Photonic quantum systems, which comprise multiple optical modes, have become an established platform for the experimental implementation of quantum walks. However, the implementation of large systems with many modes, this means for many step operations, a high and dynamic control of many different coin operations and variable graph structures typically poses a considerable challenge.
Time-multiplexed quantum walks are a versatile tool for the implementation of a highly flexible simulation platform with dynamic control of the different graph structures and propagation properties. Our time-multiplexing techniques is based on a loop geometry ensures a extremely high homogeneity of the quantum walk system, which results in highly reliable walk statistics. By introducing optical modulators we can control the dynamics of the photonic walks as well as input and output couplings of the states at different stages during the evolution of the walk.
Here we present our recent results on our time-multiplexed quantum walk experiments.[-]

Continuous quantum walks are of great interest in quantum computing and, over the last decade, my group has been studying this topic intensively. As graph theorists, one of our main goals has been to get a better understanding of the relation between the properties of a walk and the properties of the underlying graph. We have had both successes and failures. The failures lead to a number of interesting open questions, which I will present in my talk.[-]

In this talk, I will present current activities of the Computational Systems Biology group at IBM Research, Zurich, focused on the inference and exploitation of networks of molecular interactions. Focusing first on the problem of network inference, a long-standing challenge for which many methods have been proposed, I will discuss how no single inference method performs optimally across all data sets.
However, a Wisdom of the Crowds approach based on the integration of multiple inference methods can increase the robustness and high performance of the inferred networks. To that aim, we have developed COSIFER, a web-based platform that enables the inference of molecular networks using different approaches and consensus strategies. Next, I will introduce INtERAcT, an approach to extract information about molecular interactions from a text corpus in a completely unsupervised manner. INtERAcT exploits word embeddings, a state-of-the-art technology for language modelling based on deep learning that does not require text labeling for training or domain-specific knowledge, and hence, can be easily applied to different scientific domains.
Moving into the applications, I will explain how prior information about the molecular interactions in a cell can be encoded in a network, which can be further used for gene prioritization. Such strategy is exploited by NetBiTE with the goal of identifying anti-cancer drug sensitivity biomarkers. Finally, I will discuss how a probabilistic application of network dynamics can enable the reconstruction of the cell-signaling dynamics using single-cell omics.[-]

Discrepancy and discrete energy are two of the most standard ways to measure the quality of the distribution of a finite point set, and it is very well known that there is strong interplay between these concepts. One particular important example of such interplay is the classical Stolarsky principle which ties together the pairwise sum of distances and the spherical cap discrepancy. In the current talk we shall survey various manifestations of this connection between discrepancy and energy minimization.[-]

Let $q=p^r$, where $p$ is a prime number and $ ß=(\beta_1 ,\ldots ,\beta_r)$ be a basis of $\mathbb{F}_q$ over $\mathbb{F}_p$.
Any $\xi \in \mathbb{F}_q$ has a unique representation $\xi =\sum_{i=1}^r x_i \beta _i$ with $x_1,\ldots ,x_r \in \mathbb{F}_p$.
The coefficients $x_1,\ldots ,x_r$ are called the digits of $\xi$ with respect to the basis $ß$.
The analog of the Rudin-Shapiro function is $R(\xi)=x_1x_2+\cdots + x_{r-1}x_r$. For $f \in \mathbb{F}_q [X]$, non constant and $c\in\mathbb{F}_p$, we obtain some formulas for the number of solutions in $\mathbb{F}_q$ of $R(f(\xi ))=c$. The proof uses the Hooley-Katz bound for the number of zeros of polynomials in $\mathbb{F}_p$ with several variables.

This is a joint work with László Mérai and Arne Winterhof.[-]