College of Science
http://hdl.handle.net/10197/1797
20141025T15:19:50ZClustering with the multivariate normal inverse Gaussian distribution
http://hdl.handle.net/10197/6106
Clustering with the multivariate normal inverse Gaussian distribution
O'Hagan, Adrian; Murphy, Brendan; Gormley, Isobel Claire; et al.
Many modelbased clustering methods are based on a finite Gaussian mixture model. The Gaussian mixture model implies that the data scatter within each group is elliptically shaped. Hence nonelliptical groups are often modeled by more than one component, resulting in model overfitting. An alternative is to use a mean–variance mixture of multivariate normal distributions with an inverse Gaussian mixing distribution (MNIG) in place of the Gaussian distribution, to yield a more flexible family of distributions. Under this model the component distributions may be skewed and have fatter tails than the Gaussian distribution. The MNIG based approach is extended to include a broad range of eigendecomposed covariance structures. Furthermore, MNIG models where the other distributional parameters are constrained is considered. The Bayesian Information Criterion is used to identify the optimal model and number of mixture components. The method is demonstrated on three sample data sets and a novel variation on the univariate Kolmogorov–Smirnov test is used to assess goodness of fit.
20140919T00:00:00ZA 13CNMR study of azacryptand complexes
http://hdl.handle.net/10197/5894
A 13CNMR study of azacryptand complexes
Wild, Aljoscha A. C.; Fennell, Kevin; Morgan, Grace G.; Hewage, Chandralal; Malthouse, J.Paul G.
An azacryptand has been solubilised in aqueous media containing 50% (v/v) dimethyl sulphoxide. 13CNMR has been used to determine how the azacryptand is affected by zinc binding at pH 10. Using 13CNMR and 13Cenriched bicarbonate we have been able to observe the formation of 4 different carbamate derivatives of the azacryptand at pH 10. The azacryptand was shown to solubilise zinc or cadmium at alkaline pHs. Two moles of zinc are bound per mole of azacryptand and this complex binds 1 mole of carbonate. By replacing the zinc with cadmium113 we have shown that the 13CNMR signal of the 13Cenriched carbon of the bound carbonate is split into two triplets at 2.2 °C. This shows that two cadmium complexes are formed and in each of these complexes the carbonate group is bound by two magnetically equivalent metal ions. It also demonstrates that these cadmium complexes are not in fast exchange. From temperature studies we show that in the zinc complexes both complexes are in fast exchange with each other but are in slow exchange with free bicarbonate. HOESY is used to determine the position of the carbonate carbon in the complex. The solution and crystal structures of the zinc–carbonate–azacryptand complexes are compared.
20140729T00:00:00ZPiezoelectricity in collagen type II fibrils measured by scanning probe microscopy
http://hdl.handle.net/10197/5892
Piezoelectricity in collagen type II fibrils measured by scanning probe microscopy
Denning, Denise; Kilpatrick, J. I.; Hsu, T.; Rodriguez, Brian J.; et al.
The converse piezoelectric effect in collagen type II fibrils, the main collagen constituent in cartilage, was investigated using piezoresponse force microscopy. The fibrils exhibited shear piezoelectric behavior similar to that previously reported in collagen type I fibrils and followed the same cantileverfibril angle dependence present for type I. A uniform polarization directed from the amine to carboxyl termini, as seen for collagen type I, was observed in all type II fibrils studied. The shear piezoelectric coefficient, d 15, however, for type II was roughly 28–32% of the value measured for type I fibrils. Possible explanations for the reduced piezoelectric coefficient of type II collagen are provided.
20140811T00:00:00ZNanoscale characterization of βphase HxLi1−xNbO3 layers by piezoresponse force microscopy
http://hdl.handle.net/10197/5891
Nanoscale characterization of βphase HxLi1−xNbO3 layers by piezoresponse force microscopy
Manzo, Michele; Denning, Denise; Rodriguez, Brian J.; Gallo, Katia
We investigate a nondestructive approach for the characterization of proton exchanged layers in LiNbO3 with submicrometric resolution by means of piezoresponse force microscopy (PFM). Through systematic analyses, we identify a clear correlation between optical measurements on the extraordinary refractive index and PFM measurements on the piezoelectric d 33 coefficient. Furthermore, we quantify the reduction of the latter induced by proton exchange as 83 ± 2% and 68 ± 3% of the LiNbO3 value, for undoped and 5 mol. % MgOdoped substrates, respectively.
20140101T00:00:00ZThetaBurst Stimulation of Hippocampal Slices Induces NetworkLevel Calcium Oscillations and Activates Analogous Gene Transcription to Spatial Learning
http://hdl.handle.net/10197/5877
ThetaBurst Stimulation of Hippocampal Slices Induces NetworkLevel Calcium Oscillations and Activates Analogous Gene Transcription to Spatial Learning
Sheridan, Graham K.; Moeendarbary, Emad; Pickering, Mark; O'Connor, J. J.; Murphy, Keith J.
Over four decades ago, it was discovered that highfrequency stimulation of the dentate gyrus induces longterm potentiation (LTP) of synaptic transmission. LTP is believed to underlie how we process and code external stimuli before converting it to salient information that we store as 'memories'. It has been shown that rats performing spatial learning tasks display thetafrequency (3–12 Hz) hippocampal neural activity. Moreover, administering thetaburst stimulation (TBS) to hippocampal slices can induce LTP. TBS triggers a sustained rise in intracellular calcium [Ca2+]i in neurons leading to new protein synthesis important for LTP maintenance. In this study, we measured TBSinduced [Ca2+]i oscillations in thousands of cells at increasing distances from the source of stimulation. Following TBS, a calcium wave propagates radially with an average speed of 5.2 µm/s and triggers multiple and regular [Ca2+]i oscillations in the hippocampus. Interestingly, the number and frequency of [Ca2+]i fluctuations postTBS increased with respect to distance from the electrode. During the posttetanic phase, 18% of cells exhibited 3 peaks in [Ca2+]i with a frequency of 17 mHz, whereas 2.3% of cells distributed further from the electrode displayed 8 [Ca2+]i oscillations at 33 mHz. We suggest that these observed [Ca2+]i oscillations could lead to activation of transcription factors involved in synaptic plasticity. In particular, the transcription factor, NFκB, has been implicated in memory formation and is upregulated after LTP induction. We measured increased activation of NFκB 30 min postTBS in CA1 pyramidal cells and also observed similar temporal upregulation of NFκB levels in CA1 neurons following water maze training in rats. Therefore, TBS of hippocampal slice cultures in vitro can mimic the cell typespecific upregulations in activated NFκB following spatial learning in vivo. This indicates that TBS may induce similar transcriptional changes to spatial learning and that TBStriggered [Ca2+]i oscillations could activate memoryassociated gene expression.
20140620T00:00:00ZCX3CL1 is upregulated in the rat hippocampus during memoryassociated synaptic plasticity
http://hdl.handle.net/10197/5876
CX3CL1 is upregulated in the rat hippocampus during memoryassociated synaptic plasticity
Sheridan, Graham K.; Wdowicz, Anita; Pickering, Mark; Watters, Orla; Halley, Paul G.; O'Sullivan, Niamh C.; Mooney, Claire; O'Connell, David J.; O'Connor, J. J.; Murphy, Keith J.
Several cytokines and chemokines are now known to play normal physiological roles in the brain where they act as key regulators of communication between neurons, glia, and microglia. In particular, cytokines and chemokines can affect cardinal cellular and molecular processes of hippocampaldependent longterm memory consolidation including synaptic plasticity, synaptic scaling and neurogenesis. The chemokine, CX3CL1 (fractalkine), has been shown to modulate synaptic transmission and longterm potentiation (LTP) in the CA1 pyramidal cell layer of the hippocampus. Here, we confirm widespread expression of CX3CL1 on mature neurons in the adult rat hippocampus. We report an upregulation in CX3CL1 protein expression in the CA1, CA3 and dentate gyrus (DG) of the rat hippocampus 2 h after spatial learning in the water maze task. Moreover, the same temporal increase in CX3CL1 was evident following LTPinducing thetaburst stimulation in the DG. At physiologically relevant concentrations, CX3CL1 inhibited LTP maintenance in the DG. This attenuation in dentate LTP was lost in the presence of GABAA receptor/chloride channel antagonism. CX3CL1 also had opposing actions on glutamatemediated rise in intracellular calcium in hippocampal organotypic slice cultures in the presence and absence of GABAA receptor/chloride channel blockade. Using primary dissociated hippocampal cultures, we established that CX3CL1 reduces glutamatemediated intracellular calcium rises in both neurons and glia in a dose dependent manner. In conclusion, CX3CL1 is upregulated in the hippocampus during a brief temporal window following spatial learning the purpose of which may be to regulate glutamatemediated neurotransmission tone. Our data supports a possible role for this chemokine in the protective plasticity process of synaptic scaling.
20140812T00:00:00ZIdentification of a mutation in LARS as a novel cause of infantile hepatopathy
http://hdl.handle.net/10197/5794
Identification of a mutation in LARS as a novel cause of infantile hepatopathy
Casey, Jillian; McGettigan, Paul A.; LynamLennon, Niamh; Regan, Regina; Conroy, Judith; Bourke, Billy; Lynch, Sally; Ennis, Sean; et al.
Infantile hepatopathies are lifethreatening liver disorders that manifest in the first few months of life. We report on a consanguineous Irish Traveller family that includes six individuals presenting with acute liver failure in the first few months of life. Additional symptoms include anaemia, renal tubulopathy, developmental delay, seizures, failure to thrive and deterioration of liver function with minor illness. The multisystem manifestations suggested a possible mitochondrial basis to the disorder. However, known causes of childhood liver failure and mitochondrial disease were excluded in this family by biochemical, metabolic and genetic analyses. We aimed to identify the underlying risk gene using homozygosity mapping and whole exome sequencing. SNP homozygosity mapping identified a candidate locus at 5q31.3–q33.1. Whole exome sequencing identified 1 novel homozygous missense mutation within the 5q31.3–q33.1 candidate region that segregated with the hepatopathy. The candidate mutation is located in the LARS gene which encodes a cytoplasmic leucyltRNA synthetase enzyme responsible for exclusively attaching leucine to its cognate tRNA during protein translation. Knockdown of LARS in HEK293 cells did not impact on mitochondrial function even when the cells were put under physiological stress. The molecular studies confirm the findings of the patients' biochemical and genetic analyses which show that the hepatopathy is not a mitochondrialbased dysfunction problem, despite clinical appearances. This study highlights the clinical utility of homozygosity mapping and exome sequencing in diagnosing recessive liver disorders. It reports mutation of a cytoplasmic aminoacyltRNA synthetase enzyme as a possible novel cause of infantile hepatopathy and underscores the need to consider mutations in LARS in patients with liver disease and multisystem presentations.
20120701T00:00:00ZFirst implication of STRA6 mutations in isolated anophthalmia, microphthalmia and coloboma: a new dimension to the STRA6 phenotype
http://hdl.handle.net/10197/5790
First implication of STRA6 mutations in isolated anophthalmia, microphthalmia and coloboma: a new dimension to the STRA6 phenotype
Casey, Jillian; Kawaguchi, Riki; Morrissey, Maria; McGettigan, Paul A.; Nielsen, Jens Erik; Conroy, Judith; Regan, Regina; Kennedy, Breandán; Lynch, Sally; Green, Andrew; Ennis, Sean; et al.
Microphthalmia, anophthalmia, and coloboma (MAC) are structural congenital eye malformations that cause a significant proportion of childhood visual impairments. Several disease genes have been identified but do not account for all MAC cases, suggesting that additional risk loci exist. We used single nucleotide polymorphism (SNP) homozygosity mapping (HM) and targeted nextgeneration sequencing to identify the causative mutation for autosomal recessive isolated colobomatous microanophthalmia (MCOPCB) in a consanguineous Irish Traveller family. We identified a doublenucleotide polymorphism (g.1157G>A and g.1156G>A; p.G304K) in STRA6 that was homozygous in all of the MCOPCB patients. The STRA6 p.G304K mutation was subsequently detected in additional MCOPCB patients, including one individual with MatthewWood syndrome (MWS; MCOPS9). STRA6 encodes a transmembrane receptor involved in vitamin A uptake, a process essential to eye development and growth. We have shown that the G304K mutant STRA6 protein is mislocalized and has severely reduced vitamin A uptake activity. Furthermore, we reproduced the MCOPCB phenotype in a zebrafish disease model by inhibiting retinoic acid (RA) synthesis, suggesting that diminished RA levels account for the eye malformations in STRA6 p.G304K patients. The current study demonstrates that STRA6 mutations can cause isolated eye malformations in addition to the congenital anomalies observed in MWS.
20111201T00:00:00ZInterpreting map usage patterns using geovisual analytics and spatiotemporal clustering
http://hdl.handle.net/10197/5704
Interpreting map usage patterns using geovisual analytics and spatiotemporal clustering
McArdle, Gavin; Tahir, Ali; Bertolotto, Michela
Extracting meaningful information from the growing quantity of spatial data is a challenge. The issues are particularly evident with spatiotemporal data describing movement. Such data typically corresponds to movement of humans, animals and machines in the physical environment. This article considers a special form of movement data generated through human–computer interactions with online web maps. As a user interacts with a web map using a mouse as a pointing tool, invisible trajectories are generated. By examining the spatial features on the map where the mouse cursor visits, a user's interests and experience can be detected. To analyse this valuable information, we have developed a geovisual analysis tool which provides a rich insight into such user behaviour. The focus of this paper is on a clustering technique which we apply to mouse trajectories to group trajectories with similar behavioural properties. Our experiments reveal that it is possible to identify experienced and novice users of web mapping environments using an incremental clustering approach. The results can be used to provide personalised map interfaces to users and provide appropriate interventions for completing spatial tasks.
20140301T00:00:00ZHow to (Possibly) Foil Multimedia Security?
http://hdl.handle.net/10197/5700
How to (Possibly) Foil Multimedia Security?
Balado, Félix; Fournel, Thierry
Multimedia security can be foiled thanks to
Slepian’s permutation modulation. Originally proposed in 1965
for standard problems of channel and source coding in communications,
permutation codes can also provide optimum solutions
in two relevant fields: steganography (foiling hidden information
detection tests) and counterforensics (foiling forensic detection
tests). In the first scenario, permutation codes have been shown
to implement optimum perfect universal steganography (that is
to say, steganography with maximum information embedding
rate, undetectable and only relying on the empirical distribution
of the host) for histogrambased hidden information detectors.
In the second scenario, permutation codes have been shown to
implement minimumdistortion perfect counterforensics (that is
to say, forgeries which are undetectable and as close as possible to
a target forgery) for histogrambased forensic detectors. Interestingly,
both of these developments have revealed connections with
compression through theoretical bounds from the mathematical
theory of information. In steganography, the longacknowledged
duality between perfect steganography and lossless compression
has been made explicit by permutation coding. On the other
hand, a connection between counterforensics, lossy compression
and histogram specification is also shown.
13th Workshop on Information Optics (WIO2014),Neuchâtel, Switzerland, 711 July, 2014
20140701T00:00:00ZAtypical Alstrom syndrome with novel ALMS1 mutations precluded by current diagnostic criteria
http://hdl.handle.net/10197/5689
Atypical Alstrom syndrome with novel ALMS1 mutations precluded by current diagnostic criteria
Casey, Jillian; McGettigan, Paul A.; Brosnahan, Donal; et al.
We report on clinical and genetic studies in a nonconsanguineous Irish sibpair with infantile dilated cardiomyopathy and retinopathy. A diagnosis of Alström Syndrome (AS) was considered and diagnostic testing pursued. The Alströms gene (ALMS1) is very large (23 exons) and diagnostic testing of mutational hotspots (exon 6, 8 and 10) was negative. Furthermore the siblings were tall and did not have the typical phenotype of nystagmus, photophobia, obesity or hearing loss and so the AS diagnosis was removed. We then sought to identify the causative gene in this family using whole exome sequencing. Unexpectedly, the exome analysis identified novel compound heterozygous ALMS1 mutations in exon 5 (c.777delT:p.D260fs*26) and exon 20 (c.12145_12146insC:p.S4049fs*36) that segregated with the phenotype. Although the siblings show some clinical overlap with AS, their phenotype is not classical. It is plausible that their atypical presentation may be due to the location of the ALMS1 mutations outside the usual mutational hotspots. Our findings show how atypical cases of AS may be missed under the current diagnostic guidelines and support consideration of complete ALMS1 sequencing in children with two or more features, even if all of the core clinical features of AS are not present.
20140201T00:00:00ZUnexpected genetic heterogeneity for primary ciliary dyskinesia in the Irish Traveller population
http://hdl.handle.net/10197/5688
Unexpected genetic heterogeneity for primary ciliary dyskinesia in the Irish Traveller population
Casey, Jillian; McGettigan, Paul A.; Healy, Fiona; Reynolds, Alison; Kennedy, Breandán; Ennis, Sean; Slattery, Dubhfeasa; Lynch, Sally; Hogg, Claire
We present a study of five children from three unrelated Irish Traveller families presenting with primary ciliary dyskinesia (PCD). As previously characterized disorders in the Irish Traveller population are caused by common homozygous mutations, we hypothesised that all three PCD families shared the same recessive mutation. However, exome sequencing showed that there was no pathogenic homozygous mutation common to all families. This finding was supported by histology, which showed that each family has a different type of ciliary defect; transposition defect (family A), nude epithelium (family B) and absence of inner and outer dynein arms (family C). Therefore, each family was analysed independently using homozygosity mapping and exome sequencing. The affected siblings in family A share a novel 1 bp duplication in RSPH4A (NM_001161664.1:c.166dup; p.Arg56Profs*11), a radialspoke head protein involved in ciliary movement. In family B, we identified three candidate genes (CCNO, KCNN3 and CDKN1C), with a 5bp duplication in CCNO (NM_021147.3:c.258_262dup; p.Gln88Argfs*8) being the most likely cause of ciliary aplasia. This is the first study to implicate CCNO, a DNA repair gene reported to be involved in multiciliogenesis, in PCD. In family C, we identified a ~3.5kb deletion in DYX1C1, a neuronal migration gene previously associated with PCD. This is the first report of a disorder in the relatively small Irish Traveller population to be caused by >1 disease gene. Our study identified at least three different PCD genes in the Irish Traveller population, highlighting that one cannot always assume genetic homogeneity, even in small consanguineous populations.
20140501T00:00:00ZOrigin of spurious single forces in the course mechanism of volcanic seismicity
http://hdl.handle.net/10197/5682
Origin of spurious single forces in the course mechanism of volcanic seismicity
De Barros, Louis; Lokmer, Ivan; Bean, Christopher J.
Single forces are often observed in the source mechanism of volcanic seismicity. However, their underlying causative processes are still doubtful. The reliability of single force observations must be assessed, prior to analyzing them in terms of physical mechanisms. Using numerical examples, we show that source mislocation and velocity mismodeling lead to strong spurious single forces. Layering in the velocity model produces converted Swaves and source mislocations modify the wavefield at the free surface (mainly through converted S and surface waves). However, these waves can also be accurately reproduced in a homogeneous model by adding a vertical single force in the source mechanism, which mainly generates Swaves for large takeoff angles. Hence approximate velocity models can lead to the appearance of strong single forces in source inversions. We conclude that, in moment tensor inversion, while single forces can be used in some cases to accommodate mismodeling errors, they cannot be reliably used to infer physical processes.
20130715T00:00:00ZThe selective oxidation of glycerol over model Au/TiO2 catalysts  the influence of glycerol purity on conversion and product selectivity
http://hdl.handle.net/10197/5675
The selective oxidation of glycerol over model Au/TiO2 catalysts  the influence of glycerol purity on conversion and product selectivity
Sullivan, James A.; Burnham, Sarah
The activity and selectivity of a model Au/TiO2 catalyst was studied in the selective oxidation of glycerol as a function of the purity of the glycerol source. A reasonable conversion was noted when reagent grade starting materials were used. When crude glycerol from a FAME production facility was used, the activity of the catalyst was severely compromised and the selectivity of the reaction changed. Several lowcost approaches to purifying the crude glycerol were attempted but none resulted in the formation of a glycerol substrate whose conversion under reaction conditions matched that of the pure reagent grade substrate.
20140101T00:00:00ZInvestigating the source characteristics of longperiod (LP) seismic events recorded on Piton de la Fournaise volcano, La Réunion
http://hdl.handle.net/10197/5664
Investigating the source characteristics of longperiod (LP) seismic events recorded on Piton de la Fournaise volcano, La Réunion
Zecevic, Megan; De Barros, Louis; Bean, Christopher J.; O'Brien, G. S.; Brenguier, Florent
Magmatic and hydrothermal processes play a significant role in generating seismicity at active volcanoes. These signals can be recorded at the surface and can be used to obtain an insight into the volcano's internal dynamics. Long period (LP) events are of particular interest as they often accompany or precede volcanic eruptions, but they are still not well understood. Piton de la Fournaise volcano, La Réunion Island, is one of the most active volcanoes in the world however LP events are rarely recorded there. A seismic network of 20 broadband seismometers has been operational on Piton de la Fournaise volcano since November 2009. Between November 2009 and January 2011 the volcano erupted five times, but only 15 LP events were recorded. Three of these eruptions were preceded by LP events, and several LP events were recorded during an intrusive phase. A family of three repeating LP events exists within the dataset. In order to characterize these events we locate and perform moment tensor inversion on the LP family. The LP events are located within the summit crater at shallow depths (< 200 m below the surface). Inversions show that the source mechanism is best represented by a tensile crack with horizontal crack geometry. We also investigate the relationship between LP occurrence and eruptive characteristics (size of the eruption, deformation of the edifice, etc.), and we find that the events exist only during flank eruptions and can be generated by the activity of the hydrothermal system and/or by the deformation inside the crater.
20130515T00:00:00ZMoment tensor inversion for the source location and mechanism of long period (LP) seismic events from 2009 at Turrialba volcano, Costa Rica
http://hdl.handle.net/10197/5663
Moment tensor inversion for the source location and mechanism of long period (LP) seismic events from 2009 at Turrialba volcano, Costa Rica
Eyre, Thomas S.; Bean, Christopher J.; De Barros, Louis; O'Brien, G. S.; Martini, Francesca; Lokmer, Ivan; et al.
Longperiod (LP) seismic events were recorded during the temporary installation of a broadband seismic network of 13 stations from March to September 2009 on Turrialba volcano, Costa Rica. Over 6000 LPs were extracted using a modified STA/LTA method and a family consisting of 435 similar LP events has been identified. For the first time at Turrialba volcano, fullwaveform moment tensor inversion is performed to jointly determine the location and source mechanism of the events. The LPs in the family are likely to be caused by crack mechanisms dipping towards the southwest at angles of approximately 10 to 20°, located at shallow depths (< 800 m) below the active Southwest and Central craters. As the locations are so shallow, the most probable causes of crack mechanisms are hydrothermal fluids resonating within or 'pulsing' through a crack. The waveforms observed at the summit stations suggest a 'pulsing' mechanism, but source resonance with a
high degree of damping is also possible.
20130515T00:00:00ZAn irregular lattice method for elastic wave propagation
http://hdl.handle.net/10197/5660
An irregular lattice method for elastic wave propagation
O'Brien, G. S.; Bean, Christopher J.
Lattice methods are a class of numerical scheme which represent a medium as a connection of interacting nodes or particles. In the case of modelling seismic wave propagation, the interaction term is determined from Hooke′s Law including a bondbending term. This approach has been shown to model isotropic seismic wave propagation in an elastic or viscoelastic medium by selecting the appropriate underlying lattice structure. To predetermine the material constants, this methodology has been restricted to regular grids, hexagonal or square in 2D or cubic in 3D. Here, we present a method for isotropic elastic wave propagation where we can remove this lattice restriction. The methodology is outlined and a relationship between the elastic material properties and an irregular lattice geometry are derived. The numerical method is compared with an analytical solution for wave propagation in an infinite homogeneous body along with comparing the method with a numerical solution for a layered elastic medium. The dispersion properties of this method are derived from a plane wave analysis showing the scheme is more dispersive than a regular lattice method. Therefore, the computational costs of using an irregular lattice are higher. However, by removing the regular lattice structure the anisotropic nature of fracture propagation in such methods can be removed.
20111001T00:00:00ZImaging magma storage below Teide volcano (Tenerife) using scattered seismic wavefields
http://hdl.handle.net/10197/5648
Imaging magma storage below Teide volcano (Tenerife) using scattered seismic wavefields
De Barros, Louis; Martini, Francesca; Bean, Christopher J.; GarciaYeguas, A.; Ibáñez, J.
Tenerife (Canary Islands, Spain) is a volcanic island dominated by the TeidePico Viejo complex, with a summit height of 3718 m. After renewed signs of activity starting in 2004, an active seismic experiment was performed in 2007 to derive a tomographic model and identify seismic anomalies possibly associated with the magmatic system. To complement the tomography, a double beamforming analysis is applied on two orthogonal 2D profiles crossing the island to look for evidence of the existence of a magma chamber. Numerical tests allow us to investigate the best measure of coherency between traces, and show that the correlation and nth root semblance methods give better results than the classical semblance. They also demonstrate that the technique is reliable for locating scattering structures at depth, even when the velocity model is imperfect. Applying this technique to the Tenerife data set, two main anomalies can be identified: one at approximately 7–9 km b.s.l. depth in the northern part of the island, and one shallower (1–4 km b.s.l.) beneath the main summit. These structures could be linked to the magmatic system, in good agreement with previous studies. The shallowest one may be the phonolitic storage area feeding the TeidePico Viejo complex, while the deepest structure may be related to the basaltic system.
20121101T00:00:00ZTranscriptional regulation of the human thromboxane A2 receptor gene by Wilms' tumor (WT)1 and hypermethylated in cancer (HIC) 1 in prostate and breast cancers
http://hdl.handle.net/10197/5646
Transcriptional regulation of the human thromboxane A2 receptor gene by Wilms' tumor (WT)1 and hypermethylated in cancer (HIC) 1 in prostate and breast cancers
Keating, Garret L.; Reid, Helen M.; Eivers, Sarah B.; Mulvaney, Eamon P.; Kinsella, B. Therese
The prostanoid thromboxane (TX) A2 plays a central role in hemostasis and is increasingly implicated in neoplastic disease, including prostate and breast cancers. In humans, TXA2 signals through the TPα and TPβ isoforms of the T prostanoid receptor, two structurally related receptors transcriptionally regulated by distinct promoters, Prm1 and Prm3, respectively, within the TP gene. Focusing on TPα, the current study investigated its expression and transcriptional regulation through Prm1 in prostate and breast cancers. Expression of TPα correlated with increasing prostate and breast tissue tumor grade while the TXA2 mimetic U46619 promoted both proliferation and migration of the respective prostate (PC3) and breast (MCF7 and MDAMD231) derivedcarcinoma cell lines. Through 5′ deletional and genetic reporter analyses, several functional upstream repressor regions (URRs) were identified within Prm1 in PC3, MCF7 and MDAMB231 cells while sitedirected mutagenesis identified the tumor suppressors Wilms' tumor (WT)1 and hypermethylated in cancer (HIC) 1 as the transacting factors regulating those repressor regions. Chromatin immunoprecipitation (ChIP) studies confirmed that WT1 binds in vivo to multiple GCenriched WT1 ciselements within the URRs of Prm1 in PC3, MCF7 and MDAMB231 cells. Furthermore, ChIP analyses established that HIC1 binds in vivo to the HIC1(b)ciselement within Prm1 in PC3 and MCF7 cells but not in the MDAMB231 carcinoma line. Collectively, these data establish that WT1 and HIC1, both tumor suppressors implicated in prostate and breast cancers, transcriptionally repress TPα expression and thereby provide a strong genetic basis for understanding the role of TXA2 in the progression of certain human cancers.
20140601T00:00:00ZUniversal Taylor series, conformal mappings and boundary behaviour
http://hdl.handle.net/10197/5645
Universal Taylor series, conformal mappings and boundary behaviour
Gardiner, Stephen J.
A holomorphic function f on a simply connected domain Ω is said to possess a universal Taylor series about a point in Ω if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta K outside Ω (provided only that K has connected complement). This paper shows that this property is not conformally invariant, and, in the case where Ω is the unit disc, that such functions have extreme angular
boundary behaviour.
20131201T00:00:00ZBoundary Behaviour of Universal Taylor Series on Multiply Connected Domains
http://hdl.handle.net/10197/5644
Boundary Behaviour of Universal Taylor Series on Multiply Connected Domains
Gardiner, Stephen J.; Manolaki, Myrto
A holomorphic function on a planar domain Ω is said to possess a universal Taylor series about a point ζ of Ω if subsequences of the partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compact sets in C∖Ω that have connected complement. In the case where Ω is simply connected, such functions are known to be unbounded and to form a collection that is independent of the choice of ζ. This paper uses tools from potential theory to show that, even for domains Ω of arbitrary connectivity, such functions are unbounded whenever they exist. In the doubly connected case, a further analysis of boundary behaviour reveals that the collection of such functions can depend on the choice of ζ. This phenomenon was previously known only for domains that are at least triply connected. Related results are also established for universal Laurent series.
20140501T00:00:00ZStationary Boundary Points for a Laplacian Growth Problem in Higher Dimensions
http://hdl.handle.net/10197/5643
Stationary Boundary Points for a Laplacian Growth Problem in Higher Dimensions
Gardiner, Stephen J.; Sjödin, Tomas
It is known that corners of interior angle less than π/2 in the boundary of a plane domain are initially stationary for Hele–Shaw flow arising from an arbitrary injection point inside the domain. This paper establishes the corresponding result for Laplacian growth of domains in higher dimensions. The problem is treated in terms of evolving families of quadrature domains for subharmonic functions.
20140801T00:00:00ZRoutes to visible light active Cdoped TiO2 photocatalysts using carbon atoms from the Ti precursors
http://hdl.handle.net/10197/5640
Routes to visible light active Cdoped TiO2 photocatalysts using carbon atoms from the Ti precursors
Sullivan, James A.; Neville, Elaine M.; Herron, Rory; Thampi, Ravindranathan; MacElroy, J. M. Don
In this work, different thermal treatments of titanium isopropoxidederived photocatalyst precursors, designed with the purpose of generating Cdoped TiO2 photocatalysts using carbon atoms present in the TiOx gel precursors as dopants, are presented. Specifically, these look at varying the standard calcination techniques using heat treatments in He (rather than calcination in air) and lower temperature calcinations (200 °C rather than 500 °C). The formed materials are characterised using N2 physisorption, XRD, UV Visible spectroscopy and XPS and their activities in promoting the oxidation of 4chlorophenol under visiblelightonly conditions were analysed. The nature of carbon remaining on the (or in the) material is discussed found to be both surface graphitic carbon and carbon present in anionic dopant positions. The different contributions of each type of carbon to the catalytic photoactivity under visible light are discussed.
20140529T00:00:00ZFilamentous fungal biofilm for production of human drug metabolites
http://hdl.handle.net/10197/5635
Filamentous fungal biofilm for production of human drug metabolites
Amadio, Jessica; Casey, Eoin; Murphy, Cormac D.
In drug development, access to drug metabolites is essential for assessment of toxicity and pharmacokinetic studies. Metabolites are usually acquired via chemical synthesis, although biological production is potentially more efficient with fewer waste management issues. A significant problem with the biological approach is the effective halflife of the biocatalyst, which can be resolved by immobilisation. The fungus Cunninghamella elegans is well established as a model of mammalian metabolism, although it has not yet been used to produce metabolites on a large scale. Here, we describe immobilisation of C. elegans as a biofilm, which can transform drugs to important human metabolites. The biofilm was cultivated on hydrophilic microtiter plates and in shake flasks containing a steel spring in contact with the glass. Fluorescence and confocal scanning laser microscopy revealed that the biofilm was composed of a dense network of hyphae, and biochemical analysis demonstrated that the matrix was predominantly polysaccharide. The medium composition was crucial for both biofilm formation and biotransformation of flurbiprofen. In shake flasks, the biofilm transformed 86% of the flurbiprofen added to hydroxylated metabolites within 24 h, which was slightly more than planktonic cultures (76%). The biofilm had a longer effective lifetime than the planktonic cells, which underwent lysis after 2×72 h cycles, and diluting the Sabouraud dextrose broth enabled the thickness of the biofilm to be controlled while retaining transformation efficiency. Thus, C. elegans biofilm has the potential to be applied as a robust biocatalyst for the production of human drug metabolites required for drug development.
20130701T00:00:00ZHemiacetal stabilization in a chymotrypsin inhibitor complex and the reactivity of the hydroxyl group of the catalytic serine residue of chymotrypsin
http://hdl.handle.net/10197/5629
Hemiacetal stabilization in a chymotrypsin inhibitor complex and the reactivity of the hydroxyl group of the catalytic serine residue of chymotrypsin
Cleary, Jennifer A.; Doherty, William; Evans, Paul; Malthouse, J.Paul G.
The aldehyde inhibitor ZAlaAlaPheCHO has been synthesized and shown by 13CNMR to react with the active site serine hydroxyl group of alphachymotrypsin to form two diastereomeric hemiacetals. For both hemiacetals oxyanion formation occurs with a pKa value of ~ 7 showing that chymotrypsin reduces the oxyanion pKa values by ~ 5.6 pKa units and stabilizes the oxyanions of both diastereoisomers by ~ 32 kJ mol− 1. As pH has only a small effect on binding we conclude that oxyanion formation does not have a significant effect on binding the aldehyde inhibitor. By comparing the binding of ZAlaAlaPheCHO with that of ZAlaAlaPheH we estimate that the aldehyde group increases binding ~ 100 fold. At pH 7.2 the effective molarity of the active site serine hydroxy group is ~ 6000 which is ~ 7 × less effective than with the corresponding glyoxal inhibitor. Using 1HNMR we have shown that at both 4 and 25 °C the histidine pKa is ~ 7.3 in free chymotrypsin and it is raised to ~ 8 when ZAlaAlaPheCHO is bound. We conclude that oxyanion formation only has a minor role in raising the histidine pKa and that the aldehyde hydrogen must be replaced by a larger group to raise the histidine pKa > 10 and give stereospecific formation of tetrahedral intermediates. The results show that a large increase in the pKa of the active site histidine is not needed for the active site serine hydroxyl group to have an effective molarity of 6000.
20140601T00:00:00ZA role for prolyl hydroxylase domain proteins in hippocampal synaptic plasticity
http://hdl.handle.net/10197/5624
A role for prolyl hydroxylase domain proteins in hippocampal synaptic plasticity
Corcoran, Alan; Kunze, Reiner; Harney, Sarah C.; O'Connor, J. J.; et al.
Hypoxiainducible factors (HIFs) are key transcriptional regulators that play a major role in oxygen homeostasis. HIF activity is tightly regulated by oxygendependent hydroxylases, which additionally require iron and 2oxoglutarate as cofactors. Inhibition of these enzymes has become a novel target to modulate the hypoxic response for therapeutic benefit. Inhibition of prolyl4hydroxylase domains (PHDs) have been shown to delay neuronal cell death and protect against ischemic injury in the hippocampus. In this study we have examined the effects of prolyl hydroxylase inhibition on synaptic transmission and plasticity in the hippocampus. Field excitatory postsynaptic potentials (fEPSPs) and excitatory postsynaptic currents (EPSCs) were elicited by stimulation of the Schaffer collateral pathway in the CA1 region of the hippocampus. Treatment of rat hippocampal slices with low concentrations (10 µM) of the iron chelator deferosoxamine (DFO) or the 2oxoglutarate analogue dimethyloxalyl glycine (DMOG) had no effect on fEPSP. In contrast, application of 1 mM DMOG resulted in a significant decrease in fEPSP slope. Antagonism of the NMDA receptor attenuated the effects of DMOG on baseline synaptic signalling. In rat hippocampal slices pretreated with DMOG and DFO the induction of longterm potentiation (LTP) by tetanic stimulation was strongly impaired. Similarly, neuronal knockout of the single PHD family member PHD2 prevented murine hippocampal LTP. Preconditioning of PHD2 deficient hippocampi with either DMOG, DFO, or the PHD specific inhibitor JNJ42041935, did not further decrease LTP suggesting that DMOG and DFO influences synaptic plasticity primarily by inhibiting PHDs rather than unspecific effects. These findings provide striking evidence for a modulatory role of PHD proteins on synaptic plasticity in the hippocampus.
20131001T00:00:00ZThe role of permutation coding in minimumdistortion perfect counterforensics
http://hdl.handle.net/10197/5565
The role of permutation coding in minimumdistortion perfect counterforensics
Balado, Félix
This paper exploits the connection between minimumdistortion perfect counterforensics and maximumrate perfect steganography in order to provide the optimum solution to the first of these problems, in the case in which the forensic detector solely uses first order statistics. The solution relies on Slepian’s variant I permutation codes, which had previously been shown to implement maximum
rate perfect steganography when the host is memoryless (equivalently, when the steganographic detector only uses firstorder statistics). Additionally, we demonstrate a blind counterforensic strategy made possible by permutation decoding, which may also find application in image processing.
39th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May, 2014
20140501T00:00:00ZDual harmonic Kelvin probe force microscopy at the grapheneliquid interface
http://hdl.handle.net/10197/5564
Dual harmonic Kelvin probe force microscopy at the grapheneliquid interface
Collins, Liam; Kilpatrick, J. I.; Vlassiouk, Ivan V.; Weber, Stefan A. L.; Rodriguez, Brian J.; et al.
Kelvin probe force microscopy (KPFM) is a powerful technique for the determination of the contact potential difference (CPD) between an atomic force microscope tip and a sample under ambient and vacuum conditions. However, for many energy storage and conversion systems, including graphenebased electrochemical capacitors, understanding electrochemical phenomena at the solid¿liquid interface is paramount. Despite the vast potential to provide fundamental insight for energy storage materials at the nanoscale, KPFM has found limited applicability in liquid environments to date. Here, using dual harmonic (DH)KPFM, we demonstrate CPD imaging of graphene in liquid. We find good agreement with measurements performed in air, highlighting the potential of DHKPFM to probe electrochemistry at the graphene¿liquid interface.
20140401T00:00:00ZA convenient chemicalmicrobial method for developing fluorinated pharmaceuticals
http://hdl.handle.net/10197/5557
A convenient chemicalmicrobial method for developing fluorinated pharmaceuticals
Bright, Tara V.; Dalton, Fay; Elder, Victoria L.; Murphy, Cormac D.; O'Connor, Neil K.; Sandford, Graham
A significant proportion of pharmaceuticals are fluorinated and selecting the site of fluorine incorporation can be an important beneficial part a drug development process. Here we describe initial experiments aimed at the development of a general method
of selecting optimum sites on pro  drug molecules for fluorination, so that metabolic stability may be improved. Several model biphenyl derivatives were transformed by the fungus Cunninghamella elegans and the bacterium Streptomyces griseus, both of which contain cytochromes P450 that mimic oxidation processes in vivo, so that the site of oxidation could be determined. Subsequently, fluorinated biphenyl derivatives were synthesised using appropriate Suzuki  Miyaura coupling reactions, positioning the fluorine atom at the pre  determined site of microbial oxidation; the fluorinated biphenyl derivatives were incubated with the microorganisms and the degree of oxidation assessed. Biphenyl4carboxylic acid was transformed completely to 4'  hydroxybiphenyl  4  carboxylic acid by C. elegans but, in contrast, the 4' fluoro  analogue remained untransformed exemplifying the microbial oxidation – chemical fluorination concept. 2' 
Fluoroand 3'  fluoro  biphenyl  4  carboxylic acid were also transformed, but more slowly than the non  fluorinated biphenyl carboxylic acid derivative. Thus, it is possible to design compounds in an iterative fashion with a longer metabolic half  life by identifying the sites that are most easily oxidised by in vitro methods and subsequent fluorination without recourse to extensive animal studies.
20130101T00:00:00ZPolyharmonic functions of infinite order on annular regions
http://hdl.handle.net/10197/5556
Polyharmonic functions of infinite order on annular regions
Kounchev, Ognyan; Render, Hermann
Polyharmonic functions f of in nite order and type on annular regions are
systematically studied. The rst main result states that the FourierLaplace coefficients
fk;l (r) of a polyharmonic function f of in nite order and type 0 can be extended to
analytic functions on the complex plane cut along the negative semiaxis. The second
main result gives a constructive procedure via FourierLaplace series for the analytic
extension of a polyharmonic function on annular region A(r0; r1) of in nite order and
type less than 1=2r1 to the kernel of the harmonicity hull of the annular region. The
methods of proof depend on an extensive investigation of Taylor series with respect to
linear differential operators with constant coefficients.
20130601T00:00:00ZThe approximation order of polysplines
http://hdl.handle.net/10197/5519
The approximation order of polysplines
Kounchev, Ognyan; Render, Hermann
We show that the scaling spaces de ned by the polysplines of order
p provide approximation order 2p: For that purpose we re ne the re
sults on one dimensional approximation order by Lsplines obtained
in [2].
20040701T00:00:00ZVector piezoresponse force microscopy
http://hdl.handle.net/10197/5514
Vector piezoresponse force microscopy
Kalinin, S. V.; Rodriguez, Brian J.; Jesse, S.; et al.
A novel approach for nanoscale imaging and characterization of the orientation dependence of electromechanical propertiesvector piezoresponse force microscopy (Vector PFM)is described. The relationship between local electromechanical response, polarization, piezoelectric constants, and crystallographic orientation is analyzed in detail. The image formation mechanism in vector PFM is discussed. Conditions for complete threedimensional (313) reconstruction of the electromechanical response vector and evaluation of the piezoelectric constants from PFM data are set forth. The developed approach can be applied to crystallographic orientation imaging in piezoelectric materials with a spatial resolution below 10 nm. Several approaches for data representation in 2DPFM and 3DPFM are presented. The potential of vector PFM for molecular orientation imaging in macroscopically disordered piezoelectric polymers and biological systems is discussed.
20060601T00:00:00ZPolyharmonicity and algebraic support of measures
http://hdl.handle.net/10197/5511
Polyharmonicity and algebraic support of measures
Kounchev, Ognyan; Render, Hermann
Our main result states that two signed measures μ and ν with bounded
support contained in the zero set of a polynomial P(χ) are equal if they coincide on the
subspace of all polynomials of polyharmonic degree NP where the natural number NP is
explicitly computed by the properties of the polynomial P(χ). The method of proof
depends on a definition of a multivariate Markov transform which is another major
objective of the present paper. The classical notion of orthogonal polynomial of second
kind is generalized to the multivariate setting: it is a polyharmonic function which has
similar features to those in the onedimensional case.
20070201T00:00:00ZConvergence of polyharmonic splines on semiregular grids Z x aZ^n for a to 0
http://hdl.handle.net/10197/5510
Convergence of polyharmonic splines on semiregular grids Z x aZ^n for a to 0
Kounchev, Ognyan; Render, Hermann
Let
p,n
∈
N
with 2
p
≥
n
+ 2
,
and let
I
a
be a polyharmonic spline of
order
p
on the grid
Z
×
a
Z
n
which satisfies the interpolating conditions
I
a
(
j,am
) =
d
j
(
am
) for
j
∈
Z
,m
∈
Z
n
where the functions
d
j
:
R
n
→
R
and the parameter
a>
0 are given. Let
B
s
(
R
n
) be the set of all integrable
functions
f
:
R
n
→
C
such that the integral
k
f
k
s
:=
Z
R
n
b
f
(
ξ
)
(1 +

ξ

s
)
dξ
is finite. The main result states that for given
σ
≥
0 there exists a
constant
c>
0 such that whenever
d
j
∈
B
2
p
(
R
n
)
∩
C
(
R
n
)
,j
∈
Z
,
satisfy
k
d
j
k
2
p
≤
D
·
(1 +

j

σ
) for all
j
∈
Z
there exists a polyspline
S
:
R
n
+1
→
C
of order
p
on strips such that

S
(
t,y
)
−
I
a
(
t,y
)
≤
a
2
p
−
1
c
·
D
·
(1 +

t

σ
)
for all
y
∈
R
n
,t
∈
R
and all 0
<a
≤
1.
20070701T00:00:00ZOn realanalytic recurrence relations for cardinal exponential Bsplines
http://hdl.handle.net/10197/5508
On realanalytic recurrence relations for cardinal exponential Bsplines
Aldaz, J. M.; Kounchev, Ognyan; Render, Hermann
Let LN+1 be a linear differential operator of order N + 1 with constant coefficients
and real eigenvalues λ 1, ..., λ N+1, let E( N+1) be the space of all C∞solutions of
LN+1 on the real line.We show that for N 2 and n = 2, ...,N, there is a recurrence
relation from suitable subspaces εn to εn+1 involving realanalytic functions, and
with εN+1 = E(Λ N+1) if and only if contiguous eigenvalues are equally spaced.
20071001T00:00:00ZPadé approximation for a multivariate Markov transform
http://hdl.handle.net/10197/5503
Padé approximation for a multivariate Markov transform
Kounchev, Ognyan; Render, Hermann
Methods of Padè approximation are used to analyse a multivariate
Markov transform which has been recently introduced by the authors.
The first main result is a characterization of the rationality of the
Markov transform via Hankel determinants. The second main result
is a cubature formula for a special class of measure.
20081001T00:00:00ZOn the mixed Cauchy problem with data on singular conics
http://hdl.handle.net/10197/5501
On the mixed Cauchy problem with data on singular conics
Ebenfelt, Peter; Render, Hermann
We consider a problem of mixed Cauchy type for certain holomorphic partial differential
operators with the principal part Q2p(D) essentially being the (complex) Laplace operator to
a power, Δp. We provide inital data on a singular conic divisor given by P = 0, where P is a
homogeneous polynomial of degree 2p. We show that this problem is uniquely solvable if the
polynomial P is elliptic, in a certain sense, with respect to the principal part Q2p(D).
20080801T00:00:00ZThe Goursat problem for a generalized Helmholtz operator in the plane
http://hdl.handle.net/10197/5500
The Goursat problem for a generalized Helmholtz operator in the plane
Ebenfelt, Peter; Render, Hermann
We consider the Goursat problem in the plane for partial differential operators whose principal part is the pth power of the standard Laplace operator. The data is posed on a union of 2p distinct lines through the origin. We show that the solvability of this Goursat problem depends on Diophantine properties of the geometry of lines on which the data is posed.
20080901T00:00:00ZReproducing kernels for polyharmonic polynomials
http://hdl.handle.net/10197/5499
Reproducing kernels for polyharmonic polynomials
Render, Hermann
The reproducing kernel of the space of all homogeneous polynomi
als of degree
k
and polyharmonic order
m
is computed explicitly, solving a
question of A. Fryant and M.K. Vemuri.
20081001T00:00:00ZBernstein operators for exponential polynomials
http://hdl.handle.net/10197/5498
Bernstein operators for exponential polynomials
Aldaz, J. M.; Kounchev, Ognyan; Render, Hermann
Let
L
be a linear differential operator with constant coefficients of order
n
and complex eigenvalues
λ
0
,...,λ
n
. Assume that the set
U
n
of all solutions of the
equation
Lf
= 0 is closed under complex conjugation. If the length of the interval [
a,b
]
is smaller than
π/M
n
, where
M
n
:= max
{
Im
λ
j

:
j
= 0
,...,n
}
, then there exists a basis
p
n,k
,
k
= 0
,...n
, of the space
U
n
with the property that each
p
n,k
has a zero of order
k
at
a
and a zero of order
n
−
k
at
b,
and each
p
n,k
is positive on the open interval (
a,b
)
.
Under the additional assumption that
λ
0
and
λ
1
are real and distinct, our first main
result states that there exist points
a
=
t
0
<t
1
<...<t
n
=
b
and positive numbers
α
0
,..,α
n
, such that the operator
B
n
f
:=
n
X
k
=0
α
k
f
(
t
k
)
p
n,k
(
x
)
satisfies
B
n
e
λ
j
x
=
e
λ
j
x
, for
j
= 0
,
1
.
The second main result gives a sufficient condition
guaranteeing the uniform convergence of
B
n
f
to
f
for each
f
∈
C
[
a,b
].
20090401T00:00:00ZOn the Bernstein operator of S. Morigi and M. Neamtu
http://hdl.handle.net/10197/5496
On the Bernstein operator of S. Morigi and M. Neamtu
Kounchev, Ognyan; Render, Hermann
We discuss a Bernstein type operator introduced by S. Morigi and
M. Neamtu for
D
polynomials in the more general framework of exponential
polynomials
20091001T00:00:00ZShape preserving properties of generalized Bernstein operators on extended Chebyshev spaces
http://hdl.handle.net/10197/5495
Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces
Aldaz, J. M.; Kounchev, Ognyan; Render, Hermann
We study the existence and shape preserving properties of a generalized
Bernstein operator
B
n
fixing a strictly positive function
f
0
, and a second function
f
1
such
that
f
1
/f
0
is strictly increasing, within the framework of extended Chebyshev spaces
U
n
.
The first main result gives an inductive criterion for existence: suppose there exists a
Bernstein operator
B
n
:
C
[
a,b
]
→
U
n
with strictly increasing nodes, fixing
f
0
,f
1
∈
U
n
.
If
U
n
⊂
U
n
+1
and
U
n
+1
has a nonnegative Bernstein basis, then there exists a Bernstein
operator
B
n
+1
:
C
[
a,b
]
→
U
n
+1
with strictly increasing nodes, fixing
f
0
and
f
1
.
In
particular, if
f
0
,f
1
,...,f
n
is a basis of
U
n
such that the linear span of
f
0
,..,f
k
is an
extended Chebyshev space over [
a,b
] for each
k
= 0
,...,n
, then there exists a Bernstein
operator
B
n
with increasing nodes fixing
f
0
and
f
1
.
The second main result says that
under the above assumptions the following inequalities hold
B
n
f
≥
B
n
+1
f
≥
f
for all (
f
0
,f
1
)convex functions
f
∈
C
[
a,b
]
.
Furthermore,
B
n
f
is (
f
0
,f
1
)convex for all
(
f
0
,f
1
)convex functions
f
∈
C
[
a,b
]
.
20091201T00:00:00ZCauchy, Goursat and Dirichlet problems for holomorphic partial differential equations
http://hdl.handle.net/10197/5492
Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations
Render, Hermann
n this paper we survey recent results about Fischer decomposi
tions of polynomials or entire functions and their applications to holomorphic
partial di erential equations. We discuss Cauchy and Goursat problems for the
polyharmonic operator. Special emphasis is given to the KhavinsonShapiro
conjecture concerning polynomial solvability of the Dirichlet problem.
20110101T00:00:00ZThe KhavinsonShapiro conjecture and polynomial decompositions
http://hdl.handle.net/10197/5490
The KhavinsonShapiro conjecture and polynomial decompositions
Lundberg, Erik; Render, Hermann
The main result of the paper states the following: Let ψ be a polynomial
in n variables of degree t: Suppose that there exists a constant C > 0 such
that any polynomial f has a polynomial decomposition f = ψ qf + hf with
khf = 0 and deg qf deg f + C: Then deg ψ 2k. Here ∆k is the kth
iterate of the Laplace operator ∆ : As an application, new classes of domains
in Rn are identi ed for which the KhavinsonShapiro conjecture holds.
20110415T00:00:00ZPolyharmonic Hardy spaces on the complexified annulus and error estimates of cubature formulas
http://hdl.handle.net/10197/5489
Polyharmonic Hardy spaces on the complexified annulus and error estimates of cubature formulas
Kounchev, Ognyan; Render, Hermann
The present paper has a twofold contribution: first, we intro
duce a new concept of Hardy spaces on a multidimensional complexified
annular domain which is closely related to the annulus of the KleinDi
rac
quadric important in Conformal Quantum Field Theory. Secondly, for
functions in these Hardy spaces, we provide error estimate for the p
oly
harmonic GaußJacobi cubature formulas, which have been introduced
in previous papers.
20121201T00:00:00ZHarmonic divisors and rationality of zeros of Jacobi polynomials
http://hdl.handle.net/10197/5488
Harmonic divisors and rationality of zeros of Jacobi polynomials
Render, Hermann
Let
Pn
(α,β
)
(
x
)
be the Jacobi polynomial of degree
n
with parameters
αβ
The main result of the paper states the following: If
b≠
1
;
3
and
c
are nonzero rel
atively prime natural numbers then
P
(
k
+(
d
3)
=
2
;k
+(
d
3)
=
2)
n
p
b=c
6
≠ 0
for all natural
numbers
d;n
and
k
2
N
0
:
Moreover, under the above assumption, the polynomial
Q
(
x
) =
b
c
x
2
1
+
:::
+
x
2
d
1
+
b
c
1
x
2
d
is not a harmonic divisor, and the Dirichlet problem for
the cone
f
Q
(
x
)
<
0
g
has polynomial harmonic solutions for polynomial data functions.
20130801T00:00:00ZRegularity of generalized Daubechies wavelets reproducing exponential polynomials with realvalued parameters
http://hdl.handle.net/10197/5484
Regularity of generalized Daubechies wavelets reproducing exponential polynomials with realvalued parameters
Dyn, Nira; Kounchev, Ognyan; Levin, David; Render, Hermann
We investigate nonstationary orthogonal wavelets based on a nonstationary
interpolatory subdivision scheme reproducing a given set of exponentials with realvalued
parameters. The construction is analogous to the construction of Daubechies wavelets
using the subdivision scheme of DeslauriersDubuc. The main result is the existence and
smoothness of these Daubechies type wavelets.
20140901T00:00:00ZConvergence of rational Bernstein operators
http://hdl.handle.net/10197/5478
Convergence of rational Bernstein operators
Render, Hermann
In this paper we discuss convergence properties and error estimates of rational
Bernstein operators introduced by P. Pit¸ul and P. Sablonni`ere. It is shown that the
rational Bernstein operators converge to the identity operator if and only if the maximal
difference between two consecutive nodes is converging to zero. Further a Voronovskaja
theorem is given based on the explicit computation of higher order moments for the
rational Bernstein operator
20140401T00:00:00ZQuantitative determination of tip parameters in piezoresponse force microscopy
http://hdl.handle.net/10197/5475
Quantitative determination of tip parameters in piezoresponse force microscopy
Kalinin, S. V.; Jesse, S.; Rodriguez, Brian J.; et al.
One of the key limiting factors in the quantitative interpretation of piezoresponse force microscopy (PFM) is the lack of knowledge on the effective tip geometry. Here the authors derive analytical expressions for a 180 degrees domain wall profile in PFM for the point charge, sphere plane, and disk electrode models of the tip. An approach for the determination of the effective tip parameters from the wall profile is suggested and illustrated for several ferroelectric materials. The calculated tip parameters can be used selfconsistently for the interpretation of PFM resolution and spectroscopy data, i.e., linear imaging processes.
20070524T00:00:00ZReal Bargmann spaces, Fischer decompositions and Sets of uniqueness for polyharmonic functions
http://hdl.handle.net/10197/5474
Real Bargmann spaces, Fischer decompositions and Sets of uniqueness for polyharmonic functions
Render, Hermann
In this paper a positive answer is given to the following question of W.K.
Hayman: if a polyharmonic entire function of order k vanishes on k distinct ellipsoids
in the euclidean space Rn then it vanishes everywhere. Moreover a characterization of
ellipsoids is given in terms of an extension property of solutions of entire data functions
for the Dirichlet problem answering a question of D. Khavinson and H.S. Shapiro. These
results are consequences from a more general result in the context of direct sum decompositions
(Fischer decompositions) of polynomials or functions in the algebra A(BR)
of all realanalytic functions defined on the ball BR of radius R and center 0 whose
Taylor series of homogeneous polynomials converges compactly in BR. The main result
states that for a given elliptic polynomial P of degree 2k and sufficiently large radius
R > 0 the following decomposition holds: for each function f 2 A(BR) there exist
unique q, r 2 A(BR) such that f = Pq + r and kr = 0. Another application of this
result is the existence of polynomial solutions of the polyharmonic equation ku = 0 for
polynomial data on certain classes of algebraic hypersurfaces.
2000 Mathematical Subject Classification. Primary: 31B30. Secondary: 35A20,
14P99, 12Y05
20080401T00:00:00Z