scholarly journals The statistical nature of geometric reasoning

2017 ◽  
Author(s):  
Yuval Hart ◽  
Moira R. Dillon ◽  
Andrew Marantan ◽  
Anna L. Cardenas ◽  
Elizabeth Spelke ◽  
...  
Keyword(s):  
Dynamic Models ◽  
Physical World ◽  
Geometric Reasoning ◽  
Mathematical Framework ◽  
Global Orientation ◽  
Cognitive Studies ◽  
Statistical Dynamic ◽  
The Mean ◽  
Straight Lines ◽  
Triangle Completion

AbstractGeometric reasoning has an inherent dissonance: its abstract axioms and propositions refer to infinitesimal points and infinite straight lines while our perception of the physical world deals with fuzzy dots and curved stripes. How we use these disparate mechanisms to make geometric judgments remains unresolved. Here, we deploy a classically used cognitive geometric task - planar triangle completion - to study the statistics of errors in the location of the missing vertex. Our results show that the mean location has an error proportional to the side of the triangle, the standard deviation is sub-linearly dependent on the side length, and has a negative skewness. These scale-dependent responses directly contradict the conclusions of recent cognitive studies that innate Euclidean rules drive our geometric judgments. To explain our observations, we turn to a perceptual basis for geometric reasoning that balances the competing effects of local smoothness and global orientation of extrapolated trajectories. The resulting mathematical framework captures our observations and further predicts the statistics of the missing angle in a second triangle completion task. To go beyond purely perceptual geometric tasks, we carry out a categorical version of triangle completion that asks about the change in the missing angle after a change in triangle shape. The observed responses show a systematic scale-dependent discrepancy at odds with rule-based Euclidean reasoning, but one that is completely consistent with our framework. All together, our findings point to the use of statistical dynamic models of the noisy perceived physical world, rather than on the abstract rules of Euclid in determining how we reason geometrically.

Vibratory Feeding by Nonsinusoidal Vibration—Optimum Wave Form

1985 ◽  
Vol 107 (2) ◽  
pp. 188-195 ◽  
Author(s):  
S. Okabe ◽  
Y. Kamiya ◽  
K. Tsujikado ◽  
Y. Yokoyama
Keyword(s):  
Experimental Results ◽  
Wave Form ◽  
Velocity Wave ◽  
The Mean ◽  
Straight Lines ◽  
Vibratory Conveyor ◽  
Theoretical Results ◽  
Vibratory Feeding

This paper presents the conveying velocity on a vibratory conveyor whose track is vibrated by nonsinusoidal vibration. The velocity wave form of the vibrating track is approximated by six straight lines, and five distortion factors of the wave form are defined. Considering the modes of motion of the particle, the mean conveying velocity is calculated for various conditions. Referring to these results, the optimum wave form is clarified analytically. The theoretical results show that the mean conveying velocity is considerably larger than that of ordinary feeders if the proper conveying conditions are chosen. The theoretical results are confirmed by experimental results.

scholarly journals Free Will in Human Behavior and Physics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Free Will ◽  
Human Behavior ◽  
Physical World ◽  
Classical Physics ◽  
Quantum Bit ◽  
The Past ◽  
The Mean ◽  
The One

If the concept of “free will” is reduced to that of “choice” all physical world share the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly a certain goal, and the choice is only the mean, by which the aim can be achieved or not by the one who determines the target. Thus, for example, an electron has always a choice but not free will unlike a human possessing both. Consequently, and paradoxically, the determinism of classical physics is more subjective and more anthropomorphic than the indeterminism of quantum mechanics for the former presupposes certain deterministic goal implicitly following the model of human freewill behavior. Quantum mechanics introduces the choice in the fundament of physical world involving a generalized case of choice, which can be called “subjectless”: There is certain choice, which originates from the transition of the future into the past. Thus that kind of choice is shared of all existing and does not need any subject: It can be considered as a low of nature. There are a few theorems in quantum mechanics directly relevant to the topic: two of them are called “free will theorems” by their authors (Conway and Kochen 2006; 2009). Any quantum system either a human or an electron or whatever else has always a choice: Its behavior is not predetermined by its past. This is a physical law. It implies that a form of information, the quantum information underlies all existing for the unit of the quantity of information is an elementary choice: either a bit or a quantum bit (qubit).

Detection of heterozygotes for phenylketonuria by constant intravenous infusion of L-phenylalanine.

1977 ◽  
Vol 23 (9) ◽  
pp. 1661-1665 ◽  
Author(s):  
R Jagenburg ◽  
S Rödjer
Keyword(s):  
Intravenous Infusion ◽  
Elimination Rate ◽  
Mean Value ◽  
Negative Family History ◽  
Plasma Phenylalanine ◽  
Fixed Concentration ◽  
The Mean ◽  
Tyrosine Concentration ◽  
Plasma Tyrosine ◽  
Straight Lines

Abstract We measured the rate of elimination of phenylalanine by constant intravenous infusion of L-phenylalanine in 14 parents of children with phenylketonuria and in 21 subjects with a negative family history for this disease. When reciprocals of the observed elimination rates were plotted against the reciprocals of the increase in the plasma phenylalanine concentrations, approximately straight lines resulted. The theoretical maximum elimination rate, the mean value for which was 32 mmol/h in the reference subjects, was reduced by 41% in the phenylketonuric heterozygotes. The elimination rate at an increase in plasma phenylalanine concentration of 0.5 mmol/liter discriminated the phenylketonuric heterozygotes from normal homozygotes, with no overlap between the groups. A lower plasma tyrosine concentration in the phenylketonuric heterozygotes than in the reference subjects at the same rate of elimination of phenylalanine indicated an increased rate of elimination of tyrosine at a fixed concentration of this amino acid in these subjects.

Fitting straight lines to experimental data

1977 ◽  
Vol 233 (3) ◽  
pp. R94-R99 ◽  
Author(s):  
R. A. Brace
Keyword(s):  
Standard Error ◽  
Least Squares Regression ◽  
Simple Method ◽  
Mean Values ◽  
Absolute Value ◽  
Best Value ◽  
The Mean ◽  
Straight Lines ◽  
Relationship Of ◽  
Conventional Regression

The problem associated with use of statistical methods for determining a best linear relationship of the form Y = AX +B have been examined for a condition quite prevalent with experimental research, i.e., when the values of both variables are subject to essentially unknown errors. Under this condition standard least-squares regression analysis underestimates the value of the slope A. A very simple method for determining the best value of the slope and intercept has been introduced which can be used when errors are present in both variables. With this proposed method, the calculated slope is equal to the standard error of Y divided by the standard error of X (with the appropriate sign) and the intercept is found from the mean values of X and Y, i.e., B = Y - AX. The best estimate of the slope is also equal to the slope found with the conventional regression method divided by the absolute value of the correlation coefficient. The line determined with the suggested method can be considered to be a line of symmetry through the data.

scholarly journals LoRAS: an oversampling approach for imbalanced datasets

2020 ◽  
Author(s):  
Saptarshi Bej ◽  
Narek Davtyan ◽  
Markus Wolfien ◽  
Mariam Nassar ◽  
Olaf Wolkenhauer
Keyword(s):  
Data Distribution ◽  
Classification Model ◽  
Mathematical Framework ◽  
Classification Models ◽  
Local Data ◽  
Imbalanced Datasets ◽  
Minority Class ◽  
Data Space ◽  
Data Points ◽  
The Mean

AbstractThe Synthetic Minority Oversampling TEchnique (SMOTE) is widely-used for the analysis of imbalanced datasets. It is known that SMOTE frequently over-generalizes the minority class, leading to misclassifications for the majority class, and effecting the overall balance of the model. In this article, we present an approach that overcomes this limitation of SMOTE, employing Localized Random Affine Shadowsampling (LoRAS) to oversample from an approximated data manifold of the minority class. We benchmarked our algorithm with 14 publicly available imbalanced datasets using three different Machine Learning (ML) algorithms and compared the performance of LoRAS, SMOTE and several SMOTE extensions that share the concept of using convex combinations of minority class data points for oversampling with LoRAS. We observed that LoRAS, on average generates better ML models in terms of F1-Score and Balanced accuracy. Another key observation is that while most of the extensions of SMOTE we have tested, improve the F1-Score with respect to SMOTE on an average, they compromise on the Balanced accuracy of a classification model. LoRAS on the contrary, improves both F1 Score and the Balanced accuracy thus produces better classification models. Moreover, to explain the success of the algorithm, we have constructed a mathematical framework to prove that LoRAS oversampling technique provides a better estimate for the mean of the underlying local data distribution of the minority class data space.

scholarly journals ELECTROENDOSMOSIS THROUGH MAMMALIAN SEROUS MEMBRANES

1926 ◽  
Vol 9 (3) ◽  
pp. 361-373 ◽  
Author(s):  
Stuart Mudd
Keyword(s):  
Current Strength ◽  
Transport Rate ◽  
Glandular Secretion ◽  
Flow Through ◽  
The Mean ◽  
Straight Lines

The rate of electroendosmotic flow through dog and cat pericardia is found to be proportional to the current strength. The plots of current strengths against volumes of liquid transported in unit time are, in the better experiments, straight lines passing through the origin; the slopes of the lines are characteristic of the several systems. Data on transport rate with buffers of different specific resistances showed the following phenomena: 1. Decrease of the observed transport rate to a minimum between σ values of 95 and 60 ohms. 2. Changes in the membrane markedly affecting transport rate, at conductivities and osmotic pressures close to those of the blood. 3. Polarization of the membrane during the passage of current. The mean rate found for electroendosmotic transport across dog and cat serous membranes bathed in serum has been 0.19 to 0.30 (average, 0.25) c.mm. per minute per milliampere. The best experiments with dog serum and the living mesenteries of dogs under ether gave a mean rate of 0.29 c.mm. per minute per milliampere. These data, together with data from other sources, are believed to indicate a probability approaching certainty that electroendosmotic effects are a factor in glandular secretion.

scholarly journals Think globally, act locally: the role of local demographics and vaccination coverage in the dynamic response of measles infection to control

2013 ◽  
Vol 368 (1623) ◽  
pp. 20120141 ◽  
Author(s):  
M. J. Ferrari ◽  
B. T. Grenfell ◽  
P. M. Strebel
Keyword(s):  
Dynamic Models ◽  
Vaccine Coverage ◽  
National Level ◽  
Age Distribution ◽  
Local Variation ◽  
Comparative Approach ◽  
Age Of Infection ◽  
The Mean ◽  
The Impact

The global reduction of the burden of morbidity and mortality owing to measles has been a major triumph of public health. However, the continued persistence of measles infection probably not only reflects local variation in progress towards vaccination target goals, but may also reflect local variation in dynamic processes of transmission, susceptible replenishment through births and stochastic local extinction. Dynamic models predict that vaccination should increase the mean age of infection and increase inter-annual variability in incidence. Through a comparative approach, we assess national-level patterns in the mean age of infection and measles persistence. We find that while the classic predictions do hold in general, the impact of vaccination on the age distribution of cases and stochastic fadeout are mediated by local birth rate. Thus, broad-scale vaccine coverage goals are unlikely to have the same impact on the interruption of measles transmission in all demographic settings. Indeed, these results suggest that the achievement of further measles reduction or elimination goals is likely to require programmatic and vaccine coverage goals that are tailored to local demographic conditions.

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