ALBERT

Notes: Abstract: This paper considers an application of decision aiding for maritime operations, viz the design of an intelligent operator aid for dynamic route planning. The limitations of some existing methods are discussed and an Al approach is proposed that combines algorithmic and heuristic processing elements within an embedded system. The aid consists of three elements: a intelligent front end, a route planner and an explanation facility.

Notes: Abstract: Recent developments in a subarea of computer science called artificial intelligence have included the creation of expert systems that are capable of solving difficult applications problems which require expert knowledge for their solution. Such expert systems have been found to be useful in a number of applications (e.g. medicine, biochemistry and mineral exploration). In this paper the author presents an expert system for solving problems concerning income and transfer tax planning for individuals In developing this system, a theoretical structure and a set of decision rules were specified and then programmed into a rule-based system that had previously been used for medical diagnosis (Mycin [1]) Once the system was developed, its problem-solving capabilities were refined and verified by a panel of tax experts using a blind verification procedure. This verification step demonstrated that an expert system could be developed in that domain.

Notes: Abstract: The purpose of this paper is to design an expert system or an intelligent procedure' that purports to screen hazard potentials of environmental chemicals on the basis of structure-activity relationships in the study of chemical carcinogenesis, particularly with respect to analysing the current state of known structural information about chemical carcinogens and predicting the possible carcinogenicity of untested chemicals An analysis of a computerised database of known carcinogens (knowledge base) is being performed using the structure-activity trees in order to test the validity of the tree as a classification scheme (inference engine) and to evaluate trends or patterns that may exist between chemical structure and specificity for target tissue, route of administration, and animal species. Practical applications of the structure-activity tree depend on its eventual validation as a predictor of carcinogenic activity.

Notes: Abstract: Activities concerning expert systems in Japan are outlined. Expert systems are receiving increasing attention in Japan, together with fifth-generation computers. Rather than describing the details of individual systems, a variety of expert systems are briefly introduced with their aims and features.

Notes: Abstract: Analysis of the job shop scheduling domain has indicated that the crux of the scheduling problem is the determination and satisfaction of a large variety of constraints. Schedules are influenced by such diverse and conflicting factors as due date requirements, cost restrictions, production levels, machine capabilities and substitutability, alternative production processes, order characteristics, resource requirements, and resource availability. This paper describes ISIS, a scheduling system capable of incorporating all relevant constraints in the construction of job shop schedules. We examine both the representation of constraints within ISIS, and the manner in which these constraints are used in conducting a constraint-directed search for an acceptable schedule. The important issues relating to the relaxation of constraints are addressed. Finally, the interactive scheduling facilities provided by ISIS are considered.

Notes: Abstract: Log interpretation science is a controversial and rapidly changing domain. Designing interpretation models is a highly experimental process which involves trials with a computer program as an integral part of the design. Therefore conventional software engineering techniques, which require a complete specification of the problem before the program is written, are often not applicable or fail to produce high quality software. The development of expert systems has provided the techniques, tools, and capabilities to let us seek alternate methods to produce log interpretation software: exploratory programming environments and automatic programming systems. An exploratory programming environment combines the power of interactive graphics and programming tools to merge the design and programming tasks into a single process where model and program develop together. An automatic programming system will embody the knowledge of the programming process and of some log interpretation heuristics to produce log processing programs from interactive specifications expressed in familiar terms. These facilities will allow log interpretation model designers, who are non-computer specialists, to produce high quality software as the end result of a model design.

Notes: Abstract It is shown that a Thue system of the formT 1 = {(w,e)} is Church-Rosser if and only if there is a Thue systemT 2 that is Church-Rosser and is equivalent toT 1.

Notes: Abstract We associate to a maximal codeX on an alphabetA a dynamical system Ω; our main result proves that the property of unique decipherability implies that the partition of Ω associated to the letters ofA is a Bernoulli partition. Surprisingly it is possible to give two very different proofs of this result: the first one uses probability measures on monoids together with methods from automata theory; the other is based on results of entropy theory.

Notes: Abstract In contrast to the case of a single dynamical system, the asymptotic stability of orbits of control systems cannot be characterized in terms of suitably defined Lyapunov functions. It is shown that the existence of Lyapunov functions corresponds to a stronger type of asymptotic stability, which is defined by introducing higher prolongations.

Notes: Abstract Several equivalence decision algorithms for classes of grammars, program schemes, transducers follow the general pattern of the Korenjak-Hopcroft algorithm for deciding the equivalence of simple deterministic grammars. An axiomatic framework is presented which points out the essence of the Korenjak-Hopcroft algorithm and applies to numerous situations.

Notes: Abstract Call a connected planar graphG legal if it has at least two nodes, no parallel edges or self-loops and at most two terminals (degree 1 nodes) and all terminals and degree 2 nodes are exterior. This class of graphs arose in connection with a two-dimensional generating system for modeling growth by binary cell division. Showing that any permitted pattern can be generated properly requires a matching or pairing lemma. The vertex set of a legal graph withn nodes can be split intop adjacent pairs ands singletons withs p, resulting in a matching which includes at least $$2\left[ {\frac{n}{3}} \right]$$ nodes. This bound is sharp in the sense that there are legal graphs for which this matching is maximum. The matching can be implemented by a linear time algorithm. A legal graph witht terminals and n≥4 nodes has a spanning tree with at most $$\left[ {\frac{{n - t}}{2}} \right] + t$$ terminals; this bound is sharp. Such a spanning tree can be constructed by an algorithm which operates in almost linear time.

Notes: Abstract The class of readout maps of the early state space literature and the class of operators which are both causal and anticausal are compared. The first class is a subset of the second and is shown by example to be a proper subset. A characterization of the smaller class in terms of causality structure is presented. We denote this characterization by the term completely memoryless.

Notes: Abstract A simple problem concerning evaluation of programs is shown to be nonelementary recursive. The problem is the following: Given an input-free programP (i.e. all variables are initially 0) without nested loops using only instructions of the formx ← 1, x ← x + y, $$x \leftarrow x\dot - y$$ ,do x... end, doesP output 0? This problem has time complexity $$2^{2^{ {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} ^2 } } $$ }cn-levels for some constantc. Other results are presented which show how the complexity of the 0-evaluation problem changes when the nonlooping instructions are varied. For example, it is shown that 0-evaluation is PSPACE-complete even for the case when the nonlooping instructions are onlyx ← x + 1,if x = 0then y ←y $$y \leftarrow y\dot - 1$$ .

Notes: Abstract The main result of this paper is a separation result: there is a positive integerk such that for all well-behaving functionst(n), there is a language accepted by a nondeterministic (multi-tape) Turing machine in timet(n) which cannot be accepting by any deterministic (multitape) Turing machine in timeO(t(n)) and simultaneously spaceo((t(n)) 1/k ). This implies, for example that for any positive integer,l,l ≠k, there is a language accepted by an l time bounded NDTM which cannot be accepted by a DTM in time and spaceO(n l ) andO((logn) l ′) respectively for anyl′. Such a result is not provable by direct diagonalization because we do not have time to “simulate and do the opposite". We devise a different method for accomplishing the result: We first use an alternating Turing machine to speed up the simulation of a time and space bounded DTM and then argue that if our separation result did not hold, every NDTM can itself be simulated faster by another NDTM producing a contradiction to the standard hierarchy results. Some other applications of this method are also presented.

Notes: Abstract In this paper we consider the problem of uniform asymptotic stabilization of neutral delay differential systems by a suitable choice of linear feedback law, where the controller is static and at timet 0 has full knowledge ofx(t 0) ∈ ℝ n as well asx(t 0 − d) for finitely many delays present in the system. Using complex analysis in several variables in a Banach algebra context we present a solution to this problem in the form of a sufficient condition for the existence of such a stabilizing feedback gain. This condition is a weak form of (algebraic) reachability together with a condition, which we call resolvability, on the solution of an associated algebraic Riccati equation. In the case of commensurable delays our results apply to neutral systems having aD-operator which is stable in the sense of Cruz and Hale. In the non-commensurate case, our results hold for systems with aD-operator satisfying a stronger condition on the spectrum of the evolution equation, which we call formal stability. A graphical criterion, in the spirit of the multi-dimensional Nyquist theory, is presented for formal stability ofD. We find these results especially interesting in light of recent work [39] which shows that, for a special class of systems, formal stability is necessary for stabilization by a feedback gain of the type considered here. This, in fact, gives a counterexample [39] to the well known condition of Pandolfi [40]. Included among our results is an extension to the neutral case of the result in [11] which states that if the pointwise Kronecker indices are constant then the system is feedback equivalent to a delay-free system. As corollaries to this result we obtain some existing results [33] on canonical forms for time-delay systems, and, in addition, exhibit a large class of systems which are resolvable.

Notes: Abstract Sufficient conditions that a two-dimensional system with output is locally observable are presented. Known results depend on time derivatives of the output and the inverse function theorem. In some cases, no information is provided by these theories, and one must study observability by other methods. We dualize the observability problem to the controllability problem, and apply the deep results of Hermes on local controllability to prove a theorem concerning local observability.

Notes: Abstract A wordw is called recurrent with respect to a substitution if any descendant of it can regeneratew itself by iterations of the substitution. The set of recurrent words with respect to a regular (resp. context free) substitution is a regular (resp. context free) language. The set of recurrent words which are the descendants of a single fixed word with respect to a context free substitution is context free.

Notes: Abstract It is known that nondeterministic polynomial time truth-table reducibility is exactly the same as nondeterministic polynomial time Turing reducibility. Here we study the standard nondeterministic reducibilities (conjunctive, bounded truth-table, bounded positive truth-table, and many-one) and show that each is a restriction of nondeterministic polynomial time Turing reducibility corresponding to acceptance modulo a set of “oracle conditions.” Then we show that the reduction classes of these reducibilities are classes of formal languages and as such have language theoretic characterization theorems. The same program is carried out for polynomial space.

Notes: Abstract This paper deals with algebraic power series over a commutative semiringA. A characteristization result states that a power series is algebraic if and only if it is the behavior of a proper pushdown automaton. To achieve this result some topological concepts are needed to be able to solve linear equations over semirings.

Notes: Abstract In this paper a question of the controllability of nonlinear systems is considered. On the basis of theorems due to Graves, a new sufficient condition for local controllability is established.

Notes: Abstract Crossed product algebras are proposed as a framework for the study of input-output properties of linear time-varying systems. It is shown that internally stable systems with bounded continuous coefficients have transfer operators in a crossed product and conversely, that the set of all such transfer operators is dense in a crossed product. It is also shown that crossed product algebras admit causal additive decompositions, and allow a generalized frequency-domain representation.

Notes: Abstract A new technique based on Kneser's theorem is introduced, to extend the topological method of Ważewski for Caratheodory systems. In this line an existence theorem for a general boundary value problem is obtained as an application, as well as some asymptotic properties for semi-linear systems.

Notes: Abstract In this paper we give necessary and sufficient conditions for a stationary finite Volterra series to have a linear (in the controls) analytic realization, which at the same time has a Hamiltonian structure. The result generalizes that for linear systems, where the condition is that the impulse response should be an odd function, and is expressed as a particular symmetry condition on the Volterra kernals. The relation between this problem and that of the inverse problem in Newtonian mechanics is explored. The finiteness of the Volterra series implies a nilpotence condition on a certain Lie algebra defined by the realization. The additional requirement that the system be Hamiltonian adds further structure to the classical representation of a nilpotent Lie algebra by lower triangular matrices.

Notes: Abstract It is shown that for a nonlinear regulator to be structurally stable in its response to step reference and disturbance signals, it is both necessary and sufficient for the controller to be of feedback type and to incorporate integrating action in each error channel. These results constitute an extension to nonlinear systems of the well-known method of “integral control” used in the design of linear regulators; and as such they provide an additional instance of the Internal Model Principle of control theory.

Notes: Abstract This is the first of two papers concerned with the formulation of a continuous-time quantum-mechanical filter. Efforts focus on a quantum system with Hamiltonian of the formH 0+u(t)H 1, whereH 0 is the Hamiltonian of the undisturbed system,H 1 is a system observable which couples to an external classical field, andu(t) represents the time-varying signal impressed by this field. An important problem is to determine when and how the signalu(t) can be extracted from the time-development of the measured value of a suitable system observableC (invertibility problem). There exist certain quasiclassical observables such that the expected value and the measured value can be made to coincide. These are called quantum nondemolition observables. The invertibility problem is posed and solved for such observables. Since the physical quantum-mechanical system must be modelled as aninfinite-dimensional bilinear system, the domain issue for the operatorsH 0,H 1, andC becomes nontrivial. This technical matter is dealt with by invoking the concept of an analytic domain. An additional complication is that the output observableC is in general time-dependent.

Notes: Abstract Nondeterministic one-wayk-head writing finite automata are investigated. It is shown that 3-head automata with one read-write head followed by two read-only heads are as powerful as any multihead automaton. Furthermore, a new way to detect a coincidence of heads is introduced, which has as a consequence that it makes no difference, whether the heads make stationary moves ore-moves.

Notes: Abstract This paper studies the real-time behavior of constant linear systems. A function space Λ is introduced to give a precise language to discuss the working mode of systems. It is shown that a realization of a constant linear input/output map produces the desired outputs during the application of inputs. A differential equation description is derived for those systems whose weighting patterns are sufficiently smooth. The notion of topological observability in bounded time yields a necessary and sufficient condition under which the canonical realization of a constant linear input/output map has a Banach state space.

Notes: Abstract A random access machine model that has capabilities for parallel processing and string manipulation is introduced. It is shown that NP is equal to the class of sets accepted by this model in nondeterministic timeO(logn), that PSPACE is equal to the class of sets accepted by this model in deterministic polynomial time and thatP is equal to the class of sets accepted by a restricted version of this model inO(logn) space. These results generalize to arbitrary time and storage bounds.

Notes: Abstract New results concerning the space complexity of languages accepted by stack automata, alternating stack automata, and alternating pushdown automata are derived. Some of the results generalize previously known results.

Notes: Abstract Directed acyclic graphs (dags) model derivations of phrasestructure grammars analogously to the way that trees model derivations of context-free grammars. In this paper we introduce translations of such dags which naturally extend the bottom-up tree translations. Composition results of these dag-to-tree transformations are studied. It is shown that every “recursively enumerable tree language” can be obtained from a recognizable dag language by such a transduction. Tree languages obtained from some subsets of recognizable dag languages by these transductions are investigated.

Notes: Abstract A minimum algebraic structure needed in Scott-Strachey style denotational semantics for parallel programs is developed. Some elementary algebra shows that nondeterministic semantics is inherently and uniquely present. Conversely, any simple nondeterministic semantics provides uniquely a semantics for a minimal parallel computation capability.

Notes: Abstract The problem of finding periodic solutions of the matrix Riccati equations of linear control theory is interpreted geometrically as a problem of finding periodic orbits of certain one-parameter transformation groups on Grassmann manifolds. For certain control problems the vector fields which generate these groups can be written as a sum of two commuting vector fields, one a gradient vector field, the other a Killing vector field, i.e., an infinitesimal isometry of a metric on the Grassman manifold. For such vector fields, the methods of Morse theory can be adapted to study the periodic orbits. The topological data that is needed to count periodic orbits, i.e., the Poincare polynomial of certain submanifolds of the Grassmann manifold, can be derived from results proved by A. Borel.

Notes: Abstract The main result of the paper can be viewed both as a generalization of a classical results concerning colorings of graphs, as well as a very useful over-all theorem from which various specific results concerning grammar and language families can be deduced. Essentially our main result says that, when considering infinitary families obtainable by inverse morphisms, it suffices to consider their finitary parts. Various applications are given, in particular, to grammar forms and context-free languages over infinite alphabets.

Notes: Abstract Standard and nonstandard models of Propositional Dynamic Logic differ in their interpretation of loops. In Standard models, a loop is interpreted as the Kleene closure of the interpretation of its loop body; in nonstandard (Loop Invariant) models, a loop is interpreted as a program which preserves invariant assertions over the loop body. In this paper we show that both interpretations are adequate to represent loops in PDL. We demonstrate this in two ways: First we note that Standard and Loop Invariant models are distinct but not distinguishable within PDL. Second, we show that the class of Loop Invariant models is complete with respect to the Segerberg axiomatization of PDL. Since completeness of the class of Loop Invariant models implies completeness of the class of Standard models, Standard models are also complete with respect to this axiomatization.

Notes: Abstract Many computer algorithms have embedded in them a subalgorithm called a priority queue which produces on demand an element of extreme priority among elements in the queue. Queues on unrestricted priority domains have a running time of Θ(nlogn) for sequences ofn queue operations. We describe a simple priority queue over the priority domain {1,⋯,N} in which initialization, insertion, and deletion takeO(loglogD) time, whereD is the difference between the next lowest and next highest priority elements in the queue. In the case of initialization,D=Θ(N). Finding a least element, greatest element, and the neighbor in priority order of some specified element take constant time. We also consider dynamic space allocation for the data structures used. Space can be allocated in blocks of size Θ(N 1/p ), for small integerp.

Notes: Abstract It is shown that there is a length-preserving relation that is NP-complete such that the transitive closure of the relation is PSPACE-complete.

Notes: Abstract The Theory of equivalence of exterior differential systems is applied to study canonical forms under feedback for nonlinear systems in differential equation, state-space forms.

Notes: Abstract Extensive research in nonlinear system theory in recent years has shown that a number of system theoretic questions are closely related to the behaviour of the (controllability) orbits of the system. Thus orbit minimality, namely the property of the system having its state space identical to one orbit, arises naturally when dealing with controllability questions. This paper is concerned with the more general case where orbit minimality is not available, and attempts to explore various ways the orbits are patched together on the state space. Concepts like stability, attraction and asymptotic stability are defined and studied with the aid of certain sets naturally associated with the system like the limit set and the prolongational set. Since the related questions are topological in nature, the problems are set up using only the topological dynamics of the system.

Notes: Abstract A class of Σautomata is considered as a partially ordered set by homomorphism relation. We show first that some classes of automata. e.g., quasiperfect automata, perfect automata and strongly cofinal automata, are lattices, and other classes, e.g., strongly connected automata, cyclic automata and cofinal automata, are not lattices. At the same time, we give algorithms for computing the least upper bound and the greatest lower bound of given two elements in each class which forms a lattice.

Notes: Abstract It is known that ifA is a normal reductive linear operator on a Hilbert space and the linear system {A, B} is controllable, then there exists a vectorb in the range ofB such that {A, B} is controllable. It is shown that this result does not hold for an arbitrary normal operatorA.

Notes: Abstract The classical study of factorization of operators along a linearly ordered chain of orthoprojectors is extended to the more general context of partially ordered chains. With this extension the factorization theory becomes relevant to stochastic approximation, filtering and control of multidimensional systems.

Notes: Abstract A transformation is presented which converts any pushdown automaton (PDA)M 0 withn 0 states andp 0 stack symbols into an equivalent PDAM withn states and ⌈n 0 /n⌉2 p 0 stack symbols into an equivalent ofn, 1⩽n〈n 0. This transformation preserves realtime behavior but not derterminism. The transformation is proved to be the best possible one in the following sense: for each choice of the parametersn 0 + 1 stack symbols for any desired value realtime PDAM 0 such that any equivalent PDAM (whether realtime or not) havingn states must have at least ⌈(n 0 /n)2 p0⌉ stack symbols. Furthermore, the loss of deterministic behavior cannot be avoided, since for each choice ofn 0 andp 0, there is a deterministic PDAM 0 such that no equivalent PDAM with fewer states can be deterministic.

Notes: Abstract In this note we propose VLSI layouts for the cube-connectedcycles (CCC) in a three-dimensional medium. The first type of layout is for the all-active-volume mode, where computing modules are placed anywhere within the solid chip; the second type is for the one-active-layer mode, where computing modules are placed on an external face of the solid chip. In both cases we present volume × time optimal realizations. In addition, by opening the cycles of the CCC, one obtains the well-known FFT network. Both realizations use minimum volume; an all-active-volume realization with the same volume performance was earlier proposed by Rosenberg, while the present one-active-layer realization is the only optimal one that is known.

Notes: Abstract A linear recursive procedure is one each of whose executions activates at most one invocation of itself. When linear recursion cannot be replaced by iteration, it is usually implemented with a stack of size proportional to the depth of recursion. In this paper we analyze implementations of linear recursion which permit large reductions in storage space at the expense of a small increase in computation time. For example, if the depth of recursion isn, storage space can be reduced to $$\sqrt n $$ at the cost of a constant factor increase in running time. The problem is treated by abstracting any implementation of linear recursion as the pebbling of a simple graph, and for this abstraction we exhibit the optimal space-time tradeoffs.

Notes: Abstract We present a formal model for stratificational linguistics, and examine its properties such as generative power, complexity of recognition and descriptional complexity. By relating stratificational grammars to control grammars and Szilard languages, we obtain a table of language families generated by stratificational grammars under several restrictions of linguistic interest. In the process, we show that context-sensitive control grammars with leftmost derivations are no more powerful than context-free ones, and, using this, resolve two open problems of Ginsburg and Spanier. Throughout the paper, formal results are interpreted in terms of their significance for linguistic theory and practice.

Notes: Abstract We look at some decision problems concerning nondeterministic finite transducers. The problems concern finite-valuedness, finite ambiguity, equivalence, etc. For a fixedk, we give a polynomial time algorithm for deciding whether or not a transducer isk-valued. The result holds when “valued” is replaced by “ambiguous”. In fact, the following problems are decidable: 1) Given a transducer, is itk-ambiguous for somek? 2) Given two finitely ambiguous transducers, are they equivalent? For unambiguous transducers, equivalence is decidable in polynomial time.

Notes: Abstract Given a pair(X 0,D), whereX 0 is a vector field andD is a family of vector fields on a manifoldM, we can define a system affine in the control, i.e., the new family of all the vector fields of the formX 0 +uX, whereX ∈D andu is a real parameter. Such a system will be called globally controllable if each state is reachable from each other, whenever unbounded values foru are allowed. It is proved that a system affine in the control is globally controllable if and only if in any set of a suitable partition ofM there exist points locally controllable with bounded values foru. Further, it is proved that, under more restrictive assumptions, global controllability implies the existence of points locally controllable at a fixed time with bounded values foru. In the case of simply connected manifolds, a full equivalence among all the forms of controllability considered here is obtained.

Notes: Abstract A mathematical model for visual-vestibular interaction during body rotation in an illuminated visual surround is obtained by combining a previous model of the optokinetic reflex (OKR) with a simplified model of the vestibulo-ocular reflex (VOR). OKR is activated by the slip of the image of the external world on the retina, and represents a negative feedback loop around VOR. For large retinal slip velocities OKR behaves as a basically non-linear system. The validity of the model is proved via computer simulation by comparing predicted responses with the experimental results obtained in man by Koenig et al. (1978) in different situations of visual-vestibular interaction.

Notes: Abstract As in the preceding paper stick insects walk on a treadwheel and different legs are put on platforms fixed relative to the insect's body. The movement of the walking legs is recorded in addition to the force oscillations of the standing legs. The coordination between the different legs depends upon the number and arrangement of the walking legs and the legs standing on platforms. In most experimental situations one finds a coordination which is different from that of a normal walking animal.

Notes: Abstract In cortical areas direction-specific receptive fields occur systematically. Direction specifity is based on unsymmetric coupling of neurons. Such a coupling allows an exact localization of moved stimuli. For this task, the asymmetry in the time domain is compensated for by a spatial asymmetry.

Notes: Abstract A two-layer random neural net with inhibitory connections composing of threshold elements has been regarded as a model of the cerebellar cortex. Many properties of pattern separation with the model have been disclosed through consideration on the degree of pattern separation. However, we have not shown yet that the degree of pattern separation is given by some different functions which are decided by the relation between the firing rates of input patterns. The present study is intended to reveal that the functions of the degree of pattern separation are synthesized with some different partial functions, and they are differently given on the relation between the firing rates of input patterns. Simultaneously, it is proved that the number of the functions also depend on the number of connections between two layers in the model. We also disclose the properties of the degree of pattern separation, and give some suggestions on the sizes of the firing rates of mossy fibers and granule cells under the knowledge about them.

Notes: Abstract Anatomical and physiological data from lower primates, and psychophysical data from humans, is used to construct a quantitative model of the local and global map structure (functional architecture) of human striate cortex. A series of successful estimates deriving from this model are reviewed, including a prediction for the width of human ocular dominance columns, which has recently been verified. A variety of perceptual phenomena are then discussed, from the point of view of cortical, rather than retinal, topography. It is suggested that the striate cortex may be viewed as a “cyclopean retina” whose non-linear map structure, summarized in terms of a concatenated complex logarithmic pattern, suggests insights into the nature of the Mackay complimentary image, the Frazer spiral, fortification illusions, and the relationship of the second order statistics of a visual stimulus to pre-attentive (textural) segmentation. Finally, the nature of neuronal representation is considered in the context of recent models of perceptual and cognitive function. It is suggested that anatomical re-mapping at successive stages of the CNS may provide a conceptual alternative to conventional single cell and connectionist models, and offers a viable approach towards a “field” theory of vision.

Notes: Abstract The statistical properties of background spike train activity recorded from a molluscan neurone are used to identify lengths of discharge which are produced by endogeneous pacemaker mechanisms. Such pacemaker discharge has an infinitely divisible interspike interval probability density function.

Notes: Abstract Electric current was injected into a rabbit's eye with white-noise modulations of the current amplitude. A variable D.C. bias was added to the whitenoise stimulus to study the effects of stimulus bias. For each bias level, the ERG response to the electrical stimulus was cross-correlated with the random stimulus to estimate first-and second-order Wiener kernels. The kernels indicated both linear and nonlinear characteristics of the Electrical ERG. The results for the zero biased stimulus are particularly relevant for clinical testing because the root mean square (RMS) level of the stimulus was less than 0.2 mA.

Notes: Abstract In order to investigate the spectro-temporal selectivity of single auditory neurons in the auditory midbrain of the grassfrog under different stimulus conditions a stimulus ensemble consisting of tonal and natural stimuli has been constructed. The selection of characteristics of the tonal stimuli was inspired by the general properties of vocalizations of the male grassfrog. The natural stimuli contained a variety of vocalizations of various anuran species and other sounds, taken from the natural environment of the grassfrog (i.e. its biotope). The main point of interest in the present paper is the spectro-temporal characterization of acoustic stimuli. For narrowband signals a parametric description in terms of instantaneous amplitude and instantaneous frequency appears to be attractive. A more general approach, also covering wideband signals, is a description by means of the dynamic power spectrum. Both types of analysis are described. Mathematically they can be based on the theory of analytic signals. The basic principles of this theory are summarized.

Notes: Abstract Specific changes occur in the cells of the upper layers of the cat's superior colliculus when a two dimensional noise (background) is superimposed onto a deterministic signal (spot of light). Some of the measurements can be interpreted as meaning that some cells only react to certain relative movements of object (spot) and background (noise). The movement of the visual background is interpreted as environmental movement occurring due to the animal's own movement. The results of the measurements provide all the necessary presuppositions for a distinction between the animal's own velocity and that of the object (Part I). The experimental results can be interpreted with a model. The essential factor for the interpretation is the direction specific behavior of the cells which is bound up with an asymmetrical spatial coupling of the neurons with each other. The decisive advantage of asymmetrical systems for the pattern recognition of moving objects is that they can work without distortion and spatial displacement over large ranges of velocity (Part II).

Notes: Abstract The extensor tibiae muscle of Carausius is innervated by a fast (FETi), a slow (SETi) and a common inhibitor neuron (CI). Situation and shape of FETi and SETi in the ganglion correspond to Schistocerca mesothorax. In Extatosoma, a phasmid with visible cells in the ganglion, FETi does not project onto SETi. In Carausius the axons of all three neurons leave the ganglion within the same nerve (nl 3 ). FETi supplies the whole muscle except some fibres at the most distal end. SETi and CI project onto the most proximal end and the distal third.-The muscle can be divided into two parts: the proximal half being nearly exclusively FETi-innervated and the distal third being mostly triple innervated. From such preparations the time-course of the forces produced after stimulating the femoral chordotonal organ could be estimated for FETi and SETi separately. These time-courses do not correspond to those of the fast and slow channel of the previous simulation of the control-loop.-The nerve supplying the muscle is a mixed nerve, the largest sensory axons being as thick as the smaller motor axons. The conduction velocity of both types of neurons lies within the same range. The conduction time only creates a delay time of 2–5 ms in the femur-tibia-control system.

Notes: Abstract A general description of a class of schemes for pattern vision is outlined in which the visual system is assumed to form a discrete internal representation of the stimulus. These representations are discrete in that they are considered to comprise finite combinations of “components” which are selected from a fixed and finite repertoire, and which designate certain simple pattern properties or features. In the proposed description it is supposed that the construction of an internal representation is a probabilistic process. A relationship is then formulated associating the probability density functions governing this construction and performance in visually discriminating patterns when differences in pattern shape are small. Some questions related to the application of this relationship to the experimental investigation of discrete internal representations are briefly discussed.

Notes: Abstract In an associative memory with randomly distributed storage elements at least 0.05 bit per storage element can be stored.

Notes: Abstract The optomotor yaw torque response of fixed flying female houseflies, Musca domestica to three different types of visual stimuli is analyzed. In contrast to most previous investigations, the stimuli were displayed for short time intervals only in order to approximate transiently occuring visual stimuli, which mainly govern the torque generation during free flight. Monocular stimulation with a periodic pattern moving in different positions in the equatorial plane of the compound eyes reveals that (1) flight torque responses are mainly induced by progressive (front to back) motion; regressively moving stimuli are significantly less effective. (2) the strength of the response to motion in the horizontal direction depends on the position of the stimulus and (3) vertical motions do not elicit flight torque responses. Correspondingly the response to a single vertical black stripe moving clockwise in a cylindrical panorama centered around the fly is small if the stripe is in the visual field of the left eye but becomes large and strongly depending on position if the stripe enters the visual field of the right eye. The response to counterclockwise motion of the stripe is small if the stripe is in the visual field of the right eye but becomes large and strongly depending on position if the stripe enters the visual field of the left eye. Torque responses to two adjacent stripes whose intensities are modulated in time with a rectangular function can be elicited if apparent motion is generated by means of a phase difference between the intensity modulations of the two stripes. Apparent progressive motion elicits strong torque responses, apparent regressive motion is less effective. Synchronous flicker of both stripes does not elicit torque responses. The extraction of positional information from the incoming visual signals has been considered to play an important role in the orientation behaviour, and especially in the tracking behaviour of flies. The results of the experiments indicate, that under transient stimulation the evaluation of positional information is in general not mediated by formerly postulated flicker detectors but is bound to the computation of motion. These findings are implemented in a model, describing the free flight tracking behaviour of a female fly on the horizontal plane. It is shown that tracking can be achieved by a mechanism whose sensitivity to motion is parametrized in the stimulus position as outlined above. The results of the behavioural experiments are interpreted in view of electrophysiological and anatomical data on giant interneurons in the third optic ganglion of the fly.

Notes: Abstract The shape of the spatial response of the retina on a small light stimulus as found by Rodieck (1965) for the cat, and proposed for the human retina among others by Korn and von Seelen (1972), resembles a Mexican hat known as a sombrero. A model presented by Röhler (1976), using a continuous medium as a description of the retina, can lead to such a “Mexican hat” response function for a specific choice of parameters. The spatial Fourier transform of this response function has a general appearance that corresponds to that calculated for stationary signals. However, such an analysis of the model for stationary signals is incomplete. Inspection of the time-dependent equations shows that it is unstable precisely for those parameter values that give the stationary response function its desired shape. Such stationary situations cannot be physically realized since the model is unstable.

Notes: Abstract Previous results on the perception of motion indicate that perceived motion paths cannot be explained solely in terms of simple feature-specific analyzers. This is particularly true of apparent (phi) motion. In this paper we develop a dynamic network, with simple filtering and summation properties, which can predict the geometric paths of apparent motion in various spatio-temporal configurations. The network assumptions predict a non-Euclidean metric for the visual space-time of motion perception and we consider the implications of such distortions for various visual displays, including illusions.

Notes: Abstract In this paper we consider some spatial and temporal properties of visual textures which either inhibit or enhance their discrimination. From exposure time and texture mixing studies two findings emerge. First, it is clear that the spatial summation process involved in texture discrimination has a time course consistent with counting models for decision making. Secondly, the receptive field structures of salient texture features, in particular-orientation, seem to involve simple excitatory center and inhibitory surround mechanisms.

Notes: Abstract In this paper we propose a model of visual perception in which a positive feedback mechanism can reproduce the pattern stimulus on a neurons screen. The pattern stimulus reproduction is based on informations coming from the spatial derivatives of visual pattern. This information together with the response of the feature extractors provides to the reproduction of the visual pattern as neuron screen electric activity. We simulate several input patterns and prove that the model reproduces the percept.

Notes: Abstract In a series of experiments we have investigated the perception of Moiré patterns as a function of spatial density, rotation and temporal display parameters. Results indicate that the local correlation extraction process involved in the perception of these patterns is not feature specific, yet is driven by excitatory (correlated) and inhibitory (uncorrelated) information under a form of spatial summation. These results are comparable with recent results on texture discrimination where texture interpoint distance distributions (dipole statistics) have also been discovered to have excitatory and inhibitory components.

Notes: Abstract The stick insect Carausius morosus maintains the distance between the substrate and its body. The underlying feed-back servo mechanism has been analyzed in intact animals under open loop conditions by changing the body-substrate distance in a sinusoidal fashion. The center position z c has been varied as parameter and the force the animal elicits along its high axis has been measured. The response amplitude A is a nonlinear function of z c. This nonlinear relationship between A and z c is most probably caused by the relationship between the torque excerted at the joints and the measured force. The responses to sinusoidal stimulation reveal band-pass character of the feed-back loop. Due to the nonlinearity of the system the average value of the response to sinusoidal disturbances depends upon the frequency of modulation. The change of the average value with the frequency of modulation is partially due to cocontraction of the extensor and flexor muscles.

Notes: Abstract The characteristics of the response to stretch of a muscle fibre are investigated using a validated model of skeletal muscle. It is found that the model correctly predicts all the peculiar features of the stretch response: the initial rapid force rise; the subsequent slower rise; the slow decay of the force upon termination of the elongation; and the dependence of these phenomena upon stretching velocity and muscle length. The hypothesis explaining these phenomena is discussed in detail.

Notes: Abstract The threshold for rotation about the yaw axis was determined for constant acceleration stimuli as a function of their duration in the range from 3 to 25 s. From the torsion-swing model the following theoretical equation can be derived: 1 $$a_{{\text{thr}}} = {C \mathord{\left/ {\vphantom {C {\left[ {1 - \exp \left( { - {{t_s } \mathord{\left/ {\vphantom {{t_s } {\tau _1 }}} \right. \kern-\nulldelimiterspace} {\tau _1 }}} \right)} \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {1 - \exp \left( { - {{t_s } \mathord{\left/ {\vphantom {{t_s } {\tau _1 }}} \right. \kern-\nulldelimiterspace} {\tau _1 }}} \right)} \right]}}$$ , where a thr=acceleration amplitude at threshold, t s =duration of the acceleration, τ1=time constant, C=threshold for very long stimuli. According to this formula the Mulder product (i.e. the product of the threshold acceleration amplitude and the duration of the stimulus) is constant for durations up to 0.3 τ1. The best fit of this theoretical function to the somatosensory data is found for τ1=14.5 s, and C=0.220/s 2. The time within the Mulder product is constant (about 5s) is doubtless due to the mechanics of the semicircular canals. For the oculogyral data a lower value of τ1 is found. We do not have any explanation for this lower value.

Notes: Abstract An associative memory system is presented which does not require a “teacher” to provide the desired associations. For each input key it conducts a search for the output pattern which optimizes an external payoff or reinforcement signal. The associative search network (ASN) combines pattern recognition and function optimization capabilities in a simple and effective way. We define the associative search problem, discuss conditions under which the associative search network is capable of solving it, and present results from computer simulations. The synthesis of sensory-motor control surfaces is discussed as an example of the associative search problem.

Notes: Abstract Proceeding from previous studies on cells in area 18, neurophysiological experiments were carried out using combinations of deterministic and statistical stimuli. The evaluation of the results on the space, time and amplitude characteristics of the cells show that for nearly all cells in this area, pattern distorition and shift due to motion are eliminated by spatial asymmetry of the coupling and specific combinations of on-off systems. So, the extraction of features despite pattern movement is possible in area 18. The features are extracted in the low spatial frequency range.

Notes: Abstract In this account fixation and the torque response to a transient moving stripe of flying femaleMusca domestica with monocular sight was tested. This was made by either covering one eye of the fly with opaque paint or by placing a screen in front of one side of the fly's visual field. A stripe was moved with constant speed once around the fly clockwise and, after a pause, counterclockwise. The torque response of the fly was measured during the motion of the stripe and shortly beforehand. The results demonstrated that the monocular torque response to progressive (from front to back) motion and regressive (from back to front) motion essentially do not differ from the binocular response, except for the region of bionocular overlap. The beginning of the response of a fly with monocular vision to progressive motion is 11 ° (on average) before the direction of flight (0°), which means that the maximal functional binocular overlap of femaleMusca domestica is stretched at least 15° to each side (3.1). In addition, the shape of the monocular torque response to a progressively moving stripe was determined (see Figs. 5Ia and 5IIb). In other experiments similar to the ones described above, a screen was placed on one side of the fly's visual field or then on the other, (instead of covering one eye) and the torque response to the moving stripe was measured. Using this method, a delay response of 90 ms was measured. We suggest that this is the delay of the direction-sensitive component of the torque response, and therefore an additional argument for the existence of two components for the optomotor torque response. Flies with a covered eye or with a screen placed in front of one side of the visual field were able to fixate a single narrow long black stripe. This, however, was possible only when an additional offset signal was added, in order to give the stripe a constant velocity component. As a result there was a shift of the fixation towards the unobscured eye. The shift was small for the monocular flies, and it was larger (13° on average) when the screen was on one side of the fly. A new type of laser torquethrust transducer was developed and is described.

Notes: Abstract Drosophila melanogaster is able to detect a small visual object hidden in a background of identical texture, as long as there is relative motion between their retinal images. The properties of figure-ground discrimination in the walking fly are studied under experimental conditions where the positions of figure and ground oscillate sinusoidally with similar frequency and similar amplitude but with different phase. The following points have been established. (a) The average turning reaction of the stationarily walkingDrosophila depends on phase; contrary to results obtained with the flyingMusca (Reichardt and Poggio, 1979), antiphasic oscillation of figure and ground does not suppress the attrativeness of the figure. (b) A translatory response has been found which also depends on the phase difference of the oscillatory movements of figure and ground. (c) The time course of the responses and its intra- and inter-individual variability do not seem to fit into a rigid model of figure-ground discrimination.

Notes: Abstract From recent theoretical work (Poggio and Reichardt, 1981), high frequency oscillations are expected in the angular trajectory of houseflies tracking a moving target if the target's retinal position controls the flight torque by means of a stronger optomotor response to progressive than to regressive motion. Experiments designed to test this conjecture have shown that (a) asymptotic non-decaying oscillations are found in the torque of female houseflies tracking targets moving at constant angular velocity; (b) the magnitude of the oscillations grows monotonically with mean retinal excentricity of the target; (c) the period of the oscillation is around 180–200 ms. The experimental findings are consistent with the hypothesis that a “progressive-regressive mechanism” plays a significant role in the tracking behaviour of female houseflies. From this phenomenological point of view a flicker mechanism that is active only for nonzero motion is equivalent to a progressive-regressive system. The relatively long period of the oscillation requires more complex reaction dynamics than a pure single dead-time delay. As a specific example we show that a model where the reaction to progressive motion is “sticky”, holding for a longish time after the ending of the stimulus, is consistent with the experimental data.

Notes: Abstract 1. The receptive field properties of visual neurons in the retina of the catfish are studied by a white noise spatio-temporal stimulus. The spatial and temporal inputs of the stimulus are independent and lead to complete linear characterizations and local nonlinear characterizations of the neural response. 2. Horizontal cells, bipolar cells, and sustained or Type N amacrine cells all yield spatially coherent linear correlations. The horizontal cells have the shortest latency by these methods and exhibit a late depolarizing component that is wider in spatial extent than the initial hyperpolarizing component. Depolarizing Type N neurons have center-hyperpolarizing local nonlinearity. 3. Transient or Type C amacrine cells do not correlate well with the intensity of the stimulus, even though the Fast variety responds vigorously to the stimulus. 4. Ganglion cells are classified into Excitatory, Inhibitory and Biphasic classes based upon their linear correlations. Some ganglions exhibit responses dependent upon the orientation of stimulus. Although linear correlation of the Excitatory class is similar to that of the depolarizing Type N cell, the locally nonlinear character of these cell types is distinct. The receptive field of the Inhibitory ganglion cells has strong locally excitatory nonlinearity.

Notes: Abstract This paper forms a preface and introduction to a new method for the estimation of evoked potentials: a posteriori time-varying filtering. A simple evoked potential model, consisting of a transient signal and additive noise, is discussed and the underlying assumptions explicitly formulated. Assuming this model, the problem of estimating the signal from an ensemble is considered from the statistical and communication engineering point of view, along with a brief survey of the pertinent literature. It is explained why ensemble averaging, in general, does not provide the best estimate in the mean-square error sense. After a summary of the controversial aspects of timeinvariant “a posteriori ‘Wiener’ filtering”, it is indicated how that method can be generalized to a time-varying counterpart, which is able to handle the essentially transient character of evoked potential waveforms. Finally, the new method is presented on a conceptual level and its application illustrated by examples.

Notes: Abstract As the maximal K+-conductance (or K+-channel density) of the Hodgkin-Huxley equations is reduced, the stable resting membrane potential bifurcates at a subcritical Hopf bifurcation into small amplitude unstable oscillations. These small amplitude solutions jump to large amplitude periodic solutions that correspond to a repetitive discharge of action potentials. Thus the specific channel density can act as a bifurcation parameter, and can control the excitability and autorhythmicity of excitable membranes.

Notes: Abstract In addition to the asymmetry of the spatial coupling and of the specific temporal combination of excitation and inhibition, the non-linearity is very pronounced in area 18. Taking the sequence of a linear operation and a stationary nonlinear characteristic as a model, the experimental findings can be systematized and a cell classification specified which departs from the customary ones. The hypercomplex cell system probably originates in recurrent inhibition and leads to differentiation of the patterns along their contour line. Problems of cell classification and of the type of parallelism in the visual cortex are discussed.

Notes: Abstract Head movements of different species of walking beetles elicited by rotating stripe patterns have been investigated. They are of the usual type in contrast to an “inverted nystagmus” reported forTenebrio molitor in similar experimental situations. Reexamination of theTenebrio records revealed that the sign of the stimulus was interchanged by a mistake while plotting the results. Thus, the head nystagmus inTenebrio is also of the usual type, consisting of a smooth pursuit head movement followed by a faster returning phase.

Notes: Abstract A sixth order nonlinear model for horizontal head rotations in humans is analyzed using an extended parameter sensitivity analysis and a global optimization algorithm. The sensitivity analysis is used in both the direct sense, as a model fitting tool, and in the indirect sense, as a guide to experimental design. Resolution is defined in terms of the sensitivity table, and is used to interpret the sensitivity results. Using sensitivity analyses, the head and eye movement systems are compared and contrasted. Controller signal parameters are the most influential. Their variations and effects on head movement trajectories and accelerations are investigated, and the conclusions are compared with clinical neurological findings. The global optimization algorithm, in addition to automating the fitting of various types of data, is combined with time optimality theory to give theoretical time-optimal inputs to the model.

Notes: Abstract It is known (e.g., Perkel et al., 1964) that when a pacemaker neuron elicits IPSP's in another, there are domains called “paradoxical segments” where in the steady-state i) faster inhibitory discharges determine faster inhibited ones, and ii) pre- and postsynaptic spikes are “locked” in an invariant forward-and-backward positioning in time, spikes alternating in the ratios 1:1 (1 pere for 1 postsynaptic), 1:2, 2:1..., that are also the slopes of the synaptic rate-transformation. The present project examined the matter further in the inhibitory synapse upon the crayfish tonic stretch receptor neuron, confirming the above. In addition it showed that locking and alternation existed also in the segments interposed between the 1:2, 1:1 and 2:1 paradoxical segments, even though they were not as marked and apparent, and that when tests were close to each other their order became influential and hysteresis-like phenomena appeared. The main finding was that paradoxical rate-relations, locking and alternation persisted when the presynaptic train was irregularized up to interval coefficients of variation of around 0.20 (Figs. 2–5). Therefore, both phenomena may not simply be laboratory curiosities, but also have a role in natural operation where probably a substantial population of neurons exhibits that kind of irregularity. As presynaptic irregularity increased, the paradoxical segment slopes and widths decreased and locking and alternation became less clear-cut. With CV's of about 0.20, only a relatively narrow 1:1 paradoxical segment with about O slope and little locking and alternation remained (Figs. 2b, 3g, 4right, 5third row). With larger CV's, the rate relation decreased monotonically and there was no locking nor alternation (Figs. 2e, 3h, 5bottom row). The postsynaptic discharge was more regular and had fewer changes in the number of presynaptic spikes per post-synaptic interval within paradoxical segments (particularly in their centers) than in segments interposed between them (left vs. right-hand columns in Figs. 5, 6; Fig. 7): the contrast, remarkable for regular stimuli, attenuated as variability increased. The following conclusions are relevant to coding of spike trains across a synapse with IPSP's. i) With fairly regular discharges, the same postsynaptic rate may result from several presynaptic ones (e.g., may result from rates in the 1:1 and 2:1 paradoxical segments and in the interposed one, Fig.2): in some cases but not others, the precise presynaptic rate can be identified on the basis of postsynaptic CV's, interval histograms and cycle slips. ii) A small rate change in a regular presynaptic discharge will have very different postsynaptic consequences depending on where it happens: if across a paradoxical-interposed boundary, for instance, it will cause remarkable rate, pattern and correlation changes. iii) The trans-synaptic mapping of variability involves an increase for the more regular presynaptic discharges and a decrease for the more irregular ones. iv) The postsynaptic discharge was slower with IPSP's than without in most cases; however, when the control discharge was weak or absent, IPSP's accelerated it. Results are relevant also to the operation of periodically performing systems that involve neuronal correlates, indicating that it is necessary in every case to ask whether zigzag relations and locking occur. The “delay function” plots the arrival time of an IPSP (or IPSP burst) relative to the last postsynaptic spike, i.e., the “phase” (Φ in Fig. 1b), against the interval lengthening produced, i.e., the “delay” (δ). In all cases, most points clustered around a straight line (Fig. 8), whose slope and ordinate intercept were in the 0.43–0.87 and the 0.02–0.52 ranges, respectively, for single IPSP's. The slope reflects how the IPSP effectiveness depends on when it arrives in the cycle; the intercept reflects the IPSP effectiveness. Large phases often showed “aberrant” points whose ordinates were either large (and having special formal implications), or very small (perhaps reflecting conduction and synaptic delays), or clustered around a second straight segment with a large negative slope (when spontaneous rates were low) (Fig. 8c). Delay functions for widely separated pairs of IPSP's could be multi-valued, points clustering around 2 or 3 parallel straight lines. A mathematical model of pacemaker inhibitory synaptic interactions (Segundo, 1979) agreed with this embodiment insofar as some postulated properties are concerned (e.g., regular discharge, interval lengthening by IPSP's, linear delay functions with slopes around 0.7) and as to the main aspects of the preparation's behavior (i.e., zigzag rate relations and locking), but not in terms of some aspects of the postulates (e.g., interval variability, rebound) or behavior (e.g., segment boundaries, jitter in the locking, and hysteresis). The model was judged to be on the balance satisfactorily realistic.

Notes: Abstract The many indistinguishable texture pairs having identical second-, but different third- and higher-order statistics, led to the conjecture thatglobally the preattentive texture discrimination system cannot process statistical parameters of third- or higher-order. Thus in cases when iso-second-order textures yield discrimination this must be based onlocal conspicuous features calledtextons (Julesz, 1980). Here it is shown that globally even second-order statistical parameters, such as autocorrelation, cannot be processed by the textural system, and texture discrimination is solely the result of first-order statistics (density) of textons. It is also shown that the perceivable distance of statistical constraints (coherence distance) in densely packed stochastic textures is very short, four dots or less. As of now, only three texton classes were found: color, elongated blobs (line segments) of given width, orientation, and length, and the terminators (end-points) of these elongated blobs. The strength of these textons is demonstrated by several examples.

Notes: Abstract Sixty subjects were tested to assign orientation to ten dot patterns differing in their overall form and the number of dots in the pattern. The patterns were presented in four different positions in the visual field and their orientation was estimated in two ways. It was demonstrated that the assignment of orientation did not depend on the position of the pattern in the visual field as well as on the method of estimation used. A quantitative measure for the elongation of a dot pattern is proposed which correlates with the degree of ambiguity in orientation estimation. The greater the elongation the smaller the standard deviation of the estimates given. The distributions of the estimates for the ten patterns were analyzed. It was shown that they can be presented as superpositions of two or more groups of normally distributed estimates determined by some salient characteristics of the stimuli. Data are discussed from the point of view that assignment of orientation to dot patterns reveals the existence of optimization mechanisms in human brain that extract perceptual invariants from external stimulation.

Notes: Abstract Pulse-interval distributions are obtained for a counting system in which there is a gradual, rather than abrupt, increase in excitability following the registration of a pulse (relative refractoriness). The results are applicable to systems in which Poisson counting would be observed in the absence of such effects, and in which the memory reaches back at most one pulse. Choosing a particular functional form for the recovery function, the theory fits the experimentally measured distribution for the maintained discharge in the cat's retinal ganglion cell. It is also consistent with the notion that Weber's Law emerges from refractoriness in the visual system, as first proposed by van der Velden.

Notes: Abstract A hypothesis is presented which describes, in biomechanical terms, the central programs underlying horizontal eye movements in man. It is suggested that eye movements are produced by means of programmed shifts of the so-called invariant muscle characteristics (static force vs angle ϕ of gaze). These shifts lead to a change of the equilibrium point resulting from the interaction of agnnist and antagonist muscles and, as a consequence, to movement and the attainment of a new position of gaze. A reciprocal or a coactivation command to agonist and antagonist muscles occurs when their characteristics shift with respect to the coordinate ϕ in the same or opposite directions, respectively. It is proposed that during pursuit and saccadic eye movements a supperposition of the both central commands occurs. During a saccade, the reciprocal command develops evenly up to a certain level. The initial and final levels of the reciprocal command dictate the respective position of gaze and therefore the size of the saccade. The coactivation command develops to a maximum level and is slowly switched off when the new position of gaze has been achieved. The magnitude of the coactivation command seems to be not connected with an absolute position of gaze. It provides probably a stability of the movement and, in particular, prevents overshoot and oscillation during the saccade. The same timing of these commands occurs during pursuit movements, but the magnitude of the coactivation command and the rates of the development of the both commands are less in this case and correlate with the velocity of the movement. This hypothesis enables the tension changes in the muscle during saccadic and pursuit movements to be simulated in qualitative accordance with unique experimental data obtained by Collins et al. (1975). The functional significance of superposition of these motor commands and similarity in the efferent organization of eye and limb movements are discussed.