On Weak Tractability of the Clenshaw-Curtis Smolyak Algorithm

We consider the problem of integration of d-variate analytic functions defined on the unit cube with directional derivatives of all orders bounded by 1. We prove that the Clenshaw Curtis Smolyak algorithm leads to weak tractability of the problem. This seems to be the first positive tractability result for the Smolyak algorithm for a normalized and unweighted problem. The space of integrands is not a tensor product space and therefore we have to develop a different proof technique. We use the polynomial exactness of the algorithm as well as an explicit bound on the operator norm of the algorithm.Comment: 18 page

Bone Traumas in Late Antique Populations from Croatia

We present the results of the analyses of traumatic bone injuries in two Late Antique (3rd to 5th century AD) skeletal samples from Croatia: Zadar – located on the eastern Adriatic coast, and a composite skeletal series from continental Croatia consisting of skeletons from Osijek, Vinkovci, [trbinci, and Zmajevac. The osteological series from continental Croatia are related to settlements located on, or near the Danubian military border, while Zadar – 350 km to the west, is located deep in the territory of the Roman Empire. Numerous historical sources describe barbaric incursions, as well as large battles related to civil wars during the Late Antique period in continental Croatia. Conversely, there is no mention of similar events in the Zadar region. In accordance with these data our analysis tests the hypothesis that the inhabitants of continental Croatia were exposed to greater levels of violence than those living in Zadar. Analysis of bone traumas in the two series shows a similar, relatively high prevalence of long bone fractures in both samples, with a slightly higher frequency recorded in Zadar. Both series exhibit a high frequency of cranial injuries with, once again, higher frequencies recorded in the Zadar series. Additionally, two perimortem cranial fractures (one caused by a sword, the other by a blunt object) were observed in Zadar. Some of the recorded traumas in both samples resulted from accidents, but a number of injuries clearly resulted from intentional violence of lesser intensity. Further multidisciplinary research incorporating osteological, archaeological, and historical analyses is necessary to confirm the results obtained from these samples

Sex Assessment Using the Femur and Tibia in Medieval Skeletal Remains from Ireland: Discriminant Function Analysis

Sex determination based on discriminant function analysis of skeletal measurements is probably the most effective method for assessment of sex in archaeological and contemporary populations due to various reasons, but it also suffers from limitations such as population specificity. In this paper standards for sex assessment from the femur and tibia in the medieval Irish population are presented. Six femoral and six tibial measurements obtained from 56 male and 45 female skeletons were subjected to discriminant function analysis. Average accuracies obtained by this study range between 87.1 and 97%. The highest level of accuracy (97%) was achieved when using combined variables of the femur and tibia (maximum diameter of femoral head and circumference at tibial nutrient foramen), as well as two variables of the tibia (proximal epiphyseal breadth and circumference at nutrient foramen). Discriminant functions using a single variable provided accuracies between 87.1 and 96% with the circumference at the level of the tibial nutrient foramen providing the best separation. High accuracy rates obtained by this research correspond to the data recorded in other studies thus confirming the importance of discriminant function analysis in assessment of sex in both archaeological and forensic contexts

Subadult Stress in the Medieval and Early Modern Populations of Continental Croatia

Svrha rada jest analiza učestalosti i distribucije dva pokazatelja subadultnog stresa (cribrae orbitaliae i hipoplazije zubne cakline), njihove međusobne korelacije i njihova odnosa s pokazateljem nespecifičnih zaraznih bolesti – periostitisom. U radu je analizirano 415 kostura iz kontinentalne Hrvatske, s nalazišta Crkvari, Ivanec, Mala Črešnjevica, Prozorje, Nova Rača, Suhopolje, Tomaš i Torčec, koja se datiraju u srednji i novi vijek (12.-18. st.). U analiziranom uzorku muškarci su živjeli značajno duže od žena (37,2 prema 33,6 godina). Učestalost cribrae orbitaliae u ukupnom uzorku iznosi 37,2%. Djeca pokazuju statistički značajno višu učestalost cribrae orbitaliae od odraslih osoba, a poremećaj je nešto češći kod žena nego kod muškaraca. Odrasle osobe kod kojih je uočena cribra orbitalia u prosjeku žive 6,5 godina kraće od osoba kod kojih ovaj poremećaj nije prisutan. Učestalost hipoplazije zubne cakline u analiziranom uzorku iznosi 44,6%, a nešto viša učestalost zabilježena je kod žena na svim analiziranim zubima. Učestalost nespecifičnog periostitisa iznosi 48,4% s nešto višom učestalošću kod žena u odnosu na muškarce. Značajna pozitivna korelacija između cribrae orbitaliae i nespecifičnog periostitisa prisutna je na razini čitavog uzorka. Znatno kraći životni vijek, viša učestalost cribrae orbitaliae, hipoplazije zubne cakline i periostitisa kod žena sugerira da su žene bile sklonije epizodama biološkog stresa, što može biti posljedica smanjenih zaliha željeza kod žena kao rezultat reproduktivnih funkcija ili lošijeg tretmana djevojčica, posebice tijekom najranijeg djetinjstva (tijekom dojenja). Skeletni uzorak, analiziran u ovom radu, odlikuje se lošim životnim uvjetima i niskim zdravstvenim standardom koji je najvjerojatnije bio posljedica sinergističkog djelovanja anemije izazvane nedostatkom željeza, zaraznih bolesti, neodgovarajuće prehrane i parazitskih infekcija.The purpose of this paper is to analyze the frequency and distribution of two indicators of subadult stress (cribra orbitalia and enamel hypoplasia), their correlation and their relationship with an indicator of non-specific infectious diseases – periostitis. The paper contains an analysis of 415 skeletons from continental Croatia, from the sites of Crkvari, Ivanec, Mala Črešnjevica, Prozorje, Nova Rača, Suhopolje, Tomaš and Torčec, dated to the Middle Ages and the Early Modern period (12th-18th cent.). Males in the analyzed sample lived significantly longer than females (37.2 vs. 33.6 years). The frequency of cribra orbitalia in the total sample is 37.2%. The frequency of cribra orbitalia in subadults is significantly higher than in adults, and females are affected somewhat more frequently than males. Adults that exhibited cribra orbitalia lived 6.5 years shorter on the average than the individuals without this disorder. The frequency of dental enamel hypoplasia in the analyzed sample is 44.6%, with a somewhat higher frequency registered in females on all analyzed teeth. The frequency of non-specific periostitis is 48.4%, with a somewhat higher frequency in females than in males. A significant positive correlation between cribra orbitalia and non-specific periostitis is present at the level of the entire sample. A significantly shorter life span, a higher frequency of cribra orbitalia, enamel hypoplasia and periostitis in females suggests that females were more prone to the episodes of biological stress, which may have been a consequence of diminished stocks of iron in females as a result of their reproductive function or poorer treatment of young girls, particularly during earliest childhood (during breastfeeding). The skeletal sample analyzed in this paper is characterized by poor living conditions and low health standard, which was most likely a consequence of a synergic action of iron deficiency anemia, infectious diseases, inadequate diet and parasitical infections