scholarly journals Intrinsic Computation of a Monod-Wyman-Changeux Molecule

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 599
Author(s):  
Sarah Marzen
Keyword(s):  
Stochastic Process ◽  
Transfer Function ◽  
Mutual Information ◽  
Causal Structure ◽  
Excess Entropy ◽  
Sufficient Statistics ◽  
Statistical Complexity ◽  
Kinetic Rates ◽  
Causal States ◽  
The Relationship

Causal states are minimal sufficient statistics of prediction of a stochastic process, their coding cost is called statistical complexity, and the implied causal structure yields a sense ofthe process’ “intrinsic computation”. We discuss how statistical complexity changes with slight changes to the underlying model– in this case, a biologically-motivated dynamical model, that of aMonod-Wyman-Changeux molecule. Perturbations to kinetic rates cause statistical complexity to jump from finite to infinite. The same is not true for excess entropy, the mutual information between past and future, or for the molecule’s transfer function. We discuss the implications of this for the relationship between intrinsic and functional computation of biological sensory systems.

scholarly journals Process Dimension of Classical and Non-Commutative Processes

2012 ◽  
Vol 19 (01) ◽  
pp. 1250007
Author(s):  
Wolfgang Löhr ◽  
Arleta Szkoła ◽  
Nihat Ay
Keyword(s):  
Stochastic Process ◽  
Ergodic Decomposition ◽  
Statistical Complexity ◽  
Lower Semi ◽  
Decomposition Formula ◽  
Close Relationship ◽  
Natural Characteristic ◽  
Causal States ◽  
Definition Of ◽  
Process Dimension

We treat observable operator models (OOM) and their non-commutative generalisation, which we call NC-OOMs. A natural characteristic of a stochastic process in the context of classical OOM theory is the process dimension. We investigate its properties within the more general formulation, which allows one to consider process dimension as a measure of complexity of non-commutative processes: We prove lower semi-continuity, and derive an ergodic decomposition formula. Further, we obtain results on the close relationship between the canonical OOM and the concept of causal states which underlies the definition of statistical complexity. In particular, the topological statistical complexity, i.e. the logarithm of the number of causal states, turns out to be an upper bound to the logarithm of process dimension.

Pulse-Width Modulated Amplifier for DC Servo System and Its Matlab Simulation

2015 ◽  
Vol 9 (1) ◽  
pp. 625-631
Author(s):  
Ma Xiaocheng ◽  
Zhang Haotian ◽  
Cheng Yiqing ◽  
Zhu Lina ◽  
Wu Dan
Keyword(s):  
Mathematical Model ◽  
Transfer Function ◽  
Input Signal ◽  
Pulse Width ◽  
Rotation Speed ◽  
Servo Motor ◽  
Matlab Simulation ◽  
Pulse Width Modulated ◽  
Signal Changes ◽  
The Relationship

This paper introduces a mathematical model for Pulse-Width Modulated Amplifier for DC Servo Motor. The relationship between pulse-width modulated (PWM) signal and reference rotation speed is specified, and a general model of motor represented by transfer function is also put forward. When the input signal changes, the rotation speed of the servo motor will change accordingly. By changing zeros and poles, transient performance of this system is discussed in detail, and optimal ranges of the parameters is recommended at the end of discussion.

scholarly journals A Bootstrap Method to Test Granger-Causality in the Frequency Domain

2021 ◽  
Author(s):  
Matteo Farnè ◽  
Angela Montanari
Keyword(s):  
Stochastic Process ◽  
Frequency Domain ◽  
Granger Causality ◽  
Bootstrap Method ◽  
Money Stock ◽  
Bootstrap Test ◽  
Low Frequencies ◽  
Economic Output ◽  
Stationary Bootstrap ◽  
The Relationship

AbstractWe propose a bootstrap test for unconditional and conditional Granger-causality spectra in the frequency domain. Our test aims to detect if the causality at a particular frequency is systematically different from zero. In particular, we consider a stochastic process derived applying independently the stationary bootstrap to the original series. At each frequency, we test the sample causality against the distribution of the median causality across frequencies estimated for that process. Via our procedure, we infer about the relationship between money stock and GDP in the Euro Area during the period 1999–2017. We point out that the money stock aggregate M1 had a significant impact on economic output at all frequencies, while the opposite relationship is significant only at low frequencies.

scholarly journals Improvement of Snowgauge Collection Efficiency through a knowledge of solid precipitation fallspeed

2021 ◽  
Author(s):  
Nicolas R. Leroux ◽  
Julie M. Thériault ◽  
Roy Rasmussen
Keyword(s):  
Wind Speed ◽  
Transfer Function ◽  
Transfer Functions ◽  
Collection Efficiency ◽  
Particle Diameter ◽  
Field Site ◽  
Solid Precipitation ◽  
Gauge Data ◽  
The Relationship ◽  
Measured Particle

AbstractThe collection efficiency (CE) of a typical gauge-shield configuration decreases with increasing wind speed, with a high scatter for a given wind speed. The scatter in the CE for a given wind speed arises in part from the variability in the characteristics of falling snow and atmospheric turbulence. This study uses weighing gauge data collected at the Marshall Field Site near Boulder, Colorado during the WMO Solid Precipitation InterComparison Experiment (SPICE) to show that the scatter in the collection efficiency can be reduced by considering the fallspeed of solid precipitation particle types. Particle diameter and fallspeed data from a laser disdrometer were used to arrive at this conclusion. In particular, the scatter in the CE of an unshielded snow gauge and a single Alter shield snow gauge is shown to be largely produced by the variation in measured particle fallspeed. The CE was divided into two classes depending on the measured mean-event particle fallspeed. Slower-falling particles were associated with a lower CE. A new transfer function (i.e. the relationship between CE and other meteorological variables, such as wind speed or air temperature) that includes the fallspeed of the hydrometeors was developed. The RMSE of the adjusted precipitation with respect to a weighing gauge placed in a Double Fence Intercomparison Reference was lower than using previously developed transfer functions. This shows that the measured fallspeed of solid precipitation with a laser disdrometer accounts for a large amount of the observed scatter in weighing gauge collection efficiency.

DEEP CLASSES

2016 ◽  
Vol 22 (2) ◽  
pp. 249-286 ◽  
Author(s):  
LAURENT BIENVENU ◽  
CHRISTOPHER P. PORTER
Keyword(s):  
Mutual Information ◽  
Initial Segment ◽  
Computability Theory ◽  
Binary Sequences ◽  
Algorithmic Randomness ◽  
Positive Probability ◽  
Probabilistic Algorithm ◽  
Image Position ◽  
The Relationship ◽  
Mass Problems

AbstractA set of infinite binary sequences ${\cal C} \subseteq 2$ℕ is negligible if there is no partial probabilistic algorithm that produces an element of this set with positive probability. The study of negligibility is of particular interest in the context of ${\rm{\Pi }}_1^0 $ classes. In this paper, we introduce the notion of depth for ${\rm{\Pi }}_1^0 $ classes, which is a stronger form of negligibility. Whereas a negligible ${\rm{\Pi }}_1^0 $ class ${\cal C}$ has the property that one cannot probabilistically compute a member of ${\cal C}$ with positive probability, a deep ${\rm{\Pi }}_1^0 $ class ${\cal C}$ has the property that one cannot probabilistically compute an initial segment of a member of ${\cal C}$ with high probability. That is, the probability of computing a length n initial segment of a deep ${\rm{\Pi }}_1^0 $ class converges to 0 effectively in n.We prove a number of basic results about depth, negligibility, and a variant of negligibility that we call tt-negligibility. We provide a number of examples of deep ${\rm{\Pi }}_1^0 $ classes that occur naturally in computability theory and algorithmic randomness. We also study deep classes in the context of mass problems, examine the relationship between deep classes and certain lowness notions in algorithmic randomness, and establish a relationship between members of deep classes and the amount of mutual information with Chaitin’s Ω.

scholarly journals Correlated activity favors synergistic processing in local cortical networks in vitro at synaptically relevant timescales

2020 ◽  
Vol 4 (3) ◽  
pp. 678-697
Author(s):  
Samantha P. Sherrill ◽  
Nicholas M. Timme ◽  
John M. Beggs ◽  
Ehren L. Newman
Keyword(s):  
Information Processing ◽  
Mutual Information ◽  
Information Transmission ◽  
Cortical Circuits ◽  
Correlated Activity ◽  
Neural Information ◽  
Neural Information Processing ◽  
The Relationship ◽  
Information Values

Neural information processing is widely understood to depend on correlations in neuronal activity. However, whether correlation is favorable or not is contentious. Here, we sought to determine how correlated activity and information processing are related in cortical circuits. Using recordings of hundreds of spiking neurons in organotypic cultures of mouse neocortex, we asked whether mutual information between neurons that feed into a common third neuron increased synergistic information processing by the receiving neuron. We found that mutual information and synergistic processing were positively related at synaptic timescales (0.05–14 ms), where mutual information values were low. This effect was mediated by the increase in information transmission—of which synergistic processing is a component—that resulted as mutual information grew. However, at extrasynaptic windows (up to 3,000 ms), where mutual information values were high, the relationship between mutual information and synergistic processing became negative. In this regime, greater mutual information resulted in a disproportionate increase in redundancy relative to information transmission. These results indicate that the emergence of synergistic processing from correlated activity differs according to timescale and correlation regime. In a low-correlation regime, synergistic processing increases with greater correlation, and in a high-correlation regime, synergistic processing decreases with greater correlation.

scholarly journals On the convergence of quadratic variation for compound fractional Poisson processes

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Enrico Scalas ◽  
Noèlia Viles
Keyword(s):  
Stochastic Process ◽  
Random Variable ◽  
Quadratic Variation ◽  
Poisson Processes ◽  
Renewal Processes ◽  
The Relationship ◽  
Compound Renewal Processes

AbstractThe relationship between quadratic variation for compound renewal processes and M-Wright functions is discussed. The convergence of quadratic variation is investigated both as a random variable (for given t) and as a stochastic process.

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