Analysis of torque and speed ripple producing non-idealities of frequency converters in electric drives

Electric motors driven by adjustable-frequency converters may produce periodic excitation forces that can cause torque and speed ripple. Interaction with the driven mechanical system may cause undesirable vibrations that affect the system performance and lifetime. Direct drives in sensitive applications, such as elevators or paper machines, emphasize the importance of smooth torque production. This thesis analyses the non-idealities of frequencyconverters that produce speed and torque ripple in electric drives. The origin of low order harmonics in speed and torque is examined. It is shown how different current measurement error types affect the torque. As the application environment, direct torque control (DTC) method is applied to permanent magnet synchronous machines (PMSM). A simulation model to analyse the effect of the frequency converter non-idealities on the performance of the electric drives is created. Themodel enables to identify potential problems causing torque vibrations and possibly damaging oscillations in electrically driven machine systems. The model is capable of coupling with separate simulation software of complex mechanical loads. Furthermore, the simulation model of the frequency converter's control algorithm can be applied to control a real frequency converter. A commercial frequencyconverter with standard software, a permanent magnet axial flux synchronous motor and a DC motor as the load are used to detect the effect of current measurement errors on load torque. A method to reduce the speed and torque ripple by compensating the current measurement errors is introduced. The method is based on analysing the amplitude of a selected harmonic component of speed as a function oftime and selecting a suitable compensation alternative for the current error. The speed can be either measured or estimated, so the compensation method is applicable also for speed sensorless drives. The proposed compensation method is tested with a laboratory drive, which consists of commercial frequency converter hardware with self-made software and a prototype PMSM. The speed and torque rippleof the test drive are reduced by applying the compensation method. In addition to the direct torque controlled PMSM drives, the compensation method can also beapplied to other motor types and control methods.

Estimation of age- and stage-specific Catalan breast cancer survival functions using US and Catalan survival data

Background: During the last part of the 1990s the chance of surviving breast cancer increased. Changes in survival functions reflect a mixture of effects. Both, the introduction of adjuvant treatments and early screening with mammography played a role in the decline in mortality. Evaluating the contribution of these interventions using mathematical models requires survival functions before and after their introduction. Furthermore, required survival functions may be different by age groups and are related to disease stage at diagnosis. Sometimes detailed information is not available, as was the case for the region of Catalonia (Spain). Then one may derive the functions using information from other geographical areas. This work presents the methodology used to estimate age- and stage-specific Catalan breast cancer survival functions from scarce Catalan survival data by adapting the age- and stage-specific US functions. Methods: Cubic splines were used to smooth data and obtain continuous hazard rate functions. After, we fitted a Poisson model to derive hazard ratios. The model included time as a covariate. Then the hazard ratios were applied to US survival functions detailed by age and stage to obtain Catalan estimations. Results: We started estimating the hazard ratios for Catalonia versus the USA before and after the introduction of screening. The hazard ratios were then multiplied by the age- and stage-specific breast cancer hazard rates from the USA to obtain the Catalan hazard rates. We also compared breast cancer survival in Catalonia and the USA in two time periods, before cancer control interventions (USA 1975–79, Catalonia 1980–89) and after (USA and Catalonia 1990–2001). Survival in Catalonia in the 1980–89 period was worse than in the USA during 1975–79, but the differences disappeared in 1990–2001. Conclusion: Our results suggest that access to better treatments and quality of care contributed to large improvements in survival in Catalonia. On the other hand, we obtained detailed breast cancer survival functions that will be used for modeling the effect of screening and adjuvant treatments in Catalonia.

Endothelial, but not smooth muscle, peroxisome proliferator-activated receptor β/δ regulates vascular permeability and anaphylaxis.

BACKGROUND: Remodeling of quiescent vessels with increases in permeability, vasodilatation, and edema are hallmarks of inflammatory disorders. Factors involved in this type of remodeling represent potential therapeutic targets. OBJECTIVES: We investigated whether the nuclear hormone receptor peroxisome proliferator-activated receptor (PPAR) β/δ, a regulator of metabolism, fibrosis, and skin homeostasis, is involved in regulation of this type of remodeling. METHODS: Wild-type and various Pparb/d mutant mice were used to monitor dermal acute vascular hyperpermeability (AVH) and passive systemic anaphylaxis-induced hypothermia and edema. PPARβ/δ-dependent kinase activation and remodeling of endothelial cell-cell junctions were addressed by using human endothelial cells. RESULTS: AVH and dilatation of dermal microvessels stimulated by vascular endothelial growth factor A, histamine, and thrombin are severely compromised in PPARβ/δ-deficient mice. Selective deletion of the Pparb/d-encoding gene in endothelial cells in vivo similarly limits dermal AVH and vasodilatation, providing evidence that endothelial PPARβ/δ is the major player in regulating acute dermal microvessel remodeling. Furthermore, endothelial PPARβ/δ regulatory functions are not restricted to the skin vasculature because its deletion in the endothelium, but not in smooth muscle cells, also leads to reduced systemic anaphylaxis, the most severe form of allergic reaction, in which an acute vascular response plays a key role. PPARβ/δ-dependent AVH activation likely involves the activation of mitogen-activated protein kinase and Akt pathways and leads to downstream destabilization of endothelial cell-cell junctions. CONCLUSION: These results unveil not only a novel function of PPARβ/δ as a direct regulator of acute vessel permeability and dilatation but also provide evidence that antagonizing PPARβ/δ represents an important strategy to consider for moderating diseases with altered endothelial integrity, such as acute inflammatory and allergic disorders.

Clinical evolution after a non-reactive hypothermic EEG following cardiac arrest.

BACKGROUND: Lack of electroencephalography (EEG) background reactivity during therapeutic hypothermia (TH) has been associated with poor outcome in post-anoxic comatose patients. However, decision on intensive care withdrawal is based on normothermic (NT) evaluations. This study aims at exploring whether patients showing recovery of EEG reactivity in NT after a non-reactive EEG in TH differ from those remaining non-reactive. METHODS: Patients with non-reactive EEG during TH were identified from our prospective registry of consecutive comatose adults admitted after successful resuscitation from CA between April 2009 and June 2014. Variables including neurological examination, serum neuron-specific enolase (NSE), procalcitonin, and EEG features were compared regarding impact on functional outcome at 3 months. RESULTS: Seventy-two of 197 patients (37 %) had a non-reactive EEG background during TH with thirteen (18 %) evolving towards reactivity in NT. Compared to those remaining non-reactive (n = 59), they showed significantly better recovery of brainstem reflexes (p < 0.001), better motor responses (p < 0.001), transitory consciousness improvement (p = 0.008), and a tendency toward lower NSE (p = 0.067). One patient recovering EEG reactivity survived with good functional outcome at 3 months. CONCLUSIONS: Recovery of EEG reactivity from TH to NT seems to distinguish two patients' subgroups regarding early neurological assessment and transitory consciousness improvement, corroborating the role of EEG in providing information about cerebral functions. Understanding these dynamic changes encourages maintenance of intensive support in selected patients even after a non-reactive EEG background in TH, as a small subgroup may indeed recover with good functional outcome.

Social justice in education : how the function of selection in educational institutions predicts support for (non)egalitarian assessment practices

Educational institutions are considered a keystone for the establishment of a meritocratic society. They supposedly serve two functions: an educational function that promotes learning for all, and a selection function that sorts individuals into different programs, and ultimately social positions, based on individual merit. We study how the function of selection relates to support for assessment practices known to harm vs. benefit lower status students, through the perceived justice principles underlying these practices. We study two assessment practices: normative assessment-focused on ranking and social comparison, known to hinder the success of lower status students-and formative assessment-focused on learning and improvement, known to benefit lower status students. Normative assessment is usually perceived as relying on an equity principle, with rewards being allocated based on merit and should thus appear as positively associated with the function of selection. Formative assessment is usually perceived as relying on corrective justice that aims to ensure equality of outcomes by considering students' needs, which makes it less suitable for the function of selection. A questionnaire measuring these constructs was administered to university students. Results showed that believing that education is intended to select the best students positively predicts support for normative assessment, through increased perception of its reliance on equity, and negatively predicts support for formative assessment, through reduced perception of its ability to establish corrective justice. This study suggests that the belief in the function of selection as inherent to educational institutions can contribute to the reproduction of social inequalities by preventing change from assessment practices known to disadvantage lowerstatus student, namely normative assessment, to more favorable practices, namely formative assessment, and by promoting matching beliefs in justice principles.

Comprehensive Genomic Characterization of Long Non-coding RNAs across Human Cancers.

The discovery of long non-coding RNA (lncRNA) has dramatically altered our understanding of cancer. Here, we describe a comprehensive analysis of lncRNA alterations at transcriptional, genomic, and epigenetic levels in 5,037 human tumor specimens across 13 cancer types from The Cancer Genome Atlas. Our results suggest that the expression and dysregulation of lncRNAs are highly cancer type specific compared with protein-coding genes. Using the integrative data generated by this analysis, we present a clinically guided small interfering RNA screening strategy and a co-expression analysis approach to identify cancer driver lncRNAs and predict their functions. This provides a resource for investigating lncRNAs in cancer and lays the groundwork for the development of new diagnostics and treatments.

Non-wood massojen vedenpoiston arvioiminen märkäpuristuksessa

Yksivuotisten kasvien (non-wood) kuitua verrataan usein lehtipuukuituihin. Käytetyimpiä non-wood kasveja ovat vehnän olki, bambu, järviruoko ja bagassi. Non-wood massan erottaa puumassasta kuitenkin korkea silikaattipitoisuus sekä parenkyymisolupitoisuus, joka antaa massalle korkean hienoainepitoisuuden. Tämä yhdessä korkean hemiselluloosapitoisuuden ja lyhyen kuidun pituuden kanssa heikentävät voimakkaasti non-wood massan vedenpoisto-ominaisuuksia. Non-wood kuidulla voidaan korvata lehtipuumassaa hienopapereissa. Non-wood kuitu antaa paperille hyvän opasiteetin, korkean valonsirontakertoimen sekä sileän painopinnan. Massaan lisättävä pitkäkuituinen havupuumassa parantaa ajetta¬vuutta paperikoneella ja helpottaa massan vedenpoistoa. Non-wood massan vedenpoistoa voidaan tehostaa esimerkiksi poistamalla osa hienoaineesta, käyttämällä non-wood massalle sopivaa keittotapaa sekä käyttämällä märkä¬puristuksessa pitkänippityyppistä puristinratkaisua. Myös non-wood kuidun kuivaaminen parantaa vedenpoistoa. Tässä tutkimuksessa kirjallisuusosassa keskityttiin yleisimpiin paperin valmistuksessa käytettäviin non-wood kuidun lähteisiin, märkäpuristuksen teoriaan ja tapoihin tehostaa vedenpoistoa. Kokeellisessa osassa tutkittiin vehnänolkimassan käyttäytymistä märkäpuristuksessa erilaisten ominaisuuksien pohjalta. Tutkimuksen kohteena oli non-wood massan keittotapa (hapan/alkali), hienoainepitoisuus, silikaattipitoisuus sekä kuivattu/kuivaamaton kuitu. Vertailun vuoksi tutkimuksessa oli mukana myös yksi järviruokomassa. Tuloksista huomataan, että non-wood massan vedenpoistoon vaikuttaa hienoainepitoisuus, kuidun kuivaus sekä massan valmistustapa. Järviruokomassan veden¬poisto on tehokkaampaa kuin vehnänolkimassan paremman kuitu¬koostumuksensa takia. Jos hienopaperimassassa korvataan lehtipuumassaa non-wood kuidulla maksimissaan 40 %, massan vedenpoistoa voidaan hyvin arvioida erilaisten suotautuvuusmittojen, kuten freeneksen, vedenpidätyskyvyn ja suotautumisajan, avulla.

The nitric oxide pathway in pig isolated calyceal smooth muscle.

In pig and humans, whose kidneys have a multi-calyceal collecting system, the initiation of ureteral peristalsis takes place in the renal calyces. In the pig and human ureter, recent evidence suggests that nitric oxide (NO) is an inhibitory mediator that may be involved in the regulation of peristalsis. This study was designed to assess whether the NO synthase/NO/cyclic GMP pathway modulates the motility of pig isolated calyceal smooth muscle. Immunohistochemistry revealed a moderate overall innervation of the smooth muscle layer, and no neuronal or inducible NO synthase (NOS) immunoreactivities. Endothelial NOS immunoreactivities were observed in the urothelium and vascular endothelium, and numerous cyclic GMP-immunoreactive (-IR) calyceal smooth muscle cells were found. As measured by monitoring the conversion of L-arginine to L-citrulline, Ca(2+)-dependent NOS activity was moderate. Assessment of functional effects was performed in tissue baths and showed that NO and SIN-1 decreased spontaneous and induced contractions of isolated preparations in a concentration-dependent manner. In strips exposed to NO, there was a 10-fold increase of the cyclic GMP levels compared with control preparations (P < 0.01). It is concluded that a non-neuronal NOS/NO/cyclic GMP pathway is present in pig calyces, where it may influence motility. The demonstration of cyclic GMP-IR smooth muscle cells suggests that NO acts directly on these cells. This NOS/NO/cyclic GMP pathway may be a target for drugs inhibiting peristalsis of mammalian upper urinary tract. Neurourol. Urodynam. 18:673-685, 1999.

The promoter activity of human Mfn2 depends on Sp1 in vascular smooth muscle cells

AIMS: Mitofusin-2 (Mfn2) expression is dysregulated in vascular proliferative disorders and its overexpression attenuates the proliferation of vascular smooth muscle cells (VSMCs) and neointimal lesion development after balloon angioplasty. We sought to gain insight into the mechanisms that control Mfn2 expression in VSMCs. METHODS AND RESULTS: We cloned and characterized 2 kb of the 5'-flanking region of the human Mfn2 gene. Its TATA-less promoter contains a CpG island. In keeping with this, 5'-rapid amplification of cDNA ends revealed six transcriptional start sites (TSSs), of which TSS2 and TSS5 were the most frequently used. The strong CpG island was found to be non-methylated under conditions characterized by large differences in Mfn2 gene expression. The proximal Mfn2 promoter contains six putative Sp1 motifs. Sp1 binds to the Mfn2 promoter and its overexpression activates the Mfn2 promoter in VSMCs. Chemical inhibition of Sp1 reduced Mfn2 expression, and Sp1 silencing reduced transcriptional activity of the Mfn2 promoter. In keeping with this view, Sp1 and Mfn2 mRNA levels were down-regulated in the aorta early after an atherogenic diet in apolipoprotein E-knockout mice or in VSMCs cultured in the presence of low serum. CONCLUSION: Sp1 is a key factor in maintaining basal Mfn2 transcription in VSMCs. Given the anti-proliferative actions of Mfn2, Sp1-induced Mfn2 transcription may represent a mechanism for prevention of VSMC proliferation and neointimal lesion and development.

The promoter activity of human Mfn2 depends on Sp1 in vascular smooth muscle cells

AIMS: Mitofusin-2 (Mfn2) expression is dysregulated in vascular proliferative disorders and its overexpression attenuates the proliferation of vascular smooth muscle cells (VSMCs) and neointimal lesion development after balloon angioplasty. We sought to gain insight into the mechanisms that control Mfn2 expression in VSMCs. METHODS AND RESULTS: We cloned and characterized 2 kb of the 5'-flanking region of the human Mfn2 gene. Its TATA-less promoter contains a CpG island. In keeping with this, 5'-rapid amplification of cDNA ends revealed six transcriptional start sites (TSSs), of which TSS2 and TSS5 were the most frequently used. The strong CpG island was found to be non-methylated under conditions characterized by large differences in Mfn2 gene expression. The proximal Mfn2 promoter contains six putative Sp1 motifs. Sp1 binds to the Mfn2 promoter and its overexpression activates the Mfn2 promoter in VSMCs. Chemical inhibition of Sp1 reduced Mfn2 expression, and Sp1 silencing reduced transcriptional activity of the Mfn2 promoter. In keeping with this view, Sp1 and Mfn2 mRNA levels were down-regulated in the aorta early after an atherogenic diet in apolipoprotein E-knockout mice or in VSMCs cultured in the presence of low serum. CONCLUSION: Sp1 is a key factor in maintaining basal Mfn2 transcription in VSMCs. Given the anti-proliferative actions of Mfn2, Sp1-induced Mfn2 transcription may represent a mechanism for prevention of VSMC proliferation and neointimal lesion and development.

"Role of long non-coing RNAs in the stressed heart". Wisper : a novel cardiac fibroblast-enriched IncRNA that modulate fibrosis in the failing heart

LncRNAs are transcripts greater than 200 nucleotides in length with no apparent coding potential. They exert important regulatory functions in the genome. Their role in cardiac fibrosis is however unexplored. To identify IncRNAs that could modulate cardiac fibrosis, we profiled the long non-coding transcriptome in the infarcted mouse heart, and identified 1500 novel IncRNAs. These IncRNAs have unique characteristics such as high tissue and cell type specificity. Their expression is highly correlated with parameters of cardiac dimensions and function. The majority of these novel IncRNAs are conserved in human. Importantly, human IncRNAs appear to be differentially expressed in heart disease. Using a computational pipeline, we identified a super-enhancer-associated IncRNA, which is dynamically expressed after myocardial infarction. We named this particular transcript Wisper for «Wisp2 super-enhancer- derived IncRNA ». Interestingly, Wisper expression is overexpressed in cardiac fibroblasts as compared to cardiomyocytes or to fibroblasts isolated from other organs than the heart. The importance of Wisper in the biology of fibroblasts was demonstrated in knockdown experiments. Differentiation of cardiac fibroblast into myofibroblasts in vitro is significantly impaired upon Wisper knockdown. Wisper downregulation in cardiac fibroblasts results in a dramatic reduction of fibrotic gene expression, a diminished cell proliferation and an increase in apoptotic cell death. In vivo, depletion of Wisper during the acute phase of the response to infarction is detrimental via increasing the risk of cardiac rupture. On the other hand, Wisper knockdown following infarction in a prevention study reduces fibrosis and preserves cardiac function. Since WISPER is detectable in the human heart, where it is associated with severe cardiac fibrosis, these data suggest that Wisper could represent a novel therapeutic target for limiting the extent of the fibrotic response in the heart. -- Les long ARN non-codants (IncRNAs) sont des ARN de plus de 200 nucléotides qui ne codent pas pour des protéines. Ils exercent d'importantes fonctions dans le génome. Par contre, leur importance dans le développement de la fibrose cardiaque n'a pas été étudiée. Pour identifier des IncRNAs jouant un rôle dans ce processus, le transcriptome non-codant a été étudié dans le coeur de'souris après un infarctus du myocarde. Nous avons découverts 1500 nouveaux IncRNAs. Ces transcrits ont d'uniques caractéristiques. En particulier ils sont extrêmement spécifiques de sous-populations de cellules cardiaques. Par ailleurs, leur expression est remarquablement corrélée avec les paramètres définissant les dimensions du coeur et la fonction cardiaque. La majorité de ces IncRNAs sont conservés chez l'humain. Certains sont modulés dans des pathologies cardiaques. En utilisant une approche bioinformatique, nous avons identifié un IncRNA qui est associé à des séquences amplificatrices et qui est particulièrement enrichi dans les fibroblastes cardiaques. Ce transcrit a été nommé Wisper pour «Wisp2 super-enhancer-derived IncRNA ». L'importance de Wisper dans la biologie des fibroblastes cardiaques est démontrée dans des expériences de déplétion. En l'absence de Wisper, l'expression de protéines impliquées dans le développement de la fibrose est dramatiquement réduite dans les fibroblastes cardiaques. Ceux-ci montrent une prolifération réduite. Le niveau d'apoptose est largement augmenté. In vivo, la déplétion de Wisper pendant la phase aiguë de l'infarctus rehausse le risque de rupture cardiaque. Au contraire, la réduction de l'expression de Wisper pendant la phase chronique diminue la fibrose cardiaque et améliore la fonction du coeur. Puisque Wisper est exprimé dans le coeur humain, ce transcrit représente une nouvelle cible thérapeutique pour limiter la réponse fibrotique dans le coeur.

Estimation of age- and stage-specific Catalan breast cancer survival functions using US and Catalan survival data

During the last part of the 1990s the chance of surviving breast cancer increased. Changes in survival functions reflect a mixture of effects. Both, the introduction of adjuvant treatments and early screening with mammography played a role in the decline in mortality. Evaluating the contribution of these interventions using mathematical models requires survival functions before and after their introduction. Furthermore, required survival functions may be different by age groups and are related to disease stage at diagnosis. Sometimes detailed information is not available, as was the case for the region of Catalonia (Spain). Then one may derive the functions using information from other geographical areas. This work presents the methodology used to estimate age- and stage-specific Catalan breast cancer survival functions from scarce Catalan survival data by adapting the age- and stage-specific US functions. Methods: Cubic splines were used to smooth data and obtain continuous hazard rate functions. After, we fitted a Poisson model to derive hazard ratios. The model included time as a covariate. Then the hazard ratios were applied to US survival functions detailed by age and stage to obtain Catalan estimations. Results: We started estimating the hazard ratios for Catalonia versus the USA before and after the introduction of screening. The hazard ratios were then multiplied by the age- and stage-specific breast cancer hazard rates from the USA to obtain the Catalan hazard rates. We also compared breast cancer survival in Catalonia and the USA in two time periods, before cancer control interventions (USA 1975–79, Catalonia 1980–89) and after (USA and Catalonia 1990–2001). Survival in Catalonia in the 1980–89 period was worse than in the USA during 1975–79, but the differences disappeared in 1990–2001. Conclusion: Our results suggest that access to better treatments and quality of care contributed to large improvements in survival in Catalonia. On the other hand, we obtained detailed breast cancer survival functions that will be used for modeling the effect of screening and adjuvant treatments in Catalonia

Size Effect and Notch Size Effect in Metal Fatigue

It is a well known phenomenon that the constant amplitude fatigue limit of a large component is lower than the fatigue limit of a small specimen made of the same material. In notched components the opposite occurs: the fatigue limit defined as the maximum stress at the notch is higher than that achieved with smooth specimens. These two effects have been taken into account in most design handbooks with the help of experimental formulas or design curves. The basic idea of this study is that the size effect can mainly be explained by the statistical size effect. A component subjected to an alternating load can be assumed to form a sample of initiated cracks at the end of the crack initiation phase. The size of the sample depends on the size of the specimen in question. The main objective of this study is to develop a statistical model for the estimation of this kind of size effect. It was shown that the size of a sample of initiated cracks shall be based on the stressed surface area of the specimen. In case of varying stress distribution, an effective stress area must be calculated. It is based on the decreasing probability of equally sized initiated cracks at lower stress level. If the distribution function of the parent population of cracks is known, the distribution of the maximum crack size in a sample can be defined. This makes it possible to calculate an estimate of the largest expected crack in any sample size. The estimate of the fatigue limit can now be calculated with the help of the linear elastic fracture mechanics. In notched components another source of size effect has to be taken into account. If we think about two specimens which have similar shape, but the size is different, it can be seen that the stress gradient in the smaller specimen is steeper. If there is an initiated crack in both of them, the stress intensity factor at the crack in the larger specimen is higher. The second goal of this thesis is to create a calculation method for this factor which is called the geometric size effect. The proposed method for the calculation of the geometric size effect is also based on the use of the linear elastic fracture mechanics. It is possible to calculate an accurate value of the stress intensity factor in a non linear stress field using weight functions. The calculated stress intensity factor values at the initiated crack can be compared to the corresponding stress intensity factor due to constant stress. The notch size effect is calculated as the ratio of these stress intensity factors. The presented methods were tested against experimental results taken from three German doctoral works. Two candidates for the parent population of initiated cracks were found: the Weibull distribution and the log normal distribution. Both of them can be used successfully for the prediction of the statistical size effect for smooth specimens. In case of notched components the geometric size effect due to the stress gradient shall be combined with the statistical size effect. The proposed method gives good results as long as the notch in question is blunt enough. For very sharp notches, stress concentration factor about 5 or higher, the method does not give sufficient results. It was shown that the plastic portion of the strain becomes quite high at the root of this kind of notches. The use of the linear elastic fracture mechanics becomes therefore questionable.

On convergence of transforms based on parabolic scaling

This thesis studies properties of transforms based on parabolic scaling, like Curvelet-, Contourlet-, Shearlet- and Hart-Smith-transform. Essentially, two di erent questions are considered: How these transforms can characterize H older regularity and how non-linear approximation of a piecewise smooth function converges. In study of Hölder regularities, several theorems that relate regularity of a function f : R2 → R to decay properties of its transform are presented. Of particular interest is the case where a function has lower regularity along some line segment than elsewhere. Theorems that give estimates for direction and location of this line, and regularity of the function are presented. Numerical demonstrations suggest also that similar theorems would hold for more general shape of segment of low regularity. Theorems related to uniform and pointwise Hölder regularity are presented as well. Although none of the theorems presented give full characterization of regularity, the su cient and necessary conditions are very similar. Another theme of the thesis is the study of convergence of non-linear M ─term approximation of functions that have discontinuous on some curves and otherwise are smooth. With particular smoothness assumptions, it is well known that squared L2 approximation error is O(M-2(logM)3) for curvelet, shearlet or contourlet bases. Here it is shown that assuming higher smoothness properties, the log-factor can be removed, even if the function still is discontinuous.