scholarly journals The Fundamental Equations of Change in Statistical Ensembles and Biological Populations

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1395
Author(s):  
Steven A. Frank ◽  
Frank J. Bruggeman
Keyword(s):  
Probability Distribution ◽  
General Equation ◽  
Recent Article ◽  
Rate Of Change ◽  
The Other ◽  
Price Equation ◽  
Abstract Form ◽  
Statistical Ensembles ◽  
Fundamental Equations ◽  
Theoretical Results

A recent article in Nature Physics unified key results from thermodynamics, statistics, and information theory. The unification arose from a general equation for the rate of change in the information content of a system. The general equation describes the change in the moments of an observable quantity over a probability distribution. One term in the equation describes the change in the probability distribution. The other term describes the change in the observable values for a given state. We show the equivalence of this general equation for moment dynamics with the widely known Price equation from evolutionary theory, named after George Price. We introduce the Price equation from its biological roots, review a mathematically abstract form of the equation, and discuss the potential for this equation to unify diverse mathematical theories from different disciplines. The new work in Nature Physics and many applications in biology show that this equation also provides the basis for deriving many novel theoretical results within each discipline.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

On the Causal-Doxastic Theory of the Basing Relation

2002 ◽  
Vol 32 (4) ◽  
pp. 543-559 ◽  
Author(s):  
Daniel M. Mittag
Keyword(s):  
Recent Article ◽  
Causal Relation ◽  
The Other ◽  
Causal Relations ◽  
Basing Relation ◽  
In Virtue Of

If one is to believe that p justifiably, then one must believe p for, or because of, one's evidence or reasons in support of p. The basing relation is exactly this relation that obtains between one's belief and one's reasons for believing. Keith Allen Korcz, in a recent article published in this Journal, has argued that two conditions are each sufficient and are jointly necessary to establish basing relations between beliefs and reasons. One condition is formulated to account for basing relations that can obtain in virtue of causal relations between one's belief and reasons, and the other condition is supposed to account for basing relations which can be established independently of the instantiation of any such causal relation.

scholarly journals ON THE MECHANISM OF TONIC IMMOBILITY IN VERTEBRATES

1928 ◽  
Vol 11 (6) ◽  
pp. 715-741 ◽  
Author(s):  
Hudson Hoagland
Keyword(s):  
Tonic Immobility ◽  
Threshold Value ◽  
Temperature Characteristic ◽  
The State ◽  
Rate Of Change ◽  
The Other ◽  
Negative Slope ◽  
Selective Inhibitors ◽  
Initial Stimulus ◽  
Temperature Range

1. The durations of successive periods of induced tonic immobility in the lizard Anolis carolinensis was examined as a function of temperature. An automatic recording method was employed and observations were made of 12,000 to 15,000 immobilizations with six animals over a temperature range of 5° to 35°C. during 5 months. 2. The durations of the immobile periods were found to vary rhythmically in most cases. The reciprocal of the duration of the rhythm, i.e., the rate of change of the process underlying the rhythms, when plotted as a function of temperature according to the Arrhenius equation show distributions of points in two straight line groups. One of these groups or bands of points extends throughout the entire temperature range with a temperature characteristic of approximately µ = 31,000 calories, and the other covers the range of 20° to 35°C. with µ equal to approximately 9,000 calories. 3. The initial stimulus in a series of inductions of immobility appears to set off a mechanism which determines the duration of the state of quiescence. Succeeding forced recoveries seem to have no effect on the normal duration of the rhythm. 4. These results are interpreted by assuming the release, through reflex stimulation, of hormonal substances, one effective between 5° and 35°C. and the other effective between 20° and 35°C. These substances are assumed to act as selective inhibitors of impulses from so called "higher centers," allowing impulses from tonic centers to pass to the muscles. 5. In some experiments a progressive lengthening in successively induced periods of immobility was observed. The logarithm of the frequency of recovery when plotted against time in most of these cases (i.e., except for a few in which irregularities occurred) gave a linear function of negative slope which was substantially unaffected by temperature. In these cases it is assumed that a diffusion process is controlling the amount of available A substance. 6. The results are similar to those obtained by Crozier with Cylisticus convexus. The duration of tonic immobility seems to be maintained in both arthropod and vertebrate by the chemical activity of "hormonal" selective inhibitors. The details of the mechanisms differ, but there is basic similarity. 7. Injections of small amounts of adrenalin above a threshold value are found to prolong the durations of tonic immobility of Anolis, by an amount which is a logarithmic function of the "dose." It is possible that internally secreted adrenalin, above a threshold amount, may be involved in the maintenance of tonic immobility. 8. The production of tonic immobility reflexly is a problem distinct from that of the duration of immobility. It is suggested that the onset may be induced by "shock" to the centers of reflex tonus causing promiscuous discharge of these centers with accompanying inhibition of the higher centers. Such a condition may result when an animal is suddenly lifted from the substratum and overturned, or when, as in the case of Anolis, it struggles with dorsum down. This reaction of the "tonic centers" may at the same time lead to discharge of the adrenal glands by way of their spinal connections thus prolonging the state.

Ironic Reprise in Galdós' Novels

PMLA ◽  
1961 ◽  
Vol 76 (3) ◽  
pp. 233-239 ◽  
Author(s):  
Monroe Z. Hafter
Keyword(s):  
Nineteenth Century ◽  
Recent Article ◽  
The Other ◽  
Separate Study ◽  
The Unconscious ◽  
Present Essay ◽  
Spanish Novel ◽  
Artistic Representation ◽  
The Rich

A recent article of Leon Livingstone rightly calls attention to the importance of Pérez Galdós' assimilation of Cervantine irony as a forerunner of the concern of modern Spanish novelists about the autonomy of their characters. The unreality of rationalism, which Livingstone holds to be the germ of El amigo Manso, the imagination's capacity to create reality at the heart of Misericordia, lead to the even bolder experiments in the artistic representation of reality undertaken by Unamuno, Azorín, Valle-Inclán, and Pérez de Ayala. Anomalous for his time yet so pervasive in his work is Galdós' employment of “interior duplication” that a separate study would contribute to our fuller understanding of his art as well as to our measure of the advances in the Spanish novel of the latter half of the nineteenth century. The present essay focuses on Galdós' developing skill with internal repetitions from La Fontana de Oro (publ. 1870), through the rich complexities of the novels written between 1886–89, to their almost stylized simplicity in El abuelo (1897). Always related to Cervantine irony, the variety of verbal echoes, the mirroring of one character in another, the unconscious illumination each may offer the other, underscore the increasingly intimate wedding of form and matter with which Galdós came to unfold his narratives.

Timaeus 38A8–B5

1957 ◽  
Vol 77 (1) ◽  
pp. 18-23 ◽  
Author(s):  
Harold Cherniss
Keyword(s):  
Recent Article ◽  
The Other ◽  
Current Opinion ◽  
Relative Chronology ◽  
First Time

In a recent article written by Mr. G. E. L. Owen to prove that contrary to the general current opinion the composition of theTimaeusmust have antedated that of theParmenidesand its dialectical successors, it is contended that when theTimaeuswas written the analysis of negation given in theSophistcould not yet have been worked out. ‘For’, Mr. Owen writes, ‘the tenet on which the whole new account of negation is based, namely thatτὸ μὴ ὄν ἔστιν ὄντως μὴ ὄν(Soph.254D1), is contradicted unreservedly by Timaeus' assertion that it is illegitimate to sayτὸ μὴ ὄν ἔστι μὴ ὄν(38B2–3); and thereby theTimaeusat once ranks itself with theRepublicandEuthydemus.'After brushing aside Cornford's attempt to reconcile this passage of theTimaeuswith theSophist, Mr. Owen concludes his treatment of it with the words: ‘So theTimaeusdoes not tally with even a fragment of the argument in theSophist.That argument is successful against exactly the Eleatic error which, for lack of the later challenge to Father Parmenides, persists in theTimaeus.’An examination of the other arguments put forward by Mr. Owen in support of his thesis concerning the relative chronology of theTimaeusI reserve for another place. Here I propose to consider only the meaning of this one passage and whether it really does imply that theTimaeusmust have been written before Plato had conceived the doctrine enunciated in theSophist.It is a question not now raised for the first time. More than half a century ago Otto Apelt asserted that this passage of theTimaeusis enough to prove that work earlier than theSophists.His assertion did not go unchallenged; and Apelt himself appears to have lost his original confidence in it, for in his later writings on the relative chronology of the two dialogues he did not again refer to it.

scholarly journals The Probability That a Measurement Falls within a Range of Standard Deviations from an Estimate of the Mean

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Louis M. Houston
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
General Equation ◽  
Sample Sizes ◽  
The Mean ◽  
Standard Deviations ◽  
Intermediate Value ◽  
Theoretical Results

We derive a general equation for the probability that a measurement falls within a range of n standard deviations from an estimate of the mean. So, we provide a format that is compatible with a confidence interval centered about the mean that is naturally independent of the sample size. The equation is derived by interpolating theoretical results for extreme sample sizes. The intermediate value of the equation is confirmed with a computational test.

Choice of antacids for peptic ulcer - addendum

1965 ◽  
Vol 3 (12) ◽  
pp. 48-48
Keyword(s):  
Peptic Ulcer ◽  
Aluminium Hydroxide ◽  
Recent Article ◽  
The Other ◽  
The One

In a recent article (Drug Therap. Bull. April 30, 1965, p. 33) we mentioned that Asilone (Berk) and Diovol (Wallace) cost considerably more than other antacid preparations. The manufacturer has told us that Asilone is available in two versions: the one our article referred to contains aluminium hydroxide and 250 mg polymethylsiloxane per tablet, and costs 23/4 per 100 (basic NHS price); the other, Asilone 50, contains aluminium hydroxide and 50 mg polymethylsiloxane, and costs 10/- per 100 tablets. Our comment on the high cost of Asilone therefore does not apply to Asilone 50.

scholarly journals Comment on "Radiative forcings for 28 potential Archean greenhouse gases" by Byrne and Goldblatt (2014)

2015 ◽  
Vol 11 (8) ◽  
pp. 1097-1105 ◽  
Author(s):  
R. V. Kochanov ◽  
I. E. Gordon ◽  
L. S. Rothman ◽  
S. W. Sharpe ◽  
T. J. Johnson ◽  
...  
Keyword(s):  
Greenhouse Gases ◽  
Cross Sections ◽  
Spectral Region ◽  
Radiative Forcing ◽  
Recent Article ◽  
The Other ◽  
Radiative Forcings ◽  
The Status ◽  
Moderate Resolution ◽  
Spectroscopic Database

Abstract. In the recent article by Byrne and Goldblatt, "Radiative forcing for 28 potential Archean greenhouse gases", Clim. Past. 10, 1779–1801 (2014), the authors employ the HITRAN2012 spectroscopic database to evaluate the radiative forcing of 28 Archean gases. As part of the evaluation of the status of the spectroscopy of these gases in the selected spectral region (50–1800 cm−1), the cross sections generated from the HITRAN line-by-line parameters were compared with those of the PNNL database of experimental cross sections recorded at moderate resolution. The authors claimed that for NO2, HNO3, H2CO, H2O2, HCOOH, C2H4, CH3OH and CH3Br there exist large or sometimes severe disagreements between the databases. In this work we show that for only three of these eight gases a modest discrepancy does exist between the two databases and we explain the origin of the differences. For the other five gases, the disagreements are not nearly at the scale suggested by the authors, while we explain some of the differences that do exist. In summary, the agreement between the HITRAN and PNNL databases is very good, although not perfect. Typically differences do not exceed 10 %, provided that HITRAN data exist for the bands/wavelengths of interest. It appears that a molecule-dependent combination of errors has affected the conclusions of the authors. In at least one case it appears that they did not take the correct file from PNNL (N2O4 (dimer)+ NO2 was used in place of the monomer). Finally, cross sections of HO2 from HITRAN (which do not have a PNNL counterpart) were not calculated correctly in BG, while in the case of HF misleading discussion was presented there based on the confusion by foreign or noise features in the experimental PNNL spectra.

Filtration by superficial and deep glomeruli of normovolemic and volume-depleted rats

1986 ◽  
Vol 250 (1) ◽  
pp. F86-F91
Author(s):  
R. V. Pinnick ◽  
V. J. Savin
Keyword(s):  
Basement Membrane ◽  
Maximum Rate ◽  
Rate Of Change ◽  
The Other ◽  
Membrane Area ◽  
Morphometric Analyses ◽  
Three Samples ◽  
Glomerular Size ◽  
Glomerular Ultrafiltration

We measured glomerular ultrafiltration coefficient (Kf) of isolated superficial (S) and deep (D) glomeruli of normovolemic and volume-depleted rats. Filtration was induced in vitro, and Kf was calculated from the maximum rate of change in glomerular size. Basement membrane area (A) for each glomerulus was estimated from morphometric analyses, and glomerular capillary hydraulic conductivity (Lp) was calculated by the formula Lp = Kf/A. Kf of S and D glomeruli of normovolemic rats were 2.98 +/- 0.98 and 4.25 +/- 0.07 nl . min-1 . mmHg-1, respectively. In hypovolemic rats, Kf of S glomeruli fell by approximately 50% to 1.52 +/- 0.14 nl . min-1 . mmHg-1 (P less than 0.001), whereas Kf of D glomeruli remained unchanged at 4.28 +/- 0.10 nl . min-1 . mmHg-1. Lp, calculated using the peripheral capillary area, averaged 1.98 +/- 0.09 and 1.98 +/- 0.06 microliter . min-1 . mmHg-1 . cm-2 in S and D glomeruli of normovolemic rats and 1.89 +/- 0.11 microliter . min-1 . mmHg-1 . cm-2 in D glomeruli of hypovolemic rats. Lp of S glomeruli of volume-depleted rats (0.90 +/- 0.03 microliter . min-1 . mmHg-1 . cm-2) was lower than in any of the other three samples. Mild hypovolemia causes the Kf of S glomeruli to decline, whereas Kf of D glomeruli remains constant. The decrease in Kf occurs without an alteration in capillary area and is most likely due to a decrease in Lp.

scholarly journals A Comparison of Psychophysical Dose-Response Behaviour across 16 Sweeteners

Nutrients ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1632 ◽  
Author(s):  
May Wee ◽  
Vicki Tan ◽  
Ciarán Forde
Keyword(s):  
Growth Rate ◽  
Dose Response ◽  
Rate Of Change ◽  
The Other ◽  
Rebaudioside A ◽  
Glycaemic Response ◽  
Sensory Panel ◽  
Response Behaviour ◽  
Sweetness Intensity ◽  
Sugar Replacement

Reduction or replacement of sucrose while maintaining sweetness in foods is challenging, but today there are many sweeteners with diverse physical and caloric compositions to choose from. The choice of sweetener can be adapted to match reformulation goals whether these are to reduce calories, lower the glycaemic response, provide bulk or meet criteria as a natural ingredient. The current study sought to describe and compare the sweetness intensity dose-response, sweetness growth rate, sweetness potency, and potential for calorie reduction across 16 different sweeteners including sucrose. Sweetness growth rate was defined as the rate of change in sweetness intensity per unit of sweetener concentration. Sweetness potency was defined as the ratio of the concentration of a sweetener to that of sucrose at equivalent sweetness intensity, whereas the potential for calorie reduction is the caloric value of a sweetener compared to sucrose at matched sweetness intensities. Sweeteners were drawn from a range of nutritive saccharide (sucrose, dextrose, fructose, allulose (d-psicose), palatinose (isomaltulose), and a sucrose–allulose mixture), nutritive polyol (maltitol, erythritol, mannitol, xylitol, sorbitol), non-nutritive synthetic (aspartame, acesulfame-K, sucralose) and non-nutritive natural sweeteners stevia (rebaudioside A), luo han guo (mogroside V). Sweetness intensities of the 16 sweeteners were compared with a sensory panel of 40 participants (n = 40; 28 females). Participants were asked to rate perceived sweetness intensity for each sweetener series across a range of concentrations using psychophysical ratings taken on a general labelled magnitude scale (gLMS). All sweeteners exhibited sigmoidal dose-response behaviours and matched the ‘moderate’ sweetness intensity of sucrose (10% w/v). Fructose, xylitol and sucralose had peak sweetness intensities greater than sucrose at the upper concentrations tested, while acesulfame-K and stevia (rebA) were markedly lower. Independent of sweetener concentration, the nutritive sweeteners had similar sweetness growth rates to sucrose and were greater than the non-nutritive sweeteners. Non-nutritive sweeteners on the other hand had higher potencies relative to sucrose, which decreases when matching at higher sweetness intensities. With the exception of dextrose and palatinose, all sweeteners matched the sweetness intensity of sucrose across the measured range (3.8–25% w/v sucrose) with fewer calories. Overall, the sucrose–allulose mixture, maltitol and xylitol sweeteners were most similar to sucrose in terms of dose-response behaviour, growth rate and potency, and showed the most potential for sugar replacement within the range of sweetness intensities tested.

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