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Radically Reshaping Latina/o America
Latina/os are best positioned to form a broad left agenda—beyond advocating immigration reform—to tackle hemispheric inequality at its roots.
Ed Morales
What's in a name? The label "Latino" is often used to describe a monolithic interest group or voting bloc. And while criticized as inaccurate because of Latinos' diverse national, ethnic, and racial manifestations, as an organizing principal the label still conveys significant meaning—a narrative of shared experience—in both Latin America and the United States. Although Mexican Americans on the West Coast may have sharp differences with Puerto Rican migrants in New York and with Cuban Americans in Miami, what Latina/os have in common, besides a shared language and parallel cultures, is a history marked by U.S. intervention. It's the result of that intervention that has for the most part driven immigration northward. While the hemisphere's future will be determined by the continuously evolving political relationship between the United States and Latin America, the question is, what role will U.S. Latina/os play in that future?
In the 1960s and 1970s, the term "Latino" was embraced by a growing constituency of U.S.-born Latina/os who identified with the civil rights and national liberation movements of the era. They saw the term as an alternative to the Nixon administration's use of "Hispanic," a European-identified term with assimilationist connotations. But over the years, the "Latino" activist charge has waned; largely as a result of a perception created by corporate media and consumer marketers, Latina/os are now often cast as recent arrivals, imperfect English speakers, and "others" from el otro lado. This contradiction is reflected by the changing nature of U.S. Latina/o politics, in which crucial concerns around immigration policy have eclipsed, at least in public perception, the other class-based concerns of working people that historically have occupied a larger role in the left Latina/o agenda.
While free-trade policies aim to diminish borders to accommodate the flow of capital, the post-9/11 obsession with "national security" has refocused our attention on borders—whether it involves remilitarizing the one with Mexico or reasserting the class and race barriers that enforce segregation in our cities. Just as U.S. military intervention beginning in the early-twentieth century created migration flows to the north, so too as investment capital flows south, displaced populations move across the physical border, escaping, still, political persecution or economic devastation primarily caused by U.S. economic policy or U.S. support for anti-democratic governments.
The traditional view of U.S. Latina/o politics holds that the three dominant groups that wield political power are Mexicans, much of whose country was absorbed after the U.S.-Mexico war in 1848, and Puerto Ricans and Cubans, whose countries were ceded to the United States after the Spanish-American War in 1898 (with Puerto Rico still a U.S. territory). In the twentieth century, the political and cultural power and awareness of these groups matured, staking out three distinct regions of influence. Mexican descendants, who make up almost two-thirds of the U.S. Latina/o population, are concentrated in the West and Southwest; Puerto Ricans, who are born U.S. citizens and are therefore not technically immigrants, are concentrated in the Northeast; and Cuban-Americans are concentrated in South Florida.
In terms of political orientation, Mexican Americans are probably the most diverse. Although their political history has been anchored by citizenship and civil rights struggles and has produced a considerable left intelligentsia, the long-term experience of Mexican descendants in the United States has resulted in a slight uptick of conservative or libertarian tendency among class-ascendant Mexican Americans in various parts of the country. Puerto Ricans—because of factors ranging from their rejection of their colonial status, to their exposure to harsh discrimination in northern cities, to relatively low levels of educational and economic achievement—are mostly liberal-left. And Cuban exiles in South Florida, propped up by government entitlements for individuals and small businesses since their mass arrival in the early 1960s, form a bastion of right-leaning Latina/os that have been crucial to the electoral victories enjoyed by Ronald Reagan and both Bushes.
Yet these paradigms are shifting, along with Latina/os' changing fortunes in the global economy.
The neoliberal free-trade era has caused increasing migrations from Mexico and Central America as it imposes ever-harsher conditions on maquiladora and agribusiness workers on both sides of the border. Ineffectual puppet governments in Honduras, El Salvador, and Mexico also prompted immigration resulting from political violence and added new variations to the U.S. Latina/o political landscape. Beginning in the 1990s and accelerating through the 2000s, these new waves of Mexican and Central American immigration created unprecedented population flows to the U.S. south, particularly to Georgia, Virginia, and the Carolinas.
The 2006 economic crisis in Puerto Rico, caused primarily by debt speculation in U.S. bond markets, resulted in a migration of island residents of Puerto Rico to Central Florida. At the same time, mainland-raised Puerto Ricans are fleeing the Northeast, where the traditional base of manufacturing and public sector jobs has eroded greatly over the last 30 years. (This outward flow has also resulted in the growing influence in New York City of Dominicans—whose first generation of migration to U.S. shores came after the U.S. invasion of the Dominican Republic in 1965.) These phenomena, as well the waning of hardcore anti-Castro politics among newer generations of Cuban Americans, certainly threatens Florida's status as a Republican stronghold.
Other factors—like increased immigration of middle-class Colombians, Venezuelans, and Argentines to South Florida, as well as a more conservative strand of Puerto Rican migrants, some of whom are retired military personnel or members of the island's rightist pro-statehood party—are significant but will most likely not affect the Democratic bent of Florida's new Latina/o voters. But even with this new exploding Latina/o population throughout the rest of the South, it will be a generation or two before this mostly immigrant population—most of which is not eligible to vote—begins to play a significant role in electoral politics.
Whatever changes the new migrations to Florida and the U.S. South bring, the liberal Democratic political landscape of California and the Southwest has remained constant as a result of its status as the flashpoint of tension between mainstream America and Latina/os—who tend to resist the classic assimilationist path of other ethnic groups through a functional bilingualism and cultural identifications with music, dance, food, and other social practices. Even as Mexican Americans, and increasingly, naturalized Central Americans, experience some wealth accumulation and creeping interest in the tax-cutting mantras of the Republican Party, the conservative politics of fear and intolerance that has marked the mainstream response to increased migration to the region has solidified Latina/os' anti-Republican leanings. Since most Latina/os in the region are intimately connected to an undocumented immigrant, the backlash against them—manifested in discriminatory law enforcement practices and a general increase in anti-Mexican sentiment—has also negatively affected Latina/os who have been U.S. citizens for generations.
Disagreement over strategy within the immigration reform movement erupted before the president finally announced his executive action in November, which would allow four million undocumented immigrants to live and work legally in the United States. It pitted younger and more autonomous activists—some associated with the "dreamer" movement—who insisted Obama act more swiftly, against more connected advocates with closer links to the Democratic Party, who urged patience so as not to damage the party's chances in the midterm elections. Yet the Republican victories of those elections demonstrated that Obama, whose administration has overseen a record number of deportations, should have used his executive power earlier. Now that the reform process has begun, it should become clearer that it's just one part of what should be a larger Latina/o political agenda.
Immigration reform is often perceived as the most important issue for Latina/os in the United States. And for good reason: it is a human rights issue that affects so many Latina/os directly and indirectly, as anti-immigrant hostility trickles down to all Latina/os, citizens or not. The humanitarian crisis of so many people living in hiding, facing the increased deportations of the Obama era, the threat of separated families, and the lack of basic rights in the workplace, has created a situation dangerously close to apartheid. But many recent polls suggest that Latina/os, while strongly concerned with immigration reform, are equally concerned with issues that affect those with citizenship or permanent resident status: the job market, affordable housing, the erosion of voting rights, and access to higher education.
These are the issues faced by African Americans, who have been marginalized repeatedly after continuing waves of European migration, as well as Asian Americans who do not fit into the model-minority demographic, and various other marginalized constituencies, including working-class whites. For all the celebration of contributions that Latina/o immigrants make to the United States, as well as the veneration of striving undocumented dreamer college graduates—a "talented tenth" of Latina/o immigrants—the reality is that many Latina/os tend to be plagued by a pattern of downward social mobility because of their lack of access to quality education, and vulnerability to entrenched systemic racism.
It's important to understand that Latina/os come from a region, Latin America, whose societies are a product of the same colonial forces that brought together, in violent fashion, Europeans, Africans, and indigenous people. But although there was more race-mixing tolerated in Latin America, systematic race privileging has produced a society where lighter-skinned people generally accumulated more power and wealth than darker-skinned people. This means that although the theoretical "mestizo" racial unity Latina/os achieved in their home countries can sometimes hold in the United States, it can also be broken apart by the binary (black/white) racial codes of the United States. The result is that not all Latina/os are aligned in a political agenda in the way that the African American community is more known to be. Even while the furor over immigration reform has a unifying effect, Latina/o unity is not entirely assured.
Yet the growing wealth inequality in core capitalist countries worldwide has created more opportunity for diverse groups of people to come together in a common political cause. U.S. Latina/os can play a strong role in raising awareness of how labor is exploited across borders while we also are well suited to expose the exploitative and at times savage nature of U.S. foreign policy.
Turn-of-the-century Cuban revolutionary José Martí presaged this with his vision of "Our America," a call for Latin American unity as the Spanish-American War erupted. As "Americans" with a broader hemispheric perspective, U.S. Latina/os remain a group with much invested in their home countries, and a clear understanding of how free trade agreements cast a glaring light on wage inequalities on both sides of the border. We can theoretically connect issues like the downward pressure on wages—a class issue regardless of race and ethnicity—with the destructive, inequality-creating neoliberal agenda that harms our home countries. Bringing all this into focus is a more comprehensive and potentially revolutionary agenda than merely advocating for immigrants to be allowed a pathway to citizenship solely on the terms of the status quo U.S. hemispheric agenda.
While aligning with the just and noble cause of bringing undocumented immigrants out of the shadows, Latina/os should also join with other U.S. Americans to demand reinvestment in public education, the right to unionize and engage in collective bargaining, the protection of local communities from neoliberal gentrification projects, and economic justice from queer and race-based lenses. Latina/os need not only to protect our most recent arrivals from ruthless exploitation, but also to reignite the legacy of our long history in the United States and continue to engage the struggles we embraces during the civil rights era and its aftermath.
It is encouraging for now that most Latina/os remain progressive, but as a national constituency we have the potential to help move that agenda further to the left. In this historical moment, Latina/os are uniquely positioned to push American politics to truly engage with racial and class differences, the need for a universal living wage, and just foreign policy—radically reshaping "Our America."
Ed Morales is a freelance journalist and author of Living in Spanglish (St. Martin's Press). He teaches at Columbia University's Center for the Study of Ethnicity and Race, and is a NACLA contributing editor. His forthcoming book is titled Raza Matters (Verso).
Read the rest of NACLA's 2015 Winter Issue: Mapping the Moment
Tags: latino politics, Minimum Wage, employment, Foreign Policy, free trade, U.S. Intervention, José Martí


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Having tried and failed with a polar fleece applique onto a polar fleece pullover, I decided to try crochet. So I found an easy pattern for a flower, and taught myself how to crochet. I did succeed to a certain extent, making one on one day and another on the next day, to practise. Unfortunately, because I spent far too long both times, getting the hang of holding the yarn and the working piece, I now have a "repeated strain injury" in my index finger.
So be aware, all you older folks, like me, when starting something new, take it slowly, as in baby steps, and allow the joints to get used to the new activity. Oh, and do warm-ups and stretches before, during, and after. I'm not kidding.
The flower is now on hold.
I did something similar recently (about two weeks ago): for my BIL's milestone birthday I made two traditional rope fenders for his boat. The joints in my thumbs are still a bit sore and I've been doing hand and wrist stretches every day since.
Last edited by Jaye on Tue Mar 26, 2019 10:07 am, edited 1 time in total.
I have always been able to knit but with crochet I always found my fingers cramped, even when younger, never did get over it!
Oh no! I haven't knitted in a few years.... call it 25, or so. I am in search of an old pattern that I bought; I have all the yarn; asked my mom to knit it for me (I had gone back to work); she never did, but she did misplace the pattern. So I have an ISO on Ravelry.
Now that I am retired, I am getting back into more sewing, first. Then I'll pick up some knitting again.
Last edited by KimChick on Wed Mar 27, 2019 9:23 am, edited 1 time in total.
Sorry about the sore fingers .
I too got back into knitting this winter as I needed a new knitted cotton washcloth to replace my old one. Seeing all the wonderful colourful yarns available, I kept buying and buying, knitting and knitting. I ended up with quite the pile of washcloths/dishcloths (for gifts) and then knitted some colourful coasters as well. Easy peasy and very addictive!
I love to crochet. Been working on a large blanket for my sister-in-law. I have to get it done before the weather totally warms up as it will be too hot to work on. I returned to crochet a couple years ago hoping the exercise would help my stiff fingers and hands. It has certainly helped. It was pretty rough at the start.....I guess like all new activities, it's good to pace yourself.
A few years ago, my mother crocheted everyone, kids and grandkids, each a granny square afghan. I still have mine. They are very colourful with black borders individually and around the entire piece. After all those, she went back to knitting.
Right now, I'm battling dry, splitting skin and trying to hand stitch. Yesterday, hand basting zippers onto chair cushion covers, while wearing nitril gloves seemed to work well. I could push and pull the needle through faster with a decent grip.
Interesting idea....the gloves! I saw leather thimbles at the wool festival in Peterborough a couple of weeks ago. A friend said they worked well.
I know I had a leather thimble, but I can't find it anywhere. It wasn't particularly comfortable, though. Perhaps it will turn up when I don't need one, or my daughter has it.
Lo and behold, I did find my soft, plastic thimble! The leather one still hasn't turned up.


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ARTICLES MOVIES & TV 5 MOVIES THAT DON'T GET HOW LONG THINGS TAKE
5 Movies That Don't Get How Long Things Take
Tara Marie
Matt Cowan
With the magic of editing, movies can cover huge jumps in time over a span of mere seconds. That way, we never have to know how long James Bond spends sitting on the toilet after eating some bad tacos, and instead get right to the car chases and karate chops. But if you ignore the editing, how long do some of these movie scenes really take? Well, we did the calculations and found ...
5 It Takes Four Years For Starkiller Base To Destroy The Senate In The Force Awakens
In an intense scene in the Star Wars remake (search your feelings, you know it to be true) The Force Awakens, a cult of Space Nazis called the First Order activates their superweapon Starkiller Base -- a bigger, more powerful Death Star with the power to destroy entire solar systems over vast distances. Moments after the colossal beam is fired, our heroes look to the sky in horror as the Hosnian System, the seat of the Galactic Senate, is spectacularly disintegrated.
Actual Time Scale: Four Years
We know that we're talking about a science fiction universe in which both fire and sound are possible in the vacuum of space. Oh, and that literal wizards can move objects with their minds. That, too. We're not exactly expecting Stanley Kubrick levels of realism here, but most of the physics of our world -- such as gravity -- seem to remain more or less intact in the Star Wars universe. So for fun, let's imagine how long this event should have taken.
First of all, we're assuming that whatever the Starkiller beam is made from, it's moving no faster than the speed of light. It's true that spaceships in Star Wars can travel faster than light, but a beam of pure plasma or energy or whatever probably doesn't have a hyperdrive installed on it. We also know that Starkiller Base isn't in the same solar system as Hosnian Prime, because it needs to vacuum up a star before it can operate, hence its creative name. And the star in the middle of the Hosnian System is still shining at the time of impact.
R.I.P. Manatee-Pug-Face Man. May you live on with your 12 unnecessary action figures.
Best-case scenario is that Starkiller Base is orbiting the very next star over. We don't know how far that is, but we know how far our sun is from its nearest neighbor, Alpha Centauri -- a little over four light years. This means that, even if Starkiller Base is as close as it can possibly be to the Hosnian System, it still likely takes a matter of years from the moment they pull the trigger to the moment they hit their target.
"OK, now stand and wait for 1,450 days. It's going to be so cool, you guys."
So after the beam is fired and Finn and Rey escape, they could simply hop in a ship, grab a few drinks, take a little vacation, learn to play the piano, and then eventually kick on the FTL drive to mosey over to the Hosnian System to let them know that a death beam is on the way. No hurry, though -- they still have years to evacuate.
4 Gandalf's Research Journey In The Fellowship Of The Ring Covers Years
In The Lord of the Rings: The Fellowship Of The Ring, Bilbo Baggins accidentally reveals that he's carrying one of the most powerful objects in the universe when he uses it to perform party tricks. It's sort like hanging up a nuclear bomb as a pinata. Understandably concerned, Gandalf takes off on horseback to some ancient library in order to figure out which magic ring Bilbo has been carrying around -- whether it's one of the bad ones, or the really bad one. Upon concluding that it's the latter, he jumps on his horse again and rides back to Bilbo's house to warn Frodo to stop smacking the bomb with a stick.
Or to at least to not leave it in his damn junk drawer.
We assume that Gandalf's return happens the very next night, since the hobbits are all still in party mode and the banter between Gandalf and Frodo continues without skipping a beat. But if you think about it, Gandalf must have been away for much, much longer than that.
Actual Time Scale: Several Years
The library that Gandalf visits is in Minas Tirith. That's where the final battles take place in Return Of The King. You know, the same place that takes our heroes three films and around 300 hours of movie time to reach. Here it is on a map. The Shire, where the hobbits live, is in the top left, while Minas Tirith is on the bottom right, just west of Mordor's crazy square mountain range.
If we assume that Middle Earth is about the size of Eastern Europe (which is kind of what Tolkien was going for, since there weren't exactly a bunch of samurai involved), then Gandalf traveled the equivalent distance from France to Greece. On horseback. And although Gandalf is a wizard, his horse isn't established as having magical teleportation powers or anything.
So Gandalf's research trip and return could have taken years -- enough time for Sauron to figure out where the ring was and build an army. As for the hobbits still dancing and drinking when Gandalf returns? Well, that's down to the fact that nobody throws a rager like The Shire.
They're all shorter John Belushis from Animal House.
3 The Trip To Alderaan In A New Hope Takes Days
After the Star Wars cast escape from the Mos Eisley cantina on Tatooine aboard the Millennium Falcon, a matter of hours seem to pass before they reach Alderaan, only to discover that the Death Star has already made short work of it. During the journey, our heroes have only enough time to play a game of space chess and give Luke Skywalker a truncated education on the Force. Or maybe just screw with him. We can't really tell what purpose that whole blindfold/droid scene served.
"This sucks; he's actually good. Watching him take nut shots was like half our entertainment plans."
Actual Time Scale: Two Or Three Days
The trip couldn't possibly have taken place over a time span of less than a few days, even with the spurious physics of Star Wars. The real top speed of the Millennium Falcon is never stated in the Star Wars series, and Han Solo's boastful declaration that it can make the Kessel Run in less than 12 parsecs doesn't help us at all because, as nerds have been pointing out since the '70s, a parsec is a measure of distance, not time.
Wookieepedia
And to the surprise of no one, George Lucas had a pretentious explanation for that.
Luckily for us, Chris Lough over at Tor spent altogether way too much time figuring out the speed of the Falcon using hard math so that you don't have to. First of all, he used a map from the Star Wars Essential Atlas to figure out the distance between Tatooine and Alderaan: 50,855 light years.
And you thought the TI-82 your sixth-grade geometry teacher made you buy would never come in handy.
Knowing the distance between the two planets, Lough was able to calculate the top speed of the Falcon, based on scattered information available via Solo's occasional quips throughout the original trilogy, because some people truly are that dedicated to Star Wars. The Falcon can put down about 25,000 light years per day. Which is insane, but it still means that the trip between Tatooine and Alderaan (or where Alderaan used to be) took between two and three days.
So in between Jedi training and existential discussions about the Force, this whole scene mostly involved Luke, Han, and Obi-Wan sitting around for hours, making small talk or just quietly looking out the window. Hopefully they packed some books, or at the very least, a toothbrush and some clean underwear.
"Plenty of conditioner. Your hair isn't going to feather itself."
2 WALL-E's Intro Lasts Over A Century
Pixar's WALL-E is the story of an adorable robot tasked with the job of cleaning up the Earth after the humans have all left for outer space. He spends his days shoving garbage into his onboard trash compactor, compressing it into cubes, and piling it onto skyscraper-sized towers, which seem structurally unsound, to say the least. The opening scene follows WALL-E during the painstaking process of constructing one of these towers, amidst the thousands of other WALL-E units who lie dormant in the rubble, revealing that he is the last of his kind, yet still dutifully pursuing this task alone.
Because nothing says "problem-solving" like piling up mountains of scattered trash.
Actual Time Scale: Around A Century
Later in the movie, it's revealed that WALL-E has been doing this for around 700 years, but if you were mathematically inclined, you could have deduced that from the opening scene alone. We assume from context that it takes WALL-E a mere day or two to construct one of his garbage skyscrapers, but with a bit of math, you can work out that the "day" we first spend with him in that initial scene in fact covers around a hundred years of collecting, crushing, and piling garbage.
According to a blogger named Roy, who's such a fan of the movie that he's been trying to build his own WALL-E for the past four years, the dimensions of the robot's trash compactor are about 40 x 40 x 40 cm. That's an important detail, because it establishes the size of each of the "bricks" that WALL-E is using as building material. We still need to make some assumptions, since the movie doesn't tell us how high WALL-E's structures are, or how long it takes him to create and install a garbage brick. So let's be charitable and say it only takes him one minute to crush some trash, take it back to his monument, and set it in place.
And let's be honest, he does a lot of dicking around between bricks.
Assuming that one trashscraper is around the size of the Empire State Building, the math tells us that one of WALL-E's constructions contains around 50,000,000 cubes. So even if we assume WALL-E only takes a minute to put each component together -- which is figuring that little sucker's got turbo-chargers and some NOS installed -- it still takes him 95 years to build a monument. And seeing how wobbly those buildings are, it probably falls down like a Jenga tower right after he places the last brick. And you thought the intro to Up was depressing.
1 The Pirates Of The Caribbean Series Glosses Over Several Months Of Sea Travel
In the Pirates Of The Caribbean franchise, the titular pirates of said Caribbean travel pretty much the entire world over the course of four films. Between Britain, Jamaica, Haiti, Singapore, and America, our heroes wind up sailing, if not the seven seas, then at least like ... three?
Or four, if you count all that rum Jack Sparrow puts away.
Actual Time Scale: Many Months
This is, after all, set in the age of exploration. Although the movies zip between international locations as fast as Jason Bourne, the reality is that, if we're true to the time period and the type of ships used, almost every scene in these films would have been interspersed with months of slow, uneventful ocean travel. The Magellan expedition, in a more or less direct route, took more than three years to sail around the Earth, and they presumably didn't have to stop to battle zombies too many times, if at all. Based on the average speed of pirate ships at the time (8.3 mph), the shortest distance that the Black Pearl covered, from Jamaica to Haiti in the first film, would have taken at least two days. The longest would probably be the journey from Singapore to the Caribbean in the third film, which would have taken a whopping two months.
Which is still less tedious than watching On Stranger Tides once.
Most of that time having been spent cultivating scurvy and struggle-pooping over the side of a rocking ship. That's what the poop deck is for, after all.
On his better days, Matt Cowan is a columnist here at Cracked. He also does T-shirt mashups that you can buy here. Tara Marie writes a lot. You can scope her stuff out at Comics Alliance and Harlot, and complain to her about things on Twitter.
Which Sci-Fi Trope Would You Bring To The Real World, And Why? Every summer, we're treated to the same buffet of three or four science fiction movies with the same basic conceits. There's man vs. aliens, man vs. robots, man vs. army of clones, and man vs. complicated time travel rules. With virtual reality and self-driving cars fast approaching, it's time to consider what type of sci-fi movie we want to be living in for the rest of our lives. Co-hosts Jack O'Brien and Adam Tod Brown are joined by Cracked's Tom Reimann and Josh Sargent and comedians David Huntsberger, Adam Newman, and Caitlin Gill to figure out which sci-fi trope would be the best to make a reality. Get your tickets to this live podcast here!
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redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}

Photometric timeseries data are one of the fundamental observational pillars in astronomy. Interpreting these data relies critically on our ability to distinguish between the intrinsic part of the observed signal (the one that corresponds to the object of interest) and the extrinsic part (detector response, optical characteristics of the instrument, atmospheric seeing, interstellar features, \rev{etc.}). This interplay makes the observed timeseries often exceedingly complex in structure and overwhelmingly difficult to interpret. To perform high precision, high fidelity modeling of objects of interest, we need to resort to one of the following strategies: (1) make a number of simplifying assumptions that keep the model tractable; (2) include the extrinsic part of the signal in the model by introducing heuristic and/or empirical description such as, for example, Gaussian processes \citep{foremanmackey2017}; or (3) remove the extrinsic part altogether. No matter the approach, there is an omnipresent danger of attributing some of the intrinsic signal to extrinsic sources, or vice versa, as we rarely know all the sources that contribute to and all the signatures that are found in the data to a sufficient accuracy to model them adequately.

In recent years\rev{,} significant effort was invested in developing the methods for removing systematic artifacts from the \textsl{Kepler} data \citep{borucki2010}. The \textsl{Kepler} pipeline incorporates Pre-search Data Conditioning (PDC; \citealt{stumpe2012, smith2012}), within which the systematics are removed with a combination of data detrending and cotrending against weighted cotrending basis vectors derived from the time series structure most-common to all neighbors of the scientific target \citep{thompson2016}. Another detrending approach based on cotrending basis vectors is implemented within the Variational Bayes framework \citep{aigrain2017}; it can correct for discontinuities and bulk trends. The \textsl{Kepler} Guest Observer Office developed the PyKE tool for IRAF \citep{still2012}, with the \texttt{kepdetrend} and \texttt{kepcotrend} tasks for detrending the data using polynomial fits. \citet{prsa2011} used self-adjusting polynomial chains to remove trends from eclipsing binary light curves that are collected in the \textsl{Kepler} Eclipsing Binary catalog \citep{kirk2016}. An algorithm devised to detrend exoplanetary light curves based on coherent median filtering, \textsl{phasma} \citep{jansen2018}, was used to detrend 165 \textsl{Kepler} light curves. A slew of methods, either general \citep{vandenburg2014} or dedicated for a particular purpose\footnote{A comprehensive list is maintained at \texttt{https://github.com/KeplerGO/lightkurve} by the \textsl{Kepler}/K2 Guest Observer office.} have been developed for K2 \citep{howell2014} as well, and their applications and further advancements are ongoing for space surveys such as TESS \citep{ricker2015}. Utilizing and developing methods for robust, reliable detrending of the timeseries data has thus been at the forefront of modern research.

In this paper we present a detrending algorithm that targets strictly periodic variables. We make no assumptions about the functional form of the periodic signal, nor do we place any constraints on the extraneous signal. By ``extraneous'' we imply \emph{all} parts of the overall signal that are not strictly periodic, including those of an astrophysical origin. The only parameter to the algorithm is the period itself; the output is a fully disentangled periodic component of the signal and the remaining, extraneous timeseries. In Section \ref{sec:algorithm} we provide a mathematical description of the method; in Section \ref{sec:demo} we present three case studies: a synthetic signal, an eclipsing binary star and an eccentric ellipsoidal variable, also known as a \emph{heartbeat} star; in Section \ref{sec:limitations} we discuss some inherent limitations of the algorithm and in Section \ref{sec:conclusion} we provide a general discussion and conclusions.

\section{The Algorithm} \label{sec:algorithm}

Consider a signal that can be described as:
\begin{equation} \label{eq:signal}
    S(t) = X(t) + Y(t) + \varepsilon(t),
\end{equation}
where $X(t)$ is a strictly periodic signal with period $P$, $Y(t)$ is a ``baseline'' signal with no power at period $P$, and $\varepsilon(t)$ is a purely stochastic component. We will refer to signal $X(t)$ as \emph{synchronous} and signal $Y(t)$ as \emph{asynchronous}. Eq.~(\ref{eq:signal}) can then be written as:
\begin{equation} \label{eq:signal_phase}
    S(t) = X(E P \Phi(t)) + Y(t) + \varepsilon(t),
\end{equation}
where $\Phi(t) = [(t-t_\mathrm{ref}) \, \mathrm{mod} \, P] / P$ is phase on the $[0, 1)$ interval, $t_\mathrm{ref}$ is a reference time (i.e.~a phase shift), and $E$ is an integer that enumerates consecutive cycles. Let us further define the discretized counterparts of the above quantities: with $t_k$ we denote the timestamp integrated over $\Delta t_k \equiv t_{k+1/2}-t_{k-1/2}$; with $S_k \equiv S(t_k)$ the discretized signal at timestamp $t_k$; with $X_k \equiv X(\Phi_k) \equiv X(\Phi(t_k))$ the discretized synchronous component at timestamp $t_k$; with $Y_k \equiv Y(t_k)$ the discretized asynchronous component at timestamp $t_k$; and with $\varepsilon_k \equiv \varepsilon(t_k)$ the discretized stochastic component at timestamp $t_k$. Note that the discretized phase, $\Phi_k$, has its own scale that depends on $t_k$ \emph{and} the period $P$, so the sequence $\{\Phi_k\}$ will not be sorted as $t_k$ because of the modulo operator. \rev{As our goal is to disentangle the synchronous and the asynchronous components of the signal, we bundle the asynchronous and the stochastic components into one variable, $\widetilde Y_k \equiv Y_k + \varepsilon_k$.} A discretized version of Eq.~(\ref{eq:signal_phase}) can then be written as:
\begin{equation}
    S_k = X(E P \Phi_k) + \widetilde Y_k.
\end{equation}
Given an observed timeseries $O_k \equiv O(t_k)$, we note that $S_k = O_k$, i.e.~that the \emph{entire} observed signal is explained by the synchronous component $X(\Phi_k)$, asynchronous component $Y_k$ and stochastic component $\varepsilon_k$. A typical situation in astronomical observations is that $O_k$ is known, $P$ is determined to a reasonable accuracy by phase-folding, i.e.~by using Phase Dispersion Minimization (PDM; \citealt{stellingwerf1978}), Analysis of Variance (AoV; \citealt{schwarzenberg1989}) or Box Least Squares (BLS; \citealt{kovacs2002}), and $X(\Phi_k)$ and $\widetilde Y_k$ are unknown. Commonly, $\widetilde Y_k$ will either be assumed stochastic ($Y_k = 0$, $\widetilde Y_k \equiv \varepsilon_k$) or be removed from the data by detrending ($Y_k = f(t_k)$ for some detrending function $f$), and $X(\Phi_k)$ will be fit by a physical model of interest.

The synchronous component $X(\Phi_k)$ can be represented by a discrete probability density function (pdf) that describes the unknown strictly periodic signal. This means that we make no assumptions about the analytical or empirical form of the signal, just that it can be adequately represented by a discrete pdf.

The asynchronous component $\widetilde Y_k$ can be represented by the residual timeseries:
\begin{equation} \label{eq:async}
    \widetilde Y_k = O_k - X(E P \Phi_k).
\end{equation}
Next, we define the length operator on a generic discrete function $f_j \equiv f(t_j)$ as:
\begin{equation}
    \hat L f = \sum_j \left[ (f_{j+1}-f_j)^2 + (t_{j+1}-t_j)^2 \right]^{1/2}\,,
\end{equation}
where index $j$ runs over all $k$. From Eq.~(\ref{eq:async}) it follows that $X(\Phi_k)$ will be an optimal discrete pdf for the synchronous component of $O_k$ when $\hat L \widetilde Y_k = \mathrm{min}$. In other words, $X(\Phi_k)$ and $\widetilde Y_k$ will be optimally disentangled when the length of the $\{\widetilde Y_k\}$ sequence is minimal. As each $X(\Phi_k)$ pdf has a corresponding length $\hat L \widetilde Y_k$, minimizing $\hat L \widetilde Y_k$ optimizes the $X(\Phi_k)$ pdf.

To achieve this, the $X(\Phi_k)$ pdf is iteratively adjusted. Barring any obvious non-stationary trends, drifts or unit-root processes in the generative function for $\widetilde Y_k$, a reasonable starting point for the $X(\Phi_k)$ pdf is a phase-folded average of $S_k$. Otherwise, some detrending might be necessary to make the data stationary and then assign a phase-folded average to the initial $X(\Phi_k)$ pdf. Each ``bin'' $i$ of the discrete pdf affects the length of $\widetilde Y_k$ proportionally to $\partial \hat L \widetilde Y_k / \partial X_i(\Phi_k)$, so we need to take a differential step along that gradient until $\hat L \widetilde Y_k$ is minimized. Differential steps can be computed either by differential corrections (DC; \citealt{euler1755}) or by any robust heuristic methods (simulated annealing, conjugate gradients, etc.\rev{ --- see \citet{press2007} for further details}).

\bigskip

A simple form of the algorithm proceeds as follows.
\begin{description}
\item[Phase-fold the observed light curve] the composite signal $S(t)$ is optionally shifted using the time shift parameter $t_\mathrm{ref}$ (i.e.,~if we desire any particular feature in a light curve to land at any particular phase) and phased on the period of interest, $P$. This generates the undetrended phased light curve.

\item[Generate a discrete pdf for the synchronous signal] depending on the cadence of observations and on the period, we assign a number of bins $N_b$ to the discrete pdf that will describe the synchronous signal in phase space. Each pdf bin must have at least one observation. The choice for the initial pdf affects the number of iterations the algorithm will require to minimize the length of the residual curve; barring light curves that are severely dominated by the asynchronous component, a good choice for the initial pdf is the per-bin averaged phase-folded observed light curve.

\item[Compute the asynchronous curve] given observations $O_k(t_k)$ and the discrete pdf $X_k(\Phi_i)$, unfold $X_k(\Phi_i)$ to $X_k(t_j)$ for each timestamp $t_j$ in the observed dataset. As $X_k(\Phi_i)$ is discrete, linearly interpolate $X_k(t_j)$ from the two bounding bin ranges to minimize numerical artifacts. Then compute the residual curve $\widetilde Y_k \equiv O_k-X_k$.

\item[Compute partial derivatives] the slopes in the parameter space are described by the partial derivatives $\partial \hat L \widetilde Y_k/\partial X_i(\Phi_k)$, where $k$ enumerates iterations and $i$ enumerates pdf bins. These derivatives inform the algorithm how the length of the residual curve is affected by the change in each pdf bin value. We use the symmetrically discretized differences to approximate these derivatives:
\begin{equation} \label{eq:slopes}
    \frac{\partial \hat L \widetilde Y_k}{\partial X_k(\Phi_i)} \to \frac{\hat L \widetilde Y_k(\cdots X_{k,i} + \frac 12 \delta X_{k,i} \cdots) - \hat L \widetilde Y_k(\cdots X_{k,i} - \frac 12 \delta X_{k,i} \cdots)}{\delta X_{k,i}},
\end{equation}
where $\delta X_{k,i}$ is the change in the $i$-th pdf bin value.

\item[Compute an improved pdf] each per-bin pdf value is changed along the negative gradient computed in the previous step:
\begin{equation}
    X_k (\Phi_i) \to X_k(\Phi_i) - \xi \frac{\partial \hat L \widetilde Y_k}{\partial X_k(\Phi_i)},
\end{equation}
where $\xi$ is a constant that determines the step size along the slope.

\item[Iterate until the pdf is optimized] each change in the pdf reduces the length of the residual asynchronous curve. We repeat the process of modifying the pdf and computing the asynchronous curve length until the length in two consecutive steps changes by less than a prescribed tolerance $\eta$.

\end{description}

The result of this process is the \rev{separation of the strictly periodic pdf signal at period $P$ from} ``everything else\rev{,}'' i.e.~the asynchronous and the stochastic components of the net signal. This simple version of the algorithm depends on 4 parameters: number of pdf bins $N_b$, pdf per-bin value variation $\delta X_{k,i}$, descent step size $\xi$, and convergence stop criterion $\eta$. We provide some considerations on choosing the values of these parameters in Section \ref{sec:limitations} but stress that a more robust version of this algorithm could easily optimize these values as part of the execution process. \rev{We propose some efficient optimization steps in Section \ref{sec:conclusion}.}

\section{Case Studies} \label{sec:demo}

\subsection{Synthetic case}

To demonstrate and test the algorithm performance, we start with mock data. The composite signal $S(t)$ is generated using the following prescription:
\begin{equation} \label{eq:synthetic}
    S(t) = \left[ 1 + \frac 12 \sin \left( 2\pi \frac{t-t_0}{P} \right) + \frac 1{20} (t-5)^2 + e^{t/10-1} + \mathcal N(0, 0.05) \right] - 0.75 \mathcal H(5),
\end{equation}
where $X(t) \equiv 1+\sin(2\pi (t-t_0)/P)/2$ is the strictly periodic term with period $P$ and time offset $t_0$, the term $(t-5)^2/20$ is a quadratic part of the asynchronous component, $e^{t/10-1}$ is an exponential part of the asynchronous component, $\mathcal N(0, 0.05)$ is stochastic noise, and $\mathcal H(5)$ is the Heaviside step function that equals 0 for $t < 5$ and 1 for $t \geq 5$.
We generate S(t) for the time span of $10$ units, $P=0.91$ units and $t_0=0$ units. Thus, $S(t)$ is a composite function that consists of a strictly periodic signal, of a non-periodic asynchronous component with a discrete jump, and of a stochastic noise component. The top panel in Fig.~\ref{fig:synthetic} depicts a realization of this generative function.
\begin{figure}[t!]
    \centering
    \includegraphics[width=0.85\textwidth]{dps_synthetic.pdf} \\
    \caption{\textbf{Top}: synthetic (mock) signal that consists of a strictly periodic component with period $P=1$ unit, a non-periodic baseline that consists of a quadratic and an exponential function and features a discrete jump, and a stochastic noise component, cf.~Eq.~(\ref{eq:synthetic}). \textbf{Middle}: minimum length residual curve with the strictly periodic signal subtracted out. \textbf{Bottom}: strictly periodic component of the signal determined by minimizing the length of the residual curve.}
    \label{fig:synthetic}
\end{figure}

The algorithm was then run on these data with $N_b = 33$, $\delta X_{k,i} = 5 \times 10^{-4}$ units, $\xi = 10^{-3}$ and $\eta = 10^{-8}$. The results are depicted in the middle panel (asynchronous component) and in the lower panel (synchronous component). As this is a mock example, it gives us a benefit of comparing it against the known input. The synthetic data are depicted in blue, and the disentangled signal is depicted in red. Running the algorithm numerous times shows that, on average, the signal pdf is reproduced within the data uncertainty every time. This serves as proof of concept that the algorithm performs as expected.

\subsection{Eclipsing Binary Star KIC 3953981}

Astronomical objects that lend themselves readily to this algorithm's principal use are eclipsing binary stars (EBs). EBs serve as ideal astrophysical laboratories to measure their components' masses and radii: the well-understood laws of two-body dynamics and geometric considerations that lead to eclipses render inversion (the process to determine parameters from light and radial velocity curves) a tractable problem. As these masses and radii are used to calibrate the mass-radius relationship and proliferate through the rest of stellar and galactic astrophysics, as well as serve as principle distance gauges, particular effort needs to be invested to remove any and all artifacts from the observed data.

A majority of EB light curves are strictly periodic. A small number of EBs exhibit eclipse timing variations (ETVs) of the order of seconds to minutes, rarely hours. For as long as the bin size is larger than the (double) amplitude of the ETV, such light curves can also be considered strictly periodic. Any signals that are not commensurate with the orbital period (pulsations, non-synchronous spots, differential rotation effects, etc), and any dynamically variable features (transient spots, outbursts, etc) will be removed from the synchronous pdf by the algorithm. In some cases that is an added benefit as the modeling of the ``blemish''-free light curve might be favored over a complex model that includes dynamically and temporally variable effects.

We ran the algorithm on KIC 3953981, a circular, short-period eclipsing binary with orbital period $P=0.492$ days and $\mathrm{BJD}_0 \equiv t_\mathrm{ref}=54953.8225$, observed by the \textsl{Kepler} spacecraft over the course of $\sim$4 years. We used simple aperture photometry (SAP) data -- a \textsl{Kepler} pipeline deliverable that
does \emph{not} remove any trends. Given the light curve's short orbital period and smooth light curve variability, a modest number of bins, $N_b=101$, was sufficient to describe the synchronous pdf (cf.~Fig.~\ref{fig:observed}, left).
\begin{figure}[t!]
    \centering
    \includegraphics[width=0.49\textwidth]{dps_eb.pdf}
    \includegraphics[width=0.49\textwidth]{dps_heartbeat.pdf} \\
    \caption{
    \textbf{Top}: simple aperture photometry (SAP) light curve of KIC 3953981, an eclipsing binary star (left) and KIC 3547874, an eccentric ellipsoidal variable (right) observed by \textsl{Kepler}.  \textbf{Middle}: minimum length asynchronous part of the observed curve with the strictly periodic pdf subtracted out. \textbf{Bottom}: synchronous pdf determined by minimizing the length of the asynchronous curve.
    }
    \label{fig:observed}
\end{figure}
Other parameters of the algorithm were: $\delta x_{k,i} = 5 \times 10^{-4}$ normalized flux units, $\xi = 10^{-5}$ and $\eta = 10^{-8}$. Despite the demonstrably complex baseline, the algorithm performed convincingly well.

\newpage

\subsection{Eccentric Ellipsoidal Variable KIC 3547874}

Another of \textsl{Kepler} mission's notable successes was the observation of over a hundred eccentric ellipsoidal variables \citep{thompson2012}; their light curve resemblance to electro-cardiograms earned them the name of \emph{heartbeat} stars. The components in these highly eccentric binaries become highly distorted during their periastron fly-by due to the increase in tidal interaction, causing a spike in flux due to an increase in cross-section and reflection. In addition, periodic periastron ``pinches'' by tides can induce pulsations in one or both components that are commensurate with the orbital period and are revealed by the short sinusoidal oscillations in the light curve. Because of this, heartbeat stars are ideal testbeds to study tidally excited pulsations and resonance locking \citep{fuller2017, hambleton2018}.

Much like EBs, the orbital periods of hearbeat stars are largely constant, thus lending themselves readily to the algorithm. An added challenge is that, unlike EBs, heartbeat star light curves are usually very low in amplitude, and the signal is buried in noise. This makes detrending all the more difficult using conventional detrending algorithms.

We ran the algorithm on KIC 3547874, an eccentric ellipsoidal variable with orbital period $P=19.692$ days and $\mathrm{BJD}_0 \equiv t_\mathrm{ref} = 54989.421$, observed by the \textsl{Kepler} spacecraft over the course of $\sim$4 years. As before, we used the SAP data as input to the algorithm. Even though tidally induced pulsations were not evident in the original data, we used $N_b=201$ bins to make sure we have sufficient resolution to detect them (cf.~Fig.~2, right). Indeed, as the bottom panel demonstrates, the algorithm successfully extracted the signature of tidally induced pulsations at the 37$^\mathrm{th}$ harmonic of the orbital period. Other parameters of the algorithm were: $\delta x_{k,i} = 5 \times 10^{-4}$ normalized flux units, $\xi = 10^{-4}$ and $\eta = 10^{-9}$. Even though the peak-to-peak amplitude of the periastron brightening is only $\sim 0.3\%$ and the peak-to-peak amplitude of tidally induced pulsations is $\sim 0.01\%$, the algorithm was able to recover their signatures. Provided that the peak-to-peak amplitude of the background light curve is $> 2\%$, we conclude that the algorithm, despite its simplicity, performed better than expected.

\section{Limitations of the Algorithm} \label{sec:limitations}

The simple form of the algorithm presented here depends on the input light curve, the orbital period, and 4 parameters: $N_b$, $\delta X_{k,i}$, $\xi$ and $\eta$. All 4 parameters can in principle be hidden through automation, but we felt that doing so will obfuscate the clarity of the principle behind the algorithm and have opted to defer such optimization to subsequent code development. Here we discuss the roles of these parameters in more detail, along with possible optimization routes.

\begin{description}
\item[Number of bins $N_b$] measures the smoothness of the discrete pdf. If the number is too small, the pdf will not adequately capture the features present in the data; if the number is too large, the computation time cost will be prolonged and numerical errors due to low number statistics per bin \rev{may become significant}. Each additional bin adds a computation of one extra partial derivative $\partial \hat L \widetilde Y_k/\partial X_k(\Phi_i)$ and adds one extra degree of freedom. As the feature space is rarely uniform, the choice of an equidistant pdf as used above is likely inferior to advanced methods of binning data \rev{(see \citet{hogg2008} for an example)}. The algorithm in its present form also does not allow for empty pdf bins, so a reasonable value for $N_b$ has to be smaller than the number of observations per orbital period, possibly significantly smaller if a non-uniform cadence is used.

\item[Finite difference $\delta X_{k,i}$] used for the calculation of slopes in the parameter space. If $\delta X_{k,i}$ is too small, the algorithm will suffer from numerical noise. If too large, the slope will be poorly approximated and, depending on the topology of the parameter space, convergence might be compromised. The value of $\delta X_{k,i}$ is theoretically driven by the degree of linearity of the space of partial derivatives $\partial \hat L Y/\partial X_{k,i}$: $\delta X_{k,i}$ should be the same order of magnitude as the extent at which $\partial \hat L Y/\partial X_{k,i}$ is largely constant. Moreover, we adopt a single parameter for all $N_b$ finite differences $\delta X_{k,i}$, $i=1 \dots N_b$; for the same reasons as above, this can be optimized further by considering the feature properties across the phase space.

\item[Step size $\xi$] provides the extent of per-bin change of the pdf. If $\xi$ is too small, the algorithm will converge slowly; if too large, the algorithm will start to oscillate about the minimum and become unstable. This is also the most sensitive of all algorithm parameters and not trivial to estimate in advance. The telltale sign of the value of $\xi$ being too large is the oscillatory behavior of pdf corrections. The optimization process would thus identify the largest value of $\xi$ for which no oscillatory behavior is exhibited. This will vary from case to case, depending on the amplitude of the synchronous signal, the signal-to-noise ratio, and on the topology of the underlying parameter space.

\item[Convergence criterion $\eta$] determines the state at which the algorithm considers the signal pdf and the asynchronous component disentangled. If $\eta$ is too large, the two components will not be adequately separated; if too small, the number of iterations will increase to the point of inefficiency due to a high time cost, or even fail to converge if numerical artifacts prevent the difference in consecutive lengths $\hat L Y_{k+1}$ and $\hat L \widetilde Y_k$ \rev{from dipping below} $\eta$. Convergence is asymptotic and optimizing $\eta$ would imply finding a good trade-off between the accuracy of disentangling and the computational time cost based on the analysis of the asymptotic convergence behavior.

\end{description}

Another potential deficiency inherent to the simple version of the algorithm stems from using linear interpolation to compute intra-bin values of \rev{the} pdf. A more general solution would be to employ a higher order univariate spline. This issue diminishes with a sufficiently large bin number $N_b$; the telltale sign of the issue is a residual periodic signal in the asynchronous curve and an underestimated amplitude of the synchronous pdf. This is a consequence of the discrete pdf oscillating around the continuous pdf due to inadequate intra-bin interpolation, so the minimum length $\hat L Y$ will correspond to the discrete pdf with a slightly smaller amplitude rather than the correct amplitude and discrete oscillations.

A closer look at Fig.~\ref{fig:observed} might raise some eyebrows\rev{. The lower-right panel provides a likely example of one of the possible artifacts of the method. The extracted signal exhibits dips between phases 0.0 and 0.1 and between phases 0.9 and 1.0 which are unlikely to be real and are more probably caused by} (1) the tolerance $\eta$ set too high so that convergence is not yet complete; (2) the signal-to-noise ratio of observations being too low; \rev{(3) the solution corresponds to a local minimum that it cannot get out of; }or (4) that the length of the asynchronous part of the overall curve does not constrain the smoothness of the synchronous pdf adequately well. While any combination of these might be at play, the reason \rev{for the deviations in Fig.~\ref{fig:observed} is the latter: the coherence of the 37$^\mathrm{th}$ harmonic has a high spectral power that prevents \emph{collective} excursions of bins to happen and further improve the smoothness of the synchronous signal}. It is certainly possible to generalize the cost function to depend on the length of the asynchronous part of the curve \emph{and} on the smoothness of the synchronous pdf, for example by tracing the relationship between the synchronous pdf length and the asynchronous curve length via the partial derivative $\partial \hat L \widetilde Y_k/\partial \hat L X_k$\rev{, but doing this would introduce coupling parameters that would adversely affect the non-parametric nature of the pdf. We also note that the example depicted in Fig.~\ref{fig:observed} is particularly pathological and, as such, it requires special treatment that the majority of other signals do not need.}

Finally, note that the \emph{levels} of the disentangled parts are completely arbitrary. The algorithm is using euclidean distance to determine the length of the residual curve, so any and all level information is subtracted out. Thus, we cannot tell from the algorithm output alone what is the mean of the pdf nor what is the mean of the asynchronous part of the light curve. This might be inferred from modeling considerations (i.e.~expected depths of eclipses from measured luminosities of the stars), but such information would need to be applied a-posteriori to the algorithm output.

\section{Discussion} \label{sec:conclusion}

It is tempting to take the synchronous pdf to represent the astrophysical signal of interest itself. That would be incorrect; instead, it should be taken as a \emph{generating function} for the observations of that signal. In other words, if realistic observational noise (say, a Poisson shot noise) were added to the synchronous pdf, that would be a fair representation of what we might observe with an ideal instrument, i.e.~an instrument that does not modify or modulate observations. The question, then, is what we mean by ``realistic'' when we say ``realistic observational noise'' in the context of the derived pdf. As the (stochastic, non-instrumental) noise inherent in the observations from which the pdf is derived fundamentally limits the accuracy of the pdf, it is precisely that level of noise that should be added to the generating pdf. The disentangled signal, thus, is \emph{not} the pdf itself, but the pdf \emph{plus} the representative stochastic noise of the original dataset.

The algorithm can be readily applied to vast numbers of strictly periodic variables, ranging from eclipsing binaries and transiting extra-solar planets to single-modal pulsating stars. There are two principal uses for the algorithm: (1) to detrend the data and derive a generating function for the signal of interest, and (2) to determine the instrumental response, coupled with noise properties. The first use is likely intuitive to anyone working with data, while the second use might not be immediately obvious. For example, we could run the algorithm on all periodic variables observed by \textsl{Kepler} to derive the asynchronous part of their light curves and then study the dependence of that residual signal as a function of CCD position, magnitude, time, etc. Having those ``anchor'' signals, the entire CCD can be mapped and all remaining, non-periodic objects can be detrended using 2-D interpolation.

The algorithm can further be generalized to detrend \emph{any} signal that can be phase-folded. For example, including ETVs or orbital motion of the instrument due to barycentric motion, or any other effect that modulates the strictly periodic signal in a predictable manner allows us to phase-fold the data using a single period. Finally, multi-modal signals can also be detrended using the algorithm if the synchronous signal $X(t)$ in Eq.~(\ref{eq:signal}) is generalized as $\sum_i X_i(t)$, where each $X_i$ has a corresponding \emph{constant, independent} period (i.e.~it is \emph{not} a harmonic of any other input period or a combination of periods).

In this paper we deliberately refrained from optimizing and fine-tuning the algorithm to retain the clarity and to allow researchers to optimize it to their own needs that may differ from the general discussion presented above. In the online Appendix we provide complete scripts, written in \rev{P}ython 3 \citep{python1995}, to run the algorithm in jupyter notebooks and recreate the results depicted in Figs.~\ref{fig:synthetic} and \ref{fig:observed}. The notebooks and the data are also available at \texttt{http://keplerEBs.villanova.edu/DPS}.

\rev{A slightly more sophisticated, turn-key version of the code is released as open source, available from github\footnote{\texttt{https://github.com/aprsa/dips}} or via pip\footnote{\texttt{pip3 install dips}}. The released code includes three generalizations:}
\begin{description}

\item[Support for multi-processing] \rev{the computation of the slopes $\partial \hat L \widetilde Y_k/\partial X_i(\Phi_k)$ per Eq.~(\ref{eq:slopes}) is the bottleneck of the algorithm and can become a significant time sink. At the same time, the computation of the slope per bin is entirely independent and can be distributed to parallel processors when available. We use Python's \texttt{multiprocessing} module to achieve that. The computation of slopes is distributed across all available cores.}

\item[Slope-based convergence criterion] \rev{the basic algorithm presented here asserts that convergence is reached when the length change of the asynchronous curve dips below a certain threshold. This criterion is ad-hoc because it does not relate the length change and topology of the parameter space in any way. An alternative convergence criterion is to trace the magnitude of the slopes themselves and to assert convergence when the magnitude of the average down-step, i.e.~the product $\xi \left \langle \| \partial \hat L \widetilde Y_k/\partial X_i(\Phi_k) \| \right \rangle$, drops below a certain threshold. We \emph{start} with a predefined value of $\xi$ (say, $10^{-3}$) and reduce its value by an attenuation factor (say, 10\%) whenever the down-step taken was too large, i.e.~when the new length of the asynchronous curve is larger than the previous length of the asynchronous curve. Thus, as the algorithm approaches a minimum, the topology flattens and both $\xi$ and the mean absolute magnitude of the slopes tend to $0$. By connecting the tolerance for convergence with the step size, we directly relate the length of the residual curve to the topology of the parameter space.}

\item[Variable gradient descent] \rev{as stated above, the algorithm converges to \emph{a} minimum, but not necessarily to \emph{the} minimum. To avoid getting stuck in a local minimum, the algorithm does not descend along the gradient itself but, instead, along the randomly drawn gradient from the normal distribution centered on the actual gradient. The width of the distribution is a provided parameter and a reasonable value is between 5\% and 50\%. This is also known as the ``drunken sailor'' gradient descent.}

\end{description}

\rev{These additions to the algorithm make it more robust because the initial value of $\xi$ no longer affects convergence properties, tolerance is based on the shape of the parameter space and ``jittering'' the convergence path may help the algorithm avoid local minima. Of course, this cannot possibly satisfy all use cases out there so further adaptations will likely remain necessary by the users. With the source code available on github, we hope to make that task more tractable for everyone.}

\acknowledgements

The authors gratefully acknowledge support from the NSF grant \#1517460 and from the NASA grant 17-ADAP17-68 which led to the development of the presented algorithm.

redpajama_set_name: RedPajamaArXiv


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Weyes Blood & Tim Heidecker – "Oh How We Drift Away"
Later this week, the actor and comedian Tim Heidecker will release his new album Fear Of Death. Heidecker has been making vaguely satirical singer-songwriter music for a while now, and Fear Of Death seems like a more sincere embrace of the form. He recorded the album with a backing band that includes Drew Erickson, the…
For more, go to: Stereogum.com (Source)
Tim Heidecker – "Property" (Feat. Weyes Blood)
Tim Heidecker is mostly known as an actor and comedian. He did excellent work in the scene from Jordan Peele's Us, for instance, where he got brutally murdered while listening to the Beach Boys' "Good Vibrations." But Heidecker also has a side hustle making vaguely satirical '70s-style singer-songwriter music. Heidecker recorded his new album Fear…
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President goes on annual leave
15 Jan, 2022 - 00:01 2022-01-14T23:08:46+00:00 2022-01-15T00:04:10+00:00 0 Views
President Mnangagwa
Chronicle Reporter
PRESIDENT Mnangagwa has taken his annual leave which he will spend in the country.
Vice-President Dr Constantino Chiwenga is the Acting President.
In a statement yesterday, Deputy Chief Secretary for Presidential Communications in the Office of the President and Cabinet Mr George Charamba said:
"The Chief Secretary to the President and Cabinet, Dr Misheck Sibanda wishes to advise that His Excellency the President, Dr ED Mnangagwa, started his annual vacation yesterday 13th January 2022. His vacation, which runs until 5th February 2022, will be spent in the country.
During this period, Honourable Vice-President General (Retired) Dr CGDN Chiwenga is acting President."
Lockdowns worsened pre-existing dispari...20 Jan, 2022


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The Man Born to be King Archive
Identifier: Wade-A-59
PrintGenerating
Collection Organization
The Man Born to be King archive contains materials relating to the religious play of the same title by Dorothy L. Sayers. Printed copies of the play are found in folders 1-16, 40, and 42, and in the book listed under separated materials. The book, while remaining part of the archive, is now stored in the Wade Center book holdings, and may be retrieved by the archival staff upon request.
The archive is divided into 5 series: Play Scripts and Notes, Play-Related Correspondence and Fan Mail, Play-Related Press Cuttings, Heinz Geck Correspondence, and Book Photocopies. The Play Scripts and Notes series (folders 1-16) contains several scripts from the radio play The Man Born to be King (arranged chronologically), as well as production notes and directives. Some notes were handwritten by Sayers herself.
Correspondence and Fan Mail (folders 17-34) includes letters and fan mail relating to The Man Born to be King, generally arranged by correspondent's last name. Carbon copy replies from Sayers are often included next to the corresponding letters, as are enclosures such as press clippings and other items which are clearly related to certain letters. Miscellaneous notes and unrelated enclosures discovered amongst the correspondence are placed at the beginning of the series. Backs of letters may contain unidentified letters or works by Sayers.
The Press Cuttings series (folders 35-39) contains letters to the editor, book reviews, performance reviews, and topical articles which appear to have been gathered by news clippings services specifically for Dorothy L. Sayers. The clippings remain in the order they were found. More articles and reviews relating to The Man Born to be King can be found in the Wade Center article file. Consult the archivist for assistance.
The Heinz Geck Correspondence (folders 40-41) spans four years (1946-1949) and primarily includes letters between Sayers and Geck. Heinz Geck was a German prisoner of war who requested permission to translate The Man Born to be King into German. Sayers assisted him by answering questions, making suggestions, and providing notes on the play. The letters are arranged chronologically and notes that could not be linked to individual letters were placed at the back of folder 41.
The final series, Book Photocopies, (folder 42) contains copies of the cover and the inscription from the presentation copy of The Man Born to be King which Sayers gave to her husband, Mac. The book is stored in the Wade Center book holdings and may be retrieved upon request.
Created: 1940-1953, 2017
Other: Majority of material found in 1942-1944
Sayers, Dorothy L. (Sayers, Dorothy Leigh) (Person)
Copies or publication of materials by Dorothy L. Sayers require permissions from the Sayers Literary Executor.
Biographical or Historical Information
After the success of Sayers's earlier nativity play for radio, He That Should Come, which was broadcast in 1938, the Director of Religious Broadcasting for the B.B.C., J.W. Welch, wrote to Sayers in 1940 asking if she would consider writing a series of plays on the life of Jesus Christ. She agreed, and The Man Born to be King was written as a series of 12 plays spanning from Christ's birth to his death. The play cycle was first broadcast as a radio drama in 12 parts on the B.B.C. between December 1941 and October 1942.
Due to the subject matter and the use of "modern" dialogue in the plays, they were met with some opposition from various sectors. In contrast to the critics, however, were scores of individuals from many walks of life who related their appreciation of the plays in hundreds of letters to Sayers and the B.B.C. The play cycle remains one of Sayers's most significant works. The Man Born to be King was first published in book form by Victor Gollancz in 1943, shortly after its first broadcast. Several new productions of this play cycle have been broadcast over BBC radio in subsequent years.
The material in this archive was acquired at auction from Sotheby's in London by the Wade Center in 2000. The original Sotheby's lot(s) included in this archive are: Lot 290 iva-e and Lot 292 ix (fol. 21, p. 66a). Lot 290 ivb included the book in the listing of separated materials.
1.00 box : 42 folders – 2,266 pages, 1 book
The Man Born to be King archive contains materials relating to the religious play cycle of the same title by Dorothy L. Sayers including: drafts and scripts of the 12 dramas, production notes, correspondence and fan mail, press cuttings, and correspondence between Sayers and Heinz Geck, who translated the play into German.
01/1a
Researchers interested in this archive may also wish to consult the following resources in the Wade Center holdings:
"About the BBC radio broadcast of The Man Born to Be King." Glasgow Herald; the Weekly Review; Daily Telegraph (April/May 1942) AF-12458
"About the BBC radio broadcast of Man Born to Be King." Daily Telegraph (January/February 1942) AF-12461
"B.B.C. Life of Christ: Broadcast to Proceed." The (London) Times (9 January 1942): 2. AF-5960
Drakakis, John. British Radio Drama. Cambridge: Cambridge University Press, 1981.
Fairman, Marion Baker. THE NEO-MEDIEVAL PLAYS OF DOROTHY L. SAYERS. Ph.D., University of Pittsburgh, 1961. Dissertation
"Following Protest has been lodged with the B.B.C." Lord's Day Observance Society). (n.d.) AF-12627
Frieseke, Angela. DOROTHY L. SAYERS' "THE MAN BORN TO BE KING' SEINE STRUMTUR UND SEINE GESTALTUNG ALS HORSDIELZYKLUS. Ph.D., Westfalischen Wilhelms - Universitat zu Munster (Westf.), 1966. Dissertation
Gielgud, Val. "Years of the Locust." Years of the Locust. (London: Nicholson & Watson). (1947): 10-13, 44-45, 72-73, 78-79, 88-89, 92-93, 110-111, 142-43, 176-81, 196-97. AF-15920
Hampel, Michael Hans Joachim. DOROTHY L. SAYERS: CREATIVE MIND AND THE HOLY TRINITY. M.A., St. Chad's College, University of Durham, 2002. Dissertation
Hookey, Joseph Ralph. JOHN THE BAPTIST IN THE CONTEXT OF CONTEMPORARY RELIGIOUS MOVEMENTS WITHIN JUDAISM. Ph.D., University of Edinburgh, 1963. Dissertation
THE MAN BORN TO BE KING : Title pages, Dedicatory : "The Makers," Introduction, and First Play - Second Play. Incomplete. (ca. 1940-1942) 137 pp. AMs. in 116 lvs. (DLS manuscript #128)
THE MAN BORN TO BE KING : Third Play - Fifth Play, with Biblical references. (ca. 1940-1942) 146 pp. in 107 lvs.: 145 pp. AMs., 1 p. TMs. (DLS manuscript #129)
THE MAN BORN TO BE KING : Sixth Play - Eighth Play. Incomplete. Incomplete version of "Blood Sacrifice" (MS-250) found on versos of TMs. pages. (ca. 1940-1942) 172 pp. in 99 lvs. with revisions: 160 pp. AMs., 12 pp. TMs. (DLS manuscript #130)
THE MAN BORN TO BE KING : Ninth Play - Twelth Play. Fragment of "Holmes' College Career" (MS-114) and a title page from "Studies in Sherlock Holmes" (MS-212) found on versos of some cc. TMs. pages . (ca. 1940-1942) 201 pp. in 118 lvs. with revisions. (DLS manuscript #131)
"Production Notes on The Man Born to be King ." BBC Features and Drama (1967 or 1975): 14PP. AF-6022
Reviews of the book and the performance of The Man Born to be King, see the Wade Center article file, Dorothy L. Sayers review section.
Sayers, Dorothy L. Related correspondence and miscellanea in the Dorothy L. Sayers Papers folders: 314, 321-325, and 520a &b.
Wood, Bethany. Incorporation of the Incarnation: Dorothy L. Sayers's The Man Born to be King and the Wartime BBC. Master's Thesis. University of Wisconsin-Madison, 2008. Dissertation collection.
See also the Religious Illustrated Cards and Booklets Archive, folder 1.
Other materials in the Wade Center holdings may relate to the topics in this archive. See the archivist for further research assistance.
Separated Materials
(ask the archivist for retrieval):
Sayers, Dorothy L. THE MAN BORN TO BE KING. Forward by J.W. Welch. London: Victor Gollancz, 1943. 1st edition, inscribed by DLS to her husband, Mac.
Other Descriptive Information
There is an acquisition file for this collection. Materials in this archive are also described in the Sayers Manuscripts collection: DLS / MS-51, 99, 114, 250, 275-277, and the Wade Center book holdings. There is a research copy of this collection.
Processed by Laura Schmidt
Jesus Christ -- Drama.
Radio plays.
Sayers, Dorothy L.
Sayers, Dorothy L. -- Archives.
Sayers, Dorothy L. -- Correspondence.
Wade. Marion E. Wade Center
Finding Aid & Administrative Information
Laura Schmidt
Description rules
Describing Archives: A Content Standard
Physical Storage Information
Container: A-59 (Text)
Container: Cabinet 10 (Text)
Container: Drawer 1 (Text)
Part of the Marion E. Wade Center Repository
http://www.wheaton.edu/wadecenter/
Wheaton IL 60187-5593 US
wade@wheaton.edu
Description of material cited. The Man Born to be King Archive, Box #, Folder #. Marion E. Wade Center, Wheaton College, Wheaton, IL. https://archives.wheaton.edu/repositories/3/resources/428 Accessed January 19, 2021.


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A gardener has landed himself in hot water after he was spotted using his phone behind the wheel of his ride-on lawnmower - outside a police station.
The 47-year-old council gardener allegedly pulled out his phone while sat at traffic lights right outside a police station in Ely, Cardiff.
Officers then pulled over his green John Deere ride-on lawnmower. The worker told how he picked up his phone to change some music on his way between grass-cutting jobs.
But he was accused of illegally using the phone at the wheel on a public road - even though it was a lawn-mower and not a car. The worker is set to appear in front of magistrates later this month where he could face a £200 fine, six points on his licence or both.
Police were handed dashcam footage of the gardener holding his phone in his left hand as he steered with his right - and with a marked police van on the busy road just yards behind.
Cardiff Council confirmed the man was one of their employees and said he would face disciplinary action.
My comment is that I often see Police Officers using their mobile phone whilst driving. What makes them so special? Perhaps they think they are a 'cut above the rest' of us?