Semifields, relative difference sets, and bent functions

Recently, the interest in semifields has increased due to the discovery of several new families and progress in the classification problem. Commutative semifields play an important role since they are equivalent to certain planar functions (in the case of odd characteristic) and to modified planar functions in even characteristic. Similarly, commutative semifields are equivalent to relative difference sets. The goal of this survey is to describe the connection between these concepts. Moreover, we shall discuss power mappings that are planar and consider component functions of planar mappings, which may be also viewed as projections of relative difference sets. It turns out that the component functions in the even characteristic case are related to negabent functions as well as to $\mathbb{Z}_4$-valued bent functions.Comment: Survey paper for the RICAM workshop "Emerging applications of finite fields", 09-13 December 2013, Linz, Austria. This article will appear in the proceedings volume for this workshop, published as part of the "Radon Series on Computational and Applied Mathematics" by DeGruyte

Evaluation of the importance of immunological profile for pemphigus vulgaris in the light of necessity to modify compensation theory

According to the “desmoglein compensation theory,” anti-Dsg1 and anti-Dsg3 profiles are crucial for the clinical outcome of pemphigus vulgaris. However, recent studies have highlighted several cases with an incompatibility between the antibody profile and clinical manifestation. Data of 37 patients who had been diagnosed pemphigus vulgaris in our Department between January 2014-June 2016 were retrieved from our clinical database. Patients with ABSIS skin involvement scores, oral mucosa extent and severity scores, anti-Dsg1 and Dsg3 antibody profile were included in this retrospective study. Patients with discordance between clinical manifestations and immunological profile were considered as atypical clinical phenotype. Patients with missing data were excluded. In all 37 patients, Dsg1 and Dsg3 antibody titers at the baseline did not correlate with the concurrent ABSIS scores. At follow up, we detected statistically significant correlations between anti Dsg-1 profile and ABSIS skin involvement scores (p=0.006; r=0.588) and between anti-Dsg3 and ABSIS mucosal extent and severity scores (p=0.058; r=0.431). After treatment, the reduction of Dsg-1 antibody titers was statistically significant in remittent patients (p=0.027). We did not detect statistically significant reduction of Dsg-3 antibodies. Four subjects had incompatible antibody profile and clinical activity. Discordance between phenotype-antibody profile and clinical activity-Dsg titers support the idea that non-Dsg antigens may also be the target for pemphigus autoimmunity. </p

Change in Juvenile Offending Versatility Predicted by Individual, Familial, and Environmental Risks

Developmental and life-course criminology elucidate the developmental course and change of antisociality over time, considering that longitudinal trajectories differ. Specific relations between risks and different antisociality outcomes are emphasized. We assume that adolescents have different longitudinal trajectories considering the change of offending over time and that risks contribute variably to offending pathways. The current study is based on a German research project in which adolescents (N = 577) were interviewed in two German cities. Based on self-reported crime data, we utilized the slope values of offending versatility (OV) over time as outcome values in regression mixture models capturing the trends for participants over age and exhibiting two components of offending adolescents. We explored the contribution of different risks to OV, defining specific risk patterns: Acceptance of violence and peer delinquency have significant negative effects on the emergence of OV within the group of adolescents with decreasing OV. Acceptance of violence has a significant negative effect, and corporal punishment has a significant positive effect on the emergence of OV within the group of adolescents with increasing or rather stable OV. The results underline the relevance of the violence-related risk factor corporal punishment for the emergence of OV within the last-mentioned group