We introduce model-based traces, which trace behavioral models of a system’s design during its execution, allowing to combine modeldriven engineering with dynamic analysis. Specifically, we take visual inter-object scenario-based and intra-object state-based models (sequence charts and statecharts) used for a system’s design, and follow their activation and progress as they come to life at runt...

Introduction. “Singular moduli” is the classical name for the values assumed by the modular invariant j(τ) (or by other modular functions) when the argument is a quadratic irrationality. These values are algebraic numbers and have been studied intensively since the time of Kronecker and Weber. In [5], formulas for their norms, and for the norms of their differences, were obtained. Here we obtai...

Given two noncommuting matrices, A and B, it is well known that AB and BA have the same trace. This extends to cyclic permutations of products of A’s and B’s. It is shown here that for 2 × 2 matrices A and B, whose elements are independent random variables with standard normal distributions, the probability that Tr(ABAB) > Tr(AB) is exactly 1 √ 2 .

The trace of a family of sets A on a set X is A|X = {A ∩ X : A ∈ A}. If A is a family of k-sets from an n-set such that for any r-subset X the trace A|X does not contain a maximal chain, then how large can A be? Patkós conjectured that, for n sufficiently large, the size of A is at most ( n−k+r−1 r−1 ) . Our aim in this paper is to prove this conjecture.

Simple answers are given to the following and related questions: For what Hubert space operator A is it true that the smallest ideal (alternatively, the smallest norm ideal, the smallest maximal norm ideal) containing A is a norm (an intermediate norm, a principal norm) ideal? Do these ideals support a nontrivial unitary invariant positive linear functional?

We introduce model-based traces, which trace behavioral models of a system’s design during its execution, allowing to combine modeldriven engineering with dynamic analysis. Specifically, we take visual inter-object scenario-based and intra-object state-based models (sequence charts and statecharts) used for a system’s design, and follow their activation and progress as they come to life at runt...

This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, state-based modelling of components. The feedback operator on components is shown to satisfy the trace axioms of Joyal, Street and Verity. We employ McCurdy’s tube diagrams, an extension of standard string diagrams for monoidal categories, for representing and manipulating component diagra...

This Master's Thesis represents the nal part of my computer science study in Leiden. I would like to thank my supervisor Jetty Kleijn for her support.

Studies using functional cellular imaging of living flies have identified six memory traces that form in the olfactory nervous system after conditioning with odors. These traces occur in distinct nodes of the olfactory nervous system, form and disappear across different windows of time, and are detected in the imaged neurons as increased calcium influx or synaptic release in response to the con...

We present an uncertainty analysis of data taken using the Rossi technique in which the horizontal oscilloscope sweep is driven sinusoidally in time while the vertical axis follows the signal amplitude. The analysis is aimed at determining the logarithmic derivative of the amplitude as a function of time. Within the Bayesian framework used, inferences are obtained with the Markov Chain Monte Ca...