The connections between the frustrated chaos and the intermittency chaos in small Hopfield networks

In a previous paper we introduced the notion of frustrated chaos occurring in Hopfield networks [Neural Networks 11 (1998) 1017]. It is a dynamical regime which appears in a network when the global structure is such that local connectivity patterns responsible for stable oscillatory behaviors are intertwined, leading to mutually competing attractors and unpredictable itinerancy among brief appearance of these attractors. Frustration destabilizes the network and provokes an erratic ‘wavering’ among the orbits that characterize the same network when it is connected in a non-frustrated way. In this paper, through a detailed study of the bifurcation diagram given for some connection weights, we will show that this frustrated chaos belongs to the family of intermittency type of chaos, first described by Berge et al. [Order within chaos (1984)] and Pomeau and Manneville [Commun. Math. Phys. 74 (1980) 189]. Indeed, the transition to chaos is a critical one, and all along the bifurcation diagram, in any chaotic window, the duration of the intermittent cycles, between two chaotic bursts, grows as an invert ratio of the connection weight. Specific to this regime are the intermittent cycles easily identifiable as the non-frustrated regimes obtained by altering the values of these same connection weights. We will more specifically show that anywhere in the bifurcation diagram, a chaotic window always lies between two oscillatory regimes, and that the resulting chaos is a merging of, among others, the cycles at both ends. The strength (i.e. the duration of its oscillatory phase before the chaotic burst) of the first cycle decreases while the regime tends to stabilize into the second cycle (with the strength of this second cycle increasing) that will finally get the control. Since in our study, the bifurcation diagram concerns the same connection weights responsible for the learning mechanism of the Hopfield network, we will discuss the relations existing between bifurcation, learning and control of chaos. We will show that, in some cases, the addition of a slower Hebbian learning mechanism onto the Hopfield networks makes the resulting global dynamics to drive the network into a stable oscillatory regime, through a succession of intermittent and quasiperiodic regimes. Finally, we will present a series of possible logical steps to manually construct a frustrated network.     

A small-size neural network for computing with strange attractors

A small-size model for a chaotic neural network is proposed using strange attractors for computation. This network has a chaotic ground state and is capable of responding to external stimuli by constraining the network dynamics to specific parts of the ground state attractor. For parameter optimization, bifurcation diagrams are evaluated.     

The case for episodic memory in animals

The conscious recollection of unique personal experiences in terms of their details (what), their locale (where) and temporal occurrence (when) is known as episodic memory and is thought to require a ‘self-concept’, autonoetic awareness/conciousness, and the ability to subjectively sense time. It has long been held that episodic memory is unique to humans, because it was accepted that animals lack a ‘self-concept’, ‘autonoetic awareness’, and the ability to ‘subjectively sense time’. These assumptions are now being questioned by behavioral evidence showing that various animal species indeed show behavioral manifestations of different features of episodic memory such as, e.g. ‘metacognition’, ‘conscious recollection’ of past events, ‘temporal order memory’, ‘mental time travel’ and have the capacity to remember personal experiences in terms of what happened, where and when. The aim of this review is to provide a comprehensive overview on the current progress in attempts to model different prerequisites and features of human episodic memory in animals and to identify possible neural substrates of animal episodic memory. The literature covered includes behavioral and physiological studies performed with different animal species, such as non-human primates, rodents, dolphins and birds. The search for episodic memory in animals has forced researchers to define objective behavioral criteria by which different features of episodic memory can be operationalized experimentally and assessed in both animals and humans. This is especially important because the current definition of episodic memory in terms of mentalistic constructs such as ‘self’, ‘autonoetic awareness/consciousness’, and ‘subjectively sensed time’, not only hinders animal research on the neurobiology of episodic memory but also research with healthy human subjects as well as neuropsychiatric patients with impaired language or in children with less-developed verbal abilities.     

Somatic presentation of DSM III psychiatric disorders in primary care

This paper describes a study assessing the correlates and possible determinants of ‘somatisation’ by patients consulting their family doctor with a new illness. Operational criteria of ‘somatisation’ are given and the relationship between DSM III psychiatric disorders and physical illness are described. The epidemiological findings that are presented illustrate that ‘somatisation’ is a common phenomenon and accounts for a substantial proportion of ‘hidden psychiatric morbidity’ in primary care.     

Visual receptive fields of single cells in the pigeon's optic tectum

Three hundred and ninety-four units within the optic tectum of pigeons were studied using extracellular recording. According to their receptive field properties, they were classified in 4 major classes. (1) Concentrically organized fields (6%), composed of a center ‘on’ and an antagonistic surround ‘off’, or the reverse. The center and the surround had identical spectral sensitivities. Motion of a white or black spot across the center-surround evoked equally strong responses for all directions of movement. (2) Cells with homogeneous ‘on’ or ‘off’ fields (1.3%) respond well to flashes of light, but have no antagonistic surround. (3) Movement selective cells (72%) respond preferentially to moving stimuli, and poorly or not at all to static spots. According to the size of their receptive fields these were classified as ‘small’ (2°), ‘middle’ (5°) and ‘large field’ (31°). Cells with ‘large fields’ were always found at the deepest part of the electrode penetration (1100 μm to 1400 μm). (4) Directionally selective cells (21%) respond optimally to motion of the spot in one direction ‘preferred’ and not to movement in the opposite direction ‘null’. They were always recorded in the superficial range of penetration, above 1000 μm. Although the cells in the pigeon's optic tectum seem to be preferentially stimulated by moving objects, directional selectivity appears to be a characteristic of the superficial tectal layers. These results, together with other studies, suggest that the ‘output’ of the pigeon's tectum might carry directionally coded signals.     

Psychological assessment of women seeking treatment for premenstrual syndrome

One hundred (100) women who sought evaluation for premenstrual syndrome were administered a battery of standardized psychological tests, including a Minnesota Multiphasic Personality Inventory (MMPI), Beck Depression Inventory (BDI) and Short Marital Adjustment Scale (MAS), during the follicular phase of the menstrual cycle. A BDI was repeated in the luteal phase of the menstrual cycle. MMPI profiles were classified by code type using Lachar system as follows: ‘Normal’—36%; ‘Neurotic’—31%; ‘Characterological’—11%, ‘Psychotic’—5%, ‘Unclassified’—17%. A common feature of MMPI profiles was a low Scale 5 (Mf). BDI scores had several patterns; however, a significant group (25%) appeared to have clinically significant continuous depression regardless of superimposed premenstrual changes. About half of the women (42%) reported marital distress (MAS scores < 100) at the time of evaluation.     

Is the neuropathological 'gold standard' diagnosis dead? Implications of clinicopathological findings in an autosomal dominant neurodegenerative disorder

Genetically-derived neurodegenerative disorders offer a rare opportunity to test validity of neuropathological criteria for diagnosis. Implications regarding an autosomal dominant neurodegenerative disorder (PARK 8) in which four different neuropathological diagnoses were found at autopsy are discussed. We suggest that just as there is currently no clinical ‘gold standard’ for Parkinson's disease, there is no pathological ‘gold standard.’ We conclude that in certain circumstances genetic studies may provide definitive arbitration of validity of clinical and pathological diagnostic criteria.     

Reversible effects of hypoxia on neurons in mouse dorsal root ganglia in vitro

Mouse dorsal root ganglia (DRG) were isolated and maintained in a tissue chamber. Membrane potential of ‘A-type’ neurons was recorded with intracellular electrodes. When the supply of oxygen was reduced, cells depolarized by a few mV and then maintained a stable membrane potential or partially repolarized. During depolarization the action potential was reduced in amplitude and the hyperpolarizing afterpotential was depressed. Reoxygenation within 15–88 min was followed by a brief period of hyperpolarization and then complete recovery. In about 60% of the cells, invasion of the cell soma by impulses triggered by dorsal root (DR) stimulation failed during hypoxia while action potentials could still be evoked by stimulation of the peripheral nerve and by direct intracellular stimuli. Conduction from DR into the peripheral nerve stump was unchanged indicating that the blockade of DR-evoked impulse conduction occurred at the bifurcation of the axon. Results with paired pulse stimulation indicated that impulses passing the axon bifurcation leave a long lasting ( 25 ms) post-spike subnormal period. In DRG cells treated with tetraethylammonium (TEA) the calcium-mediated ‘shoulder’ of the action potential was curtailed during oxygen withdrawal. In contrast to CNS neurons, DRG cells did not show early hypoxic hyperpolarization, nor the delayed hypoxic spreading depression-like depolarization. The findings support the suggestion that the reversible depression of synaptic potentials in the CNS during the early phase of hypoxia is caused by a combination of conduction failure at axon branch points and curtailment of voltage calcium currents of presynaptic terminals, both effects resulting in reduced transmitter output.     

The assessment of alexithymia: A critical review of the literature and a psychometric study of the Toronto Alexithymia Scale-20

Objective: The objectives were to give an overview of studies on the validity of the Toronto Alexithymia Scale (TAS-20) and to present data regarding the validity of the TAS-20. Methods: The literature on the psychometric properties of the TAS-20 was reviewed and a study was conducted of its psychometric properties in a sample of students and a sample of psychiatric outpatients using a statistical method allowing identification of a stable factor structure. Results: The review revealed that the majority of studies on the TAS-20 were conducted with nonpatient samples. The factorial validity and reliability of the dimensions ‘identifying feelings’ (DIF) and ‘describing feelings’ (DDF) could be replicated in many of these studies. However, in practically all studies the dimension ‘externally oriented thinking’ (EOT) appears to be unreliable. In addition, the presupposed fantasy aspect of the alexithymia construct is not included in the TAS-20. Although many studies were conducted on the construct validity of the TAS-20, no studies have been published on its criterion validity. Some studies show a different factor structure to exist in patient samples. This was confirmed in our own study in which the dimensions ‘identifying feelings’ and ‘describing feelings’ collapsed into one single subscale. As in other studies, the reliability of the dimension ‘EOT’ was low. Conclusion: The TAS-20 has some important shortcomings with respect to validity and reliability. For the assessment of alexithymia in empirical research, it is recommended to use the TAS-20 in combination with other instruments. We do not recommend the TAS-20 to be used in clinical practice.     

SCIWORA in MRI era

The aim of this report is to discuss the use of the term ‘Spinal Cord Injury Without Radiographic Abnormality’ (SCIWORA) in the medical literature ever since MRI became commonly employed in the diagnosis of spinal cord injuries. Using the PubMed database and the keywords ‘SCIWORA and MRI’, we found 30 published articles in the English-language literature. Incidence, clinical and radiological data, and MRI findings were evaluated in all articles, which included one meta-analysis, two reviews, 10 case series, and 17 case reports. The incidence of SCIWORA among children was found to be between 3.3% and 32.0%. This wide range was directly related to patients’ age, authors’ specialty, and utilization of MRI. After MRI became commonly used for spinal injuries, the term has taken on an ambiguous meaning in the literature. In our opinion, if any pathology is detected on MRI with or without radiographic abnormality, the patients should not be classed, as SCIWORA and ‘real-SCIWORA’ should be determined as ‘Spinal Cord Injury Without Neuroimaging Abnormality’ in cases with normal MRI.     

Involvement of non-selective cationic channels in the generation of pacemaker depolarizations and firing behaviour in cultured frog melanotrophs

The firing patterns of cultured frog melanotrophs were studied using the patch-clamp technique. In the cell-attached mode, unitary currents were frequently observed as well as biphasic waveforms which were attributed to action potentials ‘leaking’ through the patch membrane An inwardly rectifying single-unit current was observed with pipette solutions containing either 100 mM K⁺ or 100 mM Na⁺. Under both conditions, these channels displayed an identical I/V relationship, yielding a unitary conductance of 110 pS. The channel opening time was extremely long (50–3000 ms) and single-channel currents showed typical relaxations, which triggered bursts of action currents. In the whole-cell configuration large (2–12 mV) fluctuations in the membrane voltage of current-clamped cells frequently occured. The deflections appeared to result from single-channel currents. Depolarizing ‘events’ often led to the discharge of action potentials. Taken together, our data provide evidence for the existence of high-conductance cationic channels in frog pars intermedia cells. These channels may, at least in some cases, be responsible for the generation of pacemaker depolarizations, thereby regulating firing behaviour. It is concluded, that the current traversing a single channel can seriously affect the membrane potential and excitability of frog melanotrophs.     

Fuzzy Lattice Neurocomputing (FLN) models

In this work it is shown how fuzzy lattice neurocomputing (FLN) emerges as a connectionist paradigm in the framework of fuzzy lattices (FL-framework) whose advantages include the capacity to deal rigorously with: disparate types of data such as numeric and linguistic data, intervals of values, ‘missing’ and ‘don't care’ data. A novel notation for the FL-framework is introduced here in order to simplify mathematical expressions without losing content. Two concrete FLN models are presented, namely ‘σ-FLN’ for competitive clustering, and ‘FLN with tightest fits (FLNtf)’ for supervised clustering. Learning by the σ-FLN, is rapid as it requires a single pass through the data, whereas learning by the FLNtf, is incremental, data order independent, polynomial (n³), and it guarantees maximization of the degree of inclusion of an input in a learned class as explained in the text. Convenient geometric interpretations are provided. The σ-FLN is presented here as fuzzy-ART's extension in the FL-framework such that σ-FLN widens fuzzy-ART's domain of application to (mathematical) lattices by augmenting the scope of both of fuzzy-ART's choice (Weber) and match functions, and by enhancing fuzzy-ART's complement coding technique. The FLNtf neural model is applied to four benchmark data sets of various sizes for pattern recognition and rule extraction. The benchmark data sets in question involve jointly numeric and nominal data with ‘missing’ and/or ‘don't care’ attribute values, whereas the lattices involved include the unit-hypercube, a probability space, and a Boolean algebra. The potential of the FL-framework in computing is also delineated.     

Putative neural substrate of normal and abnormal general movements

During the last decade it has become clear that the assessment of the quality of general movements (GMs) in foetus and young infant is a sensitive tool to evaluate the integrity of the young nervous system. GMs are movements in which all parts of the body participate. The hallmark of typical GMs is movement complexity and variation; in abnormal GMs movement complexity and variation is reduced or absent. Abnormal GMs may predict developmental outcome. Prediction on the basis of longitudinal series of GM assessments is best. Second best is prediction on the basis of an assessment at ‘fidgety’ GM age, i.e. at 2–4 months post-term. Definitely abnormal GMs at ‘fidgety’ age are related to cerebral palsy, mildly abnormal GMs to minor neurological dysfunction at school age. In the present paper the hypothesis is advanced that GM complexity and variation are brought about by the transiently present cortical subplate and that abnormal GMs are the result of damage or dysfunction of the subplate and its efferent motor connections in the periventricular white matter.     

Neuronotrophic factors and their antibodies: In vitro microassays for titration and screening

Using nerve growth factor (NGF), anti-NGF sera and dissociated neonatal mouse dorsal root ganglionic neurons we present a microculture assay methodology for (1) the titration of neuronotrophic factor (NTF) activity in monolayer culture, (2) the titration of NTF antibodies which ‘block’ NTF biological activity, (3) the titration of NTF antibodies that bind and remove (sequester) NTF from culture medium and (4) a large-scale, convenient, and rapid screening for NTF biological activity as well as for NTF ‘blocking’ or ‘sequestering’ antibodies. These quantitative and qualitative in vitro microimmunoassays should be applicable to any neuronotrophic factor or its antibody, even when the agent is only available in crude, unpurified form. Since the microculture systems permit the simultaneous screening of one thousand samples per day they should be useful for the detection and quantitation of monoclonal antibodies present in hybridoma-conditioned media.     

Reduction of insolubilized fibrinogen

Insolubilization of fibrinogen is achieved by covalent fixation onto cyanogen bromide activated agarose. When insolubilized fibrinogen (FG-ag) is reduced in order to separate the fibrinogen molecule into its chains, disc-electrophoretic patterns reveal that the (‘A’) -chains remain with the insoluble agarose whereas the (B) β-chains and the γ-chains appear in the supernatant. It is assumed that covalent fixation of fibrinogen to agarose almost exclusively takes place at the (‘A’) -chain and that the (‘A’) -chain is located at the surface of the fibrinogen molecule.     

A ventral approach to stereotaxy of the guinea pig brain

For skeletal muscles, a well-known match exists between the properties of motoneurones and those of their muscle fibres. Hence, the intramuscular distribution of different kinds of motoneuronal nerve endings (e.g. ‘slow’ versus ‘fast’) can be mapped by determining the distribution of the corresponding types of muscle fibre. As a background for further studies of motoneuronal plasticity, we needed precise measures of such distributions. Simple quantitative methods were developed for defining the position and extent of sub-populations of cells within a structure (e.g. the regional distribution of slow versus fast muscle fibres within a muscle cross-section): (a) The ‘mass vector method’ defined the relative position of the target cell cloud. A line was drawn between the calculated centre of mass for the target cells and that for the whole structure. The direction (a1) and length (a2) of this line gave a measure of the direction and degree of target cell eccentricity within the structure. (b) The ‘sector method’ delineated the region containing the target fibres. A circle around the centre of mass for the target fibres was subdivided into a number of equal sectors (standard setting: 20). The most remote point was found within each sector and a line joining these points defined the region of the target fibres. When applied to the ‘slow’ type I fibres of cross-sections from rat hindlimb muscles, the regional area estimates obtained by the sector method were highly correlated with, but 10% lower than those achieved by the well-established ‘convex hull’ method. Highly significant inter-muscular differences were observed for each one of the three new parameters described in this paper (a1, a2, b).     

Axonal transport and tissue contents of substance P in rats with long-term streptozotocin-diabetes. Effects of the aldose reductase inhibitor ‘statil’

This study examined the axonal transport of substance P-like immunoreactivity (SPLI) and its content in dorsal root ganglion, trigeminal ganglion, stomach and ileum of non-diabetic rats and two groups of rats with streptozotocin-induced diabetes of 9 months duration. One diabetic group received the aldose reductase inhibitor ‘Statil’ throughout the period of study. To reduce morbidity all diabetic animals were given twice-weekly injections of a long-acting insulin which restricted weight loss but did not prevent regular and severe hyperglycaemia. Axonal transport of SPLI was studied by measurement of accumulation at 12 h ligatures on the left sciatic nerve. There were no differences between the 3 groups either in the calculated anterograde and retrograde mean rates of accumulation (ranges 6.0 to 7.6 and 0.38 to 0.72 mm/h respectively) or mobile fractions of SPLI (means from 0.54 to 0.58). There were, however, marked reductions in anterograde and retrograde accumulations of SPLI in the constricted nerves of the ‘untreated’ diabetics (respectively 57 and 33% of controls;P < 0.01 for both). In the ‘Statil’-treated rats these deficits were attenuated (80 and 75% of controls). Diabetes also reduced the SPLI content of unligated sciatic nerve and trigeminal ganglion (65 and 75% of controls). ‘Statil’ prevented the deficit in the ganglion, but not in the nerve. ‘Statil’ treatment prevented themyo-inositol depletion and attenuated the sorbitol and fructose accumulation seen in the sciatic nerves of the untreated diabetic animals suggesting effective inhibition of aldose reductase in this tissue. The total SPLI content of the stomach and 1-cm segments of ileum were unaltered in the diabetic animals but due to the increased weights of these tissues the SPLI content per unit weight was reduced. These changes were unaffected by ‘Statil’.     

Static and dynamic fusimotor action on the response of spindle primary endings to sinusoidal stretches in the cat

In anaesthetized cats, the discharge of single spindle primary endings of flexor and extensor muscles was studied during sinusoidal stretches of the muscle (3–4 mm peak-to-peak, 1–5 Hz). In the response to each stretch, two main components could be distinguished; they were related respectively to the speed and to the amplitude of lengthening. By analogy with the usual definitions of the ‘dynamic index’ (d) and ‘position sensitivity’ (s) during ramp stretches of the same amplitude at a velocity of 35–60 mm/sec, a ‘sinusoidal dynamic index’ (D) and a ‘sinusoidal position sensitivity’ (S) were defined. Stimulation of dynamic fusimotor fibres increased D and d, S and s, while stimulation of static fusimotor fibres decreased D and d and had a less consistent effect on S and s. The total frequency variation during a sinusoidal stretch was always increased by a dynamic fusimotor action while it could be either decreased or increased by a static fusimotor action, depending on the stretch frequency and on the rate of fusimotor stimulation. These results were obtained in various muscles, without any significant difference related to their flexor or extensor function. It is concluded that in order to identify a fusimotor effect as static or dynamic during sinusoidal muscle stretch, it is necessary to use, as here, stretch parameters which elicit a dynamic component in the primary afferent response.