text:
ISSN 0439-755X
CN 11-1911/B

中国科学院心理研究所

#### Archive

25 June 2022, Volume 54 Issue 6

Reports of Empirical Studies
 For Selected: Toggle Thumbnails
Reports of Empirical Studies
 The influence of language and context on sensorimotor simulation of concrete concepts SHI Rubin, XIE Jiushu, YANG Mengqing, WANG Ruiming 2022, 54 (6):  583-594.  doi: 10.3724/SP.J.1041.2022.00583 Abstract ( 4169 )   HTML ( 382 )   PDF (410KB) ( 4809 )   Peer Review Comments How concepts are represented in the brain is an important topic in cognitive science. There are two different theories on this research question, i.e., propositional symbol theory and perceptual symbol theory. The difference between these two theories is how to treat the relationship between the internal symbol and the external archetype. The propositional symbol theory holds that the relationship between the two is arbitrary. Perceptual information does not participate in the processing of concepts. While perceptual symbols theory holds that the relationship between the two is similar. Perceptual information participates in the processing of concepts. People learn conceptual information in the vertical space. The spatial information is stored in long-term memory along with the representation of concepts. This hypothesis has been supported by many studies and is in line with the perceptual symbol theory. However, few studies have tested what factors influence sensorimotor simulation in conceptual processing. In this study, the semantic relevance judgment paradigm is used to test this question. The present study examined whether the sensorimotor simulation participates in conceptual processing in the first and second languages. Then, the present study examined how situational information modulates conceptual processing, by manipulating the intensity of spatial information and the level of semantic processing. In Experiment 1, the semantic relevance judgment paradigm is used to test whether sensorimotor simulation is involved in the second language processing and whether there is any difference between the first language and second language processing. The results of Experiment 1 show that the sensorimotor simulation has participated in the second language processing. However, there is an accuracy advantage in the sensorimotor simulation in the first language. In Experiment 2, two experiments are conducted to test the effect of the perceptual situation on sensorimotor simulation. Experiment 2a tests the influence of perceptual situation on sensorimotor simulation by changing the intensity of individual perceptual in vertical spatial axis. The results show that the sensorimotor simulation can be found in both strong and weak spatial perception. The effect of semantic processing level on perceptual motion simulation is tested in Experiment 2b. The experiment manipulates the level of semantic processing by using the semantic relevance judgment task and word judgment task. The results show that sensorimotor simulation participates in the processing of concepts, while semantic situational did not modulate this effect. The results of Experiment 2 suggest that sensorimotor stimulation may be automatic in conceptual processing. The present study conducted two experiments to test the role of sensorimotor simulation in conceptual processing. Results found that the sensorimotor simulation participates in conceptual representation, supporting the perceptual symbol theory. Furthermore, the sensorimotor simulation takes place in both Chinese and English. This finding extends the perceptual symbol theory. Finally, results found that sensorimotor stimulation may be automatic in conceptual representation and is not affected by spatial information and semantic processing.
 The influence of uncertainty and validity of expectation on the perceptual decision of motion direction PAN Yuean, JIANG Yunpeng, GUO Maojie, WU Xia 2022, 54 (6):  595-603.  doi: 10.3724/SP.J.1041.2022.00595 Abstract ( 2222 )   HTML ( 226 )   PDF (1045KB) ( 2791 )   Peer Review Comments Accurate perception of motion direction depends on current and prior information. However, it is not clear how the uncertainty of the current stimulus and the validity of expectation from prior information can be integrated into the decision-making for the directional perception. In our experiment, the validity of expectation from a cue, which appears before the stimulus, belongs to the proactive control system, while the uncertainty of stimulus, which changes by the signal-to-noise ratio, belongs to the reactive control system. It is unclear whether the proactive and reactive control systems engage in standard processing or work independently. In order to verify the integrated mechanism of the uncertainty of current sensory information and the validity of expectation from prior cue information on the perceptual decision of motion direction, two experiments were conducted. Experiment 1 employed random dot motion patterns (RDPs) to investigate the appropriate high and low uncertainty conditions. Participants should distinguish the moving direction of coherent dots (in the same direction) while noise dots move in a random direction. The PR (perceptual accuracy) values were compared for various ratios of coherent dots (100%, 80%, 70%, 60%, 20%, 0%). The results indicated that the PR of 60% ratio was significantly lower than that of 100%, while the PR of 20% ratio was significantly different from that of 0% and 60%. Consequently, 20% and 60% ratios can be considered as high and low uncertainty conditions in Experiment 2, respectively. Experiment 2 employed a task combined of associated learning and RDPs paradigm, in which a cue with high (90% correct) or low (10% correct) validity of expectation appeared before moving dots. Results showed that the PR of high uncertainty was significantly lower than that of low uncertainty and reflected a significant increase in PR with a valid cue, demonstrating an expectation effect. Moreover, there was considerable interaction between validity and uncertainty, while the expectation effect was found in both uncertainty conditions. However, the magnitude of expectation effect was lower in low uncertainty than in high uncertainty conditions, suggesting that uncertainty and validity can be influenced in standard cognitive processing. In summary, based on the present results, the prior and sensory information can be integrated into motion perception decision-making. The results can support the cooperation mechanism of proactive and reactive control systems and provide a theoretical basis to prevent traffic accidents. Investigating the effects of uncertainty and validity on the perceptual decision of motion direction of specific individuals (such as veteran or aged drivers) can be considered a future research topic.
 Sustained hyperarousal induced by acute stress in tryptophan-hydroxylase-2 genetic deficient male mice ZHOU Ping, XIAO Hua, LI Yonghui, DONG Xinwen 2022, 54 (6):  604-612.  doi: 10.3724/SP.J.1041.2022.00604 Abstract ( 856 )   HTML ( 58 )   PDF (441KB) ( 974 )   Peer Review Comments Severe stress is one of the major external triggers of emotion-related mental disorders such as post-traumatic stress disorder (PTSD). Stress-induced sustained hyperarousal state is not only a core symptom but also a contributor to other symptoms such as sleep disturbance and negative mood. Serotonin, or 5-hydroxytryptamine (5-HT), is a monoamine neurotransmitter that regulates emotional response. In addition, the 5-HT system is the target for pharmacological treatment such as selective-serotonin re-uptake inhibitors (SSRIs) for major depressive disorder, PTSD, and other emotional disorders. However, it remains unknown whether serotonin is involved in the hyperarousal state caused by severe stress, as well as the mechanism by which genetic polymorphism in serotonin regulation contributes to the vulnerability of stress-related psychiatric disorders. Tryptophan-hydroxylase-2 (Tph2) is a serotonin synthesizing enzyme that converts tryptophan to 5-hydroxytryptophan in the brain. A genetic deficiency in the expression of Tph2 may lead to a lower level of serotonin in the brain. The present study focused on the role of serotonin in the development of stress-induced hyperarousal, investigating the behavioral effect of Tph2 gene-deficiency after severe stress in a mice model. Mice lacking Tph2 (Tph2-/-) in the brain have a vitally low level of serotonin and a bad health condition, so we used heterozygous Tph2-deficient mice (Tph2+/-) which have been shown to have a mild low level of serotonin in the brain. We measured the auditory startle reflex as an indicator of arousal level at different time points after predator-exposure stress or footshock stress in both male and female Tph2+/- and wild-type mice. The predator-exposure stress was to exposure a mouse to a cat for 5 minutes with a trained experimenter protecting the mouse from direct attack from the cat. The footshock stress was to exposure a mouse to a series of footshock (1.5 mA × 5s × 5, inter-shock interval 60 ~ 120 s) in a shock chamber. Then we measured the auditory startle reflex at 1-, 2-, 10-, and 18-day post-stress. For each startle test session, a total of 30 white noise stimuli were presented to the mice in a sound-isolated chamber (90 dB, 100 dB, 110 dB, ten stimuli for each level). The results showed that the Tph2+/- male mice had a higher level of startle than the non-stressed group at 1, 2, and 10 days after footshock stress, indicating a sustained hyperarousal. However, wild-type male mice only had an increased startle response on the day after the footshock stress. For mice with predator exposure stress, both Tph2+/- male mice and wild-type male mice showed an increased startle response on the first day after the predator stress, but then returned to the same level as the non-stressed mice. We also observed a sex difference in mice’s startle response that the female mice had a lower level of startle amplitude than that of male mice at baseline test before stress. In addition, female mice with different genotypes showed minor differences in their startle response at different time points after both types of stress. The results of the study indicate that the Tph2 genotype interacts with stress types in the regulation of long-term hyperarousal after severe stress events. Our results also provide preclinical evidence that individuals with Tph2 gene deficiency may be more vulnerable to stress-induced hyperarousal and highlight the potential of targeting the serotonin system for post-traumatic intervention.
 Benefits and costs of employee boundary-spanning behavior: A meta-analytic review LAN Yuanmei, LI Chaoping, WANG Jiayan, MENG Xue 2022, 54 (6):  665-683.  doi: 10.3724/SP.J.1041.2022.00665 Abstract ( 937 )   HTML ( 63 )   PDF (518KB) ( 2091 )   Peer Review Comments Employee boundary-spanning behavior is critically important for organizations. Numerous studies have examined the relationships between employee boundary-spanning behavior and work-related outcomes. However, the findings are inconsistent among studies. This meta-analysis investigated the relationships between of employee boundary-spanning behavior and work attitude, performance, innovation, stress, and burnout, and also examined potential moderators and mediating mechanisms for those relationships based on social exchange theory. We meta-analyzed both Chinese and English primary studies on employee boundary- spanning behavior. Studies were identified with key words including “Boundary spanning”, “Boundary spanning activities/Boundary spanning activity”, “Boundary spanning behavior”, etc., in English databases including Web of Science, ProQuest (Dissertation), EBSCO, Wiley, Sage and Chinese databases of CNKI and CSSCI. Finally, 52 independent samples from 50 empirical studies (with a total sample N = 14366) were included. We chose a random-effect model to conduct the meta-analysis using the R package Psychmeta (Core team, 2020). The results showed considerable heterogeneity among the 52 independent samples, according to the heterogeneity test. The publication bias test was conducted using Egger's test, Begg test, and Failsafe number, which revealed that there was no substantial publication bias in the studies. With the Hunter-Schmidt’s meta-analytic method, employee boundary spanning behavior had significant relationships with job satisfaction and organizational commitment ($\bar{\rho }$ between 0.34 to 0.41) and performance outcomes ($\bar{\rho }$ between 0.19 to 0.31), as well as a small positive relationship with role stress ($\bar{\rho }$ = 0.14). It had no significant relationship with emotional exhaustion ($\bar{\rho }$= -0.10, 95% CI = [-0.25, 0.05]). Employees' boundary-spanning behavior has both benefits and costs. Employee type (knowledge workers-non-knowledge workers), individualism-collectivism, and power distance moderated the relationships between employee's boundary-spanning behavior and its outcomes. The relationships between employee boundary-spanning behavior and performance and innovation were stronger for knowledge workers than for nonknowledge workers, but the relationships between employee boundary-spanning behavior and job satisfaction and role stress were stronger for nonknowledge workers than for knowledge workers. Collectivism positively moderated the relationship between employee boundary-spanning behavior and job satisfaction, performance, innovation. The relationships between employee boundary-spanning behavior and job satisfaction, performance, and role stress were stronger for high power distance regions than low power distance regions. Additionally, a meta mediation analysis was conducted to examine whether work attitudes partially mediated the relationship of employee boundary-spanning behavior with work outcomes. The results revealed that employee boundary-spanning behavior had indirect impacts on performance and innovation, while having suppressing effects on stress and exhaustion. We discuss the important implications for future research and organizational practices.
 Standard errors and confidence intervals for cognitive diagnostic models: Parallel bootstrap methods LIU Yanlou 2022, 54 (6):  703-724.  doi: 10.3724/SP.J.1041.2022.00703 Abstract ( 807 )   HTML ( 42 )   PDF (1787KB) ( 1078 )   Peer Review Comments The model parameter standard error (SE; or variance-covariance matrix), which provides an estimate of the uncertainty associated with the model parameter estimate, has both theoretical and practical implications in cognitive diagnostic models (CDMs). The drawbacks of the analytic methods, such as the empirical cross-product information matrix, observed information matrix, and “robust” sandwich-type information matrix, are that they require the positive definiteness of the information matrix and may suffer from boundary problems. Another method for estimating model parameter SEs is to use the computer-intensive bootstrap method, and consequently, no study has systematically explored the performance of the bootstrap in calculating model parameter SEs and confidence intervals (CIs) in CDMs. The purpose of this research is to present two new highly efficient bootstrap methods to calculate model parameter SEs and CIs in CDMs, namely the parallel parametric bootstrap (pPB) and parallel non-parametric bootstrap (pNPB) methods. A simulation study was conducted to evaluate the performance of the pPB and pNPB methods. Five factors that may influence the performance of the model parameter SEs and CIs were manipulated. The two model specification scenarios considered in this simulation were the correctly specified and over-specified models. The sample size was set to two levels: 1, 000 and 3, 000. Three bootstrap sample sizes were manipulated: 200, 500, and 3, 000. Three levels of item quality were considered: high [$P(\mathbf{0})=0.1$, $P(\mathbf{1})=0.9$], moderate [$P(\mathbf{0})=0.2$, $P(\mathbf{1})=0.8$], and low quality [$P(\mathbf{0})=0.3$, $P(\mathbf{1})=0.7$]. The pPB and pNPB methods were used to estimate model parameter SEs and CIs. The simulation results indicated the following. (1) For the correctly specified CDMs, under the high- or moderate-item-quality conditions, the coverage rates of the 95% CIs of the model parameter SEs based on the pNPB or pPB method were reasonably close to the expected coverage rate, and the bias for each model parameter SE converged to zero, meaning that the estimated SE was almost identical to the empirical SE. The increase in the bootstrap sample size had only a slight effect on the performance of the pNPB or pPB method. Under the low-item-quality condition, the pNPB method tended to over-estimate SE, whereas a contrary trend was observed for the pPB method. (2) For the over-specified CDMs, most of the permissible item parameter SEs and almost all of the permissible structural parameter SEs exhibited good performance in terms of the 95% CI coverage rates and bias. Under most of the simulation conditions, the impermissible model parameter SEs did not exhibit good performance in approximating the empirical SEs. To the best of our knowledge, this is the first study in which the performance of the bootstrap method in estimating model parameter SEs and CIs in CDMs is systematically investigated. The pNPB or pPB appears to be a useful tool for researchers interested in evaluating the uncertainty of the model parameter point estimates. As a time-saving computational strategy, the pNPB or pPB method is substantially faster than the usual bootstrap method. The simulation and real data studies showed that 3, 000 re-samples might be adequate for the bootstrap method in calculating model parameter SEs and CIs in CDMs.


text:
Chapter 5, Problem 3PA

### Principles of Microeconomics

7th Edition
N. Gregory Mankiw
ISBN: 9781305156050

Chapter
Section

### Principles of Microeconomics

7th Edition
N. Gregory Mankiw
ISBN: 9781305156050
Textbook Problem

# Suppose the price elasticity of demand for heating oil is 02. in the short run and 0.7 in the long run.a. If the price of heating oil rises from $1.80 to$2.20 per gallon, what happens to the quantity of heating oil demanded in the short run? In the long run? (Use the midpoint method in your calculations.)b. Why might this elasticity depend on the time horizon?

Subpart (a):

To determine
Price elasticity of demand.

Explanation

By midpoint method; the percentage change in the price is calculated as follows:

Percentage change in price=(2.201.80)((2.20+1.8)2)×100=0.42×100=20%

Percentage change in price is 20%.

In the short run, when the price elasticity is 0.2, the change in quantity demanded is calculated as follows

Subpart (b):

To determine
Relevance of price elasticity of demand.

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text:
mersenneforum.org > Data processed dc and tc posts
 Register FAQ Search Today's Posts Mark Forums Read

 2019-03-06, 21:40 #1 Mark Rose     "/X\(‘-‘)/X\" Jan 2013 B8716 Posts processed dc and tc posts You may wish to not delete claims immediately lest they not be completed. It happens from time to time.
 2019-03-07, 14:56 #2 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 10,739 Posts processed dc and tc posts a collection thread for the posted cleared from the DC and TC thread.
2019-05-07, 10:18   #3
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

2·5,059 Posts

Quote:
 Originally Posted by Uncwilly You are a supermod. Next time you can put it on the list yourself. GP2 and ATH have been editing the lists too.
Which is a bit frown about, in this part of the lake... I would not recommend that all of us who, due to benevolence of the admin, appeared like the mushrooms after the rain, we start now modifying the assignment lists and so on. For many projects we have no much idea what the guyz and galz are doing there... Just my two pence... Job of the mod is to be arbiter, intervene if some sheep happens, but let the projects managers do their job... they know better what to do and what is requested, etc...

Last fiddled with by LaurV on 2019-05-07 at 10:19

2019-05-07, 16:10   #4
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

10,739 Posts

Quote:
 Originally Posted by LaurV Which is a bit frown about, in this part of the lake... I would not recommend that all of us who, due to benevolence of the admin, appeared like the mushrooms after the rain, we start now modifying the assignment lists and so on.
Sure, but I think that I am ok with Luigi doing it. George, Alex, and some others I would have no problem with.

You, on other hand, must beg for assignments and pay a steep fee.

2019-05-09, 13:45   #5
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

278616 Posts

Quote:
 Originally Posted by Uncwilly You, on other hand, must beg for assignments and pay a steep fee.
Haha, ok, ok, you won't see me here, at least, no until this ends (ETA ~20 days, over 90% done, LL+DC in parallel).

2019-05-17, 15:04   #6
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

1ABB16 Posts

Quote:
 Originally Posted by ATH You should register them in Primenet as well, everyone might not read this thread.
I would if I could. I checked they are not assigned to anyone else, via exponent details, individually, then tried to manually reserve them, individually, and got error messages.

Edit: these are being run in CUDALucas on two fast gpus. Should be done in a few days. The method I described above usually works with assignments for gpus. The error message that occurs for manual checkout of these is:
Code:
Error code: 40

Error text: No assignment available meeting CPU, program code and work preference requirements
Attached Thumbnails

Last fiddled with by kriesel on 2019-05-17 at 15:56

2019-05-17, 15:23   #7
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

10,739 Posts

Quote:
 Originally Posted by ATH You should register them in Primenet as well, everyone might not read this thread.
Quote:
 Originally Posted by kriesel I would if I could. I checked they are not assigned to anyone else, via exponent details, individually, then tried to manually reserve them, individually, and got error messages.
From the first post in this thread.
Quote:
 Originally Posted by Uncwilly The easy way to get some assignments (with Prime95):Grab the lines of the exponents that you will do. Stop Prime95. Edit your worktodo.txt, inserting the new lines, save it, and close the editor. Restart Prime95 Go to the menu Advanced-> Manual Communication Make sure "Contact PrimeNet server now" and "Send new expected completion dates to server" are checked. Hit OK After Prime95 is done communicating, look and see if any of the new exponents don't have an Assignment ID (because they were already assigned.) If they don't, stop Prime95, reopen the worktodo.txt, remove those lines, save, then restart Prime95
That should do it. mprime probably has a similar technique.

2019-05-17, 16:41   #8
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

152738 Posts

Quote:
 Originally Posted by Uncwilly From the first post in this thread. That should do it.
It does indeed. Although for gpu usage, and my crappy slow ISP, there are additional steps:
repeat the manual communication in prime95 as needed until communication completes successfully instead of giving CURL library errors;
stop prime95, cut the doublecheck assignments with new AIDs from the worktodo.txt of the prime95 instance used to reserve them, restart prime95;
stop the CUDALucas session, paste the doublecheck assignments with newly issued AIDs into the gpu worktodo.txt, and restart the CUDALucas session;
update local assignment tracking log.

Effective, though a bit tedious compared to my usual manual checkout method when it works.
I wonder if primenet will get confused by these 4 assignments completing and being reported manually in a few days, after being reserved on an old i3 laptop that could not finish one of the assignments in 3 months, and having been removed from the worktodo.txt of the regularly reporting i3 system.

2019-05-23, 15:14   #9
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

3×2,281 Posts
methods for gpus

Quote:
 Originally Posted by Uncwilly The easy way to get some assignments (with Prime95): Stop Prime95. Edit your worktodo.txt, inserting the new lines, save it, and close the editor. Restart Prime95 Go to the menu Advanced-> Manual Communication Make sure "Contact PrimeNet server now" and "Send new expected completion dates to server" are checked. Hit OK After Prime95 is done communicating, look and see if any of the new exponents don't have an Assignment ID (because they were already assigned.) If they don't, stop Prime95, reopen the worktodo.txt, remove those lines, save, then restart Prime95 If someone can post tips for the GPU's that would help.
The following assumes gpu application(s) CUDALucas etc. are already running and are not near completion of the current work item(s). Add gpu application stops and starts as appropriate if that assumption is not valid.
• Post which DC or TC candidates you're taking.
• Grab the lines of the exponents that you will do.
• Edit your gpu(s)' worktodo.txt, inserting the new lines, save it, and close the editor.
continue, with either Method 1:
• Go to https://www.mersenne.org/manual_assignment/
• Set preferred work type to Double check ll tests
• set Optional exponent range fields to one less, and one more than the exponent in the first worktodo entry added that does not yet have an AID
• click Get Assignments
• If it succeeds, copy the assignment with AID, and overwrite the corresponding gpu worktodo.txt entry that had no AID, with it, and save.
• If it fails, likely it is with error 40, no assignment available. Use a prime95 session as uncwilly described, to get the assignment, then copy that to the gpu worktodo.txt, again, overwriting the no-AID version entry.
• Repeat previous steps of method 1 for each DC or TC. Depending on how many you're doing, it can get tedious.
or continue with Method 2:
• reserve as described by uncwilly in a prime95 session.
• Copy the new assignments with AIDs from the prime95 worktodo file to the gpu(s) worktodo file(s), and save, then close the gpu worktodo file(s).
• Move the new assignments in the prime95 worktodo file, to the end of the prime95 worktodo.txt file behind some ongoing lengthy work intended for the cpu, save the prime95 worktdo file, stop and restart prime95, and check with Test, Status, that the assignments order in effect on the cpu is as intended.
For either method, wrapup:
• If you're unable to get a reservation for any exponent you posted you were taking, by either method, edit your initial post to exclude it. If the edit period already expired, post which you were unable to reserve in a new message.
Optionally: if any gpu assignment is about to expire, because manual extension does not work, try
• Open the prime95 worktodo file, temporarily put its worktodo entry at the front of the prime95 work list, save prime95 worktodo file, stop and restart prime95 computation to run at least 0.1% of completion.
• Make sure "Contact PrimeNet server now" and "Send new expected completion dates to server" are checked. Click OK, and wait for prime95 to finish talking with the primenet server
• Stop prime95, move the extended assignment to the end of the prime95 worktodo file, save and close prime95 worktodo file, restart prime95, check with Test, Status.
• After the gpu assignment completes, remove the corresponding assignment entry from the prime95 worktodo file, save and close the prime95 worktodo file, stop computation and resume in prime95, delete the prime95 save file and backup files for the few dozen iterations performed on the cpu for the completed gpu assignment.
A variant of this extension method seemed to work, in which I commented out the prime95 assignment copy and deleted the exponent's save file and bu files, on an exponent I had that was going to expire yesterday. It gained 10 weeks in the assignments report. But I see today that it is marked expired for me and assigned to someone else. Its chance of working to maintain the extension may be better if it remains in the prime95 instance's worktodo as an active entry that will be included in periodic automatic reporting of progress. By putting it at the end of the work list, behind a lengthy DC I'm running on the prime95 instance, it should report status periodically from there, and yet not use up cpu cycles partially duplicating gpu work.

A side effect of using this method for extension is it changes the assignment from manual to the prime95 instance used to extend it. At least that is what the assignments page shows.

Because this assignment or extension method might confuse Primenet about what's happening on the prime95 instance, and any expirations may count against that instance/system in getting new assignments, consider using an old slow cpu for making these reservations or extensions, where it will make little difference regarding assignment of future work via primenet.

Last fiddled with by Uncwilly on 2019-06-10 at 13:48 Reason: done at the request of the op

2019-05-30, 08:54   #10
GP2

Sep 2003

13×199 Posts

Quote:
 Originally Posted by Uncwilly GP2 can you handle the honours of posting the worktodo lines? I have no clue about them.
Lines suitable for doing a double-check with mprime would be:
Code:
PRP=1,2,87667499,-1,76,0,3,4
PRP=1,2,87595463,-1,76,0,3,4
I assume gpuOwL can understand the same format.

2019-06-10, 12:44   #11
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

3·2,281 Posts
methods for gpus (amended)

Quote:
Substitute "at least 0.1% of completion" in place of the phrase highlighted in red.

Last fiddled with by kriesel on 2019-06-10 at 12:47

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text:
Math Help - proof by contradiction

given a set with the symbols :
" - " for inverse
the constants :
0
AND the axioms:
for all a,b,c : a+(b+c) = (a+b) + c
for all a : a+0 = a
for all a : a +(-a) =0
for all a,b : a+b = b+a
1) THE uniqness of zero
2) THE uniqness of the inverse

2. Originally Posted by alexandros
given a set with the symbols :
" - " for inverse
the constants :
0
AND the axioms:
for all a,b,c : a+(b+c) = (a+b) + c
for all a : a+0 = a
for all a : a +(-a) =0
for all a,b : a+b = b+a
1) THE uniqness of zero
2) THE uniqness of the inverse
1) Let $0^,$ be a number other than zero such that for all a,

$a+0^,=a$

then, since zero is number

$0+0^,=0$

also by our fourth axiom, $0+0^,=0^,+0$ which is $0^,$ by our second axiom.

which implies $0^,$ is same as $0$....hence, zero is unique.

3. 2) The inverse of $a$ is $-a$. Assume that there exists another inverse element denoted as $a^{-1}$ such that $a^{-1}\neq-a$

Now, by the definition of inverse element, we have:

$a+a^{-1}=0$

But from the third axiom, we have:

$a+(-a)=0$

Ergo:

$a+a^{-1}=a+(-a)$

$a^{-1}=-a$

Which contradicts our original assumption $a^{-1}\neq-a$, so the inverse element must be unique.


text:
# In Note D to its 2011 financial statements, IBM includes disclosure about its derivatives as...

In Note D to its 2011 financial statements, IBM includes disclosure about its derivatives as follows: Note: AOCI represents Accumulated other comprehensive income/(loss) in Consolidated Statement of Changes in Equity. (1) See pages 76 and 77 for additional information on the purpose for entering into derivatives not designated as hedging instruments. (2) Includes changes in clean fair values of the derivative instruments in fair value hedging relationships and the periodic accrual for coupon payments required under these derivative contracts. (3) Includes basis adjustments to the carrying value of the hedged item recorded during the period and amortization of basis adjustments recorded on de-designated hedging relationships during the period. (4) Amount of gain (loss) recognized in income represents ineffectiveness on hedge relationships. (5) Instruments in net investment hedges include derivative and non-derivative instruments. At December 31, 2011, in connection with cash flow hedges of anticipated royalties and cost transactions, the company recorded net gains of $88 million (before taxes) in other comprehensive income;$191 million of gains are expected to be reclassified to net income within the next 12 months, providing an offsetting economic impact against underlying anticipated transactions. At December 31, 2011, net losses of approximately \$5 million (before taxes) were recorded in other comprehensive income/(loss) in connection with cash flow hedges of


text:
시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 512 MB 0 0 0 0.000%

## 문제

At some point or another, most computer science students have written a standard Sudoku solving program. This is yet another “put numbers in a grid’’ puzzle.

Numbers are placed in the grid so that each outlined region contains the numbers 1 to n, where n is the number of squares in the region. The same number can never touch itself, not even diagonally.

 Incomplete Grid Solution Grid

For this problem, you will write a program that takes as input an incomplete puzzle grid and outputs the puzzle solution grid.

## 입력

The first line of input contains a single decimal integer P, (1 ≤ P ≤ 100), which is the number of data sets that follow. Each data set should be processed identically and independently.

Each data set starts with a line containing the data set number K, (1 ≤ K ≤ 100), the number of rows in the input grid R, (1 ≤ R ≤ 7), and the number of columns in the input grid C, (1 ≤ C ≤ 7), separated by spaces. The next R lines contain a representation of the incomplete input grid, one row per line. The value in each cell is represented by either the digit already in that cell or a ‘-’ for an initially empty cell.

This grid is followed by a description of the separate regions in the grid. The first of these lines specifies the total number of regions. This is followed by one line for each region that specifies the cells contained in that region. Each region description consists of a decimal number N, specifying the number of cells in the region, followed by N cell descriptions separated by spaces. Each cell description consists of a left parenthesis, followed the cell’s row index, followed by a comma, followed by the cell’s row number, followed by a right parenthesis.

## 출력

For each data set, the output consists of the data set number, K, on a line by itself. This is followed by R lines containing C digits (separated by single spaces) showing the solution grid for the corresponding input data set.

## 예제 입력 1

2
1 3 5
- - - - -
- - - - -
4 - - - 1
5
1 (1,1)
2 (1,2) (1,3)
5 (2,1) (2,2) (3,1) (3,2) (3,3)
4 (2,3) (2,4) (1,4) (1,5)
3 (3,4) (3,5) (2,5)
2 7 7
- - - - - - -
4 - - - - 5 -
- - - - - - -
- - - 3 - - -
- - - - - - -
- - - - - - -
- - - - - - -
14
5 (1,1) (2,1) (3,1) (2,2) (2,3)
4 (2,4) (1,2) (1,3) (1,4)
2 (1,5) (1,6)
1 (1,7)
4 (4,1) (5,1) (6,1) (5,2)
1 (7,1)
4 (3,2) (4,2) (4,3) (5,3)
3 (7,3) (7,2) (6,2)
4 (6,3) (6,4) (7,4) (7,5)
6 (2,5) (3,5) (4,5) (3,6) (2,6) (2,7)
4 (3,7) (4,7) (4,6) (5,6)
1 (5,7)
5 (7,7) (7,6) (6,7) (6,6) (6,5)
5 (3,3) (3,4) (4,4) (5,4) (5,5)

## 예제 출력 1

1
1 2 1 2 1
3 5 3 4 3
4 2 1 2 1
2
3 1 4 2 1 2 1
4 2 5 3 6 5 4
1 3 1 4 2 3 1
2 4 2 3 1 4 2
1 3 1 5 2 3 1
4 2 4 3 4 5 2
1 3 1 2 1 3 1


text:
## Cryptology ePrint Archive: Report 2020/656

On Length Independent Security Bounds for the PMAC Family

Bishwajit Chakraborty and Soumya Chattopadhyay and Ashwin Jha and Mridul Nandi

Abstract: At FSE 2017, Gaži et al. demonstrated a pseudorandom function (PRF) distinguisher (Gaži et al., ToSC 2016(2)) on PMAC with $\Omega(\ell q^2/2^n)$ advantage, where $q$, $\ell$, and $n$, denote the number of queries, maximum permissible query length (in terms of $n$-bit blocks), and block size of the underlying block cipher. This, in combination with the upper bounds of $O(\ell q^2/2^n)$ (Minematsu and Matsushima, FSE 2007) and $O(q\sigma/2^n)$ (Nandi and Mandal, J. Mathematical Cryptology 2008(2)), resolved the long-standing problem of exact security of PMAC. Gaži et al. also showed that the dependency on $\ell$ can be dropped (i.e. $O(q^2/2^n)$ bound up to $\ell \leq 2^{n/2}$) for a simplified version of PMAC, called sPMAC, by replacing the Gray code-based masking in PMAC with any $4$-wise independent universal hash-based masking. Recently, Naito proposed another variant of PMAC with two powering-up maskings (Naito, ToSC 2019(2)) that achieves $\ell$-free bound of $O(q^2/2^n)$, provided $\ell \leq 2^{n/2}$. In this work, we first identify a flaw in the analysis of Naito's PMAC variant that invalidates the security proof. Apparently, the flaw is not easy to fix under the existing proof setup. We then formulate an equivalent problem which must be solved in order to achieve $\ell$-free security bounds for this variant. Second, we show that sPMAC achieves $O(q^2/2^n)$ bound for a weaker notion of universality as compared to the earlier condition of $4$-wise independence.

Category / Keywords: secret-key cryptography / PMAC, PMAC1, PMAC_Plus, PRF, universal hash, tight security

Date: received 31 May 2020, last revised 31 May 2020

Contact author: ashwin jha1991 at gmail com

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2020/656

[ Cryptology ePrint archive ]


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text:
# Math Help - Finding solutions to an equation

1. ## Finding solutions to an equation

The question is the following:

Find all solutions of the equation cos x = 0 such that 0</x</2pi.
--my answer is: x=pi/2 and 3pi/2.

part b says:

Find all solutions of the equation cos x = 0.
--the solutions posted for this homework shows pi/2 + 2pi(k) where k is an integer and also 3pi/2 + 2pi(k). These two are then simplified to be x=pi/2 + pi(k).

BUT THEN...

for a similar question...

Find all solutions of the equation sin x = 1/2 such that 0</x</2pi
--my answer: pi/6 and 5pi/6

part b) find all solutions of the equation sin x = 1/2
--the homework answers have two answers: x=pi/6 + 2pi(k) and x=5pi/6 + 2pi(k)

and there is no simplification.

My question is how come there was simplification in the first question but not in the second one. And how did the first one get simplified to the final equation?

thank you, sorry for the long post!

2. ## Re: Finding solutions to an equation

Originally Posted by bhuang
The question is the following:

Find all solutions of the equation cos x = 0 such that 0</x</2pi.
--my answer is: x=pi/2 and 3pi/2.

part b says:

Find all solutions of the equation cos x = 0.
--the solutions posted for this homework shows pi/2 + 2pi(k) where k is an integer and also 3pi/2 + 2pi(k). These two are then simplified to be x=pi/2 + pi(k).

BUT THEN...

for a similar question...

Find all solutions of the equation sin x = 1/2 such that 0</x</2pi
--my answer: pi/6 and 5pi/6

part b) find all solutions of the equation sin x = 1/2
--the homework answers have two answers: x=pi/6 + 2pi(k) and x=5pi/6 + 2pi(k)

and there is no simplification.

My question is how come there was simplification in the first question but not in the second one. And how did the first one get simplified to the final equation?

thank you, sorry for the long post!
all solutions in the first equation differ by exactly $\pi$ radians ; the set of all solutions in the second example do not have such a "convenient" difference.


text:
#### [SOLVED] Nice expression for minimum of three variables?

As we saw here, the minimum of two quantities can be written using elementary functions and the absolute value function.

$\min(a,b)=\frac{a+b}{2} - \frac{|a-b|}{2}$

There's even a nice intuitive explanation to go along with this: If we go to the point half way between two numbers, then going down by half their difference will take us to the smaller one. So my question is: "Is there a similar formula for three numbers?"

Obviously $\min(a,\min(b,c))$ will work, but this gives us the expression: $$\frac{a+\left(\frac{b+c}{2} - \frac{|b-c|}{2}\right)}{2} - \frac{\left|a-\left(\frac{b+c}{2} - \frac{|b-c|}{2}\right)\right|}{2},$$ which isn't intuitively the minimum of three numbers, and isn't even symmetrical in the variables, even though its output is. Is there some nicer way of expressing this function?

#### @Oscar Cunningham 2017-02-17 13:39:49

Based on Christian Blatter's answer and the trigonometric solution of the cubic equation, we can derive the following unusual solution.

Let $a$, $b$ and $c$ be real numbers. Then they are the roots of the equation

$$(x-a)(x-b)(x-c)=0$$

which can also be written as

$$x^3-(a+b+c)x^2+(ab+bc+ca)x-abc=0.$$

The trigonometric formula gives the solutions of a cubic equation in terms of its coefficients. If we substitute in the above coefficients and simplify we get an expression for the three roots, but now their size order is clear. Let $M$ be the average of $a$, $b$ and $c$, and let $P$ and $Q$ be the quadratic and geometric means of the quantities $a+b-2c$, $a-2b+c$ and $-2a+b+c$. That is:

$$M=\frac{a+b+c}3,$$ $$P=\sqrt{\frac{(a+b-2c)^2+(a-2b+c)^2+(-2a+b+c)^2}3},$$ $$Q=\sqrt[3]{(a+b-2c)(a-2b+c)(-2a+b+c)}.$$

Then we have

$$\max(a,b,c)=\frac{\sqrt 2}3P\cos\left(\frac 13\arccos\left(\sqrt 2\left(\frac QP\right)^3\right)\right)+M,$$

$$\mathrm{median}(a,b,c)=\frac{\sqrt 2}3P\cos\left(\frac 13\arccos\left(\sqrt 2\left(\frac QP\right)^3\right)+\frac{2\pi}3\right)+M,$$

$$\min(a,b,c)=\frac{\sqrt 2}3P\cos\left(\frac 13\arccos\left(\sqrt 2\left(\frac QP\right)^3\right)+\frac{4\pi}3\right)+M.$$

#### @Oscar Cunningham 2017-02-17 17:52:32

This also answers an Olympiad style inequality: "If $x+y+z=0$, $P=\sqrt{(x^2+y^2+z^2)/3}$ and $Q=\sqrt[3]{xyz}$ show that $\left|\frac QP\right|\leq\sqrt[6]2$."

#### @robjohn 2011-12-08 20:01:15

First, define $$\Delta=|a-b|+|b-c|+|c-a|\newcommand{\Mu}{\mathrm{M}}\tag{1}$$ It is somewhat intuitive that $$\frac{\Delta}{2}=\max(a,b,c)-\min(a,b,c)\tag{2}$$ For example, if $a\ge b\ge c$ then $|a-b|+|b-c|+|c-a|=2a-2c$.

Next, define $$\Sigma=a\left(1-\frac{|b-c|}{\Delta}\right)+b\left(1-\frac{|c-a|}{\Delta}\right)+c\left(1-\frac{|a-b|}{\Delta}\right)\tag{3}$$ Again, if $a\ge b\ge c$, then \begin{align} \Sigma &=a\left(\frac{2a-b-c}{2(a-c)}\right)+b\left(\frac{a-c}{2(a-c)}\right)+c\left(\frac{a+b-2c}{2(a-c)}\right)\\ &=a+c \end{align} Thus, considering the symmetry of $(3)$, it is evident that $$\Sigma=\max(a,b,c)+\min(a,b,c)\tag{4}$$ Combining $(2)$ and $(4)$ yields $$\max(a,b,c)=\frac{\Sigma}{2}+\frac{\Delta}{4}\tag{5}$$ and $$\min(a,b,c)=\frac{\Sigma}{2}-\frac{\Delta}{4}\tag{6}$$ At least $(5)$ and $(6)$ are symmetric in $a$, $b$, and $c$ since $(1)$ and $(3)$ are. That is, \begin{align} \max(a,b,c) &=\frac{a}{2}\left(\frac{|c-a|+|a-b|}{|a-b|+|b-c|+|c-a|}\right)\\ &+\frac{b}{2}\left(\frac{|a-b|+|b-c|}{|a-b|+|b-c|+|c-a|}\right)\\ &+\frac{c}{2}\left(\frac{|b-c|+|c-a|}{|a-b|+|b-c|+|c-a|}\right)\\ &+\frac{|a-b|+|b-c|+|c-a|}{4}\tag{7} \end{align} and \begin{align} \min(a,b,c) &=\frac{a}{2}\left(\frac{|c-a|+|a-b|}{|a-b|+|b-c|+|c-a|}\right)\\ &+\frac{b}{2}\left(\frac{|a-b|+|b-c|}{|a-b|+|b-c|+|c-a|}\right)\\ &+\frac{c}{2}\left(\frac{|b-c|+|c-a|}{|a-b|+|b-c|+|c-a|}\right)\\ &-\frac{|a-b|+|b-c|+|c-a|}{4}\tag{8} \end{align}

#### @Thomas Produit 2014-01-29 19:11:40

Is it possible to generalize this idea to rewrite $\min(a_1, ... a_n)$ ? Although it would be surely awful as equation I'm interested ;-)

#### @Oscar Cunningham 2014-06-30 16:36:26

If $a$, $b$ and $c$ are vectors for the vertices of a triangle then $\Sigma/2$ is its Spieker Center and $\Delta/4$ is its semiperimeter. Is there any significance to the circle about $\Sigma/2$ with radius $\Delta/4$?

#### @Oscar Cunningham 2014-06-30 17:02:57

GeoGebra suggests that this circle doesn't (as one might hope) always go through two vertices of the triangle. When the vertices are not collinear it goes through none of the points, instead going around the triangle on the outside of all the vertices.

#### @Oscar Cunningham 2017-11-17 14:00:45

a) The value $\Delta/4$ is actually half the semiperimeter. b) That circle is very close to being the Excircles Radical Circle

#### @Christian Blatter 2011-07-26 10:57:38

Here is a hint why there is no simple such formula:

In the case of two variables $a_i$ they are the zeros of the polynomial $$p(x):=(x-a_1)(x-a_2)=x^2 -(a_1+a_2)x + a_1 a_2\ .$$ Therefore by the formula for quadratic equations we have $$\min(a_1, a_2)\ =\ {a_1+a_2-\sqrt{(a_1+a_2)^2 -4a_1 a_2}\over 2} ={a_1+a_2\over2}-{|a_1-a_2|\over 2}\ .$$

Using the same idea with three variables $a_i$ we would have to look at the third degree polynomial $$q(x):=(x-a_1)(x-a_2)(x-a_3)$$ which has three real roots. Therefore we are in the "casus irreducibilis" of Cardano's formula, which can only be solved via complex numbers. Even if you would write everything out, you couldn't decide "by inspection" which root is the smallest.

#### @The Chaz 2.0 2013-05-29 17:30:55

That's good stuff.

#### @Hans Lundmark 2010-12-06 16:54:22

If you want a symmetric expression, you can take $\frac13 (\min(a,\min(b,c))+\min(b,\min(a,c))+\min(c,\min(a,b)))$. But if you rewrite it using that absolute-value trick, I still don't think it gives something that's "intuitively the minimum", I'm afraid...

#### @Qiaochu Yuan 2010-12-06 16:46:41

This probably isn't what you were thinking of, but if $a_1, ... a_n$ are non-negative, then

$$\min(a_1, ... a_n) = \lim_{k \to -\infty} \sqrt[k]{a_1^k + ... + a_n^k}$$

whereas

$$\max(a_1, ... a_n) = \lim_{k \to \infty} \sqrt[k]{a_1^k + ... + a_n^k}.$$

There are several applications of these identities (at least the second one), e.g. to functional analysis. They are also related to the way in which tropical arithmetic arises as a "limit" of ordinary arithmetic.

### [SOLVED] Finding the minimum value of a function.

• 2015-07-07 18:36:33
• Nikhil
• 125 View
• 1 Score
• Tags:   functions

### [SOLVED] Curious formula for minimum?

• 2015-05-18 20:23:02
• Antinous
• 136 View
• 4 Score
• Tags:   functions


text:
## Mini-symposium in IPMS 2O21

The Tenth International Conference “Inverse Problems: Modeling and Simulation” (IPMS2021) has now been postponed to May 22 –28, 2022. The conference takes place in Malta.

We are happy to announce that we are organizing a mini-symposium entitled “Mathematical Methods in Tomography Across the Scales” related to our SFB. The speakers are members and associated members of the SFB.

## Reconstruction Methods for Inverse Problems (19w5092)

at Banff, Alberta from Sunday, June 23 to Friday June 28, 2019

## Organizers

• Elena Beretta (NYU Abu Dhabi & Politecnico di Milano)
• Uri Ascher (University of British Columbia)
• Otmar Scherzer (University of Vienna)
• Luminita Vese (University of California, Los Angeles)

## Description

Inverse problems require to determine the cause from a set of indirect observations. Such problems appear in medical imaging, non destructive testing of materials, computerized tomography, source reconstructions in acoustics, computer vision and geophysics, to mention but a few. The 21st century is the golden age of computer imaging: Measurement devices have become enormously powerful and huge amounts of data are recorded at every eye glimpse. Moreover, computer technology has developed to such a high degree of efficiency that the evaluation of such an enormous amount of data has become possible *if* adequate mathematical and computational tools are used.

Recently, the community has been exposed to fundamentally new mathematical models (such as learning), which stimulated exciting theoretical developments and new computational algorithms for solving complicated large scale inverse problems. This workshop will survey modern and identify new mathematical and computational developments for tackling such problems.

more details

## The first SFB meeting was a success!

In the Obergurgl University Center, the initial SFB “Tomography across the scales” meeting took place, on March, 18-20.  It was attended by the Principal investigators, members, external associated researchers and candidates. The participants had the opportunity, for the first time, to meet all members and interact with people from different disciplines. The talks were interesting covering all “scales”, from mathematics and physics to medical- and bio-sciences.

Everyone is looking forward to the next meeting at the end of the year!

## Workshop “Inverse Problems in the Alps II”

Then, on March, 21-23, followed the more mathematical oriented workshop “Inverse Problems in the Alps II” co-organized by the SFB, the RICAM and the Doctoral Program “Computational Mathematics”. More than 30 participants enjoyed the talks in this wonderful location. This workshop celebrated also the 60th birthday ($$\varepsilon$$ far) of Elena Beretta,  Politecnico di Milano, Italy!


text:
# Cross-references linking to wrong equations using hyperref

I have two macros I've defined that I use to set the context in which equations are numbered in my document. One that establishes something I call a 'block' in which equations are numbered, by resetting the equation counter to 0 and setting the equation grouping to a string provided as an argument,

\newcommand{\setgroupingblock}[1]{\gdef\equationgrouping{#1:}\phantomsection\setcounter{equation}{0}}

and another that sets the section (using \setcounter{section}) and then calls my first, block-setting macro:

\newcommand{\setgroupingsection}[1]{\setcounter{section}{#1}\setgroupingblock{#1}}

I use these for a variety of reasons, to gain section-independent control over numbering of various elements (not just equations), and they use mathtools to label all of my equations as expected. However hyperref cross-reference links to these equations do not work correctly. Cross-references seem to behave as if they are numbered within sections only, ignoring 'blocks'.

I've stared at my code for a while now, but am stumped and would appreciate help sorting out what I'm doing wrong.

\documentclass{article}

\usepackage{mathtools}
\usepackage{hyperref}

% Manually set the section; set a new 'block'
\newcommand{\setgroupingsection}[1]{\setcounter{section}{#1}\setgroupingblock{#1}}
% Set a 'block' for numbering equations, overriding any section, and resetting the equation counter
\newcommand{\setgroupingblock}[1]{\gdef\equationgrouping{#1:}\phantomsection\setcounter{equation}{0}}

% Equation numbering and referencing
\renewcommand{\theequation}{\equationgrouping\arabic{equation}}
\gdef\equationgrouping{}

\begin{document}

\setgroupingsection{10} Section \textbf{10} begins here. Subsequent equations are numbered within this section, until another section is started, or a block is started.

$$q(x)=f(x)\cdot g(x)\label{eq:X}$$
$$a(i,j)=a(i,q)\cdot a(p,j)\label{eq:Y}$$

\pagebreak{}%To clearly demonstrate hyperlinking jumps in PDF

\setgroupingblock{A} Block \textbf{A} begins here. Subsequent equations are numbered within this block, until another block is started, or another section is started.

$$f(x)=x^{2}+3x\label{eq:Example1}$$
$$g(x)=\sin(\gamma^{2})\label{eq:Example2}$$
$$f(x)=\cos(\delta^{2})\label{eq:Example3}$$

\pagebreak{}%To clearly demonstrate hyperlinking jumps in PDF

\setgroupingsection{20} Section \textbf{20} begins here.

$$a(i,j)=a(i,q)\cdot a(p,j)\label{eq:Z}$$

\pagebreak{}%To clearly demonstrate hyperlinking jumps in PDF

\setgroupingblock{B} Block \textbf{B} begins here.

$$f(x)=x^{2}+3x\label{eq:Example4}$$

\pagebreak{}%To clearly demonstrate hyperlinking jumps in PDF

Numbering of equations works as desired, but hyperlinks in cross-references do not, Cross-references seem to behave as if they are numbered within sections only, ignoring blocks. For example the links to the first and second equations in block \textbf{A},\eqref{eq:Example1} and \eqref{eq:Example2} go to the corresponding equations in the most recent section before block \textbf{A}, \eqref{eq:X} and \eqref{eq:Y}; though the reference to \eqref{eq:Example3} works correctly (there is no corresponding equation in section \textbf{10} to "confuse" it with. Similarly \eqref{eq:Example4} links to \eqref{eq:Z}.

\end{document}

• If it's relevant, I get the same error described here when I compile; three times for each of the mis-linked equations. – orome Jul 30 '12 at 0:55

## 2 Answers

Package hyperref prefers \theH<counter> over \the<counter> to get unique destination names, see my answer for Change nameddest default name.

Since your equations can be numbered within section or grouping blocks, both numbers/strings can be added to \theHequation, e.g.:

\renewcommand{\theHequation}{\theHsection.\equationgrouping\arabic{equation}}

• Just to be sure I'm doing this right (since it seems to work): I should leave everything else unchanged, but add the line above, correct? – orome Jul 30 '12 at 4:08

This elaborates on Heiko's answer.

hyperref requires a unique anchor (referred to by \Hy@AnchorName within hyperref.sty). Viewing your example without

\renewcommand{\theHequation}{\theHsection.\equationgrouping\arabic{equation}}

reveals the following in your .aux file:

%...
\newlabel{eq:X}{{10:1}{1}{\relax }{equation.10.1}{}}
\newlabel{eq:Y}{{10:2}{1}{\relax }{equation.10.2}{}}
\newlabel{eq:Example1}{{A:1}{2}{\relax }{equation.10.1}{}}
\newlabel{eq:Example2}{{A:2}{2}{\relax }{equation.10.2}{}}
\newlabel{eq:Example3}{{A:3}{2}{\relax }{equation.10.3}{}}
\newlabel{eq:Z}{{20:1}{3}{\relax }{equation.20.1}{}}
\newlabel{eq:Example4}{{B:1}{4}{\relax }{equation.20.1}{}}

Note the fourth argument #4 inside the second argument of \newlabel{..}{{#1}{#2}{#3}{#4}{#5}}. This anchor, or destination, has to be unique, while yours is clearly not, causing the incorrect hyper jump.

Adding the information of both section and group makes for a unique anchor/destination with each label:

\renewcommand{\theHequation}{\theHsection.\equationgrouping\arabic{equation}}

This is the renewed .aux:

%...
\newlabel{eq:X}{{10:1}{1}{\relax }{equation.10.10:1}{}}
\newlabel{eq:Y}{{10:2}{1}{\relax }{equation.10.10:2}{}}
\newlabel{eq:Example1}{{A:1}{2}{\relax }{equation.10.A:1}{}}
\newlabel{eq:Example2}{{A:2}{2}{\relax }{equation.10.A:2}{}}
\newlabel{eq:Example3}{{A:3}{2}{\relax }{equation.10.A:3}{}}
\newlabel{eq:Z}{{20:1}{3}{\relax }{equation.20.20:1}{}}
\newlabel{eq:Example4}{{B:1}{4}{\relax }{equation.20.B:1}{}}

showing a clearly unique anchor/destination.

• LaTeX remembers the reference value in macro \@currentlabel that is then used, when a \label is written to the .aux file (example: 10:1). Package hyperref adds \@currentHref for the anchor name (example: equation.10.10:1). Forget about \Hy@AnchorName, it is only a temporary internal command inside \hyperdef, it could also be named \Hy@temp instead. – Heiko Oberdiek Jul 30 '12 at 9:54


text:
Tutorials

# Kriging geographical data

%matplotlib widget
import matplotlib.pyplot as plt
plt.ioff()
# turn of warnings
import warnings
warnings.filterwarnings('ignore')

In this example we are going to interpolate actual temperature data from the German weather service DWD.

Data is retrieved utilizing the beautiful package wetterdienst, which serves as an API for the DWD data.

For better visualization, we also download a simple shapefile of the German borderline with cartopy.

In order to keep the number of dependecies low, the calls of both functions shown beneath are commented out.

import numpy as np
import gstools as gs
def get_borders_germany():
import geopandas as gp  # 0.8.1

df = gp.read_file(shpfile)  # only use the simplest polygon
np.savetxt("de_borders.txt", list(poly.exterior.coords))

def get_dwd_temperature(date="2020-06-09 12:00:00"):
"""Get air temperature from german weather stations from 9.6.20 12:00."""
from wetterdienst.dwd import observations as obs  # version 0.13.0

settings = dict(
resolution=obs.DWDObservationResolution.HOURLY,
start_date=date,
end_date=date,
)
sites = obs.DWDObservationStations(
parameter_set=obs.DWDObservationParameterSet.TEMPERATURE_AIR,
period=obs.DWDObservationPeriod.RECENT,
**settings,
)
ids, lat, lon = sites.all().loc[:, ["STATION_ID", "LAT", "LON"]].values.T
observations = obs.DWDObservationData(
station_ids=ids,
parameters=obs.DWDObservationParameter.HOURLY.TEMPERATURE_AIR_200,
periods=obs.DWDObservationPeriod.RECENT,
**settings,
)
temp = observations.all().VALUE.values
sel = np.isfinite(temp)
# select only valid temperature data
ids, lat, lon, temp = ids.astype(float)[sel], lat[sel], lon[sel], temp[sel]
np.savetxt("temp_obs.txt", np.array([ids, lat, lon, temp]).T, header=head)

If you want to download the data again, uncomment the two following lines. We will simply load the resulting files to gain the border polygon and the observed temperature along with the station locations given by lat-lon values.

# get_borders_germany()
# get_dwd_temperature(date="2020-06-09 12:00:00")

ids, lat, lon, temp = np.loadtxt("temp_obs.txt").T

First we will estimate the variogram of our temperature data. As the maximal bin distance we choose 8 degrees, which corresponds to a chordal length of about 900 km.

bins = gs.standard_bins((lat, lon), max_dist=np.deg2rad(8), latlon=True)

bin_c, vario = gs.vario_estimate((lat, lon), temp, bins, latlon=True)
print(np.rad2deg(bins))

Now we can use this estimated variogram to fit a model to it. Here we will use a Spherical model. We select the latlon option to use the Yadrenko variant of the model to gain a valid model for lat-lon coordinates and we rescale it to the earth-radius. Otherwise the length scale would be given in radians representing the great-circle distance.

We deselect the nugget from fitting and plot the result afterwards.

## #Note

You need to plot the Yadrenko variogram, since the standard variogram still holds the ordinary routine that is not respecting the great-circle distance.

model = gs.Spherical(latlon=True, rescale=gs.EARTH_RADIUS)
model.fit_variogram(bin_c, vario, nugget=False)
ax.scatter(bin_c, vario)
print(model)

As we see, we have a rather large correlation length of 600 km.

Now we want to interpolate the data using Universal kriging. In order to tinker around with the data, we will use a north-south drift by assuming a linear correlation with the latitude. This can be done as follows:

def north_south_drift(lat, lon):
return lat

uk = gs.krige.Universal(
model=model,
cond_pos=(lat, lon),
cond_val=temp,
drift_functions=north_south_drift,
)

Now we generate the kriging field, by defining a lat-lon grid that covers the whole of Germany. The Krige class provides the option to only krige the mean field, so one can have a glimpse at the estimated drift.

# grid
g_lat = np.arange(47, 56.1, 0.1)
g_lon = np.arange(5, 16.1, 0.1)
# set pos
uk.set_pos((g_lat, g_lon), mesh_type="structured")
# get field and estimated mean drift
field = uk(return_var=False, store="temp_field")
mean = uk(only_mean=True, store="mean_field")

And that's it. Now let's have a look at the generated field and the input data along with the estimated mean:

levels = np.linspace(5, 23, 64)
fig, ax = plt.subplots(1, 3, figsize=[10, 5], sharey=True)
sca = ax[0].scatter(lon, lat, c=temp, vmin=5, vmax=23, cmap="coolwarm")
co1 = ax[1].contourf(g_lon, g_lat, uk["temp_field"], levels, cmap="coolwarm")
co2 = ax[2].contourf(g_lon, g_lat, uk["mean_field"], levels, cmap="coolwarm")

[ax[i].plot(border[:, 0], border[:, 1], color="k") for i in range(3)]
[ax[i].set_xlim([5, 16]) for i in range(3)]
[ax[i].set_xlabel("Lon in deg") for i in range(3)]
ax[0].set_ylabel("Lat in deg")

ax[0].set_title("Temperature observations at 2m\nfrom DWD (2020-06-09 12:00)")
ax[1].set_title("Interpolated temperature\nwith North-South drift")
ax[2].set_title("Estimated mean drift\nfrom Universal Kriging")

fmt = dict(orientation="horizontal", shrink=0.5, fraction=0.1, pad=0.2)
fig.colorbar(co2, ax=ax, **fmt).set_label("T in [°C]")
fig.show()

To get a better impression of the estimated north-south drift, we'll take a look at a cross-section at a longitude of 10 degree:

fig, ax = plt.subplots()
ax.plot(g_lat, uk["temp_field"][:, 50], label="Interpolated temperature")
ax.plot(g_lat, uk["mean_field"][:, 50], label="North-South mean drift")
ax.set_xlabel("Lat in deg")
ax.set_ylabel("T in [°C]")
ax.set_title("North-South cross-section at 10°")
ax.legend()
fig.show()

Interpretion of the results is now up to you! ;-)