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# How to find the probability of extra Sundays in a leap year?

What is the chance that a leap year will have 53 Sundays?

As per my trial, will it be 2/7? Since 366 days in a leap year means 52 weeks and 2 more days, so from the extra two days, the probability of Sunday is 2/7.

P.S : This was a question I found in a basic statistics book.

• 1. You say "non-leap year" in your first paragraph but your second paragraph clearly discusses leap-years (which have 366 days - contradicting the first paragraph). Please clarify your question. (You should also make clear how this question arises; is it related to coursework, for example? If not, how does it arise?) Feb 19 '17 at 6:31
• 2. Occurence of Sundays isn't a random process. Any given year will have an exact unvarying number of Sundays which is known before you observe the year. For the question to make any sense as a probability question you'd need to posit random selection of years (which you don't make any mention of), but to get anywhere we'd need to understand how years are being selected and from which notional population (the present calendar has only been around a few hundred years; the actual number of years in that with 53 Sundays probably isn't quite 2/7. Again, please clarify the nature of your question. Feb 19 '17 at 6:36
• Hello, glen_b , thanks for identifying my mistake while typing. Yes the question is for leap years only. I have edited the question as well Feb 19 '17 at 7:12
• Thanks for responding to my point 1. I've added the self-study tag -- see the comments in the help center on routine-bookwork problems (discussed under homework there but it applies to any textbook problem like this). There's additional clarification really needed in relation to point 2 (relating to what the assumed population is and the sampling model), though if you directly quote the original question the required clarification might then shift to a necessary assumption for an answer. Feb 19 '17 at 8:54

## 2 Answers

The Gregorian calendar favors five of the seven weekdays during leap years. Therefore the chance is not precisely $2/7$.

This was essentially problem B3 in the 1950 Putnam Mathematics Competition:

$n$ is chosen at random from the natural numbers. Show that the probability that December 25 in year $n$ is a Wednesday is not 1/7.

In the Gregorian Calendar, years that are multiples of $4$ are leap years (with $7\times 52 + 2=366$ days), but years that are multiples of $100$ are not leap years (and therefore have $7\times 52+1=365$ days), with the exception that years that are multiples of $400$ are leap years. (Many of us remember the most recent exception in $2000$.) This creates a $400$ year cycle containing $400/4 - 400/100 + 400/400 = 97$ leap years.

What is especially interesting is that the total number of days in this cycle is a whole multiple of seven:

$$400 \times (7\times 52 + 1) + 97 \times 1 \equiv 400+97 \equiv 71 \times 7 \equiv 0 \operatorname{mod} 7.$$

This shows that the $400$ year cycle comprises a whole number of weeks. Consequently, the pattern of days of the week is exactly the same from one cycle to the next.

We may therefore interpret the question as asking for the chance of $53$ Sundays when sampling randomly and uniformly from any $400$-year cycle of leap years. A brute-force calculation (using, say, the fact that January 1, 2001, was a Monday) shows that $28$ of the $97$ leap years in each cycle have $53$ Sundays. Therefore the chance is

$$\Pr(53\text{ Sundays}) = \frac{28}{97}.$$

Note that this does not equal $28/98 = 2/7$: it is slightly greater. Incidentally, there is the same chance of $53$ Wednesdays, Fridays, Saturdays, or Mondays and only a $27/97$ chance of $53$ Tuesdays or Thursdays.

For those who would like to make more detailed calculations (and might mistrust any mathematical simplifications), here is brute-force code that computes and examines ever day of the week for a given set of years. At the end it displays the number of years with $53$ appearances of each day of the week. It is written in R.

Here is its output for the $2001-2400$ cycle:

Friday    Monday  Saturday    Sunday  Thursday   Tuesday Wednesday
28        28        28        28        27        27        28

Here is the code itself.

leapyear <- function(y) {
(y %% 4 == 0 & !(y%% 100 == 0)) | (y %% 400 == 0)
}
leapyears <- seq(2001, length.out=400)
leapyears <- leapyears[leapyear(leapyears)]
results <- sapply(leapyears, function(y) {
table(weekdays(seq.Date(as.Date(paste0(y, "-01-01")), by="1 day", length.out=366)))
})
rowSums(results==53)

• To my mind, this shows exactly the sort of care that's required to make any sense of the question at all. Without a defined population and some random process of selecting years from it, it doesn't even make sense to talk about probability in relation to the number of Sundays in a year; I think the "2/7" (that the author of the question presumably wanted) is not readily defensible as an answer - as soon as you try,to make that work, all sorts of problems become apparent and one has to shoehorn in an artificial restriction on the considered period that's not in the question. Feb 20 '17 at 2:22

Yes, your reasoning is correct. In the long run, leap years are nearly equally likely to start on any day of the week. So the chance of the 2 extra days including a Sunday is about 2/7.

w huber points out that a quirk of the Gregorian Calendar causes the starting day of a leap year to be not quite uniformly distributed, so the true probability of 53 Sundays is 1% or so greater than 2/7. However 2/7 is almost certainly the answer that the authors of your statistics textbook intended you to find.

• To be correct, this answer requires some very specific assumptions: exactly what range of years do you have in mind? For most ranges, $2/7$ will not be the right answer.
– whuber
Feb 19 '17 at 14:48
• @w huber I have no doubt that 2/7 is the answer that was intended by the authors of the textbook that the question is from. The finessing in your answer is correct and interesting but, I would argue, doesn't help the OP learn basic statistics. Feb 19 '17 at 22:50
• I agree with most of that, especially with not helping to learn statistics--but that criticism should be leveled at the textbook, not at the solution to its exercise. What might be of especial interest here is to illustrate the process of analyzing a question--even a textbook question--and to show that sometimes the intuitively "obvious" answer is not quite correct. Surprises like this teach us much. Moreover, sometimes large consequences follow from tiny differences. (I'm working on a case now where a difference of this size changes a legal claim by a million dollars.)
– whuber
Feb 19 '17 at 23:29
• No criticism intended. Personally I'm happy with both the textbook question and with your excellent and unexpected solution. Feb 20 '17 at 3:22


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# Ampère's force law

Two current-carrying wires attract each other magnetically: The bottom wire has current I1, which creates magnetic field B1. The top wire carries a current I2 through the magnetic field B1, so (by the Lorentz force) the wire experiences a force F12. (Not shown is the simultaneous process where the top wire makes a magnetic field which results in a force on the bottom wire.)

In magnetostatics, the force of attraction or repulsion between two current-carrying wires (see first figure below) is often called Ampère's force law. The physical origin of this force is that each wire generates a magnetic field, following the Biot–Savart law, and the other wire experiences a magnetic force as a consequence, following the Lorentz force law.

## Equation

### Special case: Two straight parallel wires

The best-known and simplest example of Ampère's force law, which underlies the definition of the ampere, the SI unit of current, states that the force per unit length between two straight parallel conductors is

${\displaystyle {\frac {F_{m}}{L}}=2k_{A}{\frac {I_{1}I_{2}}{r}}}$,

where kA is the magnetic force constant from the Biot–Savart law, Fm/L is the total force on either wire per unit length of the shorter (the longer is approximated as infinitely long relative to the shorter), r is the distance between the two wires, and I1, I2 are the direct currents carried by the wires.

This is a good approximation if one wire is sufficiently longer than the other that it can be approximated as infinitely long, and if the distance between the wires is small compared to their lengths (so that the one infinite-wire approximation holds), but large compared to their diameters (so that they may also be approximated as infinitely thin lines). The value of kA depends upon the system of units chosen, and the value of kA decides how large the unit of current will be. In the SI system,[1] [2]

${\displaystyle k_{A}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ {\frac {\mu _{0}}{4\pi }}}$

with μ0 the magnetic constant, defined in SI units as[3][4]

${\displaystyle \mu _{0}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ 4\pi \times 10^{-7}}$ N / A2.

Thus, in vacuum,

the force per meter of length between two parallel conductors – spaced apart by 1 m and each carrying a current of 1 A – is exactly
${\displaystyle \displaystyle 2\times 10^{-7}}$ N / m.

### General case

The general formulation of the magnetic force for arbitrary geometries is based on iterated line integrals and combines the Biot–Savart law and Lorentz force in one equation as shown below.[5][6][7]

${\displaystyle {\vec {F}}_{12}={\frac {\mu _{0}}{4\pi }}\int _{L_{1}}\int _{L_{2}}{\frac {I_{1}d{\vec {\ell }}_{1}\ \mathbf {\times } \ (I_{2}d{\vec {\ell }}_{2}\ \mathbf {\times } \ {\hat {\mathbf {r} }}_{21})}{|r|^{2}}}}$,

where

• ${\displaystyle {\vec {F}}_{12}}$ is the total magnetic force felt by wire 1 due to wire 2 (usually measured in newtons),
• I1 and I2 are the currents running through wires 1 and 2, respectively (usually measured in amperes),
• The double line integration sums the force upon each element of wire 1 due to the magnetic field of each element of wire 2,
• ${\displaystyle d{\vec {\ell }}_{1}}$ and ${\displaystyle d{\vec {\ell }}_{2}}$ are infinitesimal vectors associated with wire 1 and wire 2 respectively (usually measured in metres); see line integral for a detailed definition,
• The vector ${\displaystyle {\hat {\mathbf {r} }}_{21}}$ is the unit vector pointing from the differential element on wire 2 towards the differential element on wire 1, and |r| is the distance separating these elements,
• The multiplication × is a vector cross product,
• The sign of In is relative to the orientation ${\displaystyle d{\vec {\ell }}_{n}}$ (for example, if ${\displaystyle d{\vec {\ell }}_{1}}$ points in the direction of conventional current, then I1>0).

To determine the force between wires in a material medium, the magnetic constant is replaced by the actual permeability of the medium.

By expanding the vector triple product and applying Stokes' theorem, the law can be rewritten in the following equivalent way:[8]

${\displaystyle {\vec {F}}_{12}=-{\frac {\mu _{0}}{4\pi }}\int _{L_{1}}\int _{L_{2}}{\frac {(I_{1}d{\vec {\ell }}_{1}\ \mathbf {\cdot } \ I_{2}d{\vec {\ell }}_{2})\ {\hat {\mathbf {r} }}_{21}}{|r|^{2}}}.}$

In this form, it is immediately obvious that the force on wire 1 due to wire 2 is equal and opposite the force on wire 2 due to wire 1, in accordance with Newton's 3rd law.

Other Languages
azərbaycanca: Amper qanunu
беларуская: Сіла Ампера
français: Force d'Ampère
Հայերեն: Ամպերի օրենք
latviešu: Ampēra spēks
македонски: Амперова сила
oʻzbekcha/ўзбекча: Amper qonuni
русский: Закон Ампера
татарча/tatarça: Ампер кануны
українська: Закон Ампера

format: plain


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# Research articles for the 2019-03-27

Appendix To 'Public Liquidity and Financial Crises'
Li, Wenhao
SSRN
This is the Appendix of the paper "Public Liquidity and Financial Crises", https://ssrn.com/abstract=3175101.

Assessment of Intellectual Capital Influence on Corporate Value as a Field for Further Investigations in Corporate Finance
Feruleva, Natalia,Ivashkovskaya, Irina
SSRN
In this paper we are going to review both theoretical studies in the field of intellectual capital measurement and empirical research, devoted to analyses of intellectual capital influence on companiesâ€™ value and financial performance. As a result, potential areas for further investigations in this field were revealed.Considering groups of intellectual capital measurement methods, we identified that direct intellectual capital methods and scorecard methods are the most appropriate for the purpose of IC components measurement. To obtain objective results of measurement it seems reasonable to develop system of proxy indicators for all intellectual capital components (human, structural and relational capitals) and subcomponents (process and innovation, client and network capitals). Basing on existing literature, we make an attempt to identify and systemize indicators, associated with intellectual capital and reveal that network capital metrics remain under-researched and deserve closer examination. It was also found that investigators should develop the system of intellectual capital indicators, taking into account industry specificity. As for empirical studies, in order to investigate the influence of intellectual capital on corporate value and financial performance, it seems reasonable to elaborate models, which include factors, associated with all intellectual capital components and subcomponents and, what is just as important, their interrelations. Furthermore, it is vital to investigate the relationships between the values of IC components for companies. The models should be adopted for both developed and developing countries. It is also important to analyze the influence of intellectual capital in various industries separately, taking into consideration phase of economic cycle.

Bank Regulatory Reforms and Institutional Equity Holdings
Bowe, Michael,Kolokolova, Olga,Michalski, Marcin
SSRN
This paper examines the effects of changes in bank regulatory environment on the risk, return, and liquidity characteristics of equity portfolios of U.S. bank holding companies between 1997 and 2016. Using a comprehensive sample of bank and hedge fund holdings data we examine the impact of the repeal of the Glass-Steagall Act, the introduction of the second and third Basel Capital Accords, and the implementation of the Dodd-Frank legislation on institutional portfolios. We document a significant increase in both the idiosyncratic volatility and illiquidity of banks' portfolios during the period of financial deregulation initiated by the formal removal of restrictions prohibiting banks from engaging in securities trading. In contrast, subsequent reforms of the bank capital requirements system and the prohibition of banks from proprietary trading activities lead to reductions in those metrics. Our results suggest that banks' restricted ability to engage in market-making can be offset by the activities of hedge funds, although the consequences of this substitution for long-term market stability remain unclear.

Calidad de la informaciÃ³n contable y el acceso al endeudamiento en BolÃvar (Accounting Quality and Debt Access in Bolivar)
SSRN

Capital Structure Choice Under Asymmetric Information and Overconfident Managers
Ji, Xiehua,Miglo, Anton
SSRN
Traditional pecking-order theory (POT) cannot explain why good-quality firms issue equity: this is often considered to be an empirical puzzle. We build a model of capital structure that has elements of both asymmetric information and behavioral finance. Firms have private information about their expected performance. The model also includes overconfident managers. Our model predicts that high-quality firms may issue equity in equilibrium, which contrasts the results in Fairchild (2005). Unlike in Fairchild (2005), managers are not equally overconfident and no exogenously given bankruptcy costs exist in our model. We test our model using a large set of data from the U.S. market and find strong empirical support.

Derivative of a Conic Problem with a Unique Solution
Enzo Busseti
arXiv

We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized residual function of [Busseti et al., 2018], the problem solution map is differentiable. We obtain the derivative, in the form of an abstract linear operator. This applies to any convex optimization problem in conic form, while a previous result [Amos et al., 2016] studied strictly convex quadratic programs. Such differentiable problems can be used, for example, in machine learning, control, and related areas, as a layer in an end-to-end learning and control procedure, for backpropagation. We accompany this note with a lightweight Python implementation which can handle problems with the cone constraints commonly used in practice.

Determinants of Financial Inclusion: New Evidence from Panel Data Analysis
Chu Khanh, Lan,Nguyen, Minh Phuong ,truong, huong
SSRN
We find evidence that favorable socioeconomic conditions in terms of income, financial development, institutional quality, population growth rate, and human development foster the development of inclusive finance. There are differences in the determinants of financial inclusion as well as its three dimensions between country groups.

Determining the Demand Elasticity in a Wholesale Electricity Market
Sergei Kulakov,Florian Ziel
arXiv

The main focus of researchers in energy markets is typically placed on the analysis of the supply side. The demand side, despite its critical importance, still requires a more profound academic investigation. In particular, the number of studies on the demand elasticity in a wholesale market is limited to merely several pieces. In this paper we extend this field of study and propose a new method for determining the demand elasticity. More specifically, we decompose the data observed in the wholesale market into individual supply and demand schedules of the market participants. These schedules are then used to construct a fundamental model of an electricity market. The main feature of our fundamental model is that our demand curve is not perfectly inelastic and is a better approximation of the true demand curve. Hence, our approach allows us to precisely compute the elasticity of the demand curve in an electricity market. Moreover, we obtain a deeper understanding of the bidding behavior of the market participants and hence can make more thorough inferences about the functioning of an electricity market or produce more accurate forecasts.

Do Mutual Funds Trade on Earnings News? The Information Content of Large Active Trades
Chen, Linda H.,Huang, Wei,Jiang, George J.
SSRN
Using monthly holdings data, we show that while mutual funds generally trade in the direction of earnings surprises, mutual fund trades in aggregate do not have predictive power for future earnings once we control for past firm performance and stock returns. We identify active trades by mutual funds, i.e., trades not passively driven by fund flows, and find that large active trades by mutual funds contain information on future earnings. Moreover, we show that large active mutual fund trades not only significantly increase market responses to earnings announcements but also help incorporate future earnings information into current stock prices. Furthermore, we show that large active mutual fund trades prior to earnings announcements have superior abnormal returns. Finally, we show evidence that mutual fund managers that actively trade on future earnings news are skilled; the top quintile skilled funds on average outperform those in the bottom quintile by 127 bps in four-factor alpha over the subsequent four quarters.

Does Reputational Capital Affect Credit Rating Agencies?: Empirical Evidence from a Natural Experiment in China
Xu, Wenming,Liu, Yan
SSRN
The subprime crisis of 2007-2008 has led major economics to reform their credit rating regulation. This paper employs a shock-based difference-in-difference research design and tests an implicit hypothesis of the gatekeeper theory supporting such reforms that reputational capital affects credit rating agencies in the Chinaâ€™s debt market. The first market-oriented evaluation in the inter-bank bond market is chosen as the source of the exogenous reputational shock. Using the Medium Term Notes (MTNs) rated by China Chengxin International Credit Rating as benchmarks, we identify a causal relationship that the average yield spread of MTNs rated by China Lianhe Credit Rating increases for around 0.230%-0.361% due to the decrease in its reputational capital. Our research provides favorable evidence to the recent reform measures that aim at increasing the disciplinary power of reputational capital.

Dynamic Optimal Restructuring Policies Under Debt Renegotiation with Positive Externalities
Tan, Yingxian,Luo, Pengfei,Yang, Jinqiang,Ling, Aifan
SSRN
This paper develops a debt renegotiation model with positive externalities by using Nash bargaining game and explores dynamic optimal downward debt restructure policies in financial distress. A novel feature of our model is the positive externalities, which imply that liquidation threat offered by the shareholders for renegotiation does not bring about any losses for both creditors and shareholders, and that the two parties always benefit from the debt renegotiation. We derive the closed-form expressions for optimal restructure policies. Moreover, we provide theoretical support for the advantages of debt renegotiation with positive externalites since it not only increases firms' value but also dramatically alleviates and even fully eliminates the inefficiency arising from asset substitution. In addition, our model may explain the violation of the absolute priority rule for firms in financial distress. Finally, we discover that firms with a relatively lower risk and larger leverage ratio are more easier to proceed to debt renegotiation, which are documented by empirical evidences.

Entangled in Cryptoassetsâ€™ Legal Nature and Governance: Searching for Clear Boundaries or Working for their Removal?
Zatti, Filippo
SSRN
The increase in the number of disputes before courts and regulatory authorities requires legal scholars to finally question the legal nature of cryptoassets. The few legislative frameworks already in force show the limits of a state-based regulation addressed both to captivate the FinTech industry through the â€˜intangible assetâ€™ of legal certainty and to avoid stifling the development of distributed ledger technology (DLT) and blockchains. However, these aims can conflict with regulatory capital market objectives, especially with market integrity and investor protection. â€˜Exchange platformsâ€™ and initial coin offerings can cause fraud and scams. Currently, these concepts affect â€˜onlyâ€™ private and commercial law, but what will happen when public law dimension is also affected? It is likely that the wait to find out will not be long if we consider the emergence of securities tokenization. Thus, the time has come to decide whether to clarify the legal boundaries between cryptoassets and fiat money, securities and commodities or to use this new technology to have more efficient and less costly financial markets by removing the legal border between crypto space and the â€˜physical world economyâ€™. Considering this aspect, the involvement of international organizations should be encouraged.

Financial Regulation: Its Objectives and Their Implementation in the European Union
Wymeersch, Eddy
SSRN
On the basis of an analysis of the objectives of financial regulation, this paper analyses the extent to which these principles are implemented in the European Union, considering the specific legal structure of its financial regulation and the implementation by national competent authorities. The resulting landscape is one of considerable diversity and complexity, creating inefficiencies and distortions. The effect of this diversity on the integration of the financial markets should not been underestimated. The European Supervisory Authorities or ESA make serious efforts to reduce the level of diversity, but more in-depth exercises are needed.

Fiscal Multipliers and Foreign Holdings of Public Debt
Broner, Fernando,Clancy, Daragh,Erce, Aitor,Martin, Alberto
SSRN
This paper explores a natural connection between fiscal multipliers and foreign holdings of public debt. Although fiscal expansions can raise domestic economic activity through various channels, they can also have crowding-out effects if the resources used to acquire public debt reduce domestic consumption and investment. These crowding-out effects are likely to be weaker when governments have access to foreign markets to place their debt, increasing the size of multipliers. We test this hypothesis on (i) post-war US data and (ii) data for a panel of 17 advanced economies from the 1980's to the present. To do so, we assemble a novel database of public debt holdings by domestic and foreign creditors for a large set of advanced economies. We combine this data with standard measures of fiscal policy shocks and show that, indeed, the size of fiscal multipliers is increasing in the share of public debt held by foreigners. In particular, the fiscal multiplier is smaller than one when the foreign share is low, such as in the U.S. in the 1950's and 1960's and Japan today, and larger than one when the foreign share is high, such as in the U.S. and Ireland today.

Forecasting Realized Correlations: A MIDAS Approach
Kostrov, Alexander,Tetereva, Anastasija
SSRN
Mixed data sampling (MIDAS) regression has received much attention in relation to modeling financial time series due to its flexibility. Previous work has mainly focused on forecasting of realized volatilities and has rarely been used to predict realized correlations. This paper considers a MIDAS approach to forecast realized correlation matrices. A MIDAS model is estimated via nonlinear least squares (NLS) using an analytical gradient-based optimization. Based on the model confidence set (MCS) procedure we discover that the introduced approach is superior compared to the established heterogeneous autoregressive (HAR) model in terms of out-of-sample forecasting accuracy. This preeminence is due to the flexible data-driven origin of the MIDAS model. The latter results in higher economic value with regard to portfolio management applications. The improvement is considerable for longer forecasting horizons both in calm times and during the periods of market turbulence.

Foreign Shareholders and Corporate Governance in Japan
Iida, Hidefusa
SSRN
Shareholders are one of the most critical players in corporate governance. Contrary to the stereotypical understanding of Japanese companies, widely held equity ownership and foreign investors constituting the largest investor category are commonly observed in large Japanese companies. Given this shareholding structure, foreign shareholders have a potentially significant influence on corporate governance in Japan; however, their role has rarely been analyzed from the perspective of corporate law. This paper argues that the current legal environment is at the halfway point in its attempt to get the most out of their potential influence. The aggressive shareholder activism by foreign investors has faced the skeptical attitude of not only the target companyâ€™s management, but also the government and the courts. Although the recent reform in corporate governance led by the government is bringing about a change in the business environment, it is too early to conclude that it will eliminate the resistance against shareholdersâ€™ activism. This paper argues that the law should prepare the environment to support mild shareholder engagement by relatively passive investors, such as those encouraging the collaboration among institutional investors.

Foreign and Domestic Loans over the Business Cycle
SSRN
During good economic times, domestic firmsâ€™ probability of obtaining loans from foreign banks increases in the firmâ€™s opacity. During downturns in the domestic economy, this relation reverses as the probability of obtaining a foreign loan decreases for all firms, but drops disproportionately for opaque borrowers. Firms that are in closer proximity to foreign banks by some measure (such as firms with a higher share of foreign sales) are always more likely to obtain foreign loans due to lower transaction costs. We derive these predictions in a formal theoretical framework and confirm them empirically using a loan-bank-firm level dataset covering forty countries during the 1999â€"2016 period.

Is Too Much Liquidity Harmful to Economic Growth?
Chu Khanh, Lan,Chu, Hung
SSRN
This paper provides evidence on the relationship between financial liquidity and economic growth. Using a panel data of 136 countries, we find that there exists a threshold above which the marginal effect of financial liquidity on economic growth becomes negative. In particular, the turning points for which domestic credit to private sector and stock market turnover start having negative effect on growth are 104% GDP and 105% respectively. Our results are robust to country income level groups, alternative model specifications, proxies for financial liquidity, and are not driven by macroeconomic volatility, banking crises, stock market crashes.

Large Shareholders and Financial Distress
Opp, Christian C.
SSRN
I examine large shareholders' externalities on other claim holders when firms are financially distressed. To this end, I develop a tractable dynamic model of the interplay between these blockholders and regular equity holders. Blockholders' information acquisition and investment decisions play a pivotal role in distressed firms' access to finance, affecting both total firm value and its distribution across claims. The impact on distress costs is non-monotone; whereas blockholders' information exacerbates debt overhang for intermediate levels of distress, it increases firms' survival chances in deep distress. These findings reveal that frictions delaying block acquisitions to "last minute" rescue interventions can in fact be efficiency-enhancing.

Loss Streaks and Turnaround in Private Family and Non-Family Firms
Kettunen, Jukka,Martikainen, Minna,Voulgaris, Georgios
SSRN
This study provides new evidence on family vs. non-family firm long-termism by showing that the loss streaks are longer in family firms compared to non-family firms. Specifically, we study whether family ownership combined with employee retention and patents contributes to the length of loss streaks and on the other hand, successful and sustainable turnaround of declining private firms. Interestingly, we show that this retrenchment strategy helps family firms to achieve a more sustainable turnaround than non-family firms. To test our hypotheses, we use a unique survey-based randomly selected dataset from Finland, an economy with a substantial presence of private family firms. In non-family firms, similar investments do contribute to shorter loss periods, but less sustainable turnaround in non-family firms. Additionally we show that within family firms the long-termism is moderated by ownership concentration. As summary our results are consistent with the notion that family firms are more long-term oriented than non-family firms.

Machine Learning for Pricing American Options in High Dimension
Ludovic Goudenège,Andrea Molent,Antonino Zanette
arXiv

In this paper we propose an efficient method to compute the price of American basket options, based on Machine Learning and Monte Carlo simulations. Specifically, the options we consider are written on a basket of assets, each of them following a Black-Scholes dynamics. The method we propose is a backward dynamic programming algorithm which considers a finite number of uniformly distributed exercise dates. On these dates, the value of the option is computed as the maximum between the exercise value and the continuation value, which is approximated via Gaussian Process Regression. Specifically, we consider a finite number of points, each of them representing the values reached by the underlying at a certain time. First of all, we compute the continuation value only for these points by means of Monte Carlo simulations and then we employ Gaussian Process Regression to approximate the whole continuation value function. Numerical tests show that the algorithm is fast and reliable and it can handle also American options on very large baskets of assets, overcoming the problem of the curse of dimensionality.

Market Dynamics: On Directional Information Derived From (Time, Execution Price, Shares Traded) Transaction Sequences
arXiv

A new approach to obtaining market--directional information, based on a non--stationary solution to the dynamic equation "future price tends to the value that maximizes the number of shares traded per unit time" [1] is presented. In our previous work[2], we established that it is the share execution flow ($I=dV/dt$) and not the share trading volume ($V$) that is the driving force of the market, and that asset prices are much more sensitive to the execution flow $I$ (the dynamic impact) than to the traded volume $V$ (the regular impact). In this paper, an important advancement is achieved: we define the "scalp--price" ${\cal P}$ as the sum of only those price moves that are relevant to market dynamics; the criterion of relevance is a high $I$. Thus, only "follow the market" (and not "little bounce") events are included in ${\cal P}$. Changes in the scalp--price defined this way indicate a market trend change --- not a bear market rally or a bull market sell--off. The software calculating the scalp--price given market observations triples (time, execution price, shares traded) is available from the authors.

Opening the Black Box of Capital Investment: The Roles of Capital Expenditure Budget and Execution
Hilary, Gilles,Ma, Mark (Shuai),Yan, Wenjia
SSRN
In spite of intensive research on capital expenditure efficiency, a firmâ€™s internal investment decision process remains largely a black box. We analyze this process by decomposing it into two stages: budgeting of capital expenditures and execution of the budget. We find that these two stages have different effects on investment efficiency and that accounting quality and board independence affect them differently. Further, while opportunistic managers massively over-execute investment budgets, managers with high ability strategically find a level of execution errors that optimizes their compensation while remaining undetected by boards. These strategic execution deviations entail significant costs for their employers.

Parallel Experimentation in a Competitive Advertising Marketplace
Xiliang Lin,Harikesh S. Nair,Navdeep S. Sahni,Caio Waisman
arXiv

When multiple firms are simultaneously running experiments on a platform, the treatment effects for one firm may depend on the experimentation policies of others. This paper presents a set of causal estimands that are relevant to such an environment. We also present an experimental design that is suitable for facilitating experimentation across multiple competitors in such an environment. Together, these can be used by a platform to run experiments "as a service," on behalf of its participating firms. We show that the causal estimands we develop are identified nonparametrically by the variation induced by the design, and present two scalable estimators that help measure them in typical high-dimensional situations. We implement the design on the advertising platform of JD.com, an eCommerce company, which is also a publisher of digital ads in China. We discuss how the design is engineered within the platform's auction-driven ad-allocation system, which is typical of modern, digital advertising marketplaces. Finally, we present results from a parallel experiment involving 16 advertisers and millions of JD.com users. These results showcase the importance of accommodating a role for interactions across experimenters and demonstrates the viability of the framework.

Participation Following Sudden Access
Fuchs-Schundeln, Nicola,Haliassos, Michael
SSRN
This paper employs the German reunification "experiment" to study how sudden access to previously unavailable financial products, supported by knowledgeable practitioners, influences participation. Findings provide new perspectives on participation and inertia. Controlling for characteristics, East Germans experienced a jump in securities participation to a level comparable to West Germans' participation immediately following reunification, and to an even higher level for consumer debt, while exhibiting inertia in previously accessible products. They showed no signs of subsequent retreat. Lower financial resources are the most important characteristic explaining lower East German participations in all asset classes, while expectations and peer effects are important drivers of the high East German debt participation. Average income among the new peers has had larger effects on East than on West German participation in both securities and consumer debt.

Pecking Order Theory for Government Finance
Miglo, Anton
SSRN
In this article we argue that asymmetric information can explain why seignorage is an inferior choice to debt for governments. We also argue that the Ricardian equivalence for governments is very similar to what the Modigliani-Miller proposition is for corporations. Our model is based on Bolton and Huang (2018) in that money for governments is similar to what equity is for corporations. In contrast to their model, our model considers rational economic agents.

Political Ties and Capital Raising in Global Markets: Evidence from Yankee Bonds
Ambrocio, Gene,Gu, Xian,Hasan, Iftekhar
SSRN
This paper examines whether state-to-state political ties help to obtain better terms when raising capital in global capital markets. Focusing on publicly issued Yankee bonds, we observe that firms from countries with close political ties to the US have been successful in reducing borrowing costs. Specifically, a one-standard-deviation improvement in such ties can lead to a 5 to 14 percent reduction in at-issue yield spreads. Such an association is more pronounced for firms located in countries that are highly indebted, in government-related industries, and during home-country recessions. Our study sheds lights on the importance of country-level political relationships in international fund-raising.

Regulating Algorithmic Insurance
Swedloff, Rick
SSRN

Stress Testing Household Balance Sheets in Luxembourg
Giordana, GastÃ³n,Ziegelmeyer, Michael
SSRN
This paper uses representative individual household data from Luxembourg to evaluate how severe economic conditions could affect bank exposure to the household sector. Information on household income, expenses and liquid assets are used to calculate household-specific probabilities of default (PD), aggregate bank exposure at default (EAD) and aggregate bank loss given default (LGD). The exercise is repeated with scenarios combining severe but plausible shocks to real estate prices, bonds and stocks, household income and interest rates. Compared to the no-shock baseline, the LGD rises by a multiple of eight, reaching 4.2% of total bank exposure to the household sector. The high-stress scenario also generates a relatively high percentage of defaults among socio-economically disadvantaged households. Our main conclusion is that bank losses appear to be quite sensitive to financial stress, despite three mitigating factors in Luxembourg: indebted households tend to hold liquid assets that can help smooth shocks, household leverage tends to decline rapidly once mortgages have been serviced several years, and loan-to-value ratios at origination appear not to be excessive.

Stress Testing Networks: The Case of Central Counterparties
Berner, Richard,Cecchetti, Stephen G.,Schoenholtz, Kermit
SSRN
Stress tests applied to individual institutions are an important tool for evaluating financial resilience. However, financial systems are typically complex, heterogeneous and rapidly changing, raising questions about the adequacy of conventional tests. In this paper, we interpret the current stress test practice from a network perspective, highlighting central counterparties (CCPs) as an example of a critical network hub. Networks that include CCPs involve deep and broad interconnections, making stress testing a challenging task. We propose supplementing both private and supervisory CCP stress tests with a high-frequency indicator constructed from a market-based estimate of the conditional capital shortfall (SRISK) of the CCP's clearing members. Applying our measure to two large CCPs, we analyze how they can transmit and amplify shocks across borders, conditional on the exhaustion of prefunded resources. Our results highlight how the network created by central clearing can act as an important transmission mechanism for shocks emanating from Europe.

The Dark Side of Licensing Cryptocurrency Exchanges as Payment Institutions
Nabilou, Hossein
SSRN
The ultimate objective of cryptocurrencies is to become a payment system substituting, complementing, or competing with the existing conventional fiat-based payment systems. Irrespective of whether such an objective could be accomplished, the functional similarities between certain cryptocurrencies and fiat money has persuaded competent authorities of certain EU Member States to grant payment institution licenses to cryptocurrency exchanges. At first blush, granting such an authorization would seem to be a step forward as it would bring otherwise unregulated cryptocurrency exchanges within the scope of the existing payment regulatory framework. However, such an authorization not only faces major legal challenges related to the definition of a payment institution, but also introduces new lesser-known risks. Aside from the semantic and definitional issues, authorizing cryptocurrency exchanges as payment institutions can bring activities and instruments - with a different risk profile than that of conventional payment instruments - within the scope of payment systems. It appears that such risks embedded in those instruments cannot be fully addressed under the existing payment laws.This paper studies two examples of unattended risks under the cryptocurrency-exchange-as-payment-institution regime. The first risk concerns the use of untethered, non-convertible, illiquid and volatile settlement assets for settlement purposes in cryptocurrency exchanges. The second risk concerns the risks associated with finality of settlements arising from the use of probabilistic finality in some of the most popular cryptocurrency blockchains. Given that in the conventional payment institutions central bank money or commercial bank money is primarily used as the settlement asset, such risks have already been addressed or otherwise taken for granted, however, in cryptocurrency exchanges, the risks involved in the settlement of liabilities with an illiquid and volatile asset relying on probabilistically final settlement mechanism cannot be dealt with by the existing applicable regulations. As the risks cannot be addressed within the current European payment regulation framework, an alternative policy option would be granting a special license to cryptocurrency businesses or introducing ring-fencing mechanism to protect the conventional payment systems from the risks of cryptocurrency payments.

The Effect of Loan Loss Recognition Timeliness in the Banking System on Firmsâ€™ Investment Efficiency
Mengistu, Muhabie Mekonnen,Ng, Jeffrey,Saffar, Walid
SSRN
In this study, we examine whether the timely recognition of loan losses by banks affects firmsâ€™ investment efficiency. The timely recognition of loan losses serves as an early warning mechanism of a bankâ€™s problem loans, which, in turn, triggers earlier scrutiny of the banks by various stakeholders. Such scrutiny increases banksâ€™ incentives to closely monitor and advise client firms about their investment decisions. Using data from over 50 countries across 21 years, we document that more timely recognition of loan losses by banks reduces firmsâ€™ investment inefficiencies (underinvestment and overinvestment). We further find that the reduction in investment inefficiencies is more pronounced in countries with stringent bank supervision, and in firms that are more opaque and have fewer investment opportunities. Finally, using the establishment of public credit registries as a shock to bank monitoring, we provide further support for a causal link between the timely recognition of loan losses and firmsâ€™ investment efficiency. Overall, our study offers new insights by showing that the accounting system used by one party (lenders) can affect the real economic decisions of the other contracting party (borrowers).

The Future of Data-Driven Finance and RegTech: Lessons from EU Big Bang II
Zetzsche, Dirk A.,Arner, Douglas W.,Buckley, Ross P.,Weber, Rolf H.
SSRN
Europeâ€™s path to digitization and datafication in finance has rested upon four apparently unrelated pillars: (1) extensive reporting requirements imposed after the Global Financial Crisis to control systemic risk and change financial sector behavior; (2) strict data protection rules reflecting European cultural concerns about dominant actors in the data processing field; (3) the facilitation of open banking to enhance competition in banking and particularly payments; and (4) a legislative framework for digital identification imposed to further the European Single Market. The paper analyzes these four pillars and suggests that together they will underpin the future of digital financial services in Europe, and â€" together â€" will drive a Big Bang transition to data-driven finance. These seemingly unrelated pillars together bolster an emerging ecosystem which aims to promote a balance among a range of sometimes conflicting objectives, including systemic risk, data security and privacy, efficiency, and customer protection. Furthermore, we argue Europeâ€™s financial services and data protection regulatory reforms have unintentionally driven the use of regulatory technologies (RegTech) by intermediaries, supervisors and regulators, thereby laying the foundations for the digital transformation of both EU financial services and financial regulation. The experiences of Europe in this process provide insights for other societies in developing regulatory approaches to the intersection of data, finance and technology.

The Impact of Gender Quota Laws on Board Composition, Risk Taking and Performance of Banks: International Evidence
Liao, Rose C.,Loureiro, Gilberto R.,Taboada, Alvaro G.
SSRN
We exploit the staggered implementation of laws mandating higher female representation on boards of directors to assess their impact on bank risk taking and performance. Using a sample of 444 banks from 39 countries between 2008 and 2017, we identify several stylized facts. First, we show that quota laws lead to a significant increase in female board representation of about 38% of the sample average. Second, post reform, female directors are generally more likely to be independent, have more executive experience, and tend to serve on more outside boards relative to their male counterparts. Third, we find an increase in bank risk taking post reforms for banks without female directors before the law is passed. Finally, we show that the impact of gender quota laws varies greatly across countries; we document positive effects of quota laws (lower risk taking and improved performance) for banks in countries with a larger female labor force, with lower gender gaps in math scores, and with stronger institutional quality, but find opposite effects in countries with smaller female labor force, higher gender gaps, and weaker institutional quality.

The Impact of Terrorist Attacks in G7 Countries on International Stock Markets and the Role of Investor Sentiment
Papakyriakou, Panayiotis,Sakkas, Athanasios,Taoushianis, Zenon
SSRN
We consider terrorism acts in G7 countries over the period 1998-2017 and examine their impact on a sample of stock market indices from 66 countries. Using an event-study methodology we find that stock markets decline significantly on the event day and on the following trading day. We further consider the investor sentiment following the attacks, based on the content of country-level news stories and social media sources, and find that indices in countries associated with higher declines in the post-event sentiment, exhibit significantly higher economic losses. Our data and results are robust to several settings; these include using samples of events from different studies, excluding the 9/11 terrorist attack from the sample of events, excluding stock market indices of G7 countries from the sample of equity data and utilizing more sophisticated event-study methodologies.

The Long-Run Determinants of Indian Government Bond Yields
Akram, Tanweer,Das, Anupam
SSRN
This paper investigates the long-term determinants of the nominal yields of Indian government bonds (IGBs). It examines whether John Maynard Keynesâ€™ supposition that the short-term interest rate is the key driver of the long-term government bond yield holds over the long run, after controlling for key economic factors. It also appraises if the government fiscal variable has an adverse effect on government bond yields over the long run. The models estimated in this paper show that in India the short-term interest rate is the key driver of the long-term government bond yield over the long run. However, the government debt ratio does not have any discernible adverse effect on IGB yields over the long run. These findings will help policy makers to (i) use information on the current trend of the short-term interest rate and other key macro variables to form their long-term outlook about IGB yields, and (ii) understand the policy implications of the governmentâ€™s fiscal stance.

The Procyclicality of Banking: Evidence from the Euro Area
Huizinga, Harry,Laeven, Luc
SSRN
Loan loss provisions in the euro area are negatively related to GDP growth, i.e., they are procyclical. Loan loss provisions tend to be more procyclical at larger and better capitalized banks. The procyclicality of loan loss provisions can explain about two-thirds of the variation of bank capitalization over the business cycle. We estimate that provisioning procyclicality in the euro area is about twice as large as in other advanced economies. This difference reflects a larger procyclicality of provisioning in euro area countries already prior to euro adoption, and the divergent growth experiences of euro area countries following the global financial crisis.

Jorda, Oscar,Schularick, Moritz,Taylor, Alan M.
SSRN
The risk premium puzzle is worse than you think. Using a new database for the U.S. and 15 other advanced economies from 1870 to the present that includes housing as well as equity returns (to capture the full risky capital portfolio of the representative agent), standard calculations using returns to total wealth and consumption show that: housing returns in the long run are comparable to those of equities, and yet housing returns have lower volatility and lower covariance with consumption growth than equities. The same applies to a weighted total-wealth portfolio, and over a range of horizons. As a result, the implied risk aversion parameters for housing wealth and total wealth are even larger than those for equities, often by a factor of 2 or more. We find that more exotic models cannot resolve these even bigger puzzles, and we see little role for limited participation, idiosyncratic housing risk, transaction costs, or liquidity premiums.

Token Offerings: A Revolution in Corporate Finance?
Momtaz, Paul P.,Rennertseder, Kathrin,SchrÃ¶der, Henning
SSRN
Token offerings or initial coin offerings (ICOs) are smart contracts based on blockchain technology designed to raise external finance without an intermediary. The new technology might herald a revolution in entrepreneurial and corporate finance, with soaring market growth rates over the last two years. This paper surveys the market evolution, offering mechanisms, and token types. Stylized facts on the pricing and long-term performance of ICOs are presented, and practical implications for this young market to thrive are discussed.

Towards hybrid price discrimination via neighbours properties in network-driven economy
Jacopo Arpetti,Antonio Iovanella
arXiv

Increased data gathering capacity, together with the spreading of data analytics techniques, has allowed an unprecedented concentration of information related to the individuals' preferences in the hands of a few gatekeepers. In such context, the traditional economic literature has been attempting to frame all the data-driven economy features. Such features, although being able to bring about a more efficient matching of people and relevant purchase opportunities, also result into distortions and disequilibria, up to market failures. Data-economy market disequilibria can be decrypted by leveraging on some of the known network properties, thus obtaining general results suitable for building a new theoretical framework for economic phenomena. Starting from the hypothesis that a digital company can always benefit from an underlying network of consumers or items related to its market, their representation can indeed provide significant competitive advantages, also enhancing the platforms' capacity to implement discriminatory practices by means of an increased ability to estimate individuals' preferences. In the present paper, we propose a measure called Information Patrimony, considering the amount of information available within the system and we look into how platforms may exploit data stemming from connected profiles within a network, with a view to obtaining competitive advantages. Such information flow may eventually allow to envisage the emergence of a new hybrid price discrimination pattern, through which platforms may influence and steer individuals' purchase choices, as well as to apply different prices to different customers.

Trade Duration Risk in Subdiffusive Financial Models
Torricelli, Lorenzo
SSRN
Subdiffusive processes can be used in finance to explicitly accommodate the presence of random waiting times between trades or ''duration'', which in turn allows the modelling of price staleness effects. Option pricing models based on subdiffusions are incomplete, as they naturally account for the presence of a market risk of trade duration. However, when it comes to pricing this risk matters are quite subtle, since the subdiffusive Levy structure is not maintained under equivalent martingale measure changes unless the price of this risk is set to zero. We argue that this shortcoming can be resolved by introducing the broader class of tempered subdiffusive models. We highlight some additional features of tempered models that are consistent with economic stylized facts, and in particular explain the role of the stability and tempering parameters in capturing the time multiscaling properties of equity prices. Finally, we show that option pricing can be performed using standard integral representations.

When Investors Call for Climate Responsibility, How Do Mutual Funds Respond?
Ceccarelli, Marco,Ramelli, Stefano,Wagner, Alexander F.
SSRN
In April 2018, the investment platform and financial advisor Morningstar introduced a new eco-label for mutual funds, the Low Carbon Designation (LCD). The unexpected release of this label induced responses by (1) investors and (2) mutual funds. First, investors flocked to funds labeled as Low Carbon. Through the end of 2018, such funds enjoyed a 3.1% increase in assets compared to otherwise similar funds. This effect was distinct from that of more generic sustainability ratings ("Globes"), and it reversed for funds that lost the label in August or November 2018. Second, managers of just-missing funds adjusted their holdings towards lower carbon risk and lower fossil fuel involvement, the two criteria used to assign the LCD. Both the rewards-for-LCD and the moving-towards-LCD effects are stronger for European funds, retail funds, funds with weak financial performance, and low-sustainability funds. Overall, the findings suggest that as investors become more sensitive to the topic of climate change, financial intermediaries also use existing investment vehicles to respond to the increasing demand for climate-conscious investment products.

Who Pays a Visit to Brussels? Cross-Border Firm Value Effects of Meetings with European Commissioners
Biguri, Kizkitza,Stahl, Jörg
SSRN
Analyzing novel data on meetings of U.S. company representatives with European Commission officials in Brussels from end 2014 to mid 2018, we find that meetings with European Commissioners are associated with substantial positive abnormal equity returns. We provide insights on the characteristics and lobbying efforts of U.S. companies that seek political access at the European Commission. Our results suggest that access to policy makers at the European Unionâ€™s executive branch is highly valuable for firms. We identify a channel that can explain the positive value effects. Compiling a novel data set on decisions of merger cases at the European Commission, we show that U.S. firms with Commission meetings are significantly more likely to receive a favorable decision than their peers without political access. In addition, we find that U.S. firms with political access disproportionately locate their European subsidiaries in countries that can be considered tax havens. This suggests that these firms have a strong interest in maintaining the current EU tax environment, which benefits multinationals. Our study contributes to the scant literature on political access to the executive branch, and it presents novel evidence on the value of political access in a cross-border setting.

Why Member Firms Hold More Cash When They Have Access to the Business Groupâ€™s Finance Company? Empirical Evidence of Tunneling from China
Peng, Hao,Liu, Hong,Jiang, Yuxiang
SSRN
In China, firms within a business group may be able to access funds provided by a parent-owned finance company within the business group. We provide direct evidence of â€˜tunnelingâ€™: where the parent of the business group requires member firms to increase their cash holdings through deposits in the groupâ€™s finance company and invest the collected deposits in the interbank market or other financial institutions, instead of lending to business group members. The parent of the business group reaps most, if not all, the profits from the finance company, at the expense of member firmsâ€™ increased holding in cash. We use the Shenzhen 2007 Anti-tunneling Guidance as the exogenous shock to identify the main results. Our results cannot be explained by the alternative hypotheses that member firms hold more cash holdings as a result of reduced bank monitoring or the parentâ€™s incentive to reallocate capital more efficiently.

Why understanding multiplex social network structuring processes will help us better understand the evolution of human behavior
Curtis Atkisson,Piotr J. Górski,Matthew O. Jackson,Janusz A. Hołyst,Raissa M. D'Souza
arXiv

Anthropologists have long appreciated that single-layer networks are insufficient descriptions of human interactions---individuals are embedded in complex networks with dependencies. One debate explicitly about this surrounds food sharing. Some argue that failing to find reciprocal food sharing means that some process other than reciprocity must be occurring, whereas others argue for models that allow reciprocity to span domains. The analysis of multi-dimensional social networks has recently garnered the attention of the mathematics and physics communities. Multilayer networks are ubiquitous and have consequences, so processes giving rise to them are important social phenomena. Recent models of these processes show how ignoring layer interdependencies can lead one to miss why a layer formed the way it did, and/or draw erroneous conclusions. Understanding the structuring processes that underlie multiplex networks will help understand increasingly rich datasets, which give better, richer, and more accurate pictures of social interactions.

Zero-Debt Policy under Asymmetric Information, Flexibility and Free Cash Flow Considerations
Miglo, Anton
SSRN
We build a model of debt for firms with investment projects for which flexibility and free cash flow problems are important issues. We focus on the factors that lead the firm to select the zero-debt policy. Our model provides an explanation of the so-called "zero-leverage puzzle" (Strebulaev and Yang (2013)). It also helps to explain why zero-debt firms often pay higher dividends compared to other firms. In addition, the model generates new empirical predictions that have not yet been tested. For example, it predicts that firms with zero-debt policy should be influenced by free cash flow considerations more than by bankruptcy cost considerations. Also the choice of zero-debt policy can be used by high-quality firms to signal their quality. This is in contrast to most traditional signalling literature such as Leland and Pyle (1977), for example, where debt serves as a signal of quality. The model can explain why the probability of selecting the zero-debt policy is positively correlated with profitability and investment size and negatively correlated with the tax rate. It also predicts that firms that are farther away from their target capital structures are less likely to select the zero-debt policy compared to firms that are close to their target levels.


text:
## Doctoral Dissertations

Winter 1997

Dissertation

Physics

#### Degree Name

Doctor of Philosophy

To advance our understanding of the magnetic storm dynamics of the outer radiation belt relativistic electrons, the magnetic storm which commenced on 9 October 1990 was analyzed in detail using data from the Combined Release and Radiation Effects Satellite (CRRES) and the Los Alamos National Laboratory geosynchronous satellite 1989enspace 046. Electron differential flux was transformed into phase space density as a function of the three adiabatic invariants. The invariants were determined by magnetic field data from CRRES and the Tsyganenko 1989 Kp driven model. The unique work of this thesis is the storm time radial diffusion modeling performed using time dependent radial diffusion coefficients (D$\sb{\rm LL}$) and a time dependent outer boundary condition. The results show that D$\sb{\rm LL}$(t), parameterized by Kp, can efficiently couple outer boundary condition variations (sources and sinks) to deep into the radiation belt interior, thus accounting for both significant flux decreases and increases throughout the region. It was found that an internal source is required to account for the gradual increase in the highest energy electrons throughout the recovery phase. A potential source mechanism is energy diffusion via wave particle interactions with whistler chorus waves which were observed by CRRES to be greatly enhanced throughout the recovery phase.


text:
listplot3d - Maple Help

plots

 listplot3d
 three-dimensional plot of a list of lists of values

 Calling Sequence listplot3d(G, options)

Parameters

 G - list of lists or rtable of numeric values

Description

 • The listplot3d function creates a 3-D plot of an $m$ by $n$ list of lists or rtable of numeric values. The x-axis and y-axis are numbered from 1 to $m$ and 1 to $n$ respectively.
 • Remaining arguments are interpreted as plot options. See plot3d/option for a list of possible options.
 • A related command is plots[surfdata].

Examples

 > $\mathrm{with}\left(\mathrm{plots}\right):$
 > $\mathrm{listplot3d}\left(\left[\left[1,2\right],\left[3,4\right],\left[5,6\right],\left[7,8\right]\right],\mathrm{color}="LightBlue"\right)$
 > $\mathrm{listplot3d}\left(\left[\mathrm{seq}\left(\left[\mathrm{seq}\left(\mathrm{sin}\left(\frac{\left(i-15\right)\left(j-10\right)}{20\mathrm{\pi }}\right),i=1..30\right)\right],j=1..20\right)\right]\right)$
 > $\mathrm{listplot3d}\left(\left[\mathrm{seq}\left(\left[\mathrm{seq}\left(\mathrm{irem}\left(j,i\right),i=1..30\right)\right],j=1..30\right)\right],\mathrm{orientation}=\left[-55,30\right],'\mathrm{style}'='\mathrm{point}','\mathrm{color}'="NavyBlue"\right)$


text:
The Universe of Discourse

Wed, 21 Feb 2007

Addenda to Apostol's proof that sqrt(2) is irrational
Yesterday I posted Tom Apostol's wonderful proof that √2 is irrational. Here are some additional notes about it.

1. Gareth McCaughan observed that:
It's equivalent to the following simple algebraic proof: if a/b is the "simplest" integer ratio equal to √2 then consider (2b-a)/(a-b), which a little manipulation shows is also equal to √2 but has smaller numerator and denominator, contradiction.
2. According to Cut-the-knot, the proof was anticipated in 1892 by A. P. Kiselev and appeared on page 121 of his book Geometry.


text:
# Problem: Draw the major, neutral organic product obtained if:(a) the reaction proceeds by the SN1 mechanism(b) the reaction proceeds by the SN2 mechanism.Draw the major, neutral organic product for each substitution reaction below. (For this question, assume that each substitution reaction goes to completion. Disregard elimination.)

Recall:

###### Problem Details

Draw the major, neutral organic product obtained if:

(a) the reaction proceeds by the SN1 mechanism

(b) the reaction proceeds by the SN2 mechanism.

Draw the major, neutral organic product for each substitution reaction below. (For this question, assume that each substitution reaction goes to completion. Disregard elimination.)


text:
### Home > CC1 > Chapter 4 > Lesson 4.1.2 > Problem4-19

4-19.

Review the Math Notes box in this lesson. Then convert each mixed number to a fraction greater than one, or each fraction greater than one to a mixed number. Homework Help ✎

1. $4\frac { 1 } { 8 }$

1. $\frac { 302 } { 3 }$

$100 \frac{2}{3}$

1. $100\frac{21}{5}$

$\frac{502}{5}$

1. $\frac { 18 } { 3 }$

Review your knowledge of mixed numbers and fractions greater than one in the Math Notes box from this lesson at the bottom of the page.

For part (a), try drawing a diagram to help visualize how many eighths are in four. Also, if you find how many eighths there are in 1, you can use multiplication to find the solution.

For part (d), you can find the mixed number by treating the fraction as a division problem. It is easier than it might seem.


text:
Economics: Elasticity Theory – #263

Question: A typical consumer behaved in the following manner with respect to purchases of butter over the past eight years:

 Year Price of Butter ($/pound) Quantity of Butter Purchased Real Income ($) Price of Margarine (\$/pound) 1 0.95 200 11000 0.65 2 1.1 180 11000 0.65 3 1.1 190 11500 0.65 4 1.1 200 11500 0.9 5 1.15 170 11500 0.9 6 0.99 190 11500 0.9 7 0.99 175 10500 0.9 8 0.99 150 10500 0.65

Compute all meaningful price, incoMeand cross-elasticity coefficients. (Remember that the effects of the other factors need to be held constant when computing any of these coefficients).


text:
Unique End of Potential Line

Fearnley, John, Gordon, Spencer, Mehta, Ruta and Savani, Rahul ORCID: 0000-0003-1262-7831
(2018) Unique End of Potential Line. .

 Text 1811.03841v1.pdf - Submitted Version Download (1MB)

Abstract

This paper studies the complexity of problems in PPAD $\cap$ PLS that have unique solutions. Three well-known examples of such problems are the problem of finding a fixpoint of a contraction map, finding the unique sink of a Unique Sink Orientation (USO), and solving the P-matrix Linear Complementarity Problem (P-LCP). Each of these are promise-problems, and when the promise holds, they always possess unique solutions. We define the complexity class UEOPL to capture problems of this type. We first define a class that we call EOPL, which consists of all problems that can be reduced to End-of-Potential-Line. This problem merges the canonical PPAD-complete problem End-of-Line, with the canonical PLS-complete problem Sink-of-Dag, and so EOPL captures problems that can be solved by a line-following algorithm that also simultaneously decreases a potential function. Promise-UEOPL is a promise-subclass of EOPL in which the line in the End-of-Potential-Line instance is guaranteed to be unique via a promise. We turn this into a non-promise class UEOPL, by adding an extra solution type to EOPL that captures any pair of points that are provably on two different lines. We show that UEOPL $\subseteq$ EOPL $\subseteq$ CLS, and that all of our motivating problems are contained in UEOPL: specifically USO, P-LCP, and finding a fixpoint of a Piecewise-Linear Contraction under an $\ell_p$-norm all lie in UEOPL. Our results also imply that parity games, mean-payoff games, discounted games, and simple-stochastic games lie in UEOPL. All of our containment results are proved via a reduction to a problem that we call One-Permutation Discrete Contraction (OPDC). This problem is motivated by a discretized version of contraction, but it is also closely related to the USO problem. We show that OPDC lies in UEOPL, and we are also able to show that OPDC is UEOPL-complete.

Item Type: Other This paper substantially revises and extends the work described in our previous preprint "End of Potential Line'' (arXiv:1804.03450). The abstract has been shortened to meet the arXiv character limit cs.CC, cs.CC, cs.DS Symplectic Admin 14 Nov 2018 08:58 10 May 2022 06:10 Author https://livrepository.liverpool.ac.uk/id/eprint/3028777


text:
# Neutral pions and chromodynamics

$\pi^0$ particles are either up-antiup or down-antidown (or strange-antistrange?) They must be opposite colors to preserve neutrality. Why don't the opposite quarks annihilate?

-
It's a metastable state--another example of a metastablestate made up of a particle antiparticle pair like this is positronium. –  Jerry Schirmer Jun 13 '13 at 23:15

Pions in general and the neutral pion is not an stable particle, its mean lifetime is $\tau=8.4 \cdot10^{-18}$ s Pion - Wikipedia
They do annihilate. Neutral pions aren't stable. Their half-life is something on the order of $10^{-17}$ seconds, which is about a millionth of the amount of time your computer takes to execute a single processor instruction.
The more fun question is 'annihilate via what reaction'? Something has to carry away the energy and angular momentum. It turns out that there are actually lots of pion decay modes, meaning lots of final states into which a pion can decay. (A slight subtlety: neutral pions are usually defined to be linear superpositions of quark antiquark pairs, roughly $|u\bar{u}\rangle - | d\bar{d}\rangle$. This is done to make them isospin eigenstates.)


text:
# 162 questions

Tagged
• x
1k
views
4
2

## max gpio current for nRF52

Hello, I just wanted to update previous similar questions for the nRF52 series, old one for nRF51 is here: https://devzone.nordicsemi.com/questi...

At page 151, section 20.4, of the nRF52832 Product Specification v1.0 I find that ... (more)

85
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no
no

## nRF52 reset behaviour on GPIO output pins

Hi. I have a board here based on the nRF52832, using SD 132 and SDK 13.0.0, with a modem on it that I'd like to keep powered on even when the Nordic is in system off mode ... (more)

58
views
1
vote
1

## Minimum pulse length to detect low level with GPIO SENSE for nRF52

Hi all

What is the minimum required length of a LOW pulse to be detected by the nRF52832 via GPIO SENSE mechanism? I couldn't find it in the product specification.

I want to wakeup the nRF with a LOW ... (more)

46
views
no
1

## Small problem with using the GPIO to power system ON/OFF

Hi, I am really new to the Nordic products and programming for that matters. But, the thing is that I am in somewhat of a hurry. I would like to use a similar code to below to the one below ... (more)

59
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no
1

## What happens to nRF51822 if GPIO is set to source less current than required?

I have a board with some LEDs that are driven in the same way as with the nRF51 DK board (i.e. there is a resistor in series with the LED and you drive the pin low to turn the ... (more)

112
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## nRF52832 one of output (p0.15) lost its power

Hi!

I have noticed strange problem with one of GPIOs - P0.15. We have tested 50 devices based on nRF52832 and 3 of them have problem with P0.15 after few days.

P0.15 pin we have connected with two ... (more)

75
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## How to send 1 byte via SPI from master to slave

Hello everyone, I'm trying to run my nrf51 with ADS1298 using SPI. nrf51 is master and ADS1298 is slave.

I configured SPI as

const nrf_drv_spi_config_t spi_config =
{
.sck_pin = 25,
.mosi_pin = 24,
.miso_pin = 23,
.ss_pin = 30,
//.irq_pin = 22,
.irq_priority = APP_IRQ_PRIORITY_HIGH,
.orc ...
(more)

69
views
3
1

## I want to digital high a gpio pin on nrf51dk, when I receive the text say "ON" from my android smartphone.How can I accomplish that using the nrf ble app uart example.I am not sure where I can compare the incoming ble data [closed]

Toggling a gpio pin upon receiving a particular string from ble uart app

69
views
1
vote
1

## Interference of bsp-module while re-configuring NFC-pins as GPIOs

Hello,

on my custom board I am trying to use pin P0.09 and P0.010 for interrupt-purposes. So I integrated the necessary adjustments as mentioned in this topic here, which resulted in an immediate 'halt' of my board, upon ... (more)

143
views
1
vote
3

## Problem using GPIO- and BSP-module simultaneously

Hello,

last week I was trying to integrate a wake-on-motion-functionality for my hardware using some interrupt-handling. While that problem is solved, I came across some kind of interdependency between initializing the GPIO- and the BSP-module simultaneaously.

Here is the code ... (more)

78
views
no
1

## Hardfault when using both UART and GPIOTE, how can I solve this problem?

Hello,

I feel like this question has an answer similar to this question, but I can't seem to get it working https://devzone.nordicsemi.com/questi...

I am using the nrf51422 chip on a board I designed myself and ... (more)

54
views
no
1

## nRF5 with input-multiplexer on ADC pin, optimization required

Hey, I am trying to sample from 10 analog sensors and stream the results via bluetooth. Since the nRF5 is on a board that only lets me access 5 Pins, I am using a 16:1 multiplexer connected to a ... (more)

137
views
1
vote
2

## Is it physically possible to set UART RX and TX to same GPIO pin?

I'm trying to implement send && recieve through one wire. Handling of pin state, if it is input or output is done via SW. Also it is going to be half-duplex only.

Is it possible to do something like this ... (more)

46
views
3
1

## GPIO act incorrectly when building with GCC

Hi,

I connected 74CH595 shift registers to nRF52DK board. When I built and upload my code with Keil everything works just fine, but if I compliled it with GCC and upload with nrfjprog, the 74CH595 cannot act properly. I need ... (more)

173
views
no
1

## Taiyo Yuden EYSHJNZXZ (nRF52832) cannot use NFC pins as GPIO

I am having trouble using GPIO P0_9 and P0_10 as GPIO pins. These are the pins designated as NFC1 and NFC2.

I am using the following sample code:

#include <stdbool.h>
#include <stdint.h>
#include "nrf_delay.h"
#include "boards.h ...
(more)

97
views
1
vote
1

## High Drive mode downsides (nRF52)

Hi,

I just had a quick question - currently I'm using standard drive mode for everything, however in one case I'm driving an IR transmitter that could really do with a little more current.

What are the downsides of ... (more)

71
views
no
1

## What are the characteristics of the nRF52832 GPIO internal 'ESD structures'?

What are the following characteristics for the 'ESD structures'/diodes pictured?

Reverse breakdown voltage, rated forward current, forward voltage

55
views
no
no

## Cannot pull down a GPIO pin which is shared with LED

Hi,

I added following code in saadc example code to set GPIO pin high/low and monitor it in the terminal. The pull up looks ok, but when I set it to low, the reading never goes down to 0 ... (more)

72
views
no
no

## Turn PWM off and back on

I am using Nordic SDK to develop an application. I need to turn PWM off and turn it back on (to produce a beeping sound from a buzzer). To do this I went into the bsp.c file and added ... (more)

438
views
2
3

## Configuring MISO pin for SPIM nrf52

Greetings I am working on an application that logs data to SPI flash device. I am having an issue where it appears that the pin configured as a MISO for SPIM is garbling up the flash device's responses. I ... (more)

71
views
no
no

## Turn off PWM LED [closed]

I have a BLE device that is using Nordic SDK 8.1 and uses PWM to control an LED. Now I want to turn the led off with PWM. To do this I set the duty cycle to 0 and ... (more)

218
views
1
vote
1

## GPIO state during deepest sleep mode

Hi, Do the nRF52 GPIOs retain their pullup/down or drive characteristics when in its deepest sleep mode? VCC is still applied, but otherwise, the chip is to consume a minimum of power, waiting for a wakeup on another GPIO ... (more)

73
views
2
1

## nrf51822 GPIO direct source with high drive setting

I directly connect GPIO pin with 24ohm resistor as follows. And I set GPIO pin as high drive,

NRF_GPIO->PIN_CNF[MY_PIN_NO] |= (GPIO_PIN_CNF_DRIVE_H0H1 << GPIO_PIN_CNF_DRIVE_Pos);

When I measure the current, I got 38mA. But it should not exceed 15mA ? What am I ... (more)

98
views
no
1

## Intentional over-voltage on nRF52 I/O Pin?

Hi all --

I have an application where I have a LDO generating 2.6V from a single lithium-ion cell. It has an EN input that I want to expose to the nRF52 with a little RC circuit to allow the ... (more)

223
views
1
vote
no

## Nordic SDK: PWM duty cycle of 0 on LED

I am using PWM on a BLE Nano using Nordic SDK. I was having problems with the PWM and decided I would set the duty cycle to 0 to see if the program was working right:

#include <stdbool.h>
#include ...
(more)

114
views
1
vote
1

## BLE Nano: Which pins are capable of PWM

I am developing on a BLE Nano 1.5 and need to use PWM to make a beeping sound from a piezo buzzer. I am wondering which pins are capable of PWM. Here is the pinout diagram:

102
views
no
no

## BLE Nano/Nordic SDK: making a quick buzz from a piezo speaker

I am working on a project using a ble nano (nrf51822) using the Nordic SDK 8.1. I started building off the ble-app-hrs in the examples of the documentation so my code is pretty similar to the example.
What I ...
(more)

44
views
1
vote
1

## GPIO high during DFU

Hello,

Id like to understand if its possible to held GPIO high during a DFU update? The usecase is as follows: 1)GSM module is usually controlled by NRF52832 and it also controls the power switch. 2)I will download ... (more)

50
views
1
vote
1

## BLE Nano Central: Use PWM

I am working on a project using a ble nano (nrf51822) using the Nordic SDK 8.1. I am trying to use PWM to control a buzzer. To do this I included the following files into my main.c:
#include ...
(more)

44
views
no
no

## Nordic SDK: swapping LEDS_ON and LEDS_OFF caused problem when checking if the LEDS are on

I am working on a project using a ble nano (nrf51822) using the Nordic SDK 8.1. In the examples I found a way to control an LED using the methods LEDS_ON and LEDS_OFF. I wanted to invert the times ... (more)

#### Statistics

• Total users: 22278
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• Resolved questions: 9667
• Total questions: 23073

## Recent blog posts

• ### Nordic Developer Zone celebrates its 4th year of helping developers succeed - Celebrate with us and win a Nordic Thingy: 52’

Posted 2017-06-23 10:12:53 by John Leonard
• ### nRF52 Development with CLion

Posted 2017-06-22 09:50:54 by dansheme
• ### Simple GPIO driver example

Posted 2017-06-22 13:38:36 by Hans Elfberg
• ### What mom didn't tell you about ble_app_att_mtu_throughput on the nRF52840 evaluation board

Posted 2017-06-16 16:12:15 by George
• ### Introducing Nordic’s new software licensing schemes

Posted 2017-06-15 11:21:39 by Reidar Martin Svendsen

## Recent questions

• ### NRF51822 to NRF51822 Over the air update (DFU)

Posted 2017-06-25 16:25:45 by wogisha
• ### Advertising with device_name Vs whitelisting

Posted 2017-06-25 14:39:12 by raju


text:
## Algebra: A Combined Approach (4th Edition)

1. Find the area of the deck with the formula A = lw. A = 35*20 = 700 2. Each gallon covers 200 sq feet, so to determine how many gallons we need, we divide the area of the deck by 200: 700 $\div$ 200 = 3.5 We need 3.5 gallons.