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A mixture of two gases A and B in the mole ratio 2 : 3 is kept in a 2 litre vessel. A second 3 litre vesselhas the same two gases in the mole ratio 3 : 5. Both gas mixtures have the same temperature and same total pressure. They are allowed to intermix the final temperature and total pressure are the same as the initial values, the final volume being 5 litres. Given that the molar masses are MB and MB, what is the mean molar mass of the final mixture?

(1) $\frac{77{M}_{A} + 123{M}_{B}}{200}$

(2) $\frac{123{M}_{A} + 77{M}_{B}}{200}$

(3) $\frac{77{M}_{A} + 123{M}_{B}}{250}$

(4) $\frac{{\text{123M}}_{\text{A}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}77{\text{M}}_{\text{B}}}{250}$


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## Thursday, December 29, 2011

### Monetary Policy & Credit Easing pt. 4: More Independent Variable Definitions

Support for Depositary Institutions

This variable will account for the Federal Reserves support of Depository Institutions through direct lending to these institutions.  Support will be measured by how much the Fed made up for any shortfalls in Depository Institutions main source of cash- time and savings deposits. Federal Reserve support for our first estimation period is operationalized as follows:

Support_{t}={TotalBorrowingFed^{DI}_{t}\ Total Time & Savings Deposits_{t}^{DI}}x 100

Where,
Support_{t}= Fed funds at depository institutions as a percentage of their main financing streams (total savings and time deposits) at time, t

TotalBorrowingFed^{DI}_{t}= Total Borrowings of Depository Institutions from the Federal Reserve (BORROW) at time, t

Total Time & Savings Deposits_{t}^{DI}= Total Time and Savings Deposits at All Depository Institutions (TOTTDP) at time, t

For our second estimation period from 4/1/01 to 4/1/11 we will use a different variable that excludes time-deposits as the series that we would ideally like to use above was discontinued in 2006.

Support_{t}={TotalBorrowingFed^{DI}_{t}\ Total Savings Deposits_{t}^{DI}}x 100

Where,
Support_{t}= Fed funds at depository institutions as a percentage of their main financing stream (total saving deposits) at time, t

TotalBorrowingFed^{DI}_{t}= Total Borrowings of Depository Institutions from the Federal Reserve (BORROW) at time, t

Total Savings Deposits_{t}^{DI}= Total Savings Deposits at all Depository Institutions (WSAVNS) at time, t

The expected beta coefficient should be positively related to short-term risk premia, as tighter credit conditions require Depository Institutions to go to the Fed for help.  Only after the risk-premia goes up and these institutions have no where else to go do they borrow from the Fed at the discount rate.

We expect the effect of lending support to depository institutions to be positively related to short-term risk premia, therefore:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

Furthermore, we expect Fed support to depository institutions to have a negative effect on long-term risk premia because of the expectations component.  As the Fed steps in with lending support, markets calm their fears about the future.  This is directly the opposite of short-term risk premia as the support in that situation is in direct response to the risk premia. Therefore,

H_{0}: ß ≥ 0 vs. H_{a}: ß < 0

Data Issues

The following time-series data were provided by FRED and the details are as follows:

(a) Total Borrowings of Depository Institutions from the Federal Reserve (BORROW), Monthly, Not Seasonally Adjusted, 1919-01-01 to 2011-10-01

(b) Total Savings Deposits at all Depository Institutions (WSAVNS), Weekly, Ending Monday, Not Seasonally Adjusted, 1980-11-03 to 2011-10-17

(c) Total Time and Savings Deposits at All Depository Institutions (DISCONTINUED SERIES) (TOTTDP), Monthly, Seasonally Adjusted, 1959-01-01 to 2006-02-01

The Federal Funds Rate

The motivation behind putting the Federal Funds rate into our regression model is simple.  This is the main policy tool that the Fed has used to manipulate short-term credit conditions and influence the rate of inflation.  The Fed controls this rate in hopes of influencing other rates such as the Prime Bank Loan Rate along with other short term credit instruments like Commercial Paper. Additionally, this variable is very easy to account for because it requires virtually zero manipulation.  Notationally we will define it in the following manner:

FF_{t}= Federal Funds rate at time, t

The expected beta coefficient should be positively related to the short-term risk premia and negatively related to long-term risk premia.  They theory is that by lowering the federal funds rate, or the rate at which banks lend to each other, the Fed is encouraging banks to lend and thus ease credit conditions.  When the Fed feels that tightening is appropriate, maybe the result of a jump in inflation expectations or an deep acceleration in the economy, they respond by raising the federal funds rate.  This tightens credit conditions and thus theoretically at least, should result in an increase in short-term risk premia. The opposite holds true for the federal funds rate effect on long-term risk premia.  Since long-term rates are a function of shorter-term rates, investors are inclined to sell Treasuries which decreases the spread between Aaa and 10 year nominal treasuries, therefore decreasing long-term risk premia.

For short-term risk premiums we expect the federal funds rate to be positively related:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

For long-term risk premiums we expect the federal funds rate to be negativity related:

H_{0}: ß ≥ 0 vs. H_{a}: ß < 0

Data Issues

We get the series for the federal funds rate from FRED and the details are as follows:

(a) Effective Federal Funds Rate (FF), Weekly, Ending Wednesday, 1954-07-07 to 2011-10-19

Interest Paid On Excess Reserves

This variable is also easy to account for because the introduction of interest paid on reserves has a direct impact on the physical quantity of excess reserves of depository institutions held at the Federal Reserve.  The motivation behind this variable is that banking institutions would not hold excess reserves with the Fed without some compensation i.e. that opportunity cost has to be greater than zero.  That is where the interest paid on excess reserves come in.  Without it there is an opportunity cost of letting the reserves sit with the fed instead of seeking more profitable safe havens for their cash. That is why we will be using the quantity of excess reserves as our explanatory variable and notationally defining it as follows:

ER_{t}= Excess Reserves of Depository Institutions at time, t

When the Fed initiated its policy of paying interest on reserves it created an incentive for banks to shore up their finances with the Fed.  It gave the Fed a way to conduct large scale asset purchases without suffering inflationary consequences. As long as the reserves are held with the Fed, they cannot be inflationary therefore an increase in excess reserves at the Fed is contractionary. Additionally, since the Fed had not initiated the policy of paying interest on reserves until October of 2008 there was no incentive for banks to hold any excess reserve balances before then. That is why our two estimation periods must have two different hypothesis tests for this variable:

For our estimation covering the 4/1/71 to 7/1/97 time period the interest paid on excess reserves policy was non-existent and therefore:

H_{0}: ß = 0 vs. H_{a}: ß ≠ 0

In other words, we are looking to not reject the null hypothesis that beta is equal to zero.

For our second estimation covering the 4/1/01 to 4/1/11 time period the interest paid on excess reserves policy was in effect, if only for a short-time before the end of the sample and therefore:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

Data Issues

We get the series from FRED and the details are as follows:

(a) Excess Reserves of Depository Institutions (EXCRESNS), Monthly, Not Seasonally Adjusted, 1959-01-01 to 2011-09-01

Control Variables: Accounting For Factors Outside of Monetary Policy

We must account for changes in the risk premia that aren't necessarily related to monetary policy.  These include things like market fear, corporate default risk and controlling for changes due to underlying fundamentals like Corporate Profits After Tax.

The Yield Curve

The motivation behind including the yield curve is due to its known predictive power of economic growth and recessionary risk. As recessionary risk increase investors are more likely to put their funds into the safest assets with the highest return.  Historically, this involves the purchase of longer-term Treasuries as they have zero default risk.  When a bond is purchased its price goes up, and its effective yield decreases so the slope of the yield curve or the spread between the most liquid and shortest maturity bond and the most liquid, longest maturity bond decreases or flattens. As this slope flattens we expect risk premia to increase for longer maturity and less liquid debt instruments. As the yield curve flattens we expect T-bills to be sold and longer-term Treasuries to be purchased.  This puts upward pressure on T-bill rates, thus narrowing the spread between Commercial Paper and T-bills and reducing the short-term risk premia.
The yield curve as we define it is the spread between the 10-Year Nominal Treasury Note rate and the 3-Month Nominal Secondary Market Treasury Bill rate.  Notationally,

YC_{t}=GS10_{t} – TB3MS_{t}

Where,

YC_{t}= Yield curve at time, t

GS10_{t}= 10-Year Treasury Constant Maturity Rate at time, t

TB3MS_{t}= 3-Month Treasury Bill: Secondary Market Rate at time, t

The beta coefficient for both of our estimation periods is expected to be negatively related to long-term risk premia. Therefore:

H_{0}: ß ≥ 0 vs. H_{a}: ß ≤ 0

The beta coefficient for both of our estimation periods is expected to be positively related to short-term risk premia. Therefore:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

Data Issues

We get the two times-series data from FRED and the details are as follows:

(a) 10-Year Treasury Constant Maturity Rate (GS10), Monthly, 1953-04-01 to 2011-09-01

(b) 3-Month Treasury Bill: Secondary Market Rate (TB3MS), Monthly, 1934-01-01 to 2011-09-01

Stock Market Volatility

We will control for market fear by including a measure of stock market volatility into our regression model. We define volatility as follows:

Volatility_{t}= CBOE DJIA Volatility Index (VXDCLS) at time, t

The motivation behind this control variable is that the returns from owning stocks become more volatile in times of fear. Thus the risk premia on assets that aren't risk free like corporate bonds may increase in response to this market volatility.

This variables is literally only relevant in the regression on long-term premiums for our second estimation period. We cannot reasonably assume it has any effect on short-term risk premia because stock market volatility signals the fear of financial markets which leads to flight to safety into longer term treasuries not short-term commercial paper. The reason is that an investor probably couldn't even have the capital to buy commercial paper to begin with and secondly when fear strikes investors tend to pour their capital into longer term treasuries because they can pick up some extra yield. This would widen the spread between Aaa and Treasuries thus increasing the risk premium.  Therefore we include this variable only in our second estimation and its only real effect will be on the long-term risk premia.

For the regression over our second estimation period, increased volatility is expected to increase the long-term risk premium:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

For the regression over our second estimation period, volatility is not expected to have an effect on short-term risk premia, therefore:

H_{0}: ß = 0 vs. H_{a}: ß ≠ 0

In other words, we are looking to not reject the null hypothesis that $\beta$ is equal to zero.

Data Issues

We get the times-series data from FRED and the details are as follows:

(a) CBOE DJIA Volatility Index (VXDCLS), Daily, Close, 1997-10-07 to 2011-11-02

Corporate Bond Default Risk

It would be prudent to control for the perceived credit default risk of the corporate bonds market. To do this we use the spread between the AAA and BAA rates bonds which would theoretically correspond to increased compensation for the risk of a default. The reason being we want to see how much the Fed's actions influence the risk premia and factor out movements in the spread that may incorporate other things like flat out default risk. Ideally we would like to use a Credit Default Swap Index to control for default risk as it would help us control directly for default risk and not other things like liquidity risk, but given the sample length data limitations we are forced to stick with what we've got.

The control variable we use for corporate default risk is the spread between Moody's rated Baa's and Aaa's. This is used because data exists for the full length of our desired samples and therefore is operationalized as follows:

Where,

BAA_{t}= Moody's Seasoned Baa Corporate Bond Yield at time, t

AAA_{t}= Moody's Seasoned Aaa Corporate Bond Yield at time, t

The beta coefficient on our corporate default control variable is expected to be positive in our regression on long-term rates since an increase in the spread between BAA and AAA would indicate that these bonds expected default risk would increase:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

In our regressions on short-term risk premia, the expected effect of this control variable is effectively zero as this variable deals with longer-term interest rates not exactly pertinent to short-term financing like commercial paper or Treasury Bills:

H_{0}: ß = 0 vs. H_{a}: ß ≠ 0

In other words, we are looking to not reject the null hypothesis that $\beta$ is equal to zero.

Data Issues

For the AAA and BAA data we use FRED:

(a) Moody's Seasoned Aaa Corporate Bond Yield (AAA), Monthly, 1919-01-01 to 2011-09-01

(b) Moody's Seasoned Baa Corporate Bond Yield (BAA), Monthly, 1919-01-01 to 2011-09-01

Corporate Profits After Tax

As corporate profits after tax increase the risk premium on corporate bonds decrease.  This fundamentally negative relationship should be controlled for in our regression model.  Operationally, this is defined as:

CP_{t} = Corporate Profits After Tax at time, t

The beta coefficient on our CP control variable should be negatively related to our dependent variables.  This is because as corporate profits after tax increase the risk that they will renege on their debt obligations will decrease. This gives us the following test.

H_{0}: ß ≥ 0 vs. H_{a}: ß < 0

Data Issues

We get the times-series data from FRED and the details are as follows:

(a) Corporate Profits After Tax (CP), Quarterly, Seasonally Adjusted Annual Rate, 1947-01-01 to 2011-04-01

Keep dancin'

Steven J.

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# Vacuum energy for Yang-Mills fields in $R^d\times S^1$: One-loop, two-loop, and beyond

Authors
Type
Published Article
Publication Date
Mar 01, 2018
Submission Date
Mar 01, 2018
Identifiers
DOI: 10.1007/BF01483877
Source
arXiv
The vacuum energy is calculated for Yang-Mills (YM) system defined in $D$ dimensional space-time of $S^1\times R^d$ ($D=d+1$), where the possibility of the YM fields to acquire the vacuum expectation values on $S^1$ is taken into account. The vacuum energy has already been obtained to the order of one-loop in many people. Here we calculate the vacuum energy in $D$ dimensions to two-loop order. With an intention to reach higher loops, an approximation method is proposed, which is especially effective in higher dimensions. By this method, we can treat the higher-loop contributions of YM interactions as easily as we treat one-loop effect. As a check, we show reproduction of the two-loop contribution ($D$-dependence of the coefficient as well as the functional form) when the coupling constant is small. This approximation method is useful not only for the Kaluza-Klein theories but also for the finite temperature-density system (as a quark-gluon plasma).


text:
# Posts Tagged ‘ Rstats ’

## Online R and Plotly Graphs: Canadian and U.S. Maps, Old Faithful with Multiple Axes, & Overlaid Histograms

February 6, 2014
By

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## What’s Warren Buffett’s \$1 Billion Basketball Bet Worth?

January 23, 2014
By

A friend of mine just alerted me to a story on NPR describing a prize on offer from Warren Buffett and Quicken Loans. The prize is a billion dollars (1B USD) for correctly predicting all 63 games in the men’s Division I college basketball tournament this March. The facebook page announcing the contest puts the odds at 1:9,223,372,036,854,775,808, […]

## Simudidactic

November 23, 2013
By

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## Montreal R User Group – Dr. Ramnath Vaidyanathan on his rCharts package

October 27, 2013
By

Monday, October 28, 2013. 6:00pm at Notman House 51 Sherbrooke W., Montreal, QC. We are very pleased to welcome back Dr. Ramnath Vaidyanathan for a talk on interactive documents as it relates to his excellent rCharts package. Bringing a laptop to follow along is highly encouraged. I would recommend installing rCharts prior to the workshop. library(devtools) pkgs <- c(‘rCharts’, ‘slidify’, ‘slidifyLibraries’) install_github(pkgs, ‘ramnathv’, ref […]

## Follow up to Johnson et al Post

October 21, 2013
By

Last week I posted a comment on a paper by Neil Johnson and colleagues that I now regret. The comment amounted to a bit of statistical pedantry on my part regarding some of the wording in the paper. It was my wording in this post, and specifically the title, which would have benefited from some […]

## P-value fallacy alive and well: Latest case in Scientific Reports

October 17, 2013
By

Erratum (10/17/13): The paper was published in Scientific Reports, an OA journal from the publishers of Nature, and not in the Journal Nature as originally reported. Clarification (10/17/13): The paper discussed here is quite good overall and very interesting. I do not believe that anything in this post calls into question any of its main […]

## Calculating AUC the hard way

October 10, 2013
By

The Area Under the Receiver Operator Curve is a commonly used metric of model performance in machine learning and many other binary classification/prediction problems. The idea is to generate a threshold independent measure of how well a model is able to distinguish between two possible outcomes. Threshold independent here just means that for any model […]

## Marginal likelihood from tempered Bayesian posteriors

October 1, 2013
By
$Marginal likelihood from tempered Bayesian posteriors$

Introduction In the previous post I showed that it is possible to couple parallel tempered MCMC chains in order to improve mixing. Such methods can be used when the target of interest is a Bayesian posterior distribution that is difficult to sample. There are (at least) a couple of obvious ways that one can temper […]

## Parallel tempering and Metropolis coupled MCMC

September 29, 2013
By
$Parallel tempering and Metropolis coupled MCMC$

Introduction Parallel tempering is a method for getting Metropolis-Hastings based MCMC algorithms to work better on multi-modal distributions. Although the idea has been around for more than 20 years, and works well on many problems, it still isn’t routinely used in applications. I think this is partly because relatively few people understand how it works, […]

## Summary stats for ABC

September 1, 2013
By
$Summary stats for ABC$

Introduction In the previous post I gave a very brief introduction to ABC, including a simple example for inferring the parameters of a Markov process given some time series observations. Towards the end of the post I observed that there were (at least!) two potential problems with scaling up the simple approach described, one relating […]


text:
# Tag Info

1

I'd suggest using the following redefinition of cite:full: \renewbibmacro*{cite:full}{% \usebibmacro{cite:full:citepages}% \printtext[bibhypertarget]{% \usedriver {\DeclareNameAlias{sortname}{labelname}} {\thefield{entrytype}}}% \usebibmacro{shorthandintro}} cite:full in the verbose styles normally just prints the whole bibliography ...

2

You can use the \DeclareNameFormat directive to throw away the first names. I just added the following line to your code \DeclareNameFormat{}{\usebibmacro{name:first-last}{}{#5}{#1}{#7}} which just omits the output of first names, as you can see in the sample page below: I have to admit it is in some parts a bit of a hacky solution as it just abuses ...

3

It is easy enough to mimic the page design of the linked-to sample_CV.tex without all the complicated hoops it jumps through. All it takes is geometry and titlesec. (I would also use enumitem to fiddle with my various list environments, but that is beside the point here.) What matters in this case is setting the margins to the width you like, and making ...

3

I solved the issue by redefining bibmacro{cite} such that it checks to see whether the entry type is @archive. Less than elegant, I'm certain, but it got the job done. MWE: \documentclass{article} \usepackage[notes,backend=biber,booklongxref=bib]{biblatex-chicago} \newbibmacro*{cite}{% \ifciteseen% {\iffieldundef{shorthand}% ...

0

I had the same issue, but my latex file had some missing references to pictures I didn't wanted in the rtf version. When I removed those it worked perfectly. So I think that the issue it may be related not to the bibliography itself but to way latex or word tackles references.

0

To suppress underlining the journal title (and allow line breaks): \makeatletter \long\def\emph#1{\ifmmode\nfss@text{\em #1}\else\hmode@bgroup\text@command{#1}\em\check@icl #1\check@icr\expandafter\egroup\fi} \makeatother You may check this post for \emph redefinition in beamer.

1

The following redefinition of \cquotation could help. \makeatletter \newcommand{\cquotation}[1]{% \begingroup \booltrue{withintextquote}% % \settowidth doesn't like paragraphs \setbox\@tempboxa\hbox{% \def\par{\hspace{3\linewidth}}% If a paragraph is included force long form %\let\par\space % Ignore paragraphs ...

1

I dealt with the problem differently, since it is not possible to use name hashes with the current UI of the package. In version 0.9 of the package (on its way to CTAN just now), the problem should be fixed. Also, I have added a second optional argument to \omitname for name prefix (aka von-part).

3

Unfortunately this is not overly easy. Instead of manipulating \mkbibnamefirst and \mkbibnameprefix, we have to manipulate the name:last-first macro directly. \renewbibmacro*{name:last-first}[4]{% \ifuseprefix {\usebibmacro{name:delim}{#3#1}% \usebibmacro{name:hook}{#3#1}% \ifblank{#3}{}{% \ifcapital ...

5

You are able to change the formatting of all last names that appear in your citations \renewcommand{\mkbibnamelast}[1]{\mkbibemph{#1}} ...and then reset the formatting before \printbibliography so that the names appear in upright font in the bibliography. Your MWE would become: \documentclass{article} \usepackage{filecontents} ...

1

Thanks for the suggestion. Surely using hashes would be more appropriate than the crude name comparison I use now. Alas, I am away from my home machine for the next four months and also extremely short of time, so chance is low I get the time to dig into this soon. Sorry about that. Of course, if anybody wants to send a patch, this would speed things up.

2

When we use editoratype = {reviser} biblatex-chicago tries to print the undefined bibstring cbyreviser. So all we have to do is to create the bibstring cbyreviser. \NewBibliographyString{cbyreviser} and populate it with appropriate text \DefineBibliographyStrings{english}{ cbyreviser = {rev\adddot}, } As a general rule of thumb: If one gets bold ...

13

Adding sortlocale = nn_NO (nn for Norwegian nynorsk, nb for Norwegian bokmål) as a package option will ensure that Aa is treated as Å, and that Å is alphabetized last. Cf. the University of Oslo’s Local guide to biblatex. \documentclass{article} \usepackage{polyglossia} \setdefaultlanguage{nynorsk} \usepackage[style = authoryear, language = nynorsk, ...

0

Your question is a bit confused, because you have tagged it as Biblatex, but your reference to apalike suggests you are using BibTeX. First off, whichever system you are using, do not try to change the format of references by changing your .bib file. That file just contains data. How it is formatted depends on other files. Each author should always and only ...

2

If we have a look at the .bbl file (as created by Biber) we can see that the simple author = {Mine, Me I.} becomes (line breaks were inserted for readability) \name{author}{1}{}{% {{hash=41274140480afc1dcd1fc7fc1b6f2529} {Mine} {M\bibinitperiod} {Me\bibnamedelima I.} {M\bibinitperiod\bibinitdelim I\bibinitperiod} {}{}{}{}}% ...

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Here is a solution which works with biblatex independent of the backend used. Since the OP asked about using bibtex, my example specifies this, but nothing depends on it. backend=biber would work at least as well. This answer is based on moewe's solution. I ran that code and read the output. biblatex suggested the defernumbers option there. Looking in the ...

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This was a bug. It should be fixed in 2.9 dev version on SF if someone could test?

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You could define a new \newbibmacro*{simp:prenote} that never prints any "vgl"/compare stuff \newbibmacro*{simp:prenote}{% \iffieldundef{prenote} {} {\printfield{prenote}% \setunit{\prenotedelim}}} (This, incidentally, is the standard definition of bibmacro{prenote} in biblatex.def.) We then use this simple bib macro in all the ...

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There is a package for it, it's called revtex4-1, which was designed for all the APS and meanwhile also for the AIP journals. To use it with Physical Review Letters style, consider the following MWE: \documentclass[aps,prl,reprint]{revtex4-1} \usepackage{blindtext} \begin{document} \title{Some random title} \author{Me} \email{mail@example.com} ...

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Caveat: I think you are using a fairly home-brewed style, which makes modifications awkward, and this is not fully tested, except on your sample .bib. I can see that some things (like the bibstrings you've used for editors) are not the same, but I hope the solution I have will work with your style, since it involves modifying a macro that I'm guessing you ...

1

The type of implementation that the OP is looking for closely matches that of the new Bibulous project. With Bibulous, customized styles are implemented with templates, so that for book and manual entry types, one can define bibliography styles with, for example, book = <author>, \enquote{<title>,} in <year>, <publisher>. manual = ...

3

5

If you only want to split @online and all other types into two bibliographies, that is as easy as \printbibliography[nottype=online] \printbibliography[type=online] The first command prints all entries save for those of type @online, while the latter prints only @online entries. We then use defernumbers=true, this options makes sure "numeric labels ...

2

Thanks @egreg. So indeed, this is what happened: On OS X I had problems with biber, and also when explicitly specifying bibtex8 as backend, that's why the backend statement was missing. On Linux, bibtex didn't work out correctly. So I added backend=biber, and then you need to re-assign the "bibtex" command in TeXMaker. In Options -> Configure Texmaker, the ...

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For @online entries, biblatex prints the URL and date even if configured with url=false. (example code was modified from @lockstep's answer) \documentclass{article} \usepackage[url=false]{biblatex} \usepackage{filecontents} \begin{filecontents}{\jobname.bib} @online{A01, author = {Author, A.}, year = {2001}, title = {Alpha}, url = ...

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Replace the literal ( and ) in your note with \bibopenparen and \bibcloseparen. Make sure they are balanced! \footnote{Here I make an insightful comment \bibopenparen Dio Cassius, \emph{Roman History}, ch. 60.19 \parencite[414–16]{fos24dio}% \bibcloseparen.}

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Search your Mendeley or exportet Bibtex Database for the string and1990. It is most likely, that Mendeley created a citation key that includes a symbol like an apostrophe ' (e.g. O'Hand1990), which is legal for the bibtex backend but illegal for biber backend. So you have two solutions: Change the citation key in Mendely to a legal string (only letters ...

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As I was suggesting in my comment, the compilation issue relies on the .bib file. Also, as @moewe identified, the use of the @proceedings category does not contain an author field. Therefore, it should be replaced either by @inproceedings or put the author in the editor field. New compilation with the appropriate .bib file syntax: ...

1

I don't think there is a definitive answer to this question at all. For one thing, I think what suits one person will not suit another. Moreover, people differ in how many entries they have to handle, where they obtain new data from and what they need to be able to do with that data later on. However, I realised that trying to explain this in comments was ...

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Here is an alternative, which enables you to use an option dead to mark that an author has died. It then adds the dagger on the first occurrence of the author's name. This may allow more "logical" markup of the .bib database. \documentclass{article} \usepackage{filecontents} \begin{filecontents}{\jobname.bib} @book{living, author = {Last, Alpha}, title ...

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I use one file and notepad++ when I'm on my windows box (jEdit on linux most of the time). My keys are (normally*) in the form Surname_Key_Words. I strip any keywords fields (manually or using a regex find/replace), because I just find thy slow down searching. A find is pretty simple: searching for Nakamura_ would only find me the following entry. ...

2

Absolute path in the \addbibresource is required with LyX, as it probably works in some temporary directory to render the output. It couldn't find the bib file as it was defined with a relative path. Hope this helps, it helped myself:-) Also make sure you are using the Unix-ish slashes even on Windows e.g. \addbibresource{C:/file.bib}. Same goes for the ...

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If you use the part field for tome information1, there is not a lot to be done in the standard styles. If you have a non-standard/custom style that moves around the part information though, you would need to tell us more about it. These four lines should do what you want. They redefine the string part to be "tomo" and print ", tomo #" after the volume. ...

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Here's a workaround with fontspec only. The trick is to define a new math symbol font for the lining figures. I wouldn't use detect-all: numbers in \SI or \num should always be typeset in math mode (hence with lining figures). \begin{filecontents}{test.bib} @Article{Hay2011, Title = {Can humans force a return to a Cretaceous' ...

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The string in question here corresponds to bytranslator, whose Italian localization can be found in the file italian.lbx; you can change the default definition using \DefineBibliographyStrings: \documentclass{article} \usepackage{fontspec} \usepackage{polyglossia} \setmainlanguage{italian} \usepackage{biblatex} \makeatletter ...

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The output of the bibliography is done done inside an environment defined by % {<name>}{<start code>}[<end code>]{<item code>} \newrobustcmd*{\defbibenvironment}[4]{% \long\csdef{blx@env@#1}{#2}% \long\csdef{blx@endenv@#1}{#3}% \long\csdef{blx@item@#1}{#4}} Every style uses this definition of modify the environment. So for ...

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You can redefine \defbibenvironment{bibliography} to include the final period. Note that this will most likely cause problems with empty bibliographies. Keep \renewcommand{\finentrypunct}{}. Take the definition of \defbibenvironment{bibliography} and add \addperiod to the line reading {\endlist}, so it reads {\addperiod\endlist}. You can find the ...

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I would discourage you from redefining the quote environment, particularly if you change its syntax to want a mandatory argument. Since this seems to be used for particular purposes, it's better to define a new environment. \begin{filecontents*}{\jobname.bib} @online{kn:gnus, author= {{David Arnold}}, title= {Writing Scientific Papers in \LaTeX}, url = ...

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I think the trick is, first, to use endnotes; second, to redefine \footnote to produce an endnote; and, third, to use a verbose citation style with biblatex rather than printing a separate list of references. For example: \documentclass{article} \usepackage{endnotes} \let\footnote\endnote \usepackage[citestyle=verbose,backend=biber]{biblatex} ...

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Here's a solution that redefines the quote environment using NewDocumentEnvironment from the xparse package. \let\oldquote\quote \let\endoldquote\endquote \RenewDocumentEnvironment{quote}{m}{% \oldquote \itshape \setlength{\rightmargin}{\leftmargin} {\Large\textbf{`}} } {% {\Large\textbf{''}} ...

2

Try the following code, it largely relies on your pseudo code above. We use a \savebox to evaluate the length. We just need to set \setlength{\availablewidth}{\linewidth}. We define a new bibmacro varwidthname. We need some new name formats for that \DeclareNameFormat{first-last-full}{% \usebibmacro{name:first-last}{#1}{#3}{#5}{#7}} ...

0

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By default biblatex does not print anything in the bibliography if the date is not set \renewbibmacro*{date+extrayear}{% \iffieldundef{\thefield{datelabelsource}year} {} {\printtext[parens]{% \iffieldsequal{year}{\thefield{datelabelsource}year} {\printdateextralabel}% {\printfield{labelyear}% ...

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To make use of biblatex's localisation capabilities we can define a new bibliography string or. \NewBibliographyString{or} \DefineBibliographyStrings{english}{% or = {or}, } \DefineBibliographyStrings{german}{% or = {oder}, } We can then define a new command that will change the "and" in \textcite to an "or". \newcommand{\useor}{% ...

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You can define a new cite command \textciteor that does that. The following code is required in the preamble: \makeatletter \DeclareCiteCommand{\cbx@textciteor} {\usebibmacro{textcite:init}} {\usebibmacro{citeindex}% \usebibmacro{textciteor}} {} {\usebibmacro{textcite:postnote}} \DeclareCiteCommand{\textciteor}[\cbx@textcite@init\cbx@textciteor] ...

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If you really want to have one set of citation commands, a good starting point seems to be the list of commands provided by biblatex (or rather its standard styles), as outlined in § 3.7 Citation Commands, p. 79 of the biblatex documentation. You should then use the appropriate command for the task at hand. I have listed some of the commands I regard as ...

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Though question. First, the \citeN, \citeNP and so commands you mention presumably have different meaning, and their differences can't be (easily) automatized, leaving the author the task to select the appropiate one. Next point is that one venue uses one set of cite commands, the other a different set. I'd wagger the sets aren't completely interchangeable, ...

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Assuming you don't want 'auto-cite' magic, then \makeatletter \renewbibmacro*{textcite}{% \iffieldequals{namehash}{\cbx@lasthash} {\usebibmacro{cite:comp}} {\usebibmacro{cite:dump}% \ifbool{cbx:parens} {\bibclosebracket\global\boolfalse{cbx:parens}} {}% \iffirstcitekey {} {\textcitedelim}% ...

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The problem ist that biblatex doesn't expand fully the argument of prefixnumbers, and so \thechapter gets written literally to the aux file. You could add this to your preamble: \makeatletter \def\blx@addprefixnumber{% \nottoggle{blx@skiplab} {\ifdef\blx@prefixnumbers {\ifundef\abx@field@shorthand ...

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This should be as easy as \makeatletter \DeclareCiteCommand{\bfullcite} {\usebibmacro{prenote}} {\renewcommand*{\newunitpunct}{\addcomma\space}% \settoggle{blx@useauthor}{false}% \settoggle{blx@useeditor}{false}% \settoggle{blx@usetranslator}{false}% \usedriver {\DeclareNameAlias{sortname}{default}} {\thefield{entrytype}}} ...

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# Implicit Differentiation

#### spoc21

[FONT=&quot]Use implicit differentiation to find [/FONT][FONT=&quot]dy/dx for xy2 - yx2 = 3xy.

My working:[/FONT]
$$\displaystyle x.(2y.dy/dx)+y^2(1)-y(2x)+dy/dx(x^2)=3x dy/dx + 3y$$

$$\displaystyle ==> 2xy dy/dx + y^2 - 2xy + dy/dx (x^2) = 3x dy/dx + 3y$$

Now Im very confused. Do we need to divide both sides, in order to separate dy/dx? Any helpful tips/suggestions would be appreciated

Thanks!
[FONT=&quot]
[/FONT]

Last edited by a moderator:

#### Silver

So $$\displaystyle xy^2 - x^2y = 3xy$$

Your working looks right although it's a little messy and I think youre dropping a sign somewhere so allow me:

$$\displaystyle y^2 + 2xy\frac{dy}{dx} - x^2\frac{dy}{dx} - 2xy = 3x\frac{dy}{dx} + 3y$$

If we throw $$\displaystyle \frac{dy}{dx}$$'s to one side and the rest to the other side:

$$\displaystyle y^2 - 2xy - 3y = 3x\frac{dy}{dx} - 2xy\frac{dy}{dx} + x^2\frac{dy}{dx}$$

Take out $$\displaystyle \frac{dy}{dx}$$ as factor on RHS

$$\displaystyle y^2 - 2xy - 3y = \frac{dy}{dx} (3x - 2xy + x^2)$$

Divide both sides by $$\displaystyle (3x - 2xy + x^2)$$ and you end up with:

$$\displaystyle \frac{y^2 - 2xy - 3y}{3x - 2xy + x^2} = \frac{dy}{dx}$$

#### spoc21

So $$\displaystyle xy^2 - x^2y = 3xy$$
Im sorry, I didn't type the question in proper notation. it's actually:
$$\displaystyle xy^2-yx^2=3xy$$

Thanks!

#### Silver

Im sorry, I didn't type the question in proper notation. it's actually:
$$\displaystyle xy^2-yx^2=3xy$$

Thanks!
It shouldn't make a difference

#### spoc21

$$\displaystyle y^2 + 2xy\frac{dy}{dx} - x^2\frac{dy}{dx} - 2xy = 3x\frac{dy}{dx} + 3y$$
I actually got $$\displaystyle + x^2\frac{dy}{dx}$$, using the product rule/chain rule of derivative.

is mine incorrect?

#### Silver

That was the sign I mentioned you dropped earlier.

Look at it this way:

$$\displaystyle xy^2 - x^2y = 3xy$$

$$\displaystyle (y^2 + 2xy\frac{dy}{dx}) - (x^2\frac{dy}{dx} + 2xy) = 3x\frac{dy}{dx} + 3y$$

$$\displaystyle y^2 + 2xy\frac{dy}{dx} - x^2\frac{dy}{dx} - 2xy = 3x\frac{dy}{dx} + 3y$$

Does that make sense?

spoc21

#### spoc21

yes, makes perfect sense, Thank you!


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# Exponent of an exponent?

If I have an expression that gives 2^3^4, would I compute this as $(2^3)^4$ or as $2^{(3^4)}$? The two answers are wildly different.

My TI gives the former but Wolfram gives the latter and I don't know which to trust more on math. I also tried reading up in textbooks on the Laws of Exponents, but I could not find the case A^B^C in any of the textbooks I can access...

EDIT: This was found as an example in a CompSci textbook, thus the notation as it was.

• en.wikipedia.org/wiki/Operator_associativity says : an exponentiation operator (if present) is right-associative – lab bhattacharjee Sep 1 '15 at 16:16
• – JuliusL33t Sep 1 '15 at 16:16
• Generally, we don't write $2\hat{\phantom:}3\hat{\phantom:}4$. We write $2^{3^4}$. And that means $2^{(3^4)}$ unambiguously. – Akiva Weinberger Sep 1 '15 at 18:54

Conventionally $a^{b^c}$ means $a^{(b^c)}$.

The other way of parsing it, $(a^b)^c$, yields a result equal to $a^{bc}$. In particular $(2^3)^4 = 2^{3\times 4} = 2^{12} = 4096$.

• Thank you, I actually had written it the way I did, though, because that was how it had been presented to me in my programming textbook. I was pretty sure it was the conventional format, but couldn't find precedent. – Falconic Katadora Sep 1 '15 at 18:02
• If it's in a programming language, you need to find out whether the ^ operator in that language is left-associative (x^y^z = (x^y)^z) or right-associative (x^y^z = x^(y^z)). Math doesn't use ^ as the exponentiation operator. – Joe Sep 2 '15 at 6:57
• Funny that this answer is the accepted one when it actually doesn't answer the question, which is about a^b^c. – Yves Daoust Sep 2 '15 at 9:39

There are a number of type-setting situations with algebraic expressions that cause problems when you try to enter them into a one-line input calculator.

For example $$\frac{2+3}{4+5}$$must be entered into a calculator as $$(2+3)/(4+5)$$The horizontal line in the fraction implies brackets around the expression in the numerator and denominator.

Similarly, the expression$$\sqrt{2+5}$$must be entered on my Casio as$$\sqrt{}(2+5)$$Here the horizontal line above the expression shows what expression is to be included in the root; the brackets in the second version do the same thing for the calculator.

Finally, if an exponent is itself an expression, that typesetting defines exactly what is in the exponent; if you can't enter the typesetting directly, you need to supply the missing information.$$2^{3^4}$$should be entered into a calculator as $$\text{2 ^ ( 3 ^ 4 )}$$

Note that when you enter 2 ^ 3 ^ 4 into Wolfram Alpha, it back translates the expression into the typeset version and then evaluates that expression correctly

In standard mathematics the notation $A \mathrel{^\wedge} B$ is not used; one does $A^B$ instead.

In some computer science (programming) applications the infix circumflex operator notation $A \mathrel{^\wedge} B$ is used (or rather the ASCII version A^B). What you point out is that this operator $\mathrel{^\wedge}$ is not associative.

So does $A \mathrel{^\wedge} B \mathrel{^\wedge} C$ mean $A \mathrel{^\wedge} (B \mathrel{^\wedge} C)$ (that is $A^{B^C}$) or $(A \mathrel{^\wedge} B) \mathrel{^\wedge} C$ (which is $(A^B)^C$)? Well, that depends on the language! For example in PARI/GP and Wolfram Alpha it would be the former, while in Visual Basic .NET and some calculators it would be the latter.

So if you are writing a computer program, find out what convention the programming language in question uses. If you are writing for a human reader, avoid $A \mathrel{^\wedge} B \mathrel{^\wedge} C$ without parenthesis because it can be ambiguous.

For similar reasons, avoid $A/B/C$ and use either $A/(B/C)$ or $(A/B)/C$. Of course, whenever it is technically possible, use "real" mathematical notation like $\frac{A}{\frac{B}{C}}$ or $\frac{\frac{A}{B}}{C}$.

PS! Out of curiosity, was the textbook using a particular programming language?

Addition: In the Java programming language, A^B is not exponentiation but instead bitwise exclusive OR (bitwise XOR). See What does the ^ operator do in Java? Since this operation is associative, A^(B^C) == (A^B)^C for XOR, there will usually not be an issue here.

• Java, it's for my Data Structures class. My professor is flabbergasted as well. – Falconic Katadora Sep 2 '15 at 1:31
• @FalconicKatadora Java?! But Java uses ^ for another purpose, so your question is not really relevant there. See updated answer above. – Jeppe Stig Nielsen Sep 2 '15 at 9:27
• It's in the textbook, not in a code snippet though. – Falconic Katadora Sep 2 '15 at 11:57
• @FalconicKatadora What is the context in the book? Why would they use ^ notation for exponentiation in a textbook on Java? – Jeppe Stig Nielsen Sep 2 '15 at 12:14
• It is in reference to infix/polish/RPN. Other than that I have no clue as to why this author would do such... This author has been known to make really odd choices in his code too though. – Falconic Katadora Sep 3 '15 at 12:56


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# portfolio optimization with uncertain returns

What is the usual method of dealing with many uncertain mean returns in portfolio optimization?

For example say you have a 3 asset portfolio with assets A, B and C. All the correlations and variances are the same.

You can't reject the null that the assets have the same mean return for (A and B) and (B and C), but you can reject the null for (A and C).

It seems there is no nonbiased way to choose the means?

Your question accurately addresses of the practical problems of applying Modern Portfolio Theory (i.e. mean-variance optimization) in practice.

Generally the correlations are considered much more difficult to accurately estimate in this context.

I am not sure I understand the question. Isn't $E(r)$ is an unbiased estimator of $r$?

You may want to look at the Black-Litterman model. It is an optimization model developed to address the practical problems in applying portfolio optimization.

A simple way that Ray Dalio suggested is using Risk-Parity portfolio. Even though Modern Portfolio Theory with mean-variance optimization gives great framework for mathematically designing a tradeoff between alpha, risk and costs, some of the drawback of this framework is that one needs to come up with 1) correct alpha and 2) correct estimation of covariance matrix.

Assuming our estimate of covariance matrix is relatively stable, then the only problem that we'd need to deal with is Alpha.

You can have a look at risk-parity optimization where you can set 1) risk contribution of each asset is equal (equal risk contribution optimization) 2) marginal risk contribution of each asset is equal.

In these framework, it removes alpha from your utility function and let the optimizer to choose the optimal portfolio only using historical available data (historical realized volatility). This may not be optimal in realizing the best sharpe, however, it could be a good alternative to the approach that you are taking if you are unsure of your alpha estimation.


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# Integration Help Please

Printable View

• December 3rd 2008, 06:43 PM
skyslimit
Integration Help Please
Can anyone help integrate. Can this be done only by taking the integration into parts??

integral
$t^2e^(-2t)$
• December 3rd 2008, 06:44 PM
vincisonfire
Yes, you should use integration by part.
$*\int t^2e^{-2t} = \frac{-t^2 e^{-2t}}{2} -\int -te^{-2t} =\frac{-t^2 e^{-2t}}{2} +\int te^{-2t}$

$\frac{-t^2 e^{-2t}}{2} +\int te^{-2t}=\frac{-t^2 e^{-2t}}{2} +\frac{-te^{-2t}}{2} + \int \frac{e^{-2t}}{2}$

$=\frac{-t^2 e^{-2t}}{2} +\frac{-te^{-2t}}{2} + \frac{-e^{-2t}}{4}$