Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere

We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot product kernels defined on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0. We illustrate our results with examples, among them the integral operator generated by a Gaussian kernel. Finally, we sketch complex versions of our results to cover the cases when the sphere sits in a Hermitian space.

Canine heartworm disease in Porto Velho: first record, distribution map and occurrence of positive mosquitoes

The aim of this study was to make the first report on canine heartworm disease in the state of Rondônia and confirm its transmission in this state. Blood samples were randomly collected from 727 dogs in the city of Porto Velho. The samples were analyzed to search for microfilariae and circulating antigens, using three different techniques: optical microscopy on thick blood smears stained with Giemsa; immunochromatography; and PCR. Mosquitoes were collected inside and outside the homes of all the cases of positive dogs and were tested using PCR to search for DNA of Dirofilaria immitis. Ninety-three blood samples out of 727 (12.8%) were positive according to the immunoassay technique and none according to the thick smear method. Among the 93 positive dogs, 89 (95.7%) were born in Porto Velho. No difference in the frequency of infection was observed between dogs raised indoors and in the yard. PCR on the mosquitoes resulted in only one positive pool. This result shows that the transmission of canine heartworm disease is occurring in the city of Porto Velho and that there is moderate prevalence among the dogs. The techniques of immunochromatography and PCR were more effective for detecting canine heartworm than thick blood smears. The confirmation of canine heartworm disease transmission in Porto Velho places this disease in the ranking for differential diagnosis of pulmonary nodules in humans in Rondônia.

Humoral autoimmune response heterogeneity in the spectrum of primary biliary cirrhosis

Objective To compare autoantibody features in patients with primary biliary cirrhosis (PBC) and individuals presenting antimitochondria antibodies (AMAs) but no clinical or biochemical evidence of disease. Methods A total of 212 AMA-positive serum samples were classified into four groups: PBC (definite PBC, n = 93); PBC/autoimmune disease (AID; PBC plus other AID, n = 37); biochemically normal (BN) individuals (n = 61); and BN/AID (BN plus other AID, n = 21). Samples were tested by indirect immunofluorescence (IIF) on rat kidney (IIF-AMA) and ELISA [antibodies to pyruvate dehydrogenase E2-complex (PDC-E2), gp-210, Sp-100, and CENP-A/B]. AMA isotype was determined by IIF-AMA. Affinity of anti-PDC-E2 IgG was determined by 8 M urea-modified ELISA. Results High-titer IIF-AMA was more frequent in PBC and PBC/AID (57 and 70 %) than in BN and BN/AID samples (23 and 19 %) (p < 0.001). Triple isotype IIF-AMA (IgA/IgM/IgG) was more frequent in PBC and PBC/AID samples (35 and 43 %) than in BN sample (18 %; p = 0.008; p = 0.013, respectively). Anti-PDC-E2 levels were higher in PBC (mean 3.82; 95 % CI 3.36–4.29) and PBC/AID samples (3.89; 3.15–4.63) than in BN (2.43; 1.92–2.94) and BN/AID samples (2.52; 1.54–3.50) (p < 0.001). Anti-PDC-E2 avidity was higher in PBC (mean 64.5 %; 95 % CI 57.5–71.5 %) and PBC/AID samples (66.1 %; 54.4–77.8 %) than in BN samples (39.2 %; 30.9–37.5 %) (p < 0.001). PBC and PBC/AID recognized more cell domains (mitochondria, nuclear envelope, PML/sp-100 bodies, centromere) than BN (p = 0.008) and BN/AID samples (p = 0.002). Three variables were independently associated with established PBC: high-avidity anti-PDC-E2 (OR 4.121; 95 % CI 2.118–8.019); high-titer IIF-AMA (OR 4.890; 2.319–10.314); antibodies to three or more antigenic cell domains (OR 9.414; 1.924–46.060). Conclusion The autoantibody profile was quantitatively and qualitatively more robust in definite PBC as compared with AMA-positive biochemically normal individuals.

On existence and uniqueness of positive solutions to a class of fractional boundary value problems

[EN] The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ′ ( 0 ) = 0 , where 2 < α ≤ 3 and D 0 + α is the Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem in partially ordered metric spaces. The autonomous case of this problem was studied in the paper [Zhao et al., Abs. Appl. Anal., to appear], but in Zhao et al. (to appear), the question of uniqueness of the solution is not treated. We also present some examples where we compare our results with the ones obtained in Zhao et al. (to appear). 2010 Mathematics Subject Classification: 34B15

Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems

[EN] We establish the existence and uniqueness of a positive and nondecreasing solution to a singular boundary value problem of a class of nonlinear fractional differential equation. Our analysis relies on a fixed point theorem in partially ordered sets.

Mechanism of resistance to tyrosine kinase inhibitors in philadelphia-positive acute lymphblastic leukaemia (all): from genetic alterations to impaired RNA editing

The Ph chromosome is the most frequent cytogenetic aberration associated with adult ALL and it represents the single most significant adverse prognostic marker. Despite imatinib has led to significant improvements in the treatment of patients with Ph+ ALL, in the majority of cases resistance developed quickly and disease progressed. Some mechanisms of resistance have been widely described but the full knowledge of contributing factors, driving both the disease and resistance, remains to be defined. The observation of rapid development of lymphoblastic leukemia in mice expressing altered Ikaros (Ik) isoforms represented the background of this study. Ikaros is a zinc finger transcription factor required for normal hemopoietic differentiation and proliferation, particularly in the lymphoid lineages. By means of alternative splicing, Ikaros encodes several proteins that differ in their abilities to bind to a consensus DNA-binding site. Shorter, DNA nonbinding isoforms exert a dominant negative effect, inhibiting the ability of longer heterodimer partners to bind DNA. The differential expression pattern of Ik isoforms in Ph+ ALL patients was analyzed in order to determine if molecular abnormalities involving the Ik gene could associate with resistance to imatinib and dasatinib. Bone marrow and peripheral blood samples from 46 adult patients (median age 55 yrs, 18-76) with Ph+ ALL at diagnosis and during treatment with imatinib (16 pts) or dasatinib (30 pts) were collected. We set up a fast, high-throughput method based on capillary electrophoresis technology to detect and quantify splice variants. 41% Ph+ ALL patients expressed high levels of the non DNA-binding dominant negative Ik6 isoform lacking critical N-terminal zinc-fingers which display abnormal subcellular compartmentalization pattern. Nuclear extracts from patients expressed Ik6 failed to bind DNA in mobility shift assay using a DNA probe containing an Ikaros-specific DNA binding sequence. In 59% Ph+ ALL patients there was the coexistence in the same PCR sample and at the same time of many splice variants corresponded to Ik1, Ik2, Ik4, Ik4A, Ik5A, Ik6, Ik6 and Ik8 isoforms. In these patients aberrant full-length Ikaros isoforms in Ph+ ALL characterized by a 60-bp insertion immediately downstream of exon 3 and a recurring 30-bp in-frame deletion at the end of exon 7 involving most frequently the Ik2, Ik4 isoforms were also identified. Both the insertion and deletion were due to the selection of alternative splice donor and acceptor sites. The molecular monitoring of minimal residual disease showed for the first time in vivo that the Ik6 expression strongly correlated with the BCR-ABL transcript levels suggesting that this alteration could depend on the Bcr-Abl activity. Patient-derived leukaemia cells expressed dominant-negative Ik6 at diagnosis and at the time of relapse, but never during remission. In order to mechanistically demonstrated whether in vitro the overexpression of Ik6 impairs the response to tyrosine kinase inhibitors (TKIs) and contributes to resistance, an imatinib-sensitive Ik6-negative Ph+ ALL cell line (SUP-B15) was transfected with the complete Ik6 DNA coding sequence. The expression of Ik6 strongly increased proliferation and inhibited apoptosis in TKI sensitive cells establishing a previously unknown link between specific molecular defects that involve the Ikaros gene and the resistance to TKIs in Ph+ ALL patients. Amplification and genomic sequence analysis of the exon splice junction regions showed the presence of 2 single nucleotide polymorphisms (SNPs): rs10251980 [A/G] in the exon2/3 splice junction and of rs10262731 [A/G] in the exon 7/8 splice junction in 50% and 36% of patients, respectively. A variant of the rs11329346 [-/C], in 16% of patients was also found. Other two different single nucleotide substitutions not recognized as SNP were observed. Some mutations were predicted by computational analyses (RESCUE approach) to alter cis-splicing elements. In conclusion, these findings demonstrated that the post-transcriptional regulation of alternative splicing of Ikaros gene is defective in the majority of Ph+ ALL patients treated with TKIs. The overexpression of Ik6 blocking B-cell differentiation could contribute to resistance opening a time frame, during which leukaemia cells acquire secondary transforming events that confer definitive resistance to imatinib and dasatinib.

Persistent currents in quantum rings

In this thesis, three different types of quantum rings arestudied. These are quantum rings with diamagnetic,paramagnetic or spontaneous persistent currents. It turns out that the main observable to characterizequantum rings is the Drude weight. Playing a key role inthis thesis, it will be used to distinguish betweendiamagnetic (positive Drude weight) and paramagnetic(negative Drude weight) ring currents. In most models, theDrude weight is positive. Especially in the thermodynamiclimit, it is positive semi-definite. In certain modelshowever, intuitivelysurprising, a negative Drude weight is found. This rareeffect occurs, e.g., in one-dimensional models with adegenerate ground state in conjunction with the possibilityof Umklapp scattering. One aim of this thesis is to examineone-dimensional quantum rings for the occurrence of anegative Drude weight. It is found, that the sign of theDrude weight can also be negative, if the band structurelacks particle-hole symmetry. The second aim of this thesis is the modeling of quantumrings intrinsically showing a spontaneous persistentcurrent. The construction of the model starts from theextended Hubbard model on a ring threaded by anAharonov-Bohm flux. A feedback term through which thecurrent in the ring can generate magnetic flux is added.Another extension of the Hamiltonian describes the energystored in the internally generated field. This model isevaluated using exact diagonalization and an iterativescheme to find the minima of the free energy. The quantumrings must satisfy two conditions to exhibit a spontaneousorbital magnetic moment: a negative Drude weight and aninductivity above the critical level. The magneticproperties of cyclic conjugated hydrocarbons likebenzene due to electron delocalization [magnetic anisotropy,magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)]---that have become important criteriafor aromaticity---can be examined using this model. Corrections to the presented calculations are discussed. Themost substantial simplification made in this thesis is theneglect of the Zeeman interaction of the electron spins withthe magnetic field. If a single flux tube threads a quantumring, the Zeeman interaction is zero, but in mostexperiments, this situation is difficult to realize. In themore realistic situation of a homogeneous field, the Zeemaninteraction has to be included, if the electrons have atotal spin component in the direction of the magnetic field,or if the magnetic field is strong.

Depicting the role of CDKN2A/ARF alterations in adult BCR-ABL1-positive acute lymphoblastic leukemia patients: from genomic deletions to prognostic impact

This 9p21 locus, encode for important proteins involved in cell cycle regulation and apoptosis containing the p16/CDKN2A (cyclin-dependent kinase inhibitor 2a) tumor suppressor gene and two other related genes, p14/ARF and p15/CDKN2B. This locus, is a major target of inactivation in the pathogenesis of a number of human tumors, both solid and haematologic, and is a frequent site of loss or deletion also in acute lymphoblastic leukemia (ALL) ranging from 18% to 45% 1. In order to explore, at high resolution, the frequency and size of alterations affecting this locus in adult BCR-ABL1-positive ALL and to investigate their prognostic value, 112 patients (101 de novo and 11 relapse cases) were analyzed by genome-wide single nucleotide polymorphisms arrays and gene candidate deep exon sequencing. Paired diagnosis-relapse samples were further available and analyzed for 19 (19%) cases. CDKN2A/ARF and CDKN2B genomic alterations were identified in 29% and 25% of newly diagnosed patients, respectively. Deletions were monoallelic in 72% of cases and in 43% the minimal overlapping region of the lost area spanned only the CDKN2A/2B gene locus. The analysis at the time of relapse showed an almost significant increase in the detection rate of CDKN2A/ARF loss (47%) compared to diagnosis (p = 0.06). Point mutations within the 9p21 locus were found at very low level with only a non-synonymous substition in the exon 2 of CDKN2A. Finally, correlation with clinical outcome showed that deletions of CDKN2A/B are significantly associated with poor outcome in terms of overall survival (p = 0.0206), disease free-survival (p = 0.0010) and cumulative incidence of relapse (p = 0.0014). The inactivation of 9p21 locus by genomic deletions is a frequent event in BCR-ABL1-positive ALL. Deletions are frequently acquired at the leukemia progression and work as a poor prognostic marker.

Heteroatom containing polycyclic aromatic hydrocarbons with positive charge - synthesis and characterization

The synthesis and characterization of various heteroatom containing PAHs with positive charge were investigated in this work: 1. A series of 2-phenyl-benzo[8,9]quinolizino[4,5,6,7-fed]phenanthridinylium (PQP) salts with different alkyl chains and anions were synthesized. The synthesis of the extended derivates of PQP salts with two fused benzene rings, 2-phenyl-naphthacene[1,2]quinolizino[3,4,5,6-def]benzo[i]phenanthridinium (DBPQP) tetrafluoroborate was also developed. The self-assembly behavior of these amphiphilic PAHs was investigated in methanolic solution as well as in the bulk. Various aggregates with different morphologies such as fibers, tubes and vesicals were obtained from their solution. All of these morphology changes could be ascribed to the changes in intermolecular interactions which resulting from the difference in the molecular structures such as aromatic cores, alkyl chains and counterions. 2. The synthetic strategy of oxygen containing positively charged PAHs, benzo[5,6]naphthaceno[1,12,11,10-jklmna]xanthylium (BNAX) salts and its dibenzo derivates, DBNAX salts were developed. With a similar method, sulfur containing benzo[5,6]naphthaceno[1,12,11,10-jklmna]thioxanthylium (BNATX) salts were also synthesized. Various BNAX salts with different alkyl chains could be obtained and their supramolecular behavior were investigated. A discotic liquid crystalline behavior was observed for di- (3-25) and tridodecyl (3-27) substituted BNAX salts and both compounds exhibited large unit cell in their 2D-WAXS patterns which could be attributed to the formation of dimer structures. By drop casting their methanolic solution on silicon wafers, similar nanoscaled fibers from monododecyl substituted BNAX bromide 3-24 and DBNAX bromide 3-35 could be observed. 3. A novel synthetic method toward nitrogen containing 14-phenyl-dibenzo[jk,mn]naphtho[2,1,8-fgh]thebenidinium (DBNT) salts was also developed. In this method, the undehydrogenated precursor of DBNT, dibenzoacridinium salt could be produced directly from the reaction between dibenzoxanthenylium derivates and amine/aniline in reasonable yields. Various DBNT salts with different alkyl and alkylphenyl chains on their nitrogen atom were synthesized in this two-step method. The self-assembly behavior of two alkylated DBNT salts, 4-15a and 4-18b was also studied in this work. Compound 4-15a formed nanoscaled fibers and helical aggregates were obtained from 4-18b in their methanolic solutions. 4. Various ionic complexes were derived by complexing PQP and DBPQP cations with different sulfate/sulfonate group containing anionic surfactants. The ionic complexes resulting from the ionic self-assembly (ISA) method exhibited self-assembly behavior which was controllable by the species and shape of cations and anions. Various aggregates such as nanofibers and spherical aggregates could be produced from their methanolic solution in a defined manner conveniently.

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

Factorization method and irregular inclusions in electrical impedance tomography

In electrical impedance tomography, one tries to recover the conductivity inside a physical body from boundary measurements of current and voltage. In many practically important situations, the investigated object has known background conductivity but it is contaminated by inhomogeneities. The factorization method of Andreas Kirsch provides a tool for locating such inclusions. Earlier, it has been shown that under suitable regularity conditions positive (or negative) inhomogeneities can be characterized by the factorization technique if the conductivity or one of its higher normal derivatives jumps on the boundaries of the inclusions. In this work, we use a monotonicity argument to generalize these results: We show that the factorization method provides a characterization of an open inclusion (modulo its boundary) if each point inside the inhomogeneity has an open neighbourhood where the perturbation of the conductivity is strictly positive (or negative) definite. In particular, we do not assume any regularity of the inclusion boundary or set any conditions on the behaviour of the perturbed conductivity at the inclusion boundary. Our theoretical findings are verified by two-dimensional numerical experiments.