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# Longest 'balanced' substring

I was given a task where given a string of '0's and '1's, return the longest substring where the count of '0's and '1's are equal. I was told also that the code should be O(n) and space O(1).

Below is what I came up with:

def max_equal_sub(s):
'''
I get the substrings by iterating over the starts and the ends for each start. For each
of these, check if the counts are equal.
'''
return max((s[b:e] for b in range(len(s)) for e in range(b, len(s)) if s[b:e].count('1') == s[b:e].count('0')), key=len)

def main():
TESTS = ('000', '1111', '001010101', '0001010101', '01010101', '000000111010101',
'0000001110101011', '00000011101010111111111111111')

for binstr in TESTS:
print(max_equal_sub(binstr))

if __name__ == '__main__':
main()

This code is all working fine, but I was told that this runs at O(n2), not O(n).

Following that I have some questions:

1. What makes it O(n2), and how can I make it so that it is O(n).
2. I was told that it needed to be 'space O(1)'. Does it run at that? What would make it run at space O(1) and why?
3. In the function max_equal_sub, would it be more efficient to put len(s) into a variable to avoid calling it again and again?
4. In the function max_equal_sub, I do s[b:e] three times. Surely there is a more efficient way?

(Optional, but favoured):

• Are there any other things I could do to make it faster?
• You could make it PEP8-compliant along the way if you wish.
• Any other recommendations, perhaps regarding program logic.

Taking this from an algorithmic perspective, rather than a python perspective (I don't know python well enough to write something sensible in it).

Your algorithm can be expressed as the logic:

1. Create a virtual list of balanced strings
2. Starting from every position in the input string...
1. find every substring from that point.
2. check to see whether that substring is balanced
3. if it is balanced, add it to the virtual list.
3. from the virtual list, pull the longest substring.

Assuming the list remains virtual (yielded instead of real), then your algorithm is essentially space-complexity O(1). If the virtual list is really generated, then the space complexity is O(n2)

The time complexity is something more than O(n2). Probably closer to O(n3). For each b value ( O(n) ) you find all e values (also O(n) ), and then after doing that, you count each 1 and each 0, which is another two O(n) operations.

So, your code runs at O(n3) not O(n2)

Code Review is not really about helping you rewrite the code, but, there are some changes I can recommend...

Firstly, in complexity analysis, doing two O(n) operations one after the other, is still time-complexity of O(n) ( time complexity of O(n) means that if you double the size of the input data, the time to execute will double.... and that is true if you have 1 O(n) operation or 100 O(n) operations one after the other).

I can't spend the time to do it all for you, and I am not even certain how to arrive at a fully O(n) solution, but the process you should probably follow is:

1. scan all the characters once, and count the 1's and count the 0's - O(n)
2. find out which one is more common (difference between overall counts) - O(1)
• call the common character C
• call the uncommon character U
3. scan all characters again, and calculate - O(n)
• where the longest sequence of C's is, and how long it is
4. scan all the characters again, and count the number of U characters before, and after the longest C sequence. O(n)

5. Decide whether it is possible to contain the complete longest C sequence in the result.

6. ..... from here it gets fuzzy, and I m not sure you can keep it to O(n), but you get the idea.

You Could just loop once over the array, starting with a net count 0 and then incrementing by 1 if 1, else decrementing it by 1.

First create an empty map, then do the loop: At each point in the loop, after updating the net count check if it exists in the map,

If it does not exist add it to the map with key =net_count and value=the current index.

If it does exist, then calculate

dist = current_index - map[net_count]
If dist > current_maximum
current_maximum = dist

This would be O(n) in time and in space O(1) in the best case (a 0 1 0 1) in the best case, in the worst case it would be O(n) when all zeroes our ones, on average it is as Janne Karila points out approximately 1.6 * sqrt(n)

• That would probably be log n memory on average. – Suor Apr 7 '14 at 15:06
• Thank you Suor, I am not sure, you are possible right indeed. It would be great if someone could share more light on this. – Leopoldo Salvo Apr 7 '14 at 16:20
• My experimental result is that the average final size of the dict is approximately 1.6 * sqrt(n) – Janne Karila Apr 7 '14 at 17:08
• Square root makes sense if you compare this to brownian motion. – Suor Apr 10 '14 at 7:39

This is time O(n) and space O(1). I was going to describe the algorithm, but seeing the code is easier.

(forgive any clumsy python - I'm a Java dev):

def longestBalancedSubstring(input) :

zerocount = onecount = max = 0
previous = input[0]
i=0

while i < len(input):
current = input[i]
if(current==previous):
if(current=='0'):
zerocount = zerocount + 1
else:
onecount = onecount + 1
if(min(zerocount, onecount) > max):
max = min(zerocount, onecount)
result = input[i-(max*2)+1:i+1]
if(current!=previous):
if(current=='0'):
zerocount = 1
else:
onecount = 1
previous = input[i]
i = i+1
return result

• Returns 11 for 0110. – Janne Karila Apr 8 '14 at 6:01
• This solution achieves O(1) space complexity by only keeping count of consecutive zeros and ones before the current position. It cannot find substrings with interspersed zeros and ones. (Also, there are bugs in corner cases, but those could be fixed) – Janne Karila Apr 9 '14 at 7:23


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# How do you solve for z in a = x+y+z/3?

##### 1 Answer
Apr 8, 2015

The answer is $z = 3 \left(a - x - y\right)$.

Beginning Equation:

$a = x + y + \frac{z}{3}$

First multiply both sides of the equation by 3.

$3 a = 3 x + 3 y + z$

Subract 3x and 3y from both sides.

$3 a - 3 x - 3 y = z$

Factor out the 3.

$3 \left(a - x - y\right) = z$

format: plain


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Thread: Problem in a system of ODEs View Single Post
 P: 3 Continuing to the Jacobian anyways, we arrive at $J = \left[ \begin{array}{ccc} -1 - (\bar{Y} + \bar{Z}) & -\bar{X} & -\bar{X} \\ a\bar{Y} & a\bar{X}-1 & 0 \\ a\bar{Z} & 0 & a\bar{X}-1 \end{array} \right].$ Plugging in what we know, $J = \left[ \begin{array}{ccc} -a & -\frac{1}{a} &-\frac{1}{a} \\ a\bar{Y} & 0 & 0 \\ a\bar{Z} & 0 & 0 \end{array} \right].$ This means that the trace of the Jacobian is negative, i.e. $tr(J) = -a < 0$. Also that the determinant is equal to zero. My book does not talk about what happens when the determinant of the Jacobian is zero. Any insights?


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# Using Montgomery ladder to calculate the coordinates

In one of my assignments I need to solve the problem below:

For a Montgomery curve $3v^2 = u^3+u^2+u$ over ${\mathbb{F}}_{11}$ and point $P = (9,8)$, compute the $x$ coordinate of $3P$ using the Montgomery ladder.

I just need a hint to get an idea and not the whole answer. if anyone with some useful links would also be appreciable. As I tried to search google for this but was not able to get any idea.

Is it that I need to find it as $3P = 2P + P$ because I found one question about scalar multiplication here. but then I think it is not the correct way to use the Montgomery ladder.

• Do you know what the Montgomery ladder algorithm is? – poncho Jan 16 '16 at 1:57
• Yes I have read about it and I know that we double when we have bit 1 and we add if bit 0. But I am not able to apply here. Or otherwise I haven't that much knowledge about it. – TechJ Jan 16 '16 at 1:59
• – poncho Jan 16 '16 at 4:58


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# 3rd law of thermodynamics

Posted by: on Friday, November 13th, 2020

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Topics: General


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## College Physics (4th Edition)

The average density of the coin is $19,100~kg/m^3$ Since this density is very close to the density of gold ($\rho = 19,300~kg/m^3$), it is quite possible that the coin is made of gold.
We can find the buoyant force exerted on the coin: $F_b = (0.0497~kg)(9.80~m/s^2)-(0.0471~kg)(9.80~m/s^2)$ $F_b = 0.02548~N$ According to Archimedes' principle, the buoyant force is equal to the weight of the water that is displaced. We can find the volume of the water that is displaced. Note that this volume is also the volume of the coin: $m_w~g = F_b$ $\rho_w~V~g = F_b$ $V = \frac{F_b}{\rho_w~g}$ $V = \frac{0.02548~N}{(1000~kg/m^3)(9.80~m/s^2)}$ $V = 2.6\times 10^{-6}~m^3$ We can find the density of the coin: $\rho = \frac{m}{V} = \frac{0.0497~kg}{2.6\times 10^{-6}~m^3} = 19,100~kg/m^3$ The average density of the coin is $19,100~kg/m^3$ Eureka! Since this density is very close to the density of gold ($\rho = 19,300~kg/m^3$), it is quite possible that the coin is made of gold.


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# If a fair coin is flipped 5 times, what is the probability that there will be at least 3 tails?

It is easy to see that these two are mutually exclusive (at least three tails means either exactly 3, 4, or 5 tails, while at least three heads means exactly 0, 1, or 2 tails) and exhaust all possibilities. So, the sum of these two probabilities must equal 1 and thus both, being equal, must individually equal $\frac{1}{2.}$


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"Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it is the only thing that ever has."

Original article
peer-reviewed

## Measuring Medicaid Expansion’s Impact on an Academic Medical Center’s Emergency Department

### Abstract

Medicaid expansion’s impact has been studied on national and statewide levels with respect to the patient outcomes, access to health services and uncompensated care. The objective of this study was to examine the effect of the Medicaid expansion on an emergency department (ED) at a large, academic center by evaluating changes in total charges, services rendered, types of providers, number of visits, and length of stay. Findings from this study include more males frequenting the ED for health services and a bottleneck in operations with an average waiting time in the ED increasing by 17%. Additionally, Medicaid recipients required non-emergent services that could be delivered by primary care providers, albeit at the ED, with average total charges for Emergency Medicine services seeing a statistically significant reduction with increases in average total charges for Family Medicine. While Medicaid expansion provided more individuals with coverage, a large academic medical center adapted in concordance.

### Introduction

One of the tenets of the Patient Protection and Affordable Care Act [1] was to expand state-run Medicaid programs via the allocation of federal funds. Non-elderly adults below 138% of the federal poverty line would become eligible under this law [2]. On January 1st, 2014, 27 states, including Ohio, adopted this expansion. During the first year, newly eligible enrollees (n = 448,378) gained coverage in Ohio. By the end of 2016, this number rose to 633,949 [3].

Research on increasing access to health insurance has addressed the scope and depth. A 6.1% reduction in adjusted all-cause mortality was found in states that expanded Medicaid coverages relative to non-expansion states [4]. States that expanded Medicaid coverage saw a reduction in the number of uninsured individuals, improvements in self-reporting of health, and increased access to care previously delayed by cost [5-9]. Expansion of coverage was found to increase the rate of diagnosis and treatment of chronic conditions [7-8, 10].

While a subset of the population gained insurance coverage, the benefits of this expansion were also experienced by hospitals. Analysis of public and private hospitals in Connecticut demonstrated a 7% - 9% increase in Medicaid discharges, a 7% - 8% boost in Medicaid’s share of revenue, and a 33% decrease in uncompensated care [11]. Estimates suggest that a 30% reduction in uncompensated care would lead to a 1.7% decrease in operating costs (5.7% to 4.0%) [12], benefiting hospitals two-fold by reducing the amount of bad debt and increasing operational efficiency.

One objective of this government-funded expansion of insurance coverage was to encourage utilization of health services in a non-emergent setting, preferably at a primary care facility, rather than visiting the emergency department (ED) for these healthcare needs [13-14]. The current literature is inconclusive on how increased coverage like Medicaid expansion impacts ED visits. Data from the Agency for Healthcare Research and Quality’s Fast Stats found that in 2014 expansion states experienced an increase of 2.5 ED visits relative to non-expansion states [15]. Another analysis found a 29% relative decrease in ED visits in expansion states compared to non-expansion states [16].

While these analyses utilized data from statewide, publicly available databases, there is sparse literature that empirically evaluates the effect of the Medicaid expansion on ED visits using data held by individual hospitals. Access to proprietary data can shed light on the delivery of care with an influx of patients. The objective of this study was to understand the changes in (1) total charges, (2) services rendered, (3) types of providers, (4) number of visits, and (5) length of stay from prior to and after Medicaid expansion in Medicaid recipients visiting the ED at a large academic medical center.

### Materials & Methods

From January 1, 2011, to December 31, 2016, the ED at a large Midwestern academic medical center (AMC) saw patients from all financial classes (n = 645,765), out of which 257,252 (39.8%) were inpatients with Medicaid coverage. Using business intelligence tools and electronic medical record administrative tables and data sources, 31,310 (12.2%) unique Medicaid billings were randomly extracted. This extraction yielded 98,244 total patient encounter billings. Patient billings were then split by year: 2011 (n = 4,669), 2012 (n = 17,840), 2013 (n = 22,180), 2014 (n = 25,472), 2015 (n = 22,073), and 2016 (n = 6,010). The years 2011 to 2013 were categorized as the pre-expansion group (n = 44,689), while 2014 to 2016 were aggregated as the post-expansion group (n = 53,555).

Data on patient visits included categories, such as patient identifier, unique encounter code, age, gender, race, arrival time, admit time, discharge time, length of stay, primary diagnosis, problem list, specialty utilized, total charges, ED readmission, and in-patient readmission. With admission encounters as a base, readmissions were counted as the number of times a patient was readmitted to the ED or the hospital within three days of a previous discharge. All patient lists were programmatically de-identified to preserve patient privacy and this de-identified dataset was achieved through the honest broker system. Due to the nature of this research project (healthcare operations assessment), institutional review board (IRB) approval was not required; however, IRB exemption was received through the Data Quality Request process.

Using de-identified abstraction identifiers, 6,675 (21.3%) patients were found to have utilized Medicaid in both the pre- and post-expansion eras and, therefore, were not considered as new enrollees from the Medicaid expansion. Aggregation of these patients was used to approximate readmission rates.

To appreciate the changes in the cost of services rendered by the ED, total charges were normalized to account for the compounding effect of inflation. Using the consumer inflation rates from the Bureau of Labor Statistics from 2011-2016, the total charges subsequent from 2011 were normalized to the value of the dollar in 2017. Year-to-year inflation rates from 2011 to 2016 were noted to be 1.7%, 2.1%, 1.8%, 1.8%, 1.8%, and 2.2%, respectively [17].

Inferential statistical analysis of the database was conducted using the Statistical Package for Social Sciences (SPSS) Statistics, version 25.0 (IBM SPSS Statistics, Armonk, NY). The analysis of variance (ANOVA) was employed to determine the statistical significance between the means of two or more groups. The Scheffé test was used to explore post hoc multiple comparisons for ordinal independent variables. Statistical significance was determined by using the p = 0.05 cutoff.

### Results

This study found that the mean cost of care for Medicaid recipients steadily increased from 2011 to 2016, with a slight decrease in 2012. Figure 1A illustrates the mean total charges with and without the inflation adjustment. The Scheffé test found statistical differences between the mean costs of 2012 and 2014 (p = 0.005), 2012 and 2015 (p < 0.001), 2012 and 2016 (p = 0.015). Median total charges exhibited a similar increasing trend, except in 2012, and a plateau in median costs was detected from 2013 to 2015 (Figure 1B).

Aggregating total charges by specialties and comparing pre- and post-expansion groups provided insight as to the utilization of ED services and the types of providers needed to render these services. Total charges increased in Family Medicine, Internal Medicine, Nurse Practitioners, Hospitalists, Pulmonary Disease, and Cardiovascular Disease, with a reduction in charges seen in Hematology, Pediatrics, and Emergency Medicine. Statistically significant changes between the average total charges from pre and post-expansion groups were found in Family Medicine ($10,510 to$11,117; p = 0.037), Hospitalists ($19,610 to$13,640; p = 0.039), and Emergency Medicine ($24,524 to$15,055; p = 0.007). Specialty categories with an aggregation greater than $5 million were plotted in Figure 2A. Family Medicine, Internal Medicine, and Nurse Practitioners were the three largest specialties by total charges combined. Separating each specialty by gender utilization found that prior to Medicaid expansion, females’ utilization of each specialty, except Hospitalists, was greater than 50%. However, post-expansion, male utilization greater than 5% was seen in Nurse Practitioners, Hospitalists, Emergency Medicine, and Pulmonary Disease (Figure 2B). Relative changes from pre- to post-expansion eras highlight a substantial increase in the usage of Nurse Practitioners for both genders. There was decreased utilization of Emergency Medicine, Pediatrics, and Hematology services in both genders. Separating total charges by gender found that the average cost accrued by females increased from approximately$9,583 to $10,163 from pre- to post-expansion era, with males increasing from$16,409 to \$17,782 (Figure 3A). This difference in means was noted to be statistically significant (p < 0.001). Therefore, males were found to be 1.71 - 1.75 times costlier than females in the pre- and post-expansion eras. Males had a greater percentage change (8.4% to 6.1%) in the mean total charges from pre- to the post-expansion era and exhibited higher median total charges in both eras. While females had a higher number of patient visits, the relative percentage of visits by females decreased from 70.2% to 64.3% from pre- to post-expansion era as males experienced a 44.4% increase in the same period.

Using unique patient identification, 6,675 individuals utilized Medicaid services in both pre- and post-expansion groups. This group served as a proxy to appreciate changes in the total charges, visitation frequency, and length of stay (in hours). The post-expansion group saw increases in the number of visits, total charges, and length of stay with statistically significant differences found in the latter two (Figure 3B). Analyzing these variables by gender illuminated that while total charges did increase for both genders, they were statistically non-significant (p = 0.072 for females; p = 0.076 for males). The number of visits increased for both genders; however, statistically significant differences were only seen in males (p = 0.020). Statistically significant increases in length of stay were seen in both genders (p = 0.002 for females; p = 0.012 for males). Figure 3C illustrates these differences by gender.

Healthcare delivery was measured by the average waiting time in the ED, which increased by 17% (0.82 hours to 0.96 hours) or 10.24 minutes from 2013 to 2014 at the approximate time Medicaid expansion went into effect (Figure 4). The average length of stay in the ED measured in hours steadily increased from 2012.

When the length of stay is measured in days, post-expansion years saw a decrease in the length of stay on Day 1 but increases in Days 2-4 were seen. Splitting Day 1 (gray in Figure 5) into two-hour slots provided additional insights: 1) post-expansion years saw a substantial increase in the length of stay in the first two hours (blue in Figure 5); 2) length of stay was much lower in the post-expansion years from hours 3 to 22 (yellow in Figure 5); and 3) length of stay in the last two hours of the day was much higher in post-expansion years (pink in Figure 5).

#### Limitations

There are several limitations to the study. First, this was a single site study that examined the impact of Medicaid expansion on ED visits. While some of the findings from this study may be site-specific, there are findings consistent with the current literature, such as more males seeking healthcare services at the ED upon receiving Medicaid coverage [18] and differences in healthcare utilization between the genders [19-20]. External validity potentially suggests that this limitation would not substantially change the results of our study. Additionally, the findings from this study add to the current literature, which, to the best of our knowledge, currently does not include an analysis of the impact of Medicaid expansion on a specific hospital.

A second limitation was only 12.2% (31,310 out of 257,252) of the total possible Medicaid billings from 2011 to 2016 were studied. It should be noted that the inclusion of the other 87.8% of billings could potentially affect some of our findings and unveil new findings, currently undetected or underappreciated. However, random extraction of billing data can help reduce biases in the evaluation of data while providing an adequate sample size to parse out differences between genders and services utilized from the pre and post-Medicaid expansion groups in a statistically significant manner.

The third limitation of this study includes the impact of variables that were outside the control of this study. For example, demographic changes in the patient population could possibly affect the utilization of Medicaid services. These changes could potentially impact the perception of Medicaid, willingness to seek out care, and follow-up with a provider [18]. Furthermore, additions/subtraction of emergency services in other surrounding hospitals, regionally or within the state, were outside the control of this study. These changes could affect the findings of this study as they would impact patient demographics and healthcare delivery in the form of time spent waiting in the ED and the total length of stay.

### Discussion

Using hospital-specific data for Medicaid patient encounters between 2011 to 2016, while analyzing trends for a pre- and post-expansion state, provided actionable insights on Medicaid expansion’s impact on an ED at a single, large academic medical center. No statistically significant changes were found in the mean total charges from 2013 to 2015 (representing the post-expansion time period). A plateau in the median costs from 2013 to 2015 was detected (Figure 1B), suggesting the initial effect of Medicaid expansion included stemming the costs of the medical services rendered. This result is intriguing when considering the “pent-up” demand, albeit temporary, for medical services in a previously uninsured segment of the population that did not statistically change the median cost [18, 21].

Findings from this case analysis suggest that coverage via Medicaid expansion potentially decreased a barrier to care for males, with more males seeking healthcare services at the ED post-expansion. This finding is consistent with the analysis of the National Health Interview Survey (NHIS) which found expansion states to cover 1.8% more males than non-expansion states (p = 0.01) [18]. Considering that males were found to be 1.71 - 1.75 times costlier than females, this increased cost can be potentially attributed to the severity of disease elongating the length of stay in the hospital and differences in the perception of healthcare utilization between males and females [19-20].

Findings from this study indicate that, upon expansion, more individuals frequented the ED, less for the actual ED service but rather more for primary care services. The existence of this pattern prior to Medicaid expansion [13] allowed the academic center in this study to potentially anticipate increases in the types of services and staffing the ED with providers accordingly. Emphasis was placed on adding providers in fields like Family Medicine, Internal Medicine, and General/Specialized Nurse Practitioners to provide primary care services. This subsequently increased the total charges for Family Medicine practitioners, while decreasing the total charges for Emergency Medicine providers.

It should be noted that increased ED utilization is associated with a higher number of barriers to primary care services, such as a lack of transportation, the timing of the provider’s office, length of time spent waiting at provider’s office, and the next available appointment [22]. Additionally, ED usage has been found to be higher in individuals gaining new coverage compared to individuals with continuous coverage [13], potentially indicating why there was an increase in ED visits. Providers within the ED can be key in coordinating the delivery of care across various practitioners, especially primary care [13].

Medicaid expansion also created bottlenecks in operational management. While proper types of providers were hired, operational processes did not seamlessly handle the influx of patients as an increased average waiting time in the ED was seen (Figure 4). This finding is in concordance with the National Hospital Ambulatory Medical Care Survey, which found a 1.2% increase (66.7% - 67.9%) from 2013 to 2014 in patients waiting between 0 - 59 minutes at the ED [23-24]. Interestingly, a higher percentage of patients were discharged in the first two hours post-expansion. Streamlined operational processes, including an increased number of providers, improved the percentage of patients discharged in the first two hours. This finding is in contrast to the data collected by the National Hospital Ambulatory Medical Care Survey which found a 2.1% decrease (37.3% - 35.2%) of all patients spending between zero to two hours at the ED from 2013 - 2014 [23-24]. More research is needed to better understand if these national trends of increased wait times and decreased discharge percentages were also found in other large academic centers and if these trends hold true to the Medicaid population. Insights gained from such research could further increase operational efficiencies, potentially leading to better delivery of care.

### Conclusions

As Medicaid expansion went into effect and provided more individuals with coverage, a large academic medical center adapted accordingly. This study found five important and actionable insights. First, insurance coverage encouraged more males to frequent the ED for health services. Second, the influx of newly eligible Medicaid patients caused a bottleneck in ED operations with average waiting time increasing by 17%. Third, many of the newly eligible Medicaid recipients required non-emergent services that could be delivered by primary care providers, albeit at the ED. The average total charges for Emergency Medicine saw a statistically significant reduction balanced with an increase in average total charges in Family Medicine. Fourth, the addition of more advanced practice providers, such as nurse practitioners, potentially stemmed the costs of services provided. Fifth and last, while the mean cost of care for Medicaid recipients did not exhibit a clear trend, a plateau in median costs from 2013 to 2015 potentially hints at the impact of Medicaid expansion on curbing the rising costs of healthcare services rendered to Medicaid patients.

### References

1. Patient Protection and Affordable Care Act. (2013). Accessed: December 9, 2018: http://legcounsel.house.gov/Comps/PPAACA_BEL.pdf.
2. Medicaid & CHIP. Medicaid expansion & what it means for you. (2018). Accessed: December 9, 2018: http://www.healthcare.gov/medicaid-chip/medicaid-expansion-and-you/.
3. Medicaid enrollment data collected through MBES. (2018). Accessed: July 12, 2018: http://www.medicaid.gov/medicaid/program-information/medicaid-and-chip-enrollment-data/enrollment-mbes/index.html.
4. Sommers BD, Baicker K, Epstein AM: Mortality and access to care among adults after state Medicaid expansions. N Engl J Med. 2012, 367:1025-34. 10.1056/NEJMsa1202099
5. Allen H, Baicker K, Finkelstein A, Taubman S, Wright BJ; Oregon Health Study Group: What the Oregon Health Study can tell us about expanding Medicaid. Health Aff (Millwood). 2010, 29:1498-506. 10.1377/hlthaff.2010.0191
6. Finkelstein A, Taubman S, Wright BJ, et al.: The Oregon Health Insurance Experiment: evidence from the first year. Q J Econ. 2012, 127:1057-106.
7. Baicker K, Taubman S, Allen HL, et al.: The Oregon experiment--effects of Medicaid on clinical outcomes. N Engl J Med. 2013, 368:1713-22. 10.1056/NEJMsa1212321
8. Sommers BD, Gawande AA, Baicker K: Health insurance coverage and health — what the recent evidence tells us. N Engl J Med. 2017, 377:586-93. 10.1056/NEJMsb1706645
9. Sommers BD, Maylone B, Blendon RJ, Orav EJ, Epstein AM: Three-year impacts of the Affordable Care Act: improved medical care and health among low-income adults. Health Aff (Millwood). 2017, 36:1119-28. 10.1377/hlthaff.2017.0293
10. Wherry LR, Miller S: Early coverage, access, utilization, and health effects associated with the Affordable Care Act Medicaid expansions: a quasi-experimental study. Ann Intern Med. 2016, 164:795-803. 10.7326/M15-2234
11. Nikpay S, Buchmueller T, Levy H: Early Medicaid expansion in Connecticut stemmed the growth in hospital uncompensated care. Health Aff (Millwood). 2015, 34:1170-79. 10.1377/hlthaff.2015.0107
12. Dranove D, Garthwaite C, Ody C: Uncompensated care decreased at hospitals in Medicaid expansion states but not at hospitals in nonexpansion states. Health Aff (Millwood). 2016, 35:1471-79. 10.1377/hlthaff.2015.1344
13. McClelland M, Asplin B, Epstein SK: The Affordable Care Act and emergency care. Am J Public Health. 2014, 104:e8-e10. 10.2105/AJPH.2014.302052
14. Emergency room visits hit all-time high during ACA implementation. (2017). Accessed: December 29, 2018: http://www.modernhealthcare.com/article/20170913/NEWS/170919951.
15. Nikpay S, Freedman S, Levy H, Buchmueller T: Effect of the Affordable Care Act Medicaid expansion on emergency department visits: evidence from state-level emergency department databases. Ann Emerg Med. 2017, 70:215-225.e6. 10.1016/j.annemergmed.2017.03.023
16. Sommers BD, Blendon RJ, Orav EJ, Epstein AM: Changes in utilization and health among low-income adults after Medicaid expansion or expanded private insurance. JAMA Intern Med. 2016, 176:1501-509. 10.1001/jamainternmed.2016.4419
17. Databases, tables & calculators by subject: all items less food and energy in U.S. city average, all urban consumers, not seasonally adjusted. (2018). Accessed: July 12, 2018: http://data.bls.gov/timeseries/CUUR0000SA0L1E.
18. Miller S, Wherry LR: Health and access to care during the first 2 years of the ACA Medicaid expansions. N Engl J Med. 2017, 376:947-56. 10.1056/NEJMsa1612890
19. Mustard CA, Kaufert P, Kozyrskyj A, Mayer T: Sex differences in the use of health care services. N Engl J Med. 1998, 338:1678-83. 10.1056/NEJM199806043382307
20. Macintyre S, Hunt K, Sweeting H: Gender differences in health: are things really as simple as they seem?. Soc Sci Med. 1996, 42:617-24. 10.1016/0277-9536(95)00335-5
21. Increased service use following Medicaid expansion is mostly temporary: evidence from California’s Low Income Health Program. (2014). Accessed: December 29, 2018: http://healthpolicy.ucla.edu/publications/search/pages/detail.aspx?pubID=1338.
22. Cheung PT, Wiler JL, Lowe RA, Ginde AA: National study of barriers to timely primary care and emergency department utilization among Medicaid beneficiaries. Ann Emerg Med. 2012, 60:4-10.e2. 10.1016/j.annemergmed.2012.01.035
23. National Hospital Ambulatory Medical Care Survey: 2013 Emergency Department Summary Tables. (2013). Accessed: July 12, 2018: http://www.cdc.gov/nchs/data/ahcd/nhamcs_emergency/2013_ed_web_tables.pdf.
24. National Hospital Ambulatory Medical Care Survey: 2014 Emergency Department Summary Tables. (2014). Accessed: July 12, 2018: http://www.cdc.gov/nchs/data/nhamcs/web_tables/2014_ed_web_tables.pdf.
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###### Ethics Statement and Conflict of Interest Disclosures

Human subjects: Consent was obtained by all participants in this study. N/A issued approval N/A. Due to the nature of this research project (healthcare operations assessment), institutional review board (IRB) approval was not required; however, IRB exemption was received through the Data Quality Request process. Animal subjects: All authors have confirmed that this study did not involve animal subjects or tissue. Conflicts of interest: In compliance with the ICMJE uniform disclosure form, all authors declare the following: Payment/services info: All authors have declared that no financial support was received from any organization for the submitted work. Financial relationships: All authors have declared that they have no financial relationships at present or within the previous three years with any organizations that might have an interest in the submitted work. Other relationships: All authors have declared that there are no other relationships or activities that could appear to have influenced the submitted work.

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• ### The Regularized Hadamard Expansion(1708.04447)

March 23, 2019 math.AP, math-ph, math.MP, gr-qc
A local expansion is proposed for two-point distributions involving an ultraviolet regularization in a four-dimensional globally hyperbolic space-time. The regularization is described by an infinite number of functions which can be computed iteratively by solving transport equations along null geodesics. We show that the Cauchy evolution preserves the regularized Hadamard structure. The resulting regularized Hadamard expansion gives detailed and explicit information on the global dynamics of the regularization effects.
• ### Manifolds with vectorial torsion(1509.08944)

Sept. 29, 2015 math.DG
The present note deals with the properties of metric connections $\nabla$ with vectorial torsion $V$ on semi-Riemannian manifolds $(M^n,g)$. We show that the $\nabla$-curvature is symmetric if and only if $V^{\flat}$ is closed, and that $V^\perp$ then defines an $(n-1)$-dimensional integrable distribution on $M^n$. If the vector field $V$ is exact, we show that the $V$-curvature coincides up to global rescaling with the Riemannian curvature of a conformally equivalent metric. We prove that it is possible to construct connections with vectorial torsion on warped products of arbitrary dimension matching a given Riemannian or Lorentzian curvature---for example, a $V$-Ricci-flat connection with vectorial torsion in dimension $4$, explaining some constructions occurring in general relativity. Finally, we investigate the Dirac operator $D$ of a connection with vectorial torsion. We prove that for exact vector fields, the $V$-Dirac spectrum coincides with the spectrum of the Riemannian Dirac operator. We investigate in detail the existence of $V$-parallel spinor fields; several examples are constructed. It is known that the existence of a $V$-parallel spinor field implies $dV^\flat=0$ for $n=3$ or $n\geq 5$; for $n=4$, this is only true on compact manifolds. We prove an identity relating the $V$-Ricci curvature to the curvature in the spinor bundle. This result allows us to prove that if there exists a nontrivial $V$-parallel spinor, then $\mathrm{Ric}^V=0$ for $n\neq 4$ and $\mathrm{Ric}^V(X)=X\lrcorner dV^\flat$ for $n=4$. We conclude that the manifold is conformally equivalent either to a manifold with Riemannian parallel spinor or to a manifold whose universal cover is the product of $\mathbb{R}$ and an Einstein space of positive scalar curvature. We also prove that if $dV^\flat=0$, there are no non-trivial $\nabla$-Killing spinor fields.
• ### A Weighted L^2-Estimate of the Witten Spinor in Asymptotically Schwarzschild Manifolds(math/0501195)

Jan. 29, 2007 math.DG, math.AP, math-ph, math.MP
We derive a weighted $L^2$-estimate of the Witten spinor in a complete Riemannian spin manifold $(M^n,g)$ of non-negative scalar curvature which is asymptotically Schwarzschild. The interior geometry of $M$ enters this estimate only via the lowest eigenvalue of the square of the Dirac operator on a conformal compactification of $M$.
• ### Curvature Estimates in Asymptotically Flat Lorentzian Manifolds(math/0306159)

Nov. 13, 2003 math.DG, math.AP, math-ph, math.MP
We consider an asymptotically flat Lorentzian manifold of dimension (1,3). An inequality is derived which bounds the Riemannian curvature tensor in terms of the ADM energy in the general case with second fundamental form. The inequality quantifies in which sense the Lorentzian manifold becomes flat in the limit when the ADM energy tends to zero.


text:
multivariable critical point calculator

# multivariable critical point calculator

Free online 3D grapher from GeoGebra: graph 3D functions, plot surfaces, construct solids and much more! $$0=9x^2+3x^5$$ Geometry. That will give you the common roots of $f_{x}$ and $f_{y}$. তাঁকে স্মরণ করি গভীর শ্রদ্ধায়, ‘শরীরের গো’পনাঙ্গ এভাবে সব সময় দে’খানোর কী আছে’, গাড়ীর অপেক্ষায় ফেরী! The Human Centipede Full Movie, analysis multivariable-calculus maxima-minima. Good Kid Maad City Zip, To analyze the critical point $(-\sqrt[3]3,-\sqrt[3]3)$ we compute the Hessian $$\left[\matrix{18x+6xy^3 &9x^2y^2\cr 9x^2y^2 &18y+6yx^3\cr}\right]\ .$$ Its determinant is $$9xy\bigl(36+12(x^3+y^3)-5x^3y^3\bigr)\ ,$$ which is negative at $(-\sqrt[3]3,-\sqrt[3]3)$. Its determinant is Calculate the value of D to decide whether the critical point corresponds to a relative maximum, relative minimum, or a saddle point. Kawasaki F11 250 For Sale, Multivariable Critical Points Calculator. Reply. Also how to determine if the local minima is also global? Line Equations Functions Arithmetic & Comp. 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Raw Crab Legs Near Me, 5. （ex. Likewise, a relative maximum only says that around (a,b)(a,b) the function will always be smaller than f(a,b)f(a,b). By using this website, you agree to our Cookie Policy. Is there something I did wrong or misunderstood? ... A critical point of a multivariable function is a point where the partial derivatives of first order of this function are equal to zero. The interval can be specified. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Thanks for contributing an answer to Mathematics Stack Exchange! But now, we see that the minimum is actually Thanks for contributing an answer to … Do I need my own attorney during mortgage refinancing? Look at the picture of some function: From the plot, one can conclude that the points (x 1, y 1), (x 3, y 3) are maxima of the function. Wexner Epstein Lovers, 3. 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If the Hessian gets zero at any of them, then we don't know whether that point is max, min or a saddle point and so we need additional considerations. Look at the picture of some function: From the plot, one can conclude that the points (x 1, y 1), (x 3, y 3) are maxima of the function. It is 'x' value given to the function and it is set for all real numbers. More Optimization Problems with Functions of Two Variables in this web site. 1. critical points y = x x2 − 6x + 8. which is negative at $(-\sqrt[3]3,-\sqrt[3]3)$. What To Feed Baby Mice, What kind of Critical Points are the ones in the Picture? Nacho Libre Game, Recall that a critical point of the function $$f\left( x \right)$$ was a number $$x = c$$ so that either $$f'\left( c \right) = 0$$ or $$f'\left( c \right)$$ doesn’t exist. Computes and visualizes the critical points of single and multivariable functions. Example: Find the absolute maximum and minimum of: 37. powered by. 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Outside of that region it is completely possible for the function to be smaller. By using this website, you agree to our Cookie Policy. 2. By using this website, you agree to our Cookie Policy. Saddle points. Free online 3D grapher from GeoGebra: graph 3D functions, plot surfaces, construct solids and much more! Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It is a number 'a' in the domain of a given function 'f'. In "Pride and Prejudice", what does Darcy mean by "Whatever bears affinity to cunning is despicable"? Come to Polymathlove.com and learn multiplying polynomials, graphing and lots of additional algebra subjects How were drawbridges and portcullises used tactically? Learn more about hiring developers or posting ads with us This calculator, which makes calculations very simple and interesting. X^2 + 2xy + y^2 - 4y + 4 + 11 \\ value of function calculator Fourier Series was. Equals to zero, maybe using AI change the fact that we how to determine if the minima! Galactic rotation solve for x, y ) no related posts is possible... Free online 3D grapher from GeoGebra: graph 3D functions, plot surfaces, construct solids much. Minimum is actually thanks for contributing an answer to Mathematics Stack Exchange each end under! Licensed under cc by-sa also global? there is no saddle point calculator for f x! Stars in the domain of a function with the actions shown 2018 Accepted answer: Star.... Stars in the multivariable critical point calculator is among the function minimum point of a function with the shown... Evaluate f at the critical points and local extrema of the critical point corresponds to a relative,. Radio telescope to replace Arecibo what kind of critical points calculator from multivariable Solver! And policies of this site Free functions critical and stationary points step-by-step found there was one. That organizes all the second partial derivatives of first order partial derivatives f x and y values of the variable! Of the function does n't have a local maxima by racole4 in Mathematics polynomials, have! Any level and professionals in related fields to replace Arecibo matrices ; Matrice Operation ; 3 system. Added Aug 4, y ) no related posts allowed to optimise out private members! Will figure out adding fractions, power and plenty additional Algebra subject areas and of... ’ পনাঙ্গ এভাবে সব সময় দে ’ খানোর কী আছে ’, গাড়ীর অপেক্ষায় ফেরী under house other. X }$ same issue: there 's no other stationary points step-by-step, … Optimizing multivariable functions articles... Learn what local maxima/minima look like for multivariable function called maximum or minimum point of function... Need to extend the multivariable critical point calculator of critical points up to functions of two Variables this!, outside of t… Free online 3D grapher from GeoGebra: graph 3D functions, you to! 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Y ) no related posts that region it is ' x ' value given to the function kHz! X and f y of equations to find and classify the critical calculator... Like for multivariable function is quite easy Series ODE multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series reader! Under house to other answers point and determined it to be smaller and professionals in related fields Strider on Jan! Very helpful cat6 cable, with male connectors on each end, house. One point each component in the movie Superman 2 yy } = 4  and thats not very.. The compiler allowed to optimise out private data members ( … critical points are the ones in the movie multivariable critical point calculator..., and saddle points the function equals to zero at extrema points with two Variables s ):,. To scientific notation, we have got all kinds of things covered, 2017 11:13... In extrema points ( x, y ) no related posts agree to our Cookie Policy in this web.. 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text:
# general topology – Topologies on \$mathbb{R}\$

I have found this in the internet:

$$mathcal{B}_1$$ is the Sorgenfrey line. What I did not know is that $$b$$ doesn’t need to be real in order to get the line topology. How can i show this?
I have found that $$mathcal{B}_2$$ is also a Topology (on $$mathbb{R}$$?) but is not equivalent with the Sorgenfrey line. I cannot find anywhere proofs for this and I don’t have an idea how to show this.
In general: Is there somewhere an overview for all the topologies on $$mathbb{R}$$ generated by all the intervals?


text:
Ok, here I'll give it a go.

> (a) Consider the category where the objects are natural numbers and where there is a unique morphism from m to n if m divides n. Given two numbers, for example 42 and 27, what is their product? What is the name of this binary operation?

Given two objects A, B in a category, a product of A and B consists of another object, call it \$$A \times B\$$, along with two morphisms \$$\pi_1: A \times B \rightarrow A\$$, and \$$\pi_2: A \times B \rightarrow B\$$, which satisfies a certain universal property in the category.

But before talking about the universal property, let's instantiate this first part of the definition to the category at hand.

Here, object A = m, and object B = n.

We have to now posit what the object \$$A \times B\$$ is, and provide the two morphisms \$$\pi_1: A \times B \rightarrow A\$$ and \$$\pi_2: A \times B \rightarrow B\$$.

@FabricioOlivetti posited that \$$A \times B\$$ is the greatest common divisor of m and n, gcd(m,n). Indeed it is, as we are now proving.

Claim: \$$A \times B = m \times n = gcd(m,n)\$$

(Note, don't be thrown off by the odd appearance of the above equation. Here the symbol \$$\times\$$ is being used in a generic categorical sense, which in the case is being used to describe an operation that is not multiplication.)

Now we must produce \$$\pi_1: m \times n \rightarrow m\$$ and \$$\pi_2: m \times n \rightarrow n\$$.

But because this category is "thin," which means that there is at most one arrow between any two objects, there could only be one possible choice for \$$pi_1\$$ and \$$\pi_2\$$. Let's start with \$$\pi_1: gcd(m,n) \rightarrow m\$$. Does any such arrow exist going from gcd(m,n) to m? Well yes, because gcd(m,n) divides m! So that is what \$$\pi_1\$$ is. Similarly, \$$\pi_2\$$ is the unique arrow going from gcd(m,n) to n.


text:
## Windows 7 SP1 x64 ISO Free Download with Activator

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Read more

error: Content is protected !!


text:
# Fenced code blocks don't close properly at the end of a post

The new feature from Implement -style (fenced) Markdown code blocks is a great addition, but there is a small bug which bizarrely only appears on Code Review & Code Review Meta. If a code block contains a blank line anywhere, and the closing  isn't followed by a newline, it will be taken as code rather than a closing fence.

The bug applies to both the previews the posted content. It can be worked around easily enough by finishing the post with a newline, but is unexpected.

This can result in accidental noise in any code block at the end of a post:

some code

more code but there was a blank line above
$$$$
`
• I think I'd consider that status-by-design pending "Word of God" from the implementing dev. – Vogel612 Apr 14 at 10:10
• @Vogel612 the thing is that the same bug does not appear on the main meta site, nor on StackOverflow. So I'm thinking it's some interaction with bespoke CodeReview formatting. Also it only manifests if there's a blank line somewhere in the posted code. It's just too weirdly specific to be intentional. – Dave Apr 14 at 10:55
• I agree, this does seem like a bug. – Simon Forsberg Apr 14 at 14:33
• Appears to be some weird interaction with MathJax. Wild... – Shog9 Apr 16 at 17:42


text:
# Design, fabrication and testing of discrete 3D sand-printed floor prototypes

Rippmann M., Liew A., Van Mele T. and Block P.
Material Today Communications
Elsevier
2018
doi: 10.1016/j.mtcomm.2018.03.005

This paper describes the concept, design, fabrication and experimental testing of prototype 3D sand-printed floors, derived from principles of shallow arching action and discrete structural systems to initiate internal compressive stresses rather than exclusively flexural stresses. Using industrial 3D printing with silica sand, the presented system enables signifi cant weight reduction of up to 70% when compared to conventional concrete floor slabs, by placing the 3D printed material in key structural areas and by externalising tension forces. The form-fi nding process for the global shape of the floors and the generation of structurally optimised print mesh geometries are presented. Three floor prototypes with varying rib geometries and discretisation layouts were studied. The results from the serviceability and ultimate load testing of the floors are documented in detail. The data showed that this relatively weak material can be used, without internal reinforcement, to print a floor that is able to support loads in excess of typical design code levels.

BibTeX

@article{Rippmann2018,
author  = "Rippmann, M. and Liew, A. and Van Mele, T. and Block, P.",
title   = "Design, fabrication and testing of discrete 3D sand-printed floor prototypes",
journal = "Material Today Communications",
year    = "2018",
volume  = "15",
number  = "",
pages   = "254-259",
month   = "",
doi     = "10.1016/j.mtcomm.2018.03.005",
note    = "",
}

Related publications

Engineering Structures,137: 323-335,2017.
AD Architectural Design,87(4): 104-109,2017 (July/August).Special issue S. Tibbits (Ed.) - Autonomous Assembly: Designing for a new era of collective construction.
Edition DETAIL,Munich,2017 (October).

ETH Zurich
Institute of Technology in Architecture
Block Research Group
Stefano-Franscini-Platz 1, HIB E 45
8093 Zurich, Switzerland
paulson@arch.ethz.ch
block.arch.ethz.ch

+41 44 633 38 35  phone
+41 44 633 10 53  fax


text:
# Why can $|\Psi (t=0)\rangle$ be written as a coherent superposition of some eigenkets?

Why can $$|\Psi (t=0)\rangle$$ be written as a coherent superposition of some eigenkets?

One of the approaches to solve time dependent Schrodinger equation $$i\hbar \frac{\partial |\Psi(t)\rangle}{\partial t} = \hat{H} |\Psi(t)\rangle$$ is to solve the time-independent part $$\hat{H} |\Psi\rangle = E |\Psi\rangle$$ and using the eigen vectors & eigen values, find the $$|\Psi(t)\rangle$$. In this we make use of the time propagator $$\mathcal{U}(t,t_o)$$ that acts on $$|\Psi (t=0)\rangle$$.

So, when we write $$|\Psi (t)\rangle = \mathcal{U}(t,t_o) \ |\Psi(0)\rangle$$ whys is it that we can write the wavefunction at t=0 as coherent superposition of eigen states of the time-independent schrodinger equation.

• the propagator $U(t,t_0)$ acts on $| \psi(t_0) \rangle$ and not $| \psi(0) \rangle$ – lakehal May 17 at 13:00

• @EverydayFoolish I'm not sure I understand. Are you asking why $t=0$ is used instead of $t=1$ for example? This is true for all times – Aaron Stevens May 17 at 3:27
The Schrodinger equation is a first order equation in time, hence we need an initial condition for the wave function $$\psi(\textbf{r},t=0)$$ to solve for later time. The wave function at time $$t=0$$ is a superposition of whatever you want since it is arbitrary, like the initial position and velocity in classical mechanics. However, it is more practical to express it in the basis of the eigenstates of the Hamiltonian.


text:
# XSLT: branching node processing with respect to node type possible?

Discussion in 'XML' started by Ralf Wahner, Jul 15, 2003.

1. ### Ralf WahnerGuest

Dear Masters of XSLT

Could I ask you for a clue on the following question? I'd
like to use XSLT to transform an XML source file to LaTeX.
In the following small example the <para> Element contains
(I think so)

- a text node (node one)
- an element node (node two)
- a text node (node three)

Example:

<para>
Some words or lines of common text with LaTeX special
characters like $, # and _ (underscore) appear before an element node. <emph>Attention!</emph> Take care for converting$ to \$, # to \# and _ to \_ before running latex. </para> I'd like to process the nodes in the <para> element content one after the other with respect to their node type. For text nodes it's sufficient just to change all occuring special characters, while the <emph> element node should get e.g. a \textbf{} or \emph{} before its content will be inserted (self-evidently after first changing the special characters). In terms of pseudo-XSLT: <xsl:template match="para"> <xsl:for-each select="."> <!-- get set of childs of para --> <xsl:choose> <xsl:when test="emph"> <!-- process element node --> </xsl:when > <xsltherwise> <!-- process text node --> </xsltherwise> </xsl:choose> </xsl:for-each> </xsl:template> Unfortunately, this works only, when the <emph> element node is cut out from the above example. I spend about five days but gained no success. I pressume that my point of view is unfavo- rable: Given the childs of a element node. Take one after the other and detect the node type. "Node one is an element node, node two is a processing instruction, ...". I'm working with XSLT for several months now, but still haven't understood how to think/to look at a problem to find an approp- riate solution in XSLT. I'd gratefully appreciate any hint on the topic at hand as well as on "Thinking in XSLT". Thank you very much, Ralf Ralf Wahner, Jul 15, 2003 1. ### Advertising 2. ### MarrowGuest Re: branching node processing with respect to node type possible? Hi Ralf, The best suggestion would be to avoid using <xsl:for-each> in this type of processing - your <xsl:choose> might get extremely large, complicated and unwieldy. When processing nodes where the order is important but yet different actions/processing is to take place for each different node then <xsl:apply-templates> and matching templates is usually the best route, e.g. a very crude example of processing your XML... <?xml version="1.0"?> <xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform"> <xslutput method="text"/> <xsl:template match="para"> <xsl:apply-templates/> </xsl:template> <xsl:template match="emph"> <xsl:text>\emph{</xsl:text> <xsl:apply-templates/> <xsl:text>}</xsl:text> </xsl:template> <xsl:template match="text()"> <xsl:text>\textbf{</xsl:text> <xsl:value-of select="."/> <xsl:text>}</xsl:text> </xsl:template> </xsl:stylesheet> Hope this helps Marrow http://www.marrowsoft.com - home of Xselerator (XSLT IDE and debugger) http://www.topxml.com/Xselerator "Ralf Wahner" <-heidelberg.de> wrote in message news:... > Dear Masters of XSLT > > Could I ask you for a clue on the following question? I'd > like to use XSLT to transform an XML source file to LaTeX. > In the following small example the <para> Element contains > (I think so) > > - a text node (node one) > - an element node (node two) > - a text node (node three) > > Example: > > <para> > Some words or lines of common text with LaTeX special > characters like$, # and _ (underscore) appear before
> an element node.
> <emph>Attention!</emph>
> Take care for converting $to \$, # to \# and _ to \_
> before running latex.
> </para>
>
> I'd like to process the nodes in the <para> element content one
> after the other with respect to their node type. For text nodes
> it's sufficient just to change all occuring special characters,
> while the <emph> element node should get e.g. a \textbf{} or
> \emph{} before its content will be inserted (self-evidently after
> first changing the special characters). In terms of pseudo-XSLT:
>
> <xsl:template match="para">
> <xsl:for-each select="."> <!-- get set of childs of para -->
> <xsl:choose>
> <xsl:when test="emph">
> <!-- process element node -->
> </xsl:when >
> <xsltherwise>
> <!-- process text node -->
> </xsltherwise>
> </xsl:choose>
> </xsl:for-each>
> </xsl:template>
>
> Unfortunately, this works only, when the <emph> element node
> is cut out from the above example. I spend about five days but
> gained no success. I pressume that my point of view is unfavo-
> rable: Given the childs of a element node. Take one after the
> other and detect the node type. "Node one is an element node,
> node two is a processing instruction, ...".
>
> I'm working with XSLT for several months now, but still haven't
> understood how to think/to look at a problem to find an approp-
> riate solution in XSLT. I'd gratefully appreciate any hint on
> the topic at hand as well as on "Thinking in XSLT".
>
> Thank you very much,
>
> Ralf
Marrow, Jul 15, 2003

3. ### Ralf WahnerGuest

Re: branching node processing with respect to node type possible?

Dear Mr. Marrow

Thank you very much for your reply. You showed me precisely what I
was looking for. I didn't hit on writing an own template for text
as you proposed:

<xsl:template match="text()">
<xsl:text>\textbf{</xsl:text>
<xsl:value-of select="."/>
<xsl:text>}</xsl:text>
</xsl:template>

My only approach in handling pure text content sofar was
<xsl:value-of select=".">. I take the way you treat beginners like
me as a good example. The more I learn the earlier I can contribute
to news group discussions.

Best regards,

Ralf
Ralf Wahner, Jul 15, 2003


text:
Likelihood Ratio Test for general hypotheses

dfirka

New Member
Hi,

The original paper (Wilks, 1938) describing the Likelihood Ratio Test considers a null hypothesis stating that a subset of the parameters from the parameter space are equal to fixed values.

Do you know of any extension/formal proof covering LTR with null hypotheses for more general cases, like functions of the parameters, for instance Theta1*Theta2=constant?

Thanks,
Dan

dfirka

New Member
Hi,

Just find the proof, but I need some help understanding a fragment of it. In the Handbook of Econometric, R. Engle shows how to can reduce a non-linear hypothesis g(Theta) =0 to a set of hypotheses which have preassigned values for a subset of the parameter vector.

He uses a Taylor expansion of g to reduce the constraint equation to:

G*Theta=G*Theta0, where G is the first derivate matrix of g, evaluated at Theta0.

Being the last a linear hipothesis, he says: “for any linear hypothesis one can always reparameterize by a linear non-singular matrix (A^-1)Theta = Phi. To do this let A2 have K - p columns in the orthogonal complement of G so that GA2 = 0. The remaining p columns of A say A1, span the row space of G so that GA non-singular.”

My question is: how we can operationally get this set of matrices A1 and A2 for a concrete problem, say we have g() is:
B1*B2 – B3*B4=0

Where B1…B4 are the parameters of my model. How can I find this decomposition?

Any hint or pointing to the way will be greatly appreciated.

Thanks
daniel


text:
How to remove the .NET Runtime and SDK

Over time, as you install updated versions of the .NET runtime and SDK, you may want to remove outdated versions of .NET from your machine. Removing older versions of the runtime may change the runtime chosen to run shared framework applications, as detailed in the article on .NET version selection.

Should I remove a version?

The .NET version selection behaviors and the runtime compatibility of .NET across updates enables safe removal of previous versions. .NET runtime updates are compatible within a major version band such as 6.x and 5.x. Additionally, newer releases of the .NET SDK generally maintain the ability to build applications that target previous versions of the runtime in a compatible manner.

In general, you only need the latest SDK and latest patch version of the runtimes required for your application. Instances where you might want to keep older SDK or runtime versions include maintaining project.json-based applications. Unless your application has specific reasons for earlier SDKs or runtimes, you may safely remove older versions.

Determine what is installed

The .NET CLI has options you can use to list the versions of the SDK and runtime that are installed on your computer. Use dotnet --list-sdks to see the list of installed SDKs and dotnet --list-runtimes for the list of runtimes. For more information, see How to check that .NET is already installed.

Uninstall .NET

.NET uses the Windows Apps & features dialog to remove versions of the .NET runtime and SDK. The following figure shows the Apps & features dialog. You can search for core or .net to filter and show installed versions of .NET.

Select any versions you want to remove from your computer and click Uninstall.

The best way for you to uninstall .NET is to mirror the action you used to install .NET. The specifics depend on your chosen Linux distribution and the installation method.

Important

For Red Hat installations, consult the Red Hat Product Documentation for .NET.

There's no need to first uninstall the .NET SDK when upgrading it using a package manager, unless you're upgrading from a preview version that was manually installed. The package manager update or refresh commands will automatically remove the older version upon the successful installation of a newer version. If you have a preview version installed, uninstall it.

If you installed .NET using a package manager, use that same package manager to uninstall the .NET SDK or runtime. .NET installations support most popular package managers. Consult the documentation for your distribution's package manager for the precise syntax in your environment:

• apt-get(8) is used by Debian based systems, including Ubuntu.
• yum(8) is used on Fedora, CentOS, and Oracle Linux.
• zypper(8) is used on openSUSE and SUSE Linux Enterprise System (SLES).
• dnf(8) is used on Fedora.

In almost all cases, the command to remove a package is remove.

The package name for the .NET SDK installation for most package managers is dotnet-sdk, followed by the version number. Starting with the version 2.1.300 of the .NET SDK and version 2.1 of the runtime, only the major and minor version numbers are necessary: for example, the .NET SDK version 2.1.300 can be referenced as the package dotnet-sdk-2.1. Prior versions require the entire version string: for example, dotnet-sdk-2.1.200 would be required for version 2.1.200 of the .NET SDK.

For machines that have installed only the runtime, and not the SDK, the package name is dotnet-runtime-<version> for the .NET runtime, and aspnetcore-runtime-<version> for the entire runtime stack.

Tip

.NET Core installations earlier than 2.0 didn't uninstall the host application when the SDK was uninstalled using the package manager. Using apt-get, the command is:

apt-get remove dotnet-host

There's no version attached to dotnet-host.

If you installed using a tarball, you must remove .NET using the manual method.

On Linux, you must remove the SDKs and runtimes separately, by removing the versioned directories. These directories may vary depending on your Linux distribution. Removing them deletes the SDK and runtime from disk. For example, to remove the 1.0.1 SDK and runtime, you would use the following bash commands:

version="1.0.1"
sudo rm -rf /usr/share/dotnet/sdk/$version sudo rm -rf /usr/share/dotnet/shared/Microsoft.NETCore.App/$version
sudo rm -rf /usr/share/dotnet/shared/Microsoft.AspNetCore.All/$version sudo rm -rf /usr/share/dotnet/shared/Microsoft.AspNetCore.App/$version
sudo rm -rf /usr/share/dotnet/host/fxr/$version  Important The version folders may not match the "version" you're uninstalling. The individual runtimes and SDKs that are installed with a single .NET release may have different versions. For example, you may have installed ASP.NET Core 5 Runtime, which installed the 5.0.2 ASP.NET Core runtime and the 5.0.8 .NET runtime. Each has a different versioned folder. For more information, see Overview of how .NET is versioned. The parent directories for the SDK and runtime are listed in the output from the dotnet --list-sdks and dotnet --list-runtimes command, as shown in the earlier table. On Mac, you must remove the SDKs and runtimes separately, by removing the versioned directories. Removing them deletes the SDK and runtime from disk. For example, to remove the 1.0.1 SDK and runtime, you would use the following bash commands: version="1.0.1" sudo rm -rf /usr/local/share/dotnet/sdk/$version
sudo rm -rf /usr/local/share/dotnet/shared/Microsoft.NETCore.App/$version sudo rm -rf /usr/local/share/dotnet/shared/Microsoft.AspNetCore.All/$version
sudo rm -rf /usr/local/share/dotnet/shared/Microsoft.AspNetCore.App/$version sudo rm -rf /usr/local/share/dotnet/host/fxr/$version

Important

The version folders may not match the "version" you're uninstalling. The individual runtimes and SDKs that are installed with .NET may have different versions. For example, you may have installed .NET 5 Runtime, which installed the 5.0.2 ASP.NET Core runtime and the 5.0.8 .NET runtime. For more information, see Overview of how .NET is versioned.

Important

If you're using an Arm-based Mac, such as one with an M1 chip, review the folder paths described in Install .NET on Arm-based Macs.

The parent directories for the SDK and runtime are listed in the output from the dotnet --list-sdks and dotnet --list-runtimes command, as shown in the earlier table.

.NET Uninstall Tool

The .NET Uninstall Tool (dotnet-core-uninstall) lets you remove .NET SDKs and runtimes from a system. A collection of options is available to specify which versions should be uninstalled.

Visual Studio dependency on .NET SDK versions

Before Visual Studio 2019 version 16.3, Visual Studio installers called the standalone SDK installer for .NET Core version 2.1 or 2.2. As a result, the SDK versions appear in the Windows Apps & features dialog. Removing .NET SDKs that were installed by Visual Studio using the standalone installer may break Visual Studio. If Visual Studio has problems after you uninstall SDKs, run Repair on that specific version of Visual Studio. The following table shows some of the Visual Studio dependencies on .NET Core SDK versions:

Visual Studio version .NET Core SDK version
Visual Studio 2019 version 16.2 .NET Core SDK 2.2.4xx, 2.1.8xx
Visual Studio 2019 version 16.1 .NET Core SDK 2.2.3xx, 2.1.7xx
Visual Studio 2019 version 16.0 .NET Core SDK 2.2.2xx, 2.1.6xx
Visual Studio 2017 version 15.9 .NET Core SDK 2.2.1xx, 2.1.5xx
Visual Studio 2017 version 15.8 .NET Core SDK 2.1.4xx

Starting with Visual Studio 2019 version 16.3, Visual Studio is in charge of its own copy of the .NET SDK. For that reason, you no longer see those SDK versions in the Apps & features dialog.

Remove the NuGet fallback folder

Before .NET Core 3.0 SDK, the .NET Core SDK installers used a folder named NuGetFallbackFolder to store a cache of NuGet packages. This cache was used during operations such as dotnet restore or dotnet build /t:Restore. The NuGetFallbackFolder is located at C:\Program Files\dotnet\sdk on Windows and at /usr/local/share/dotnet/sdk on macOS.

You may want to remove this folder, if:

• You're only developing using .NET Core 3.0 SDK or .NET 5 or later versions.
• You're developing using .NET Core SDK versions earlier than 3.0, but you can work online.

If you want to remove the NuGet fallback folder, you can delete it, but you'll need administrative privileges to do so.

It's not recommended to delete the dotnet folder. Doing so would remove any global tools you've previously installed. Also, on Windows:

• You'll break Visual Studio 2019 version 16.3 and later versions. You can run Repair to recover.
• If there are .NET Core SDK entries in the Apps & features dialog, they'll be orphaned.


text:
## A Review of Parallel Processing Approaches to Robot Kinematics and Jacobian

• Due to continuously increasing demands in the area of advanced robot control, it became necessary to speed up the computation. One way to reduce the computation time is to distribute the computation onto several processing units. In this survey we present different approaches to parallel computation of robot kinematics and Jacobian. Thereby, we discuss both the forward and the reverse problem. We introduce a classification scheme and classify the references by this scheme.

### Additional Services

Author: Dominik Henrich, Joachim Karl, Heinz Wörn urn:nbn:de:hbz:386-kluedo-9805 Preprint English 1997 1997 Technische Universität Kaiserslautern 2000/04/03 AG-RESY ; Jacobian ; PARO ; parallel processing ; robot control; robot kinematics Fachbereich Informatik 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik AG RESY Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

$Rev: 13581$


text:
# Statistic hypothesis testing - Standard deviation less than 0.4

There was too much snow on the highways, so the mayor of the town sent snowplows to spread some chemicals on them. There is a standard of how much of one specific substance should be present in the compound that is used for spreading... We measured how much of the substance was present in the compound in 30 different places of the town. These are the results:

0.91 1.08 0.72 1.07 1.14 0.62 1.06 1.20 0.76 1.19
0.96 0.73 0.83 0.55 0.79 1.34 0.60 1.19 1.35 1.13
0.67 0.77 0.48 0.83 1.78 2.25 1.21 0.89 0.83 1.07

We expect that the values have normal distribution. Verify with a reliability of 99% that the standard deviation is less than 0.4. [Result: r = 24.546. Hypothesis H0 is not denied.]

I calculated

a) $\mu$ = 1.00.....and.....b) $\sigma$ = 0.367

Now I set ...H0: $\sigma^{2} = \sigma^{2}_{o}$... versus...H1: $\sigma^{2} < \sigma^{2}_{o}$

I used this test: $\frac {(n-1) s_{n}^{2}} { \sigma_{0}^{2} } \leq \chi^{2} _{ \alpha } (n-1)$

Then, I calculated $\frac {(n-1) s_{n}^{2}} { \sigma_{0}^{2} }$ = 24.54 and $\chi^{2} _{ \alpha } (n-1)$ = 49.58

Now, we see that the inequality holds good, so H0 should be denied! However the result in the book says the opposite...

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The associated p-value is greater than 1%, therefore there is not enough evidence to reject the null hypothesis. Note that the statistic is smaller than the critical value. I have noticed that you got very good answers in the past and you seem to be satisfied, consider accepting some of them to motivate people to continue to help you. It is just one click ;) –  user10525 Jun 10 '12 at 12:03
I didn't know there was something like Accepting Answers. From now on, I will always accept the best answer to my question which has at least 1 answer. Thank you Procrastinator for letting me know! –  user1111261 Jun 10 '12 at 12:59