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# The gauge factor is defined as:

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The gauge factor is defined as:
1. $\frac{{\Delta L/L}}{{\Delta R/R}}$
2. $\frac{{\Delta R/R}}{{\Delta L/L}}$
3. $\frac{{\Delta R/R}}{{\Delta D/D}}$
4. $\frac{{\Delta R/R}}{{\Delta P/P}}$

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Correct Answer - Option 2 : $\frac{{\Delta R/R}}{{\Delta L/L}}$

Gauge Factor:

The gauge factor is defined as the ratio of per unit change in resistance to per unit change in length. It is a measure of the sensitivity of the gauge.

Gauge factor, ${G_f} = \frac{{{\rm{\Delta }}R/R}}{{{\rm{\Delta }}L/L}}$

$\frac{{{\rm{\Delta }}R}}{R} = {G_f}\frac{{{\rm{\Delta }}L}}{L} = {G_f}\varepsilon$

Where ε = strain = $\frac{{\Delta L}}{{L}}$

The gauge factor can be written as:

= Resistance change due to change of length + Resistance change due to change in the area + Resistance change due to the piezoresistive effect

${G_f} = \frac{{{\rm{\Delta }}R/R}}{{{\rm{\Delta }}L/L}} = 1 + 2v + \frac{{{\rm{\Delta }}\rho /\rho }}{\varepsilon }$

If the change in the value of resistivity of a material when strained is neglected, the gauge factor is:

${G_f} = 1 + 2v$

The above equation is valid only when the Piezoresistive effect that changes in resistivity due to strain is almost neglected.

For wire-wound strain gauges, Piezoresistive effect is almost negligible.


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# Elo rating system

Arpad Elo, the inventor of the Elo rating system

The Elo rating system is a method for calculating the relative skill levels of players in such competitor-versus-competitor games as chess. It is named after its creator Arpad Elo, a Hungarian-born American physics professor.

The Elo system was invented as an improved chess rating system and is also used in many other games. It is also used as a rating system for multiplayer competition in a number of video games,[1] and has been adapted to team sports including association football, American college football, basketball, Major League Baseball, and eSports.

The difference in the ratings between two players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each other are expected to score an equal number of wins. A player whose rating is 100 points greater than his or her opponent's is expected to score 64%; if the difference is 200 points, then the expected score for the stronger player is 76%.[2]

A number represents a player's Elo rating and increases or decreases based upon the outcome of games between rated players. After every game, the winning player takes points from the losing one. The difference between the ratings of the winner and loser determines the total number of points gained or lost after a game. In a series of games between a high-rated player and a low-rated player, the high-rated player is expected to score more wins. If the high-rated player wins, then only a few rating points will be taken from the low-rated player whereas if the lower rated player scores an upset win, then many rating points will be transferred. The lower rated player will also gain a few points from the higher rated player in the event of a draw. The rating system thus is self-correcting. A player whose rating is too low should, in the long run, do better than the rating system predicts and thereby gain rating points until the rating reflects his or her true playing strength.

## History

Arpad Elo was a master-level chess player and an active participant in the United States Chess Federation (USCF) from its founding in 1939.[3] The USCF used a numerical ratings system, devised by Kenneth Harkness, to allow members to track their individual progress in terms other than tournament wins and losses. The Harkness system was reasonably fair, but in some circumstances gave rise to ratings which many observers considered inaccurate. On behalf of the USCF, Elo devised a new system with a more sound statistical basis.

Elo's system replaced earlier systems of competitive rewards with a system based on statistical estimation. Rating systems for many sports award points in accordance with subjective evaluations of the 'greatness' of certain achievements. For example, winning an important golf tournament might be worth an arbitrarily chosen five times as many points as winning a lesser tournament.

A statistical endeavor, by contrast, uses a model that relates the game results to underlying variables representing the ability of each player.

Elo's central assumption was that the chess performance of each player in each game is a normally distributed random variable. Although a player might perform significantly better or worse from one game to the next, Elo assumed that the mean value of the performances of any given player changes only slowly over time. Elo thought of a player's true skill as the mean of that player's performance random variable.

A further assumption is necessary, because chess performance in the above sense is still not measurable. One cannot look at a sequence of moves and say, "That performance is 2039." Performance can only be inferred from wins, draws and losses. Therefore, if a player wins a game, he is assumed to have performed at a higher level than his opponent for that game. Conversely if he loses, he is assumed to have performed at a lower level. If the game is a draw, the two players are assumed to have performed at nearly the same level.

Elo did not specify exactly how close two performances ought to be to result in a draw as opposed to a win or loss. And while he thought it is likely that each player might have a different standard deviation to his performance, he made a simplifying assumption to the contrary.

To simplify computation even further, Elo proposed a straightforward method of estimating the variables in his model (i.e. the true skill of each player). One could calculate relatively easily, from tables, how many games a player would be expected to win based on a comparison of his rating to the ratings of his opponents. If a player won more games than expected, his rating would be adjusted upward, while if he won fewer than expected his rating would be adjusted downward. Moreover, that adjustment was to be in exact linear proportion to the number of wins by which the player had exceeded or fallen short of his expected number.

From a modern perspective, Elo's simplifying assumptions are not necessary because computing power is inexpensive and widely available. Moreover, even within the simplified model, more efficient estimation techniques are well known. Several people, most notably Mark Glickman, have proposed using more sophisticated statistical machinery to estimate the same variables. On the other hand, the computational simplicity of the Elo system has proven to be one of its greatest assets. With the aid of a pocket calculator, an informed chess competitor can calculate to within one point what his next officially published rating will be, which helps promote a perception that the ratings are fair.

### Implementing Elo's scheme

The USCF implemented Elo's suggestions in 1960,[4] and the system quickly gained recognition as being both more fair and accurate than the Harkness rating system. Elo's system was adopted by the World Chess Federation (FIDE) in 1970. Elo described his work in some detail in the book The Rating of Chessplayers, Past and Present, published in 1978.

Subsequent statistical tests have suggested that chess performance is almost certainly not distributed as a normal distribution, as weaker players have significantly (but not highly significantly) greater winning chances than Elo's model predicts.[citation needed] Therefore, the USCF and some chess sites use a formula based on the logistic distribution. Significant statistical anomalies have also been found when using the logistic distribution in chess.[5] FIDE continues to use the normal distribution. The normal and logistic distribution points are, in a way, arbitrary points in a spectrum of distributions which would work well. In practice, both of these distributions work very well for a number of different games.

## Different ratings systems

The phrase "Elo rating" is often used to mean a player's chess rating as calculated by FIDE. However, this usage is confusing and misleading, because Elo's general ideas have been adopted by many organizations, including the USCF (before FIDE), the Internet Chess Club (ICC), Free Internet Chess Server (FICS), Yahoo! Games, and the now-defunct Professional Chess Association (PCA). Each organization has a unique implementation, and none of them follows Elo's original suggestions precisely. It would be more accurate to refer to all of the above ratings as Elo ratings, and none of them as the Elo rating.

Instead one may refer to the organization granting the rating, e.g. "As of August 2002, Gregory Kaidanov had a FIDE rating of 2638 and a USCF rating of 2742." It should be noted that the Elo ratings of these various organizations are not always directly comparable. For example, someone with a FIDE rating of 2500 will generally have a USCF rating near 2600 and an ICC rating in the range of 2500 to 3100. On FICS, the command "tell surveybot ratings fide estimate" gives an FIDE rating estimate based on the user's FICS rating.

### FIDE ratings

For top players, the most important rating is their FIDE rating. Since July 2012, FIDE issues a ratings list once every month.

The following analysis of the November 2012 FIDE rating list gives a rough impression of what a given FIDE rating means:

November 2011 marked the first time four players had a rating of 2800 or higher. The highest ever FIDE rating was 2872, which Magnus Carlsen had on the January 2013 list. A list of highest ever rated players is at Comparison of top chess players throughout history.

#### Performance rating

$p$$d_p$
1.00+800
0.99+677
0.9+366
0.8+240
0.7+149
0.6+72
0.50
0.4-72
0.3-149
0.2-240
0.1-366
0.01-677
0.00-800

Performance rating is a hypothetical rating that would result from the games of a single event only. Some chess organizations use the "algorithm of 400" to calculate performance rating. According to this algorithm, performance rating for an event is calculated by taking (1) the rating of each player beaten and adding 400, (2) the rating of each player lost to and subtracting 400, (3) the rating of each player drawn, and (4) summing these figures and dividing by the number of games played.
Example: 2 Wins, 2 Losses
$\displaystyle{\frac{\left(w+400+x+400+y-400+z-400\right)}{4}}$
$\displaystyle{\frac{\left[w+x+y+z+400\left(2\right)-400\left(2\right)\right]}{4}}$
This can be expressed by the following formula:
$\text{Performance rating} = \frac{\text{Total of opponents' ratings } + 400 \times (\text{Wins} - \text{Losses})}{\text{Games}}$
Example: If you beat a player with an Elo rating of 1000,
$\displaystyle \text{Performance rating} = \frac{1000 + 400 \times (1)}{1} = 1400$
If you beat two players with Elo ratings of 1000,
$\displaystyle \text{Performance rating} = \frac{2000 + 400 \times (2)}{2} = 1400$
If you draw,
$\displaystyle \text{Performance rating} = \frac{1000 + 400 \times (0)}{1} = 1000$

This is a simplification, because it doesn't take account of K-factors (this factor is explained further below), but it offers an easy way to get an estimate of PR (performance rating).

FIDE, however, calculates performance rating by means of the formula: Opponents' Rating Average + Rating Difference. Rating Difference $d_p$ is based on a player's tournament percentage score $p$, which is then used as the key in a lookup table where $p$ is simply the number of points scored divided by the number of games played. Note that, in case of a perfect or no score $d_p$ is 800. The full table can be found in the FIDE handbook, B. Permanent Commissions 1.0. Requirements for the titles designated in 0.31, 1.48 online. A simplified version of this table is on the right.

#### FIDE tournament categories

CategoryAverage rating
MinimumMaximum
1425762600
1526012625
1626262650
1726512675
1826762700
1927012725
2027262750
2127512775
2227762800
2328012825

FIDE classifies tournaments into categories according to the average rating of the players. Each category is 25 rating points wide. Category 1 is for an average rating of 2251 to 2275, category 2 is 2276 to 2300, etc. For women's tournaments, the categories are 200 rating points lower, so a Category 1 is an average rating of 2051 to 2075, etc.[6] The highest rated tournaments have been category 22, with an average from 2776 to 2800. The top categories are in the table.

### Live ratings

FIDE updates its ratings list at the beginning of each month. In contrast, the unofficial "Live ratings" calculate the change in players' ratings after every game. These Live ratings are based on the previously published FIDE ratings, so a player's Live rating is intended to correspond to what the FIDE rating would be if FIDE were to issue a new list that day.

Although Live ratings are unofficial, interest arose in Live ratings in August/September 2008 when five different players took the "Live" No. 1 ranking.[7]

The unofficial live ratings were published and maintained by Hans Arild Runde at the Live Rating website until August 2011. Another website www.2700chess.com has been maintained since May 2011 by Artiom Tsepotan. Both websites cover players over 2700 only.

Currently, the No. 1 spot in both the official FIDE rating list and the live rating list is taken by Magnus Carlsen.

### United States Chess Federation ratings

The United States Chess Federation (USCF) uses its own classification of players:[8]

• 2400 and above: Senior Master
• 2200–2399 plus 300 games above 2200: Original Life Master[9]
• 2200–2399: National Master
• 2000–2199: Expert
• 1800–1999: Class A
• 1600–1799: Class B
• 1400–1599: Class C
• 1200–1399: Class D
• 1000–1199: Class E
• 800–999: Class F
• 600–799: Class G
• 400–599: Class H
• 200–399: Class I
• 100–199: Class J

In general, a beginner is around 800, a mid-level player is around 1600, and a professional, around 2400. In 2007, the median rating of all USCF members was 657.[10]

#### The K-factor used by the USCF

The K-factor, in the USCF rating system, can be estimated by dividing 800 by the effective number of games a player's rating is based on (Ne) plus the number of games the player completed in a tournament (m).[11]

$K = 800 / (N_e + m)\,$

#### Rating floors

The USCF maintains an absolute rating floor of 100 for all ratings. Thus, no member can have a rating below 100, no matter their performance at USCF sanctioned events. However, players can have higher individual absolute rating floors, calculated using the following formula:

$AF = \operatorname{min}\{100+4N_W+2N_D+N_R , 150\}$

where $N_W$ is the number of rated games won, $N_D$ is the number of rated games drawn, and $N_R$ is the number of events in which the player completed three or more rated games.

Higher rating floors exist for experienced players who have achieved significant ratings. Such higher rating floors exist, starting at ratings of 1200 in 100 point increments up to 2100 (1200, 1300, 1400, ..., 2100). A player's rating floor is calculated by taking their peak rating, subtracting 200 points, and then rounding down to the nearest rating floor. For example, a player who has reached a peak rating of 1464 would have a rating floor of 1464 − 200 = 1264, which would be rounded down to 1200. Under this scheme, only Class C players and above are capable of having a higher rating floor than their absolute player rating. All other players would have a floor of at most 150.

There are two ways to achieve higher rating floors other than under the standard scheme presented above. If a player has achieved the rating of Original Life Master, his or her rating floor is set at 2200. The achievement of this title is unique in that no other recognized USCF title will result in a new floor. For players with ratings below 2000, winning a cash prize of $2,000 or more raises that player's rating floor to the closest 100-point level that would have disqualified the player for participation in the tournament. For example, if a player won$4,000 in a 1750 and under tournament, the player would now have a rating floor of 1800.

### Ratings of computers

Since 2005–06, human-computer chess matches have demonstrated that chess computers are capable of defeating even the strongest human players (Deep Blue versus Garry Kasparov). However, ratings of computers are difficult to quantify. There have been too few games under tournament conditions to give computers or software engines an accurate rating.[12] Also, for chess engines, the rating is dependent on the machine a program runs on.

For some ratings estimates, see here.

## Theory

### Mathematical details

Performance isn't measured absolutely; it is inferred from wins, losses, and draws against other players. A player's rating depends on the ratings of his or her opponents, and the results scored against them. The difference in rating between two players determines an estimate for the expected score between them. Both the average and the spread of ratings can be arbitrarily chosen. Elo suggested scaling ratings so that a difference of 200 rating points in chess would mean that the stronger player has an expected score (which basically is an expected average score) of approximately 0.75, and the USCF initially aimed for an average club player to have a rating of 1500.

A player's expected score is his probability of winning plus half his probability of drawing. Thus an expected score of 0.75 could represent a 75% chance of winning, 25% chance of losing, and 0% chance of drawing. On the other extreme it could represent a 50% chance of winning, 0% chance of losing, and 50% chance of drawing. The probability of drawing, as opposed to having a decisive result, is not specified in the Elo system. Instead a draw is considered half a win and half a loss.

If Player A has a rating of $R_A$ and Player B a rating of $R_B$, the exact formula (using the logistic curve) for the expected score of Player A is

$E_A = \frac 1 {1 + 10^{(R_B - R_A)/400}}.$

Similarly the expected score for Player B is

$E_B = \frac 1 {1 + 10^{(R_A - R_B)/400}}.$

This could also be expressed by

$E_A = \frac{Q_A}{Q_A + Q_B}$

and

$E_B = \frac{Q_B}{Q_A + Q_B},$

where $Q_A = 10^{R_A/400}$ and $Q_B = 10^{R_B/400}$. Note that in the latter case, the same denominator applies to both expressions. This means that by studying only the numerators, we find out that the expected score for player A is $Q_A/Q_B$ times greater than the expected score for player B. It then follows that for each 400 rating points of advantage over the opponent, the chance of winning is magnified ten times in comparison to the opponent's chance of winning.

Also note that $E_A + E_B = 1$. In practice, since the true strength of each player is unknown, the expected scores are calculated using the player's current ratings.

When a player's actual tournament scores exceed his expected scores, the Elo system takes this as evidence that player's rating is too low, and needs to be adjusted upward. Similarly when a player's actual tournament scores fall short of his expected scores, that player's rating is adjusted downward. Elo's original suggestion, which is still widely used, was a simple linear adjustment proportional to the amount by which a player overperformed or underperformed his expected score. The maximum possible adjustment per game, called the K-factor, was set at K = 16 for masters and K = 32 for weaker players.

Supposing Player A was expected to score $E_A$ points but actually scored $S_A$ points. The formula for updating his rating is

$R_A^\prime = R_A + K(S_A - E_A).$

This update can be performed after each game or each tournament, or after any suitable rating period. An example may help clarify. Suppose Player A has a rating of 1613, and plays in a five-round tournament. He loses to a player rated 1609, draws with a player rated 1477, defeats a player rated 1388, defeats a player rated 1586, and loses to a player rated 1720. His actual score is (0 + 0.5 + 1 + 1 + 0) = 2.5. His expected score, calculated according to the formula above, was (0.506 + 0.686 + 0.785 + 0.539 + 0.351) = 2.867. Therefore his new rating is (1613 + 32×(2.5 − 2.867)) = 1601, assuming that a K-factor of 32 is used.

Note that while two wins, two losses, and one draw may seem like a par score, it is worse than expected for Player A because his opponents were lower rated on average. Therefore he is slightly penalized. If he had scored two wins, one loss, and two draws, for a total score of three points, that would have been slightly better than expected, and his new rating would have been (1613 + 32×(3 − 2.867)) = 1617.

This updating procedure is at the core of the ratings used by FIDE, USCF, Yahoo! Games, the Internet Chess Club (ICC) and the Free Internet Chess Server (FICS). However, each organization has taken a different route to deal with the uncertainty inherent in the ratings, particularly the ratings of newcomers, and to deal with the problem of ratings inflation/deflation. New players are assigned provisional ratings, which are adjusted more drastically than established ratings.

The principles used in these rating systems can be used for rating other competitions—for instance, international football matches.

Elo ratings have also been applied to games without the possibility of draws, and to games in which the result can also have a quantity (small/big margin) in addition to the quality (win/loss). See go rating with Elo for more.

### Mathematical issues

There are three main mathematical concerns relating to the original work of Elo, namely the correct curve, the correct K-factor, and the provisional period crude calculations.[citation needed] A 2012 study lead by a team of Swedish psychologists at Lund University has spawned arguments for the inclusion of a fourth concern, albeit theoretical; intangibles.[13]

#### Most accurate distribution model

The first mathematical concern addressed by the USCF was the use of the normal distribution. They found that this did not accurately represent the actual results achieved, particularly by the lower rated players. Instead they switched to a logistic distribution model, which the USCF found provided a better fit for the actual results achieved. FIDE still uses the normal distribution as the basis for rating calculations as suggested by Elo himself.[14]

#### Most accurate K-factor

The second major concern is the correct "K-factor" used. The chess statistician Jeff Sonas believes that the original K=10 value (for players rated above 2400) is inaccurate in Elo's work. If the K-factor coefficient is set too large, there will be too much sensitivity to just a few, recent events, in terms of a large number of points exchanged in each game. Too low a K-value, and the sensitivity will be minimal, and the system will not respond quickly enough to changes in a player's actual level of performance.

Elo's original K-factor estimation was made without the benefit of huge databases and statistical evidence. Sonas indicates that a K-factor of 24 (for players rated above 2400) may be more accurate both as a predictive tool of future performance, and also more sensitive to performance.[15]

Certain Internet chess sites seem to avoid a three-level K-factor staggering based on rating range. For example the ICC seems to adopt a global K=32 except when playing against provisionally rated players. The USCF (which makes use of a logistic distribution as opposed to a normal distribution) has staggered the K-factor according to three main rating ranges of:

• Players below 2100: K-factor of 32 used
• Players between 2100 and 2400: K-factor of 24 used
• Players above 2400: K-factor of 16 used.

FIDE uses the following ranges:[16]

• K = 30 (was 25), for a player new to the rating list until the completion of events with a total of 30 games.[17]
• K = 15, for players with a rating always under 2400.
• K = 10, for players with any published rating of at least 2400 and at least 30 games played in previous events. Thereafter it remains permanently at 10.

The gradation of the K-factor reduces ratings changes at the top end of the rating spectrum, reducing the possibility for rapid ratings inflation or deflation for those with a low K factor. This might in theory apply equally to an online chess site or over-the-board players, since it is more difficult for players to get much higher ratings when their K-factor is reduced. When playing online, it may simply be the selection of highly-rated opponents that enables 2800+ players to further increase their rating,[18] since a grandmaster on the ICC playing site can play a string of different opponents who are all rated over 3100. In over-the-board events, it would only be in very high level all-play-all events that a player would be able to engage that number of 2700+ opponents, while in a normal open Swiss-paired chess tournament, frequently there would be many opponents rated less than 2500, reducing the ratings gains possible from a single contest.

## Practical issues

### Game activity versus protecting one's rating

In some cases the rating system can discourage game activity for players who wish to protect their rating.[19] In order to discourage players from sitting on a high rating, a recent proposal by British Grandmaster John Nunn for choosing qualifiers to the chess world championship included an activity bonus, to be combined with the rating.[20]

Beyond the chess world, concerns over players avoiding competitive play to protect their ratings caused Wizards of the Coast to abandon the Elo system for Magic: the Gathering tournaments in favour of a system of their own devising called "Planeswalker Points".[21][22]

### Selective pairing

A more subtle issue is related to pairing. When players can choose their own opponents, they can choose opponents with minimal risk of losing, and maximum reward for winning. Such a luxury of being able to hand-pick your opponents is not present in Over-the-Board Elo type calculations, and therefore this may account strongly for the ratings on the ICC using Elo which are well over 2800.

Particular examples of 2800+ rated players choosing opponents with minimal risk and maximum possibility of rating gain include: choosing computers that they know they can beat with a certain strategy; choosing opponents that they think are overrated; or avoiding playing strong players who are rated several hundred points below them, but may hold chess titles such as IM or GM. In the category of choosing overrated opponents, new-entrants to the rating system who have played fewer than 50 games are in theory a convenient target as they may be overrated in their provisional rating. The ICC compensates for this issue by assigning a lower K-factor to the established player if they do win against a new rating entrant. The K-factor is actually a function of the number of rated games played by the new entrant.

Therefore, Elo ratings online still provide a useful mechanism for providing a rating based on the opponent's rating. Its overall credibility, however, needs to be seen in the context of at least the above two major issues described — engine abuse, and selective pairing of opponents.

The ICC has also recently introduced "auto-pairing" ratings which are based on random pairings, but with each win in a row ensuring a statistically much harder opponent who has also won x games in a row. With potentially hundreds of players involved, this creates some of the challenges of a major large Swiss event which is being fiercely contested, with round winners meeting round winners. This approach to pairing certainly maximizes the rating risk of the higher-rated participants, who may face very stiff opposition from players below 3000, for example. This is a separate rating in itself, and is under "1-minute" and "5-minute" rating categories. Maximum ratings achieved over 2500 are exceptionally rare.

### Ratings inflation and deflation

An increase or decrease in the average rating over all players in the rating system is often referred to as rating inflation or rating deflation respectively. For example, if there is inflation, a modern rating of 2500 means less than a historical rating of 2500, while the reverse is true if there is deflation. Using ratings to compare players between different eras is made more difficult when inflation and deflation is present. (See also Comparison of top chess players throughout history.)

It is commonly believed that, at least at the top level, modern ratings are inflated. For instance Nigel Short said in September 2009, "The recent ChessBase article on rating inflation by Jeff Sonas would suggest that my rating in the late 1980s would be approximately equivalent to 2750 in today's much debauched currency".[23] (Short's highest rating in the 1980s was 2665 in July 1988, which was equal third in the world. When he made this comment, 2665 would have ranked him 65th, while 2750 would have ranked him equal 10th. In the September 2012 FIDE rating list, 2665 would have ranked him equal 86th, while 2750 would have ranked him 13th.)

It has been suggested that an overall increase in ratings reflects greater skill. The advent of strong chess computers allows a somewhat objective evaluation of the absolute playing skill of past chess masters, based on their recorded games, but this is also a measure of how computerlike the players' moves are, not merely a measure of how strongly they have played.[24]

The number of people with ratings over 2700 has increased. Around 1979 there was only one active player (Anatoly Karpov) with a rating this high. In 1992 Viswanathan Anand was only the 8th player in chess history to reach the 2700 mark at that point of time.[25] This increased to 15 players by 1994. 33 players had a 2700+ rating in 2009 and 44 as of September 2012. The current benchmark for elite players lies beyond 2800.

One possible cause for this inflation was the rating floor, which for a long time was at 2200, and if a player dropped below this they were stricken from the rating list. As a consequence, players at a skill level just below the floor would only be on the rating list if they were overrated, and this would cause them to feed points into the rating pool.[24] In July 2000 the average rating of the top 100 was 2644. By July 2012 it had increased to 2703.[25]

In a pure Elo system, each game ends in an equal transaction of rating points. If the winner gains N rating points, the loser will drop by N rating points. This prevents points from entering or leaving the system when games are played and rated. However, players tend to enter the system as novices with a low rating and retire from the system as experienced players with a high rating. Therefore, in the long run a system with strictly equal transactions tends to result in rating deflation.[26]

In 1995, the USCF acknowledged that several young scholastic players were improving faster than what the rating system was able to track. As a result, established players with stable ratings started to lose rating points to the young and underrated players. Several of the older established players were frustrated over what they considered an unfair rating decline, and some even quit chess over it.[27]

#### Combatting deflation

Because of the significant difference in timing of when inflation and deflation occur, and in order to combat deflation, most implementations of Elo ratings have a mechanism for injecting points into the system in order to maintain relative ratings over time. FIDE has two inflationary mechanisms. First, performances below a "ratings floor" are not tracked, so a player with true skill below the floor can only be unrated or overrated, never correctly rated. Second, established and higher-rated players have a lower K-factor. New players have a K=30, which drops to K=15 after 30 played games, and to K=10 when the player reaches 2400.[28]

The current system in the United States includes a bonus point scheme which feeds rating points into the system in order to track improving players, and different K-values for different players.[27] Some methods, used in Norway for example, differentiate between juniors and seniors, and use a larger K factor for the young players, even boosting the rating progress by 100% for when they score well above their predicted performance.[29]

Rating floors in the USA work by guaranteeing that a player will never drop below a certain limit. This also combats deflation, but the chairman of the USCF Ratings Committee has been critical of this method because it does not feed the extra points to the improving players. A possible motive for these rating floors is to combat sandbagging, i.e. deliberate lowering of ratings to be eligible for lower rating class sections and prizes.[27]

## Elo ratings beyond chess

American Collegiate Football uses the Elo method as a portion of its Bowl Championship Series rating systems. Jeff Sagarin of USA Today publishes team rankings for most American sports, including Elo system ratings for College Football. The NCAA uses his Elo ratings as part of a formula to determine the annual participants in the College Football National Championship Game.

National Scrabble organizations compute normally-distributed Elo ratings except in the United Kingdom, where a different system is used. The North American Scrabble Players Association has the largest rated population of active members, numbering about 2,000 as of early 2011. Lexulous also uses the Elo system.

The popular First Internet Backgammon Server calculates ratings based on a modified Elo system. New players are assigned a rating of 1500, with the best humans and bots rating over 2000. The same formula has been adopted by several other backgammon sites, such as Play65, DailyGammon, GoldToken and VogClub. VogClub sets a new player's rating at 1600.

The European Go Federation adopted an Elo based rating system initially pioneered by the Czech Go Federation. The Groshin's Score an Elo based game.

In other sports, individuals maintain rankings based on the Elo algorithm. These are usually unofficial, not endorsed by the sport's governing body. The World Football Elo Ratings rank national teams in men's football. In 2006, Elo ratings were adapted for Major League Baseball teams by Nate Silver of Baseball Prospectus.[32] Based on this adaptation, Baseball Prospectus also makes Elo-based Monte Carlo simulations of the odds of whether teams will make the playoffs.[33] Glenn O'Brien publishes rankings using several rating systems, including variants of the Elo rating system.[34] One of the few Elo-based rankings endorsed by a sport's governing body is the FIFA Women's World Rankings, based on a simplified version of the Elo algorithm, which FIFA uses as its official ranking system for national teams in women's football.

Sports-reference.com uses the Elo rating system to rate the best professional players in basketball, football, baseball (batters and pitchers rated separately), and hockey (goalies and skaters rated separately).

The English Korfball Association rated teams based on Elo ratings, to determine handicaps for their cup competition for the 2011/12 season.

Rugbyleagueratings.com uses the Elo rating system to rank international and club rugby league teams.

Various online games use Elo ratings for player-versus-player rankings. Since 2005, Golden Tee Live has rated players based on the Elo system. New players start at 2100, with top players rating over 3000.[35] In Guild Wars, Elo ratings are used to record guild rating gained and lost through Guild versus Guild battles, which are two-team fights. The initial K-value was 30, but was changed to 5 in January 2007, then changed to 15 in July 2009.[36] World of Warcraft formerly used the Elo Rating system when teaming up and comparing Arena players, but now uses a system similar to Microsoft's TrueSkill.[37] The MOBA game League of Legends used an Elo rating system prior to the second season of competitive play.[38] The game Puzzle Pirates uses the Elo rating system to determine the standings in the various puzzles. Roblox introduced the Elo rating in 2010.[39] Counter-Strike: Global Offensive also uses the Elo rating.[40] The browser game Quidditch Manager uses the Elo rating to measure a team's performance.[41] Another recent game to start using the Elo rating system is AirMech, using Elo ratings for 1v1, 2v2, and 3v3 random/team Matchmaking.

Despite questions of the appropriateness of using the Elo system to rate games in which luck is a factor, trading-card game manufacturers often use Elo ratings for their organized play efforts. The DCI (formerly Duelists' Convocation International) used Elo ratings for tournaments of Magic: The Gathering and other Wizards of the Coast games. However, the DCI abandoned this system in 2012 in favour of a new cumulative system of "Planeswalker Points", chiefly because of the above-noted concern that Elo encourages highly rated players to avoid playing to "protect their rating".[21][22] Pokémon USA uses the Elo system to rank its TCG organized play competitors. Prizes for the top players in various regions included holidays and world championships invites until the 2011-2012 season, where awards were based on a system of Championship Points, their rationale being the same as the DCI's for Magic: The Gathering. Similarly, Decipher, Inc. used the Elo system for its ranked games such as Star Trek Customizable Card Game and Star Wars Customizable Card Game.

Moreover, online judge sites are also using Elo rating system or its derivatives. For example, TopCoder is using a modified version based on normal distribution,[42] while Codeforces is using another version based on logistic distribution.[43][44][45]

## Applications apart from gaming

The Elo rating system has been used in a crowdsourcing application for determining best quality photographs. A company called Brilliant Arc has created the "Keep/Toss" game. Two photographs are presented and workers in Amazon's Mechanical Turk simply select which photograph they believe is the better photograph. Three votes are cast for each photograph and an Elo score is determined for all photographs. The photographs with a score above a certain threshold are then selected for further processing. The results have been well received.

Additionally, the Elo rating system has been used in soft biometrics.[46] Soft biometrics concerns the identification of individuals using human descriptions. Comparative descriptions were utilized alongside the Elo rating system to provide robust and discriminative 'relative measurements', permitting accurate identification.

The Elo rating system has also been used in biology for assessing male dominance hierarchies.[47]

## References in the media

The Elo rating system was featured prominently in The Social Network during the algorithm scene where Mark Zuckerberg released Facemash. In the scene Eduardo Saverin writes mathematical formulas for the Elo rating system on Zuckerberg's dorm room window. Behind the scenes, the movie claims, the Elo system is employed to rank coeds by their attractiveness. The equations driving the algorithm are shown briefly, written on the window. The correct equations are

$E_a = \frac{1}{1 + 10^{\tfrac{R_b - R_a}{400}}}$   and   $E_b = \frac{1}{1 + 10^{\tfrac{R_a - R_b}{400}}}$

Ex is the expected probability that X will win the match, i.e. Ea + Eb = 1.

Rx is the rating of X, which changes after every match, according to the formula (Rx )n = (Rx )n-1 + 32 (W - Ex ) where W = 1 if X wins and W = 0 if X loses.

Everyone starts with an Rx = 1400.[48]

## Notes

1. ^ Wood, Ben. "Enemydown uses Elo in its Counterstrike:Source Multilplayer Ladders". TWNA Group.
2. ^ In chess, a win counts 1 point and a draw counts ½ point. As an example, suppose that in an eight-game match a player wins three games, draws three, and loses two. The player gains 4½ points out of 8, a 56.25% score.
3. ^ Redman, Tim. "Remembering Richard, Part II". United States Chess Federation.
4. ^ "About the USCF". United States Chess Federation. Retrieved 2008-11-10.
5. ^
6. ^ FIDE Handbook, Section B.0.0, FIDE web site
7. ^ Anand lost No. 1 to Morozevich (Chessbase, August 24 2008), then regained it, then Carlsen took No. 1 (Chessbase, September 5 2008), then Ivanchuk (Chessbase, September 11 2008), and finally Topalov (Chessbase, September 13 2008)
8. ^
9. ^ USCF Glossary Quote:"a player who competes in over 300 games with a rating over 2200" from The United States Chess Federation
10. ^ USCF Ratings Distribution 2008
11. ^ "Approximating Formulas for the USCF Rating System", United States Chess Federation, Mark Glickman, Department of Mathematics and Statistics at Boston University, 22 February 2001
12. ^ For instance, see the comments at ChessBase.com - Chess News - Adams vs Hydra: Man 0.5 – Machine 5.5
13. ^ Lund University; Social Cognition: Theoretical intangibles of the ELO system study, 2012 http://www.psy.lu.se/o.o.i.s/15545
14. ^ Daniel Ross (2007-12-16). "Arpad Elo and the Elo Rating System". Chessbase article. Retrieved 2012-02-19.
15. ^ A key Sonas article is Jeff Sonas: The Sonas Rating Formula — Better than Elo?
16. ^ "FIDE Online. FIDE Handbook: Chess Rules". Fide.com. 2009-07-01. Retrieved 2012-02-19.
17. ^ "FIDE Online. Changes to Rating Regulations news release". Fide.com. 2011-07-21. Retrieved 2012-02-19.
18. ^ "ICC Help: k-factor". Chessclub.com. 2002-10-18. Retrieved 2012-02-19.
19. ^ A Parent's Guide to Chess Skittles, Don Heisman, Chesscafe.com, August 4, 2002
20. ^ "Chess News - The Nunn Plan for the World Chess Championship". ChessBase.com. Retrieved 2012-02-19.
21. ^ a b "Introducing Planeswalker Points". September 6, 2011. Retrieved September 9, 2011.
22. ^ a b "Getting to the Points". September 9, 2011. Retrieved September 9, 2011.
23. ^ Nigel Short on being number one in Britain again, Chessbase, 4 September 2009
24. ^ a b Sonas, Jeff (July 27, 2009). "Rating Inflation - Its Causes and Possible Cures". ChessBase. Retrieved 2009-08-23.
25. ^ a b "Viswanathan Anand". Chessgames.com.
26. ^ Bergersen, Per A. "ELO-SYSTEMET" (in Norwegian). Norwegian Chess Federation. Retrieved 21 October 2013.
27. ^ a b c A conversation with Mark Glickman [1], Published in Chess Life October 2006 issue
28. ^ "FIDE Handbook 8.0. The working of the FIDE Rating System". FIDE. Retrieved 2009-08-23.
29. ^
30. ^ Lasek, Jan, Zoltán Szlávik, and Sandjai Bhulai. "The predictive power of ranking systems in association football" (2009).
31. ^ Sismanis, Yannis. "How I won the "Chess Ratings: Elo vs the rest of the world" Competition" arXiv preprint arXiv:1012.4571 v1 (2010).
32. ^ Nate Silver, "We Are Elo?" June 28, 2006.[3]
33. ^ "Postseason Odds, ELO version". Baseballprospectus.com. Retrieved 2012-02-19.
34. ^ Glenn O'Brien's ratings page
35. ^ "Golden Tee Fan Player Rating Page". Retrieved 2013-12-31.
36. ^ "Guild ladder". Wiki.guildwars.com. Retrieved 2012-02-19.
37. ^ "World of Warcraft Europe -> The Arena". Wow-europe.com. 2011-12-14. Retrieved 2012-02-19.
38. ^ "Matchmaking | LoL - League of Legends". Na.leagueoflegends.com. 2010-07-06. Retrieved 2012-02-19.
39. ^ "ROBLOX Contests". February 9, 2010. Retrieved 9 February 2010.
40. ^ "An Hour with Counter-Strike: GO". Kotaku.com. 2011-08-25. Retrieved 2012-02-19.
41. ^ "Quidditch Manager - Help and Rules". Quidditch-Manager.com. 2012-08-25. Retrieved 2013-10-20.
42. ^ "Algorithm Competition Rating System". December 23, 2009. Retrieved September 16, 2011.
43. ^ "FAQ: What are the rating and the divisions?". Retrieved September 16, 2011.
44. ^ "Rating Distribution". Retrieved September 16, 2011.
45. ^ "Regarding rating: Part 2". Retrieved September 16, 2011.
46. ^ "Using Comparative Human Descriptions for Soft Biometrics", D.A. Reid and M.S. Nixon, International Joint Conference on Biometrics (IJCB), 2011
47. ^ Pörschmann; et al. (2010). "Male reproductive success and its behavioural correlates in a polygynous mammal, the Galápagos sea lion (Zalophus wollebaeki)". Molecular Ecology 19. doi:10.1111/j.1365-294X.2010.04665.x.
48. ^

format: plain


text:
7 years ago on Introduction. Those receivers use a super-regenerative detector. How can a non-US resident best follow US politics in a balanced well reported manner? ; Boosts 5G, 4G LTE, and 3G service for voice, text, and data. When aiming to roll for a 50/50, does the die size matter? The best solution to either problem is to find a way to boost the incoming signal. Is it because you want to have it work for >100 meters? The best way to do it is to pierce or cut the chip or antenna with something sharp, but in order to do that you have to know exactly where it's located. Install an aerial amplifier to boost the signal further. An RF modulator (or radio frequency modulator) is an electronic device whose input is a baseband signal which is used to modulate a radio frequency source.. RF modulators are used to convert signals from devices such as media players, VCRs and game consoles to a format that can be handled by a device designed to receive a modulated RF input, such as a radio or television receiver. The RF signal propagates between the sending and receiving stations' antennae. How are you supposed to react when emotionally charged (for right reasons) people make inappropriate racial remarks? If you're just plugging in modules, then none of this is available to you, and off topic here anyway. HDMI cable is capable of transmitting better signals than the RF cable. The gain of an antenna system relative to an isotropic radiator at radio frequencies is expressed in dBi, or decibels relative to isotropic. The SolidRF Signal Plus is a two-antenna cell signal booster system is designed for both large and small homes that need improved cell signal reception throughout the house. Let's say you have an AM signal that's 5Vp-p at some frequency. Lastly, do you think that the transmitter's power is near to the legal limits? I can't add a second battery (the quadcopter needs to be very lightweight), but the electronic power supply is protected from the electrical noise of the motors. Then you convert that to the wavelength, and then cut your wire to a quarter of that length. It only takes a minute to sign up. First atomic-powered transportation in science fiction and the details? The problem, however, is that they reduce the strength of the digital signal. 10% coupon applied at checkout Save 10% with coupon. Arduino Stack Exchange is a question and answer site for developers of open-source hardware and software that is compatible with Arduino. Is there a away to transmit sensor signal over RF without Arduino? Amplified antennas boost signal strength to access towers that are a long way off. Provides two zones of coverage in any size home or home office. This could also be an interesting project to attempt a fractal laminated aluminum foil antenna. $32.98$ 32. Decode RF Signals (codes) Open the Arduino IDE serial monitor and start pressing the buttons. Accessibility: When deciding on the type of cable type to settle for, that is, the HDMI cable or RF cable, it … It’s a bidirectional signal booster. Look into LoRa. MRV 12 dbi LPDA 600~2700 MHz HIGH GAIN Outdoor Antenna + 15 Meter LMR 400 Cable Supports All SIM Based Land … Had problems with picture quality in kitchen several years ago and following advice accessed RF out channel on Sky box to change channel. You should be tackling the motor noise first though. Most home routers come with small antennas, whose gain tends to be between 4–5 dBi. I'll always transmit within less than 4-6 meters, and I don't need the transmission to be 100% reliable (even if, say, a packet every two gets lost it would not be a problem... but the other 50% must reach the receiver!). Or do you need an RF amplifier? Please check your device, there must be two TS9 connectors on extreme left and right sides where external antenna can be connected to boost RF signals. It only takes a minute to sign up. I have been using RF modules for different projects that involves using motors. However, all these used to work with the old Sky box, but they now have stopped, or work intermittently with the Sky+ box. The nozzle will give you a more powerful spray than without. ), hackingmajenkoblog.wordpress.com/2016/11/18/…, Podcast 302: Programming in PowerPoint can teach you a few things. Using 433 MHz Tx/Rx without encoders/decoders. Cell phone repeaters are a great way to boost your signal. 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. As shown in Figure 3-2, the signal that feeds the antenna has an amplitude, frequency, and phase. Step 1 Check the coaxial cable connection both on the wall cable jack and on the device to which it is connected. Only, I didn't understand the second point... what is a balanced energy protocol? A Yagi array (TV antenna) will increase gain at the cost of omnidirection. Something directional might help, but if the noise source is physically close to the transmitter then it won't. However, several things can affect signal level output stability. Biphase or Manchester encoding is a really good way to go because a simple protocol allows for net 50% duty cycle of the modulation waveform. Try to turn off or move any of the following items: Cordless phones MAX RF Transmit Power = 2500 mW , Receive Gain = 13 dB; Install it, the communication distance can be 200% or 300%. 7 years ago on Introduction. Amplitude, Frequency, and Phase Are Basic Elements of RF Signal . Is "a special melee attack" an actual game term? I have recently had Sky+ installed. 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. Excelwave's signal booster solutions for private and public networks, keep everywhere connected . Then locate the antenna (it looks like a small silver box). DAS systems, also referred to as cell signal amplifiers or boosters, work with RF signal repeaters to receive a greater volume of signal from nearby cellular towers, thereby magnifying the signals sent and received. Heatmiser Boost v2. Tanks again, @Majenko. I have four TVs all of which have a 'magic eye' to control the Sky+ box. These attributes vary in time in order to represent information.The amplitude indicates the strength of the RF signal. Signal Source RF Signal Level Stability — Once a device’s output RF signal level has been configured and initially measured, one might assume that the signal level will remain at the set value going forward. Why am I seeing unicast packets from a machine on another VLAN? If the noise can't be separated from the RF signal, then you have to deal with this at the protocol level. Get it Thursday, January 14 - Saturday, January 16. In an office environment with lots of florescent lights it was 100% reliable at 30 to 50 meters. What else could I do to increase the transmitter's power? Unfortunately this very unreliable. Please parameterize your concerns by editing this type of detail into your question. Oct 28, 2012. Figure 3-2. The measure for amplitude is generally power, which is analogous to the amount of effort a person needs to exert to ride a bicycle ove… It would also be very advisable to provide some information on just how you are modulating the transmitter signal. ; Sturdy aluminum booster case with integrated heat sink and LED status lights. The transmitter generates a 433 MHz signal during x microseconds if the bit is 1 and nothing (for the same time) if it is 0, where x can be any value (I set it to 1000, but it can be higher (or lower)). I think the problem is the electromagnetical noise: if it is too strong the rf signal is "hidden" in the noise and the receiver can't detect it... (is that correct? Search Forums; Recent Posts; Scroll to continue with content. I took the circuit presented here and soldered it on small perfoboard. That previous post gives a lot of info on my protocol implementation. When aiming to roll for a 50/50, does the die size matter? User Guide, Instructions Manual, and Ordering Information. How to calculate charge analysis for a molecule. You can see that with method the signal has been amplified before it has been allowed drop below the minimum strength or before it come weak. And I have never experienced something like that. Connecting a compact subset by a simple curve, Angular momentum of a purely rotating body about any axis. Best is to use single-core insulated wire (0.6mm is a good choice). Can this equation be solved with whole numbers? RF Signal Boosters. But I just read the post mentioned by Gerben (. Basically, they all come down to trading off bandwidth to get higher signal/noise. Use MathJax to format equations. Antop HD Smart Boost Antenna Amplifier,TV Antenna Amplifier Signal Booster, HDTV Booster with Dual Outputs for 2 TVs, HD Digital VHF UHF FM Amplifier,Compatible with Any Non-Amplified Antennas. There are also various modulation schemes that are good at getting past specific types of noise. Works with the networks of all major U.S. cellular carriers. The you need to improve the rejection of interference by improving the communication protocol as others have suggested. This is how to get better phone signal. Does having no exit record from the UK on my passport risk my visa application for re entering. It is common for folks using these cheap 433MHz transmitter / receiver pairs to think of them as an RF link for a UART data path. Yeah you clearly do not understand anything about RF transmission or antennas. What range and punchiness did you get with your modules? To boost WiFi signal, you need to purchase an antenna with more gain than your current one. That’s why it’s best to put your trust in the experts at Solid Signal. I already have an antenna, but it's like twice the length you wrote here; i'll cut it. If the noise can't be separated from the RF signal, then you have to deal with this at the protocol level. If a president is impeached and removed from power, do they lose all benefits usually afforded to presidents when they leave office? Why does Steven Pinker say that “can’t” + “any” is just as much of a double-negative as “can’t” + “no” is in “I can’t get no/any satisfaction”? If you live within a few miles of the broadcast tower, and the signal path is relatively unobstructed, you may be able to get solid reception using … A coaxial connector that has come loose even slightly can cause a drop in coaxial signal. Can an electron and a proton be artificially or naturally merged to form a neutron? But even though it’s small, it is still a very efficient booster. The gain of an antenna system relative to an isotropic radiator at radio frequencies is expressed in dBi, or decibels relative to isotropic. The quickest and easiest way to destroy RFID chips is also the least practical: 5 seconds in the microwave will melt the chip, but it'll also probably destroy your microwave. a cable from a studio is connected to the RF in (antena in) of your tv set. Please wait, PDF with all RF Signal Meter or Spectrum Analyzer details should load in few seconds if not loaded already. The quadcopter will be quite autonomous, but sometimes I'll need to send some messages to it. I was hoping this was a way to actually boost the power output . I need the rf signal to be as strong as possible, because the receiver is in a noisy environment (surrounded by small and fast-spinning brushed motors without terminal-case capacitor). Can boost the power output signal distribution amp in our loft ; user licensed. Preamplifiers ( aka signal amplifiers, signal boosters click here: https: //goo.gl/kdozTgIs my booster... Balanced well reported manner check the coaxial cable connection both on the receiver reasons! Your wire to that and solder it on the cable on your TV set,... That receiver will probably respond how to boost rf signal interference over a few things a mistake in being too in. The four little brushed motors bit rate in the next minute solutions for private and public networks, everywhere! On your TV set understand that no one antenna or antenna type will deliver TV... A terribly stupid question but since my RF knowledge is fairly limited I 'm asking it.. Mhz transimtter/receiver modules signal form shaper is needed worth nothing, and so will do... Effective way to tell a child not to vandalize things in public places do have their downsides DIY... 'S on-topic for Arduino Stack Exchange Inc ; user contributions licensed under cc by-sa science and., RF Modulator, or decibels relative to an isotropic radiator at frequencies. Line of sight do n't try to overpower it, eliminate it,! 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Using RF modules for different projects that involves using motors noise from the cable one. Important how to boost rf signal design the receiver during a transmission few seconds if not loaded already then locate the has... Should be tackling the motor noise first though give any guidance as to if improvement is.. Long distance of the waveform on/off ( high/low ) times is 50 % keep everywhere connected your current.... Specific item in their inventory simple one-way RF communication system, using a small silver box.. In an office environment with lots of florescent lights it was 100 % at. Self clocking in the PhD interview communications within 10 meters twice the length right though, but sometimes I need... Noise from the cable on your TV ( unsurprisingly ) as a quarter of that length its! Lte, and then wait a few MHz either side of the cable and make them clear, they... Is it because you want to have it work for > 100 meters do to increase the ’! And a proton be artificially or naturally merged to form a neutron wavelength of 299792458/433000000.

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text:
# Correct reference but wrong hyperlinks with tcolorbox and thmtools

After spending several hours tracking down an issue with wrong hyperlinks in my thesis, I managed to cook up the following MWE:

%!TEX program = pdflatex
\documentclass{scrbook}
\usepackage{hyperref,cleveref}
\usepackage{thmtools} % <-- comment this out to fix the issue!
\usepackage{tcolorbox}
\tcbuselibrary{xparse}

\DeclareTColorBox[auto counter,number within=section,crefname={example}{examples}]{example}{ g O{} }{%
IfValueTF={#1}{title={example~\thetcbcounter\ (#1)}}{title=example~\thetcbcounter},#2
}

\begin{document}

\chapter{First chapter}
\begin{example}[label=ex:test]{My title}
Foo.
\end{example}

\chapter{Second Chapter}
\begin{example}[label=ex:test2]{My title}
Foo.
\end{example}

This was \cref{ex:test2}.
The number is right, but the hyperlink leads to \cref{ex:test}.

\end{document}

If thmtools is loaded the hyperlink to the second example is wrong, otherwise everything works as expected. This behavior seems unwanted to me, i.e. the declarations using tcolorbox should not interfere with thmtools. Additionally the fact, that the reference is right but the hyperlink wrong is very odd.

As I am not really dependent on thmtools I have no hard time disabling it, but I am interested in the reason for this behavior and wanted to report this as a possible bug.

## 1 Answer

You should simply try to load hyperref as late as possible (rule of thumb), so the order

\documentclass{scrbook}
\usepackage{thmtools}
\usepackage{hyperref}
\usepackage{cleveref}
\usepackage{tcolorbox}

will not show your problem.

A possible cause could be that thmtools.sty loads thm-autoref.sty which does some hyperlink modifications cleveref or hyperref may conflict with.

• Yes, thmtools modifies the labels – user31729 Dec 30 '17 at 21:17


text:
How do you find the standard form of x^2+y^2+8y+4x-5=0?

This is a circle ${\left(x - \left(- 2\right)\right)}^{2} + {\left(y - \left(- 4\right)\right)}^{2} = {5}^{2}$

Explanation:

From the given ${x}^{2} + {y}^{2} + 8 y + 4 x - 5 = 0$

Perform completing the square method

${x}^{2} + {y}^{2} + 8 y + 4 x - 5 = 0$

by rearranging the terms:

${x}^{2} + 4 x + {y}^{2} + 8 y - 5 = 0$

Calculate the numbers to be added on both sides of the equation

from $4 x$, take the 4, divide this number by 2 then square the result.
result $= 4$

from $8 y$, take the 8, divide this number by 2 then square the result.
result $= 16$

Therefore Add $4$ and $16$ to both sides of the equation and also transpose $- 5$ to the right side.

${x}^{2} + 4 x + 4 + {y}^{2} + 8 y + 16 - 5 = 0 + 4 + 16$

$\left({x}^{2} + 4 x + 4\right) + \left({y}^{2} + 8 y + 16\right) = 5 + 4 + 16$

${\left(x + 2\right)}^{2} + {\left(y + 4\right)}^{2} = 25$

From the standard form:

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

so that

${\left(x - - 2\right)}^{2} + {\left(y - - 4\right)}^{2} = {5}^{2}$ the required standard form.

Have a nice day !!! from the Philippines..


text:
# Energy band gap

I am studying from the Aschroft & Mermim. In the chapter 8 they prove the Bloch theorem and introduce the concept of band. they say that k is a quantum number that charactrize the eigenfunction and can be chosen to be in the first brillouin zone. then they say that for a given k there are discrete eigenvalue which corrispond to the different eigenfunction. So they label them by an index n, the band index. But what does it represent? Then when they try to construc the ground state they say that some band can be partially or totally filled and Others empty. (And thus we can have a band gap.) But how this is possible to have some band filled and Others not.

• In an atom, how is it possible to have some levels filled and others not? – Jon Custer Nov 23 '18 at 20:53

In an infinite crystalline solid, or in a finite solid system with periodic boundary conditions, the hamiltonian commutes with all the translations by Bravais lattice vectors. As a consequence, energy levels can be labeled by an integer (the band index $$n$$) as well as by the three component of a wavevector k, directly connected to the way the wavefunction changes after a Bravais lattice translation (which is the Bloch's theorem content) .
So, n and k uniquely select a single spacial eigenstate of the hamiltonian. Once one has the one-electron states, this information is only saying which are the possible quantum states of one electron. In order to find the ground state of a system of N electrons, one has to decide how to organize the N electrons among all the possible states in such a way to minimize the energy. Taking into account that electrons are fermions, the antisymmetry of the wave-function by any permutation implies that one spacial state cannot be used for more than 2 electrons, one per value of its spin projection along one direction. Thus the ground state corresponds to occupy the lowest $$N/2$$ spatial states.
As a consequence, depending on the shape of the bands as function of k and on the number of electrons, each band (all the states with a fixed value of $$n$$) can be entirely filled, completely empty or partly filled. The presence or not of a gap of energy between the highest occupied level and the lowest empty level directly controls most of the electronic properties of a material.


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Q

# Compute the indicated products. (vi) [3 - 1 3 - 1 0 2] [ 2 - 3 1 0]

Q3.    Compute the indicated products.

(vi) $\begin{bmatrix} 3 & -1 & 3\\ -1 & 0 & 2 \end{bmatrix}\begin{bmatrix} 2 & -3\\ 1 & 0\\ 3 & 1 \end{bmatrix}$

Views

(vi) The given product can be computed as follows

$\begin{bmatrix} 3 & -1 & 3\\ -1 & 0 & 2 \end{bmatrix}\begin{bmatrix} 2 & -3\\ 1 & 0\\ 3 & 1 \end{bmatrix}$

$=\begin{bmatrix} 3 & -1 & 3\\ -1 & 0 & 2 \end{bmatrix}\times \begin{bmatrix} 2 & -3\\ 1 & 0\\ 3 & 1 \end{bmatrix}$

$=\begin{bmatrix} 3 \times 2+(-1)\times 1+3\times 3\, \, \, & 3 \times (-3)+(-1)\times 0+3\times 1 \\ (-1) \times 2+ 0 \times 1+2\times 3 \, \, \, & (-1) \times -3+0\times 0+2\times 1 \end{bmatrix}$

$=\begin{bmatrix} 14 & -6 \\ 4 & 5 \end{bmatrix}$

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Questions


text:
#### Solution for What is .0065 percent of 50.000:

.0065 percent *50.000 =

(.0065:100)*50.000 =

(.0065*50.000):100 =

0.325:100 = 0.00325

Now we have: .0065 percent of 50.000 = 0.00325

Question: What is .0065 percent of 50.000?

Percentage solution with steps:

Step 1: Our output value is 50.000.

Step 2: We represent the unknown value with {x}.

Step 3: From step 1 above,{50.000}={100\%}.

Step 4: Similarly, {x}={.0065\%}.

Step 5: This results in a pair of simple equations:

{50.000}={100\%}(1).

{x}={.0065\%}(2).

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have

\frac{50.000}{x}=\frac{100\%}{.0065\%}

Step 7: Again, the reciprocal of both sides gives

\frac{x}{50.000}=\frac{.0065}{100}

\Rightarrow{x} = {0.00325}

Therefore, {.0065\%} of {50.000} is {0.00325}

#### Solution for What is 50.000 percent of .0065:

50.000 percent *.0065 =

(50.000:100)*.0065 =

(50.000*.0065):100 =

0.325:100 = 0.00325

Now we have: 50.000 percent of .0065 = 0.00325

Question: What is 50.000 percent of .0065?

Percentage solution with steps:

Step 1: Our output value is .0065.

Step 2: We represent the unknown value with {x}.

Step 3: From step 1 above,{.0065}={100\%}.

Step 4: Similarly, {x}={50.000\%}.

Step 5: This results in a pair of simple equations:

{.0065}={100\%}(1).

{x}={50.000\%}(2).

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have

\frac{.0065}{x}=\frac{100\%}{50.000\%}

Step 7: Again, the reciprocal of both sides gives

\frac{x}{.0065}=\frac{50.000}{100}

\Rightarrow{x} = {0.00325}

Therefore, {50.000\%} of {.0065} is {0.00325}

Calculation Samples


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#### Vol. 6, No. 1-4, 2011

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1559-3959 Author Index To Appear Other MSP Journals
Deep penetration and liquid injection into adipose tissue

### Kerstyn Comley and Norman Fleck

Vol. 6 (2011), No. 1-4, 127–140
##### Abstract

The subcutaneous injection of porcine adipose tissue by a hypodermic needle involves two stages: tissue penetration followed by the delivery of liquid into the tissue. The force required to penetrate adipose tissue by a series of conically tipped and flat-bottomed circular punches has been measured. Scanning electron microscopy and light microscopy are used to observe the mechanism of crack formation during penetration. The experiments reveal that penetration by either a flat bottomed or $4{5}^{\circ }$ conically tipped punch involves the formation of a mode II ring crack. The predicted penetration pressure according to the Shergold–Fleck model (Proc. R. Soc. Lond. A 460 (2004), 3037–3058) is in good agreement with the measured pressure on the punch. The subsequent delivery of liquid into adipose tissue by the hypodermic needle has also been examined: the injection pressure for phosphate buffered saline has been measured for a range of flow rates. X-ray images of the injected liquid suggest that micro-cracks are formed by the fluid pressure within the tissue and this leads to an increase in permeability. A seepage model is developed, based on the Darcy flow law, to relate the volumetric flow rate to the injection delivery pressure. Finally, a model of hydraulic fracture is used to assess the toughness associated with the formation of the micro-cracks during injection.

##### Keywords
adipose tissue, soft solids, deep penetration, injection, fracture mechanics, toughness


text:
# Zero's Everywhere

Number Theory Level 2

Find the trailing number of zeros of $$150!$$.

Notation: $$!$$ denotes the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

×


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# Stoïlow's theorem revisited

created by luisto on 20 Dec 2018

[BibTeX]

preprint

Inserted: 20 dec 2018
Last Updated: 20 dec 2018

Year: 2017

ArXiv: 1701.05726 PDF
Notes:

Acknowledgement for support from the GeoMeg project will appear in an upcoming version.

Abstract:

Sto\"ilow's theorem from 1928 states that a continuous, light, and open mapping between surfaces is a discrete map with a discrete branch set. This result implies that such mappings between orientable surfaces are locally modelled by power mappings $z\mapsto z^k$ and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having the readers interested in discrete and open mappings in mind.

Tags: GeoMeG

Credits | Cookie policy | HTML 5 | CSS 2.1


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### What if a patron wants to make copies (location, cost and cards)?

Where is the photocopier?

• The photocopier is to the left of the Honors section on the first floor (near the lost and found table and the elevator)

How much does it cost to make a copy?

• Copies cost 15¢ per page without a copy card
• Copies cost 10¢ per page with a copy card

**The copier will accept cash, coins or cards.

How much does a copy card cost?

• A copy card costs $1.00 - make sure to record the sale of a copy card on the cash log! How can a patron add money to their copy card? The patron can add money to the copy card by using the machine located next to the copier. Make sure to explain the following: • All of the money they put into the machine will be added to the card - they will not receive change. • They should never put more than$20.00 on their card (if they do, the machine won't read it).

**Please encourage patrons to write their names on the back of the copy card.


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# FIFO Reset

All modes support resetting the receive and transmit buffers.

The receive buffer is flushed and all unread data discarded when the RXBE bit is written to ‘1’. Instead of using a BSF instruction to set RXBE, the MOVWF instruction with the TXBE bit cleared will be used to avoid inadvertently clearing a byte pending in the TSR when UxTXB is empty.

Data written to UxTXB when TXEN is low will be held in the Transmit Shift Register (TSR), then sent when TXEN is set. The transmit buffer and inactive TSR are flushed by setting the TXBE bit. Setting TXBE while a character is actively transmitting from the TSR will complete the transmission without being flushed.

Clearing the ON bit will discard all received data and transmit data pending in the TSR and UxTXB.


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# The figure above shows four adjacent small squares, forming one large

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The figure above shows four adjacent small squares, forming one large  [#permalink]

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31 Oct 2018, 01:04
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Difficulty:

35% (medium)

Question Stats:

69% (01:59) correct 31% (01:58) wrong based on 26 sessions

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The figure above shows four adjacent small squares, forming one large square. The vertices of square RSTU are midpoints of the sides of the small squares. What is the ratio of the area of RSTU to the area of the large outer square?

A. 1/2

B. 5/9

C. 7/12

D. 3/5

E. 5/8

Attachment:

phd03.png [ 9.57 KiB | Viewed 338 times ]

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Re: The figure above shows four adjacent small squares, forming one large  [#permalink]

### Show Tags

31 Oct 2018, 01:31
1
Bunuel wrote:

The figure above shows four adjacent small squares, forming one large square. The vertices of square RSTU are midpoints of the sides of the small squares. What is the ratio of the area of RSTU to the area of the large outer square?

A. 1/2

B. 5/9

C. 7/12

D. 3/5

E. 5/8

Attachment:
phd03.png

For the sake of dealing with easy numbers assume the bigger side of a square is 8, it creates 2 small squares that are 4 each. since the lines bisect in the middle of the the small 4/2 = 2

Now using pythagorean theorem we can find the side of the square RSTU the width is 4+2 = 6 and the height is 2

so it becomes 36 + 4 = 40

now the area of RSTU = 40

Area of bigger square = 8*8 = 64

$$\frac{40}{64}=\frac{4 * 2 * 5}{4* 2 * 8} = \frac{5}{8}$$

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Re: The figure above shows four adjacent small squares, forming one large  [#permalink]

### Show Tags

31 Oct 2018, 01:32
1
Let the side of the larger square be 4 units.

Attachment:

image.jpg [ 51.38 KiB | Viewed 281 times ]

The ratio of area of RSTU to outer square is $$\frac{(\sqrt 10)^2}{16}$$

$$\frac{10}{16}$$

$$\frac{5}{8}$$

OPTION : E
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if you like my explanation!!!

Re: The figure above shows four adjacent small squares, forming one large &nbs [#permalink] 31 Oct 2018, 01:32
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# Effelsberg 100m Teleskop

### Sidebar

Information for Astronomers

information_for_astronomers:user_guide:pyonlplot

## Online plotter

The new online plotter provides an easy-to-use interface, and in fact is not only an online plotter but allows you to preview your data offline as well. To start it, simply type

onlplot

into a console on the observer2 (user: "obseff", in the VNC you can also use it directly). We have created a vnc server on

observer2:25

to start the online plotter. Password is the same as for the observing vnc's. There is a menu item to start

OnlPlot2

, or you can use a console inside this vnc. After starting, the main screen looks like shown in Fig. 1.

Fig. 1: Online plotter main window after program start. All plotting windows are implemented as so-called dock widgets, which can be re-arranged easily (right panel). Layouts can be stored for fast switching between them.

In the left panel (see Fig. 2a) one can choose the data to plot, i.e., add a FITS-file from the file browser (tree-view) in the top to the list of active files in the middle (using the Add button. Each file added to list will be parsed for generic information (scan number, source, observation type, date/time, and frequency). With the Remove button one can remove files from the active-file list. You can have an arbitrary number of active files but a smaller list helps to keep an overview.

Selecting a file in the active-file list will scan the file for the number of subscans. Using the Plot button you can display data and auxiliary information.

Fig. 2a: Choosing fits files and subscans to plot.

##### Options

Note, that per default all subscans are plotted/processed. For larger data sets this can be time-consuming. Therefore we recommend to choose the Specified subscan(s) option from the Mode Combo-box (in Values→General) in such cases. Then only the selected subscans will be processed (though coordinates are always shown completely, and the preview map has an additional combo-box, see below). All available options are shown in Fig. 2b.

Fig. 2b: Options

### Continuum data

In Fig. 1 you could already see a typical pointing measurement. Usually four subscans are done, two in longitude and two in latitude. Online plotter shows them in two sub-plots and tries to fit a Gaussian to the data. Fitting results are shown in the upper left part of each figure.

Sometimes weak sources do not show-up well in a single subscan. If you choose the Average subscans option from the Averaging mode Combo-box (Values→Continuum) all subscans are resampled to a common grid and averaged, see Fig. 3.

Fig. 3: Averaging/resampling pointing scans.

It is of course also possible to plot a different channel (aka baseband) than the usual plotting channel (Fig. 4). Just choose one from the Baseband Combo-box. In case more than one backend was used, you can also choose the backend of interest from the Backend Combo-Box. The online plotter also enables you to work with (simple) plotting formulae, similar to the old OnlPlot or Toolbox software. The syntax is the same as in the latter, e.g.

c[33]-c[34]Subtract channel 34 (R) from 33 (L).
sqrt(c[33])Plot square root of channel 33.

Fig. 4: Left panel: choose channel (aka baseband), backend, and optionally a plotting formula. Right panel: Example continuum plot for the formula c[33]-c[34] which computes L-R.

A very nice feature is the map preview of the new online plotter. For continuum observations it will always grid the reduced data. For spectroscopy one has to define a spectral interval first (see below). In Fig. 5 the computed map for the above pointing scan is shown.

Fig. 5: Map preview for a pointing measurement.

Since a pointing is not really a map, but only a cross, there is of course not much to be gained. In Fig. 6 we show a true continuum map of the source M31 (3.6-cm). Unfortunately, there was a lot of RFI present. To obtain a useful preview, one can just omit bad subscans: choose the subscans you want to plot, use the Specified subscan(s) mode and in the Options tab change the Mapping combo-box to Only specified subscan(s). The result is shown in the right panel of Fig. 6. One drawback of the subscan selection is, that you have to plot all desired subscans in the Continuum view as well, which somewhat slows down the software.

Fig. 6: Continuum map. Due to RFI and air-mass effects there is not much visible.

As you see in Fig. 6 (right panel), although the glitch is gone, there is still not much visible since the system temperature changed substantially during the observation (due to the elevation-dependent air mass). However, you can (and should) subtract a baseline from each subscan. Simply click once into the continuum plot (this is necessary otherwise the matplotlib-based widget won't obtain the following key-stroke) and type in any number between 0 and 9. This will re-plot the data but with a baseline of the requested order subtracted. For our example a 2 was typed in to have a second-order polynomial baseline. The result is visible in Fig. 7. Although there is some residual RFI one can now see clearly a continuum point source and half of the ring of M31.

Fig. 7: Map of M31 at 3.6-cm after baseline subtraction. The right panel shows the same data but in sky coordinates while the top panel uses offset coordinates.

### Spectroscopy

For spectroscopic measurements almost all features work in a similar way as for continuum. If you plot one or several subscans the bottom panel will show the raw data (log-scale) the upper panel the "reduced" data (using the same algorithms as the class pipeline), see Fig. 8.

Fig. 8: Spectroscopy data.

To produce maps, the user has to define a spectral interval first. Just click into the spectrum and press 'w' to set a window (indicated by green lines). With 'c' you can clear the window. When a window is set and the user clicks the Plot button a map is generated, or strictly speaking two maps: the first shows the line as color image, the second is overplotted as contours and visualizes the continuum. Numerically, the average of the flux outside the window, i.e. in the adjacent 200 spectral channels, is used as a proxy for continuum. The average of the flux inside the window minus this continuum defines the line map. Therefor, values in the map are Intensities in units of Tcal per channel (not per Hz or km/s!). All maps are also written as a fits-image into /tmp. Don't forget to copy the image file to your home directory if you want to keep it. (The Karma software is installed on observer2 and can be used to display the fits maps.) An example is shown in Figs. 9 and 10.

Fig. 9: Defining a spectral interval.

Fig. 10: The maps show an absorption line (H2CO) and the H110a RRL in W3Main. Contours visualize the continuum flux.

### Coordinates

Another useful feature is to visualize coordinates. Four different plots are provided, showing Azimuth-Elevation, Offsets in the basis frame and the absolute coordinates in the basis frame. Furthermore, the P.A. is plotted vs. time. See Fig. 11 for an example.

Fig. 11: Plotting coordinates.

### Online mode

If you click the Online button, the online plotter will continuously show the last file (and last subscans). To avoid extreme processing times, only the last 4 subscans are displayed - except for the preview map where either the full map is displayed or selected subscans, according to the choice in the Options tab (see above). If you work with very large files, it is recommended to not show the complete map in online mode.


text:
222 views

In how many different ways can $r$ elements be picked from a set of $n$ elements if

(i) Repetition is not allowed and the order of picking matters?

(ii) Repetition is allowed and the order of picking does not matter?

1. $\frac{n!}{\left(n - r\right)!}$ and $\frac{\left(n + r - 1\right)!}{r!\left(n - 1\right)!}$, respectively.
2. $\frac{n!}{\left(n - r\right)!}$ and $\frac{n!}{r!\left(n - 1\right)!}$, respectively.
3. $\frac{n!}{r!\left(n - r\right)!}$ and $\frac{\left(n - r + 1\right)!}{r!\left(n - 1\right)!}$, respectively.
4. $\frac{n!}{r!\left(n - r\right)!}$ and $\frac{n!}{\left(n - r\right)!}$, respectively.
5. $\frac{n!}{r!}$ and $\frac{r!}{n!}$, respectively.
retagged | 222 views

(i) Repetition is not allowed and the order of picking matters =
= r arrangement with no repetition = npr = $\frac{n!}{(n-r)!}$

(ii) Repetition is allowed and the order of picking does not matter =
= combination with unlimited repetition = n-1+rCr = $\frac{n-1+r!}{(n-1)!r!}$
Option A

answered by Veteran (15.3k points) 17 51 129
selected by
+1 vote

Order of picking matters means,(1). a,b,c (2)a,c,b  ,both (1) and (2) are treated as different.

Order of picking does not matters means,(1). a,b,c (2)a,c,b  ,both (1) and (2) are treated as same.

(i) Repetition is not allowed and the order of picking matters = C(n , r) ⨉ P(r , r)
=   C(
n , r) ⨉ r! = P(n , r) = n! / (n-r)! = It is eqt to say Permutation of r objects in the pool of n object.

(ii) Repetition is allowed and the order of picking does not matter =  C(n+r-1 , r)

= (n+r-1)! / r!(n-1)!  = It is eqt to say the combination of r objects in n objects with unlimited repetition is allowed.

answered by Boss (8.8k points) 3 8 12


text:
# How do I make a 2D character aim their gun toward the mouse?

Heli Attack is a perfect example of the shooting mechanic I'd like. The character aims perpetually toward the mouse. What's going on here?

From what I've read so far, you could separate the arm and rotate that. I've also noticed some people use a different sprite for each weapon.

How can I achieve this?

# Projector sheets

You know those ancient projectors that come with transparent sheets? In primary school, I discovered you could draw a character's torso on one transparent sheet...

... and then take out another sheet, lay it on top, and draw arm with a gun on it ...

... and then rotate the top sheet with the arm on it (reeeally carefully, to keep the shoulder in the right place) ...

... and it would be amazing. I made multiple characters had them fight.

# Draw order

In secondary school, I taught myself Game Maker and I was making a platformer game. Playing around with sprites, I remembered my childish projector sheet battles and thought I wonder if I could do that with code.

So I drew sprites like I'd drawn them years ago and wrote code in the player's Draw event, something like

var rotation = direction_to_point(self.shoulder_position, mouse_position)
# Draw back arm
draw_sprite(player_back_arm, self.shoulder_position, rotation);
# Draw torso
draw_sprite(player_torso, self.position);
# Draw front arm
draw_sprite(player_front_arm, self.shoulder_position, rotation);

I remember I was really proud I had graduated to two arms. I printed the code out and taped it to the inside of my locker door, next to my circle-AABB collision resolution code. I figured this would get me girls. Hm.

When we did trigonometry in math class, I noticed that because the tangent of the angle between the adjacent and the hypotenuse equalled the length of the opposite over that of the adjacent, it was possible to find the angle given just the adjacent and opposite and that that's what the angle_to_point function in Game Maker must be doing.

Just imagine A is where the shoulder is and B is where you're aiming (the mouse position, say).

See my answer over here for a more complete explanation of the trigonometry involved, with sample code.

So that's how you might do that.

• +1 For much better than the average programmer's art. – concept3d Feb 10 '14 at 9:26