This essay considers a mode of thought and a tradition of composition inculcated by four Latin writers, the translator of Anatolius of Laodicea’s De ratione paschali (post ad 283, ante ad 402), Evagrius of Antioch’s translation of Athanasius’s Life of Saint Antony (c ad 360–74), Jerome’s Biblia Vulgata (ad 382) and Sulpicius Severus’s Vita Sancti Martini (ad 397), based upon the Life of Antony, and his latercus (ad 410), based upon the work of Anatolius, all texts known in these islands during the period from ad 410–25 to the seventh century. A simple calculus of literary composition in the anonymous Lindisfarne Life of Saint Cuthbert, dedicated to Eadfrith bishop of Lindisfarne in ad 698, is exhibited in the iconographic elements of the Evangelists’ portraits in the Lindisfarne Gospels, written and illuminated by Eadfrith. The same calculus is displayed both in the iconographic designs and in the inscriptions in Northumbrian Old English and Latin on the Franks Casket of c ad 700 and on the Ruthwell Cross of c ad 730–5.

Calculus removed from the molar teeth of four American mastodons (Mammut americanum) contained opal phytoliths which reflect major dietary components. Three samples contained abundant grass phytoliths (ca. 86% of total), with long cells and trapezoidal pooid short cells dominant (ca. 25 and 31%, respectively). Dicot phytoliths from hackberry (Celtis sp.) seeds and indeterminate deciduous trees were rare (1–3%), though well preserved, whereas phytoliths from conifer trees were not recognizable in any of the samples. Comparative analysis of calculus from modern and fossil browsers and mixed feeders implies that dicots and conifers are nearly invisible in the phytolith record. This scarcity may result from poor preservation, low silica production in woody taxa, and/or animals' selection of young, silica-poor leaves and shoots. However, abundant grass phytoliths in the mixed feeders suggest that presence versus absence of grass phytoliths may distinguish mixed feeders and grazers from browsers. Mastodons are traditionally considered browsers, but grass phytolith assemblages in three individual mastodons contained similarly high concentrations of pooids, suggesting that these grasses were a significant part of the diet. Abundant pooid phytoliths, in addition to diatoms, indicate that these mastodons grazed in a cool, moist late Pleistocene environment, possibly near water.

The paper describes a novel means of performing calculus operations on poorly understood engineering functions using networks of radial Gaussian neurons. The network architecture and training algorithm used for this purpose is described briefly. Once trained, a network can be converted into a form that provides the differential or integral of the learned function, by a simple substitution of the type of activation function used at the hidden neurons. A range of substitute activation functions, for conversion to first- and second-order partial differential and integral forms of the network, are derived. Following this, the technique is tested on a selection of calculus operations for two example civil engineering problems: assessing motion in tall structures; and modeling moisture penetration in porous materials. The converted networks produced in these experiments provide accurate models of the actual differentials and integrals of the function the original networks had been taught. A method of improving the accuracy of results by training the original network beyond the region in which the converted networks operate, is described. The paper concludes by identifying some areas for further development of the technique.

Extracorporeal shock wave lithotripsy is a rather new therapeutical method in the treatment of sialolithiasis. The objective was to evaluate retrospectively the results of the extracorporeal shock wave lithotripsy therapy performed with a Minilith SL 1 lithotripter on 167 out-patients with symptomatic stones (average size 5.94 mm) of the salivary glands over an observation period of seven years. A successful treatment with total stone disintegration was achieved in 51 (31 per cent) patients. In 92 (55 per cent) patients treatment was partially successful, with disappearance of the symptoms but a sonographically still identifiable stone. Treatment failure occurred in 24 (14 per cent) patients who then underwent surgery. The mean follow-up period was 35.6 months (minimum three, maximum 83), after which 83.2 per cent of the initially successfully treated patients were still free of symptoms.Therefore, extracorporeal shock wave lithotripsy, as a non-invasive treatment alternative with few side effects, is an efficient technique for the therapy of sialolithiasis in selected patients.

Treatment of salivary stones includes both surgical and non-surgical techniques. Surgical approaches range from excision of the sialolith, for those near the duct orifice, to removal of the affected salivary gland and its associated duct, for stones near the hilum of the gland. We present a case of two sialoliths triggering an acute infection in a residual Wharton's duct, 12 years after the removal of the associated submandibular gland. Excision of the sialoliths and treatment of the infected duct via sialodochoplasty was successfully performed in this patient. If the Wharton's duct is not removed with the associated submandibular gland, the potential for infection and continuous growth of dormant calcifications exists. We also address the aetiology, pathogenesis, and management of patients with sialolithiasis in the absence of a major salivary gland.

Perinephric abscesses often present with flank pain and signs of sepsis, and are known to discharge to the skin. We report a case of a young patient presenting with a 48-hour history of painful swelling in her right renal angle following a urinary tract infection and no overt signs or symptoms of sepsis. Plain abdominal films showed a perinephric abscess secondary to a staghorn calculus in the upper pole of the right kidney. On incision and drainage, 700 mL of pus was drained freely. The patient recovered well but required partial nephrectomy.

Subcutaneous abscess as a result of intra-abdominal pathology is a recognized but rare complication. This case illustrates that subcutaneous abscesses may have underlying intra-abdominal pathology without overt signs of sepsis.

For constant linear systems we are introducing integral reconstructors and generalized proportional-integral controllers, which permit to bypass the derivative term in the classic PID controllers and more generally the usual asymptotic observers. Our approach, which is mainly of algebraic flavour, is based on the module-theoretic framework for linear systems and on operational calculus in Mikusiński's setting. Several examples are discussed.