Jan Philipp Pade

Motivational Salience Modulates Hippocampal Repetition Suppression and Functional Connectivity in Humans

Repetition suppression (RS) is a rapid decrease of stimulus-related neuronal responses upon repeated presentation of a stimulus. Previous studies have demonstrated that negative emotional salience of stimuli enhances RS. It is, however, unclear how motivational salience of stimuli, such as reward-predicting value, influences RS for complex visual stimuli, and which brain regions might show differences in RS for reward-predicting and neutral stimuli. Here we investigated the influence of motivational salience on RS of complex scenes using event-related functional magnetic resonance imaging. Thirty young healthy volunteers performed a monetary incentive delay task with complex scenes (indoor vs. outdoor) serving as neutral or reward-predicting cue pictures. Each cue picture was presented three times. In line with previous findings, reward anticipation was associated with activations in the ventral striatum, midbrain, and orbitofrontal cortex (OFC). Stimulus repetition was associated with pronounced RS in ventral visual stream areas like the parahippocampal place area (PPA). An interaction of reward anticipation and RS was specifically observed in the anterior hippocampus, where a response decrease across repetitions was observed for the reward-predicting scenes only. Functional connectivity analysis further revealed specific activity-dependent connectivity increases of the hippocampus and the PPA and OFC. Our results suggest that hippocampal RS is sensitive to reward-predicting properties of stimuli and might therefore reflect a rapid, adaptive neural response mechanism for motivationally salient information.

Reduction of interaction delays in networks

Delayed interactions are a common property of coupled natural systems and therefore arise in a variety of different applications. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed connections. Such systems are often modeled by delay differential equations with discrete delays. In realistic situations, these delays are not identical on different connections. We show that by a componentwise timeshift transformation it is often possible to reduce the number of different delays and simplify the models without loss of information. We identify dynamic invariants of this transformation, determine its capabilities to reduce the number of delays and interpret these findings in terms of the topology of the underlying graph. In particular, we show that networks with identical sums of delay times along the fundamental semicycles are dynamically equivalent and we provide a normal form for these systems. We illustrate the theory using a network motif of coupled Mackey-Glass systems with 8 different time delays, which can be reduced to an equivalent motif with three delays.

Improving Network Structure can lead to Functional Failures

In many real-world networks the ability to synchronize is a key property for their performance. Recent work on undirected networks with diffusive interaction revealed that improvements in the network connectivity such as making the network more connected and homogeneous enhances synchronization. However, real-world networks have directed and weighted connections. In such directed networks, understanding the impact of structural changes on the network performance remains a major challenge. Here, we show that improving the structure of a directed network can lead to a failure in the network function. For instance, introducing new links to reduce the minimum distance between nodes can lead to instabilities in the synchronized motion. This effect only occurs in directed networks. Our results allow to identify the dynamical importance of a link and thereby have a major impact on the design and control of directed networks.

Spectra of Laplacian matrices of weighted graphs: structural genericity properties

This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called the algebraic connectivity) and its associated eigenvector (the so-called Fiedler vector). Here we prove that, given a Laplacian matrix, it is possible to perturb the weights of the existing edges in the underlying graph in order to obtain simple eigenvalues and a Fiedler vector composed of only nonzero entries. These structural genericity properties with the constraint of not adding edges in the underlying graph are stronger than the classical ones, for which arbitrary structural perturbations are allowed. These results open the opportunity to understand the impact of structural changes on the dynamics of complex systems.

The Dynamical Impact of a Shortcut in Unidirectionally Coupled Rings of Oscillators

We study the destabilization mechanism in a unidirectional ring of identical oscillators, perturbed by the introduction of a long-range connection. It is known that for a homogeneous, unidirectional ring of identical Stuart-Landau oscillators the trivial equilibrium undergoes a sequence of Hopf bifurcations eventually leading to the coexistence of multiple stable periodic states resembling the Eckhaus scenario. We show that this destabilization scenario persists under small non-local perturbations. In this case, the Eckhaus line is modulated according to certain resonance conditions. In the case when the shortcut is strong, we show that the coexisting periodic solutions split up into two groups. The first group consists of orbits which are unstable for all parameter values, while the other one shows the classical Eckhaus behavior.