Tropical Density Estimation of Phylogenetic Trees.

Much evidence from biological theory and empirical data indicates that, gene trees, phylogenetic trees reconstructed from different genes (loci), do not have to have exactly the same tree topologies. Such incongruence between gene trees might be caused by some "unusual" evolutionary events, such as meiotic sexual recombination in eukaryotes or horizontal transfers of genetic material in prokaryotes. However, most of the gene trees are constrained by the tree topology of the underlying species tree, that is, the phylogenetic tree depicting the evolutionary history of the set of species under consideration. In order to discover "outlying" gene trees which do not follow the "main distribution(s)" of trees, we propose to apply the "tropical metric" with the max-plus algebra from tropical geometry to a non-parametric estimation of gene trees over the space of phylogenetic trees. In this research we apply the "tropical metric," a well-defined metric over the space of phylogenetic trees under the max-plus algebra, to non-parametric estimation of gene trees distribution over the tree space. Kernel density estimator (KDE) is one of the most popular non-parametric estimation of a distribution from a given sample, and we propose an analogue of the classical KDE in the setting of tropical geometry with the tropical metric which measures the length of an intrinsic geodesic between trees over the tree space. We estimate the probability of an observed tree by empirical frequencies of nearby trees, with the level of influence determined by the tropical metric. Then, with simulated data generated from the multispecies coalescent model, we show that the non-parametric estimation of the gene tree distribution using the tropical metric performs better than one using the Billera-Holmes-Vogtmann (BHV) metric developed by Weyenberg et al. in terms of computational times and accuracy. We then apply it to Apicomplexa data.

Biologically plausible local synaptic learning rules robustly implement deep supervised learning.

In deep neural networks, representational learning in the middle layer is essential for achieving efficient learning. However, the currently prevailing backpropagation learning rules (BP) are not necessarily biologically plausible and cannot be implemented in the brain in their current form. Therefore, to elucidate the learning rules used by the brain, it is critical to establish biologically plausible learning rules for practical memory tasks. For example, learning rules that result in a learning performance worse than that of animals observed in experimental studies may not be computations used in real brains and should be ruled out. Using numerical simulations, we developed biologically plausible learning rules to solve a task that replicates a laboratory experiment where mice learned to predict the correct reward amount. Although the extreme learning machine (ELM) and weight perturbation (WP) learning rules performed worse than the mice, the feedback alignment (FA) rule achieved a performance equal to that of BP. To obtain a more biologically plausible model, we developed a variant of FA, FA_Ex-100%, which implements direct dopamine inputs that provide error signals locally in the layer of focus, as found in the mouse entorhinal cortex. The performance of FA_Ex-100% was comparable to that of conventional BP. Finally, we tested whether FA_Ex-100% was robust against rule perturbations and biologically inevitable noise. FA_Ex-100% worked even when subjected to perturbations, presumably because it could calibrate the correct prediction error (e.g., dopaminergic signals) in the next step as a teaching signal if the perturbation created a deviation. These results suggest that simplified and biologically plausible learning rules, such as FA_Ex-100%, can robustly facilitate deep supervised learning when the error signal, possibly conveyed by dopaminergic neurons, is accurate.

Tropical support vector machines: Evaluations and extension to function spaces.

Support Vector Machines (SVMs) are one of the most popular supervised learning models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical SVMs classify data points using a tropical hyperplane under the tropical metric with the max-plus algebra. In this paper, first we show generalization error bounds of tropical SVMs over the tropical projective torus. While the generalization error bounds attained via Vapnik-Chervonenkis (VC) dimensions in a distribution-free manner still depend on the dimension, we also show numerically and theoretically by extreme value statistics that the tropical SVMs for classifying data points from two Gaussian distributions as well as empirical data sets of different neuron types are fairly robust against the curse of dimensionality. Extreme value statistics also underlie the anomalous scaling behaviors of the tropical distance between random vectors with additional noise dimensions. Finally, we define tropical SVMs over a function space with the tropical metric.

Assessing the Impacts of Correlated Variability with Dissociated Timescales.

Despite the profound influence on coding capacity of sensory neurons, the measurements of noise correlations have been inconsistent. This is, possibly, because nonstationarity, i.e., drifting baselines, engendered the spurious long-term correlations even if no actual short-term correlation existed. Although attempts to separate them have been made previously, they were ad hoc for specific cases or computationally too demanding. Here we proposed an information-geometric method to unbiasedly estimate pure short-term noise correlations irrespective of the background brain activities without demanding computational resources. First, the benchmark simulations demonstrated that the proposed estimator is more accurate and computationally efficient than the conventional correlograms and the residual correlations with Kalman filters or moving averages of length three or more, while the best moving average of length two coincided with the propose method regarding correlation estimates. Next, we analyzed the cat V1 neural responses to demonstrate that the statistical test accompanying the proposed method combined with the existing nonstationarity test enabled us to dissociate short-term and long-term noise correlations. When we excluded the spurious noise correlations of purely long-term nature, only a small fraction of neuron pairs showed significant short-term correlations, possibly reconciling the previous inconsistent observations on existence of significant noise correlations. The decoding accuracy was slightly improved by the short-term correlations. Although the long-term correlations deteriorated the generalizability, the generalizability was recovered by the decoder with trend removal, suggesting that brains could overcome nonstationarity. Thus, the proposed method enables us to elucidate the impacts of short-term and long-term noise correlations in a dissociated manner.

Identification of midbrain dopamine neurons using features from spontaneous spike activity patterns.

Although dopamine neurons are considered essential in various brain functions, their specific roles are under debate, partially due to the difficulty to identify dopamine neurons among surrounding neurons deep in the brain based only on the extracellularly recorded electric activities. Thus, a handy method to identify dopamine and non-dopamine neurons based on the spontaneous activity patterns is desired. Here we tried to discriminate optogenetically-identified dopamine neurons from other types of neurons and obtained 86.0% success.

The Level of IgA Antibodies to Endothelial Cells Correlates with Histological Evidence of Disease Activity in Patients with Lupus Nephritis.

Anti-endothelial cell antibodies (AECA) are frequently detected in patients with systemic lupus erythematosus (SLE), but their pathological role remains unclear. We recently developed a solubilized cell surface protein capture enzyme-linked immunosorbent assay (CSP-ELISA) to detect antibodies against membrane proteins involved in autoimmune reactions. In this study, sera from 51 patients with biopsy-proven lupus nephritis (LN), 25 with SLE without renal involvement (non-LN SLE), 42 disease control (DC) subjects, and 80 healthy control (HC) subjects were tested for IgG- and IgA-AECA for human umbilical vein endothelial cells (HUVEC) and human glomerular EC (HGEC) by using CSP-ELISA. IgG- and IgA-AECA titers were significantly higher in LN and non-LN SLE patients than in the DC or HC (P < 0.001) groups. IgG- and IgA-AECA titers for HUVEC corresponded well with those for HGEC. The IgA-AECA level correlated with the SLE disease activity index and with histological evidence of active lesions (cellular proliferations, hyaline thrombi and wire loops, leukocytic infiltration, and fibrinoid necrosis) in LN patients (P < 0.001). The sensitivity of IgA-AECA as a diagnostic test for histological evidence of active lesions in LN patients was 0.92, with a specificity of 0.70. The significant correlation of IgA-AECA with glomerular hypercellularity indicates that IgA-AECA are associated with endothelial damage in LN.

Hodge-Kodaira decomposition of evolving neural networks.

Although it is very important to scrutinize recurrent structures of neural networks for elucidating brain functions, conventional methods often have difficulty in characterizing global loops within a network systematically. Here we applied the Hodge-Kodaira decomposition, a topological method, to an evolving neural network model in order to characterize its loop structure. By controlling a learning rule parametrically, we found that a model with an STDP-rule, which tends to form paths coincident with causal firing orders, had the most loops. Furthermore, by counting the number of global loops in the network, we detected the inhomogeneity inside the chaotic region, which is usually considered intractable.

Dynamical system design for silicon neurons using phase reduction approach.

In the present paper, we apply a computer-aided phase reduction approach to dynamical system design for silicon neurons (SiNs). Firstly, we briefly review the dynamical system design for SiNs. Secondly, we summarize the phase response properties of circuit models of previous SiNs to clarify design criteria in our approach. From a viewpoint of the phase reduction theory, as a case study, we show how to tune circuit parameters of the resonate-and-fire neuron (RFN) circuit as a hybrid type SiN. Finally, we demonstrate delay-induced synchronization in a silicon spiking neural network that consists of the RFN circuits.

The dorsomedial striatum encodes net expected return, critical for energizing performance vigor.

Decision making requires an actor to not only steer behavior toward specific goals but also determine the optimal vigor of performance. Current research and models have largely focused on the former problem of how actions are directed while overlooking the latter problem of how they are energized. Here we designed a self-paced decision-making paradigm, which showed that rats' performance vigor globally fluctuates with the net value of their options, suggesting that they maintain long-term estimates of the value of their current state. Lesions of the dorsomedial striatum (DMS) and, to a lesser degree, in the ventral striatum impaired such state-dependent modulation of vigor, rendering vigor to depend more exclusively on the outcomes of immediately preceding trials. The lesions, however, spared choice biases. Neuronal recordings showed that the DMS is enriched in net value-coding neurons. In sum, the DMS encodes one's net expected return, which drives the general motivation to perform.

Odor representations in olfactory cortex: distributed rate coding and decorrelated population activity.

VIDEO ABSTRACT: How information encoded in neuronal spike trains is used to guide sensory decisions is a fundamental question. In olfaction, a single sniff is sufficient for fine odor discrimination but the neural representations on which olfactory decisions are based are unclear. Here, we recorded neural ensemble activity in the anterior piriform cortex (aPC) of rats performing an odor mixture categorization task. We show that odors evoke transient bursts locked to sniff onset and that odor identity can be better decoded using burst spike counts than by spike latencies or temporal patterns. Surprisingly, aPC ensembles also exhibited near-zero noise correlations during odor stimulation. Consequently, fewer than 100 aPC neurons provided sufficient information to account for behavioral speed and accuracy, suggesting that behavioral performance limits arise downstream of aPC. These findings demonstrate profound transformations in the dynamics of odor representations from the olfactory bulb to cortex and reveal likely substrates for odor-guided decisions.

Autoantibodies directed against labile epitopes on cell surface proteins in autoimmune disease patients: proposal of a novel ELISA for the detection of anti-endothelial cell antibodies.

This article describes a novel method for detecting anti-endothelial cell antibodies (AECAs). Sera from patients with systemic vasculitis or inflammatory conditions have been reported to contain antibodies (Abs) that bind to endothelial cells (EC), i.e., AECAs. AECAs are known to play immunogenic effects by triggering EC activation and vascular damage, but the immunopathological role of AECAs is not clear. Sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) and Western blotting have previously been used for detecting target antigens of AECAs. However, we assumed that these methods are not appropriate for searching genuine target antigens (Ags) on cell surface, and developed a novel solubilized cell surface protein-capture ELISA (CSP-ELISA). Ags were obtained as cell surface proteins from the plasma membrane of human umbilical vein endothelial cells (HUVECs); these cell surface proteins were biotinylated, solubilized with detergent, and captured on ELISA wells coated with NeutrAvidin™ biotin binding protein (NeuAvi). AECA titers in serum from 126 autoimmune disease patients and 122 healthy donors were tested. AECAs were detected in 28 of 36 (78%) of systemic lupus erythematosus (SLE) patients; in 13 of 16 (81%) of mixed connective tissue disease (MCTD) patients; and in 5 of 9 (56%) of systemic sclerosis (SSc) patients. Relatively weak denaturation of antigens on ELISA wells caused loss of binding of these autoantibodies (autoAbs). Thus, this newly developed CSP-ELISA method enables the detection of Abs to the labile epitopes of autoantigens (autoAgs) such as membrane proteins, and this method is generally applicable to various kinds of membrane proteins and the Abs against them. We propose CSP-ELISA for measuring AECAs in serum samples for routine laboratory testing.

Analytical investigation of the effects of lateral connections on the accuracy of population coding.

We studied how lateral connections affect the accuracy of a population code by using a model of orientation selectivity in the primary visual cortex. Investigating the effects of lateral connections on population coding is a complex problem because these connections simultaneously change the shape of tuning curves and correlations between neurons. Both of these changes caused by lateral connections have to be taken into consideration to correctly evaluate their effects. We propose a theoretical framework for analytically computing the Fisher information, which measures the accuracy of a population code, in stochastic spiking neuron models with refractory periods. Within our framework, we accurately evaluated both the changes in tuning curves and correlations caused by lateral connections and their effects on the Fisher information. We found that their effects conflicted with each other and the answer to whether or not the lateral connections increased the Fisher information strongly depended on the intrinsic properties of the model neuron. By systematically changing the coupling strengths of excitations and inhibitions, we found the parameter regions of lateral connectivities where sharpening of tuning curves through Mexican-hat connectivities led to an increase in information, which is in contrast to some previous findings.

Balanced excitatory and inhibitory inputs to cortical neurons decouple firing irregularity from rate modulations.

In vivo cortical neurons are known to exhibit highly irregular spike patterns. Because the intervals between successive spikes fluctuate greatly, irregular neuronal firing makes it difficult to estimate instantaneous firing rates accurately. If, however, the irregularity of spike timing is decoupled from rate modulations, the estimate of firing rate can be improved. Here, we introduce a novel coding scheme to make the firing irregularity orthogonal to the firing rate in information representation. The scheme is valid if an interspike interval distribution can be well fitted by the gamma distribution and the firing irregularity is constant over time. We investigated in a computational model whether fluctuating external inputs may generate gamma process-like spike outputs, and whether the two quantities are actually decoupled. Whole-cell patch-clamp recordings of cortical neurons were performed to confirm the predictions of the model. The output spikes were well fitted by the gamma distribution. The firing irregularity remained approximately constant regardless of the firing rate when we injected a balanced input, in which excitatory and inhibitory synapses are activated concurrently while keeping their conductance ratio fixed. The degree of irregular firing depended on the effective reversal potential set by the balance between excitation and inhibition. In contrast, when we modulated conductances out of balance, the irregularity varied with the firing rate. These results indicate that the balanced input may improve the efficiency of neural coding by clamping the firing irregularity of cortical neurons. We demonstrate how this novel coding scheme facilitates stimulus decoding.

Estimating spiking irregularities under changing environments.

We considered a gamma distribution of interspike intervals as a statistical model for neuronal spike generation. A gamma distribution is a natural extension of the Poisson process taking the effect of a refractory period into account. The model is specified by two parameters: a time-dependent firing rate and a shape parameter that characterizes spiking irregularities of individual neurons. Because the environment changes over time, observed data are generated from a model with a time-dependent firing rate, which is an unknown function. A statistical model with an unknown function is called a semiparametric model and is generally very difficult to solve. We used a novel method of estimating functions in information geometry to estimate the shape parameter without estimating the unknown function. We obtained an optimal estimating function analytically for the shape parameter independent of the functional form of the firing rate. This estimation is efficient without Fisher information loss and better than maximum likelihood estimation. We suggest a measure of spiking irregularity based on the estimating function, which may be useful for characterizing individual neurons in changing environments.

Organization and structure of hox gene loci in medaka genome and comparison with those of pufferfish and zebrafish genomes.

We isolated BAC clones that cover the entire hox gene loci in the medaka fish Oryzias latipes. The BAC clones were characterized by the Southern hybridization with many hox gene probes isolated in our previous study and by PCR using primers designed for selective amplification of respective hox genes. Then, the BAC clones have been subjected to shotgun sequencing. The results revealed the organization of the entire hox gene loci. Forty-six hox genes in total are encoded in seven clusters as follows: 10 hox genes in Aa cluster; 5 in Ab; 9 in Ba; 4 in Bb; 10 in Ca; 6 in Da; and 2 in Db. Together with the information on the hox gene loci registered in the Fugu genome database and in the Danio genome database, the physical maps of three fish genomes were constructed and compared one another. Not only numbers of hox genes but also the distances between the neighboring hox genes are highly similar between medaka and fugu. As for six clusters, Aa, Ab, Ba, Bb, Ca and Da that are commonly present in the three fishes, only few or no differences were found in each cluster. Thus, the hox gene sets should have been well conserved once they had been established in respective species.

A measure of local variation of inter-spike intervals.

It has been revealed in our recent study that cortical neurons are categorized into distinct types, according to a new measure of the local variation of inter-spike intervals, L(V). In this paper, we obtain values of the local variation L(V) and a conventional coefficient of variation C(V) for a variety of model point processes. While the value of C(V) undergoes large changes by rate fluctuation of the point processes, the value of L(V) does not undergo large changes by rate fluctuation, and is principally determined by the form of intrinsic interval distribution of the original model point process.

Pulse-coupled resonate-and-fire models.

We analyze two pulse-coupled resonate-and-fire neurons. Numerical simulation reveals that an antiphase state is an attractor of this model. We can analytically explain the stability of antiphase states by means of a return map of firing times, which we propose in this paper. The resultant stability condition turns out to be quite simple. The phase diagram based on our theory shows that there are two types of antiphase states. One of these cannot be seen in coupled integrate-and-fire models and is peculiar to resonate-and-fire models. The results of our theory coincide with those of numerical simulations.