Collective stability of networks of winner-take-all circuits

The neocortex has a remarkably uniform neuronal organization, suggesting that common principles of processing are employed throughout its extent. In particular, the patterns of connectivity observed in the superficial layers of the visual cortex are consistent with the recurrent excitation and inhibitory feedback required for cooperative-competitive circuits such as the soft winner-take-all (WTA). WTA circuits offer interesting computational properties such as selective amplification, signal restoration, and decision making. But, these properties depend on the signal gain derived from positive feedback, and so there is a critical trade-off between providing feedback strong enough to support the sophisticated computations, while maintaining overall circuit stability. We consider the question of how to reason about stability in very large distributed networks of such circuits. We approach this problem by approximating the regular cortical architecture as many interconnected cooperative-competitive modules. We demonstrate that by properly understanding the behavior of this small computational module, one can reason over the stability and convergence of very large networks composed of these modules. We obtain parameter ranges in which the WTA circuit operates in a high-gain regime, is stable, and can be aggregated arbitrarily to form large stable networks. We use nonlinear Contraction Theory to establish conditions for stability in the fully nonlinear case, and verify these solutions using numerical simulations. The derived bounds allow modes of operation in which the WTA network is multi-stable and exhibits state-dependent persistent activities. Our approach is sufficiently general to reason systematically about the stability of any network, biological or technological, composed of networks of small modules that express competition through shared inhibition.Comment: 7 Figure

Competition through selective inhibitory synchrony

Models of cortical neuronal circuits commonly depend on inhibitory feedback to control gain, provide signal normalization, and to selectively amplify signals using winner-take-all (WTA) dynamics. Such models generally assume that excitatory and inhibitory neurons are able to interact easily, because their axons and dendrites are co-localized in the same small volume. However, quantitative neuroanatomical studies of the dimensions of axonal and dendritic trees of neurons in the neocortex show that this co-localization assumption is not valid. In this paper we describe a simple modification to the WTA circuit design that permits the effects of distributed inhibitory neurons to be coupled through synchronization, and so allows a single WTA to be distributed widely in cortical space, well beyond the arborization of any single inhibitory neuron, and even across different cortical areas. We prove by non-linear contraction analysis, and demonstrate by simulation that distributed WTA sub-systems combined by such inhibitory synchrony are inherently stable. We show analytically that synchronization is substantially faster than winner selection. This circuit mechanism allows networks of independent WTAs to fully or partially compete with each other.Comment: in press at Neural computation; 4 figure

Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks

Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of the CSPs planar four-color graph coloring, maximum independent set, and Sudoku on this substrate, and provide mathematical proofs that guarantee these graph coloring problems will convergence to a solution. The network is composed of non-saturating linear threshold neurons. Their lack of right saturation allows the overall network to explore the problem space driven through the unstable dynamics generated by recurrent excitation. The direction of exploration is steered by the constraint neurons. While many problems can be solved using only linear inhibitory constraints, network performance on hard problems benefits significantly when these negative constraints are implemented by non-linear multiplicative inhibition. Overall, our results demonstrate the importance of instability rather than stability in network computation, and also offer insight into the computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018

Prevalence of vitamin D deficiency in an inpatient population in the Swiss canton of Basel-Country

AIMS: Vitamin D deficiency remains very common in the general population. Adding to the importance of this issue is the discovery that vitamin D plays a role in many other tissues apart from the bone, including muscle, brain, prostate, breast and colon. In this study, we investigated the prevalence of vitamin D deficiency in a large group of patients hospitalised in the cantonal hospital Basel-Country, and analysed the dependence of serum vitamin D concentrations on gender, time of the year and age. METHODS: We retrospectively analysed anonymised data received from the central laboratory of the cantonal hospital Basel-Country. The pool of data contains values obtained between 2013 and 2017 from 8861 patients aged between 18 and 102 years. If sequential measurements were available from a patient, only the first was used for the analyses. Vitamin D deficiency was defined as a serum concentration of <50 nmol/l and severe deficiency as 75 nmol/l. RESULTS: Mean ± standard deviation serum vitamin D concentration was 52.5 ± 30.5 nmol/l, with women having a higher mean of 55.5 ± 31.5 nmol/l as compared with 48.1 ± 28.6 nmol/l in men (p <10-5). Of the 8861 first measurements taken within the observation period, 4527 (51%) were vitamin D deficient with levels <50 nmol/l, including 1860 (21.0%) with levels <25 nmol/l. There was only a weak positive association of average vitamin D levels with age (p = 0.06). Women reached peak concentrations of 56.9 ± 35.4 nmol/l in the age group 90-102 years, whereas men reached peaks of 50.3 ± 31.9 nmol/l in 50-59-year-olds. Mean autumn and spring concentrations differed less (51.6 ± 29.6 vs 52.7 ± 30.7 nmol/l, respectively, p = 0.38) than mean summer and winter concentrations (57.1 ± 29.5 vs 48.0 ± 31.2 nmol/l, respectively, p 75 nmol/l, only 22.1% of measured values indicated adequate vitamin D levels. This issue should be addressed in order to improve quality of life and reduce medical costs.

State-Dependent Computation Using Coupled Recurrent Networks

Although conditional branching between possible behavioral states is a hallmark of intelligent behavior, very little is known about the neuronal mechanisms that support this processing. In a step toward solving this problem, we demonstrate by theoretical analysis and simulation how networks of richly interconnected neurons, such as those observed in the superficial layers of the neocortex, can embed reliable, robust finite state machines. We show how a multistable neuronal network containing a number of states can be created very simply by coupling two recurrent networks whose synaptic weights have been configured for soft winner-take-all (sWTA) performance. These two sWTAs have simple, homogeneous, locally recurrent connectivity except for a small fraction of recurrent cross-connections between them, which are used to embed the required states. This coupling between the maps allows the network to continue to express the current state even after the input that elicited that state iswithdrawn. In addition, a small number of transition neurons implement the necessary input-driven transitions between the embedded states. We provide simple rules to systematically design and construct neuronal state machines of this kind. The significance of our finding is that it offers a method whereby the cortex could construct networks supporting a broad range of sophisticated processing by applying only small specializations to the same generic neuronal circuit

Computation in Dynamically Bounded Asymmetric Systems

Previous explanations of computations performed by recurrent networks have focused on symmetrically connected saturating neurons and their convergence toward attractors. Here we analyze the behavior of asymmetrical connected networks of linear threshold neurons, whose positive response is unbounded. We show that, for a wide range of parameters, this asymmetry brings interesting and computationally useful dynamical properties. When driven by input, the network explores potential solutions through highly unstable ‘expansion’ dynamics. This expansion is steered and constrained by negative divergence of the dynamics, which ensures that the dimensionality of the solution space continues to reduce until an acceptable solution manifold is reached. Then the system contracts stably on this manifold towards its final solution trajectory. The unstable positive feedback and cross inhibition that underlie expansion and divergence are common motifs in molecular and neuronal networks. Therefore we propose that very simple organizational constraints that combine these motifs can lead to spontaneous computation and so to the spontaneous modification of entropy that is characteristic of living systems

Nanofibers: Friend or Foe?

Since the early 1990s nanofibers, particularly those of a carbonaceous content [1] have received heightened interest due to their advantageous physico-chemical characteristics (e.g., high strength, stiffness, semi-conductor, increased thermal conductivity and one of the highest Young’s modulus [2]).[...

Digital videodensitometric measurement of aortic regurgitation

A videodensitometric method for quantification of aortic regurgitation which requires neither measurement of cardiac output nor determination of enddiastolic and endsystolic left ventricular volumes has been developed. The injection of 20 ml of contrast medium into the left ventricle is digitally recorded at 25 images s−1 during 20 s using an equipment for digital subtraction angiography (Digitron 2, Siemens). The Digitron computes 2 ‘time dilution curves' (TDC) from the unsubtracted image sequence, for 2 regions of interest drawn around the angiographic enddiastolic and endsystolic left ventricular silhouettes. Enddiastolic and endsystolic points of the TDC are then entered into a VAX-750 computer, which calculates the ejection fraction (EF), the forward ejection fraction (FEF) and the regurgitant fraction (RGF). This is performed by a complex fitting algorithm based on a physical model of the washout process of contrast medium, which reconstructs the two best enddiastolic and endsystolic baselines in the washout parts of the two TDC. The EF, FEF and RGF obtained in 9 regurgitant and 11 nonregurgitant patients have been compared with the corresponding values EFv, FEFv and RGFv obtained by a conventional technique (Cardiogreen and biplane LV area-length volumetry). Regression analysis yielded: EF = 0.88 × EFv (regression line forced through the origin), r = 0.77, FEF = 0.76 × FEFv + 3, r = 0.96, RGF = 0.94 × RGFv + 5, r = 0.98 (v stands for volumetry

Long-term (10 years) prognostic value of a normal thallium-201 myocardial exercise scintigraphy in patients with coronary artery disease documented by angiography

In order to assess the prognostic significance of normal exercise thallium-210 myocardial scintigraphy in patients with documented coronary artery disease, we studied the incidence of cardiac death and non-fatal myocardial infarction in 69 symptomatic patients without prior Q wave myocardial infarction, who demonstrated one or more significant coronary lesions (stenosis ≤70%) on an angiogram performed within 3 months of scintigraphy (Group 1). These patients were compared to a second group of 136 patients with an abnormal exercise scintigram, defined by the presence of reversible defect(s) and angiographically proven coronary artery disease (Group 2), and to a third group of 102 patients with normal exercise scintigraphy without significant coronary lesions (stenosis ≥30%) or with normal coronary angiography (Group 3). In contrast to coronary lesions observed in Group 2, patients in Group I presented more frequently with single- vessel disease (83% vs 35%, P>0·0001) and with more distal lesions (55% vs 23%, P>0·0001). Over a mean follow-up period of 8·6 years, one fatal and eight non-fatal cases of myocardial infarction were observed in Group 1. The majority of patients in Group 1 were treated medically: only 24 (35%) underwent myocardial revascularization, usually by coronary angioplasty. There was no significant difference in the incidence of combined major cardiac events (cardiac death, non-fatal myocardial infarction) in patients with normal exercise scintigraphy, with or without documented coronary artery disease (Groups 1 and 3), while the incidence was higher in Group 2. However, while the mortality remained very low in Group 1, the incidence of non-fatal myocardial infraction was not different from that of Group 2, where most patients underwent revascularization procedures. In conclusion, patients with coronary artery disease and a normal exercise thallium-201 myocardial scintigram usually have mild coronary lesions (single-vessel disease, distal location) and good long-term prognosis, with a low incidence of cardiac deat