971 resultados para Average rate


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Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.

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Climate change will influence the living conditions of all life on Earth. For some species the change in the environmental conditions that has occurred so far has already increased the risk of extinction, and the extinction risk is predicted to increase for large numbers of species in the future. Some species may have time to adapt to the changing environmental conditions, but the rate and magnitude of the change are too great to allow many species to survive via evolutionary changes. Species responses to climate change have been documented for some decades. Some groups of species, like many insects, respond readily to changes in temperature conditions and have shifted their distributions northwards to new climatically suitable regions. Such range shifts have been well documented especially in temperate zones. In this context, butterflies have been studied more than any other group of species, partly for the reason that their past geographical ranges are well documented, which facilitates species-climate modelling and other analyses. The aim of the modelling studies is to examine to what extent shifts in species distributions can be explained by climatic and other factors. Models can also be used to predict the future distributions of species. In this thesis, I have studied the response to climate change of one species of butterfly within one geographically restricted area. The study species, the European map butterfly (Araschnia levana), has expanded rapidly northwards in Finland during the last two decades. I used statistical and dynamic modelling approaches in combination with field studies to analyse the effects of climate warming and landscape structure on the expansion. I studied possible role of molecular variation in phosphoglucose isomerase (PGI), a glycolytic enzyme affecting flight metabolism and thereby flight performance, in the observed expansion of the map butterfly at two separate expansion fronts in Finland. The expansion rate of the map butterfly was shown to be correlated with the frequency of warmer than average summers during the study period. The result is in line with the greater probability of occurrence of the second generation during warm summers and previous results on this species showing greater mobility of the second than first generation individuals. The results of a field study in this thesis indicated low mobility of the first generation butterflies. Climatic variables alone were not sufficient to explain the observed expansion in Finland. There are also problems in transferring the climate model to new regions from the ones from which data were available to construct the model. The climate model predicted a wider distribution in the south-western part of Finland than what has been observed. Dynamic modelling of the expansion in response to landscape structure suggested that habitat and landscape structure influence the rate of expansion. In southern Finland the landscape structure may have slowed down the expansion rate. The results on PGI suggested that allelic variation in this enzyme may influence flight performance and thereby the rate of expansion. Genetic differences of the populations at the two expansion fronts may explain at least partly the observed differences in the rate of expansion. Individuals with the genotype associated with high flight metabolic rate were most frequent in eastern Finland, where the rate of range expansion has been highest.

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Dispersal is a highly important life history trait. In fragmented landscapes the long-term persistence of populations depends on dispersal. Evolution of dispersal is affected by costs and benefits and these may differ between different landscapes. This results in differences in the strength and direction of natural selection on dispersal in fragmented landscapes. Dispersal has been shown to be a nonrandom process that is associated with traits such as flight ability in insects. This thesis examines genetic and physiological traits affecting dispersal in the Glanville fritillary butterfly (Melitaea cinxia). Flight metabolic rate is a repeatable trait representing flight ability. Unlike in many vertebrates, resting metabolic rate cannot be used as a surrogate of maximum metabolic rate as no strong correlation between the two was found in the Glanville fritillary. Resting and flight metabolic rate are affected by environmental variables, most notably temperature. However, only flight metabolic rate has a strong genetic component. Molecular variation in the much-studied candidate locus phosphoglucose isomerase (Pgi), which encodes the glycolytic enzyme PGI, has an effect on carbohydrate metabolism in flight. This effect is temperature dependent: in low to moderate temperatures individuals with the heterozygous genotype at the single nucleotide polymorphism (SNP) AA111 have higher flight metabolic rate than the common homozygous genotype. At high temperatures the situation is reversed. This finding suggests that variation in enzyme properties is indeed translated to organismal performance. High-resolution data on individual female Glanville fritillaries moving freely in the field were recorded using harmonic radar. There was a strong positive correlation between flight metabolic rate and dispersal rate. Flight metabolic rate explained one third of the observed variation in the one-hour movement distance. A fine-scaled analysis of mobility showed that mobility peaked at intermediate ambient temperatures but the two common Pgi genotypes differed in their reaction norms to temperature. As with flight metabolic rate, heterozygotes at SNP AA111 were the most active genotype in low to moderate temperatures. The results show that molecular variation is associated with variation in dispersal rate through the link of flight physiology under the influence of environmental conditions. The evolutionary pressures for dispersal differ between males and females. The effect of flight metabolic rate on dispersal was examined in both sexes in field and laboratory conditions. The relationship between flight metabolic rate and dispersal rate in the field and flight duration in the laboratory were found to differ between the two sexes. In females the relationship was positive, but in males the longest distances and flight durations were recorded for individuals with low flight metabolic rate. These findings may reflect male investment in mate locating. Instead of dispersing, males with high flight metabolic rate may establish territories and follow a perching strategy when locating females and hence move less on the landscape level. Males with low metabolic rate may be forced to disperse due to low competitive success or may show adaptations to an alternative strategy: patrolling. In the light of life history trade-offs and the rate of living theory having high metabolic rate may carry a cost in the form of shortened lifespan. Experiments relating flight metabolic rate to longevity showed a clear correlation in the opposite direction: high flight metabolic rate was associated with long lifespan. This suggests that individuals with high metabolic rate do not pay an extra physiological cost for their high flight capacity, rather there are positive correlations between different measures of fitness. These results highlight the importance of condition.

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In this paper, we present the design and characterization of a vibratory yaw rate MEMS sensor that uses in-plane motion for both actuation and sensing. The design criterion for the rate sensor is based on a high sensitivity and low bandwidth. The required sensitivity of the yawrate sensor is attained by using the inplane motion in which the dominant damping mechanism is the fluid loss due to slide film damping i.e. two-three orders of magnitude less than the squeeze-film damping in other rate sensors with out-of-plane motion. The low bandwidth is achieved by matching the drive and the sense mode frequencies. Based on these factors, the yaw rate sensor is designed and finally realized using surface micromachining. The inplane motion of the sensor is experimentally characterized to determine the sense and the drive mode frequencies, and corresponding damping ratios. It is found that the experimental results match well with the numerical and the analytical models with less than 5% error in frequencies measurements. The measured quality factor of the sensor is approximately 467, which is two orders of magnitude higher than that for a similar rate sensor with out-of-plane sense direction.

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In this paper we give the performance of MQAM OFDM based WLAN in presence of single and multiple channels Zigbee interference. An analytical model for getting symbol error rate (SER) in presence of single and multiple channel Zigbee interference in AWGN and Rayleigh fading channel for MQAM OFDM system is given. Simulation results are compared with analytical symbol error rate (SER) of the MQAM-OFDM system. For analysis we have modeled the Zigbee interference using the power spectral density (PSD) of OQPSK modulation and finding the average interference power for each sub-carrier of the OFDM system. Then we have averaged the SER over all WLAN sub-carriers. Simulations closely match with the analytical models. It is seen from simulation and analytical results that performance of WLAN is severely affected by Zigbee interference. Symbol error rate (SER) for 16QAM and 64QAM OFDM system is of order of 10(-2) for SIR (signal to interference ratio) of 20dB and 30dB respectively in presence of single Zigbee interferer inside the WLAN frequency band for Rayleigh fading channel. For SIR values more than 30dB and 40dB the SER approaches the SER without interference for 16QAM and 64QAM OFDM system respectively.

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Mutation and recombination are the fundamental processes leading to genetic variation in natural populations. This variation forms the raw material for evolution through natural selection and drift. Therefore, studying mutation rates may reveal information about evolutionary histories as well as phylogenetic interrelationships of organisms. In this thesis two molecular tools, DNA barcoding and the molecular clock were examined. In the first part, the efficiency of mutations to delineate closely related species was tested and the implications for conservation practices were assessed. The second part investigated the proposition that a constant mutation rate exists within invertebrates, in form of a metabolic-rate dependent molecular clock, which can be applied to accurately date speciation events. DNA barcoding aspires to be an efficient technique to not only distinguish between species but also reveal population-level variation solely relying on mutations found on a short stretch of a single gene. In this thesis barcoding was applied to discriminate between Hylochares populations from Russian Karelia and new Hylochares findings from the greater Helsinki region in Finland. Although barcoding failed to delineate the two reproductively isolated groups, their distinct morphological features and differing life-history traits led to their classification as two closely related, although separate species. The lack of genetic differentiation appears to be due to a recent divergence event not yet reflected in the beetles molecular make-up. Thus, the Russian Hylochares was described as a new species. The Finnish species, previously considered as locally extinct, was recognized as endangered. Even if, due to their identical genetic make-up, the populations had been regarded as conspecific, conservation strategies based on prior knowledge from Russia would not have guaranteed the survival of the Finnish beetle. Therefore, new conservation actions based on detailed studies of the biology and life-history of the Finnish Hylochares were conducted to protect this endemic rarity in Finland. The idea behind the strict molecular clock is that mutation rates are constant over evolutionary time and may thus be used to infer species divergence dates. However, one of the most recent theories argues that a strict clock does not tick per unit of time but that it has a constant substitution rate per unit of mass-specific metabolic energy. Therefore, according to this hypothesis, molecular clocks have to be recalibrated taking body size and temperature into account. This thesis tested the temperature effect on mutation rates in equally sized invertebrates. For the first dataset (family Eucnemidae, Coleoptera) the phylogenetic interrelationships and evolutionary history of the genus Arrhipis had to be inferred before the influence of temperature on substitution rates could be studied. Further, a second, larger invertebrate dataset (family Syrphidae, Diptera) was employed. Several methodological approaches, a number of genes and multiple molecular clock models revealed that there was no consistent relationship between temperature and mutation rate for the taxa under study. Thus, the body size effect, observed in vertebrates but controversial for invertebrates, rather than temperature may be the underlying driving force behind the metabolic-rate dependent molecular clock. Therefore, the metabolic-rate dependent molecular clock does not hold for the here studied invertebrate groups. This thesis emphasizes that molecular techniques relying on mutation rates have to be applied with caution. Whereas they may work satisfactorily under certain conditions for specific taxa, they may fail for others. The molecular clock as well as DNA barcoding should incorporate all the information and data available to obtain comprehensive estimations of the existing biodiversity and its evolutionary history.

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A vibration isolator is described which incorporates a near-zero-spring-rate device within its operating range. The device is an assembly of a vertical spring in parallel with two inclined springs. A low spring rate is achieved by combining the equivalent stiffness in the vertical direction of the inclined springs with the stiffness of the vertical central spring. It is shown that there is a relation between the geometry and the stiffness of the individual springs that results in a low spring rate. Computer simulation studies of a single-degree-of-freedom model for harmonic base input show that the performance of the proposed scheme is superior to that of the passive schemes with linear springs and skyhook damping configuration. The response curves show that, for small to large amplitudes of base disturbance, the system goes into resonance at low frequencies of excitation. Thus, it is possible to achieve very good isolation over a wide low-frequency band. Also, the damper force requirements for the proposed scheme are much lower than for the damper force of a skyhook configuration or a conventional linear spring with a semi-active damper.

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The first aim of the current study was to evaluate the survival of total hip arthroplasty (THA) in patients aged 55 years and older on a nation-wide level. The second aim was to evaluate, on a nation wide-basis, the geographical variation of the incidence of primary THA for primary OA and also to identify those variables that are possibly associated with this variation. The third aim was to evaluate the effects of hospital volume: on the length of stay, on the numbers of re-admissions and on the numbers of complications of THR on population-based level in Finland. The survival of implants was analysed based on data from the Finnish Arthroplasty Register. The incidence and hospital volume data were obtained from the Hospital Discharge Register. Cementless total hip replacements had a significantly reduced risk of revision for aseptic loosening compared with cemented hip replacements. When revision for any reason was the end point in the survival analyses, there were no significant differences found between the groups. Adjusted incidence ratios of THA varied from 1.9- to 3.0-fold during the study period. Neither the average income within a region nor the morbidity index was associated with the incidence of THA. For the four categories of volume of total hip replacements performed per hospital, the length of the surgical treatment period was shorter for the highest volume group than for the lowest volume group. The odds ratio for dislocations was significantly lower in the high volume group than in the low volume group. In patients who were 55 years of age or older, the survival of cementless total hip replacements was as good as that of the cemented replacements. However, multiple wear-related revisions of the cementless cups indicate that excessive polyethylene wear was a major clinical problem with modular cementless cups. The variation in the long-term rates of survival for different cemented stems was considerable. Cementless proximal porous-coated stems were found to be a good option for elderly patients. When hip surgery was performed on with a large repertoire, the indications to perform THAs due to primary OA were tight. Socio-economic status of the patient had no apparent effect on THA rate. Specialization of hip replacements in high volume hospitals should reduce costs by significantly shortening the length of stay, and may reduce the dislocation rate.

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This paper deals with low maximum-likelihood (ML)-decoding complexity, full-rate and full-diversity space-time block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna (2 x 2) and the 4 transmit antenna, 2 receive antenna (4 x 2) MIMO systems. Presently, the best known STBC for the 2 2 system is the Golden code and that for the 4 x 2 system is the DjABBA code. Following the approach by Biglieri, Hong, and Viterbo, a new STBC is presented in this paper for the 2 x 2 system. This code matches the Golden code in performance and ML-decoding complexity for square QAM constellations while it has lower ML-decoding complexity with the same performance for non-rectangular QAM constellations. This code is also shown to be information-lossless and diversity-multiplexing gain (DMG) tradeoff optimal. This design procedure is then extended to the 4 x 2 system and a code, which outperforms the DjABBA code for QAM constellations with lower ML-decoding complexity, is presented. So far, the Golden code has been reported to have an ML-decoding complexity of the order of for square QAM of size. In this paper, a scheme that reduces its ML-decoding complexity to M-2 root M is presented.

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In this paper, we present a low-complexity algorithm for detection in high-rate, non-orthogonal space-time block coded (STBC) large-multiple-input multiple-output (MIMO) systems that achieve high spectral efficiencies of the order of tens of bps/Hz. We also present a training-based iterative detection/channel estimation scheme for such large STBC MIMO systems. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed multistage likelihood ascent search (M-LAS) detector in conjunction with the proposed iterative detection/channel estimation scheme at low complexities. The fact that we could show such good results for large STBCs like 16 X 16 and 32 X 32 STBCs from Cyclic Division Algebras (CDA) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot based training for channel estimation and turbo coding) establishes the effectiveness of the proposed detector and channel estimator. We decode perfect codes of large dimensions using the proposed detector. With the feasibility of such a low-complexity detection/channel estimation scheme, large-MIMO systems with tens of antennas operating at several tens of bps/Hz spectral efficiencies can become practical, enabling interesting high data rate wireless applications.

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Introduction: The epidemic of obesity has been accompanied by an increase in the prevalence of the metabolic syndrome, type 2 diabetes, and non-alcoholic fatty liver disease (NAFLD). However, not all obese subjects develop these metabolic abnormalities. Hepatic fat accumulation is related to hepatic insulin resistance, which in turn leads to hyperglycemia, hypertriglyceridemia, and a low HDL cholesterol con-centration. The present studies aimed to investigate 1) how intrahepatic as compared to intramyocellular fat is related to insulin resistance in these tissues and to the metabolic syndrome (Study I); 2) the amount of liver fat in subjects with and without the metabolic syndrome, and which clinically available markers best reflect liver fat content (Study II); 3) the effect of liver fat on insulin clearance (Study III); 4) whether type 2 diabetic patients have more liver fat than age-, gender-, and BMI-matched non-diabetic subjects (Study IV); 5) how type 2 diabetic patients using exceptionally high doses of insulin respond to addition of a PPARγ agonist (Study V). Subjects and methods: The study groups consisted of 45 (Study I), 271 (Study II), and 80 (Study III) non-diabetic subjects, and of 70 type 2 diabetic patients and 70 matched control subjects (Study IV). In Study V, a total of 14 poorly controlled type 2 diabetic patients treated with high doses of insulin were studied before and after rosiglitazone treatment (8 mg/day) for 8 months. In all studies, liver fat content was measured by proton magnetic resonance spectroscopy, and sub-cutaneous and intra-abdominal fat content by MRI. In addition, circulating markers of insulin resistance and serum liver enzyme concentrations were determined. Hepatic (i.v. insulin infusion rate 0.3 mU/kg∙min combined with [3-3H]glucose, Studies I, III, and V) and muscle (1.0 mU/kg min, Study I) insulin sensitivities were measured by the euglycemic hyperinsulinemic clamp technique. Results: Fat accumulation in the liver rather than in skeletal muscle was associated with features of insulin resistance, i.e. increased fasting serum (fS) triglycerides and decreased fS-HDL cholesterol, and with hyperinsulinemia and low adiponectin concentrations (Study I). Liver fat content was 4-fold higher in subjects with as compared to those without the metabolic syndrome, independent of age, gender, and BMI. FS-C-peptide was the best correlate of liver fat (Study II). Increased liver fat was associated with both impaired insulin clearance and hepatic insulin resistance independent of age, gender, and BMI (Study III). Type 2 diabetic patients had 80% more liver fat than age-, weight-, and gender-matched non-diabetic subjects. At any given liver fat content, S-ALT underestimated liver fat in the type 2 diabetic patients as compared to the non-diabetic subjects (Study IV). In Study V, hepatic insulin sensitivity increased and glycemic control improved significantly during rosiglitazone treatment. This was associated with lowering of liver fat (on the average by 46%) and insulin requirements (40%). Conclusions: Liver fat is increased both in the metabolic syndrome and type 2 diabetes independent of age, gender, and BMI. A fatty liver is associated with both hepatic insulin resistance and impaired insulin clearance. Rosi-glitazone may be particularly effective in type 2 diabetic patients who are poorly controlled despite using high insulin doses.

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Tavoitteena oli tutkia 40-vuotiaiden miesten terveyskäyttäytymistä, terveysuskomuksia ja miesten saamaa terveysneuvontaa Helsingissä. 273 miestä vastasi kyselyyn ja osallistui terveystutkimuksiin. Terveydentilan perusteella miehet arvioitiin matalan (n=145) ja korkean (n=128) riskin ryhmiin. Khin neliö-testillä tutkittiin elämäntapa- ja riskitekijöitä koetun terveyden (hyvä, keskinkertainen/huono) luokissa ja verrattiin matalan ja korkean riskin ryhmiä em. tekijöiden osalta. Askeltavalla logistisella regressiomallilla analysoitiin tulosmuuttujia taustatekijöiden, terveyskäyttäytymisen, terveysuskomusten ja kliinisten riskitekijöiden avulla sekä arvioitiin oireiden ja vaivojen suhdetta koettuun terveydentilaan. Korkeassa riskissä olevien terveyttä seurattiin vuosina 2001–2004 analysoimalla mini-intervention vaikutusta terveysriskeihin ja elintapoihin varianssianalyysin avulla (ANOVA) (n=46). Matalasta vastausprosentista johtuen (39.6%), ei-vastanneiden aineistoa kerättiin käyttämällä syvähaastattelua (n=28) sekä puhelinkyselyä (n=40). Lopullinen aineisto koostui 341 miehestä. Tulokset osoittivat, että miehillä oli sydän- ja verisuonitautiriskejä. Kaksi kolmesta osallistuneista oli ylipainoisia tai lihavia, yli kolmanneksella vyötärönympärys oli ≥100 cm, ja yli 40%:llä oli diastolinen verenpaine ≥90 mmHg. Yli puolet tupakoi päivittäin ja 40% käytti alkoholia runsaasti. Ristiriitaisuutta ilmensi se, että huolimatta riskitekijöistä noin puolet miehistä koki terveydentilansa hyväksi. Sairauden tai vamman puute, hyvä suun terveydentila ja normaali vyötärönympärys olivat yhteydessä hyväksi koettuun terveydentilaan. Suora yhteys voitiin havaita omaisten tarjoaman neuvonnan ja vähäisen alkoholin käytön välillä. Masennus ja unettomuus olivat voimakkaasti yhteydessä loppuun palamiseen. Miehillä oli erilaisia fyysisiä ja psyykkisiä oireita, jotka korreloivat voimakkaasti masennuksen kanssa. Pieni määrä miehistä koki saaneensa terveysneuvontaa hoitohenkilökunnalta verrattuna perheenjäseniltä saatuun ohjaukseen. Korkeariskisten miesten (n=46) arvot parantuivat merkitsevästi lyhyellä aikavälillä. Kolesteroliarvoja lukuunottamatta ne palautuivat kolmen vuoden kuluttua alkumittausarvoja kohti. Laadullinen tutkimus osoitti, että “ei-vastanneet“ eivät osallistuneet projektiin, sillä he olivat oireettomia tai kiireisiä. Heillä todettiin samoja terveysriskejä kuin projektiin osallistuneilla. Syvähaastattelussa miehet toivat esille kokemuksiaan huolista, vihan tunteista, peloista ja yksinäisyydestä. Hoidonantajien on tärkeää ymmärtää ristiriidat miesten subjektiivisen ja objektiivisen terveydentilan välillä, mikä auttaa havaitsemaan esteitä terveyskäyttäytymiselle. Yhä enemmän tarvitaan yhteistyötä yksityisen ja julkisen terveydenhuollon välillä varmistamaan terveystottumusten jatkuminen miesten keskuudessa.

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Background and aims. Since 1999, hospitals in the Finnish Hospital Infection Program (SIRO) have reported data on surgical site infections (SSI) following major hip and knee surgery. The purpose of this study was to obtain detailed information to support prevention efforts by analyzing SIRO data on SSIs, to evaluate possible factors affecting the surveillance results, and to assess the disease burden of postoperative prosthetic joint infections in Finland. Methods. Procedures under surveillance included total hip (THA) and total knee arthroplasties (TKA), and the open reduction and internal fixation (ORIF) of femur fractures. Hospitals prospectively collected data using common definitions and written protocol, and also performed postdischarge surveillance. In the validation study, a blinded retrospective chart review was performed and infection control nurses were interviewed. Patient charts of deep incisional and organ/space SSIs were reviewed, and data from three sources (SIRO, the Finnish Arthroplasty Register, and the Finnish Patient Insurance Centre) were linked for capture-recapture analyses. Results. During 1999-2002, the overall SSI rate was 3.3% after 11,812 orthopedic procedures (median length of stay, eight days). Of all SSIs, 56% were detected after discharge. The majority of deep incisional and organ/space SSIs (65/108, 60%) were detected on readmission. Positive and negative predictive values, sensitivity, and specificity for SIRO surveillance were 94% (95% CI, 89-99%), 99% (99-100%), 75% (56-93%), and 100% (97-100%), respectively. Of the 9,831 total joint replacements performed during 2001-2004, 7.2% (THA 5.2% and TKA 9.9%) of the implants were inserted in a simultaneous bilateral operation. Patients who underwent bilateral operations were younger, healthier, and more often males than those who underwent unilateral procedures. The rates of deep SSIs or mortality did not differ between bi- and uni-lateral THAs or TKAs. Four deep SSIs were reported following bilateral operations (antimicrobial prophylaxis administered 48-218 minutes before incision). In the three registers, altogether 129 prosthetic joint infections were identified after 13,482 THA and TKA during 1999-2004. After correction with the positive predictive value of SIRO (91%), a log-linear model provided an estimated overall prosthetic joint infection rate of 1.6% after THA and 1.3% after TKA. The sensitivity of the SIRO surveillance ranged from 36% to 57%. According to the estimation, nearly 200 prosthetic joint infections could occur in Finland each year (the average from 1999 to 2004) after THA and TKA. Conclusions. Postdischarge surveillance had a major impact on SSI rates after major hip and knee surgery. A minority of deep incisional and organ/space SSIs would be missed, however, if postdischarge surveillance by questionnaire was not performed. According to the validation study, most SSIs reported to SIRO were true infections. Some SSIs were missed, revealing some weakness in case finding. Variation in diagnostic practices may also affect SSI rates. No differences were found in deep SSI rates or mortality between bi- and unilateral THA and TKA. However, patient materials between these two groups differed. Bilateral operations require specific attention paid to their antimicrobial prophylaxis as well as to data management in the surveillance database. The true disease burden of prosthetic joint infections may be heavier than the rates from national nosocomial surveillance systems usually suggest.

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In secondary steelmaking, the enhancement of the reaction rate in the low carbon period during the decarburization of steel is considered the most effective method to produce ultralow carbon steel. In a previous study, it was revealed that the surface reaction is dominant during the final stage of the actual refining process. In order to improve the surface reaction rate, it is necessary to enlarge the reaction region, which is usually achieved by increasing the plume eye area. In this study, water model experiments were carried out to estimate the influence of bottom stirring conditions on the gas-liquid reaction rate; for this purpose, the deoxidation rate during the bottom bubbling process was measured. Five types of nozzle configurations were used to study the effect of the plume eye area on the reaction rate at various gas flow rates. The results reveal that the surface reaction rate is influenced by the gas flow rate and the plume eye area. An empirical correlation was developed for the reaction rate and the plume eye area. This correlation was applied to estimate the gas-liquid reaction rate mat the bath surface.