Stochastic Syncing in Sinusoidally Driven Atomic Orbital Memory.

Stochastically fluctuating multiwell systems are a promising route toward physical implementations of energy-based machine learning and neuromorphic hardware. One of the challenges is finding tunable material platforms that exhibit such multiwell behavior and understanding how complex dynamic input signals influence their stochastic response. One such platform is the recently discovered atomic Boltzmann machine, where each stochastic unit is represented by a binary orbital memory state of an individual atom. Here, we investigate the stochastic response of binary orbital memory states to sinusoidal input voltages. Using scanning tunneling microscopy, we investigated orbital memory derived from individual Fe and Co atoms on black phosphorus. We quantify the state residence times as a function of various input parameters such as frequency, amplitude, and offset voltage. The state residence times for both species, when driven by a sinusoidal signal, exhibit synchronization that can be quantitatively modeled by a Poisson process based on the switching rates in the absence of a sinusoidal signal. For individual Fe atoms, we also observe a frequency-dependent response of the state favorability, which can be tuned by the input parameters. In contrast to Fe, there is no significant frequency dependence in the state favorability for individual Co atoms. Based on the Poisson model, the difference in the response of the state favorability can be traced to the difference in the voltage-dependent switching rates of the two different species. This platform provides a tunable way to induce population changes in stochastic systems and provides a foundation toward understanding driven stochastic multiwell systems.

Postoperative Delirium After Intracranial Surgery: A Retrospective Cohort Study.

BACKGROUND: The clinical relevance of postoperative delirium (POD) in neurosurgery remains unclear and should be investigated because these patients are vulnerable. Hence, we investigated the impact of POD, by means of incidence and health outcomes, and identified independent risk factors. METHODS: Adult patients undergoing an intracranial surgical procedure in the Erasmus Medical Center Rotterdam between June 2017 and September 2020 were retrospectively included. POD incidence, defined by a Delirium Observation Screening Scale (DOSS) ≥3 or antipsychotic treatment for delirium within 5 days after surgery, was calculated. Logistic regression analysis on the full data set was conducted for the multivariable risk factor and health outcome analyses. RESULTS: After including 2901 intracranial surgical procedures, POD was present in 19.4% with a mean onset in days of 2.62 (standard deviation, 1.22) and associated with more intensive care unit admissions and more discharge toward residential care. Onset of POD was not associated with increased length of hospitalization or mortality. We identified several independent nonmodifiable risk factors such as age, preexisting memory problems, emergency operations, craniotomy compared with burr-hole surgery, and severe blood loss. Moreover, we identified modifiable risk factors such as low preoperative potassium and opioid and dexamethasone administration. CONCLUSIONS: Our POD incidence rates and correlation with more intensive care unit admission and discharge toward residential care suggest a significant impact of POD on neurosurgical patients. We identified several modifiable and nonmodifiable risk factors, which shed light on the pathophysiologic mechanisms of POD in this cohort and could be targeted for future intervention studies.

An atomic Boltzmann machine capable of self-adaption.

The quest to implement machine learning algorithms in hardware has focused on combining various materials, each mimicking a computational primitive, to create device functionality. Ultimately, these piecewise approaches limit functionality and efficiency, while complicating scaling and on-chip learning, necessitating new approaches linking physical phenomena to machine learning models. Here, we create an atomic spin system that emulates a Boltzmann machine directly in the orbital dynamics of one well-defined material system. Utilizing the concept of orbital memory based on individual cobalt atoms on black phosphorus, we fabricate the prerequisite tuneable multi-well energy landscape by gating patterned atomic ensembles using scanning tunnelling microscopy. Exploiting the anisotropic behaviour of black phosphorus, we realize plasticity with multi-valued and interlinking synapses that lead to tuneable probability distributions. Furthermore, we observe an autonomous reorganization of the synaptic weights in response to external electrical stimuli, which evolves at a different time scale compared to neural dynamics. This self-adaptive architecture paves the way for autonomous learning directly in atomic-scale machine learning hardware.

Bayesian neural networks with variable selection for prediction of genotypic values.

BACKGROUND: Estimating the genetic component of a complex phenotype is a complicated problem, mainly because there are many allele effects to estimate from a limited number of phenotypes. In spite of this difficulty, linear methods with variable selection have been able to give good predictions of additive effects of individuals. However, prediction of non-additive genetic effects is challenging with the usual prediction methods. In machine learning, non-additive relations between inputs can be modeled with neural networks. We developed a novel method (NetSparse) that uses Bayesian neural networks with variable selection for the prediction of genotypic values of individuals, including non-additive genetic effects. RESULTS: We simulated several populations with different phenotypic models and compared NetSparse to genomic best linear unbiased prediction (GBLUP), BayesB, their dominance variants, and an additive by additive method. We found that when the number of QTL was relatively small (10 or 100), NetSparse had 2 to 28 percentage points higher accuracy than the reference methods. For scenarios that included dominance or epistatic effects, NetSparse had 0.0 to 3.9 percentage points higher accuracy for predicting phenotypes than the reference methods, except in scenarios with extreme overdominance, for which reference methods that explicitly model dominance had 6 percentage points higher accuracy than NetSparse. CONCLUSIONS: Bayesian neural networks with variable selection are promising for prediction of the genetic component of complex traits in animal breeding, and their performance is robust across different genetic models. However, their large computational costs can hinder their use in practice.

Role of Synaptic Stochasticity in Training Low-Precision Neural Networks.

Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights naturally gives prominence to exponentially rare dense regions of solutions with a number of desirable properties such as robustness and good generalization performance, while typical solutions are isolated and hard to find. Binary solutions of the standard perceptron problem are obtained from a simple gradient descent procedure on a set of real values parametrizing a probability distribution over the binary synapses. Both analytical and numerical results are presented. An algorithmic extension that allows to train discrete deep neural networks is also investigated.

Learning Universal Computations with Spikes.

Providing the neurobiological basis of information processing in higher animals, spiking neural networks must be able to learn a variety of complicated computations, including the generation of appropriate, possibly delayed reactions to inputs and the self-sustained generation of complex activity patterns, e.g. for locomotion. Many such computations require previous building of intrinsic world models. Here we show how spiking neural networks may solve these different tasks. Firstly, we derive constraints under which classes of spiking neural networks lend themselves to substrates of powerful general purpose computing. The networks contain dendritic or synaptic nonlinearities and have a constrained connectivity. We then combine such networks with learning rules for outputs or recurrent connections. We show that this allows to learn even difficult benchmark tasks such as the self-sustained generation of desired low-dimensional chaotic dynamics or memory-dependent computations. Furthermore, we show how spiking networks can build models of external world systems and use the acquired knowledge to control them.

Quantitative analysis of task selection for brain-computer interfaces.

OBJECTIVE: To assess quantitatively the impact of task selection in the performance of brain-computer interfaces (BCI). APPROACH: We consider the task-pairs derived from multi-class BCI imagery movement tasks in three different datasets. We analyze for the first time the benefits of task selection on a large-scale basis (109 users) and evaluate the possibility of transferring task-pair information across days for a given subject. MAIN RESULTS: Selecting the subject-dependent optimal task-pair among three different imagery movement tasks results in approximately 20% potential increase in the number of users that can be expected to control a binary BCI. The improvement is observed with respect to the best task-pair fixed across subjects. The best task-pair selected for each subject individually during a first day of recordings is generally a good task-pair in subsequent days. In general, task learning from the user side has a positive influence in the generalization of the optimal task-pair, but special attention should be given to inexperienced subjects. SIGNIFICANCE: These results add significant evidence to existing literature that advocates task selection as a necessary step towards usable BCIs. This contribution motivates further research focused on deriving adaptive methods for task selection on larger sets of mental tasks in practical online scenarios.

Emerging phenomena in neural networks with dynamic synapses and their computational implications.

In this paper we review our research on the effect and computational role of dynamical synapses on feed-forward and recurrent neural networks. Among others, we report on the appearance of a new class of dynamical memories which result from the destabilization of learned memory attractors. This has important consequences for dynamic information processing allowing the system to sequentially access the information stored in the memories under changing stimuli. Although storage capacity of stable memories also decreases, our study demonstrated the positive effect of synaptic facilitation to recover maximum storage capacity and to enlarge the capacity of the system for memory recall in noisy conditions. Possibly, the new dynamical behavior can be associated with the voltage transitions between up and down states observed in cortical areas in the brain. We investigated the conditions for which the permanence times in the up state are power-law distributed, which is a sign for criticality, and concluded that the experimentally observed large variability of permanence times could be explained as the result of noisy dynamic synapses with large recovery times. Finally, we report how short-term synaptic processes can transmit weak signals throughout more than one frequency range in noisy neural networks, displaying a kind of stochastic multi-resonance. This effect is due to competition between activity-dependent synaptic fluctuations (due to dynamic synapses) and the existence of neuron firing threshold which adapts to the incoming mean synaptic input.

Time-integrated position error accounts for sensorimotor behavior in time-constrained tasks.

Several studies have shown that human motor behavior can be successfully described using optimal control theory, which describes behavior by optimizing the trade-off between the subject's effort and performance. This approach predicts that subjects reach the goal exactly at the final time. However, another strategy might be that subjects try to reach the target position well before the final time to avoid the risk of missing the target. To test this, we have investigated whether minimizing the control effort and maximizing the performance is sufficient to describe human motor behavior in time-constrained motor tasks. In addition to the standard model, we postulate a new model which includes an additional cost criterion which penalizes deviations between the position of the effector and the target throughout the trial, forcing arrival on target before the final time. To investigate which model gives the best fit to the data and to see whether that model is generic, we tested both models in two different tasks where subjects used a joystick to steer a ball on a screen to hit a target (first task) or one of two targets (second task) before a final time. Noise of different amplitudes was superimposed on the ball position to investigate the ability of the models to predict motor behavior for different levels of uncertainty. The results show that a cost function representing only a trade-off between effort and accuracy at the end time is insufficient to describe the observed behavior. The new model correctly predicts that subjects steer the ball to the target position well before the final time is reached, which is in agreement with the observed behavior. This result is consistent for all noise amplitudes and for both tasks.

Irregular dynamics in up and down cortical states.

Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a biologically motivated stochastic model of up and down transitions. The model is constituted by a simple bistable rate dynamics, where the synaptic current is modulated by short-term synaptic processes which introduce stochasticity and temporal correlations. A complete analysis of our model, both with mean-field approaches and numerical simulations, shows the appearance of complex transitions between high (up) and low (down) neural activity states, driven by the synaptic noise, with permanence times in the up state distributed according to a power-law. We show that the experimentally observed large fluctuation in up and down permanence times can be explained as the result of sufficiently noisy dynamical synapses with sufficiently large recovery times. Static synapses cannot account for this behavior, nor can dynamical synapses in the absence of noise.

Multipoint approximations of identity-by-descent probabilities for accurate linkage analysis of distantly related individuals.

We propose an analytical approximation method for the estimation of multipoint identity by descent (IBD) probabilities in pedigrees containing a moderate number of distantly related individuals. We show that in large pedigrees where cases are related through untyped ancestors only, it is possible to formulate the hidden Markov model of the Lander-Green algorithm in terms of the IBD configurations of the cases. We use a first-order Markov approximation to model the changes in this IBD-configuration variable along the chromosome. In simulated and real data sets, we demonstrate that estimates of parametric and nonparametric linkage statistics based on the first-order Markov approximation are accurate. The computation time is exponential in the number of cases instead of in the number of meioses separating the cases. We have implemented our approach in the computer program ALADIN (accurate linkage analysis of distantly related individuals). ALADIN can be applied to general pedigrees and marker types and has the ability to model marker-marker linkage disequilibrium with a clustered-markers approach. Using ALADIN is straightforward: It requires no parameters to be specified and accepts standard input files.

Effect of linkage disequilibrium between markers in linkage and association analyses.

Contributions to Group 17 of the Genetic Analysis Workshop 15 considered dense markers in linkage disequilibrium (LD) in the context of either linkage or association analysis. Three contributions reported on methods for modeling LD or selecting a subset of markers in linkage equilibrium to perform linkage analysis. When all markers were used without modeling LD, inflated evidence for linkage was observed when parental genotypes were missing. All methods for handling LD led to some decreased linkage evidence. Two groups performed a genome-wide association scan using either mixed models to account for known or unknown relatedness between individuals, trend tests or combination statistics. All methods failed to detect four of the eight simulated loci because of low LD in some regions. Three groups performed association analysis using simulated dense markers on chromosome 6, where a simulated HLA-DRB1 locus played a major role in disease susceptibility along with two additional loci of smaller effect. The overall conditional genotype method correctly identified both additional loci while a novel transmission disequilibrium test-statistic to combine studies with non-overlapping markers identified one HLA locus after stratifying on the parental HLA-DRB1 genotypes; LD mapping using the Malécot model mapped two loci in this region, even when using greatly reduced marker density. While LD between markers appears to be a nuisance that may cause spurious linkage results with missing parental genotypes in linkage analysis, association analysis thrives on LD, and disease genes fail to be detected in regions of low LD.

Haplotype inference in general pedigrees using the cluster variation method.

We present CVMHAPLO, a probabilistic method for haplotyping in general pedigrees with many markers. CVMHAPLO reconstructs the haplotypes by assigning in every iteration a fixed number of the ordered genotypes with the highest marginal probability, conditioned on the marker data and ordered genotypes assigned in previous iterations. CVMHAPLO makes use of the cluster variation method (CVM) to efficiently estimate the marginal probabilities. We focused on single-nucleotide polymorphism (SNP) markers in the evaluation of our approach. In simulated data sets where exact computation was feasible, we found that the accuracy of CVMHAPLO was high and similar to that of maximum-likelihood methods. In simulated data sets where exact computation of the maximum-likelihood haplotype configuration was not feasible, the accuracy of CVMHAPLO was similar to that of state of the art Markov chain Monte Carlo (MCMC) maximum-likelihood approximations when all ordered genotypes were assigned and higher when only a subset of the ordered genotypes was assigned. CVMHAPLO was faster than the MCMC approach and provided more detailed information about the uncertainty in the inferred haplotypes. We conclude that CVMHAPLO is a practical tool for the inference of haplotypes in large complex pedigrees.

Input-driven oscillations in networks with excitatory and inhibitory neurons with dynamic synapses.

Previous work has shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons can reveal oscillatory activity. For example, Börgers and Kopell (2003) have shown that oscillations occur when the excitatory neurons receive a sufficiently large input. A constant drive to the excitatory neurons is sufficient for oscillatory activity. Other studies (Doiron, Chacron, Maler, Longtin, & Bastian, 2003; Doiron, Lindner, Longtin, Maler, & Bastian, 2004) have shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons reveal oscillatory activity only if the excitatory neurons receive correlated input, regardless of the amount of excitatory input. In this study, we show that these apparently contradictory results can be explained by the behavior of a single model operating in different regimes of parameter space. Moreover, we show that adding dynamic synapses in the inhibitory feedback loop provides a robust network behavior over a broad range of stimulus intensities, contrary to that of previous models. A remarkable property of the introduction of dynamic synapses is that the activity of the network reveals synchronized oscillatory components in the case of correlated input, but also reflects the temporal behavior of the input signal to the excitatory neurons. This allows the network to encode both the temporal characteristics of the input and the presence of spatial correlations in the input simultaneously.

Modeling linkage disequilibrium in exact linkage computations: a comparison of first-order Markov approaches and the clustered-markers approach.

Recent studies have shown that linkage disequilibrium (LD) between single-nucleotide polymorphism (SNP) markers is widespread. Assuming linkage equilibrium has been shown to cause false positives in linkage studies where parental genotypes are not available. Therefore, linkage analysis methods that can deal with LD are required to accurately analyze SNP marker data sets. We compared three approaches to deal with LD between markers: 1) The clustered-markers approach implemented in the computer program MERLIN; 2) The standard hidden Markov model (HMM) multipoint model augmented with a first-order Markov model for the allele frequencies of the founders, in which we considered both a Bayesian and a maximum-likelihood implementation of this approach; 3) The 'independent' SNPs approach, i.e., removing SNPs from the data set until the remaining SNPs have low levels of LD.We evaluated these approaches on the Illumina 6K SNP data set of affected sib-pairs of Problem 2. We found that the first-order Markov model was able to account for most of the strong LD in this data set. The difference between the Bayesian and maximum- likelihood implementation was small. An advantage of the first-order Markov model is that it does not require the user to specify parameters.

The cluster variation method for efficient linkage analysis on extended pedigrees.

BACKGROUND: Computing exact multipoint LOD scores for extended pedigrees rapidly becomes infeasible as the number of markers and untyped individuals increase. When markers are excluded from the computation, significant power may be lost. Therefore accurate approximate methods which take into account all markers are desirable. METHODS: We present a novel method for efficient estimation of LOD scores on extended pedigrees. Our approach is based on the Cluster Variation Method, which deterministically estimates likelihoods by performing exact computations on tractable subsets of variables (clusters) of a Bayesian network. First a distribution over inheritances on the marker loci is approximated with the Cluster Variation Method. Then this distribution is used to estimate the LOD score for each location of the trait locus. RESULTS: First we demonstrate that significant power may be lost if markers are ignored in the multi-point analysis. On a set of pedigrees where exact computation is possible we compare the estimates of the LOD scores obtained with our method to the exact LOD scores. Secondly, we compare our method to a state of the art MCMC sampler. When both methods are given equal computation time, our method is more efficient. Finally, we show that CVM scales to large problem instances. CONCLUSION: We conclude that the Cluster Variation Method is as accurate as MCMC and generally is more efficient. Our method is a promising alternative to approaches based on MCMC sampling.

Linear theory for control of nonlinear stochastic systems.

We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of nonlinear control problems that can be formulated as a path integral and where the noise plays the role of temperature. The path integral displays symmetry breaking and there exists a critical noise value that separates regimes where optimal control yields qualitatively different solutions. The path integral can be computed efficiently by Monte Carlo integration or by a Laplace approximation, and can therefore be used to solve high dimensional stochastic control problems.

Coincidence detection with dynamic synapses.

Recent experimental findings show that the efficacy of transmission in cortical synapses depends on presynaptic activity. In most neural models, however, the synapses are regarded as static entities where this dependence is not included. We study the role of activity-dependent (dynamic) synapses in neuronal responses to temporal patterns of afferent activity. Our results demonstrate that, for suitably chosen threshold values, dynamic synapses are capable of coincidence detection (CD) over a much larger range of frequencies than static synapses. The phenomenon appears to be valid for an integrate-and-fire as well as a Hodgkin-Huxley neuron and various types of CD tasks.

Associative memory with dynamic synapses.

We have examined a role of dynamic synapses in the stochastic Hopfield-like network behavior. Our results demonstrate an appearance of a novel phase characterized by quick transitions from one memory state to another. The network is able to retrieve memorized patterns corresponding to classical ferromagnetic states but switches between memorized patterns with an intermittent type of behavior. This phenomenon might reflect the flexibility of real neural systems and their readiness to receive and respond to novel and changing external stimuli.

Storage capacity of attractor neural networks with depressing synapses.

We compute the capacity of a binary neural network with dynamic depressing synapses to store and retrieve an infinite number of patterns. We use a biologically motivated model of synaptic depression and a standard mean-field approach. We find that at T=0 the critical storage capacity decreases with the degree of the depression. We confirm the validity of our main mean-field results with numerical simulations.