scholarly journals A Quick and Easy Way to Estimate Entropy and Mutual Information for Neuroscience

2021 ◽  
Vol 15 ◽  
Author(s):  
Mickael Zbili ◽  
Sylvain Rama
Keyword(s):  
Mutual Information ◽  
Sampling Bias ◽  
Computationally Efficient ◽  
Mathematical Methods ◽  
Text And Image ◽  
Experimental Conditions ◽  
Histological Data ◽  
Series Of Experiments ◽  
Entropy Encoding ◽  
Analytical Tools

Calculations of entropy of a signal or mutual information between two variables are valuable analytical tools in the field of neuroscience. They can be applied to all types of data, capture non-linear interactions and are model independent. Yet the limited size and number of recordings one can collect in a series of experiments makes their calculation highly prone to sampling bias. Mathematical methods to overcome this so-called “sampling disaster” exist, but require significant expertise, great time and computational costs. As such, there is a need for a simple, unbiased and computationally efficient tool for estimating the level of entropy and mutual information. In this article, we propose that application of entropy-encoding compression algorithms widely used in text and image compression fulfill these requirements. By simply saving the signal in PNG picture format and measuring the size of the file on the hard drive, we can estimate entropy changes through different conditions. Furthermore, with some simple modifications of the PNG file, we can also estimate the evolution of mutual information between a stimulus and the observed responses through different conditions. We first demonstrate the applicability of this method using white-noise-like signals. Then, while this method can be used in all kind of experimental conditions, we provide examples of its application in patch-clamp recordings, detection of place cells and histological data. Although this method does not give an absolute value of entropy or mutual information, it is mathematically correct, and its simplicity and broad use make it a powerful tool for their estimation through experiments.

scholarly journals A quick and easy way to estimate entropy and mutual information for neuroscience

2020 ◽  
Author(s):  
Mickael Zbili ◽  
Sylvain Rama
Keyword(s):  
Mutual Information ◽  
Sampling Bias ◽  
Computationally Efficient ◽  
Mathematical Methods ◽  
Text And Image ◽  
Electrophysiological Signals ◽  
Histological Data ◽  
Multiple Trials ◽  
Series Of Experiments ◽  
Analytical Tools

AbstractCalculations of entropy of a signal or mutual information between two variables are valuable analytical tools in the field of neuroscience. They can be applied to all types of data, capture nonlinear interactions and are model independent. Yet the limited size and number of recordings one can collect in a series of experiments makes their calculation highly prone to sampling bias. Mathematical methods to overcome this so called “sampling disaster” exist, but require significant expertise, great time and computational costs. As such, there is a need for a simple, unbiased and computationally efficient tool for reliable entropy and mutual information estimation. In this paper, we propose that application of entropy-coding compression algorithms widely used in text and image compression fulfill these requirements. By simply saving the signal in PNG picture format and measuring the size of the file on the hard drive, we can reliably estimate entropy through different conditions. Furthermore, with some simple modifications of the PNG file, we can also estimate mutual information between a stimulus and the observed responses into multiple trials. We show this using White noise signals, electrophysiological signals and histological data. Although this method does not give an absolute value of entropy or mutual information, it is mathematically correct, and its simplicity and broad use make it a powerful tool for their estimation through experiments.

Effect of combined citicoline and glutamate antibodies on acute, generalized convusions induced by pentylenetetrazole in mice

2018 ◽  
pp. 24-29
Author(s):  
М.Н. Карпова ◽  
Л.В. Кузнецова ◽  
Н.Ю. Клишина ◽  
Л.А. Ветрилэ
Keyword(s):  
Drug Combination ◽  
Subcutaneous Injection ◽  
Seizure Activity ◽  
Experimental Conditions ◽  
Slow Progression ◽  
Experiment Control ◽  
Effective Doses ◽  
Experimental Justification ◽  
Series Of Experiments ◽  
The Brain

Цель исследования. На 2 моделях острых генерализованных судорог (ОГС), вызванных конвульсантом пентилентетразолом (ПТЗ), изучить эффективность сочетанного применения ноотропа цитиколина - препарата с противосудорожным действием, нейрорегенеративной, нейропротекторной активностью и антител (АТ) к глутамату, обладающих противосудорожной активностью. Методика. Эксперименты выполнены на мышах-самцах линии C57Bl/6 (n = 87) массой 22-28 г. Эффективность сочетанного применения цитиколина и АТ к глутамату изучали на двух моделях ОГС. Выполнено 2 серии экспериментов. В 1-й серии ОГС вызывали внутривенным введением 1% раствора ПТЗ со скоростью 0,01 мл/с. Для изучения эффективности сочетанного применения препаратов определяли минимальное противосудорожное действие цитиколина (Цераксон, «Nicomed Ferrer Internaсional, S.A.») и АТ к глутамату при их внутрибрюшинном введении. С этой целью цитиколин вводили в дозах 500 и 300 мг/кг за 1 ч до введения ПТЗ, АТ к глутамату - в дозах 5 и 2,5 мг/кг за 1 ч 30 мин до введения ПТЗ. АТ к глутамату получали путем гипериммунизации кроликов соответствующим конъюгированным антигеном. Во 2-й серии ОГС вызывали подкожным введением ПТЗ в дозе 85 мг/кг. Для изучения эффективности сочетанного действия изучаемых препаратов последние вводили в минимально действующих дозах, установленных в 1-й серии экспериментов. Контролем во всех сериях опытов служили животные, которым вводили в аналогичных условиях и в том же объеме физиологический раствор. Результаты. Показано, что сочетанное применение цитиколина и АТ к глутамату в минимально действующих дозах (300 и 2,5 мг/кг соответственно) при моделировании ОГС не вызывало повышения судорожной активности мозга и усиления противосудорожных свойств препаратов. Заключение. Cочетанное применение цитиколина и АТ к глутамату в минимально действующих дозах не вызывало повышения судорожной активности мозга, что свидетельствует о безопасности совместного применения препаратов. Проведенное исследование может служить также экспериментальным обоснованием возможности использования сочетанного применения данных препаратов при судорогах с целью замедления прогрессирования нейродегенеративных процессов и благоприятного влияния на когнитивные функции. Aim. To study the effectivity of a combination of citicoline, a nootropic substance with neuroregenerative, neuroprotective, and anticonvulsant actions, and glutamate antibodies (АB) with an anticonvulsant action in two models of acute generalized convulsions (AGC) caused by the convulsant pentylenetetrazole (PTZ). Methods. Experiments were conducted on C57Bl/6 mice (n = 87) weighing 22-28 g. Effects of combined citicoline and glutamate АB were studied on two models of AGС. In the first series of experiments, AGС was induced by intravenous infusion of a 1% PTZ solution at 0.01 ml/sec. In the second series, AGС was induced by a subcutaneous injection of PTZ 85 mg/kg. To evaluate efficacy of the drug combination minimum intraperitoneal anticonvulsant doses of citicoline (Tserakson, Nicomed Ferrer Internacional, S.A.) and glutamate АB were determined. To this purpose, citicoline was administered at 500 and 300 mg/kg 1 h prior to PTZ, and glutamate АB was administered at 5 and 2.5 mg/kg 90 min prior to PTZ. Glutamate АB was obtained by hyperimmunization of rabbits with a respective conjugated antigen. In the second series of experiments, AGС was induced by a subcutaneous injection of PTZ 85 mg/kg. To evaluate the effect of the drug combination, the drugs were administered at the minimum effective doses determined in the first series of experiment. Control animals were injected with the same volume of saline in the same experimental conditions. Results. The combination of citicoline and glutamate AB used at minimum effective doses of 300 and 2.5 mg/kg, respectively, did not increase the seizure activity in the brain and enhanced anticonvulsant properties of the drugs in two models of AGС. Conclusion. The combination of citicoline and glutamate AT at minimum effective doses did not increase the convulsive activity in the brain, which supported safety of the drug combination. Besides, this study can serve as an experimental justification for using the drug combination in convulsions to favorably influence cognitive functions and slow progression of neurodegenerative processes.

Development of embryonic rat eyes in organ culture

Development ◽  
1968 ◽  
Vol 19 (3) ◽  
pp. 407-414
Author(s):  
R. Christy Armstrong ◽  
Joel J. Elias
Keyword(s):  
Organ Culture ◽  
Culture Medium ◽  
Folic Acid Deficiency ◽  
Experimental Conditions ◽  
Acid Deficiency ◽  
Series Of Experiments ◽  
Development In Vitro ◽  
Ocular System

Abnormalities of the ocular system which appear in organ culture in Waymouth's medium with freshly added glutamine (Armstrong & Elias, 1968) resemble those caused by transitory pteryolglutamic acid (PGA or folic acid) deficiency in vivo (Armstrong & Monie, 1966). The configurations of such malformations as lens herniations, retinal diverticula, and rosette-like formations of the retina are remarkably similar in both cases. The experiments reported in this paper were undertaken in an effort to understand the mechanisms involved in the production of similar abnormalities by two very different experimental conditions: the addition of glutamine in vitro and the transitory deficiency of PGA in vivo. One series of experiments involved the effects of manipulation of the PGA and glutamine content of the culture medium on eye development in vitro. Parallel studies on PGA-deficiency in vivo were undertaken in conjunction with organ-culture experiments in order to compare the effects on abnormal eye morphogenesis.

Sonometric Evaluation of Eustachian Tube Function Using Broadband Stimuli

1980 ◽  
Vol 89 (3_suppl) ◽  
pp. 178-184 ◽  
Author(s):  
Krishna G. Murti ◽  
Erdem I. Cantekin ◽  
Richard M. Stern ◽  
Charles D. Bluestone
Keyword(s):  
Eustachian Tube ◽  
A Priori ◽  
Broadband Noise ◽  
Ear Canal ◽  
Experimental Conditions ◽  
Diagnostic Significance ◽  
Tube Function ◽  
Series Of Experiments ◽  
Sound Conduction ◽  
Clinical Instrument

New measurements of acoustical transmission through the eustachian tube (ET) have been obtained in a series of experiments directed toward the development of a clinical instrument to assess ET function behind an intact tympanic membrane (TM). Using a sound conduction method, a sound source was placed in one nostril, and the acoustical energy that was transmitted through the ET was measured by a microphone placed in the ear canal. The present study used a broadband noise as the acoustical stimulus, in contrast to the tonal stimuli employed in previous investigations. This stimulus was chosen because it is believed to reduce the variability in the data due to intersubject differences in the acoustics of the nasopharynx and ET, and to avoid any a priori assumptions concerning the specific frequencies that would be of greatest diagnostic significance. Averaged spectra of the sound transmitted to the ear canal were obtained for three experimental conditions: acoustical source present during subject swallowing, source present with no swallowing, and subject swallowing with source absent. A Bayesian classification scheme based on the statistics of these spectra was used in classifying subjects into one of two possible categories, normal and abnormal ET function. A comparison was made between sonometric classification and classification based on a tympanometric ET function test. Correlation between the two methods was 87.1%.

scholarly journals A computationally efficient estimator for mutual information

2008 ◽  
Vol 464 (2093) ◽  
pp. 1203-1215 ◽  
Author(s):  
Dafydd Evans
Keyword(s):  
Data Analysis ◽  
Mutual Information ◽  
Time Complexity ◽  
Exploratory Data Analysis ◽  
Nearest Neighbour ◽  
Computationally Efficient ◽  
One Dimensional ◽  
Exploratory Data ◽  
Efficient Alternative ◽  
Computationally Expensive

Mutual information quantifies the determinism that exists in a relationship between random variables, and thus plays an important role in exploratory data analysis. We investigate a class of non-parametric estimators for mutual information, based on the nearest neighbour structure of observations in both the joint and marginal spaces. Unless both marginal spaces are one-dimensional, we demonstrate that a well-known estimator of this type can be computationally expensive under certain conditions, and propose a computationally efficient alternative that has a time complexity of order ( N  log  N ) as the number of observations N →∞.

Simulation of fuel bed ignition by wildland firebrands

2018 ◽  
Vol 27 (8) ◽  
pp. 550 ◽  
Author(s):  
O. V. Matvienko ◽  
D. P. Kasymov ◽  
A. I. Filkov ◽  
O. I. Daneyko ◽  
D. A. Gorbatov
Keyword(s):  
Mathematical Model ◽  
Pinus Sylvestris ◽  
Mathematical Modelling ◽  
Thermal Energy ◽  
Ignition Time ◽  
Pine Bark ◽  
Bark Sample ◽  
Airflow Velocity ◽  
Experimental Conditions ◽  
Series Of Experiments

A 3-D mathematical model of fuel bed (FB) ignition initiated by glowing firebrands originating during wildland fires is proposed. In order to test and verify the model, a series of experiments was conducted to determine the FB ignition time by a single pine bark and twig firebrand (Pinus sylvestris). Irrespective of the pine bark sample sizes and experimental conditions, the ignition of the FB was not observed. Conversely, pine twigs, under certain parameters, ignited the FB in the range of densities (60–105 kg m−3) and with the airflow velocity of ≥2 m s−1. The results of the mathematical modelling have shown that a single pine bark firebrand ≤5 cm long with a temperature of T ≤ 1073 K does not ignite in the flaming mode the FB, and only the thermal energy of larger particles is sufficient for flaming ignition of the adjacent layers of the FB. The analysis of the results has shown that the firebrand length is a major factor in the initiation of ignition. Comparison of the calculated and observed FB ignition times by a single firebrand have shown that our modelling accords well with the experimental results.

Multimodal Analysis in Qualitative Research: Extending Grounded Theory Through the Lens of Social Semiotics

2020 ◽  
pp. 107780042097874
Author(s):  
Vivien Sommer
Keyword(s):  
Grounded Theory ◽  
Digital Technology ◽  
Research Approach ◽  
Social Semiotics ◽  
Audiovisual Material ◽  
Text And Image ◽  
Multimodal Data ◽  
Multimodal Analysis ◽  
Analytical Tools ◽  
Analyze Data

Digital technology has made it easier for researchers to conduct and produce multimodal data. In terms of a social semiotic understanding, multimodal means that data are produced from different sign resources, such as field protocols combined with visual recordings or document analysis consisting of audiovisual material. The increase in multimodal data brings the challenge of developing analytical tools not only to collect data but also to examine them. In this article, I introduce a research approach for how to integrate multimodal data within the framework of grounded theory by extending the coding process with a social semiotic understanding of data as a combination of different sign modes. This approach makes it possible not only to analyze data based on different modes separately but also to analyze their combination, for example, the interweaving of text and image.

The measurement and prediction of sustained temperature oscillations in a chemical reactor

1969 ◽  
Vol 309 (1496) ◽  
pp. 1-26 ◽  
Keyword(s):  
Mathematical Analysis ◽  
Methyl Chloride ◽  
Chemical Reactor ◽  
Vapour Phase ◽  
Gas Temperature ◽  
Experimental Conditions ◽  
Temperature Oscillations ◽  
Series Of Experiments ◽  
Steady Oscillations

Steady oscillations in the recorded gas temperature have been observed in a series of experiments in which the vapour-phase chlorination of methyl chloride was carried out. The instability was reproducible and persisted within a sharply defined range of reaction temperatures. A mathematical analysis of the dynamics of the reacting system is found to predict closely the nature and frequency of the oscillations and the range of experimental conditions within which they occur.

scholarly journals Steady State Relation between Cytoplasmic Free Ca2+ Concentration and Force in Intact Frog Skeletal Muscle Fibers

1998 ◽  
Vol 111 (4) ◽  
pp. 505-519 ◽  
Author(s):  
Masato Konishi ◽  
Masaru Watanabe
Keyword(s):  
Skeletal Muscle ◽  
Steady State ◽  
Isometric Force ◽  
Muscle Fibers ◽  
Skinned Fibers ◽  
Hill Coefficient ◽  
Experimental Conditions ◽  
Skeletal Muscle Fibers ◽  
Force Relation ◽  
Series Of Experiments

The steady state relation between cytoplasmic Ca2+ concentration ([Ca2+]i) and force was studied in intact skeletal muscle fibers of frogs. Intact twitch fibers were injected with the dextran-conjugated Ca2+ indicator, fura dextran, and the fluorescence signals of fura dextran were converted to [Ca2+]i using calibration parameters previously estimated in permeabilized muscle fibers (Konishi and Watanabe. 1995. J. Gen. Physiol. 106:1123–1150). In the first series of experiments, [Ca2+]i and isometric force were simultaneously measured during high K+ depolarization. Slow changes in [Ca2+]i and force induced by 15–30 mM K+ appeared to be in equilibrium, as instantaneous [Ca2+]i versus force plot tracked the common path in the rising and relaxation phases of K+ contractures. In the second series of experiments, 2,5-di-tert-butylhydroquinone (TBQ), an inhibitor of the sarcoplasmic reticulum Ca2+ pump, was used to decrease the rate of decline of [Ca2+]i after tetanic stimulation. The decay time courses of both [Ca2+]i and force were dose-dependently slowed by TBQ up to 5 μM; the instantaneous [Ca2+]i– force relations were nearly identical at ≥1 μM TBQ, suggesting that the change in [Ca2+]i was slow enough to reach equilibrium with force. The [Ca2+]i–force data obtained from the two types of experiments were consistent with the Hill curve using a Hill coefficient of 3.2–3.9 and [Ca2+]i for half activation (Ca50) of 1.5–1.7 μM. However, if fura dextran reacts with Ca2+ with a 2.5-fold greater Kd as previously estimated from the kinetic fitting (Konishi and Watanabe. 1995. J. Gen. Physiol. 106:1123–1150), Ca50 would be 3.7–4.2 μM. We also studied the [Ca2+]–force relation in skinned fibers under similar experimental conditions. The average Hill coefficient and Ca50 were estimated to be 3.3 and 1.8 μM, respectively. Although uncertainties remain about the precise levels of [Ca2+]i, we conclude that the steady state force is a 3rd to 4th power function of [Ca2+]i, and Ca50 is in the low micromolar range in intact frog muscle fibers, which is in reasonable agreement with results obtained from skinned fibers.

Sign in / Sign up

Export Citation Format

Share Document