87,008 research outputs found
Can biological quantum networks solve NP-hard problems?
There is a widespread view that the human brain is so complex that it cannot
be efficiently simulated by universal Turing machines. During the last decades
the question has therefore been raised whether we need to consider quantum
effects to explain the imagined cognitive power of a conscious mind.
This paper presents a personal view of several fields of philosophy and
computational neurobiology in an attempt to suggest a realistic picture of how
the brain might work as a basis for perception, consciousness and cognition.
The purpose is to be able to identify and evaluate instances where quantum
effects might play a significant role in cognitive processes.
Not surprisingly, the conclusion is that quantum-enhanced cognition and
intelligence are very unlikely to be found in biological brains. Quantum
effects may certainly influence the functionality of various components and
signalling pathways at the molecular level in the brain network, like ion
ports, synapses, sensors, and enzymes. This might evidently influence the
functionality of some nodes and perhaps even the overall intelligence of the
brain network, but hardly give it any dramatically enhanced functionality. So,
the conclusion is that biological quantum networks can only approximately solve
small instances of NP-hard problems.
On the other hand, artificial intelligence and machine learning implemented
in complex dynamical systems based on genuine quantum networks can certainly be
expected to show enhanced performance and quantum advantage compared with
classical networks. Nevertheless, even quantum networks can only be expected to
efficiently solve NP-hard problems approximately. In the end it is a question
of precision - Nature is approximate.Comment: 38 page
Using synchronous Boolean networks to model several phenomena of collective behavior
In this paper, we propose an approach for modeling and analysis of a number
of phenomena of collective behavior. By collectives we mean multi-agent systems
that transition from one state to another at discrete moments of time. The
behavior of a member of a collective (agent) is called conforming if the
opinion of this agent at current time moment conforms to the opinion of some
other agents at the previous time moment. We presume that at each moment of
time every agent makes a decision by choosing from the set {0,1} (where
1-decision corresponds to action and 0-decision corresponds to inaction). In
our approach we model collective behavior with synchronous Boolean networks. We
presume that in a network there can be agents that act at every moment of time.
Such agents are called instigators. Also there can be agents that never act.
Such agents are called loyalists. Agents that are neither instigators nor
loyalists are called simple agents. We study two combinatorial problems. The
first problem is to find a disposition of instigators that in several time
moments transforms a network from a state where a majority of simple agents are
inactive to a state with a majority of active agents. The second problem is to
find a disposition of loyalists that returns the network to a state with a
majority of inactive agents. Similar problems are studied for networks in which
simple agents demonstrate the contrary to conforming behavior that we call
anticonforming. We obtained several theoretical results regarding the behavior
of collectives of agents with conforming or anticonforming behavior. In
computational experiments we solved the described problems for randomly
generated networks with several hundred vertices. We reduced corresponding
combinatorial problems to the Boolean satisfiability problem (SAT) and used
modern SAT solvers to solve the instances obtained
Model of human collective decision-making in complex environments
A continuous-time Markov process is proposed to analyze how a group of humans
solves a complex task, consisting in the search of the optimal set of decisions
on a fitness landscape. Individuals change their opinions driven by two
different forces: (i) the self-interest, which pushes them to increase their
own fitness values, and (ii) the social interactions, which push individuals to
reduce the diversity of their opinions in order to reach consensus. Results
show that the performance of the group is strongly affected by the strength of
social interactions and by the level of knowledge of the individuals.
Increasing the strength of social interactions improves the performance of the
team. However, too strong social interactions slow down the search of the
optimal solution and worsen the performance of the group. In particular, we
find that the threshold value of the social interaction strength, which leads
to the emergence of a superior intelligence of the group, is just the critical
threshold at which the consensus among the members sets in. We also prove that
a moderate level of knowledge is already enough to guarantee high performance
of the group in making decisions.Comment: 12 pages, 8 figues in European Physical Journal B, 201
Markovian Dynamics on Complex Reaction Networks
Complex networks, comprised of individual elements that interact with each
other through reaction channels, are ubiquitous across many scientific and
engineering disciplines. Examples include biochemical, pharmacokinetic,
epidemiological, ecological, social, neural, and multi-agent networks. A common
approach to modeling such networks is by a master equation that governs the
dynamic evolution of the joint probability mass function of the underling
population process and naturally leads to Markovian dynamics for such process.
Due however to the nonlinear nature of most reactions, the computation and
analysis of the resulting stochastic population dynamics is a difficult task.
This review article provides a coherent and comprehensive coverage of recently
developed approaches and methods to tackle this problem. After reviewing a
general framework for modeling Markovian reaction networks and giving specific
examples, the authors present numerical and computational techniques capable of
evaluating or approximating the solution of the master equation, discuss a
recently developed approach for studying the stationary behavior of Markovian
reaction networks using a potential energy landscape perspective, and provide
an introduction to the emerging theory of thermodynamic analysis of such
networks. Three representative problems of opinion formation, transcription
regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see
http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm
On the Steady State of Continuous Time Stochastic Opinion Dynamics with Power Law Confidence
This paper introduces a class of non-linear and continuous-time opinion
dynamics model with additive noise and state dependent interaction rates
between agents. The model features interaction rates which are proportional to
a negative power of opinion distances. We establish a non-local partial
differential equation for the distribution of opinion distances and use Mellin
transforms to provide an explicit formula for the stationary solution of the
latter, when it exists. Our approach leads to new qualitative and quantitative
results on this type of dynamics. To the best of our knowledge these Mellin
transform results are the first quantitative results on the equilibria of
opinion dynamics with distance-dependent interaction rates. The closed form
expressions for this class of dynamics are obtained for the two agent case.
However the results can be used in mean-field models featuring several agents
whose interaction rates depend on the empirical average of their opinions. The
technique also applies to linear dynamics, namely with a constant interaction
rate, on an interaction graph
Reality Inspired Voter Models: A Mini-Review
This mini-review presents extensions of the voter model that incorporate
various plausible features of real decision-making processes by individuals.
Although these generalizations are not calibrated by empirical data, the
resulting dynamics are suggestive of realistic collective social behaviors.Comment: 13 pages, 16 figures. Version 2 contains various proofreading
improvements. V3: fixed one trivial typ
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