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Chrystopher L. Nehaniv

Publications and source records attributed to Chrystopher L. Nehaniv.

31 records · Page 2Linked to original sources
arXiv2020

Algebraic Structure and Complexity of Bootstrap Percolation with External Inputs

In this paper a modification of the standard Bootstrap Percolation model is introduced. In our modification a discrete time update rule is constructed that allows for non-monotonicity - unlike its classical counterpart. External inputs to drive the system into desirable states are also included in the model. The algebraic structure and complexity properties of the system are inferred by studying the system's holonomy decomposition. We introduce methods of inferring the pools of reversibility for the system. Dependence of system complexity on process parameters is presented and discussed.

math.DS↗
arXiv2020

Exploring Tetris as a Transformation Semigroup

Tetris is a popular puzzle video game, invented in 1984. We formulate two versions of the game as a transformation semigroup and use this formulation to view the game through the lens of Krohn-Rhodes theory. In a variation of the game upon which it restarts if the player loses, we find permutation group structures, including the symmetric group $S_5$ which contains a non-abelian simple group as a subgroup. This implies, at least in a simple case, that iterated Tetris is finitarily computationally universal.

math.GR↗
arXiv2019

Measuring Time with Minimal Clocks

Being able to measure time, whether directly or indirectly, is a significant advantage for an organism. It allows for the timely reaction to regular or predicted events, reducing the pressure for fast processing of sensory input. Thus, clocks are ubiquitous in biology. In the present paper, we consider minimal abstract pure clocks in different configurations and investigate their characteristic dynamics. We are especially interested in optimally time-resolving clocks. Among these, we find fundamentally diametral clock characteristics, such as oscillatory behavior for purely local time measurement or decay-based clocks measuring time periods of a scale global to the problem. We include also sets of independent clocks ("clock bags"), sequential cascades of clocks and composite clocks with controlled dependency. Clock cascades show a "condensation effect" and the composite clock shows various regimes of markedly different dynamics.

q-bio.OT↗
arXiv2018

Robots Learning to Say `No': Prohibition and Rejective Mechanisms in Acquisition of Linguistic Negation

`No' belongs to the first ten words used by children and embodies the first active form of linguistic negation. Despite its early occurrence the details of its acquisition process remain largely unknown. The circumstance that `no' cannot be construed as a label for perceptible objects or events puts it outside of the scope of most modern accounts of language acquisition. Moreover, most symbol grounding architectures will struggle to ground the word due to its non-referential character. In an experimental study involving the child-like humanoid robot iCub that was designed to illuminate the acquisition process of negation words, the robot is deployed in several rounds of speech-wise unconstrained interaction with naïve participants acting as its language teachers. The results corroborate the hypothesis that affect or volition plays a pivotal role in the socially distributed acquisition process. Negation words are prosodically salient within prohibitive utterances and negative intent interpretations such that they can be easily isolated from the teacher's speech signal. These words subsequently may be grounded in negative affective states. However, observations of the nature of prohibitive acts and the temporal relationships between its linguistic and extra-linguistic components raise serious questions over the suitability of Hebbian-type algorithms for language grounding.

cs.CL↗
arXiv2017

Simulating and Reconstructing Neurodynamics with Epsilon-Automata Applied to Electroencephalography (EEG) Microstate Sequences

We introduce new techniques to the analysis of neural spatiotemporal dynamics via applying $ε$-machine reconstruction to electroencephalography (EEG) microstate sequences. Microstates are short duration quasi-stable states of the dynamically changing electrical field topographies recorded via an array of electrodes from the human scalp, and cluster into four canonical classes. The sequence of microstates observed under particular conditions can be considered an information source with unknown underlying structure. $ε$-machines are discrete dynamical system automata with state-dependent probabilities on different future observations (in this case the next measured EEG microstate). They artificially reproduce underlying structure in an optimally predictive manner as generative models exhibiting dynamics emulating the behaviour of the source. Here we present experiments using both simulations and empirical data supporting the value of associating these discrete dynamical systems with mental states (e.g. mind-wandering, focused attention, etc.) and with clinical populations. The neurodynamics of mental states and clinical populations can then be further characterized by properties of these dynamical systems, including: i) statistical complexity (determined by the number of states of the corresponding $ε$-automaton); ii) entropy rate; iii) characteristic sequence patterning (syntax, probabilistic grammars); iv) duration, persistence and stability of dynamical patterns; and v) algebraic measures such as Krohn-Rhodes complexity or holonomy length of the decompositions of these. The potential applications include the characterization of mental states in neurodynamic terms for mental health diagnostics, well-being interventions, human-machine interface, and others on both subject-specific and group/population-level.

q-bio.NC↗
arXiv2017

The maximal subgroups and the complexity of the flow semigroup of finite (di)graphs

The flow semigroup, introduced by John Rhodes, is an invariant for digraphs and a complete invariant for graphs. After collecting together previous partial results, we refine and prove Rhodes's conjecture on the structure of the maximal groups in the flow semigroup for finite, antisymmetric, strongly connected digraphs. Building on this result, we investigate and fully describe the structure and actions of the maximal subgroups of the flow semigroup acting on all but $k$ points for all finite digraphs and graphs for all $k\geq 1$. A linear algorithm (in the number of edges) is presented to determine these so-called `defect $k$ groups' for any finite (di)graph. Finally, we prove that the complexity of the flow semigroup of a 2-vertex connected (and strongly connected di)graph with $n$ vertices is $n-2$, completely confirming Rhodes's conjecture for such (di)graphs.

math.CO↗
arXiv2017

Time as it could Be measured in Artificial Living Systems

Being able to measure time, whether directly or indirectly, is a significant advantage for an organism. It permits it to predict regular events, and prepare for them on time. Thus, clocks are ubiquitous in biology. In the present paper, we consider the most minimal abstract pure clocks and investigate their characteristics with respect to their ability to measure time. Amongst other, we find fundamentally diametral clock characteristics, such as oscillatory behaviour for local time measurement or decay-based clocks measuring time periods in scales global to the problem. We include also cascades of independent clocks ("clock bags") and composite clocks with controlled dependency; the latter show various regimes of markedly different dynamics.

q-bio.OT↗
arXiv2015

Computational Holonomy Decomposition of Transformation Semigroups

We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty lies in the strict separation of several different ideas appearing in the holonomy method. The steps of the proof and the constructions are illustrated with computed examples.

math.GR↗
arXiv2014

Computational Understanding and Manipulation of Symmetries

For natural and artificial systems with some symmetry structure, computational understanding and manipulation can be achieved without learning by exploiting the algebraic structure. Here we describe this algebraic coordinatization method and apply it to permutation puzzles. Coordinatization yields a structural understanding, not just solutions for the puzzles.

cs.AI↗
arXiv2012

Interaction Histories and Short Term Memory: Enactive Development of Turn-taking Behaviors in a Childlike Humanoid Robot

In this article, an enactive architecture is described that allows a humanoid robot to learn to compose simple actions into turn-taking behaviors while playing interaction games with a human partner. The robot's action choices are reinforced by social feedback from the human in the form of visual attention and measures of behavioral synchronization. We demonstrate that the system can acquire and switch between behaviors learned through interaction based on social feedback from the human partner. The role of reinforcement based on a short term memory of the interaction is experimentally investigated. Results indicate that feedback based only on the immediate state is insufficient to learn certain turn-taking behaviors. Therefore some history of the interaction must be considered in the acquisition of turn-taking, which can be efficiently handled through the use of short term memory.

cs.AI↗
arXiv2010

On Straight Words and Minimal Permutators in Finite Transformation Semigroups

Motivated by issues arising in computer science, we investigate the loop-free paths from the identity transformation and corresponding straight words in the Cayley graph of a finite transformation semigroup with a fixed generator set. Of special interest are words that permute a given subset of the state set. Certain such words, called minimal permutators, are shown to comprise a code, and the straight ones comprise a finite code. Thus, words that permute a given subset are uniquely factorizable as products of the subset's minimal permutators, and these can be further reduced to straight minimal permutators. This leads to insight into structure of local pools of reversibility in transformation semigroups in terms of the set of words permuting a given subset. These findings can be exploited in practical calculations for hierarchical decompositions of finite automata. As an example we consider groups arising in biological systems.

math.GR↗
arXiv2009

Subgroup Chains and Lagrange Coordinatizations of Finite Permutation Groups

We give a general constructive proof for hierarchical coordinatizations (Lagrange Decompositions) of permutation groups. The generalization originates from the investigation of how the subgroup chains of finite permutation groups yield different coordinate systems. The study is motivated by the practical needs and the verification of an existing computational implementation. Large scale machine calculated examples are also presented.

math.GR↗