Analytic and probabilistic problems in discrete geometry

The thesis concentrates on two problems in discrete geometry, whose solutions are obtained by analytic, probabilistic and combinatoric tools. The first chapter deals with the strong polarization problem. This states that for any sequence u1,...,un of norm 1 vectors in a real Hilbert space H , there exists a unit vector \vartheta \epsilon H , such that \sum 1 over [ui, v]2 \leqslant n2. The 2-dimensional case is proved by complex analytic methods. For the higher dimensional extremal cases, we prove a tensorisation result that is similar to F. John's theorem about characterisation of ellipsoids of maximal volume. From this, we deduce that the only full dimensional locally extremal system is the orthonormal system. We also obtain the same result for the weaker, original polarization problem. The second chapter investigates a problem in probabilistic geometry. Take n independent, uniform random points in a triangle T. Convex chains between two fixed vertices of T are defined naturally. Let Ln denote the maximal size of a convex chain. We prove that the expectation of Ln is asymptotically \alpha n1/3, where \alpha is a constant between 1:5 and 3:5 - we conjecture that the correct value is 3. We also prove strong concentration results for Ln, which, in turn, imply a limit shape result for the longest convex chains

Structure and Magnetic Properties of the Radical Cation Salt of a TTF-based NiII Complex

Chemical oxidation of a TTF-based NiII complex with I2 produces the corresponding radical cation salt 1, [Ni2Cl2(L)2](I3)2(I5)2(I2)(H2O)2(C4H8O)3, (L=4,5-bis(2-pyridylmethylsulfanyl)-4',5'-ethylenedithiotetrathiafulvalene). The results of magnetic susceptibility measurements show the occurrence of intramolecular magnetic exchange interactions in 1. The lack of close S···S contacts, confirmed by crystal structure analysis, results in an insulating behavio

Altered mitochondrial response to activation of T-cells in neonate

Mitochondrial functions have a major impact on T-cell functionality. In this study we characterized whether mitochondrial function in the neonatal T-cells differs from that in the adult T-cells during short T-cell activation. METHODS: We used fow cytometry methods to test mitochondrial mass and to monitor mitochondrial Ca(2+) levels, mitochondrial potential and superoxide generation in parallel with cytoplasmic Ca(2+) levels during phythohaemagglutinine-induced activation of CD4+ and CD8+ T-cells of 12 term neonates and 11 healthy adults. RESULTS: Baseline mitochondrial mass of CD4+ and CD8+ cells was lower in the neonate than in the adult. In comparison with the adult, neonatal resting CD4+ T-cells had lower cytoplasmic Ca(2+) levels and this was associated with normal activation induced Ca(2+)-response. During short-term activation cytoplasmic Ca(2+)-response was lower in neonatal than in adult CD8+ T-cells. Mitochondrial Ca(2+) uptake was increased in CD4+ neonatal T cells while it decreased in CD8+ T-cells. Mitochondrial depolarization was increased in CD4+ and decreased in CD8+ neonatal T-cells compared to adults. Superoxide generation was higher and equal in neonatal CD4+ and CD8+ cells, respectively, compared to the adult ones. CONCLUSION: Our data suggest that neonatal T-cells exhibit marked differences in mitochondrial function and superoxide generation compared to adult T-cells

Your place or mine? The neural dynamics of personally familiar scene recognition suggests category independent familiarity encoding.

Recognizing a stimulus as familiar is an important capacity in our everyday life. Recent investigation of visual processes has led to important insights into the nature of the neural representations of familiarity for human faces. Still, little is known about how familiarity affects the neural dynamics of non-face stimulus processing. Here we report the results of an EEG study, examining the representational dynamics of personally familiar scenes. Participants viewed highly variable images of their own apartments and unfamiliar ones, as well as personally familiar and unfamiliar faces. Multivariate pattern analyses were used to examine the time course of differential processing of familiar and unfamiliar stimuli. Time-resolved classification revealed that familiarity is decodable from the EEG data similarly for scenes and faces. The temporal dynamics showed delayed onsets and peaks for scenes as compared to faces. Familiarity information, starting at 200 ms, generalized across stimulus categories and led to a robust familiarity effect. In addition, familiarity enhanced category representations in early (250-300 ms) and later (>400 ms) processing stages. Our results extend previous face familiarity results to another stimulus category and suggest that familiarity as a construct can be understood as a general, stimulus-independent processing step during recognition

Person identity-specific adaptation effects in the ventral occipito-temporal cortex

Identifying the faces of familiar persons requires the ability to assign several different images of a face to a common identity. Previous research showed that the occipito-temporal cortex, including the fusiform and the occipital face areas, is sensitive to personal identity. Still, the viewpoint, facial expression, and image-independence of this information are currently under heavy debate. Here we adapted a rapid serial visual stimulation paradigm (Johnston et al., 2016) and presented highly variable ambient-face images of famous persons to measure fMRI adaptation. FMRI adaptation is considered as the neuroimaging manifestation of repetition suppression, a neural phenomenon currently explained as a correlate of reduced predictive error responses for expected stimuli. We revisited the question of image-invariant identity-specific encoding mechanisms of the occipito-temporal cortex, using fMRI adaptation with a particular interest in predictive mechanisms. Participants were presented with trials containing eight different images of a famous person, images of eight different famous persons, or seven different images of a particular famous person followed by an identity change to violate potential expectation effects about person identity. We found an image-independent adaptation effect of identity for famous faces in the fusiform face area. However, in contrast to previous electrophysiological studies, using similar paradigms, no release of the adaptation effect was observed when identity-specific expectations were violated. Our results support recent multivariate pattern analysis studies, showing image-independent identity encoding in the core face-processing areas of the occipito-temporal cortex. These results are discussed in the frame of recent identity-processing models and predictive mechanisms

The neural dynamics of familiarity-dependent face identity representation

Recognizing a face as belonging to a given identity is essential in our everyday life. Clearly, the correct identification of a face is only possible for familiar people, but ‘familiarity’ covers a wide range—from people we see every day to those we barely know. Although several studies have shown that the processing of familiar and unfamiliar faces is substantially different, little is known about how the degree of familiarity affects the neural dynamics of face identity processing. Here, we report the results of a multivariate EEG analysis, examining the representational dynamics of face identity across several familiarity levels. Participants viewed highly variable face images of 20 identities, including the participants' own face, personally familiar (PF), celebrity and unfamiliar faces. Linear discriminant classifiers were trained and tested on EEG patterns to discriminate pairs of identities of the same familiarity level. Time-resolved classification revealed that the neural representations of identity discrimination emerge around 100ms post-stimulus onset, relatively independently of familiarity level. In contrast, identity decoding between 200 and 400ms is determined to a large extent by familiarity: it can be recovered with higher accuracy and for a longer duration in the case of more familiar faces. In addition, we found no increased discriminability for faces of PF persons compared to those of highly familiar celebrities. One's own face benefits from processing advantages only in a relatively late time-window. Our findings provide new insights into how the brain represents face identity with various degrees of familiarity and show that the degree of familiarity modulates the available identity-specific information at a relatively early time window

Decrease in alpha-1 antiproteinase antitrypsin is observed in primary Sjogren's syndrome condition

Primary Sjogren’s syndrome (pSS) is a systemic autoimmune disease that is characterized by the infiltration of immune cells. Although the loss of salivary gland function is a major manifestation observed in pSS, the factors that could promote these changes in salivary gland tissue in pSS is not yet determined. Herein, we provide evidence that loss of alpha-1 antiproteinase antitrypsin could contribute to the induction of pSS. Alpha-1 antiproteinase antitrypsin belongs to the family of serpin proteins that function as protease inhibitors and protect secretory cells against proteases, especially to elastases that is secreted from lymphocytes. Importantly, expression of alpha-1 antiproteinase antitrypsin was decreased (more than 3-fold), along with an increase in elastase expression, in pSS samples when compared with age-matched non-SS-SICCA patients. Consistent with the human data, loss of alpha-1 antiproteinase antitrypsin, as well as an increase in immune infiltration, was observed in IL14α transgenic mice that exhibit SS like symptoms. Moreover, an age-dependent increase in elastase expression was observed in IL14α transgenic mice along with a decrease in total saliva secretion. Importantly, a 4-fold increase in microRNA132 expression, but not in other microRNAs, and increased DNA methylation in the promoter/noncoding region of serpina gene was observed in pSS, which could be responsible for the inhibition of alpha-1 antiproteinase antitrypsin expression in salivary gland cells of pSS patients. Together, these findings demonstrate that epigenetic regulations that include DNA methylation and microRNAs that could modulate the expression of alpha-1 antiproteinase antitrypsin in salivary glands and could be involved in the onset of pSS

Embedding variables in finite dimensional models

Global problems associated with the transformation from the Arnowitt, Deser and Misner (ADM) to the Kucha\v{r} variables are studied. Two models are considered: The Friedmann cosmology with scalar matter and the torus sector of the 2+1 gravity. For the Friedmann model, the transformations to the Kucha\v{r} description corresponding to three different popular time coordinates are shown to exist on the whole ADM phase space, which becomes a proper subset of the Kucha\v{r} phase spaces. The 2+1 gravity model is shown to admit a description by embedding variables everywhere, even at the points with additional symmetry. The transformation from the Kucha\v{r} to the ADM description is, however, many-to-one there, and so the two descriptions are inequivalent for this model, too. The most interesting result is that the new constraint surface is free from the conical singularity and the new dynamical equations are linearization stable. However, some residual pathology persists in the Kucha\v{r} description.Comment: Latex 2e, 29 pages, no figure

The Bb fragment of complement factor B acts as a B cell growth factor.

The process of B cell growth and differentiation into plasma cells is highly regulated and may be influenced by a large number of inflammatory mediators, including complement components. We have studied the regulatory influence of Bb, a 60-kD peptide created during the cleavage of complement Factor B by Factor D and C3b. Purified Bb alone had no effect on proliferation and differentiation of human splenic or tonsillar B cells. However, when B cells were activated by Staphylococcus aureus Cowan I (SAC), Bb enhanced proliferation in a dose-dependent manner. Bb also enhanced proliferation when cocultured with SAC and suboptimal concentrations of purified 60-kD B cell growth factor (HMW-BCGF), a previously described lymphokine that is known to possess growth-promoting activity. However, Bb had no effect on cells treated with optimal concentrations of HMW-BCGF. Like HMW-BCGF, Bb's major effect was on the larger in vivo activated B cells. Half-maximal enhancement of proliferation was reached at a Bb concentration of 1-10 nM. Of note is the fact that antibody to Factor B recognized HMW-BCGF, and an mAb to HMW-BCGF also recognized Factor B and Bb, but not Ba. Moreover, radiolabeled Bb bound saturably to activated B cells and to an EBV-transformed human B cell line. The binding of Bb was inhibited by HMW-BCGF but not by Ba or IgG. Thus, Bb is antigenically and functionally related to HMW-BCGF, and can act as a B cell growth and differentiation factor at potentially physiologic concentrations. These data suggest that Bb may be important in amplifying the immune response in areas of inflammation. Since complement activation occurs at inflammatory sites long before induction of HMW-BCGF synthesis, Bb may be an early signal for the clonal expansion of antigen-activated B cells