Biological systems need to process information in real time and must trade off accuracy of presentation and coding costs. Here we operationalize this trade-off and develop an information-theoretic framework that selectively extracts information of the input past that is predictive about the output future, obtaining a generalized eigenvalue problem. Thereby, we unravel the input history in terms of structural phase transitions correspond-ing to additional dimensions of a state space. We elucidate the relation to canonical correlation analysis and give a numerical example. Altogether, this work relates information-theoretic optimization to the joint problem of system identification and model reduction.

Urban car transportation is a cause of climate change but is also associated with additional burdens such as traffic congestion and air pollution. Studies of external costs and potential impacts of travel demand management help to define policy instruments that mitigate the damaging impact of transportation. Here, we analyze different externalities of car transportation in Beijing and show that social costs induced by motorized transportation are equivalent to about 7.5-15.0% of Beijing's GDP. Congestion and air pollution contribute the most with climate change costs being the most uncertain. We show that a road charge could not only address congestion but also has environmental benefits. The paper investigates the role of demand elasticities and demonstrates that joint demand and supply-side policies provide considerable synergies.

Acoustic communication signals often involve temporal sequences in which the relative durations of individual elements, such as sound pulses and brief pauses, but not their absolute durations, convey meaning. Decoding such signals requires an explicit or implicit calculation of the ratios between time intervals. Using grasshopper communication as a model, we demonstrate how this seemingly difficult computation can be solved in real time by a small set of auditory neurons. One of these cells, an ascending interneuron, generates bursts of action potentials in response to the rhythmic syllable-pause structure of grasshopper calls. Our data show that these bursts are preferentially triggered at syllable onset; the number of spikes within the burst is linearly correlated with the duration of the preceding pause. Integrating the number of spikes over a fixed time window therefore leads to a total spike count that reflects the species-characteristic syllable-to-pause ratio while being invariant to playing back the call faster or slower. Such a time-scale invariant recognition is essential under natural conditions, as grasshoppers do not thermoregulate - the call of a sender sitting in the shade will be slower than that of a grasshopper in the sun. Our results show that time-scale invariant stimulus recognition can be implemented at the single-cell level without directly calculating the ratio between pulse and interpulse durations.