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spores and cells Q2 and show significant growth Q2 over time which saturates after free particles were consumed by structures so |
that density dependent equilibrium emerges Fig 2). After the growth phase we observe clear ratio of spore populations to cell populations |
Q3 Fig 3). By fitting the observed data to classical population model from biology we show that the structures follow known population |
dynamics of natural organisms Q4 Fig .3) suggesting the emergence of sort of self generating ecosystem This is further supported |
by identifying clear material cycles that emerge in the system as they are also known from ecology Fig 3). Based on those findings |
we conclude that we found novel model capable of capturing rich set of phenomena known from natural systems with minimal set of computational |
complexity We here report our first findings and assume that further analysis of the system will yield more fascinating insights |
and phenomena very prominent model in Artificial Life research and research of self organization emergence and complexity was the |
game of life (\ cite citation :10}), which consists of cells of binary state dead or alive in discrete grid world following simple |
rules of local interaction These rules mimic simple ecological rules overpopulation Allee effect partner finding in reproduction |
and create rich set of patterns that are attributed with distinct names ., called pond glider comb It was found that the populations |
of cells in the GOL develops into balanced population density what is not surprising as the microscopic rules in the GOL mimic the |
basic mechanisms of density regulated growth (\ cite citation :8}). We took such ground breaking and classical models Game of Life |
logistic growth and self propelled particles ), which were extensively studied in tens of thousands of analysis and articles as reference |
and created system here that is even closer to the singularity of the origin of life and the ecological equilibria emerging afterwards |
ecology ): Random particles moving in continuous space and interacting in an asynchronous way forming patterns of life like shape |
and complexity self reproducing self sustaining self repairing and developing into well balanced ecology Also in our model we look |
for minimalistic set of rules achieving maximum of diversity of patterns that emerge We think that PPS is currently the most simple |
bottom up model operating in continuous space and without required synchrony of agents PPS work synchronously and asynchronously |
data not shown that can demonstrate morphogenesis from scratch Thus we propose PPS as the most simple protocell model This article |
is preliminary version of an article currently under preparation to be submitted to high ranking scientific journal section Acknowledgments |
This article was written in cooperation of and .: discovered the PPS and the interesting parameter setting and implemented the first |
programs of those PPS conducted the systematic numerical analysis and statistical evaluation and produced all graphs of this article |
The text of this article was equally written together by and Early variants of such minimalistic algorithm to produce coordinated |
group behaviours of agents were investigated by the EU ICT FP7 project CoCoRo #270382. Currently we further explore those systems |
with the funding of the EU-H2020 FET-PROACTIVE project subCULTron \#640967 and the project REBODIMENT (Austrian Science Fund, FWF), |
23943-N13. begin thebibliography }{1} bibitem citation :1} Langton Computation at the edge of chaos Phase transitions and emergent |
computation textit Physica {\ bf 42}, 12-37 (1970) bibitem citation :2} Peret ’o, J. Controversies on the origin of life. \textit{Int.\ Microbiol.\ ␣␣ {\bf 8}, 23-31 (2005). |
\bibitem{citation:3} Haken, H. \textit{Synergetics: Nonequilibrium Phase Transitions and Self-Organization in Physics} (Springer, Berlin, 1978). |
\bibitem{citation:4} Fellermann, H., Rasmussen, S., Ziock, H. J. \& Sol\’e, R. V. Life cycle of minimal protocell dissipative particle dynamics study. |
\textit{Artif.\ Life\ {\bf 13(4)}, 319-345 (2007). \bibitem{citation:5} Erskine, A. \& Herrmann, J. M. Cell Division Behaviour in Heterogeneous Swarm Environment. ␣␣ \textit{In Advances in Artificial Life, ECAL} {\bf 12}, 35-42 (2013). |
\bibitem{citation:6} Vicsek, T., Czir\’ok, A., Ben-Jacob, E., Cohen, I. \& Shochet, O. Novel type of phase transition in system of self-driven particles. |
\textit{Phys.\ Rev.\ Lett.\ {\bf 75(6)}, 1226 (1995). \bibitem{citation:7} Hamann, H., Schmickl, T. \& Crailsheim, K. Self-organized pattern formation in swarm system as transient phenomenon of non-linear dynamics. ␣␣ \textit{Math. Comput. Model Dyn. Syst.} {\bf 18(1)}, 39-50 (2012) |
␣␣ \bibitem{citation:8} Verhulst, P. F. La Loi d’ Accroissement de la Population textit Nouv Mem Acad Roy Soc Belle lettr Bruxelles |
{\ bf 18}, (1845). bibitem citation :9} Schmickl \& Karsai The interplay of sex ratio male success and density independent mortality |
affects population dynamics textit Ecol Modell .} {\ bf 221(8)}, 1089-1097 (2010). bibitem citation :10} 14. Gardner Mathematical |
games The fantastic combinations of John Conway ’s new solitaire game “life’ ’. \textit{Sci. Am.} {\bf 223(4)}, (1970). \end{thebibliography} |
\end{multicols} \begin{figure}[p] ␣␣␣␣ \centering ␣␣␣␣ \includegraphics[width=1\textwidth]{ArxivFig1.png} ␣␣␣␣ \caption{\textbf{Screenshots of independent runs at the same timestep (100,000), at which color in visualization is determined by local neighborhood density.} Particles with more than 15 neighboring particles ... |
␣␣␣␣ \label{fig:Figure1} \end{figure} \begin{figure}[p] ␣␣␣␣ \centering ␣␣␣␣ \includegraphics[width=1\textwidth]{ArxivFig2.png} ␣␣␣␣ \caption{\textbf{Functional boxplot (a) number of cells (blue) and spores (red) at each timestep of independent runs (seen in Figure 1), (b) example timesteps, statistically compared.} Fi... |
␣␣␣␣ \label{fig:Figure2} \end{figure} \begin{figure}[p] ␣␣␣␣ \centering ␣␣␣␣ \includegraphics[width=1\textwidth]{ArxivFig3.png} ␣␣␣␣ \caption{\textbf{Detailed analysis of one extended run (run number 5).} Figure 3a: Number of cells and spores at each timestep with fitted logistic growth model. Figure 3b and 3c: Analysi... |
# Source: arxiv 1601.06755 # Title: The Utility of Hedged Assertions in the Emergence of Shared Categorical Labels # Sections: all # Downloaded: 2026-03-03T02:00:59.293844+00:00 |
The Utility of Hedged Assertions in the Emergence of Shared Categorical Labels Abstract We investigate the emergence of shared concepts in a community of language users using a multi-agent simulation. We extend results showing that negated assertions are of use in developing shared categories, to include assertions mod... |
INTRODUCTION An evolutionary approach to semantics enables the development in robots and autonomous agents of flexible, mutable concepts that could be learnt through interaction and can change over time |
. This approach is investigated by Eyre and Lawry in , in which they develop a model of language evolution based in the label semantics framework. They show that using a mixture of positive and negated assertions enables the development of languages that are both shared, and discriminate effectively between elements wi... |
1.1 A representation model for concepts We model concepts within the label semantics framework , combined with prototype theory and the conceptual spaces model of concepts |
. Prototype theory offers an alternative to the classical theory of concepts, basing categorization on proximity to a prototype. This approach is based on experimental results where human subjects were found to view membership in a concept as a matter of degree, with some objects having higher membership than others |
. Fuzzy set theory , in which an object [MATH] has a graded membership [MATH] in a concept [MATH] , was proposed as a formalism for prototype theory. However, numerous objections to its suitability have been made |
Conceptual spaces theory renders concepts as convex regions of a conceptual space - a geometrical structure with quality dimensions and a distance metric. Examples are: the RGB colour cube, pictured in figure ; physical dimensions of height, breadth and depth; or the taste tetrahedron. Since concepts are convex regions... |
Label semantics is a random set approach to concepts which quantifies an agent’s uncertainty about the extent of application of a concept. We refer to this as subjective uncertainty |
to emphasise that it concerns the definition of concepts and categories, in contrast to stochastic uncertainty which concerns the state of the world. Lawry and Tang |
combine the label semantics approach with conceptual spaces and prototype theory, to give a formalisation of concepts as based on a prototype and a threshold, located in a conceptual space. |
Within this framework, agents use sets of labels [MATH] to describe an underlying conceptual space [MATH] with distance metric [MATH] between points. The conceptual space could be, as mentioned, the RGB colour space. Labels [MATH] would then be concepts such as ‘red’, ‘blue’, ‘purple’, ‘orange’ and so on. These labels ... |
In this model, however, agents are uncertain as to exactly where the thresholds lie. To illustrate this, consider the concept ‘tall’. It is easy to point out a tall person, and to point out a person who is not tall, but it is difficult to specify the exact threshold between ‘tall’ and ‘not tall’. This uncertainty conce... |
The threshold [MATH] is uncertain, however, so there is some probability that [MATH] in figure is actually wide enough to include the object [MATH] , i.e. that [MATH] is appropriate to describe [MATH] . The appropriateness [MATH] of a label [MATH] to describe an element [MATH] is then given by the probability that [MAT... |
[EQUATION] Figure shows how this appropriateness measure works in a setup similar to that in figure This appropriateness measure is similar to Zadeh’s description of fuzzy membership in a concept |
1.2 Linguistic hedges Hedges are words or phrases such as ‘very’, ‘quite’, ‘strictly speaking’ which modify the domain of application of a concept. In particular, ‘very’, and ‘quite’ respectively contract or expand the domain of application of a concept, so that, for example, ‘very tall’ applies to fewer people than do... |
uses operations of concentration and dilation to render these ideas. Concentration is described as [MATH] and dilation is often rendered as [MATH] . However, we argue, as do |
, that Zadeh’s formulae are, to an extent, arbitrary, since the notion of taking a power of a membership value does not correspond to anything that language users might do. Rather, it simply has some of the right effects. As with |
, we take a semantic approach. In , we propose that a concept ‘very [MATH] ’ or ‘quite [MATH] ’ be rendered by considering that the prototype of ‘very/quite [MATH] ’ is equal to that of the base concept [MATH] , but that the threshold of the hedged concept ‘very/quite [MATH] ’ is respectively smaller or larger than tha... |
Our model of the hedges ‘very’ and ‘quite’ therefore requires simply that [MATH] and that [MATH] . We implement this model in a version of the multi-agent simulation created in |
in order to investigate how the use of these hedges in a model of language helps the emergence of shared categories across a community of language users. |
METHODS 2.1 Overview To investigate the utility of hedged assertions we implement a multi-agent simulation of a version of the category game |
, following , in which shared categories develop over time as a result of the interactions of the category users. An overview of the game is as follows. Agents use labels to describe a conceptual space [MATH] . At each timestep, agents are randomly paired into speakers and listeners, and each pair is shown a distinct e... |
2.2 Conceptual models Each agent is equipped with the same number [MATH] of labels [MATH] , with point prototypes [MATH] , where [MATH] . At the start of the simulations the [MATH] are uniformly distributed around the space. Thresholds [MATH] are also randomly initiated, and considered to be some multiple of a base thr... |
Each agent therefore has a label set [MATH] . These labels can be hedged to form a set [MATH] . Hedged concepts have the same prototype [MATH] as basic labels, but a scaled threshold [MATH] or [MATH] where [MATH] and [MATH] . Agents can assert positive or negated, hedged or basic labels, giving an assertion set [MATH] ... |
2.3 Assertion model At each timestep, half the agents are designated speaker agents and make assertions, determined by the assertion model used.The assertion model is based on the probability of making a particular assertion [MATH] , given that the object being described is [MATH] . Following methods in |
, we calculate the posterior probability of each [MATH] , given an element [MATH] . The assertion made by a speaker agent is the assertion with the highest probability. The posterior probability of each [MATH] , given [MATH] , is determined by the appropriateness of the assertion [MATH] to describe [MATH] , i.e. [MATH]... |
We first consider which sets of labels that are appropriate to describe [MATH] . The probability that any particular set of labels [MATH] are appropriate to describe [MATH] is given by a probability mass function [MATH] . One way of determining [MATH] is via the consonant selection function introduced in |
. This states: Definition 1 (Consonant selection function) Given non-zero appropriateness measures on basic labels [MATH] ordered such that [MATH] for [MATH] , the consonant selection function identifies the mass function |
[EQUATION] Because we have ordered the labels by [MATH] , if the label [MATH] is appropriate to describe [MATH] , all labels [MATH] must also be appropriate to describe [MATH] . The quantity [MATH] corresponds to the idea that [MATH] in some sense lies between the thresholds [MATH] and [MATH] , so that [MATH] is approp... |
Example 2 (Determining the mass function) Suppose we are determining the mass function for subsets [MATH] , given the point [MATH] , as illustrated in figure |
Suppose that [MATH] [MATH] [MATH] [MATH] [MATH] [MATH] , giving us the order [MATH] . We may then assign probabilities to subsets of labels according to the consonant selection function: |
[EQUATION] Having determined the probability mass function on sets of labels, a mass assignment on sets of assertions is then defined. |
Definition 3 (Mass assignment on assertions) [MATH] is defined such that: [EQUATION] where [MATH] , and [MATH] is defined recursively by |
[EQUATION] This definition has the implication that for [MATH] [MATH] Then the probability of an assertion [MATH] being made, given that an object [MATH] is being described, can be calculated by summing over [MATH] that contain [MATH] |
Definition 4 Given a prior distribution on [MATH] , a posterior distribution given an object [MATH] can be calculated by: [EQUATION] |
Here, [MATH] The value of [MATH] for one particular label [MATH] is a product of two elements: the prior probability [MATH] of making a positive assertion (or [MATH] for a negated assertion); and the prior probability of making a hedged assertion, given by [MATH] for making an assertion hedged with the word ‘very’, [MA... |
The prior probability of asserting any particular label [MATH] is uniform across [MATH] . Hence the value of [MATH] calculated above should be divided by [MATH] , giving, for example, |
[EQUATION] Example 5 (Determining the posterior probability of assertion) Suppose, for an easy example, we want to calculate the probability of asserting ‘very [MATH] ’, given object [MATH] , as in example . We need to calculate |
[EQUATION] where [MATH] . However, the only subset [MATH] ‘very [MATH] ’ is [MATH] , so [EQUATION] Suppose, for a more involved example, the label set [MATH] is as in example , with [MATH] [MATH] [MATH] , and we want to determine [MATH] . The prior probability [MATH] . So we have: |
[EQUATION] Having calculated the probability of each assertion, the speaker agent makes the most probable assertion [MATH] 2.4 Updating algorithms |
Once the speaker agent has made assertion [MATH] , the listener agent computes [MATH] based on its current label set. If [MATH] , where [MATH] is a parameter that can be thought of as the age of the speaker agent, the listener agent updates its label set [MATH] by moving the prototype and/or changing the threshold of t... |
. A label defined by [MATH] and [MATH] is updated to [MATH] and [MATH] . Values for [MATH] and [MATH] are sought, such that [MATH] |
2.4.1 Case 1: [MATH] Recall that [MATH] , so that for [MATH] [EQUATION] The label [MATH] is updated to [MATH] , where [MATH] and [MATH] , such that [MATH] , and minimising the distance between the interpretations as measured by the Haussdorff distance between the two neighbourhoods, |
[EQUATION] To minimise the update, we set [MATH] , so: [EQUATION] which gives [EQUATION] To update [MATH] we will always want [MATH] [MATH] , as we are dealing with a positive label. |
Substituting [MATH] into equation (*), we obtain [EQUATION] Then if [MATH] , i.e. [MATH] , the quantity ( ) can be minimised by setting [MATH] so [MATH] . Otherwise, we have [MATH] [MATH] |
Since [MATH] is a random variable, so is the choice between [MATH] and [MATH] . We therefore need a concrete updating rule. We update [MATH] and [MATH] with the expected values of [MATH] and [MATH] respectively. [MATH] , so |
[EQUATION] We can therefore calculate [EQUATION] and [EQUATION] 2.4.2 Case 2: [MATH] By an entirely similar argument, we obtain [EQUATION] |
and [EQUATION] So at each timestep, each listener agent, for whom [MATH] , updates the relevant label using the the quantities [MATH] [MATH] |
2.5 Performance metrics Performance metrics from are used, measuring the Average Pairwise Distance between label sets (APD) and the Average Label Overlap (ALO). APD measures the difference in label sets in the community, and ALO indicates the extent to which an agent’s concepts overlap. We seek low values for each metr... |
APD is calculated using the Haussdorff distance between two neighbourhoods as given in equation . The difference between the label sets of any one pair of agents is given by |
[EQUATION] where [MATH] is the number of labels each agent has and [MATH] and [MATH] refer to distinct agents. This is averaged over pairs of agents. There are [MATH] agents, therefore [MATH] pairs, giving: |
[EQUATION] ALO is the extent to which labels overlap. To calculate this, we take the maximum value of the intersection of a pair of labels, as measured by a min rule. We average this value over pairs of labels. The overlap within an individual’s label set is therefore |
[EQUATION] Averaged across the population this is: [EQUATION] where [MATH] siginifies agent [MATH] ’s label overlap. 2.6 Simulation process |
Simulations with [MATH] agents were run for [MATH] timesteps. Agent weights [MATH] were updated at each timestep in increments of [MATH] . When [MATH] , agents are reborn with randomised labels and [MATH] . 20 simulations are run for each reported combination of parameters. |
show that if [MATH] then performance of the system changes from low ALO and high APD to vice versa at approximately [MATH] . We ran simulations in a slightly extended range for comparison, varying the prior probabilities [MATH] [MATH] and [MATH] of asserting the different hedges ‘very’, ‘basic’, and ‘quite’. We present... |
RESULTS The results presented show performance against the two metrics after [MATH] simulation timesteps. By this point, the population has generally reached a steady state in which performance does not greatly change. |
Figure shows the steady state of APD achieved after [MATH] timesteps for a range of values [MATH] . Three sets of results are presented: results using unhedged assertions; results with a high prior probability of using contraction hedges; and results from simulations with a high prior probability of asserting expansion... |
A high prior of asserting contracted labels reduces minimum APD achieved from [MATH] when [MATH] or [MATH] to [MATH] when [MATH] (figure ). Performing a paired t-test across the 20 simulations gives the mean difference between these values as [MATH] . This difference is statistically significant with [MATH] and with 95... |
With a high prior probability of asserting expanded labels, lower values of ALO can be achieved when the probability of asserting positive labels is [MATH] , decreasing to [MATH] compared to [MATH] , figure 11 . The mean difference between these values across the 20 simulations is 0.083, which is statistically signific... |
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