scholarly journals Weak Bi-Center and Critical Period Bifurcations of a Z2-Equivariant Quintic System

2021 ◽  
Vol 31 (08) ◽  
pp. 2150117
Author(s):  
Yusen Wu
Keyword(s):  
Numerical Analysis ◽  
Computer Algebra ◽  
Critical Period ◽  
Computer Algebra System ◽  
Center Problem ◽  
Critical Periods ◽  
Symbolic Calculation ◽  
Weak Center

With the help of computer algebra system-Mathematica, this paper considers the weak center problem and local critical periods for bi-center of a [Formula: see text]-equivariant quintic system with eight parameters. The order of weak bi-center is identified and the exact maximum bifurcation number of critical periods generated from the bi-center is given via the combination of symbolic calculation and numerical analysis.

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

scholarly journals Demand Response Coupled with Dynamic Thermal Rating for Increased Transformer Reserve and Lifetime

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1378
Author(s):  
Ildar Daminov ◽  
Rémy Rigo-Mariani ◽  
Raphael Caire ◽  
Anton Prokhorov ◽  
Marie-Cécile Alvarez-Hérault
Keyword(s):  
Ambient Temperature ◽  
Demand Response ◽  
Thermal Model ◽  
Critical Period ◽  
Optimization Problem ◽  
Integrated Management ◽  
Critical Periods ◽  
Network Access ◽  
Maximal Amplitude ◽  
Demand Response Program

(1) Background: This paper proposes a strategy coupling Demand Response Program with Dynamic Thermal Rating to ensure a transformer reserve for the load connection. This solution is an alternative to expensive grid reinforcements. (2) Methods: The proposed methodology firstly considers the N-1 mode under strict assumptions on load and ambient temperature and then identifies critical periods of the year when transformer constraints are violated. For each critical period, the integrated management/sizing problem is solved in YALMIP to find the minimal Demand Response needed to ensure a load connection. However, due to the nonlinear thermal model of transformers, the optimization problem becomes intractable at long periods. To overcome this problem, a validated piece-wise linearization is applied here. (3) Results: It is possible to increase reserve margins significantly compared to conventional approaches. These high reserve margins could be achieved for relatively small Demand Response volumes. For instance, a reserve margin of 75% (of transformer nominal rating) can be ensured if only 1% of the annual energy is curtailed. Moreover, the maximal amplitude of Demand Response (in kW) should be activated only 2–3 h during a year. (4) Conclusions: Improvements for combining Demand Response with Dynamic Thermal Rating are suggested. Results could be used to develop consumer connection agreements with variable network access.

Critical periods for functional and anatomical compensation in lateral suprasylvian visual area following removal of visual cortex in cats

1984 ◽  
Vol 52 (5) ◽  
pp. 941-960 ◽  
Author(s):  
L. Tong ◽  
R. E. Kalil ◽  
P. D. Spear
Keyword(s):  
Visual Cortex ◽  
Critical Period ◽  
Ocular Dominance ◽  
Direction Selectivity ◽  
Visual Area ◽  
Critical Periods ◽  
Cortex Lesion ◽  
Thalamic Projections ◽  
Adult Cats ◽  
Visual Cortical

Previous experiments have found that neurons in the cat's lateral suprasylvian (LS) visual area of cortex show functional compensation following removal of visual cortical areas 17, 18, and 19 on the day of birth. Correspondingly, an enhanced retino-thalamic pathway to LS cortex develops in these cats. The present experiments investigated the critical periods for these changes. Unilateral lesions of areas 17, 18, and 19 were made in cats ranging in age from 1 day postnatal to 26 wk. When the cats were adult, single-cell recordings were made from LS cortex ipsilateral to the lesion. In addition, transneuronal autoradiographic methods were used to trace the retino-thalamic projections to LS cortex in many of the same animals. Following lesions in 18- and 26-wk-old cats, there is a marked reduction in direction-selective LS cortex cells and an increase in cells that respond best to stationary flashing stimuli. These results are similar to those following visual cortex lesions in adult cats. In contrast, the percentages of cells with these properties are normal following lesions made from 1 day to 12 wk of age. Thus the critical period for development of direction selectivity and greater responses to moving than to stationary flashing stimuli in LS cortex following a visual cortex lesion ends between 12 and 18 wk of age. Following lesions in 26-wk-old cats, there is a decrease in the percentage of cells that respond to the ipsilateral eye, which is similar to results following visual cortex lesions in adult cats. However, ocular dominance is normal following lesions made from 1 day to 18 wk of age. Thus the critical period for development of responses to the ipsilateral eye following a lesion ends between 18 and 26 wk of age. Following visual cortex lesions in 2-, 4-, or 8-wk-old cats, about 30% of the LS cortex cells display orientation selectivity to elongated slits of light. In contrast, few or no cells display this property in normal adult cats, cats with lesions made on the day of birth, or cats with lesions made at 12 wk of age or later. Thus an anomalous property develops for many LS cells, and the critical period for this property begins later (between 1 day and 2 wk) and ends earlier (between 8 and 12 wk) than those for other properties.(ABSTRACT TRUNCATED AT 400 WORDS)

The Maple computer algebra system: A review

1995 ◽  
Vol 10 (3) ◽  
pp. 329-337 ◽  
Author(s):  
John Hutton ◽  
James Hutton
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
System A

scholarly journals The ex-illiterate brain: The critical period, cognitive reserve and HAROLD model

2009 ◽  
Vol 3 (3) ◽  
pp. 222-227 ◽  
Author(s):  
Maria Vania Silva Nunes ◽  
Alexandre Castro-Caldas ◽  
Dolores Del Rio ◽  
Fernado Maestú ◽  
Tomás Ortiz
Keyword(s):  
Recognition Test ◽  
Cognitive Skills ◽  
Critical Period ◽  
Cognitive Reserve ◽  
Brain Activity ◽  
High Educational Level ◽  
Critical Periods ◽  
Language Recognition ◽  
Regular Time ◽  
The Brain

Abstract The lifelong acquisition of cognitive skills shapes the biology of the brain. However, there are critical periods for the best use of the brain to process the acquired information. Objectives: To discuss the critical period of cognitive acquisition, the concept of cognitive reserve and the HAROLD (Hemispheric Asymmetry Reduction in Older adults) model. Methods: Seven women who learned how to read and to write after the age of 50 (ex-illiterates) and five women with 10 years of regular schooling (controls) were submitted to a language recognition test while brain activity was being recorded using magnetoencephalography. Spoken words were delivered binaurally via two plastic tubs terminating in ear inserts, and recordings were made with a whole head magnetometer consisting of 148 magnetometer coils. Results: Both groups performed similarly on the task of identifying target words. Analysis of the number of sources of activity in the left and right hemispheres revealed significant differences between the two groups, showing that ex-illiterate subjects exhibited less brain functional asymmetry during the language task. Conclusions: These results should be interpreted with caution because the groups were small. However, these findings reinforce the concept that poorly educated subjects tend to use the brain for information processing in a different way to subjects with a high educational level or who were schooled at the regular time. Finally, the recruiting of both hemispheres to tackle the language recognition test occurred to a greater degree in the ex-illiterate group where this can be interpreted as a sign of difficulty performing the task.

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