Best N Term Approximation Spaces for Tensor Product Wavelet Bases

We consider best N term approximation using anisotropic tensor product wavelet bases ("sparse grids"). We introduce a tensor product structure ⊗q on certain quasi-Banach spaces. We prove that the approximation spaces Aαq(L2) and Aαq(H1) equal tensor products of Besov spaces Bαq(Lq), e.g., Aαq(L2([0,1]d)) = Bαq(Lq([0,1])) ⊗q · ⊗q Bαq · ·(Lq([0,1])). Solutions to elliptic partial differential equations on polygonal/polyhedral domains belong to these new scales of Besov space

Preliminary Analysis of Quality of Contour Lines Using Smoothing Algorithms

In this paper several well-known filtering techniques were compared in the purpose of automatic line generalization. The used methods for line simplification are digital first order low-pass filter, Savitzky-Golay (SG) filter and Whittaker filter. Two versions of the algorithm for line feature generalization were tested, from source scale 1:25 000 towards target scale of 1:100 000 and from source scale 1:25 000 towards scale of 1:50 000. Also, GPS data filtering for the target scale 1:50 000 was tested. The first version of the algorithm considers that there are no control data, and the filtering parameter is dictated by the desired accuracy for the target scale. The second version involves control data in the target scale. This means that the optimal value for the filtering parameter is the value for which the difference between input and control data is the smallest. Analysis showed that the SG filter yielded the best results in general. The proposed filters can be considered as a new solution for automated cartographic line simplification

Evaluation of Circle of Willis Aneurysms with Spiral Computed Tomographic Angiography

The aim of this retrospective study is to evaluate the specificity and sensitivity of spiral computed tomographic angiograohy (SCTA) in the detection of intracranial aneurysms. Patients were included in this study on the ground of the SCTA, digital subtraction angiography, magnetic resonance angiography, neurosurgeons operative findings and autopsy reports. Scanning protocol was slice thickness of 1mm, reconstruction interval of 0.5 mm, pitch 1. Flow rate was 3–4 ml/s, with standard scan delay time of 15–20s. In 18 patients with average age of 49.3 years SCTA results were positive for cerebral aneurysms and confirmed with other methods. On a per aneurysm basis SCTA sensitivity for detection of aneurysms was 89.47% specificity was 86.96%, positive predictive value of 85.00% and negative predictive value of 90.91%. SCTA should be used for the detection of cerebral aneurysms, especially for aneurysms with maximum diameter larger than 5mm

The Value of Hormone Receptor Assessment in Ultrasound Guided Core Needle Biopsy of the Breast

Breast cancer is the most common cancer in women in Western countries after skin tumors. Successful treatment depends on many factors, relies on clinical examination, diagnostic procedures, pathologic evaluation, and good therapy decision. The Pathologic diagnosis should be the determining factor in the decision on therapeutic approach. There are several methods of obtaining tissue samples. The percutaneous ultrasound guided breast Core needle biopsy (CNB) is one of them. The Aim of this Study is to evaluate our experience in the accuracy of hormone receptors assessment in ultrasound guided CNB. In our institution, in last 12 month 60 women (with 67 lesions) underwent Breast CNB. The CNB was performed with 16 Gauge semiautomatic biopsy needle with 15 Gauge coordinated introducer needle. 3-6 specimen (mean 4) were taken during the procedure. We analyzed five factors (histological type, histological grade, estrogen and progesterone receptor status, and HER2 from the biopsied sample. All results were presented at the Multidisciplinary Oncology Team. In addition to demographic data and morphological features of the lesion, we analyzed five pathological factors (histological type, histological grade, estrogen and progesterone receptor status, and HER2 from the biopsied sample. All results were presented at the Multidisciplinary Oncology Team. Ultrasound-guided CNB has proven to be a reliable technique for performing a biopsy for breast. It is a good and reliable, complication free method, for preoperative staging, operative planning as well for prognostic value. It is a cost-effective method, can be performed quickly and in outpatient population, does not deform the breast and multiple lesions can be biopsied. This technique shows a high sensitivity value and offers many advantages over other imaging methods to guide a biopsy. All advantages have made this technique the most widespread used technique to perform a biopsy for a suspicious breast lesion

A Case of Transient Constrictive Pericarditis in a 42 year old Patient

We report a case of 42 year old patient with acute idiopathic pericarditis in whom we describe transient cardiac constriction, consisting of the temporary development of features of constrictive pericarditis with subsequent return to normality after medical therapy alone. After a mean of 6 months, there have been no recurrences of constrictive physiology or clinical symptoms. The results of our study suggest that patients who have constrictive features early in the course of their illness and are hemodynamically stable should be considered for a trial of conservative therapy before pericardiectomy is pursued

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Contribution to the development of the modified sigmoid function used for modeling the subsidence caused by underground mining

V magistrskem delu je obravnavan matematični model konsolidacijskega procesa na primeru posedanja površine v odkopnem prostoru Premogovnika Velenje. Ustreznost prilagojenega modela se je dokazala na podlagi primerjave modela s štiri in pet parametrično logistično funkcijo. Statistična analiza podatkov terminskih izmer točk, ki so del ene izmed štirih opazovalnih mrež, je bila izvedena v programu Wolfram Mathematica. Analiza zajema prileganje posameznega modela k podatkom na osnovi nelinearne regresije, statističnih testov ocenjenih modelov in njihovih parametrov ter napovedi časovnega razvoja posedkov. Vsi trije modeli se dobro prilegajo. Na to, da je modificirana sigmoidna funkcija najprimernejša kažejo boljši rezultati analize, manjša občutljivost parametrov in manjša kompleksnost modela. Enostavna programska koda za napoved časovnega razvoja posedkov omogoča tudi nazoren prikaz dinamike posedanja in določanje terminov naslednje ter končne izmere. Termina naslednje in končne izmere služita za časovno opredelitev vseh izmer, ki se morajo izvajati v času aktivnega posedanja. Končna izmera se izvede v času konsolidacije, ko so nadaljnji posedki zanemarljivi in se lahko monitoringom območja zaključi.The thesis discusses a mathematical model of subsidence on the surface in the excavation area of Premogovnik Velenje. Adequacy of the adjusted model was confirmed by comparison with the four and five parameter logistic function. Statistical analysis of data, which were obtained with epoch measurements of points, that are a part of four observational networks, was carried out with the Wolfram Mathematica software. Analysis encompasses fitting of each model to data based on nonlinear regression, statistical tests of estimated models and their parameters and the prediction of subsidence development. All models are a good fit. Most applicable model is the modified sigmoid function due to better analysis results, less sensitive parameters and reduced model complexity. A simple program code enables subsidence prediction, graphical display of subsidence dynamic and the time estimation of the next and final epoch measurement

Hybrid prediction model of surface dynamics subsidence above underground excavation

Učinki podzemnega rudarjenja se odražajo na površini v obliki posedanja terena, kar povzroča poškodbe infrastrukture znotraj in v širšem območju rudarskega prostora. V zadnjih desetletjih je zavedanje pomembnosti varovanja življenjskega okolja in posledično tudi površinskih objektov privedlo do razvoja različnih modelnih pristopov za napoved posedanja površine nad podzemnimi odkopi. Ti se razlikujejo glede na metode rudarjenja in naravnih značilnosti območja posameznih nahajališč mineralnih surovin. Raziskave v doktorski disertaciji smo razdelili v tri sklope, kjer smo si za cilj postavili razvoj hibridnega napovednega modela, ki združuje več preizkušenih rešitev in omogoča napoved posedanja za katero koli površinsko točko. V okviru predhodnih raziskav smo v prvem sklopu proučili pogoste metode spremljanja posedkov površine. Na podlagi praktičnosti in natančnosti smo za izvedbo monitoringa posedkov izbrali metodo fotogrametrije UAV. V drugem sklopu smo naredili analizo razvoja posedanja točke in med sabo primerjali različne napovedne modele. Glede na dobljene rezultate smo za napoved posedanja točke kot najprimernejši model izbrali modificirano sigmoidno funkcijo, s katero smo v zahtevanih mejah natančnosti interpolirali in ekstrapolirali izmerjene posedke. Omenjena napoved posedkov temelji na oceni trenda posedkov in napovedi časa naslednje ter končne meritve, ko se začne konsolidacija in je nadaljnje posedanje zanemarljivo. V tretjem sklopu smo pojasnili teorijo hibridnega modela za napoved dinamičnega ugrezanja z razdelitvijo vplivnega območja na pravokotne sektorje, pri čemer je vsak sektor vseboval oblak točk in ravnino, ki se najbolje prilega tem točkam. Tako je mogoče napoved posedkov implementirati v režim monitoringa posedkov. Vsako ravnino smo definirali s centroidom, katerih višine smo uporabili, kot vhodni podatek za izračun parametrov modificirane sigmoidne funkcije. Razvit hibridni model, ki vključuje sigmoidno funkcijo, računsko mrežo s sektorji in primerjavo oblakov točk, lahko uporabimo za optimizacijo sanacije površine nad podzemnim odkopom. To dosežemo s pravočasnim odkrivanjem območij intenzivnega posedanja in kategorizacijo sektorjev računske mreže. Hibridni model smo uspešno verificirali na dejanskih podatkih posedanja površine v najbolj aktivnem odkopnem območju Premogovnika Velenje. Predlagana metoda je dobra osnova za napoved posedanja površine, kjer konvencionalen monitoring ni mogoč, ter omogoča prilagoditev nadaljnjih meritev posedkov glede na predvideno dinamiko posedanja terena, kar je časovno in stroškovno učinkovito.The effects of underground mining are reflected on the surface in the form of ground subsidence, which causes damage to infrastructure in the wider mining area. In recent decades, awareness of the importance of protecting the environment, and thus surface structures, has led to the development of various modeling approaches for predicting surface subsidence over underground mining excavations. These differ depending on the mining methods and the natural conditions in the area of each mineral deposit. The dissertation research was divided into three sections, and our goal was to develop a hybrid prediction model that combines several tested solutions and allows prediction of subsidence for any surface point. As part of the preliminary research, we examined common methods for monitoring surface subsidence in the first section. For reasons of practicality and accuracy, we chose the UAV photogrammetry method for monitoring ground subsidence. In the second part, we analyzed the development of the subsidence of a point and compared different prediction models. Based on the obtained results, we selected the modified sigmoid function as the most suitable model for point subsidence prognosis, which we used to interpolate and extrapolate the measured subsidence values within the required accuracy limits. The mentioned subsidence prediction is based on the assessment of the subsidence trend and the prediction of the time of the next and final measurement, when the consolidation starts and further subsidence is negligible. In the third part, the theory of the hybrid model for dynamic subsidence prediction was explained, in which the area of influence is divided into rectangular sectors, each sector containing a cloud of points and a plane that best fits these points. In this way, it is possible to implement subsidence prediction in the monitoring regime. Each plane was defined by a centroid whose heights were used as input data for calculating the parameters of the modified sigmoid function. The developed hybrid model, which includes a sigmoid function, a computational grid with sectors, and a point cloud comparison, can be used to optimize surface remediation over an underground excavation. This is achieved by identifying areas of intense subsidence and categorizing sectors of the computational grid. The hybrid model was successfully verified on actual surface subsidence data in the most active mining area of the Velenje Coal Mine (slo. Premogovnik Velenje). The proposed method is a good basis for prediction of surface subsidence in areas where conventional monitoring is not possible, and enables time- and cost-efficient adjustment of further subsidence measurements based on the predicted dynamics of terrain subsidence

Best N term approximation spaces for tensor product wavelet bases

ISSN:0176-4276ISSN:1432-094