scholarly journals Quantum Calcium-Ion Interactions with EEG

Sci ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 7 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Closed Form ◽  
Path Integral ◽  
Stochastic Systems ◽  
Analytic Solution ◽  
Short Term Memory ◽  
Mathematical Physics ◽  
Modest Improvement ◽  
Classical Physics ◽  
Arbitrary Time ◽  
Eeg Data

Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. Objective: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. Conclusions: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.

scholarly journals Quantum Calcium-Ion Interactions with EEG

Sci ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 20 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Closed Form ◽  
Path Integral ◽  
Stochastic Systems ◽  
Analytic Solution ◽  
Short Term Memory ◽  
Mathematical Physics ◽  
Modest Improvement ◽  
Classical Physics ◽  
Arbitrary Time ◽  
Eeg Data

Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. Objective: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. Conclusions: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.

scholarly journals Quantum Calcium-Ion Interactions with EEG

Sci ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 7
Author(s):  
Lester Ingber
Keyword(s):  
Closed Form ◽  
Path Integral ◽  
Stochastic Systems ◽  
Analytic Solution ◽  
Short Term Memory ◽  
Mathematical Physics ◽  
Modest Improvement ◽  
Classical Physics ◽  
Arbitrary Time ◽  
Eeg Data

Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. Objective: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. Conclusions: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.

scholarly journals Recurrent neural network-based acute concussion classifier using raw resting state EEG data

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Karun Thanjavur ◽  
Arif Babul ◽  
Brandon Foran ◽  
Maya Bielecki ◽  
Adam Gilchrist ◽  
...  
Keyword(s):  
Neural Network ◽  
Recurrent Neural Network ◽  
Resting State ◽  
Short Term Memory ◽  
Characteristic Curve ◽  
Health Concern ◽  
Adolescent Athletes ◽  
Individual Level ◽  
Diffuse Brain Injury ◽  
Eeg Data

AbstractConcussion is a global health concern. Despite its high prevalence, a sound understanding of the mechanisms underlying this type of diffuse brain injury remains elusive. It is, however, well established that concussions cause significant functional deficits; that children and youths are disproportionately affected and have longer recovery time than adults; and that individuals suffering from a concussion are more prone to experience additional concussions, with each successive injury increasing the risk of long term neurological and mental health complications. Currently, the most significant challenge in concussion management is the lack of objective, clinically- accepted, brain-based approaches for determining whether an athlete has suffered a concussion. Here, we report on our efforts to address this challenge. Specifically, we introduce a deep learning long short-term memory (LSTM)-based recurrent neural network that is able to distinguish between non-concussed and acute post-concussed adolescent athletes using only short (i.e. 90 s long) samples of resting state EEG data as input. The athletes were neither required to perform a specific task nor expected to respond to a stimulus during data collection. The acquired EEG data were neither filtered, cleaned of artefacts, nor subjected to explicit feature extraction. The LSTM network was trained and validated using data from 27 male, adolescent athletes with sports related concussion, benchmarked against 35 non-concussed adolescent athletes. During rigorous testing, the classifier consistently identified concussions with an accuracy of > 90% and achieved an ensemble median Area Under the Receiver Operating Characteristic Curve (ROC/AUC) equal to 0.971. This is the first instance of a high-performing classifier that relies only on easy-to-acquire resting state, raw EEG data. Our concussion classifier represents a promising first step towards the development of an easy-to-use, objective, brain-based, automatic classification of concussion at an individual level.

An investment model with entry and exit decisions

2000 ◽  
Vol 37 (2) ◽  
pp. 547-559 ◽  
Author(s):  
J. Kate Duckworth ◽  
Mihail Zervos
Keyword(s):  
Dynamic Programming ◽  
Closed Form ◽  
Production Scheduling ◽  
Analytic Solution ◽  
Investment Model ◽  
Programming Approach ◽  
Entry And Exit ◽  
Dynamic Programming Approach ◽  
Exit Decisions ◽  
Parameter Values

We consider an investment model which generalizes a number of models that have been studied in the literature. The model involves entry and exit decisions as well as decisions relating to production scheduling. We then address the problem of its valuation from the standpoint of the dynamic programming approach. Our analysis results in a closed form analytic solution that can take qualitatively different forms depending on parameter values.

Some Properties of R. G. D. Allen's Treatment of Kalecki's 1935 Model of Business Cycles

2002 ◽  
Vol 24 (4) ◽  
pp. 463-474
Author(s):  
John V. Baxley ◽  
John C. Moorhouse
Keyword(s):  
Business Cycles ◽  
Business Cycle ◽  
Mathematical Models ◽  
Closed Form ◽  
Analytic Solution ◽  
John Maynard Keynes

More than sixty-five years have passed since Michal Kalecki (1935) published one of the first formal mathematical models of business cycles. His paper presents a closed-form analytic solution. This characteristic, among others, sets Kalecki's work apart from that of contemporary literary business cycle theorists such as Friedrich A. Hayek (1935) and John Maynard Keynes (1936).

scholarly journals Using AI-Based Classification Techniques to Process EEG Data Collected during the Visual Short-Term Memory Assessment

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Milos Antonijevic ◽  
Miodrag Zivkovic ◽  
Sladjana Arsic ◽  
Aleksandar Jevremovic
Keyword(s):  
Visual Information ◽  
Short Term Memory ◽  
Support Vector ◽  
Short Term ◽  
Term Memory ◽  
Memory Assessment ◽  
Visual Short Term Memory ◽  
Eeg Data ◽  
Short Period

Visual short-term memory (VSTM) is defined as the ability to remember a small amount of visual information, such as colors and shapes, during a short period of time. VSTM is a part of short-term memory, which can hold information up to 30 seconds. In this paper, we present the results of research where we classified the data gathered by using an electroencephalogram (EEG) during a VSTM experiment. The experiment was performed with 12 participants that were required to remember as many details as possible from the two images, displayed for 1 minute. The first assessment was done in an isolated environment, while the second assessment was done in front of the other participants, in order to increase the stress of the examinee. The classification of the EEG data was done by using four algorithms: Naive Bayes, support vector, KNN, and random forest. The results obtained show that AI-based classification could be successfully used in the proposed way, since we were able to correctly classify the order of the images presented 90.12% of the time and type of the displayed image 90.51% of the time.

Nonlinear Oscillator Stochastic Response and Survival Probability Determination via the Wiener Path Integral

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
Yuanjin Zhang ◽  
Ioannis A. Kougioumtzoglou
Keyword(s):  
Closed Form ◽  
Path Integral ◽  
Survival Probability ◽  
Nonlinear Oscillator ◽  
Transition Probability ◽  
Computational Cost ◽  
Discrete Version ◽  
Stochastic Response ◽  
Transition Probability Density ◽  
Approximate Analytical Expression

A Wiener path integral (WPI) technique based on a variational formulation is developed for nonlinear oscillator stochastic response determination and reliability assessment. This is done in conjunction with a stochastic averaging/linearization treatment of the problem. Specifically, first, the nonlinear oscillator is cast into an equivalent linear one with time-varying stiffness and damping elements. Next, relying on the concept of the most probable path, a closed-form approximate analytical expression for the oscillator joint transition probability density function (PDF) is derived for small time intervals. Finally, the transition PDF in conjunction with a discrete version of the Chapman–Kolmogorov (C–K) equation is utilized for advancing the solution in short-time steps. In this manner, not only the nonstationary response PDF but also the oscillator survival probability and first-passage PDF are determined. In comparison with existing numerical path integral schemes, a significant advantage of the proposed WPI technique is that closed-form analytical expressions are derived for the involved multidimensional integrals; thus, the computational cost is kept at a minimum level. The hardening Duffing and the bilinear hysteretic oscillators are considered as numerical examples. Comparisons with pertinent Monte Carlo simulation (MCS) data demonstrate the reliability of the developed technique.

scholarly journals Closed-Form Analytic Solution of Cloud Dissipation for a Mixed-Layer Model

2017 ◽  
Vol 74 (8) ◽  
pp. 2525-2556 ◽  
Author(s):  
Bengu Ozge Akyurek ◽  
Jan Kleissl
Keyword(s):  
Boundary Conditions ◽  
Closed Form ◽  
Mixed Layer ◽  
Analytic Solution ◽  
Cloud Base ◽  
Layer Model ◽  
Stratocumulus Clouds ◽  
Initial And Boundary Conditions ◽  
Cloud Thickness ◽  
Mixed Layer Model

Abstract Stratocumulus clouds play an important role in climate cooling and are hard to predict using global climate and weather forecast models. Thus, previous studies in the literature use observations and numerical simulation tools, such as large-eddy simulation (LES), to solve the governing equations for the evolution of stratocumulus clouds. In contrast to the previous works, this work provides an analytic closed-form solution to the cloud thickness evolution of stratocumulus clouds in a mixed-layer model framework. With a focus on application over coastal lands, the diurnal cycle of cloud thickness and whether or not clouds dissipate are of particular interest. An analytic solution enables the sensitivity analysis of implicitly interdependent variables and extrema analysis of cloud variables that are hard to achieve using numerical solutions. In this work, the sensitivity of inversion height, cloud-base height, and cloud thickness with respect to initial and boundary conditions, such as Bowen ratio, subsidence, surface temperature, and initial inversion height, are studied. A critical initial cloud thickness value that can be dissipated pre- and postsunrise is provided. Furthermore, an extrema analysis is provided to obtain the minima and maxima of the inversion height and cloud thickness within 24 h. The proposed solution is validated against LES results under the same initial and boundary conditions.

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