Abstract:
We study the dynamics of the `batch' minority game with market-impact correction using generating functional techniques to carry out the quenched disorder average. We find that the assumption of weak long-term memory, which one usually makes in order to calculate ergodic stationary states, breaks down when the persistent autocorrelation becomes larger than c_c=0.772... We show that this condition, remarkably, coincides with the AT-line found in an earlier static calculation. This result suggests a new scenario for ergodicity breaking in disordered systems.

Abstract:
During the last decade, we have gained much insight into the mechanisms that open and close a sensitive period of plasticity in the visual cortex. This brings the hope that novel treatments can be developed for brain injuries requiring renewed plasticity potential and neurodevelopmental brain disorders caused by defective synaptic plasticity. One of the central mechanisms responsible for opening the sensitive period is the maturation of inhibitory innervation. Many molecular and cellular events have been identified that drive this developmental process, including signaling through BDNF and IGF-1, transcriptional control by OTX2, maturation of the extracellular matrix, and GABA-regulated inhibitory synapse formation. The mechanisms through which the development of inhibitory innervation triggers and potentially closes the sensitive period may involve plasticity of inhibitory inputs or permissive regulation of excitatory synapse plasticity. Here, we discuss the current state of knowledge in the field and open questions to be addressed. 1. Sensitive Periods of Plasticity Many things can be learned more easily during childhood than in adulthood, including speaking a new language, playing an instrument, or performing a sport. This is the consequence of how our brain develops. It seems to make sense to learn these skills in a rather permanent way when we are young so that we can take advantage of them when we are adults. This is not only true for learning skills or facts but reflects a general property of brain development where periods of enhanced experience-dependent plasticity in different cortical and subcortical brain regions are essential for achieving functional and reliable connectivity between brain areas. During the last decade, it has become clear that specific molecular and cellular mechanisms are in place that regulate the onset and offset of these sensitive periods [1], indicating that they are not simply the consequence of the brain regions involved becoming optimized but actively regulated periods of enhanced plasticity. Sensitive periods are not only essential for normal brain development, they are also protective in cases of brain damage during childhood. In the young brain, cortical areas are not yet fully committed to specific tasks and damage can still be compensated for by other brain areas taking over the lost functionality [2]. But sensitive periods can also cause important problems. If plasticity does not occur in a proper fashion during these periods, lifelong problems may occur. This can occur if the provided inputs are inadequate.

Abstract:
We study the magnetic properties of nanoscale magnetic films with large perpendicular anisotropy comparing polarization microscopy measurements on Co_28Pt_72 alloy samples based on the magneto-optical Kerr effect with Monte Carlo simulations of a corresponding micromagnetic model. We focus on the understanding of the dynamics especially the temperature and field dependence of the magnetisation reversal process. The experimental and simulational results for hysteresis, the reversal mechanism, domain configurations during the reversal, and the time dependence of the magnetisation are in very good qualitative agreement. The results for the field and temperature dependence of the domain wall velocity suggest that for thin films the hysteresis can be described as a depinning transition of the domain walls rounded by thermal activation for finite temperatures.

Abstract:
We study the dynamics of supervised on-line learning of realizable tasks in feed-forward neural networks. We focus on the regime where the number of examples used for training is proportional to the number of input channels N. Using generating function techniques from spin glass theory, we are able to average over the composition of the training set and transform the problem for N to infinity to an effective single pattern system, described completely by the student autocovariance, the student-teacher overlap and the student response function, with exact closed equations. Our method applies to arbitrary learning rules, i.e. not necessarily of a gradient-descent type. The resulting exact macroscopic dynamical equations can be integrated without finite-size effects up to any degree of accuracy, but their main value is in providing an exact and simple starting point for analytical approximation schemes. Finally, we show how, in the region of absent anomalous response and using the hypothesis that (as in detailed balance systems) the short-time part of the various operators can be transformed away, one can describe the stationary state of the network succesfully by a set of coupled equations involving only four scalar order parameters.

Abstract:
We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques \`{a} la De Dominicis. The control parameters in this model are the ratio $\alpha=p/N$ of the number $p$ of possible values for the external information over the number $N$ of trading agents, and the statistical properties of the agents' decision noise parameters. The presence of decision noise is found to have the general effect of damping macroscopic oscillations, which explains why in certain parameter regions it can effectively reduce the market volatility, as observed in earlier studies. In the limit $N\to\infty$ we (i) solve the first few time steps of the dynamics (for any $\alpha$), (ii) calculate the location $\alpha_c$ of the phase transition (signaling the onset of anomalous response), and (iii) solve the statics for $\alpha>\alpha_c$. We find that $\alpha_c$ is not sensitive to additive decision noise, but we arrive at non-trivial phase diagrams in the case of multiplicative noise. Our theoretical results find excellent confirmation in numerical simulations.

Abstract:
We study the dynamics of the batch minority game, with random external information, using generating functional techniques a la De Dominicis. The relevant control parameter in this model is the ratio $\alpha=p/N$ of the number $p$ of possible values for the external information over the number $N$ of trading agents. In the limit $N\to\infty$ we calculate the location $\alpha_c$ of the phase transition (signaling the onset of anomalous response), and solve the statics for $\alpha>\alpha_c$ exactly. The temporal correlations in global market fluctuations turn out not to decay to zero for infinitely widely separated times. For $\alpha<\alpha_c$ the stationary state is shown to be non-unique. For $\alpha\to 0$ we analyse our equations in leading order in $\alpha$, and find asymptotic solutions with diverging volatility $\sigma=\order(\alpha^{-{1/2}})$ (as regularly observed in simulations), but also asymptotic solutions with vanishing volatility $\sigma=\order(\alpha^{{1/2}})$. The former, however, are shown to emerge only if the agents' initial strategy valuations are below a specific critical value.

Abstract:
We solve the dynamics of the on-line minority game, with general types of decision noise, using generating functional techniques a la De Dominicis and the temporal regularization procedure of Bedeaux et al. The result is a macroscopic dynamical theory in the form of closed equations for correlation- and response functions defined via an effective continuous-time single-trader process, which are exact in both the ergodic and in the non-ergodic regime of the minority game. Our solution also explains why, although one cannot formally truncate the Kramers-Moyal expansion of the process after the Fokker-Planck term, upon doing so one still finds the correct solution, that the previously proposed diffusion matrices for the Fokker-Planck term are incomplete, and how previously proposed approximations of the market volatility can be traced back to ergodicity assumptions.

Abstract:
The conserved NineTeen protein complex (NTC) is an integral subunit of the spliceosome and required for intron removal during pre-mRNA splicing. The complex associates with the spliceosome and participates in the regulation of conformational changes of core spliceosomal components, stabilizing RNA-RNA- as well as RNA-protein interactions. In addition, the NTC is involved in cell cycle checkpoint control, response to DNA damage, as well as formation and export of mRNP-particles. We have identified the Num1 protein as the homologue of SPF27, one of NTC core components, in the basidiomycetous fungus Ustilago maydis. Num1 is required for polarized growth of the fungal hyphae, and, in line with the described NTC functions, the num1 mutation affects the cell cycle and cell division. The num1 deletion influences splicing in U. maydis on a global scale, as RNA-Seq analysis revealed increased intron retention rates. Surprisingly, we identified in a screen for Num1 interacting proteins not only NTC core components as Prp19 and Cef1, but several proteins with putative functions during vesicle-mediated transport processes. Among others, Num1 interacts with the motor protein Kin1 in the cytoplasm. Similar phenotypes with respect to filamentous and polar growth, vacuolar morphology, as well as the motility of early endosomes corroborate the genetic interaction between Num1 and Kin1. Our data implicate a previously unidentified connection between a component of the splicing machinery and cytoplasmic transport processes. As the num1 deletion also affects cytoplasmic mRNA transport, the protein may constitute a novel functional interconnection between the two disparate processes of splicing and trafficking.

Abstract:
We study the dynamics of on-line learning in large perceptrons, for the case of training sets with a structural bias of the input vectors, by deriving exact and closed macroscopic dynamical laws using non-equilibrium statistical mechanical tools. In sharp contrast to the more conventional theories developed for homogeneously distributed or only weakly biased data, these laws are found to describe a non-trivial and persistently non-deterministic macroscopic evolution, and a generalisation error which retains both stochastic and sample-to-sample fluctuations, even for infinitely large networks. Furthermore, for the standard error-correcting microscopic algorithms (such as the perceptron learning rule) one obtains learning curves with distinct bias-induced phases. Our theoretical predictions find excellent confirmation in numerical simulations.

Abstract:
The absorption and emission spectra of most luminescent, pi-conjugated, organic molecules are the mirror image of each other. In some cases, however, this symmetry is severely broken. In the present work, the asymmetry between the absorption and fluorescence spectra in molecular systems consisting of para-linked phenyl rings is studied. The vibronic structure of the emission and absorption bands is calculated from ab-initio quantum chemical methods and a subsequent, rigorous Franck-Condon treatment. Good agreement with experiment is achieved. A clear relation can be established between the strongly anharmonic double-well potential for the phenylene ring librations around the long molecular axis and the observed deviation from the mirror image symmetry. Consequences for related compounds and temperature dependent optical measurements are also discussed.