutic ratio in the treatment of patients with locally advanced nasopharyngeal and paranasal sinus tumors by using split-course concomitant infusion cisplatin chemotherapy and hyperfractionated radiotherapy. METHODS AND MATERIALS: From 1983 to 1993, 21 patients with locally advanced nasopharyngeal and paranasal sinus tumors (T3 and T4, or recurrent tumors involving the facial bones and/or the base of the skull) were treated with a regimen of split-course hyperfractioned radiotherapy (1.2 Gy/fraction/bid) and concomitant infusion cisplatin (5-10 mg/m2/24 h). The therapy was given in three separate 2-week sessions with 1 to 2 week breaks between sessions. Seventeen of 21 patients were treated with curative intent with cumulative radiation doses ranging from 64.8 to 70.8 Gy. Four patients were treated with palliative intent to a total dose of less than 60 Gy or to a limited field due to previous irradiation. RESULTS: Sixteen of 17 patients (94%) treated curatively achieved a complete response. Of the 16 patients who achieved complete response, 7 patients (50%) were alive at the time of analysis (36 to 126 months). One patient was alive at 4 years with no evidence of disease, and died in 10 years at the age of 80 of unknown cause. Two patients died of local recurrence at 21 and 45 months and one patient died of a cerebrovascular accident at 12 months with disease status unknown. Five patients died of distant metastases. The one patient who had a partial response died in 25 months with local disease and metastases to the bone and lung. Four patients that were previously irradiated received a reduced total dose or treated to a limited irradiation field. All had near complete responses, but died within a year of treatment, with the exception of one patient who died at 23 months. Acute reactions included intense erythema of the mucosa in all patients. Five of 21 (23%) developed punctate mucositis and 3 of 21 (14%) developed confluent mucositis. Hematologically, one patient developed neutropenia (1800 WBC/mm3) and one developed thrombocytopenia (38,000/mm3). A rising creatinine was observed in three patients (2.0, 1.7, 1.7) all of whom were treated with the higher 10 mg/m2/day dose of infusional cisplatin. In all three of these cases, the creatinine slowly returned to normal over a 6-month period. Hormonal evaluations were performed in three patients and all were within normal ranges. There was no evidence of neck fibrosis or trismus. One patient with gross recurrent disease of the orbit developed blindness of the involved eye due to corneal opacification. The orbital area had been reirradiated in this patient. CONCLUSIONS: Concomitant infusion cisplatinum with hyperfractionated radiation improved tumor control, but did not increase normal tissue injury. Acute reactions were minimized by splitting the treatment with a 1- to 2-week break after each 2 weeks of radiation treatment. Late complications were not increased by using a hyperfractionated radiation regimen. The local failure rate was only 18% (3 of 17 patients), but the distant failure rate was 35% (6 patients). Further investigation is needed to prove if adjuvant chemotherapy after concomitant chemoradiation improves survival by decreasing the distant failure in such advanced cases.     

Influence of bromodeoxyuridine radiosensitization on malignant glioma patient survival: a retrospective comparison of survival data from the Northern California Oncology Group (NCOG) and Radiation Therapy Oncology Group trials (RTOG) for glioblastoma multiforme and anaplastic astrocytoma

PURPOSE: To examine the effect of treatment using Bromodeoxyuridine (BrdU) during radiation therapy on malignant glioma patient survival by comparing historical survival data from several large clinical trials. METHODS: A retrospective analysis of patient data from Radiation Therapy Oncology Group (RTOG) trials 74-01, 79-18, and 83-02 and the Northern California Oncology Group (NCOG) study 6G-82-1 was conducted. Patient data was supplied by both groups, and analyzed by the RTOG. Pretreatment characteristics including age, extent of surgery, Karnofsky Performance Status (KPS), and histopathology were collected; the only treatment variable evaluated was the use of BrdU during radiation therapy. Radiation dose, dose-fractionation schedule, use of chemotherapy, and/or type of chemotherapy was not controlled for in the analyses. Univariate and multivariate analyses were conducted to examine the potential treatment effect of BrdU on patient survival. RESULTS: Data from 334 patients treated with BrdU on NCOG 6G-82-1 and 1743 patients treated without BrdU on 3 RTOG studies was received. Patients were excluded from the review if confirmation of eligibility could not be obtained, if the patient was ineligible for the study they entered, if central pathology review was not done, or if radiotherapy data was not available. Patients treated according to the RTOG studies had to start radiotherapy within 4 weeks of surgery; no such restriction existed for the NCOG studies. To ensure comparability between the studies, patients from the NCOG studies who began treatment longer than 40 days from surgery were also excluded. The final data set included 296 cases from the NCOG studies (89%) and 1478 cases from the RTOG studies (85%). For patients with glioblastoma multiforme (GBM) the median survival was 9.8 months in the RTOG studies and 13.0 months in the NCOG trial (p < 0.0001). For patients with AA the median survival was 35.1 months for the RTOG studies and 42.8 months in the NCOG trial (p = 0.126). Univariate results showed consistent results favoring BrdU among patients over 30 years of age, across the extent of surgery, and for GBM patients. A proportional hazards regression model that included treatment, histopathology, KPS, age, and extent of surgery demonstrated that treatment with BrdU was included in the best model only for the GBM group of patients (risk ratio 0.83). CONCLUSIONS: Because of the heterogeneity of the treatment groups, including potentially important differences in pathology reviewers assessment of nonglioblastoma cases, differences in radiation dose and schedules, and chemotherapy during or after radiation, these analyses cannot provide the definitive answer as to whether BrdU given during radiation therapy improves survival in patients with malignant glioma. There does appear to be a favorable treatment effect seen in patients with GBM, with a lesser effect in patients with AA.     

ATM: from gene to function

The identification of ATM , the gene responsible for the pleiotropic recessive disease ataxia telangiectasia, has initiated extensive research to determine the functions of its multifaceted protein product. The ATM protein belongs to a family of protein kinases that share similarities at their C-terminal region with the catalytic domain of phosphatidylinositol 3-kinases. Studies with ataxia telangiectasia (A-T) cells and Atm-deficient mice have shown that ATM is a key regulator of multiple signaling cascades which respond to DNA strand breaks induced by damaging agents or by normal processes, such as meiotic or V(D)J recombination. These responses involve the activation of cell cycle checkpoints, DNA repair and apoptosis. Other roles outside the cell nucleus might be carried out by the cytoplasmic fraction of ATM. In addition, ATM appears to function as a 'caretaker', suppressing tumorigenesis in specific T cell lineages.     

Counting information: A note on physicalized numbers

Existing work on the ultimate limits of computation has urged that the apparatus of real numbers should be eschewed as an investigative tool and replaced by discrete mathematics. The present paper argues for a radical extension of this viewpoint: not only the continuum but all infinitary constructs including the rationals and the potential infinite sequence of whole numbers need to be eliminated if a self-consistent investigative framework is to be achieved.