From infinite to two dimensions through the functional renormalization group.

We present a novel scheme for an unbiased, nonperturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, the dynamical mean field theory and the functional renormalization group. Physically, this allows for a systematic inclusion of nonlocal correlations via the functional renormalization group flow equations, after the local correlations are taken into account nonperturbatively by the dynamical mean field theory. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half filling.

FoxP2 and olfaction: divergence of FoxP2 expression in olfactory tubercle between different feeding habit bats.

FoxP2 is a member of the winged helix/forkhead class of transcription factors. Despite FoxP2 is found to have particular relevance to speech and language, the role of this gene is broader and not yet fully elucidated. In this study, we investigated the expression of FoxP2 in the brains of bats with different feeding habits (two frugivorous species and three insectivorous species). We found FoxP2 expression in the olfactory tubercle of frugivorous species is significantly higher than that in insectivorous species. Difference of FoxP2 expression was not observed within each of the frugivorous or insectivorous group. The diverse expression patterns in olfactory tubercle between two kinds of bats indicate FoxP2 has a close relation with olfactory tubercle associated functions, suggesting its important role in sensory integration within the olfactory tubercle and such a discrepancy of FoxP2 expression in olfactory tubercle may take responsibility for the different feeding behaviors of frugivorous and insectivorous bats.

Turning a first order quantum phase transition continuous by fluctuations: general flow equations and application to d-wave Pomeranchuk instability.

We derive renormalization group equations which allow us to treat order parameter fluctuations near quantum phase transitions in cases where an expansion in powers of the order parameter is not possible. As a prototypical application, we analyze the nematic transition driven by a d-wave Pomeranchuk instability in a two-dimensional electron system. We find that order parameter fluctuations suppress the first order character of the nematic transition obtained at low temperatures in mean-field theory, so that a continuous transition leading to quantum criticality can emerge.

Soft fermi surfaces and breakdown of Fermi-liquid behavior.

Electron-electron interactions can induce Fermi surface deformations which break the point-group symmetry of the lattice structure of the system. In the vicinity of such a "Pomeranchuk instability" the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We show that critical Fermi surface fluctuations near a d-wave Pomeranchuk instability in two dimensions lead to large anisotropic decay rates for single-particle excitations, which destroy Fermi-liquid behavior over the whole surface except at the Brillouin zone diagonal.

Fine control of call frequency by horseshoe bats.

The auditory system of horseshoe bats is narrowly tuned to the sound of their own echoes. During flight these bats continuously adjust the frequency of their echolocation calls to compensate for Doppler-effects in the returning echo. Horseshoe bats can accurately compensate for changes in echo frequency up to 5 kHz, but they do so through a sequence of small, temporally-independent, step changes in call frequency. The relationship between an echo's frequency and its subsequent impact on the frequency of the very next call is fundamental to how Doppler-shift compensation behavior works. We analyzed how horseshoe bats control call frequency by measuring the changes occurring between many successive pairs of calls during Doppler-shift compensation and relating the magnitude of these changes to the frequency of each intervening echo. The results indicate that Doppler-shift compensation is mediated by a pair of (echo)frequency-specific sigmoidal functions characterized by a threshold, a slope, and an upper limit to the maximum change in frequency that may occur between successive calls. The exact values of these parameters necessarily reflect properties of the underlying neural circuitry of Doppler-shift compensation and the motor control of vocalization, and provide insight into how neural feedback can accommodate the need for speed without sacrificing stability.

Dynamical mean-field theory for pairing and spin gap in the attractive hubbard model.

We solve the attractive Hubbard model for arbitrary interaction strengths within dynamical mean-field theory. We compute the transition temperature for superconductivity and analyze electron pairing in the normal phase. The normal state is a Fermi liquid at weak coupling and a non-Fermi-liquid state with a spin gap at strong coupling. Away from half filling, the quasiparticle weight vanishes discontinuously at the transition between the two normal states.

d-wave superconductivity and pomeranchuk instability in the two-dimensional hubbard model

We present a systematic stability analysis for the two-dimensional Hubbard model, which is based on a new renormalization group method for interacting Fermi systems. The flow of effective interactions and susceptibilities confirms the expected existence of a d-wave pairing instability driven by antiferromagnetic spin fluctuations. More unexpectedly, we find that strong forward scattering interactions develop which may lead to a Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface.

Robustness and variability of neuronal coding by amplitude-sensitive afferents in the weakly electric fish eigenmannia.

We investigated the variability of P-receptor afferent spike trains in the weakly electric fish, Eigenmannia, to repeated presentations of random electric field AMs (RAMs) and quantified its impact on the encoding of time-varying stimuli. A new measure of spike timing jitter was developed using the notion of spike train distances recently introduced by Victor and Purpura. This measure of variability is widely applicable to neuronal responses, irrespective of the type of stimuli used (deterministic vs. random) or the reliability of the recorded spike trains. In our data, the mean spike count and its variance measured in short time windows were poorly correlated with the reliability of P-receptor afferent spike trains, implying that such measures provide unreliable indices of trial-to-trial variability. P-receptor afferent spike trains were considerably less variable than those of Poisson model neurons. The average timing jitter of spikes lay within 1-2 cycles of the electric organ discharge (EOD). At low, but not at high firing rates, the timing jitter was dependent on the cutoff frequency of the stimulus and, to a lesser extent, on its contrast. When spikes were artificially manipulated to increase jitter, information conveyed by P-receptor afferents was degraded only for average jitters considerably larger than those observed experimentally. This suggests that the intrinsic variability of single spike trains lies outside of the range where it might degrade the information conveyed, yet still allows for improvement in coding by averaging across multiple afferent fibers. Our results were summarized in a phenomenological model of P-receptor afferents, incorporating both their linear transfer properties and the variability of their spike trains. This model complements an earlier one proposed by Nelson et al. for P-receptor afferents of Apteronotus. Because of their relatively high precision with respect to the EOD cycle frequency, P-receptor afferent spike trains possess the temporal resolution necessary to support coincidence detection operations at the next stage in the amplitude-coding pathway.

Encoding and processing of sensory information in neuronal spike trains

Recently, a statistical signal-processing technique has allowed the information carried by single spike trains of sensory neurons on time-varying stimuli to be characterized quantitatively in a variety of preparations. In weakly electric fish, its application to first-order sensory neurons encoding electric field amplitude (P-receptor afferents) showed that they convey accurate information on temporal modulations in a behaviorally relevant frequency range (<80 Hz). At the next stage of the electrosensory pathway (the electrosensory lateral line lobe, ELL), the information sampled by first-order neurons is used to extract upstrokes and downstrokes in the amplitude modulation waveform. By using signal-detection techniques, we determined that these temporal features are explicitly represented by short spike bursts of second-order neurons (ELL pyramidal cells). Our results suggest that the biophysical mechanism underlying this computation is of dendritic origin. We also investigated the accuracy with which upstrokes and downstrokes are encoded across two of the three somatotopic body maps of the ELL (centromedial and lateral). Pyramidal cells of the centromedial map, in particular I-cells, encode up- and downstrokes more reliably than those of the lateral map. This result correlates well with the significance of these temporal features for a particular behavior (the jamming avoidance response) as assessed by lesion experiments of the centromedial map.

Neural circuitry for communication and jamming avoidance in gymnotiform electric fish.

Over the past decade, research on the neural basis of communication and jamming avoidance in gymnotiform electric fish has concentrated on comparative studies of the premotor control of these behaviors, on the sensory processing of communication signals and on their control through the endocrine system, and tackled the question of the degree to which these behaviors share neural elements in the sensory-motor command chain by which they are controlled. From this wealth of investigations, we learned, first, how several segregated premotor pathways controlling a single central pattern generator, the medullary pacemaker nucleus, can provide a large repertoire of behaviorally relevant motor patterns. The results suggest that even small evolutionary modifications in the premotor circuitry can yield extensive changes in the behavioral output. Second, we have gained some insight into the concerted action of the brainstem, the diencephalon and the long-neglected forebrain in sensory processing and premotor control of communication behavior. Finally, these studies shed some light on the behavioral significance of multiple sensory brain maps in the electrosensory lateral line lobe that long have been a mystery. From these latter findings, it is tempting to interpret the information processing in the electrosensory system as a first step in the evolution towards the 'distributed hierarchical' organization commonly realized in sensory systems of higher vertebrates.

Segregation of behavior-specific synaptic inputs to a vertebrate neuronal oscillator.

Although essential for understanding the mechanisms underlying sensorimotor integration and motor control of behaviors, very little is known about the degree to which different behaviors share neural elements of the sensorimotor command chain by which they are controlled. Here, we provide, to our knowledge, the first direct physiological evidence that various modulatory premotor inputs to a vertebrate central pattern generator, the pacemaker nucleus in gymnotiform electric fish, carrying distinctly different behavioral information, can remain segregated from their various sites of origin in the diencephalon to the synaptic termination sites on different target neurons in the medullary pacemaker nucleus. During pharmacological activation of each of the premotor inputs originating from the three prepacemaker nuclei so far identified, we determined in vivo the changes in input resistance in the neuronal elements of the pacemaker nucleus, i.e., relay cells and pacemaker cells. We found that each input yields significantly different effects on these cells; the inputs from the two diencephalic prepacemaker nuclei, PPnC and PPnG, which resulted in increased oscillator activity, caused significantly lower input resistances in relay and pacemaker cells, respectively, exhibiting drastically different time courses. The input from the sublemniscal prepacemaker nucleus, which resulted in reduced oscillator activity, however, caused a significant increase in input resistance only in relay cells. Considering that the sensory pathways processing stimuli yielding these behaviors are separated as well, this study indicates that sensorimotor control of different behaviors can occur in strictly segregated channels from the sensory input of the brain all through to the synaptic input level of the final premotor command nucleus.

Feature extraction by burst-like spike patterns in multiple sensory maps.

In most sensory systems, higher order central neurons extract those stimulus features from the sensory periphery that are behaviorally relevant (e.g.,Marr, 1982; Heiligenberg, 1991). Recent studies have quantified the time-varying information carried by spike trains of sensory neurons in various systems using stimulus estimation methods (Bialek et al., 1991; Wessel et al., 1996). Here, we address the question of how this information is transferred from the sensory neuron level to higher order neurons across multiple sensory maps by using the electrosensory system in weakly electric fish as a model. To determine how electric field amplitude modulations are temporally encoded and processed at two subsequent stages of the amplitude coding pathway, we recorded the responses of P-type afferents and E- and I-type pyramidal cells in the electrosensory lateral line lobe (ELL) to random distortions of a mimic of the fish's own electric field. Cells in two of the three somatotopically organized ELL maps were studied (centromedial and lateral) (Maler, 1979; Carr and Maler, 1986). Linear and second order nonlinear stimulus estimation methods indicated that in contrast to P-receptor afferents, pyramidal cells did not reliably encode time-varying information about any function of the stimulus obtained by linear filtering and half-wave rectification. Two pattern classifiers were applied to discriminate stimulus waveforms preceding the occurrence or nonoccurrence of pyramidal cell spikes in response to the stimulus. These signal-detection methods revealed that pyramidal cells reliably encoded the presence of upstrokes and downstrokes in random amplitude modulations by short bursts of spikes. Furthermore, among the different cell types in the ELL, I-type pyramidal cells in the centromedial map performed a better pattern-recognition task than those in the lateral map and than E-type pyramidal cells in either map.

A method to biotinylate and histochemically visualize ibotenic acid for pharmacological inactivation studies.

Ibotenic acid (IA) and kainic acid (KA) are commonly used tools to selectively inactivate neuronal perikarya, eventually leading to their degeneration, without affecting fibers of passage. Reversible inactivations and experimental paradigms that do not allow for long survival times, however, do not permit for histological verification of the site and extent of the lesion by identifying the area showing gliosis. We describe here a method in which IA and KA were conjugated with biotin and thus could be easily visualized histochemically. We pressure-injected biotinylated IA and KA into various hindbrain areas of the electrosensory system in electric fish while monitoring neuronal responses at the injection site and assessing effects on the behavior. Whereas the effects of biotinylated IA did not differ from those of the unbiotinylated form, biotinylated KA lost its physiological activity. Thus, only biotinylated IA could be used successfully. The size of the gliosis seen after a survival time of seven days was similar to the extent of biotin label observed after injection of comparable volumes of biotinylated IA. Moreover, this method resulted in labeling of individual neurons presumably affected by IA and yielded information about their projection patterns which was comparable to labeling seen after intracellular injections of neurobiotin or biocytin.

A sensory brain map for each behavior?

Multiple brain maps are commonly found in virtually every vertebrate sensory system. Although their functional significance is generally relatively little understood, they seem to specialize in processing distinct sensory parameters. Nevertheless, to yield the stimulus features that ultimately elicit the adaptive behavior, it appears that information streams have to be combined across maps. Results from current lesion experiments in the electrosensory system, however, suggest an alternative possibility. Inactivations of different maps of the first-order electrosensory nucleus in electric fish, the electrosensory lateral line lobe, resulted in markedly different behavioral deficits. The centromedial map is both necessary and sufficient for a particular electrolocation behavior, the jamming avoidance response, whereas it does not affect the communicative response to external electric signals. Conversely, the lateral map does not affect the jamming avoidance response but is necessary and sufficient to evoke communication behavior. Because the premotor pathways controlling the two behaviors in these fish appear to be separated as well, this system illustrates that sensory-motor control of different behaviors can occur in strictly segregated channels from the sensory input of the brain all through to its motor output. This might reflect an early evolutionary stage where multiplication of brain maps can satisfy the demand on processing a wider range of sensory signals ensuing from an enlarged behavioral repertoire, and bridging across maps is not yet required.

From stimulus encoding to feature extraction in weakly electric fish.

Animals acquire information about sensory stimuli around them and encode it using an analogue or a pulse-based code. Behaviourally relevant features need to be extracted from this representation for further processing. In the electrosensory system of weakly electric fish, single P-type electroreceptor afferents accurately encode the time course of random modulations in electric-field amplitude. We applied a stimulus estimation method and a signal-detection method to both P-receptor afferents and their targets, the pyramidal cells in the electrosensory lateral-line lobe. We found that although pyramidal cells do not accurately convey detailed information about the time course of the stimulus, they reliably encode up- and downstrokes of random modulations in electric-field amplitude. The presence of such temporal features is best signalled by short bursts of spikes, probably caused by dendritic processing, rather than by isolated spikes. Furthermore, pyramidal cells outperform P-receptor afferents in signalling the presence of temporal features in the stimulus waveform. We conclude that the sensory neurons are specialized to acquire information accurately with little processing, whereas the following stage extracts behaviourally relevant features, thus performing a nonlinear pattern-recognition task.

Motor control of the jamming avoidance response of Apteronotus leptorhynchus: evolutionary changes of a behavior and its neuronal substrates.

The two closely related gymnotiform fishes, Apteronotus and Eigenmannia, share many similar communication and electrolocation behaviors that require modulation of the frequency of their electric organ discharges. The premotor linkages between their electrosensory system and their medullary pacemaker nucleus, which controls the repetition rate of their electric organ discharges, appear to function differently, however. In the context of the jamming avoidance response, Eigenmannia can raise or lower its electric organ discharge frequency from its resting level. A normally quiescent input from the diencephalic pre-pacemaker nucleus can be recruited to raise the electric organ discharge frequency above the resting level. Another normally active input, from the sublemniscal pre-pacemaker nucleus, can be inhibited to lower the electric organ discharge frequency below the resting level (Metzner 1993). In contrast, during a jamming avoidance response, Apteronotus cannot lower its electric organ discharge frequency below the resting level. The sublemniscal pre-pacemaker is normally completely inhibited and release of this inhibition allows the electric organ discharge frequency to rise during the jamming avoidance response. Further inhibition of this nucleus cannot lower the electric organ discharge frequency below the resting level. Lesions of the diencephalic pre-pacemaker do not affect performance of the jamming avoidance response. Thus, in Apteronotus, the sublemniscal pre-pacemaker alone controls the changes of the electric organ discharge frequency during the jamming avoidance response.

Anatomical basis for audio-vocal integration in echolocating horseshoe bats.

Neurophysiological recordings suggest that audio-vocal neurons located in the paralemniscal tegmentum of the midbrain in horseshoe bats provide an interface between the pathways for auditory sensory processing and those for the motor control of vocalization. To verify these physiological results anatomically, the projection pattern of the audio-vocally active area in the paralemniscal tegmentum was investigated by using extracellular tracer injections of wheat germ agglutinin conjugated to horseradish peroxidase. Several nuclei of the lemniscal auditory pathway (dorsal nucleus of the lateral lemniscus, central nucleus of the inferior colliculus, lateral superior olive) as well as the nucleus of the central acoustic tract appear to project to the paralemniscal tegmentum. Other possible sources of afferent projections are a small but distinctly labeled structure within the lateral hypothalamic area, the substantia nigra pars compacta, the deep mesencephalic nucleus, the rostral portion of the inferior colliculus, the deep and intermediate layers of the superior colliculus, and several small areas in the rhombencephalic reticular formation. No direct efferent projection from the audio-vocally active area of the paralemniscal tegmentum to primarily auditory structures was found. Instead, the main targets were structures that are involved in the control of different motor patterns. These targets include the deep and intermediate layers of the superior colliculus and the dorsomedial portion of the facial nucleus, both of which most probably control pinna movements in cats, and the reticular formation medial and caudal to the facial nucleus and rostral to the nucleus ambiguus, which represents an area involved in the control of vocalization. Hence, the anatomical projection pattern suggests that the paralemniscal tegmentum in horseshoe bats serves as a link between the processing of auditory information and the control of vocalization and related motor patterns.