Z wie Zufall

Article for general public (2013)

Z4 parafermions in time-reversal invariant topological insulators

Scientific Conference (2015, April)

(Z_2)^n-Superalgebra and (Z_2)^n-Supergeometry

Doctoral thesis (2014)

The present thesis deals with a development of linear algebra, geometry and analysis based on (Z_2)^n-superalgebras: associative unital algebras which are (Z_2)^n-graded (for some natural number n) and ... [more ▼]

The present thesis deals with a development of linear algebra, geometry and analysis based on (Z_2)^n-superalgebras: associative unital algebras which are (Z_2)^n-graded (for some natural number n) and graded-commutative, i.e., satisfying ab = (-1)^<deg(a),deg(b)> ba, for all homogeneous elements a, b of respective degrees deg(a), deg(b) in (Z_2)^n, and < . , . > denoting the usual scalar product. This generalization widens the range of applications of supergeometry to many mathematical structures -- the algebra of quaternions H and more generally Clifford algebras, Deligne algebra of superdifferential forms, higher vector bundles ... -- and appears also in physics -- for describing anyons, paraparticles -- proving its worth and relevance. In this dissertation, we first focus on (Z_2)^n-superalgebra theory: we define and characterize the notions of trace, determinant and Berezinian of matrices over graded-commutative algebras. Special attention is given to the case of Clifford algebras, where our study gives a new approach to treat the classical problem of finding a “good” determinant for matrices with non-commuting (quaternionic) entries. Further, we undertake the study of (Z_2)^n-graded differenital geometry. Privileging the ringed space approach, we define (smooth) (Z_2)^n-supermanifolds modeling their algebras of functions on the (Z_2)^n-commutative algebra of formal power series in graded variables, and develop the theory along the lines of supergeometry. Notable results are: the graded Berezinian and its cohomological interpretation (essential to establish integration theory); the theorem of morphism, which states that a morphism of (Z_2)^n-supermanifolds can be recovered from its coordinate expression; an analogous of Batchelor-Gawedzki theorem for (Z_2)^n-supermanifolds. [less ▲]

Z_2^n-Supergeometry I: Manifolds and Morphisms

E-print/Working paper (2014)

Die Zahl der aktiven palmaren Schweißdrüsen (PSI, palmar sweat index) als psychophysiologischer Parameter.

in Zeitschrift für Experimentelle und Angewandte Psychologie (1989), 36

Two laboratory studies were carried out to assess the behavior of the active palmar sweat glands in both an active and a passive coping situation. Stressor in study I was watching a distressing film, in ... [more ▼]

Two laboratory studies were carried out to assess the behavior of the active palmar sweat glands in both an active and a passive coping situation. Stressor in study I was watching a distressing film, in study II mental arithmetic. Subjects were male students, 17 in experiment I, 20 in experiment II. Both experiments involved a 10-minute baseline phase, a 10-minute stress period, and a follow-up of 10 minutes. PSI was assessed at 90-sec intervals and averaged across phases, as were readings in SCL, SCR, heart rate, diastolic and systolic blood pressure. PSI could be determined in 16 subjects of each study. In both experiments PSI increased significantly from baseline to stress (p less than 0.1%) and decreased from stress to follow-up (p less than 0.1%), and thus proved to be the most sensitive indicator for stress. The interrater reliability for counting the number of active sweat glands was high when the area for evaluation was defined unambiguously. Since the assessment of the PSI does not require a sophisticated technology and is thus also applicable in field research, we suggest giving more consideration to this variable. [less ▲]

Zahlentheorie und Geometrie vereint in der Serre-Vermutung

in Essener Unikate (2008), 33

ZAP

Report (2011)

Zasada rządów prawa w polityce zewnętrznej Unii Europejskiej (Rule of law in the European Union’s external policy)

in Przegląd Prawa Konstytucyjnego (Review of Constitutional Law) (2013), 2013(2), 157-175

Rule of law, whose core is „the access to an independent judiciary and judicial review”, fulfills in EU external policy two functions. Firstly, according to the art. 21 of TEU, all EU external actions ... [more ▼]

Rule of law, whose core is „the access to an independent judiciary and judicial review”, fulfills in EU external policy two functions. Firstly, according to the art. 21 of TEU, all EU external actions have to be subdued to the rule of law. Secondly, promoting and consolidating the rule of law is one the objectives of EU external action. In most constitutional systems, a wide margin of appreciation is left as regards to foreign policy and judicial review is considerably limited. In case of EU, the Court’s jurisdiction over EU external policy is differentiated and reflects the old pillar structure. The question which arises here is whether it can be accommodated with the disposition of the art. 2 of TEU, which states that the European Union which is a single legal entity „is founded on the value of rule of law”, and with the principle of EU external policy coherence. [less ▲]

Zebrafish models of Dravet syndrome: discovery of antiseizure drug leads and analysis of behavioural comorbidities

Doctoral thesis (2018)

Dravet syndrome (DS) is one of the most frequent genetic epilepsies, with an incidence of 1/30,000. Most DS patients are pharmacoresistant, in that they do not respond adequately to currently available ... [more ▼]

Dravet syndrome (DS) is one of the most frequent genetic epilepsies, with an incidence of 1/30,000. Most DS patients are pharmacoresistant, in that they do not respond adequately to currently available anticonvulsant drugs (ASDs). Beside the seizure occurrence in these patients, many DS patients also suffer from cognitive impairment that can be aggravated by some of the seizure medications prescribed. Preclinical models such as mouse models of Dravet syndrome have been developed and described to exhibit cognitive deficits similar to those of DS patients, but are only suitable for the evaluation of small number of compounds, thereby limiting their utility for drug discovery. An animal model with higher screening throughput would therefore be of value for drug discovery efforts focused on seizure reduction and decrease of the comorbidities associated with DS. Recent studies on zebrafish have demonstrated its ability to be a promising in vivo model for DS. Two different zebrafish DS models - one based on a loss-of-function mutation in the zebrafish ortholog of SCN1A, the other based on an antisense knockdown of this gene - exhibit seizure-like behaviour and epileptiform discharges that are exacerbated by hyperthermia. The mutant line was also described to display greater anxiety levels. In this Doctoral thesis project, we are investigating these zebrafish DS models with regard to (1) their seizure occurrence and potential reduction following exposure to several anticonvulsant drug candidates, and (2), their cognitive functions in order to determine possible similarities with cognitive impairment in human DS patients. Our results indicate these zebrafish DS models to exhibit memory impairment and higher anxiety levels. These findings provide an initial insight into the resemblance between human patients and zebrafish in terms of comorbidities. Finally, we also identified several novel anticonvulsant compounds and drug candidates with antiseizure activity in these zebrafish DS models. [less ▲]

Zehntropie

Presentation (2014, January)