We review recent developments in the control of deterministic and stochastic nonlinear dynamics by time-delayed feedback methods [1]. We point out how to overcome the alleged odd number limitation for unstable periodic orbits, and discuss the control of complex chaotic or noise-induced space-time patterns. Our findings are applied to a selection of models ranging from semiconductor nanostructures, like resonant-tunneling diodes [2], to neural systems. [1] E. Sch{\"o}ll and H.G. Schuster (Eds.): Handbook of Chaos Control (Wiley-VCH, Weinheim, 2008), second completely revised and enlarged edition. [2] E. Sch{\"o}ll, Nonlinear spatio-temporal dynamics and chaos in semiconductors (Cambridge University Press, Cambridge, 2001).

Living organisms need to obtain and process information crucial for their survival. Information processing in living systems, ranging from signal transduction in a single cell to image processing in the human brain, are performed by biological circuits (networks), which are driven out of equilibrium. These biochemical and neural circuits are inherently noisy. However, certain accuracy is required to carry out proper biological functions. How do biological networks process information with noisy components? What is the free energy cost of accurate biological computing? Is there a fundamental limit for its performance of the biological functions? In this talk, we will describe our recent work in trying to address these general questions in the context of two basic cellular computing tasks: sensory adaptation for memory encoding [1,2]; biochemical oscillation for accurate timekeeping [3].

[1] The energy-speed-accuracy trade-off in sensory adaptation, G. Lan, P. Sartori, S. Neumann, V. Sourjik, and Yuhai Tu, Nature Physics 8, 422-428, 2012.
[2] Free energy cost of reducing noise while maintaining a high sensitivity, Pablo Sartori and Yuhai Tu, Phys. Rev. Lett. 2015. 115: 118102.
[3] The free-energy cost of accurate biochemical oscillations, Y. Cao, H. Wang, Q. Ouyang, and Yuhai Tu, Nature Physics 11, 772, 2015.

In nature, insects, fish, birds and other animals flock. A simple two-dimensional model due to Vicsek et al treats them as self-propelled particles that move with constant speed and, at each time step, tend to align their velocities to an average of those of their neighbors except for an alignment noise (conformist rule). The distribution function of these active particles satisfies a kinetic equation. Flocking appears as a bifurcation from an uniform distribution of particles whose order parameter is the average of the directions of their velocities (polarization). This bifurcation is quite unusual: it is described by a system of partial differential equations that are hyperbolic on the short time scale and parabolic on a longer scale. Uniform solutions provide the usual diagram of a pitchfork bifurcation but disturbances about them obey the Klein-Gordon equation in the hyperbolic time scale. Then there are persistent oscillations with many incommensurate frequencies about the bifurcating solution, they produce a shift in the critical noise and resonate with a periodic forcing of the alignment rule. These predictions are confirmed by direct numerical simulations of the Vicsek model. In addition, if the active particles may choose with probability p at each time step to follow the conformist Vicsek rule or to align their velocity contrary or almost contrary to the average one, the bifurcations are of either period doubling or Hopf type and we find stable time dependent solutions. Numerical simulations demonstrate striking effects of alignment noise on the polarization order parameter: maximum polarization length is achieved at an optimal nonzero noise level. When contrarian compulsions are more likely than conformist ones, non-uniform polarized phases appear as the noise surpasses threshold.

Sequence and timing are two fundamental aspects of many critical motor actions that humans and animals must learn and perform. Human speech is a familiar example. How precisely timed action sequences are controlled by networks of neurons, and how such neural networks form through experience, are poorly understood.

Songbirds are excellent animal models for investigating these problems. Male songbirds learn to sing songs with exquisite temporal complexity and precision, similar to human speech. Unlike human brains, songbird brains are experimentally accessible. Indeed, the wealth of experimental data on songbirds makes them ideal systems for computational modeling.

In this talk, I will present a computational study of production and learning of timed action sequence, using birdsong as a concrete example. First, I will advance the idea that associative chains of neurons, also called "synfire chains" in some context, are fundamental building blocks of sequence generating networks. I will show experimental evidence of their existence in the songbird brain, including the recent discovery of a critical property of song controlling neurons, which was predicted by a computational analysis of the robustness of the associative chain dynamics against imperfects in the connectivity and other sources of noise. Second, I will demonstrate computationally that associative chains can form simply through a self-organized process, which depends on ubiquitously observed properties of neurons, including spike-time dependent plasticity of synapses, axonal remodeling, and spontaneous activity. This result suggests that associative chains are stable "attractors" of neural connectivity. The process is robust against death and renewal of neurons, which naturally occur in songbird brain. Finally, I will illustrate that associative chains are also useful for sequence recognition tasks, such as song recognition in songbirds, thus can serve as the neural substrate of sensory-motor integration.

Henry Greenside (hsg@phy.duke.edu) will be the host for his visit.

My group studies colloidal suspensions, which are solid micron-sized particles in a liquid. We use an optical confocal microscope to view the motion of these colloidal particles in three dimensions. In some experiments, these particles arrange into a crystalline lattice, and thus the sample is analogous to a traditional solid. We study the interface between colloidal crystals and colloidal liquids, and find that this interface is quite sharply defined. In other experiments, the sample is analogous to a glass, with particles randomly packed together. The particles correspond to individual molecules in a traditional glass, and the sample exhibits glassy behavior when the particle concentration is high. This allows us to directly study the microscopic behavior responsible for the macroscopic viscosity divergence of glasses.

A consensus is emerging that discontinuous shear thickening (DST) in dense suspensions marks a transition from a flow state where particles remain well separated by lubrication layers, to one dominated by frictional contacts. We show here that reasonable assumptions about contact proliferation predict two distinct types of DST in the absence of inertia. The first occurs at densities above the jamming point of frictional particles; here the thickened state is completely jammed and (unless particles deform) cannot flow without inhomogeneity or fracture. The second regime shows strain-rate hysteresis and arises at somewhat lower densities where the thickened phase flows smoothly. DST is predicted to arise when finite-range repulsions defer contact formation until a characteristic stress level is exceeded.

I will describe two simple models that incorporate only hard-sphere and geometrical constraints, yet provide quantitatively accurate predictions for the structural and mechanical properties of frictional packings of granular media and proteins. We first model static friction between grains by considering nominally spherical particles with periodically spaced asperities on the surface of the grains. This model captures the dependence of the average packing fraction and number of interparticle contacts on the static friction coefficient obtained from experiments, and has significant advantages over other models. Second, in the spirit of the Ramachandran map for the backbone dihedral angles of proteins, we develop a model for nonpolar amino acids that allows us to predict the allowed conformations of sidechain dihedral angles. Our predictions are quantitatively similar to the sidechain dihedral angle distributions obtained from known crystal structures. These two examples emphasize the power of simple physical models, which are able to predict important properties of soft and biological materials.