Benson's Theorem for Partial Geometries

In 1970 Clark Benson published a theorem in the Journal of Algebra stating a congruence for generalized quadrangles. Since then this theorem has been expanded to other specific geometries. In this thesis the theorem for partial geometries is extended to develop new divisibility conditions for the existence of a partial geometry in Chapter 2. Then in Chapter 3 the theorem is applied to higher dimensional arcs resulting in parameter restrictions on geometries derived from these structures. In Chapter 4 we look at extending previous work with partial geometries with α = 2 to uncover potential partial geometries with higher values of α. Finally the theorem is extended to strongly regular graphs in Chapter 5. In addition we obtain expressions for the multiplicities of the eigenvalues of matrices related to the adjacency matrices of these graphs. Finally, a four lesson high school level enrichment unit is included to provide students at this level with an introduction to partial geometries, strongly regular graphs, and an opportunity to develop proof skills in this new context.

Noninvasive assessment of acute ureteral obstruction with diffusion-weighted MR imaging: a prospective study

PURPOSE: To prospectively assess the potential of noninvasive diffusion-weighted magnetic resonance (MR) imaging to depict changes in microperfusion and diffusion in patients with acute unilateral ureteral obstruction. MATERIALS AND METHODS: The local ethics committee approved the study protocol. Informed consent was obtained. Diffusion-weighted MR imaging was performed in 21 patients (two women, 19 men; mean age, 43 years +/- 10 [standard deviation]) with acute unilateral ureteral obstruction due to a calculus diagnosed at unenhanced computed tomography. A control group (one woman, 15 men; mean age, 44 years +/- 12) underwent the same MR protocol. Standard processing yielded an apparent diffusion coefficient (ADC) ADCT; the separation of microperfusion and diffusion contributions yielded the perfusion fraction FP and the pure diffusion coefficient ADCD. ADCT, ADCD, and FP were compared between obstructed and contralateral unobstructed kidneys and with control values. For statistical analysis, nonparametric rank tests were used. A P value of less than .05 was considered significant. RESULTS: No significant differences were observed between the ADCT of the medulla or cortex of the obstructed and unobstructed kidneys. Compared with control kidneys, only medullary ADCT was slightly increased in the obstructed kidney (P < .04). However, the ADCD in the medulla of the obstructed and unobstructed kidneys was significantly higher than that in control subjects (201 x 10(-5) mm2/sec +/- 16 and 199 x 10(-5) mm2/sec +/- 20 vs 189 x 10(-5) mm2/sec +/- 12; P < .008 and P < .03, respectively). FP of the cortex of the obstructed kidney was significantly lower than that in the unobstructed kidney (20.2% +/- 4.8 vs 24.0% +/- 5.8; P < .002); FP of the medulla was slightly lower in the obstructed kidney than in the unobstructed kidney (18.3% +/- 5.9 vs 20.7% +/- 6.4; P = .05). CONCLUSION: Diffusion-weighted MR imaging allows noninvasive detection of changes in renal perfusion and diffusion during acute unilateral ureteral obstruction, as exemplified in patients with a ureteral calculus.

Clinical outcomes following subgingival application of a novel erythritol powder by means of air polishing in supportive periodontal therapy: a randomized, controlled clinical study

OBJECTIVES The aim of this prospective, randomized, controlled clinical study was to compare the clinical outcomes of the subgingival treatment with erythritol powder by means of an air-polishing (EPAP) device and of scaling and root planing (SRP) during supportive periodontal therapy (SPT). METHOD AND MATERIALS 40 patients enrolled in SPT were randomly assigned to two groups of equal size. Sites had to show signs of inflammation (bleeding on probing [BOP]-positive) and a probing pocket depth (PPD) of ≥ 4 mm, however, without presence of detectable subgingival calculus. During SPT, these sites were treated with EPAP or SRP, respectively. Full mouth and site-specific plaque indices, BOP, PPD, and clinical attachment level (CAL) were recorded at baseline (BL) and at 3 months, whereas the percentage of study sites positive for BOP (BOP+) was considered as primary outcome variable. Additionally, patient comfort using a visual analog scale (VAS) and the time needed to treat per site was evaluated. RESULTS At 3 months, mean BOP level measured 45.1% at test sites and 50.6% at control sites, respectively, without a statistically significant difference between the groups (P > .05). PPD and CAL slightly improved for both groups with comparable mean values at 3 months. Evaluation of patient tolerance showed statistically significantly better values among patients receiving the test treatment (mean VAS [0-10], 1.51) compared to SRP (mean VAS [0-10], 3.66; P = .0012). The treatment of test sites was set to 5 seconds per site. The treatment of control sites, on the other hand, lasted 85 seconds on average. CONCLUSION The new erythritol powder applied with an air-polishing device can be considered a promising modality for repeated instrumentation of residual pockets during SPT. CLINICAL RELEVANCE With regard to clinical outcomes during SPT, similar results can be expected irrespective of the two treatment approaches of hand instrumentation or subgingival application of erythritol powder with an air-polishing device in sites where only biofilm removal is required.

Histological evaluation of human intrabony periodontal defects treated with an unsintered nanocrystalline hydroxyapatite paste

OBJECTIVES The aim of the study was to clinically and histologically evaluate the healing of human intrabony defects treated with open flap surgery (OFD) and application of a new, resorbable, fully synthetic, unsintered, nanocrystalline, phase-pure hydroxyapatite (nano-HA). MATERIALS AND METHODS Six patients, each of them displaying very advanced intrabony defects around teeth scheduled for extraction due to advanced chronic periodontitis and further prosthodontic considerations, were included in the study. Following local anaesthesia, mucoperiosteal flaps were reflected; the granulation tissue was removed, and the roots were meticulously debrided by hand and ultrasonic instruments. A notch was placed at the most apical extent of the calculus present on the root surface or at the most apical part of the defect (if no calculus was present) in order to serve as a reference for the histological evaluation. Following defect fill with nano-HA, the flaps were sutured by means of mattress sutures to allow primary intention healing. At 7 months after regenerative surgery, the teeth were extracted together with some of their surrounding soft and hard tissues and processed for histological analysis. RESULTS The postoperative healing was uneventful in all cases. At 7 months following surgery, mean PPD reduction and mean CAL gain measured 4.0 ± 0.8 and 2.5 ± 0.8 mm, respectively. The histological analysis revealed a healing predominantly characterized by epithelial downgrowth. Limited formation of new cementum with inserting connective tissue fibers and bone regeneration occurred in three out of the six biopsies (i.e. 0-0.86 and 0-1.33 mm, respectively). Complete resorption of the nano-HA was found in four out of the six biopsies. A few remnants of the graft particles (either surrounded by newly formed mineralized tissue or encapsulated in connective tissue) were found in two out of the six biopsies. CONCLUSION Within their limits, the present results indicate that nano-HA has limited potential to promote periodontal regeneration in human intrabony defects. CLINICAL RELEVANCE The clinical outcomes obtained following surgery with OFD + nano-HA may not reflect true periodontal regeneration.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Online disclosure and privacy concerns: a study of Moroccan and American facebook users

In using online social networks to connect and interact with people has become extremely popular all around the world. Thelargest Social Networking Site (SNS), Facebook, offers its services in over 70 languages and increasingly relies oninternational users to grow its membership. Aiming to understand the role of culture in SNS participation, this study adopts a‘privacy calculus’ perspective to examine the differences in participation patterns between American and MoroccanFacebook users. Survey results show that Moroccans users disclose less on Facebook than US users, yet perceive moredamage should their privacy on Facebook be violated. American users, on the other hand, have lower privacy concerns, trustfellow SNS members and legal system more, and disclose more in their profile. From a practical standpoint, the resultsindicate that SNS providers cannot rely on the same methods to encourage user participation and disclosure in differentcountries.

Privacy Calculus on Social Networking Sites: Explorative Evidence from Germany and USA

Worldwide social networks, like Facebook, face fierce competition from local platforms when expanding globally. To remain attractive social network providers need to encourage user self-disclosure. Yet, little research exists on how cultural differences impact selfdisclosure on these platforms. Addressing this gap, this study explores the differences in perceptions of disclosure-relevant determinants between German and US users. Survey of Facebook members indicates that German users expect more damage and attribute higher probability to privacy-related violations. On the other hand, even though American users show higher level of privacy concern, they extract more benefits from their social networking activities, have more trust in the service provider and legal assurances as well as perceive more control. These factors may explain a higher level of self-disclosure indicated by American users. Our results provide relevant insights for the social network providers who can adjust their expansion strategy with regard to cultural differences.

Limit theorems for nondegenerate U-statistics of continuous semimartingales

This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

On restricted families of projections in ℝ3

We study projections onto non-degenerate one-dimensional families of lines and planes in R 3 . Using the classical potential theoretic approach of R. Kaufman, one can show that the Hausdorff dimension of at most 12 -dimensional sets [Math Processing Error] is typically preserved under one-dimensional families of projections onto lines. We improve the result by an ε , proving that if [Math Processing Error], then the packing dimension of the projections is almost surely at least [Math Processing Error]. For projections onto planes, we obtain a similar bound, with the threshold 12 replaced by 1 . In the special case of self-similar sets [Math Processing Error] without rotations, we obtain a full Marstrand-type projection theorem for 1-parameter families of projections onto lines. The [Math Processing Error] case of the result follows from recent work of M. Hochman, but the [Math Processing Error] part is new: with this assumption, we prove that the projections have positive length almost surely.

Measurement of the total cross section from elastic scattering in pp collisions at √s=7TeV with the ATLAS detector

A measurement of the total pp cross section at the LHC at √s = 7 TeV is presented. In a special run with high-β* beam optics, an integrated luminosity of 80 μb−1 was accumulated in order to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable t . The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the |t | range from 0.01 GeV2 to 0.1 GeV2 to extrapolate to |t | →0, the total cross section, σtot(pp→X), is measured via the optical theorem to be: σtot(pp→X) = 95.35± 0.38 (stat.)± 1.25 (exp.)± 0.37 (extr.) mb, where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation to |t | → 0. In addition, the slope of the elastic cross section at small |t | is determined to be B = 19.73 ±0.14 (stat.) ±0.26 (syst.) GeV−2.

Granular computing as a tool of human data interaction - a cognitive cities use case

The article proposes granular computing as a theoretical, formal and methodological basis for the newly emerging research field of human–data interaction (HDI). We argue that the ability to represent and reason with information granules is a prerequisite for data legibility. As such, it allows for extending the research agenda of HDI to encompass the topic of collective intelligence amplification, which is seen as an opportunity of today’s increasingly pervasive computing environments. As an example of collective intelligence amplification in HDI, we introduce a collaborative urban planning use case in a cognitive city environment and show how an iterative process of user input and human-oriented automated data processing can support collective decision making. As a basis for automated human-oriented data processing, we use the spatial granular calculus of granular geometry.