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# Which carbons in pyrrole have the highest electron density?

In pyrrole, which carbon atoms have the greatest electron density?

In the resonance structures of pyrrole, all carbons can formally bear a negative charge, so it's not immediately obvious which one is most electron-rich:

My book claims that because resonance forms 1c and 1d are greater contributors to the resonance hybrid than 1b and 1e, the α-carbons (which bear the negative formal charge in 1c and 1d) are more electron-rich. Is this really the case?

Interesting question, more subtle than I realized!

Theoretical approach: I would turn to resonance and induction as the rationale for electronic properties. I think all of your resonance forms may contribute about equally to the resonance hybrid. This suggests that all four carbons would share roughly the same amount of electron density. However, we must also consider the inductive effect of the nitrogen atom, which draws some electron density away from C2 and C5 through the sigma bonds. This would imply that the two proximal carbons (closest to N) are more electron-deficient, and the distal (more distant) pair of carbons are more electron-rich.

Experimental considerations: Orthocresol has a good point that pyrroles are observed to form bonds with electrophiles at the proximal carbons (2/5). However, I think this trend may be due to the superior stability of the intermediate produced by that pathway (3 significant resonance forms) versus a distal (3/4) attack (2 significant forms). The cation from a proximal attack is better stabilized by resonance than the distal-attack cation. I expect that pyrrole forming C2 bonds with electrophiles has more to do with the stability of the intermediate of that pathway than necessarily greater electron density on C2. What I did not expect, but read on Wikipedia, is this:

Unlike furan and thiophene, [pyrrole] has a dipole in which the positive end lies on the side of the heteroatom, with a dipole moment of $1.58\ \mathrm{D}$.

This is experimental evidence demonstrating that the electron density is lower on the proximal side (C2,5) and greater on the distal side (C3,4). Besides molecular modeling of the electron density clouds, I think the molecular dipole moment is about the most conclusive evidence one can hope for.

It really comes down to the context: in an undergrad first-semester course, you might be expected to say the distal carbons have more density because the nitrogen withdraws from the proximal carbons. In more advanced courses, you might take orthocresol's perspective and base your answer in reactivity, concluding the proximal have more electron density. But I expect a doctorate researcher would probably conduct molecular modeling and compute the electron distributions using quantum mechanics, and perhaps conduct a few experiments to measure the dipole. And at that level, I think C3 and C4 have the honey.

• But the key has the answer as C2 and C5 by following the inductive effect (may be 'cause I'm still in high school C3 and C4 and dipole moment were all neglected or remain unnoticed) so shall I take C2,5 or C3,4? And thank you for the detailed answer, it helped a lot :) – Harini Dec 14 '16 at 16:07
• That is bizarre. Unless there are more than college-level concepts at play here that I'm not aware of, I would say with certainty that the inductive effect would /lessen/ the electron density at C2/5. The nitrogen withdraws electrons from the proximal carbons due to its higher electronegativity. I cannot see how any "inductive effect" here could make C2/5 more electron-rich. This is highschool, you say? Perhaps your teacher is mistaken. I would be interested to hear their logic. – electronpusher Dec 15 '16 at 3:48
• There is no 'most stable resonance structure'. These are all part of the same description as a singular structure is an incomplete description. – Martin - マーチン Dec 20 '16 at 20:02
• Of course Martin, it is only a colloquial phrase for intuitive rationalizations. Would you prefer "the relative weights of the molecular orbital wavefunction vector components are likely nearly equal in magnitude"? – electronpusher Dec 20 '16 at 20:16
• @electronpusher That's a silly question: Yes, of course. A bit simpler would be all resonance forms have a relative similar contribution to the overall bonding situation. I find such colloquialism very bad, as for the untrained eye and mind they suggest something that isn't true at all. And especially this association continues to linger around. And that is very bad, since it is much harder to unlearn something than learning something new. – Martin - マーチン Dec 21 '16 at 15:31

That is really not a fair question and even with a computational approach the differences are more or less marginal. The approach by electron pusher is certainly the way to go, and here is the computations to back it up.
See if you can find the carbon with the highest electron density in the following plot showing the value of the electron density for the calculation on the DF-M06L/def-TZVPP level of theory.

I have then performed an analysis of the electron density with the Quantum Theory of Atoms in Molecules (QTAIM). The following shows the Laplacian of the electron density, with the zero-flux surfaces in blue that divide the molecule.

When we integrate over the electron density in these basins, we know at which atom "are the most electrons", subtracting the nuclear charge, we get the overall charge. This should tell us, which carbons have the higher overall density.

  1 (C )    Charge:    0.015912     Volume:    83.414 Bohr^3
2 (C )    Charge:    0.406209     Volume:    76.122 Bohr^3
3 (N )    Charge:   -1.248690     Volume:    95.264 Bohr^3
4 (C )    Charge:    0.406204     Volume:    76.122 Bohr^3
5 (C )    Charge:    0.015911     Volume:    83.414 Bohr^3
6 (H )    Charge:   -0.012007     Volume:    48.338 Bohr^3
7 (H )    Charge:    0.004155     Volume:    47.506 Bohr^3
8 (H )    Charge:    0.004162     Volume:    47.506 Bohr^3
9 (H )    Charge:   -0.012006     Volume:    48.338 Bohr^3
10 (H )    Charge:    0.420149     Volume:    28.032 Bohr^3

And for reference we need the numbering in the table:

TL;DR (1) The α-carbons to the nitrogen have a higher positive charge, hence the lower total electron density than the β-carbons.

Let's have another look at the π-orbitals to see where the reactivity towards electrophiles comes from.

TL;DR (2) The highest electron density of the HOMO is at the α-carbons; electrophiles react there.

Please don't nag about the numbering, I recycled the calculation from another post, where I did not pay much attention to that. Sorry.

Ad. I agree with the analysis of the dipole moment since all $\ce{C/N-H}$ bonds are in plane. The calculation predicts 1.9 D (away from nitrogen, see here for the direction confusion). This is quite nicely explained in Ron's answer to Pyrrole and furan dipole moments.

The electron density on a particular atom not only depends on resonance but also on inductive-effect. And in case when resonance structures doesn't give a clear answer to the question we go for other effects like inductive effect, no bond resonance etc. So, here by just looking at resonating structures you will not get the answer — for that go for inductive effect and then you will see a clear difference between the electron-densities on different carbons of pyrrole.

• Out of curiosity, how do you explain that when pyrrole donates electrons to electrophiles, the bond forms on C2/5? – electronpusher Dec 16 '16 at 3:44
• It has been already explained in any of the above comments...the intermediate carbocation is resonance stabilised to a greater extent than that in case of an attack at 3/4 or can say at beta position. For more you can go through Gilchrist's book on Heterocycles.Thank You. – user38876 Dec 18 '16 at 20:29
• So you say the distal carbon will be more electron densed as cited in electronpusher's answer? – Harini Dec 20 '16 at 19:09
• Yeaah! Two factors are just confusing you...in case of electron density only resonance can't give you a clear picture hence you will go for inductive effect... But when you will start looking at the site of attack you will have to look at the stability of the resulting intermediate. – user38876 Dec 20 '16 at 19:14
• Wah!! Thanks I got it cleared :) but do give a look at Martin's answer for this question.he has explained it in a new perspective.. :) – Harini Dec 21 '16 at 18:21


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# Homology torsion in the double branched cover of a tangle?

Let $$T$$ be a locally unknotted $$2$$-tangle in $$B^3$$ and $$\Sigma(T)$$ be its double branched cover. Can $$H_1(\Sigma(T))$$ have a non-trivial torsion? (Obviously, not for rational tangles.)

• I feel like there should be plenty of alternating tangles with this property, such as pretzel or algebraic tangles. – Ian Agol Apr 28 at 4:34

An example (similar to Ken's and related to Ian's comment): take the pretzel tangle P(-3,-3,3) drawn below; its double branched cover has homology $$Z \oplus Z/3 \oplus Z/3$$. This is from my paper (Embedding tangles in links, J. Knot Theory Ramif.,9, No. 4 (2000), 523-530).

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# Mixtures¶

A convenient property of submodular functions is that the addition of two of them is still a submodular function. More generally, the linear combination of any number of submodular functions (assuming non-negative weights) is still a submodular function. Because of this, a mixture of submodular functions can be optimized using the same algorithms as an individual submodular function. Mixtures can be useful in situations where there are different important aspects of data that are each submodular.

The general form of a mixture function is

$f(X) = \sum\limits_{i=1}^{M} \alpha_{i} g_{i}(X)$

where $$f$$ indicates the mixture function, $$M$$ is the number of functions in the mixture, $$X$$ is a subset, $$\alpha_{i}$$ is the weight of the $$i$$-th function and $$g_{i}$$ is the $$i$$-th function.

## API Reference¶

This file contains code that implements mixtures of submodular functions.

class apricot.functions.mixture.MixtureSelection(n_samples, functions, weights=None, metric='ignore', initial_subset=None, optimizer='two-stage', optimizer_kwds={}, n_jobs=1, random_state=None, verbose=False)[source]

A selection approach based on a mixture of submodular functions.

This class implements a simple mixture of submodular functions for the purpose of selecting a representative subset of the data. The user passes in a list of instantiated submodular functions and their respective weights to the initialization. At each iteration in the selection procedure the gains from each submodular functions will be scaled by their respective weight and added together.

This class can also be used to add regularizers to the selection procedure. If a submodular function is mixed with another submodular function that acts as a regularizer, such as feature based selection mixed with a custom function measuring some property of the selected subset.

Parameters: n_samples : int The number of samples to return. submodular_functions : list The list of submodular functions to mix together. The submodular functions should be instantiated. weights : list, numpy.ndarray or None, optional The relative weight of each submodular function. This is the value that the gain from each submodular function is multiplied by before being added together. The default is equal weight for each function. initial_subset : list, numpy.ndarray or None, optional If provided, this should be a list of indices into the data matrix to use as the initial subset, or a group of examples that may not be in the provided data should beused as the initial subset. If indices, the provided array should be one-dimensional. If a group of examples, the data should be 2 dimensional. optimizer : string or optimizers.BaseOptimizer, optional The optimization approach to use for the selection. Default is ‘two-stage’, which makes selections using the naive greedy algorithm initially and then switches to the lazy greedy algorithm. Must be one of ‘random’ : randomly select elements (dummy optimizer) ‘modular’ : approximate the function using its modular upper bound ‘naive’ : the naive greedy algorithm ‘lazy’ : the lazy (or accelerated) greedy algorithm ‘approximate-lazy’ : the approximate lazy greedy algorithm ‘two-stage’ : starts with naive and switches to lazy ‘stochastic’ : the stochastic greedy algorithm ‘sample’ : randomly take a subset and perform selection on that ‘greedi’ : the GreeDi distributed algorithm ‘bidirectional’ : the bidirectional greedy algorithm Default is ‘two-stage’. optimizer_kwds : dict, optional Arguments to pass into the optimizer object upon initialization. Default is {}. n_jobs : int, optional The number of cores to use for processing. This value is multiplied by 2 when used to set the number of threads. If set to -1, use all cores and threads. Default is -1. random_state : int or RandomState or None, optional The random seed to use for the random selection process. Only used for stochastic greedy. verbose : bool, optional Whether to print output during the selection process. pq : PriorityQueue The priority queue used to implement the lazy greedy algorithm. n_samples : int The number of samples to select. submodular_functions : list A concave function for transforming feature values, often referred to as phi in the literature. weights : numpy.ndarray The weights of each submodular function. ranking : numpy.array int The selected samples in the order of their gain with the first number in the ranking corresponding to the index of the first sample that was selected by the greedy procedure. gains : numpy.array float The gain of each sample in the returned set when it was added to the growing subset. The first number corresponds to the gain of the first added sample, the second corresponds to the gain of the second added sample, and so forth.
fit(self, X, y=None, sample_weight=None, sample_cost=None)[source]

Run submodular optimization to select the examples.

This method is a wrapper for the full submodular optimization process. It takes in some data set (and optionally labels that are ignored during this process) and selects n_samples from it in the greedy manner specified by the optimizer.

This method will return the selector object itself, not the transformed data set. The transform method will then transform a data set to the selected points, or alternatively one can use the ranking stored in the self.ranking attribute. The fit_transform method will perform both optimization and selection and return the selected items.

Parameters: X : list or numpy.ndarray, shape=(n, d) The data set to transform. Must be numeric. y : list or numpy.ndarray or None, shape=(n,), optional The labels to transform. If passed in this function will return both the data and th corresponding labels for the rows that have been selected. sample_weight : list or numpy.ndarray or None, shape=(n,), optional The weight of each example. Currently ignored in apricot but included to maintain compatibility with sklearn pipelines. sample_cost : list or numpy.ndarray or None, shape=(n,), optional The cost of each item. If set, indicates that optimization should be performed with respect to a knapsack constraint. self : MixtureSelection The fit step returns this selector object.
fit_transform(self, X, y=None, sample_weight=None, sample_cost=None)

Run optimization and select a subset of examples.

This method will first perform the fit step and then perform the transform step, returning a transformed data set.

Parameters: X : list or numpy.ndarray, shape=(n, d) The data set to transform. Must be numeric. y : list or numpy.ndarray or None, shape=(n,), optional The labels to transform. If passed in this function will return both the data and the corresponding labels for the rows that have been selected. Default is None. sample_weight : list or numpy.ndarray or None, shape=(n,), optional The sample weights to transform. If passed in this function will return the selected labels (y) and the selected samples, even if no labels were passed in. Default is None. sample_cost : list or numpy.ndarray or None, shape=(n,), optional The cost of each item. If set, indicates that optimization should be performed with respect to a knapsack constraint. X_subset : numpy.ndarray, shape=(n_samples, d) A subset of the data such that n_samples < n and n_samples is the integer provided at initialization. y_subset : numpy.ndarray, shape=(n_samples,), optional The labels that match with the indices of the samples if y is passed in. Only returned if passed in. sample_weight_subset : numpy.ndarray, shape=(n_samples,), optional The weight of each example.
transform(self, X, y=None, sample_weight=None)

Transform a data set to include only the selected examples.

This method will return a selection of X and optionally selections of y and sample_weight. The default setting is to select items based on the ranking determined in the fit step with examples in the same order as that ranking. Optionally, the whole data set can be returned, with the weights corresponding to samples that were not selected set to 0. This setting can be controlled by setting pipeline=True.

Parameters: X : list or numpy.ndarray, shape=(n, d) The data set to transform. Must be numeric. y : list or numpy.ndarray or None, shape=(n,), optional The labels to transform. If passed in this function will return both the data and the corresponding labels for the rows that have been selected. Default is None. sample_weight : list or numpy.ndarray or None, shape=(n,), optional The sample weights to transform. If passed in this function will return the selected labels (y) and the selected samples, even if no labels were passed in. Default is None. X_subset : numpy.ndarray, shape=(n_samples, d) A subset of the data such that n_samples < n and n_samples is the integer provided at initialization. y_subset : numpy.ndarray, shape=(n_samples,), optional The labels that match with the indices of the samples if y is passed in. Only returned if passed in. sample_weight_subset : numpy.ndarray, shape=(n_samples,), optional The weight of each example.


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## Universality or Non-Universality of Absorption Cross Sections for Extended Objects

• Abstract: The calculation of absorption cross sections for minimal scalars in supergravity backgrounds is an important aspect of the investigation of AdS/CFT correspondence and requires a matching of appropriate wave functions. The low energy case has attracted particular attention. In the following the dependence of the cross section on the matching point is investigated. It is shown that the low energy limit is independent of the matching point and hence exhibits universality. In the high energy limit the independence is not maintained, but the result is believed to possess the correct energy dependence.

### Additional Services

Author: D.K. Park, H. J. W. Müller-Kirsten urn:nbn:de:hbz:386-kluedo-11130 Preprint English 2000 2000 Technische Universität Kaiserslautern 2001/02/16 Fachbereich Physik 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

$Rev: 13581$


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eISSN 2233-6052  l  pISSN 2210-9099

Sung and Etemadifar: Multilevel Analysis of Socio-Demographic Disparities in Adulthood Obesity Across the United States Geographic Regions

Abstract

ObjectivesThe objective of this study was to examine the socio-demographic disparities in obesity among US adults across 130 metropolitan and micropolitan statistical areas.

MethodsThis study used data from the 2015 Behavioral Risk Factor Surveillance System and Selected Metropolitan/Micropolitan Area Risk Trend of 159,827 US adults aged 18 years and older. Data were analyzed using the multilevel linear regression models.

ResultsAccording to individual level analyses, socio-demographic disparities in obesity exist in the United States. Individuals with low socioeconomic status were associated with a higher body mass index. The participants from the Midwest United States tend to have higher body mass index than those who from the South. According to metropolitan and micropolitan statistical area level analyses, secondly, there were significant differences in obesity status between different areas and the relation of obesity with 5 socio-demographic factors varied across different areas. According to geospatial mapping analyses, even though obesity status by metropolitan and micropolitan statistical area level has improved overtime, differences in body mass index between United States regions are increasing from 2007 to 2015.

ConclusionSocio-demographic and regional disparities in obesity status persist among US adults. Hence, these findings underscore the need to take socio-environmental factors into account when planning obesity prevention on vulnerable populations and areas.

Keywords: body mass index; environment; obesity

2. Participants from the South MMSAs areas have higher BMI compared to those who reside in other MMSAs areas.

3. Obesity and socio-demographic status are influenced by geographic areas (130 MMSAs).

Materials and MethodsThis study used data from the 2015 Behavioral Risk Factor Surveillance System (BRFSS) and Selected Metropolitan/Micropolitan Area Risk Trends (SMART). The BRFSS is the nation’s premier system of health-related telephone surveys that collected state data on US residents regarding their health-related risk behaviors, chronic health conditions, and use of preventive services. Established in 1984 in 15 states, BRFSS now collects data in 50 states as well as the District of Columbia and 3 United States territories. BRFSS completes more than 400,000 adult interviews each year, making it the largest continuously conducted health survey system in the world. BRFSS data are generally used to provide state-level estimates. BRFSS and SMART data are used to provide small area-level estimates for MMSAs which were determined by the Office of Management and Budgets. Hence, in order to create localized health information that can help public health practitioners identify local emerging health problems, plan and assess local responses, the Centers for Disease Control and Prevention analyzes BRFSS and SMART data. This specific data selected for this study was from 2015 and was city and countywide including 159,827 US adults aged 18 years and older [35]. This study did not require approval from the institutional review board because the BRFSS data was secondary data that did not include personal information.

1. Why MMSAs selected rather than another type of local administrative unit?MMSAs represent geographic areas that satisfy standard definitions determined by the United States Office of Management and Budget (OMB), which are used by the Census Bureau and other federal, state, and local governmental entities. MMSAs consist of counties and the BRFSS collects data about county of residence. This county information allows the reporting of information by MMSAs. Some cities and counties were excluded from SMART and BRFSS. In order for an MMSA to be included in SMART BRFSS there must be at least 500 respondents within the MMSA and the weighting criteria must be applicable. In order for a county to be included, the county must be within a selected MMSA and the weighting criteria must be applicable at the county level. The State’s BRFSS Coordinator handles these cases [35].

2. Measures

2.1. Dependent variable: obesity

BMI was used as a measure of obesity and it was computed by dividing an individual’s weight by their height squared. BMI is closely linked with percentage body fat and total body fat [36]. Individuals with a BMI of 25 kg/m2 to 29 kg/m2 were regarded as overweight, and individuals with a BMI of 30 kg/m2 or more were considered obese [37].

2.2. Independent variables: socio-demographic variables

Gender was categorized into males and females. Age was categorized into 18–44 years and ≥ 45 years. The education level was categorized into higher education (≥ college diploma) and lower education (< college diploma). Race was categorized into Non-White or Hispanic and Non-Hispanic White. The household income level was categorized into ≥ $50,000 and <$50,000. Regions were categorized into 5 groups (South, Northeast, Midwest, West, Puerto Rico).

2.3. Control variables

Physical activity was categorized into yes and no. Fruit consumption was categorized into ≤ 1 time per month and ≥ 1 time per week.

3. Statistical AnalysisDescriptive statistics with using chi-square (Table 1) and line graph analysis are presented in Figure 1. All descriptive analyses were carried out using STATA (version 15.0, StataCorp LLC., College Station, TX).A mainland United States map of average adult BMI (≥ 18 years) by MMSAs levels in 2007, 2011, and 2015 was created using Arc GIS 10.6 with R (Figure 2).To examine the socio-demographic and regional disparities in adulthood obesity among US adults across 130 MMSAs, 3 multilevel linear regression models of BMI were conducted using STATA. Firstly, the null hypothesis model was implemented (Model I) to determine whether there was a difference in obesity status and these statistical areas. Secondly, the random-intercepts model (Model II) was implemented which considers individual-level predictors in the fixed part to examine how the 6 socio-demographic variables affect obesity status after adjusting for obesity-related health behaviors such as physical activity and fruit consumption. Finally, the random-slope model (Model III) was implemented to examine whether or not obesity status and with the 5 socio-demographic variables varied across the 130 MMSAs.

ResultsTable 1 shows the percentages of obesity rate among US adults ≥ 18 years (N = 159,827). The average percentage of obese people (BMI ≥ 30) in the 130 MMSAs was 29.06% (SD = 4.44). Men were slightly more likely to be obese than women (29.41% versus 29.15%). Participants who were ≥ 45 years were more likely to be obese than those aged 18–44 years (30.60% versus 25.87%). Participants with a higher education (≥ college diploma) were less likely to be obese than those who had a lower education (< college diploma) (24.05% versus 33.45%). Non-White or Hispanic participants were more likely to be obese than Non-Hispanic White participants (33.38% versus 28.03%). Participants with a higher income (≥ $50,000) were less likely to be obese than those with lower income (<$50,000) (26.05% versus 33.05%). Participants from the South and the Midwest were more likely to be obese than those from the Northeast and the West (31.08% and 31.65% versus 29.96% and 25.72%).Table 2 shows the results of multilevel linear regression of socio-demographic status and BMI among US adults (≥ 18 years) in 130 MMSAs (N = 159,827). The average coefficient of Model I was 28.147. The metropolitan and micropolitan statistical area level residual variance at Model I was significant at the 0.001 level, which means that there were significant differences in obesity status between the 130 MMSAs. Model II, III show the unstandardized coefficients from the multilevel linear regression model of the association between socio-demographic variables and obesity status among US adults. According to full model (Model III), firstly, men were associated with higher BMI than women (B = 0.592, p < 0.001). Secondly, participants who were ≥ 45 years were associated with higher BMI than those aged 18–44 years (B = 0.709, p < 0.001). Thirdly, participants with higher education (≥ college diploma) were associated with lower BMI than those who with lower education (< college diploma) (B = −0.743, p < 0.001). Fourthly, Non-White or Hispanic participants were associated with higher BMI than Non-Hispanic white (B = 1.008, p < 0.001). Fifthly, participants with higher income (≥ $50,000) were associated with lower BMI than those who with lower income (<$50,000) (B = −0.292, p < 0.001). Finally, participants from the Midwest MMSAs areas were associated with higher BMI than those who from the South MMSAs areas (B = 0.504, p < 0.01). On the other hand, participants from the West MMSAs areas were associated with lower BMI than those who from South MMSAs areas (B = −0.576, p < 0.01).Random slope model (Model III) analysis shows that the metropolitan and MMSA-level residuals were all significant at the 0.001 level. It means that the obesity status relationship with the 6 socio-demographic variables varies across the 130 MMSAs.Figure 1 displays the association between prevalence of obesity according to the areas (130 MMSAs) and socioeconomic status such as education levels and household income levels. As shown in Figure 1, areas with a higher prevalence of obesity tended to have a higher proportion of people with a lower level of education and a lower household income.Figure 2 displays a mainland United States map of the average adult BMI (≥18 years) by MMSAs levels in 2007, 2011, and 2015. As shown in maps on the left, the mean BMI of all MMSAs has decreased overtime. As shown in both maps, there were no significant differences in BMI according to regions in 2007. However, over time, differences in BMI between the regions widened.

DiscussionThis study is one of the first studies in the United States to examine socio-demographic and regional disparities in adulthood obesity by MMSAs. Multilevel analysis was used to examine the socio-demographic disparities in obesity and examine how this relationship is affected by the geographic areas (130, MMSAs).

< $50,000 73,496 (45.98) 33.05 Region South 44,932 (28.11) 31.08 Northeast 32,401 (20.27) 29.96 Midwest 46,575 (29.14) 31.65 West 33,372 (20.88) 25.72 Puerto Rico 2,547 (1.59) 29.88 MMSA level (n =130) % of obese people in the MMSA where participants live (mean, SD) 29.06 4.44 BRFSS = behavioral risk factor surveillance system; MMSA = metropolitan and micropolitan statistical area; SMART = selected metropolitan/micropolitan area risk trends. Table 2 Multilevel linear regression of socio-demographic status and BMI among US adults (≥ 18 years) (N = 159,827). Model I Model II Model III Coef (SE) Coef (SE) Coef (SE) Fixed effect (individual level) Intercept 28.147*** (0.071) 27.105*** (0.103) 27.058*** (0.118) Gender Male 0.600*** (0.033) 0.592*** (0.040) Female (Ref) Age (y) ≥ 45 0.721*** (0.037) 0.709*** (0.052) 18–44 (Ref) Education level ≥ College −0.790*** (0.036) −0.743*** (0.049) < College (Ref) Race Non-White or Hispanic 1.067*** (0.043) 1.008*** (0.079) Non-Hispanic White (Ref) Income level ≥$50,000 −0.295*** (0.037) −0.292*** (0.039)
< \$50,000 (Ref)

Region Northeast −0.359* (0.166) −0.293 (0.195)
Midwest 0.432** (0.142) 0.504** (0.165)
West −0.657*** (0.160) −0.576** (0.187)
Puerto Rico −1.468* (0.618) −1.227 (0.927)
South (Ref)

Physical activity No 1.800*** (0.040) 1.800*** (0.040)
Yes (Ref)

Fruit consumption ≤ 1 per mo 0.427*** (0.036) 0.422*** (0.036)
≥ 1 per wk (Ref)

Random effect (Between MMSAs)

Intercept 0.774*** (0.053) 0.596*** (0.043) 0.653*** (0.053)

Slopes for gender 0.192*** (0.052)

Slopes for age 0.350*** (0.046)

Slopes for education level 0.324*** (0.052)

Slopes for race 0.654*** (0.073)

Slopes for income level 0.106*** (0.078)
* p < 0.05,
** p < 0.01
*** p < 0.001
BMI = body mass index; MMSA = metropolitan and micropolitan statistical area.


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Karya, built on Mon Jul 24 11:39:07 PDT 2017 (patch 33511aca01257b76b88de7c7a2763b7a965c084e)

Derive.Symbols

Description

Some standard call names. These are used to construct calls symbolically, or so instruments can override standard symbols.

ToExpr and generator are useful for constructing symbolic expressions.

Synopsis

# Documentation

Call used by the infix = syntax.

Cause notes to be stronger or weaker.

Cause notes to be stronger or weaker.


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Math Required?

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mjamer    122
Hello, I would like to learn OpenGL programming, however I''m not that good with math. The last math class I had was about 15 years ago, and that was a semester of geometry. That brings my math background to algebra I and half of geometry. I''ve done alot of research, but my findings make me feel as though I''ll be learning math for 2 lifetimes before I can begin really understanding how to do things in OpenGL. So I come to you all, experts at this stuff, to give me a bit of guidance. I''m married with a child, and work a full time job. I wont be able to really make time to attend any colleges or night classes. What I''d like to know, is what math is required to fully enjoy programming in OpenGL with no limitations other than the hardware itself. My programming background is superb (not to toot my horn!), I''ve been programming in both C and ASM for over 15 years, that part I can handle. It''s just the math. What math is required, and what books or websites can I learn from at home on my own time? Thanks! Mike

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nathanSDK    122
This is a pretty good book:

Mathematics for Computer Graphics Applications
by Michael E. Mortenson

Available at Amazon.com for $45 new. You may also want to just go to a used bookstore and get some books on linear algebra (matrices, vectors, etc.). Don''t know how much more you really need to know than that. Websites: (found on a www.google.com search in about a minute) This looks good: http://mathworld.wolfram.com/ specifically to get started: http://mathworld.wolfram.com/topics/VectorAlgebra.html http://mathworld.wolfram.com/topics/Matrices.html Also, a lot of introductory game programming books usually have either a section at the beginning or an appendix that explains some of the basic math needed. Share this post Link to post Share on other sites mjamer 122 Thanks for the reply NathanSDK, I will look into purchasing the math book you reccomended. I just hope it starts slow enough for me to grasp it. The links you provided are as I suggested, seemingly a lifetime to learn just what that stuff means. I''m sure one day I''ll be able to browse around wolfram with confidince and understanding, but I''m just not there yet. An example as to how unknowledgeable I am, I do have the Alan Watt - 3d Games real-time rendering and software technology, and 3d game engine design - David Eberly. Both of these books blow me away with the math in just the first 2 chapters. I need away to learn up to and including what they''re talking about. If I need to start over with basic algebra, so be it. Just need to know where I should start for this. =) Thanks again, Mike Share this post Link to post Share on other sites nathanSDK 122 A better option may actually be to take an online class. That way you could also ask the instructor if you got stuck. I have read a review of www.gameinstitute.com and it seems like they have a pretty neat program. The particular class you would want to take would be: Game Mathematics. At$95 it's not that steep, and the
material looks pretty comprehensive.

In regards to those links, I looked again and you may want
to just use those as one of many references instead of a
starting point. :-)

I think your best bet might be to take the Game Institute
class. This link is a review on the Game
Institute "school". Granted, there's a link to it their front
page, but I remember reading it before it was there and believe
it is an honest report.

[edit: fixed links for real this time! =)]

[edited by - nathanSDK on June 9, 2002 10:06:46 PM]

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llvllatrix    340
Hi, im in high school and learned most of my 3d math from www.sosmath.com. I learnt enough to build my own (ineffeicient) 3d api (something like a primative opengl thing, but with no textures). 3D Math isn''t that hard, mostly matricies and vectors. You can pick it up on the fly, and its not worth paying for.

Im just curious. You have been programming for 15 years and dont know much about math? I thought programming was math. Then again i have spent no time in the industry. What am i in for?

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Jedi of Myth    122
mjamer, a lot of Opengl is basic geometry and algebra. At the very least, knowledge about Cartesian Geometry to plot polygons to the screen is the least you need to start.

Don''t feel that you need to know a lot of theory behind concepts in OpenGL in order to get them to work. I myself am still learning a lot of the ropes in 3D graphics (I started this January.) For me, I try and obtain a working knowledge of a concept first and then go back to the theory when I''m comfortable.

In short, my advice is to take your time, learn at your own pace, and practice with what you know.

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Guest Anonymous Poster
Vectors and Matricies are really important, try to learn those...they are really easy also. I dont know what books are good though because I learned it in college.

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glDino    122
||v||atrix,

I just graduated from high school myself, and I am entering Drexel university as a software engineering major in a couple months. Having looked through the required courses for my major, I am in for a good deal of mathematics (at least 9 courses including calculus and statistics) This really frightened me, so I did a search on the internet to see what other software engineers thought about their jobs. One guy said that whenever his work required any intensive mathematics, he collaborated with a mathematician So maybe there is a light at the end of the tunnel for those not so mathematically inclined, like myself... at least I keep telling myself that!

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yellowjon    144
You could in theory, never learn linear algebra or calculus, and get by fine in 3d game programming. All you would have to do is take the given formulas and put them into the program. On the other hand, if you understand the math, you would understand how the stuff works and what happens when things go wrong. I started programming in opengl in Junior year of high school (before I linear algebra) and I was even able to program my own 3d engine with software rendering in java, so I know that it can be done. However, I think you will find that you''ll start wanting to learn some of the math that goes on behind the scenes. I started to look up matrices and vector math online, and learned a great deal. Now I''m a math major in college!

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mjamer    122
Thank you everyone, with all the replies I have a pretty clear picture on proceeding. I appreciate everyone''s help!

||v||atrix,
How do I program without knowing advanced math? By not knowing I know any advanced math. With the exception of way out there theoretical math, the rest is just built with +,-,*, and / that''s how I work, things make sense in programming. I''m sure some mathematician would label things as this formula or that discipline, but to me it''s just getting the job done. As glDino said, when it isn''t simple problem solving mathematics, an expert will be referred to.

If you''re worried you need to know alot of math to be a programmer, think of a musician, a guitarist perhaps. There is quite a bit of math in music/music theory, more than one would imagine. Yet there are some brilliant guitarists, and musicians that have never learned to read music, or have ever studied music theory. I''m willing to wager that if you asked a few of them, or even your local neighborhood guy that learned by ear the mathematics behind what he does, he''ll not know. Sometimes I guess ya know but you don''t know you know, and it''s ok! =)

Thanks again to everyone!
Mike


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# Parallax background positions when jumping

I am currently building my first Mobile game. The concept is pretty simple, it's a sideways scroller.

I have implemented 5 layers to act as parallax scrolling, these are working quite well for general movement. However they look a bit weak when jumping, I would like to apply some sort of ratio which gives a 3d effect to the jump. I made a basic attempt, however it just looks a bit naff.

I have struggled to find any tutorials on this , could anyone provide any help?

As requested, here is some example code

    backgroundJumpEnd = function(){
transition.to(hills,{time=600,y=153})
transition.to(hills2,{time=600,y=153})
transition.to(hills3,{time=600,y=153})
transition.to(tree,{time=600,y=153})
transition.to(trees,{time=600,y=180})
transition.to(cloudsBig,{time=500,y=cloudsBig.y-6})
transition.to(cloudsBig2,{time=500,y=cloudsBig2.y-6})
transition.to(cloudsSmall,{time=500,y=cloudsSmall.y-2})
transition.to(cloudsSmall2,{time=500,y=cloudsSmall2.y-2})
transition.to(sky,{time=500,y=sky.y-3})
transition.to(sky2,{time=500,y=sky2.y-3})
transition.to(sky3,{time=500,y=sky3.y-3 })
transition.to(floor,{time=500,y=floor.y-15})
}

backgroundJumpStart = function (){
transition.to(hills , {time=500, y=180,onComplete=backgroundJumpEnd })
transition.to(hills2,{time=500,y=180})
transition.to(hills3,{time=500,y=180})
transition.to(tree,{time=500,y=185})
transition.to(trees,{time=500,y=220})
transition.to(cloudsBig,{time=500,y=cloudsBig.y+6})
transition.to(cloudsBig2,{time=500,y=cloudsBig2.y+6})
transition.to(cloudsSmall,{time=500,y=cloudsSmall.y+2})
transition.to(cloudsSmall2,{time=500,y=cloudsSmall2.y+2})
transition.to(sky,{time=500,y=sky.y+3})
transition.to(sky2,{time=500,y=sky2.y+3})
transition.to(sky3,{time=500,y=sky3.y+3})
transition.to(floor,{time=500,y=floor.y+15})
}

• I guess you should specify what programming language you're using by adding a tag. – user1306322 Mar 5 '13 at 12:37
• I was after a kind of general ratio / guide really. I didn't want to get too hung up on languages or frameworks, more principles of how this can work effectively – user499846 Mar 5 '13 at 12:55
• Why exactly do you think it looks poor when a sprite jumps? It should look exactly the same. Could you give an example of what you want it to look like? – Tony Mar 5 '13 at 17:26
• Try using the golden ratio. – aglassman Mar 5 '13 at 17:29
• @tony hey, so horizontal scrolling seems to look and feel fine, however vertically the I have played around with a few different ratios however it doesn't seem to give any depth of field. It seems to be a common technique used in most Mobile games - (ski safari - wimp are a couple of examples) but I can't seem to find any resources or tutorials, everything seems to cover horizontal only – user499846 Mar 5 '13 at 23:13

I have used Parallax background in my game and I don't understand, why should the vertical and horizontal ratio should be any different. I have only 3 layers. Static background, parallax layer that moves half the speed as the front (game) layer. In my game, there's a lot of vertical and horizontal movement and it simply looks the best when the vertical and horizontal movement is the same.

Now adding one more layer that moves 1/4 of the speed horizontally (so it is further), why shouldn't it be the same ratio vertically?

If I just consider mathematical point of view, parallax layers are like slices of the real world. We make a lot of simplifications when making games, so let's do some:

Draw a hypothetical line from your eye all the way the infinity, so the line is perpendicular to your body. The point in infinity never moves.

When you move left one meter, the start point of the line moves one meter to the left. The point that we will consider placement of parallax layer with horizontal ratio 0.5 (let's call it X, it moves half the distance) will move half a meter left. Now go back and duck. The line will move 1 meter down (depends on your height, really...) and the point X moves half a meter down, doesn't it?

So doesn't it look "weak" simply because your run left and right for a long distance, but you jump only a little?

TLDR: Same ratio.

It's hard to answer without seeing what you have and how it compares to what you want.

First thing's first, change all those values to variables. That'll make it much easier to update.

Second, your JumpStart and JumpEnd have different time values for your hills, which from what little I know of your code, should make things look weird. Also, their y values are different, which should slowly pull them out of sync.

Third, a picture would help. Most parallax games use foreground, midground, and background. Occasionally, games throw in more layers, but they're not necessary. This naturally groups your elements into the segments that move together (the further you get from the screen, the less they should move). With the code you have here, it's hard to tell which elements should move more than others.


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# Generate Constrained Vector of Random Numbers?

I'm having trouble creating a random vector $\vec{V}$ starting with a standard 0:1 randon number generator subject to the following set of constraints: (given parameters $D$, $L$, and $\theta$)

1. The vector $\vec{V}$ must be $N$ units long
2. The elements must have an average of $\theta$
3. No 2 successive elements may differ by more than +/-10 (i.e. $|V_i-V_{i+1}|\leq 10$)
4. $D = \sum_i(L*cos(V_i-\theta))$

I'm having the most problems with the last one. Any ideas?

Edit
New thought on the problem: I've noticed that constraints (2) and (4) can be simplified by setting $\theta$ to 0 and then once a valid vector for $\theta==0$ is found, add $\theta$ to all elements to bias the mean to the true $\theta$ again.

-
Do you want the result to have any particular distribution? –  joriki Apr 10 '13 at 5:07
Not picky, but it would be nice if the original random numbers used were a uniform distribution. Makes the coding easier later. –  CodeFusionMobile Apr 10 '13 at 5:19
To that end, I would even accept a trivial solution to the constraints that could be randomly perturbed in some way. –  CodeFusionMobile Apr 10 '13 at 5:22


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# model on trigonometry in real life

Over the course of 6 months we have seen our daughter's confidence in math grow. Trigonometry is a branch of mathematics that helps us to find the angles and distances of objects. Currently he is a senior and scored in the 85th percentile on the SAT in math with the help of Mathnesium instruction on the SAT. This resource is designed for UK teachers. Do archaeologists use trigonometry? We used tutors and attempted to help her at home. I seriously have not had one complaint in over a year of our relationship with you all! She enjoys coming here and her grades have improved. Use technology to write a trigonometric model, as applied in Example 4. Although my students doesn't attend as often now as he has in the past, having Mathnasium as a continuing resource for homework assistance and test prep is really invaluable. We are so glad that we decided to join Mathnasium. Even in projectile motion you have a lot of application of trigonometry. Round your answer to the nearest tenth.. Show Answer I had great experience with it , the teachers are very helpful and willing to teach your kid as long your kid is ready to be taught they will do everything in their power to get them on track. I highly recommend Mathnasium to any student and parent. Great place to learn with amazing staffs. Trigonometry will help to solve for that third side of your triangle which will lead the plane in the right direction, the plane will actually travel with the force of wind added on to its course. I would definitely recommend them! Definitely one of the best place for any student expecting to be challenged. All of the teachers in the Pflugerville Mathnasium are friendly, helpful and super supportive. The successful reality rapper, T.I. The angle of elevation from a point 43 feet from the base of a tree on level ground to the top of the tree is 30°. My son enjoys his time at Mathnasium. For example music, as you know sound travels in waves and this pattern though not as regular as a sine or cosine function, is still useful in developing computer music. They have put forth every effort to ensure that he has mastered the content. It is used naval and aviation industries. It is used in cartography (creation of maps). It has been a wonderful resource to have the support he needed to close the gaps he had. Trigonometry is used in satellite systems and astronomy, aviation, engineering, land Even with the transition to virtual! It’s March, which means March Madness for fans of college basketball. In physics, trigonometry is used to find the components of vectors, model the mechanics of waves (both physical and electromagnetic) and oscillations, sum the strength of fields, and use dot and cross products. Trigonometry is used to divide up the excavation sites properly into equal areas of work. 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Example $$\PageIndex{1}$$: (Continuation of Progress Check 2.16) Now that we have determined that $V(t) = 35\cos(\dfrac{5\pi}{3}t) + 105$ (where $$t$$ is measured in seconds since the heart was full and $$V(t)$$ is measured in milliliters) is a model for the amount of blood in the heart, we can use this model to determine other values associated with the amount of blood in the heart. This was around 2000 years ago. He doesn’t really jump straight along the Y axis, it is a slightly curved path or a parabolic path that he takes to tackle the obstacles on his way. Mathnasium is where students in ... It’s that time of year again! My daughter absolutely loves Mathnasium in Pflugerville, Texas. They were able to help him increase his score in just five weeks. 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As you know Gaming industry is all about IT and computers and hence Trigonometry is of equal importance for these engineers. It is a great experience, it's very helpful. And this means sound engineers need to know at least the basics of trigonometry. We are so gllad we found Mathnasium!!! Great Staff And Great Owner (SanJay) that make the program fun for our daughter and makes sure to keep us included step by step with all of her progress. Can trigonometry be used in everyday life? The wind plays an important role in how and when a plane will arrive where ever needed this is solved using vectors to create a triangle using trigonometry to solve. My son enjoyed tutoring from Mathnasium. She is more confident now as a freshman in high school because of their tutoring. My daughter looks forward to attending her classes and learning various math techniques. By clicking the 'Submit' button below, you confirm that we have your express written consent to contact The Pflugerville location staff have completely turned our daughter's dread of math into interest. It is used naval and aviation industries. Previous section Problems Next section Problems. SO Is trigonometry really relevant in your day to day activities? Go Pflugerville Team!!! Categories & Ages. The instructors are all great. I am very satisfied with the feedback and progress monitoring that has been given out! Does this ever show up in real life?" Thank you for all you've done, and all you continue to do for my son! He complains that at school he just gets a bunch of red x’s and never knows what he did wrong and just fails the assignment. The Mathnasium in Pflugerville, TX is absolutely amazing. Their commitment to excellence and their dedication to their students are exceptional. She feels more confident at school. you by telephone, email, and/or text messages and that you have reviewed and agree to our, This site uses cookies to monitor the performance of this website and improve your browsing experience. View US version. We are only 5 week in and our daughter has had positive feedback. We love Mathnasium! I can see the improvement in her math understanding and being able to able the lessons in the every day world to get the answers she needs. Flight engineers have to take in account their speed, distance, and direction along with the speed and direction of the wind. He doesn’t really jump straight along the Y axis, it is a slightly curved path or a parabolic path that he takes to tackle the obstacles on his way. They can also use it to measure the distance from underground water systems. We have built a great partnership over the last 3 years and my child is doing exceptional well in Algebra I. Trigonometry and its applications: Trigonometry is used PPT. Felt they listened to my concerns of my childs challenges and they helped with focusing on my son's weaknesses and challenges as well as give him the confidence he needed. Learn trigonometry for free—right triangles, the unit circle, graphs, identities, and more. She gained confidence, caught up with her class and excel at the end ... they targeted her specific weaknesses and got her to much better place in logical thinking and truly understanding math! Real life contexts for trig and Pythagoras, including gradients of roads, felling trees, surveying roads, landing aircraft. Presentation Summary : Trigonometry and its applications: Trigonometry is used widely in the real life applications. My daughter's confidence with math has increased greatly since she began over a year ago. The six different identities are used to find either the length of one one or more sides of a shape, or the angle at which different materials should be placed at. The tutors have been great and more importantly patient with my son. My son has always struggled in math and now he has a little more confidence thanks to Mathnasium and his hard work. About this resource. Excellent staff, flexible and cooperative. strongly recommend. In physics, trigonometry is used to find the components of vectors, model the mechanics of waves (both physical and electromagnetic) and oscillations, sum the strength of fields, and use dot and cross products. That has been a real confidence killer for him. Problem-solving skills. Looking forward. He feels comfortable learning and says he’s happy doing math because you not only teach him, but if he gets a problem wrong, you show the right way. I can see a difference in her confidence when spraking about math. The Pythagorean Theorem is a statement in geometry that shows the relationship between the lengths of the sides of a right triangle – a triangle with one 90-degree angle. I wish all the other fixes in life were this easy. Another answer According to Morris Kline, in his book named- Mathematical Thought from Ancient to Modern Times, proclaimed that ‘trigonometry was first developed in connection with astronomy, with applications to navigation and construction of calendars. Use this location during the summer months in 2017. Model data with a sine or cosine function. Really was the smartest and most efficient program for us. We have noticed great improvement with our sons Math class due to the addition of Mathnasium! The Real Life of T.I. The … For example, if a plane is travelling at 234 mph, 45 degrees N of E, and there is a wind blowing due south at 20 mph. They were patient and very knowledgeable. Info. Trigonometry Trigonometry is derived from Greek words trigonon (three angles) and metron ( measure). Marine biologists often use trigonometry to establish measurements. Trigonometry - Real Life Uses. In marine engineering trigonometry is used to build and navigate marine vessels. There are following real life application of trigonometry: In Measuring the Height and Building or Mountain As we have studied that the trigonometry defines the relationship between sides and angles of a triangle. and the many other such things where it becomes necessary to use trigonometry. My son says he wishes all his classes at school were taught this way . Report a problem. Thus, if we consider that building or mountain as the perpendicular and the base of building is on the plane road. From the director, Kendall, and owner of the Pflugerville Mathnasium to our son's wonderful teacher, Matt, J has learned well and comes out of his sessions there upbeat. I cant give enough praise to the awesome owner Sunjay and the amazing director Kendall. Some real life applications of the trigonometric functions include architecture, biology, cartography (creation of maps), chemistry, geophysics, engineering, medical imaging (CT scans and ultrasounds), music theory, pharmacology, psychology, visual perception, etc. My son has benefited by the tutoring in his math and Physics classes all through high school. I hope you find it useful. Emma has grown tremendously with your help.   pflugerville@mathnasium.com. However, the origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and India more than 4000 years ago. Great Team and I love the Communication!!! Trigonometry in Criminology. Trigonometry is a very different subject than most of the math we encounter in our lives previously, and it takes a different way of thinking to understand. My is doing much better with the guidance and support with his math and physics class. 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Also trigonometry has its applications in satellite systems. He shares this with me each time and I am automatically able to see their areas of need and what he is currently working in! I am so very thankful for the service you provide. We recommend them to anyone who has a child struggling with math. While she has a curriculum she is working through, she values the time spent on homework review. The time and care given to help each student succeed is extraordinary. We didn't just want for our daughter to make good grades on tests. The sine and cosine functions are fundamental to the theory of periodic functions, those that describe the sound and light waves. Answers included on the end of the sheet. It is used in oceanography in calculating the height of tides in oceans. The one on one attention and positive reinforcement are moving him through the math curriculum that the teacher in the regular classroom could not accomplish. Thanks for providing a good learning environment. Thanks you and we plan to go to Mathnasium for SAT and ACT prep. Trigonometry is one of the basic math classes that you typically take in high school, and you also need it as a core course for almost any bachelor's degree. For example music, as you know sound travels in waves and this pattern though not as regular as a sine or cosine function, is still useful in developing computer music. Created: Dec 28, 2012. After meeting and working with your teachers his understanding increased and he passed the class. For example, to find out how light levels at different depths affect the ability of algae to photosynthesize. My son’s grade and understanding have improved tremendously. Examples of Trigonometry Being Used in Construction Jobs. In Chapter 4, you will use both perspectives to graph trigonometric functions and solve application problems involving angles and trian-gles.You will also learn how to graph and evaluate inverse trigonometric functions. 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Electrical engineers use trigonometry to model this flow and the change of direction, with the sine function used to model voltage. In a very short time, she has completely changed how she views herself and her ability to learn. Read: Height & Distance Important Questions Now, this building or mountain baseline is considered as the base of the triangle. You guys have been extremely wonderful with Meisi and so patient and understanding with my family! Sometimes when we talk about learning calculus, we talk about some of the amazing jobs you can get as a result. Mathnasium attempts to get to know the students and determines a teaching style that is effective for each student. They have helped my son succeed in every area of Math. In just one month, our 8th grade daughter is back to her old self. She knows now that there are multiple ways to learn math and that she can learn anything. All rights reserved. The height of the building, the width length etc. Math Enrichment and Accelerated Programs in Pflugerville. We had an extraordinary experience with our five kids in Mathnasium. Every time you flip on a light switch or turn on the television, you’re benefiting from one of trigonometry's many uses. Our son was failing math terribly. Trigonometry can be used to roof a house, to make the roof inclined ( in the case of single individual bungalows) and the height of the roof in buildings etc. In physics, trigonometry is used to find the components of vectors, model the mechanics of waves (both physical and electromagnetic) and oscillations, sum the strength of fields, and use dot and cross products. Teens listen to rap because they like the beat and lyrics. Her passion and support helped my son believe in himself. And the good music that these sound engineers produce is used to calm us from our hectic, stress full life – All thanks to trigonometry. The team did an amazing job of tailoring and implementing Math Instruction for my son's SAT. Archaeologists identify different tools used by the civilization, using trigonometry can help them in these excavate. I'd recommend it to anyone without a second thought. Trigonometry is even used in the investigation of a crime scene. 12: Introduction to Trigonometry and Angles. Free worksheet(pdf) and answer key on real world applications of sohchatoa. Trigonometry can be used to roof a house, to make the roof inclined and the height of the roof in buildings etc. This is a good worksheet for independent learners and those needing extension work. Mathnasium is great. The answer is most definitely yes. He started to do better on tests. To find out more about cookies or learn how to change your cookie settings, please see our. As we know sound travels in waves and frequencies. I came in for calculus 2 tutoring, it's hard to find good college level tutors and they were awesome! My child was getting D's in math and shortly after joining Mathnasium started getting A's. What is the height of the tree? In physics, trigonometry is used to find the components of vectors, model the mechanics of waves (both physical and electromagnetic) and oscillations, sum the strength of fields, and use dot and cross products. She feels that she is able to learn Algebra and that gives her confidence to try. While she still has to work a little harder than most, she relies on the methods she learned at Mathnasium. Mathnasium did a great job identifying my child's gaps in math and did an incredible job at filling those gaps. We have seen such an attitude change. I always recommend Mathanasium as a great resource in math. March Mathness - The Statistics Behind Building the Perfect Bracket. After continuous 2 hour sessions every week from April into the summer as well as Fall. Also supports the maths needed in BTEC Engineering and Construction. 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The team is very knowledgeable, patient, and encouraging. Mathematics; Mathematics / Geometry and measures / 2D properties of shapes; Archaeologists identify different tools used by the civilization, using trigonometry can help them in these excavate. I have seen such an improvement with her. I am very happy with the progress that my son has made in math. It's changed how my daughter thinks about math, and I'm excited for my son to be old enough to attend next year. It's been only one month and Mischa's teacher already sees a difference. They have patience and care about your kids. Nicholas [LAST NAME REMOVED] has been doing well and is performing much better. And this means sound engineers need to know at least the basics of trigonometry. Even in projectile motion you have a lot of application of trigonometry. The assessments given were definitely an eye opener and helped us as parents see where he needed to improve most. 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Learning to handle an array of topics is critical to future progress as opposed to facing struggles down the road since math is very cumulative. This is done by analyzing given data about the Ferris wheel, plotting a few known points on the graph of the model, and finally creating the equation of the function. They go beyond the contracted hours to ensure the students fully grasp the mathematical concepts. It is a study of relationships in mathematics involving lengths, heights and angles of different triangles. It was a good way to keep the kids working on math facts through the summer. In physics, trigonometry is used to find the components of vectors, model the mechanics of waves (both physical and electromagnetic) and oscillations, sum the strength of fields, and use dot and cross products. They focus on progress and not rote learning. Trigonometry spreads its applications into various fields such as architects, surveyors, astronauts, physicists, engineers and even crime scene investigators. This place makes learning math more enjoyable and the tutors truly care about their students. We appreciate your willingness to make adjustments to the schedule. My child fills out a what I worked on sheet and ponders 3 things that are asked if him to complete! A computer cannot obviously listen to and comprehend music as we do, so computers represent it mathematically by its constituent sound waves. Due to his hard work in Math I can see his esteem and confidence change in such a positive way! They can also use it to measure the distance from underground water systems. 30. After his first day at Mathnasium, his confidence was soaring and he came out of the class excitedly telling me that he could do math after all! It is extensively used in architecture, astronomy, electronics, The Real Life of T.I. It is used in navigation in order to pinpoint a location. Architects use trigonometry to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles. He is more confident about his ability to complete math problems. For that reason, many people just want to get it over with when trig comes up in school. Kendall (Office Mgr @ the Pflugerville location) and her staff are extraordinary. Then a friend recommended Mathnasium. One word describes Mathnasium Pflugerville and the team of wonderful leaders...AMAZING!!! Our son has made leaps and bounds with his grades due to Mathnasium! In construction we need trigonometry to calculate the following: Architects use trigonometry to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles. Thanks Sunjay to you and your outstanding team! 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29/12/2020


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Now showing items 1-4 of 4

• #### A high order numerical method for solving nonlinear fractional differential equation with non-uniform meshes

We introduce a high-order numerical method for solving nonlinear fractional differential equation with non-uniform meshes. We first transform the fractional nonlinear differential equation into the equivalent Volterra integral equation. Then we approximate the integral by using the quadratic interpolation polynomials. On the first subinterval $[t_{0}, t_{1}]$, we approximate the integral with the quadratic interpolation polynomials defined on the nodes $t_{0}, t_{1}, t_{2}$ and in the other subinterval $[t_{j}, t_{j+1}], j=1, 2, \dots N-1$, we approximate the integral with the quadratic interpolation polynomials defined on the nodes $t_{j-1}, t_{j}, t_{j+1}$. A high-order numerical method is obtained. Then we apply this numerical method with the non-uniform meshes with the step size $\tau_{j}= t_{j+1}- t_{j}= (j+1) \mu$ where $\mu= \frac{2T}{N (N+1)}$. Numerical results show that this method with the non-uniform meshes has the higher convergence order than the standard numerical methods obtained by using the rectangle and the trapzoid rules with the same non-uniform meshes.
• #### High-Order Numerical Methods for Solving Time Fractional Partial Differential Equations

In this paper we introduce a new numerical method for solving time fractional partial differential equation. The time discretization is based on Diethelm’s method where the Hadamard finite-part integral is approximated by using the piecewise quadratic interpolation polynomials. The space discretization is based on the standard finite element method. The error estimates with the convergence order O(τ^(3−α) +h^2 ),0
• #### Higher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth Data

Two higher order time stepping methods for solving subdiffusion problems are studied in this paper. The Caputo time fractional derivatives are approximated by using the weighted and shifted Gr\"unwald-Letnikov formulae introduced in Tian et al. [Math. Comp. 84 (2015), pp. 2703-2727]. After correcting a few starting steps, the proposed time stepping methods have the optimal convergence orders $O(k^2)$ and $O(k^3)$, respectively for any fixed time $t$ for both smooth and nonsmooth data. The error estimates are proved by directly bounding the approximation errors of the kernel functions. Moreover, we also present briefly the applicabilities of our time stepping schemes to various other fractional evolution equations. Finally, some numerical examples are given to show that the numerical results are consistent with the proven theoretical results.
• #### On the behavior of the solutions for linear autonomous mixed type difference equation

A class of linear autonomous mixed type difference equations is considered, and some new results on the asymptotic behavior and the stability are given, via a positive root of the corresponding characteristic equation.


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# Z-score/percentile rank question

1. Jul 6, 2011

### ACHQ

SO the entrance to a college is based off of two factors: 54% grade point average, and 46% supplemental application. Both factors are standardized by the college using a z-score.

If a student is ranked in the only ~55 percentile for his grade point average, what percentile rank (approximately) would be needed on their supplemental application in order to be among the ~85 percentile of applicants?

(This is not homework and relates to an actual application)

Thanks

2. Jul 7, 2011

### chiro

I'm going to base my calculations off the assumption that your percentile is calculated using the formula:

Final Percentile = 100 x [ (Percentile Probability of GPA From Normal Distribution) x 0.54
+ (Percentile of Supplemental Application) x 0.46 ]
= 100 x [0.54 x P1 + 0.46 x P2] %

We are given in your example P1 = 0.55, and you want Final Percentile (FP) = 85%.

Using some algebra we get:

85 = 100 x [0.54 x 0.55 + 0.46 x P2] (P2 is supp application percentile probabilty)

Arranging terms and solving for P2 we get

P2 = 1.202173913

This means with 55 percentile for GPA you can not possibly get 85% percentile.

If you want to know the maximum percentile let P2 = 1 (100% percentile) and you find that your maximum overall percentile is 0.46 + 0.55 x 0.54 = 0.757 or roughly 76% percentile (rounded up)

In the above I'm assuming 99 percentile is top 1% and that the percentiles are weighted like you said above (54% GPA, the rest application).

3. Jul 7, 2011

### uart

I'm reading the question a little different chiro. I'm thinking that if they normalize both the GPA and the Supp to Z scores and then form the weighted average of those two Z scores, then the result will no longer be a Z score and will have to get normalized again - which changes the outcome somewhat.

Here's my thinking on this.

Start with Z score, N(0,1), and times by 0.54. The resulting variance is 0.54^2 x 1^2. And similar for the other one.

Let X3 = 0.54 Z1 + 0.46 Z2. This the sum of normal RV's variance 0.54^2 and 0.46^2 therefore variance of X3 is 0.54^2 + 0.46^2 = 0.5032. (stdev = 0.7094).

So X3 is not as yet a Z score since the variance in not unity. So we need to use Z3 = X3/sd3 which is normal.

Putting it all together, for the percentiles the OP states when can look up the normal cdf and find we have Z1=0.15, Z2=? and Z3=1.04

$$Z_3 = \frac{0.54 Z_1 + 0.46 Z_2 }{0.7094}$$

Putting in the given data and solving for Z2 I get Z2=1.43, corresponding to about the 92nd to 93rd percentile.

I think this is correct but to be honest I'm not 100% sure.

4. Jul 7, 2011

### chiro

Yeah I think you're right uart. The assumption that the weights are purely linear is probably not the best way to describe the problem.

5. Jul 9, 2011

### ACHQ

The linear assumption isn't really correct. The reason being is that they normalize both the GPA and the Supp to Z scores and then take the top ~15% of the "weighted average score". uart seems to be on the right track, I myself couldn't figure out the math behind it, but that number 92-93rd percentile seems to make sense.

I know for a fact that individuals that score in the 55-65 percentile for the GPA component do get into that college, based off of their supplemental application. I just wanted to put a number estimate on how stellar of a supplemental application one would need if they fell into that GPA range.

Thanks!

6. Aug 25, 2011

### ACHQ

So if the college's admission criteria were: 27% GPA, 27% Standardized test, 46% Supplementary application (again all have been Z-scored individually), would the same formula still apply, except instead of the variance being 0.54^2 + 0.46^2 = 0.5032 (stdev = 0.7094). It would be 0.27^2 + 0.27^2 +0.46^2 = 0.3974 (stdev = 0.5978)????

7. Aug 25, 2011

### uart

Yes, that would be correct. The weighted sum of the Z-scores would not itself be a z-score but could be considered a random variable with zero mean and stdev of approx 0.5978 as you calculated. So dividing it by this stdev will turn it back into a z-score.

8. Aug 31, 2011

### ACHQ

Ok I get everything except for one thing...

Why is the variance of each sum equal to : 0.27^2, 0.27^2, 0.46^2 respectively (i.e. why is the variance equal to the %weight squared?)

Thanks!


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# Recombinant Protein Expression: How to Choose the Right Affinity Tag

So, you have selected a protein for biochemical studies and have cloned it into a tag-containing vector. After successfully expressing your protein in a soluble form, all you need to do is pick it out from the proteome pool of the expression system, such as E. coli or insect host cells.

An affinity tag, just like an identity card, allows you to identify and separate your protein from hundreds of others (a VIP status, sort of!). Protein purification affinity tags enable your protein to bond with resin-attached molecules, leaving behind other, non-tagged proteins (no tag, nothing to brag).

This short introduction to commonly used affinity tags will help you select the best one for your experimental conditions and obtain a joyful, “proteinaceous” reward for your hard work.

## 6X-His (hexahistidine) Tag

Hexahistidine tags are one of the most commonly used affinity tags. It utilizes the ability of histidine to coordinate with transition metal ions, such as Ni2+, Co2+, and Cu2+. Owing to its small size, it is non-toxic and does not interfere with the immunogenicity or physiochemical properties of the protein.

One should proceed with caution if using denaturing agents, such as urea, or reducing agents, such as dithiothreitol (DTT), as they may disturb the metal-ion resin.

A 6x-His tag is a great option for experiments involving a prokaryotic expression system. I achieved >95% purity of a cytoplasmic protein from Leishmania sp. in a single step using a Ni-nitrilotriacetic acid (NTA) resin. Moreover, you can regenerate and re-use the resin numerous times (a boon during fund crunch in the lab), given that conditions are amenable during each purification cycle.

## Glutathione-S-transferase (GST) Tag

This tag works on the principle of GST’s affinity for immobilized glutathione. A GST tag can increase the solubility of your expressed protein in a prokaryotic system. You can remove the 26-kDa tag while the fusion protein is still bound to the glutathione resin, or you can elute the tagged protein. Tag removal is recommended as it may affect the properties of the fusion protein.

The elution procedure is mild, thus preserving the protein’s immunogenicity and properties. GST-based purification gives good yields. However, if your purification procedure requires the use of reducing agents, such as DTT or $\beta$-mercaptoethanol ($\beta$-ME), denaturing agents, such as urea or guanidine HCl, or detergents, GST-based chromatographic purification may be less effective.

Watch out for co-elution of an unwelcomed guest (70-kDa E. coli chaperonin) with your protein. In such a situation, treat the lysate with 5 mM MgCl2 and ATP before eluting.

## Maltose-Binding Protein (MBP)

The main aim of this tag is to increase the solubility of the fusion protein, thus it may be your tag of choice when purifying membrane or lipophilic proteins. MBP-based purification helped me obtain decent expression and yield of a membrane protein that was difficult to achieve with a 6X-His-tag.

This tag gives a good yield; however, the size of the MBP tag (46 kDa) could be a concern if your downstream application is immunization. In such a scenario, you should consider removing the tag to avoid altering the protein’s immunogenicity.

The MBP-fusion protein bound to an amylose resin is eluted by running maltose in the elution buffer. This method is fairly resistant to denaturants, reducing agents, and detergents. However, any amylase activity in the cell lysate may reduce the efficiency of the amylose resin.

## Calmodulin-Binding Protein (CBP)

This procedure utilizes the C-terminal domain of myosin light-chain kinase (MLCK) as a purification tag. In the presence of low levels of calcium, CBP has a high affinity for resin-attached calmodulin. Combined with superaffinity, smaller (4 kDa) size, and mild elution conditions, CBP tags are good if you are dealing with a delicate or finicky protein.

It can withstand low levels of notorious (yet sometimes essential) components such as denaturants, detergents, and reducing agents.

## Streptavidin/Biotin-Based Tag

Who is not aware of the great affinity that biotin and streptavidin have for each other? Well, you can utilize it for protein purification by biotinylating your protein of interest and making it ‘pretty’ in avidin’s eyes (avidin-attached resins)!

Non-specific binding during purification is negligible in this method; however, the use of denaturing agents is a big ‘no-no’. This is widely used for immobilizing biotinylated fusion proteins on surface plasmon resonance (SPR) chips for functional studies.

## Strep-Tag® Peptide System

This is a modification of the streptavidin/biotin-based purification system. The target protein is fused to a short peptide (9 amino acids) known as Strep-tag, which binds to a streptavidin. The protein is eluted by using biotin in the elution buffer. This system achieves a high purification efficiency even with low-expressing proteins.

The Strep-Tactin®/Strep-tag II system achieves even higher purification efficiency by utilizing engineered forms of streptavidin and an eight-peptide tag. This system is free from the drawbacks associated with metal-ion based resins, which can cause protein aggregation and protein precipitation by chelation. Additionally, you can reuse the resin multiple times.

Once you are finished with your purification, you can always choose to remove the tag, depending upon downstream experiments/assays. So, go ahead and choose a tag based on your protein’s comfort and liking.

Feel free to share your experiences working with the protein purification affinity tag of your choice in the comments below. I wish you good luck in achieving high protein yields!

## References

1. Kimple M.E., et al. Overview of affinity tags for protein purification. Curr Protoc Protein Sci, Chapter 9, Unit 9.9 (2013). doi: 10.1002/0471140864.ps0909s36
2. Zhao X., et al. Several affinity tags commonly used in chromatographic purification. J Anal Methods Chem, 581093 (2013). doi: 10.1155/2013/581093

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