Implications of interrupted eye–head gaze shifts for resettable integrator reset.

Abstract The neural circuit responsible for saccadic eye movements is generally thought to resemble a closed loop controller. Several models of the saccadic system assume that the feedback signal of such a controller is an efference copy of "eye displacement", a neural estimate of the distance already travelled by the eyes, provided by the so-called "resettable integrator" (RI). The speed, with which the RI is reset, is thought to be fast or instantaneous by some authors and gradual by others. To examine this issue, psychophysicists have taken advantage of the target-distractor paradigm. Subjects engaged in it, are asked to look to only one of two stimuli (the "target") and not to a distractor presented in the diametrically opposite location and they often generate movement sequences in which a gaze shift towards the "distractor" is followed by a second gaze shift to the "target". The fact that the second movement is not systematically erroneous even when very short time intervals (about 5 ms) separate it from the first movement has been used to question the verisimilitude of gradual RI reset. To explore this matter we used a saccade-generating network that relies on a RI coupled to a head controller and a model of the rotational vestibulo-ocular reflex. An analysis of the activation functions of model units provides disproof by counterexample: "targets" can be accurately acquired even when the RI of the saccadic burst generator is not reset at all after the end of the first, interrupted eye-head gaze shift to the distractor and prior to the second, complete eye-head gaze shift to the "target"

Recent Advances in Σ-definability over Continuous Data Types

The purpose of this paper is to survey our recent research in computability and definability over continuous data types such as the real numbers, real-valued functions and functionals. We investigate the expressive power and algorithmic properties of the language of Sigma-formulas intended to represent computability over the real numbers. In order to adequately represent computability we extend the reals by the structure of hereditarily finite sets. In this setting it is crucial to consider the real numbers without equality since the equality test is undecidable over the reals. We prove Engeler's Lemma for Sigma-definability over the reals without the equality test which relates Sigma-definability with definability in the constructive infinitary language L_{omega_1 omega}. Thus, a relation over the real numbers is Sigma-definable if and only if it is definable by a disjunction of a recursively enumerable set of quantifier free formulas. This result reveals computational aspects of Sigma-definability and also gives topological characterisation of Sigma-definable relations over the reals without the equality test. We also illustrate how computability over the real numbers can be expressed in the language of Sigma-formulas

Comparing the degrees of enumerability and the closed Medvedev degrees

We compare the degrees of enumerability and the closed Medvedev degrees and find that many situations occur. There are nonzero closed degrees that do not bound nonzero degrees of enumerability, there are nonzero degrees of enumerability that do not bound nonzero closed degrees, and there are degrees that are nontrivially both degrees of enumerability and closed degrees. We also show that the compact degrees of enumerability exactly correspond to the cototal enumeration degrees

Algorithmic iteration for computational intelligence

Machine awareness is a disputed research topic, in some circles considered a crucial step in realising Artificial General Intelligence. Understanding what that is, under which conditions such feature could arise and how it can be controlled is still a matter of speculation. A more concrete object of theoretical analysis is algorithmic iteration for computational intelligence, intended as the theoretical and practical ability of algorithms to design other algorithms for actions aimed at solving well-specified tasks. We know this ability is already shown by current AIs, and understanding its limits is an essential step in qualifying claims about machine awareness and Super-AI. We propose a formal translation of algorithmic iteration in a fragment of modal logic, formulate principles of transparency and faithfulness across human and machine intelligence, and consider the relevance to theoretical research on (Super)-AI as well as the practical import of our results

Complex type 4 structure changing dynamics of digital agents: Nash equilibria of a game with arms race in innovations

The new digital economy has renewed interest in how digital agents can innovate. This follows the legacy of John von Neumann dynamical systems theory on complex biological systems as computation. The Gödel-Turing-Post (GTP) logic is shown to be necessary to generate innovation based structure changing Type 4 dynamics of the Wolfram-Chomsky schema. Two syntactic procedures of GTP logic permit digital agents to exit from listable sets of digital technologies to produce novelty and surprises. The first is meta-analyses or offline simulations. The second is a fixed point with a two place encoding of negation or opposition, referred to as the Gödel sentence. It is postulated that in phenomena ranging from the genome to human proteanism, the Gödel sentence is a ubiquitous syntactic construction without which escape from hostile agents qua the Liar is impossible and digital agents become entrained within fixed repertoires. The only recursive best response function of a 2-person adversarial game that can implement strategic innovation in lock-step formation of an arms race is the productive function of the Emil Post [58] set theoretic proof of the Gödel incompleteness result. This overturns the view of game theorists that surprise and innovation cannot be a Nash equilibrium of a game

A competitive integration model of exogenous and endogenous eye movements

We present a model of the eye movement system in which the programming of an eye movement is the result of the competitive integration of information in the superior colliculi (SC). This brain area receives input from occipital cortex, the frontal eye fields, and the dorsolateral prefrontal cortex, on the basis of which it computes the location of the next saccadic target. Two critical assumptions in the model are that cortical inputs are not only excitatory, but can also inhibit saccades to specific locations, and that the SC continue to influence the trajectory of a saccade while it is being executed. With these assumptions, we account for many neurophysiological and behavioral findings from eye movement research. Interactions within the saccade map are shown to account for effects of distractors on saccadic reaction time (SRT) and saccade trajectory, including the global effect and oculomotor capture. In addition, the model accounts for express saccades, the gap effect, saccadic reaction times for antisaccades, and recorded responses from neurons in the SC and frontal eye fields in these tasks. © The Author(s) 2010

Deficits in visuo-spatial working memory, inhibition and oculomotor control in boys with ADHD and their non-affected brothers.

Few studies have assessed visuo-spatial working memory and inhibition in attention-deficit/hyperactivity disorder (ADHD) by recording saccades and consequently little additional knowledge has been gathered on oculomotor functioning in ADHD. Moreover, this is the first study to report the performance of non-affected siblings of children with ADHD, which may shed light on the familiality of deficits. A total of 14 boys with ADHD, 18 non-affected brothers, and 15 control boys aged 7-14 years, were administered a memory-guided saccade task with delays of three and seven seconds. Familial deficits were found in accuracy of visuo-spatial working memory, percentage of anticipatory saccades, and tendency to overshoot saccades relative to controls. These findings suggest memory-guided saccade deficits may relate to a familial predisposition for ADHD