scholarly journals Memory and Markov Blankets

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1105
Author(s):  
Thomas Parr ◽  
Lancelot Da Costa ◽  
Conor Heins ◽  
Maxwell James D. Ramstead ◽  
Karl J. Friston
Keyword(s):  
Steady State ◽  
Conditional Independence ◽  
Initial Conditions ◽  
Theoretical Biology ◽  
State Density ◽  
Biological Entity ◽  
Apparent Paradox ◽  
Markov Blanket ◽  
Time Required ◽  
The Brain

In theoretical biology, we are often interested in random dynamical systems—like the brain—that appear to model their environments. This can be formalized by appealing to the existence of a (possibly non-equilibrium) steady state, whose density preserves a conditional independence between a biological entity and its surroundings. From this perspective, the conditioning set, or Markov blanket, induces a form of vicarious synchrony between creature and world—as if one were modelling the other. However, this results in an apparent paradox. If all conditional dependencies between a system and its surroundings depend upon the blanket, how do we account for the mnemonic capacity of living systems? It might appear that any shared dependence upon past blanket states violates the independence condition, as the variables on either side of the blanket now share information not available from the current blanket state. This paper aims to resolve this paradox, and to demonstrate that conditional independence does not preclude memory. Our argument rests upon drawing a distinction between the dependencies implied by a steady state density, and the density dynamics of the system conditioned upon its configuration at a previous time. The interesting question then becomes: What determines the length of time required for a stochastic system to ‘forget’ its initial conditions? We explore this question for an example system, whose steady state density possesses a Markov blanket, through simple numerical analyses. We conclude with a discussion of the relevance for memory in cognitive systems like us.

scholarly journals Modules or Mean-Fields?

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 552 ◽  
Author(s):  
Thomas Parr ◽  
Noor Sajid ◽  
Karl J. Friston
Keyword(s):  
Steady State ◽  
Message Passing ◽  
Mean Field Theory ◽  
Functional Anatomy ◽  
Mean Field ◽  
State Density ◽  
Stochastic Dynamical Systems ◽  
Conditional Independency ◽  
The Brain ◽  
Non Equilibrium

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

scholarly journals Post-translational processing of urea amidolyase in Saccharomyces cerevisiae.

1982 ◽  
Vol 2 (7) ◽  
pp. 800-804 ◽  
Author(s):  
R A Sumrada ◽  
G Chisholm ◽  
T G Cooper
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Steady State ◽  
State Level ◽  
Steady State Level ◽  
Prosthetic Group ◽  
Apparent Paradox ◽  
Multifunctional Protein ◽  
Group A ◽  
Time Required ◽  
Sequential Induction

Urea amidolyase catalyzes the two reactions (urea carboxylase and a allophanate hydrolase) associated with urea degradation in Saccharomyces cerevisiae. Past work has shown that both reactions are catalyzed by a 204-kilodalton, multifunctional protein. In view of these observations, it was surprising to find that on induction at 22 degrees C, approximately 2 to 6 min elapsed between the appearance of allophanate hydrolase and urea carboxylase activities. In search of an explanation for this apparent paradox, we determined whether or not a detectable period of time elapsed between the appearance of allophanate hydrolase activity and activation of the urea carboxylase domain by the addition of biotin. We found that a significant portion of the protein produced immediately after the onset of induction lacked the prosthetic group. A steady-state level of biotin-free enzyme was reached 16 min after induction and persisted indefinitely thereafter. These data are consistent with the suggestion that sequential induction of allophanate hydrolase and urea carboxylase activities results from the time required to covalently bind biotin to the latter domain of the protein.

scholarly journals A Note on Migration Perturbation and Convergence Rates to a Steady State

2020 ◽  
Vol 11 (4) ◽  
pp. 17-30
Author(s):  
Lawrence Edward Blume ◽  
Aleksandra Andreevna Lukina
Keyword(s):  
Steady State ◽  
Brain Drain ◽  
Population Model ◽  
Convergence Rates ◽  
Population Distribution ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Distribution Vector ◽  
Time Required ◽  
The Brain

Using tools developed in the Markov chains literature, we study convergence times in the Leslie population model in the short and middle run. Assuming that the population is in a steady-state and reproduces itself period after period, we address the following question: how long will it take to get back to the steady-state if the population distribution vector was affected by some shock as, for instance, the “brain drain”? We provide lower and upper bounds for the time required to reach a given distance from the steady-state.

A Fuzzy Cognitive Mapping Approach to the Conference Selection Problem

2020 ◽  
Vol 19 (06) ◽  
pp. 1451-1484
Author(s):  
Cigdem Kadaifci ◽  
Umut Asan ◽  
Y. Ilker Topcu
Keyword(s):  
Steady State ◽  
Cognitive Mapping ◽  
Initial Conditions ◽  
Mathematical Formulation ◽  
Threshold Function ◽  
Fuzzy Cognitive Mapping ◽  
Factors Affecting ◽  
Threshold Functions ◽  
Time Required ◽  
Academic Conferences

Academic conferences are popular platforms for academicians to share their research with colleagues, get feedback, and stay up to date on recent academic studies. Conferences also provide opportunities for the participants to express themselves, expand their network, and become socialized. However, academicians are forced to choose a limited number of conferences to participate due to several different factors such as time required for preparing a research, traveling and lodging expenses, and conference fees. At this multi-criteria decision problem, relevant factors can be used to evaluate the alternatives (i.e., academic conferences to participate) and prioritization of these factors would be necessary in advance. To address this issue, this study suggests an improved fuzzy cognitive mapping (FCM) approach to analyze factors affecting the choice of academic conferences to participate. The classical FCM allows to observe the dynamic behavior of complex systems during time. While the approach is widely used in different areas, it has considerable drawbacks: (i) producing same steady state values under different initial conditions and (ii) yielding completely different steady state values when different threshold functions are used. The new approach provides a mathematical formulation that produces steady state values sensitive to initial conditions. Since the selection of the threshold function in classical FCM is a highly subjective choice, the proposed approach offers an alternative way to obtain comparable values.

Post-translational processing of urea amidolyase in Saccharomyces cerevisiae

1982 ◽  
Vol 2 (7) ◽  
pp. 800-804
Author(s):  
R A Sumrada ◽  
G Chisholm ◽  
T G Cooper
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Steady State ◽  
State Level ◽  
Steady State Level ◽  
Prosthetic Group ◽  
Apparent Paradox ◽  
Multifunctional Protein ◽  
Group A ◽  
Time Required ◽  
Sequential Induction

Urea amidolyase catalyzes the two reactions (urea carboxylase and a allophanate hydrolase) associated with urea degradation in Saccharomyces cerevisiae. Past work has shown that both reactions are catalyzed by a 204-kilodalton, multifunctional protein. In view of these observations, it was surprising to find that on induction at 22 degrees C, approximately 2 to 6 min elapsed between the appearance of allophanate hydrolase and urea carboxylase activities. In search of an explanation for this apparent paradox, we determined whether or not a detectable period of time elapsed between the appearance of allophanate hydrolase activity and activation of the urea carboxylase domain by the addition of biotin. We found that a significant portion of the protein produced immediately after the onset of induction lacked the prosthetic group. A steady-state level of biotin-free enzyme was reached 16 min after induction and persisted indefinitely thereafter. These data are consistent with the suggestion that sequential induction of allophanate hydrolase and urea carboxylase activities results from the time required to covalently bind biotin to the latter domain of the protein.

scholarly journals Future climates: Markov blankets and active inference in the biosphere

2020 ◽  
Vol 17 (172) ◽  
pp. 20200503 ◽  
Author(s):  
Sergio Rubin ◽  
Thomas Parr ◽  
Lancelot Da Costa ◽  
Karl Friston
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Solar Radiation ◽  
Theoretical Biology ◽  
Metabolic Rates ◽  
Markov Blanket ◽  
Gaia Hypothesis ◽  
The Earth ◽  
Internal States ◽  
Non Equilibrium

We formalize the Gaia hypothesis about the Earth climate system using advances in theoretical biology based on the minimization of variational free energy. This amounts to the claim that non-equilibrium steady-state dynamics—that underwrite our climate—depend on the Earth system possessing a Markov blanket. Our formalization rests on how the metabolic rates of the biosphere (understood as Markov blanket's internal states) change with respect to solar radiation at the Earth's surface (i.e. external states), through the changes in greenhouse and albedo effects (i.e. active states) and ocean-driven global temperature changes (i.e. sensory states). Describing the interaction between the metabolic rates and solar radiation as climatic states—in a Markov blanket—amounts to describing the dynamics of the internal states as actively inferring external states. This underwrites climatic non-equilibrium steady-state through free energy minimization and thus a form of planetary autopoiesis.

Time consumption and quality of an automated fusion tool for SPECT and MRI images of the brain

2003 ◽  
Vol 42 (05) ◽  
pp. 215-219
Author(s):  
G. Platsch ◽  
A. Schwarz ◽  
K. Schmiedehausen ◽  
B. Tomandl ◽  
W. Huk ◽  
...  
Keyword(s):  
Data Sets ◽  
3D Mri ◽  
Clinical Routine ◽  
Fusion Procedure ◽  
3D Data ◽  
Mri Scans ◽  
2D Data ◽  
Time Required ◽  
The Brain ◽  
Manual Correction

Summary: Aim: Although the fusion of images from different modalities may improve diagnostic accuracy, it is rarely used in clinical routine work due to logistic problems. Therefore we evaluated performance and time needed for fusing MRI and SPECT images using a semiautomated dedicated software. Patients, material and Method: In 32 patients regional cerebral blood flow was measured using 99mTc ethylcystein dimer (ECD) and the three-headed SPECT camera MultiSPECT 3. MRI scans of the brain were performed using either a 0,2 T Open or a 1,5 T Sonata. Twelve of the MRI data sets were acquired using a 3D-T1w MPRAGE sequence, 20 with a 2D acquisition technique and different echo sequences. Image fusion was performed on a Syngo workstation using an entropy minimizing algorithm by an experienced user of the software. The fusion results were classified. We measured the time needed for the automated fusion procedure and in case of need that for manual realignment after automated, but insufficient fusion. Results: The mean time of the automated fusion procedure was 123 s. It was for the 2D significantly shorter than for the 3D MRI datasets. For four of the 2D data sets and two of the 3D data sets an optimal fit was reached using the automated approach. The remaining 26 data sets required manual correction. The sum of the time required for automated fusion and that needed for manual correction averaged 320 s (50-886 s). Conclusion: The fusion of 3D MRI data sets lasted significantly longer than that of the 2D MRI data. The automated fusion tool delivered in 20% an optimal fit, in 80% manual correction was necessary. Nevertheless, each of the 32 SPECT data sets could be merged in less than 15 min with the corresponding MRI data, which seems acceptable for clinical routine use.

Steady-State Dynamic Response of a Limited Slip System

1968 ◽  
Vol 35 (2) ◽  
pp. 322-326 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Slip System ◽  
External Load ◽  
Initial Conditions ◽  
Viscous Damping ◽  
Steady State Response ◽  
Response Curves ◽  
State Response ◽  
System Nonlinearity

The steady-state response of a system constrained by a limited slip joint and excited by a trigonometrically varying external load is discussed. It is shown that the system may possess such features as disconnected response curves and jumps in response depending on the strength of the system nonlinearity, the level of excitation, the amount of viscous damping, and the initial conditions of the system.

Steady-state levels of pro-dynorphin-related end-products from the brain of the amphibian, Xenopus laevis

1989 ◽  
Vol 479 (1) ◽  
pp. 162-166 ◽  
Author(s):  
Catherine A. Sei ◽  
Robert Richard ◽  
Robert M. Dores
Keyword(s):  
Steady State ◽  
Xenopus Laevis ◽  
End Products ◽  
Steady State Levels ◽  
The Brain

scholarly journals Disease control as an optimization problem

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0257958
Author(s):  
Miguel Navascués ◽  
Costantino Budroni ◽  
Yelena Guryanova
Keyword(s):  
Disease Control ◽  
Stochastic Models ◽  
Optimization Problem ◽  
Initial Conditions ◽  
Optimization Theory ◽  
Model Parameters ◽  
Grid Search ◽  
Brute Force ◽  
Time Required ◽  
Policy Optimization

In the context of epidemiology, policies for disease control are often devised through a mixture of intuition and brute-force, whereby the set of logically conceivable policies is narrowed down to a small family described by a few parameters, following which linearization or grid search is used to identify the optimal policy within the set. This scheme runs the risk of leaving out more complex (and perhaps counter-intuitive) policies for disease control that could tackle the disease more efficiently. In this article, we use techniques from convex optimization theory and machine learning to conduct optimizations over disease policies described by hundreds of parameters. In contrast to past approaches for policy optimization based on control theory, our framework can deal with arbitrary uncertainties on the initial conditions and model parameters controlling the spread of the disease, and stochastic models. In addition, our methods allow for optimization over policies which remain constant over weekly periods, specified by either continuous or discrete (e.g.: lockdown on/off) government measures. We illustrate our approach by minimizing the total time required to eradicate COVID-19 within the Susceptible-Exposed-Infected-Recovered (SEIR) model proposed by Kissler et al. (March, 2020).

Sign in / Sign up

Export Citation Format

Share Document