scholarly journals Mathematical Models of Consciousness

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 609
Author(s):  
Johannes Kleiner
Keyword(s):  
Mathematical Models ◽  
Conscious Experience ◽  
Theory Building ◽  
Mathematical Representation ◽  
Mathematical Framework ◽  
Physical Domain ◽  
Mathematical Structures ◽  
Building Process ◽  
Key Characteristics ◽  
Epistemic Context

In recent years, promising mathematical models have been proposed that aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully motivated, their mathematical formalism has not. In this article, we aim to remedy this situation. We give an account of what warrants mathematical representation of phenomenal experience, derive a general mathematical framework that takes into account consciousness’ epistemic context, and study which mathematical structures some of the key characteristics of conscious experience imply, showing precisely where mathematical approaches allow to go beyond what the standard methodology can do. The result is a general mathematical framework for models of consciousness that can be employed in the theory-building process.

Abstraction and Representational Capacity in Computational Structures

2019 ◽  
pp. 210-229
Author(s):  
Michael Weisberg
Keyword(s):  
Mathematical Models ◽  
Computational Models ◽  
Mathematical Structure ◽  
Narrative Form ◽  
Mathematical Structures ◽  
Computational Structure ◽  
Representational Capacity ◽  
Computational Structures

Michael Weisberg’s book Simulation and Similarity argued that although mathematical models are sometimes described in narrative form, they are best understood as interpreted mathematical structures. But how can a mathematical structure be causal, as many models described in narrative seem to be? This chapter argues that models with apparently narrative form are actually computational structures. It explores this suggestion in detail, examining what computational structure consists of, the resources it offers modelers, and why attempting to re-describe computational models as imaginary concrete systems fails even more dramatically than it does for mathematical models.

scholarly journals An Organizing Principle for the Water-Energy-Food Nexus

2020 ◽  
Vol 12 (19) ◽  
pp. 8135
Author(s):  
Chad W. Higgins ◽  
Majdi Abou Najm
Keyword(s):  
Climate Change ◽  
Research Community ◽  
Future Generations ◽  
Mathematical Representation ◽  
Mathematical Framework ◽  
Natural Processes ◽  
Anthropogenic Inputs ◽  
Complex Interactions ◽  
Management Concept ◽  
Growth Habits

The nexus between water, energy, and food has recently evolved as a resource-management concept to deal with this intimately interwoven set of resources, their complex interactions, and the growing and continuously changing internal and external set of influencing factors, including climate change, population growth, habits and lifestyles alternations, and the dynamic prices of water, energy, and food. While an intriguing concept, the global research community is yet to identify a unifying conceptual and mathematical framework capable of adapting to integrate gathered knowledge and ensuring inclusivity by accounting for all significant interactions and feedbacks (including natural processes and anthropogenic inputs) within all nexus domains. We present an organizing roadmap for a conceptual and mathematical representation of the nexus. Our hope is that this representation will organize the nexus research and formalize a way for a generalizable framework that can be used to advance our understanding of those complex interactions, with hope that such an approach will lead to a more resilient future with sustained resources for the future generations.

scholarly journals Models for predicting damage due to accidents at energy objects and in energy systems of enterprises

2019 ◽  
Vol 110 ◽  
pp. 02041
Author(s):  
Irina Zaychenko ◽  
Nadezhda Grashchenko ◽  
Tatiana Saurenko ◽  
Vladimir Anisimov ◽  
Evgeniy Anisimov ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Energy Management ◽  
Stochastic Models ◽  
Energy Security ◽  
Economic Losses ◽  
Mathematical Representation ◽  
Security Measures ◽  
Short Period ◽  
Change Function ◽  
Supply Systems

Achieving energy security by preventing and timely eliminating the consequences of accidents at energy facilities and in energy supply systems of enterprises is one of the important tasks of energy management. The basis for planning appropriate energy security measures is the prediction of damage from these accidents. The purpose of forecasting is to assess the possibility of an accident occurring at some point in time and leading to a particular damage, and to assess the magnitude of this damage. The article proposed methodological approaches to the construction of mathematical models of such prediction. In this case, as an indicator of damage, the economic losses caused by these accidents are taken. The simulation is based on the representation of this indicator in the form of a step change function of the magnitude of losses in the event of an accident. Depending on the amount of information available in the period prior to forecasting, the mathematical representation of the forecasting problem is reduced to the construction of conditionally determined or stochastic models. Conditionally determined models allow obtaining acceptable damage estimates with a short period of retrospection and small amounts of information, and stochastic models with significantly large amounts. At the same time, the principle of “maximum uncertainty” formalized in the form of maximum entropy is the basis for removing uncertainty in the construction of both conditionally determined and stochastic models. Its use has allowed increasing the objectivity of forecasts by minimizing the subjective information used in modeling. The proposed approaches to the construction of mathematical models for predicting accidents at energy facilities and power supply systems of enterprises are the basis for creating specific techniques for solving relevant energy management tasks both at the micro level at the scale of individual enterprises and at the macro level at the scale of industries, regions and the state as a whole.

Load-Transmitter Constraint Sets: Part II—A Building Block Based Methodology for the Synthesis of Compliant Mechanisms

2010 ◽  
Author(s):  
Girish Krishnan ◽  
Charles Kim ◽  
Sridhar Kota
Keyword(s):  
Compliant Mechanisms ◽  
Load Flow ◽  
Flow Path ◽  
Mathematical Representation ◽  
Mathematical Framework ◽  
Systematic Design ◽  
Shape Morphing ◽  
Load Paths ◽  
Block Based ◽  
Extensive Computation

Designers have always conceptualized of load flow as a part of their initial design process for mechanisms and structures. However, the lack of mathematical representation of load flow makes it inappropriate to be included in systematic design processes. Load Transmitter Constraint (LTC) sets provide a mathematical framework for visualizing load paths in compliant mechanisms. In this paper we propose a systematic design methodology for compliant mechanisms by systematic combination of LTC sets. This enables the designer to conceptualize load flow and choose relevant LTC sets to enforce it. Apart from being intuitive this process gives an understanding of the importance of each member in the mechanism. Furthermore this theory enables accurate and deterministic design for given motion specification without the aid of extensive computation. In this paper we propose guidelines for the design of mechanisms with a single load flow path and multi load flow path, particularly relevant in shape morphing applications.

Modeling and prototyping of a soft closed-chain modular gripper

2019 ◽  
Vol 46 (1) ◽  
pp. 135-145 ◽  
Author(s):  
Muddasar Anwar ◽  
Toufik Al Khawli ◽  
Irfan Hussain ◽  
Dongming Gan ◽  
Federico Renda
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Chain Structure ◽  
Mathematical Representation ◽  
Mathematical Framework ◽  
Complex Objects ◽  
Content Type ◽  
Design And Optimization ◽  
Closed Chain

Purpose This paper aims to present a soft closed-chain modular gripper for robotic pick-and-place applications. The proposed biomimetic gripper design is inspired by the Fin Ray effect, derived from fish fins physiology. It is composed of three axisymmetric fingers, actuated with a single actuator. Each finger has a modular under-actuated closed-chain structure. The finger structure is compliant in contact normal direction, with stiff crossbeams reorienting to help the finger structure conform around objects. Design/methodology/approach Starting with the design and development of the proposed gripper, a consequent mathematical representation consisting of closed-chain forward and inverse kinematics is detailed. The proposed mathematical framework is validated through the finite element modeling simulations. Additionally, a set of experiments was conducted to compare the simulated and prototype finger trajectories, as well as to assess qualitative grasping ability. Findings Key Findings are the presented mathematical model for closed-loop chain mechanisms, as well as design and optimization guidelines to develop controlled closed-chain grippers. Research limitations/implications The proposed methodology and mathematical model could be taken as a fundamental modular base block to explore similar distributed degrees of freedom (DOF) closed-chain manipulators and grippers. The enhanced kinematic model contributes to optimized dynamics and control of soft closed-chain grasping mechanisms. Practical implications The approach is aimed to improve the development of soft grippers that are required to grasp complex objects found in human–robot cooperation and collaborative robot (cobot) applications. Originality/value The proposed closed-chain mathematical framework is based on distributed DOFs instead of the conventional lumped joint approach. This is to better optimize and understand the kinematics of soft robotic mechanisms.

Inside the Municipal Lobby: Explaining Local Government Influence on the New EU Public Procurement Directives

2018 ◽  
Vol 16 (1) ◽  
pp. 193-214 ◽  
Author(s):  
Tom Verhelst
Keyword(s):  
Local Government ◽  
Causal Model ◽  
Public Procurement ◽  
Theory Building ◽  
Process Tracing ◽  
Opportunity Structure ◽  
Distinctive Character ◽  
Government Influence ◽  
Building Process ◽  
The Eu

Despite a challenging context, local authorities succeeded in influencing one of the most fiercely debated issues of the new EU Public Procurement Directives (2014): the (conditional) exemption of public-public cooperation (PPC). Using theory-building process-tracing this paper analyses the PPC-case to design a parsimonious causal model of successful municipal lobbying under challenging circumstances. The model represents a composed mechanism that triggered municipal lobby influence through the interplay of three basic parts: a strategic lobby campaign deployed by a strong protagonist, an external opportunity structure underpinning and strengthening the latter and a significantly receptive EU decision-making arena. Furthermore, the case suggests that in challenging lobby cases local government can profit from its distinctive character as an electorally legitimised and politically connected interest group to promote its interests in the EU polity.

scholarly journals An algorithm for discovering Lagrangians automatically from data

2015 ◽  
Vol 1 ◽  
pp. e31 ◽  
Author(s):  
Daniel J.A. Hills ◽  
Adrian M. Grütter ◽  
Jonathan J. Hudson
Keyword(s):  
Mathematical Models ◽  
Prior Knowledge ◽  
Model Building ◽  
Mechanical Systems ◽  
Future Evolution ◽  
Least Action ◽  
Building Process ◽  
Principle Of Least Action ◽  
Insight Into ◽  
Model Building Process

An activity fundamental to science is building mathematical models. These models are used to both predict the results of future experiments and gain insight into the structure of the system under study. We present an algorithm that automates the model building process in a scientifically principled way. The algorithm can take observed trajectories from a wide variety of mechanical systems and, without any other prior knowledge or tuning of parameters, predict the future evolution of the system. It does this by applying the principle of least action and searching for the simplest Lagrangian that describes the system’s behaviour. By generating this Lagrangian in a human interpretable form, it can also provide insight into the workings of the system.

scholarly journals Understanding the concept of π numbers for elementary school pre-service teachers on circle materials

2020 ◽  
Vol 8 (1) ◽  
pp. 12-19
Author(s):  
Dyah Worowirastri Ekowati ◽  
Beti Istanti Suwandayani
Keyword(s):  
Elementary School ◽  
Mathematical Models ◽  
The Other ◽  
Mathematical Representation ◽  
Research Subjects ◽  
Other Hand

This research aims to describe the understanding of the concept of π numbers for elementary school pre-service teachers on circle materials. The research was conducted qualitatively and the type of research conducted was descriptive. The instruments used in this research were observation, interviews, and documentation. The research subjects involved were 45 elementary school pre-service teachers. The results of the research showed that understanding the concept of π numbers for elementary school pre-service teachers had the advantage of classifying objects based on whether or not the requirements that form the concept are fulfilled, identifying the characteristics of operations or concepts and developing the important requirements and/or sufficient requirements of a concept. On the other hand, understanding the concept of π numbers for elementary school pre-service teachers had weaknesses in indicators when applying the concept logically, giving examples or not examples of concepts learned, presenting concepts in various forms of mathematical representation (tables, graphs, diagrams, drawings, sketches, mathematical models, or others) and linking various concepts in Mathematics and out of Mathematics.

scholarly journals A Synergistic Workspace for Human Consciousness Revealed by Integrated Information Decomposition

2020 ◽  
Author(s):  
Andrea I. Luppi ◽  
Pedro A.M. Mediano ◽  
Fernando E. Rosas ◽  
Judith Allanson ◽  
John D. Pickard ◽  
...  
Keyword(s):  
Information Processing ◽  
Human Brain ◽  
Information Integration ◽  
Conscious Experience ◽  
Human Information Processing ◽  
Loss Of Consciousness ◽  
Mathematical Framework ◽  
Human Consciousness ◽  
The Brain ◽  
Integrated Information

AbstractA central goal of neuroscience is to understand how the brain synthesises information from multiple inputs to give rise to a unified conscious experience. This process is widely believed to require integration of information. Here, we combine information theory and network science to address two fundamental questions: how is the human information-processing architecture functionally organised? And how does this organisation support human consciousness? To address these questions, we leverage the mathematical framework of Integrated Information Decomposition to delineate a cognitive architecture wherein specialised modules interact with a “synergistic global workspace,” comprising functionally distinct gateways and broadcasters. Gateway regions gather information from the specialised modules for processing in the synergistic workspace, whose contents are then further integrated to later be made widely available by broadcasters. Through data-driven analysis of resting-state functional MRI, we reveal that gateway regions correspond to the brain’s well-known default mode network, whereas broadcasters of information coincide with the executive control network. Demonstrating that this synergistic workspace supports human consciousness, we further apply Integrated Information Decomposition to BOLD signals to compute integrated information across the brain. By comparing changes due to propofol anaesthesia and severe brain injury, we demonstrate that most changes in integrated information happen within the synergistic workspace. Furthermore, it was found that loss of consciousness corresponds to reduced integrated information between gateway, but not broadcaster, regions of the synergistic workspace. Thus, loss of consciousness may coincide with breakdown of information integration by this synergistic workspace of the human brain. Together, these findings demonstrate that refining our understanding of information-processing in the human brain through Integrated Information Decomposition can provide powerful insights into the human neurocognitive architecture, and its role in supporting consciousness.

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