Plumbing emergencies are common in Chicago, and until one strikes, you don't really know if there is a leak in your fixtures. This is why initiatives like the Fix a Leak Week are being used to prevent plumbing emergencies.
REALTOR® Sonia Anaya, broker-owner of America Real Estate in Chicago, has received the 2016 Illinois REALTORS® Political Involvement Award. The award is given to individuals for outstanding political and legislative service to the REALTOR® organization.
The Boulder Group, a net leased investment brokerage firm, has completed the sale of a single tenant new construction Dollar General located at 1107 N Santa Fe Avenue in Princeville, Illinois for $1,145,681.
The Boulder Group, a net leased investment brokerage firm, has completed the sale of a single tenant core located PNC Bank Ground Lease located at 1640 W Fullerton Avenue in Chicago, IL for $6,000,000. The Property is located in the Lincoln Park neighborhood, one of Chicago's wealthiest and most expensive communities with average single-family home prices of approximately one million dollars.


text:
'The Flash' & 'Legends of Tomorrow' Hit Series Low Ratings
by William Outlaw on March 8, 2017
Could the CW superhero monopoly be collapsing? For some reason or another, viewers have stopped tuning into Flash and Legends of Tomorrow specifically this season. After dropping 18% in the 18-49 demographic compared to Season 2, The Flash has now reached the 0.9 rating with 2.49 million viewers in that demo, marking a season and series low. Similarly, Legends of Tomorrow dropped a whole tenth of a point from last week, coming to a 0.5 rating and 1.55 million viewers, which is also a series low. Arrow hit its own series low just a few weeks ago as well.
Although both of these numbers sound pretty bad (and they would be on another network), The Flash is still the highest rated show on the CW, and Legends is still tied in third with Arrow. Unfortunately, each DC show is undergoing massive year to year loss in viewers. Supergirl, which is in second place at the moment, is suffering from an astounding 53% drop from last season. However, the series started out on CBS where there are many more viewers anyway. Still, Flash is dropping 20% season to season and Arrow is dropping 29%. Legends is curiously actually doing the best in these terms with only a 17% drop from last season.
Thankfully neither show is in a danger of cancelling since, as I said earlier, they are still the top shows on the CW. If you are a fan of the CW DC shows, be sure to show your support. We wouldn't want another Constantine fiasco on our hands.
For more on Flash, Legends of Tomorrow, Supergirl and Arrow, be sure to come back to Heroic Hollywood!
Source: Screener and TV Series Finale
William Outlaw

redpajama_set_name: RedPajamaCommonCrawl


text:
Laws of Logic Lead to New Restrictions on the Big Bang
By Charlie Wood
Physicists are translating commonsense principles into strict mathematical constraints on how our universe must have behaved at the beginning of time.
Patterns in the ever-expanding arrangement of galaxies might reveal secrets of the universe's first moments.
Dave Whyte for Quanta Magazine
AdS/CFTBig BangbootstrapCMBcosmologyinflationphysicstheoretical physicsAll topics
For over 20 years, physicists have had reason to feel envious of certain fictional fish: specifically, the fish inhabiting the fantastic space of M.C. Escher's Circle Limit III woodcut, which shrink to points as they approach the circular boundary of their ocean world. If only our universe had the same warped shape, theorists lament, they might have a much easier time understanding it.
Escher's fish lucked out because their world comes with a cheat sheet — its edge. On the boundary of an Escher-esque ocean, anything complicated happening inside the sea casts a kind of shadow, which can be described in relatively simple terms. In particular, theories addressing the quantum nature of gravity can be reformulated on the edge in well-understood ways. The technique gives researchers a back door for studying otherwise impossibly complicated questions. Physicists have spent decades exploring this tantalizing link.
Inconveniently, the real universe looks more like the Escher world turned inside out. This "de Sitter" space has a positive curvature; it expands continuously everywhere. With no obvious boundary on which to study the straightforward shadow theories, theoretical physicists have been unable to transfer their breakthroughs from the Escher world.
"The closer we get to the real world, the fewer tools we have and the less we understand the rules of the game," said Daniel Baumann, a cosmologist at the University of Amsterdam.
But some Escher advances may finally be starting to bleed through. The universe's first moments have always been a mysterious era when the quantum nature of gravity would have been on full display. Now multiple groups are converging on a novel way to indirectly evaluate descriptions of that flash of creation. The key is a new notion of a cherished law of reality known as unitarity, the expectation that all probabilities must add up to 100%. By determining what fingerprints a unitary birth of the universe should have left behind, researchers are developing powerful tools to check which theories clear this lowest of bars in our shifty and expanding space-time.
Unitarity in de Sitter space "was not understood at all," said Massimo Taronna, a theoretical physicist at the National Institute for Nuclear Physics in Italy. "There is a huge jump that has happened in the last couple of years."
The unfathomable ocean that theorists aim to plumb is a brief but dramatic stretch of space and time that many cosmologists believe set the stage for all we see today. During this hypothetical era, known as inflation, the infant universe would have ballooned at a truly incomprehensible rate, inflated by an unknown entity akin to dark energy.
Cosmologists are dying to know exactly how inflation might have happened and what exotic fields might have driven it, but this era of cosmic history remains hidden. Astronomers can see only the output of inflation — the arrangement of matter hundreds of thousands of years after the Big Bang, as revealed by the cosmos's earliest light. Their challenge is that countless inflationary theories match the final observable state. Cosmologists are like film buffs struggling to narrow down the possible plots of Thelma and Louise from its final frame: the Thunderbird hanging frozen in midair.
The final frame of Thelma and Louise (left) and the cosmic microwave background radiation (right) both depict the last instant of an epic saga.
Roland Neveu / PictureLux / The Hollywood Archive / Alamy Stock Photo; ESA, Planck Collaboration
Yet the task may not be impossible. Just as currents in the Escher-like ocean can be deciphered from their shadows on its boundary, perhaps theorists can read the inflationary story from its final cosmic scene. In recent years, Baumann and other physicists have sought to do just that with a strategy called bootstrapping.
Cosmic bootstrappers strive to winnow the crowded field of inflationary theories with little more than logic. The general idea is to disqualify theories that fly in the face of common sense — as translated into stringent mathematical requirements. In this way, they "hoist themselves up by their bootstraps," using math to evaluate theories that can't be distinguished using current astronomical observations.
One such commonsense property is unitarity, an elevated name for the obvious fact that the sum of the odds of all possible events must be 1. Put simply, flipping a coin must produce a heads or a tails. Bootstrappers can tell at a glance whether a theory in the Escher-like "anti-de Sitter" space is unitary by looking at its shadow on the boundary, but inflationary theories have long resisted such simple treatment, because the expanding universe has no obvious edge.
Physicists can check a theory for unitarity by laboriously calculating its predictions from moment to moment and verifying that the odds always add up to 1, the equivalent of watching a whole movie with an eye for plot holes. What they really want is a way to glance at the end of an inflationary theory — the film's final frame — and instantly know whether unitarity has been violated during any previous scene.
But the concept of unitarity is linked closely to the passage of time, and they've struggled to understand what shape the fingerprints of unitarity would take in this final frame, which is a static, timeless snapshot. "For many years the confusion was, 'How the hell can I get information about time evolution … in an object where time doesn't exist at all?'" said Enrico Pajer, a theoretical cosmologist at the University of Cambridge.
Last year, Pajer helped bring the confusion to an end. He and his colleagues found a way to figure out if a particular theory of inflation is unitary by looking only at the universe it produces.
In the Escher world, checking shadow theories for unitarity can be done on a cocktail napkin. These boundary theories are, in practice, quantum theories of the sort we might use to understand particle collisions. To check one for unitarity, physicists describe two particles pre-crash with a mathematical object called a matrix, and post-crash with another matrix. For a unitarity collision, the product of the two matrices is 1.
Where do physicists get these matrices? They start with the pre-crash matrix. When space holds still, a movie of a particle collision looks the same played forward or backward, so researchers can apply a simple operation to the initial matrix to find the final matrix. Multiply those two together, check the product, and they're done.
But expanding space ruins everything. Cosmologists can work out the post-inflation matrix. Unlike particle collisions, however, an inflating cosmos looks quite different in reverse, so until recently it was unclear how to determine the pre-inflation matrix.
"For cosmology we would have to exchange the end of inflation with the beginning of inflation," Pajer said, "which is crazy."
Last year, Pajer, along with his colleagues Harry Goodhew and Sadra Jazayeri, figured out how to calculate the initial matrix. The Cambridge group rewrote the final matrix to accommodate complex numbers as well as real numbers. They also defined a transformation involving swapping positive energies for negative energies — analogous to what physicists might do in the particle collision context.
But had they found the right transformation?
Pajer then set out to verify that these two matrices really do capture unitarity. Using a more generic theory of inflation, Pajer and Scott Melville, also at Cambridge, played the birth of the universe forward frame by frame, looking for illegal unitarity violations in the traditional way. In the end, they showed that this painstaking process gave the same result as the matrix method.
The new method allows them to skip the moment-by-moment calculation. For a general theory involving particles of any mass and any spin communing via any force, they could see if it is unitary by checking the final outcome. They had discovered how to reveal the plot without watching the movie.
The new matrix test, known as the cosmological optical theorem, soon proved its power. Pajer and Melville found that a lot of possible theories violated unitarity. In fact, the researchers ended up with so few valid possibilities that they wondered if they could make some predictions. Even without a specific theory of inflation in hand, could they tell astronomers what to search for?
Cosmic Triangle Test
One revealing imprint of inflation is the way galaxies are distributed across the sky. The simplest pattern is the two-point correlation function, which, roughly speaking, gives the odds of finding two galaxies separated by particular distances. In other words, it tells you where the universe's matter is.
Our universe's matter is spread out in a special way, observations have found, with dense spots stuffed full of galaxies that come in a variety of sizes. The theory of inflation arose in part to explain this peculiar finding.
The universe started out quite smooth overall, the thinking goes, but quantum wiggles imprinted space with tiny dollops of extra matter. As space expanded, these dense spots stretched out even as the tiny ripples continued to arise. When inflation stopped, the young cosmos was left with dense spots ranging from small to large, which would go on to become galaxies and galaxy clusters.
All theories of inflation nail this two-point correlation function. To distinguish between competing theories, researchers need to measure subtler, higher-point correlations — relationships between the angles formed by a trio of galaxies, for instance.
Typically, cosmologists propose a theory of inflation involving certain exotic particles, and then play it forward to calculate the three-point correlation functions it would leave in the sky, giving astronomers a target to search for. In this way, researchers tackle theories one by one. "There are many, many, many possible things you could look for. Infinitely many, in fact," said Daan Meerburg, a cosmologist at the University of Groningen.
Pajer has turned that process around. Inflation is thought to have left ripples in the fabric of space in the form of gravitational waves. Pajer and his collaborators started with all possible three-point functions describing these gravitational waves and checked them with the matrix test, eliminating any functions that failed unitarity.
In the case of a certain type of gravitational wave, the group found that unitary three-point functions are few and far between. In fact, only three pass the test, the researchers announced in a preprint posted in September. The result "is very remarkable," said Meerburg, who was not involved. If astronomers ever detect primordial gravitational waves — and efforts are ongoing — these will be the first signs of inflation to look for.
Positive Signs
The cosmological optical theorem guarantees that the probabilities of all possible events add up to 1, just as a coin is certain to have two sides. But there is another way of thinking about unitarity: The odds of each event must be positive. No coin can have a negative chance of landing on tails.
Victor Gorbenko, a theoretical physicist at Stanford University, Lorenzo Di Pietro of the University of Trieste in Italy, and Shota Komatsu of CERN in Switzerland recently approached unitarity in de Sitter space from this perspective. What would the sky look like, they wondered, in bizarro universes that broke this law of positivity?
Taking inspiration from the Escher world, they were intrigued by the fact that anti-de Sitter space and de Sitter space share one fundamental feature: Viewed properly, each can look the same at all scales. Zoom in near the boundary of Escher's Circle Limit III woodcut, and the shrimpy fish have identical proportions to the whoppers in the middle. Similarly, quantum ripples in the inflating universe generated dense spots large and small. This common property, "conformal symmetry," recently allowed Taronna, who has been working with Charlotte Sleight, a theoretical physicist at Durham University in the U.K., to port a popular mathematical technique for breaking apart boundary theories between the two worlds.
Video: David Kaplan explores the leading cosmological explanation for the origin of the universe.
Gorbenko's group further developed the tool, which let them take the end of inflation in any universe — the hodgepodge of density ripples — and break it into a sum of wavelike patterns. For unitary universes, they found, each wave would have a positive coefficient. Any theories predicting negative waves would be no good. They described their test in a preprint in August. Simultaneously, an independent group led by João Penedones of the Swiss Federal Institute of Technology Lausanne arrived at the same result.
The positivity test is more exact than the cosmological optical theorem, but less ready for real data. Both positivity groups made simplifications, including stripping out gravity and assuming flawless de Sitter structure, that will need to be modified to fit our messy, gravitating universe. But Gorbenko calls these steps "concrete and doable."
Cause for Hope
Now that bootstrappers are closing in on the notion of what unitarity looks like for the outcome of a de Sitter expansion, they can move on to other classic bootstrapping rules, such as the expectation that causes should come before effects. It's not currently clear how to see the traces of causality in a timeless snapshot, but the same was once true of unitarity.
"That's the most exciting thing that we still don't fully understand," said Taronna. "We don't know what is not causal in de Sitter."
As bootstrappers learn the ropes of de Sitter space, they hope to zero in on a few correlation functions that next-generation telescopes might actually spot — and the few theories of inflation, or even gravity, that could have produced them. If they can pull it off, our swollen universe might someday look as transparent as the world of Escher's fish.
"After many years of working in de Sitter," Taronna said, "we are finally starting to understand what the rules of a mathematically consistent theory of quantum gravity are."
Update: November 12, 2021
This article has been edited to clarify how the positivity test for unitarity was developed. Massimo Taronna and Charlotte Sleight first imported a tool for breaking apart boundary theories from Anti de Sitter space to de Sitter Space. Then the groups of Gorbenko and Penedones extended it to arrive at the positivity test.
Mathematicians Find Structure in Biased Polynomials


This study investigated the hypothesis that the coupled contribution of all body segments to the whole-body response during both walking and managing unexpected perturbations is characterized by similar features which do not depend on the laterality (i.e., right versus left sides), but can be influenced by the direction (e. g., north, east, south, etc.) of the perturbation. The whole-body angular momentum was estimated as summation of segmental angular momenta, while 15 young adults managed ten unexpected unilateral perturbations during walking. Then, the Principal component analysis was used to extract primitive features describing intersegment coordination. Results showed that intersegment coupling was similar even though the reactive response to the perturbations elicited more consistent motor schemes across body segments than during walking, especially in the frontal plane. The direction of the perturbation significantly (p < 0.05) affected angular momentum regulation documenting the attitude of the central nervous system to interpret multiple sensory inputs in order to produce context-dependent reactive responses. With respect to the side, results highlighted anisotropic features of the elicited motor schemes that seemed to depend on subjects' dominance. Finally, results confirm that the coordination of upper and lower body segments is synergistically achieved strengthening the hypothesis that it may result from common neural pathways.


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CheckPoint: Teaching as a Professional Career Resource: Ch.1 of Introduction to Teaching Write a 200- to 300- word paper in which you list 3 to 5 factors that define teaching as a professional career. Elaborate on how these factors are employed by teachers on a daily basis.
Identify internal or external rewards that affect recruitment and retention of quality teachers. How do such rewards influence recruitment or retention? How might these rewards shift as new accountability-centered teacher reforms are proposed, such as merit pay and competency testing?
In your opinion, will teacher reforms, such as comprehensive testing of teachers or requiring ongoing professional development, attract or intimidate individuals from joining the teaching profession? How do the reforms affect your own desire to enter the profession? Explain your answers.
Use a Microsoft® Excel or Word table function to propose and create a schedule of school-related tasks for a typical teaching day from the time you arrive at school until the time you leave school at the end of the day. Remember to take into account the education level you expect to teach (elementary or secondary).
Search the Internet for three time management tips for teachers.
List the tips, in a separate document and answer this question: How do you think these tips will affect your daily schedule as an educator? Provide a comment on how each one serves to improve your success or reduce your daily stress.
Format your sources according to APA standards.
When you are finished, click the Submit Answers for Gradingbutton at the bottom.
Scroll down to question 5 to read the feedback.
Schedule a brief (15-minute) interview with a teacher or a teacher's aide. The interview may be in person, by phone, via e-mail, or in an instant message chat.
Is it best to adjust instruction to teach in accordance with individual learning styles or should students experience and be encouraged to participate in activities that require learning styles other than those they naturally prefer? In other words, if a child's preferred learning style is visual and field independent (prefers to work alone), should all instruction be based on visual, independent activities, or should the student also be accountable for participation in group activities that incorporate other modes of learning: for example, bodily/kinesthetic, auditory, and so forth? Explain your answer then respectfully respond to a classmate's post with an opposing viewpoint.
AED 201 WEEK 4 CHECKPOINT SOCIOECONOMIC STATUS, STUD.ACHIEV.
Identifythe name and location of the school or school district you're investigating; include this information in your response.
Locate and recordinformation that would indicate SES of the school or district (such as household income, students eligible for free/reduced lunch fee program, education level of parents, and so forth).
Locate and recordinformation that would indicate student achievement (such as performance on standardized tests).
Compare and discussactual student achievement scores with your expectations based on your observations of SES. Did your observations match your expectations? Explain why or why not.
Search the Web to see how your community might be involved at the school or district you're investigating. School, district, city, chamber of commerce, county, or state Web sites may provide information. What programs, if any, exist for the school or district that address the needs of students having low SES? What types of programs should or could the school, district, or community provide?
Discuss at least one program.
Discuss, in 250 to 300-words, how one of the events has shaped today's classroom and how that event is still reflected in today's classroom.
Readp. 134 of the text, which discusses the way one school district addresses the needs of a group of at-risk students.
Use the Internet and Library databases to research one or more exemplary programs in your state, school district, or community that help meet the needs of the selected group of at-risk students.
Writea 700- to 1,100-word paper that includes your description of the category of at-risk students you chose and the programs you found for the selected type of at-risk students.
Determine which factors may explain that most of the higher per-pupil expenditures are found in the Northeastern and upper-Midwest states and the lower per-pupil expenditures are found in the South and West. In your opinion, what must happen to create a balance in school funding across regions?
Many U.S. citizens believe that parents and students must have the right to school choice. Others, however, believe school choice creates greater stratification and segregation among public schools. For example, some argue strong schools have better equipped students and weaker schools have more challenging, less-prepared students.
Consult the roster posted in the Mainforum to determine the school choice viewpoint your instructor assigned to you. After reviewing Ch. 8 and Internet articles relating to school vouchers, post an informed statement from a parent's point of view that is meant to persuade voters to support your position.
Cite your sources according to APA standards.
Format yourpaper according to APA standards.
Are there certain curricular areas in which technology is more useful than in others? Explain your answer.
Use Appendix A to help you create a Professional Development Plan—a component that may be added to your professional portfolio.
What professional development programs might you enroll in to help you prepare to meet the diverse needs of today's learners?


First Night Buffalo – Monday, December 31st from 5 to 10 p.m. at the Buffalo Niagara Convention Center, 153 Franklin St. in downtown Buffalo. It's Buffalo's biggest drug- and alcohol-free New Year's Eve celebration, with family activities throughout the evening. Tickets are $8 in advance at WNY Wegmans stores, children 2 and under are free; tickets will be $10 at the door. Find out more about First Night at www.firstnightbuffalo.org.
Buffalo Ball Drop – Monday, December 31st beginning at 10:30 p.m. at the Electric Tower in downtown Buffalo. The free event, in its 25th year, will feature live music throughout the night and the ball drop and fireworks display at midnight.
Hard Rock Café New Year's Eve Guitar Drop – Monday, December 31st at 8 p.m. at the Hard Rock Café Niagara Falls USA, 333 Prospect St. in Niagara Falls. The fourth annual Guitar Drop will feature a free outdoor concert from Everclear with special guests Eve 6 and The Albrights. Food and beverages will be available on the street and in the 103.3 The EDGE heated Party Tent, open to the general public. Find out more about the event at the HRC website.
Gateway Harbor Ball Drop – Monday, December 31st beginning at 6 p.m. at Gateway Harbor Canal Park in the Tonawandas. Family activities include two alcohol-free kids' fun zones and a merchant scavenger hunt, along with music from High Horse in the heated tent on Sweeney St. along with food vendors. For the 21-and-over crowd, there's a Pub Crawl through Tonawanda and North Tonawanda ($10 pre-sale, $15 day of event). Get complete details at www.gatewayballdrop.com.
New Year's Eve at Holiday Valley – Monday, December 31st beginning at 9 p.m. in the Holiday Valley Lodge, located on Route 219 in Ellicottville. The indoor family-friendly event will feature dancing, games, cocktails and mocktails. Outside, the Snowcat Parade begins at 11:15 p.m. on the slopes, followed by the Torchlight Parade at 11:30 p.m.; fireworks will lead up to midnight. Find out more about the event at www.holidayvalley.com.


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The building of the University Library, located at the heart of the Guyanese University Campus has to be a driving force within the University and contribute to its regional radiance. It is a structuring facility for all the buildings that constitute the Guyanese University Campus : its vocation is to gather books and readers in a unique place dedicated to knowledge, an open and generous place within the University. It is about providing a cultural and documentary service of quality and also materialise the image of the regional community, therefore one of the main issues is to give to the building of the University Library a physical, social and symbolic identity that will impact the one of the neighbourhood and of the city.
Our aim is to give to this unique building for its program and its central position, a proper architecture – identifiable by its volumetry and its uses – combined to an opening upon the whole University.
The main architectural choice is the creation of an open peripheral space : unlike a construction cast in one piece with no dialogue with the surrounding, the building is wrapped up with a peripheral space of variable dimensions called "gallery" or peristyle. This gallery is an open space, a place where the students meet and pass through, an extra room between inside and outside, sheltered from sun and rain.
Additional wealth, the peristyle forms a place to exchange, a public space taken over – and even "the space for the public" – which connects the library to the rest of the University : the library is a place for studying that is not cut off from the rest of the world, all it takes to see the life of the University Campus is to look up when sitting at a reading table and have a look at the traffic and motions in the gallery. This one is made of a filter : a slope of wooden lace carefully placed around a concrete core.
• to offer a building of great unity and create a landmark on the University Campus.
The construction industry in general, is a field highly consumer for the primary resources (water, energy, raw material) and great waste producer. Our thought has naturally been brought towards an Amazonian Environmental Quality process, version of the High Environmental Quality certification (HQE®) in tropical and subtropical countries.
_ international : greenhouse effect ; ozone layer (refrigerants from the air conditioning).
The sun protection of the building rests on the principle of the double-skin façade. All the facades and particularly the W/E facades are protected by this wooden filter that forms a very effective brise soleil, a second roof protects the programmatic heart from the solar radius very intense in Guyana (proximity of the Equator).
It is a decisive condition : it consists in providing a diffuse light into the room so that any angle with which one takes a book, there are no embarrassing reflections.
The project offers a gentle and enveloping light, as a result of the many openings spread over the facade : the generous light first filteres by the wooden skin is then released in a homogeneous manner inside the building.
With the same logic, the artificial light is regularly distributed in order to avoid any brutal dazzling light or source of reflections and backlighting.
By implementation of absorbing materials : soundproof ceiling, plaster wall lining for sound insulation of the Mezzanine and the training / exhibition rooms, etc, offer inside calm inviting concentration.
The library is considered as an open space, with wide reception spaces, diverse reading and research spaces and the possibility of lending books. It is also a facility that combines traditional documentation and modern technologies.
The building is composed of 2 parts : one that receives the public and one reserved for administration and its technical rooms.
The spaces dedicated to the public are located on the ground floor and on the mezzanine ; the ones for the administration on the ground floor and the upper level.
Patios and rifts mark this dissociation and improve the lighting at the centre of the building.
Once coming through the gallery – true threshold – the library is reached through a double door entrance space open on a wide entrance hall.
Into the hall there are : a waiting area, a reception desk, and in the back the sanitaries (the central position of this desk allows to control at a distance away from the reading room).
After going through the access control, the visitor directly reaches the lending desk, the press room, or the temporary exhibition space.
The documentary room largely extends in the whole space located behind the reception desk and the temporary exhibition space.
Two patios have been set up in order to bring natural light at the core of the building between the public part and the administrative part, and also in anticipation of an extension requested in the program. The central patio therefore becomes the heart of the connection element organised in a thematic garden.
– in the documentary room, spaces dedicated to individual consultation : individual work cubicles and research networks ; reachable directly from the large central staircase or from a smaller staircase on the side. This configuration offers privileged workplaces that have a clear view over the large room located below.
– a "box" or an autonomous volume that contains the multimedia training room on one side and the exhibition room on the other. The latter is also reachable from a staircase that gives onto the entrance hall.
The entrance to the administrative part is direct from the ground floor, taking the elevator or stairs located on the side of the patio. The offices and the common premises are divided on both sides of the staircase ; they all benefit from natural lighting and views outside and to the patio.


I'm often in our local public library but I'd never thought to look for our Dinner Club Mysteries before. And, there they were, all three of them. I'm so delighted the series is available in our branch in Half Moon Bay, anyway. Now, our food adventures, and our sleuthing skills, can be shared with all readers. I know I should feel more humble about all this but I'm just so excited. I want to spread the word.
Of course, I'm a big supporter of libraries and have been since I was a child. I thank my parents for that. I spent many hours lost in a book, slumped in a chair in the kids section. It was a regular weekly visit and I've continued that tradition, as best I can, to this day. That's also where my love of mysteries started, reading Trixie Belden and Nancy Drew.
I guess that's where I got hooked on cookbooks also because, just between us, my Mom wasn't much of a cook. Of course, her meals were always well-balanced and nutritious, but not very creative. I remember the first time I walked past the display of cookbooks at the library. Those covers set my mouth watering and once I peered inside, it just kept getting better.
So, here's to libraries and to everyone who uses them! See you between the covers.
To celebrate National Library Week, I'm having a draw for any book of your choice in the Dinner Club Mysteries, to be sent to your local public library. I'm thinking, smaller regional libraries in particular. So if you'd like to submit your library's name, just add your email addy and I'll make the draw tomorrow at 6 PM.
We are a small town of less than 3,000 population and we are the county seat. :) I would like to submit Stone County Library in Mountain View, AR.
Here's to libraries, be they large or small.
Our local library had so much activity they had to build another one nearby to handle it all!
Donamaekutska7@gmail.com our library needs to add on its very popular.
Your books are already in residence at my library.
Just wanted to add that this is Jefferson County, Indiana.


text:
\section{Introduction}
\label{introduction}

\subsection{Warehousing in e-commerce}
\label{warehousing}

Warehousing occupies a central role in a supply chain. According to \cite{Gu2007}, the primary purposes of a warehouse are to act as a buffer to adapt to the variability of the production flow; to consolidate products; and to add marginal value such as pricing, labelling or customisation.

The recent and massive development of e-commerce introduces great challenges in the \emph{Business to Customer} segment. E-commerce involves enormous volumes of orders, and online sales keep growing in number: in 2016, e-commerce sales grew by 23.7\%, accounting for 8.7\% of the total market \citep{Boysen2019ManualProblem}. These orders consist, on average, of very few items: the same authors mention that the average number of items per order at Amazon is only 1.6. E-commerce also faces great demand uncertainty, with fast-changing demand trends, and the need to satisfy orders quickly \citep{Yaman2012ReleaseDelivery, Boysen2019ManualProblem, Boysen2019WarehousingSurvey}. Amazon, for instance, offers customers \emph{Prime}, a differentiated service that used to offer delivery within two days and is now, under certain conditions, promising same-day delivery. Moreover, with easily accessible alternatives available to customers, online retailers face high competitive pressure, and the link between logistics performance and customer loyalty is much stronger compared to other industries \citep{Ramanathan2010TheE-commerce}.

Parts-to-picker Automated Storage and Retrieval Systems (AS/RS), with the typical single, aisle-captive crane retrieving bins from a static rack, have been used for several decades and have proven their superior operational efficiency compared to manual systems, at the cost of an essential initial investment \citep{Roodbergen2009}. However, some limitations of AS/RS become apparent when facing new challenges posed by the rise of e-commerce: cranes are sensitive points of failure; expandability is complicated and expensive; batching and zoning require consolidation and a delay-sensitive dependency between operators; and a single crane per aisle can only perform so many cycles. According to \cite{Davarzani2015}, ``adaptation is urgent'' to keep up with the growing demand.

\subsection{Robotic Mobile Fulfillment System}
\label{RMFS}

Kiva Systems created the first RMFS in 2006, this company was later bought by Amazon and re-branded Amazon Robotics in 2012 \citep{Wurman2008CoordinatingWarehouses, Azadeh2017RobotizedOpportunities,Boysen2019WarehousingSurvey}. However, RMFSs, also referred to as rack-moving mobile robot based warehouses, or Kiva warehouses, are not limited to Amazon warehouses. Other companies have developed their own systems: for instance, Alibaba's Zhu Que robots, the Quicktron robots (Huawei), the Open Shuttles by Knapp, CarryPick by Swisslog, Butler by GreyOrange, the Locus Robotics system and others \citep{Kirks2012CellularSystems, Boysen2019WarehousingSurvey}.

This new type of automated warehouse involves a large fleet of small robots that move freely around the storage area to retrieve shelves full of items and bring them to operators for picking (possibly after waiting in a queue) before returning to a storage location. Interestingly, when a robot is loaded, it must travel along the aisles, but when unloaded, it can pass under stored shelves to take shortcuts. This type of operations is equivalent to a mini-load with dual-command cycles system with a fleet of non-aisle-captive robots \citep{Roodbergen2009}. For a more detailed description of an RMFS and its advantages compared to traditional systems, the interested reader is referred to the following references: \cite{Wurman2008CoordinatingWarehouses}; \cite{DAndrea2008FutureFacilities}; \cite{Enright2011OptimizationSystems}; and \cite{Azadeh2017RobotizedOpportunities}.

\cite{Rimele2020RoboticApplications} present a mathematical modelling framework that formalises optimisation opportunities in an RMFS. Because e-commerce promises fast delivery of small orders, the fulfilment of requests follows what can be called an \emph{order streaming} logic \citep{Banker2018NewAutomation}, which ``drops orders [...] to the floor as soon as they are received''. Because of this specificity, the option of batching requests is minimal, and the system needs to account for uncertainty and adapt online to newly revealed orders. Among the operational decisions, the real-time storage allocation problem can leverage the great storage flexibility of the system. When a robot leaves a picking station, it does not need to store the shelf in its initial location but can choose \emph{any} free location. This allows for the real-time adaptation of the storage layout in response to the demand, thereby minimising the travelling time of the robots, which translates into increasing an upper bound of the throughput.

\subsection{Contributions and paper structure}
\label{contribution}

This work focuses on a specific operational control aspect of a Robotic Mobile Fulfillment System for e-commerce, namely the problem of learning an effective dynamic storage policy. When a robot is available at an operator's station, a decision must be made in real-time about which storage location to use to minimise the average cycle time of the robots. To make such a decision, one can use information about the next request to process, statistical insights about the demand, and other input regarding the current state of the warehouse's layout. This information at a given time step defines a state's representation in an environment that we approximate as a partially observable Markov decision process (POMDP). We propose the application of a variant of a Q-learning agent \citep{Watkins1989LearningRewards,Hessel2018Rainbow:Learning, Mnih2015}, a Reinforcement Learning (RL) algorithm, to learn an efficient dynamic storage policy that aims at minimising the average cycle time. More precisely, we implement a Differential Double Q-learning agent with experience relays to minimise the average travelling time of the robots. Inspired by \emph{Class-based} storage policies, the decision on where to return a shelf is made based on a discretisation of the storage area into zones. A discrete event simulator is used to evaluate the performance of our method compared to baselines on different levels of skewed demand distributions. To further improve the performance of our method, we propose an extension using a rollout strategy over a fixed horizon of already-revealed requests. This strategy is also applicable to the baseline methods from the literature.

The presentation of our proposed approach is organised as follows. Section \ref{problem_definition} first formalises the optimisation problem of dynamically allocating storage locations to shelves, then presents a literature review related to storage policies in automated warehouses and operational control applications specific to RMFS. Section \ref{methodology} presents our methodology, with a discretisation of the storage area into zones, the system representation as a POMDP, and the reinforcement learning variant of a Q-learning agent used to learn an efficient storage policy, as well as the rollout strategy to further improve performance. Section \ref{sec:simulation_study} explains how we generated data in our simulations and shows results obtained by our method compared with baselines from the literature. Finally, Section \ref{conclusions} summarises the obtained results and discusses future research avenues.

\section{Problem definition and literature}
\label{problem_definition}

\subsection{Decision-making framework}
\label{decision_making_framework}

In this section, we present the storage allocation decision-making framework, as well as the relevant literature on the topic.

For the case of an e-commerce Amazon-type warehouse, a modelling of operational decisions is proposed by \cite{Rimele2020RoboticApplications}, with a stochastic dynamic optimisation formulation. In this formulation, an incoming request corresponds to a single item type and consolidation of orders, if any, is assumed to take place in the downstream sections of the warehouse. Orders are revealed online and are considered available for fulfilment as soon as they arrive, with no batching. An \emph{event} corresponds to a robot being available for a task. The tasks of a robot correspond to a sequence of \emph{dual-command (DC) cycles} for which the total time can be decomposed into: (i) storage access time; (ii) interleaving (or transition) time to retrieval location; (iii) retrieval time; and (iv) waiting time at the picking station's queue (see arcs on the left side of Figure \ref{fig:cycles}). To create those cycles, storage and retrieval decisions must be made. After the picking operation, the robot is available at the picking station, and it has to perform a \emph{storage task}, which consists in selecting an available location for storage. When the shelf has been stored, the robot needs to perform a \emph{retrieval task}, which consists in choosing which order to fulfil next, from which shelf, and which picking station. Besides those two typical tasks, we also consider an \emph{opportunistic task}, a task that can only occur in a particular situation where a requested item is stored on a shelf currently being carried by the robot. In this case, the robot can go directly to the back of the waiting line at the operator, without passing by the storage area (right side of Figure \ref{fig:cycles}).

\begin{figure}
\centering
\includegraphics[width=110mm]{figures/dc_and_opportunistic_cycles.jpg}
\caption{Dual-command cycle (left) and opportunistic task (right)}
\label{fig:cycles}
\end{figure}

In this work, we focus on optimising storage decisions only. It is assumed that an external system provides the sequence of orders and the decisions on which shelf and picking station to use. To be more precise, this system simply considers orders already revealed and yet to be fulfilled and dynamically sequences them by increasing deadlines, as an emergency rule. If an order requires a shelf carried by another robot, this order is temporarily skipped to be processed by that other robot as an opportunistic task. Also, opportunistic tasks are performed as often as possible. The objective is to minimise the average travelling time, which is directly related to the maximal throughput capacity of the warehouse \citep{Park2012OrderModels}. We make other simplification assumptions similar to the ones enumerated in the simulation study in \cite{Rimele2020RoboticApplications}. We consider one picking station only, an item is associated with exactly one shelf in the considered storage area, replenishment is explicitly ignored even if some orders could correspond to replenishment tasks, travelling and processing times are deterministic and, finally, congestion of robots in the aisles is ignored.

\subsection{Storage policies}
\label{storage_policies}

Commonly used and studied storage policies for AS/RS are \emph{Random} storage policy or policies based on the container's turnover rate. The former gives a container an equal probability to occupy any available location. While this method is space-efficient and easy to implement in practice, it can obviously result in poor accessibility and low productivity during operations. The latter method is typically expressed as a full-turnover-based storage assignment or a class-based storage assignment. A full-turnover-based assignment locates the most-requested containers closest to the Input/Output (I/O) point; however, a practical concern appears when new containers enter and leave the system, or when the turnover rates change. In \emph{Class-based} storage, storage locations are clustered into a given number of classes based on their proximity to the I/O point (see left side of Figure \ref{fig:class_zone_layouts}). Then, a container is assigned to a zone based on its turnover rate; its storage within this zone is random. While this method benefits from both \emph{Random} storage and full-turnover-based assignments, it requires the definition of the number of classes and their dimensions. Numerous analytical and simulation studies such as \cite{Hausman1976OptimalSystems}, \cite{Graves1977Storage-RetrievalSystems}, \cite{Schwarz1978SchedulingResults}, \cite{Bozer1984Travel-TimeSystems}, and \cite{Gagliardi2012OnSystems} show that \emph{Class-based} storage assignment demonstrates the best performance and practicality. However, while those applications generally apply to both single and dual-command cycles system, it seems they have been more driven by the former. In another simulation study, \cite{VandenBerg2000SimulationSystem} find out that for dual-command cycles, selecting the storage location that minimises the cumulative distance from the I/O point to the storage location, plus the distance from the storage location to the following retrieval location, gives the best average completion time. This decision rule is often referred to as the \emph{Shortest Leg} storage policy.

\subsection{RMFS-related work}
\label{rmfs_related_work}
Some recent work focuses more specifically on RMFS, either on storage decisions or closely related topics like performance measures and others.
\cite{Lamballais2017EstimatingSystem} use queueing network models to analytically estimate maximum order throughput, average cycle times, and robot utilisation. Using these models allows one to quickly evaluate different layouts or robot zoning strategies. Among their results, they show the good accuracy of their models compared to simulations. They also show that the throughput is quite insensitive to the length-to-width ratio of the storage area, but is more strongly affected by the location of the picking stations. Also using queueing network models, \cite{Roy2019} study the effect of dedicating robots exclusively to either retrieval tasks or replenishment tasks, or a combination of both. They find that the latter reduces the picking time by up to one third, but increases the replenishment time up to three times. They also study the allocation to multiple classes and conclude that allocating robots to least congested classes results in a similar performance as a dedicated zone policy.

\cite{Boysen2017Parts-to-pickerEnvironment} study the problem of synchronising the processing of orders at a picking station with the visits of the shelves carried by robots. By considering a given set of orders, and a capacity to process orders simultaneously, their objective is to minimise the number of visits of shelves to the picking station. They propose a MIP model, a decomposition approach, and different heuristics and show that they can halve the robot fleet size.

Regarding storage allocation, \cite{Weidinger2018StorageWarehouses} define a \emph{Rack Assignment Problem}, which assigns each stopover (return of a rack) of a given set (batching) to an open storage location. They consider the time at which each rack visits the picking station to be known. They propose a MIP model as a special case of an interval scheduling problem, with the surrogate objective of minimising the total loaded distance. The model formalises the fact that two stopovers can occupy the same storage location only if their storage intervals cannot overlap. They do not consider robots individually, but instead they expect that a robot will always be available for the task. They propose solving their model using an Adaptive Large Matheuristic Search (ALMS), and compare their results with other storage policies, such as those presented in Section \ref{storage_policies}. On their surrogate objective, ALMS demonstrates good performance, outperforming the other policies on the total travel time (unloaded robots are considered to travel twice as fast as loaded ones). Similar to the finding of \cite{VandenBerg2000SimulationSystem}, the authors note the very good performance of the \emph{Shortest Leg} policy; compared to their method, it only increases the travel distance by 3.49\% and the size of the robot fleet by 2.17\%, without batching.

\cite{Yuan2018} propose a fluid model to assess the performance of velocity-based storage policies in terms of travelling time to store and retrieve shelves. They find that when the items are stowed randomly within a shelf, a 2-class or 3-class storage policy reduces the travelling time between 6 to 12\%. This theoretical result is validated by simulation. Additionally, they find that if items are stowed together based on their velocity, the travelling distances considered can be reduced by up to 40\%.

In situations when batching or zoning requires consolidation, different options can be considered. \cite{Boysen2019ManualProblem} consider a manual consolidation with put walls (sorting shelves). They propose a MIP to optimise the release sequence of bins from intermediate storage so that orders are quickly sorted on the put wall and idle times of operators are minimised. In a case where the intermediate storage uses an AS/RS that serves the consolidation area with a conveyor belt, \cite{Boysen2018OptimizingProblem} propose a MIP model for the minimum order spread sequencing problem, which consists in minimising the number of conveyor segments between the first and last occurrence of an order.

\cite{Merschformann2019DecisionSystems} use a discrete event simulator presented in \cite{Merschformann2018RAWSim-O:Systems}, which considers most, if not all, of the operational decisions occurring in an RMFS. They test a multitude of combinations of decision rules concerning, for instance, the assignment to a picking or replenishment station, the robot selection, storage allocation, etc. They observe significant performance differences between distinct combinations, as well as strong cross-dependencies between some decision rules, suggesting there may be some benefit to exploring integrated approaches.

\section{Methodology}
\label{methodology}

This section presents our method for solving the dynamic storage allocation problem in an RMFS. We first define the notion of zones that we use in our storage policy. Then, we explain the representation of the system as a POMDP and the features extraction. In Section \ref{sec:rl_method}, we describe the variant of Q-learning, a Reinforcement Learning agent, that we use. Section \ref{sec:imple_details} presents implementation details essential to the success of the method. Finally, Section \ref{sec:rollout} describes a look-ahead rollout strategy to enhance our storage policy, by making better-informed decisions using already-revealed orders.

\subsection{Storage zones definition}
\label{zones_definition}

In this work, inspired by \emph{Class-based} storage policies from the literature, we propose optimising a policy that will allocate shelves to classes instead of exact locations. Contrary to the standard \emph{Class-based} storage assignment presented in Section \ref{storage_policies}, the online assignment to a class is not only made based on the turnover rate of the shelf to store, but also on a set of diverse features. Since we are interested in minimising dual-command cycle completion times, as opposed to the access to storage or retrieval time alone (like in single command cycles), the interleaving time between a storage location and the next retrieval location is essential. With the usual definition of classes distributed with an increasing distance from the picking station, such as in Figure \ref{fig:class_zone_layouts} (left), the access and retrieval times depend directly on the assigned class, but the interleaving time is quite random. For instance, in the ideal case where we store and retrieve shelves from the same storage class 2, we see that the cycle can either be very good (if the two locations are adjacent), or very bad if the locations are at the two extremities. To better account for the importance of interleaving time, we propose another definition of classes, which we now call \emph{zones} as represented in Figure \ref{fig:class_zone_layouts} (right). These zones are now clustered into regular shapes such that locations within the same zone are close to each other and such that the zones are distributed in an increasing distance from the picking station. With this new zone definition, a storage and a retrieval from the same zone would entail a short interleaving time and, thus, a good cycle. Note that the selection of the exact storage location within a zone is arbitrarily made by choosing the open location closest to the picking station.

\begin{figure}
\centering
\subfigure{\resizebox*{5.5cm}{!}{\includegraphics{figures/class_based.png}}}\hspace{5pt}
\subfigure{\resizebox*{5.5cm}{!}{\includegraphics{figures/rl_zone_based.png}}}
\caption{Concentric class-based storage layout (left) vs. proposed zones layout (right)} \label{fig:class_zone_layouts}
\end{figure}

\subsection{System representation}
\label{system_representation}

\cite{Rimele2020RoboticApplications} model the storage and retrieval operations in an AS/RS as a Markov Decision Process (MDP), which gives a full representation of the warehouse, including all of the revealed orders, as a state of the system when an event occurs (corresponding to the need for a storage decision here). Instead of giving such a complete representation of the current state of the warehouse, we propose a \emph{Partially Observable} MDP (POMDP), where only some characteristics of the real state are used as state representation. In the traditional \emph{Class-based} storage policy, for instance, the representation of the state is simply the turnover rate of the shelf to store, and based on this information the robot knows which class to assign it to.

We decided to represent a state with some more characteristics (features), given below:
\begin{itemize}
\setlength\itemsep{0.2em}
\item Average turnover rate of the shelf to store
\item Relative rank of the shelf's turnover rate
\item Zone of the next retrieval task (one-hot encoding, one feature per zone)
\item Occupation levels of each zone (one feature per zone)
\item For each zone, the number of robots that are currently moving toward the zone to retrieve a shelf
\end{itemize}

An extra feature is used to encode whether the next task is an opportunistic one (the shelf is not stored but is already being carried by the robot). In total, if $n$ denotes the number of zones, there are $3n+3$ scalars in the features vector.

The intuitive idea is that there must be a balance between greedily minimising the immediate cycle time, similar to the \emph{Shortest Leg} storage policy, and minimising the future access time, similar to a turnover-based storage policy as presented in Section \ref{storage_policies}. The objective is to learn a policy that, based on the above set of features, will aim at minimising the average cycle time.

\subsection{Reinforcement learning method}
\label{sec:rl_method}

We propose using a Reinforcement Learning (RL) method to learn an efficient storage policy. The field of RL offers a diversity of methods to solve decision problems whose objectives are defined recursively by a Bellman equation, introduced in dynamic programming (DP). Compared to traditional DP methods that require complete information about the model and probability distributions, RL methods can learn from repeated experiences, even in large state and action space, when using function approximations. As presented by \cite{Sutton2018ReinforcementIntroduction}, in RL the decision-maker, or agent, interacts with its environment. At every time step $t$, and based on the current representation of the state $S_t$, the agent selects an action $A_t$, which impacts the environment and receives from it a reward $R_{t+1}$ and a new state representation $S_{t+1}$. Based on repeated experiences, the goal of the agent is to learn a policy that maximises the onward cumulative sum of rewards. Note that the agent is not necessarily given the complete state characteristics; it can only be given a partial representation through a POMDP. The state representation defined in Section \ref{system_representation} is the partially observable state given to the agent in our approach. In value-based RL, given a policy $\pi$, the agent learns the State-Action value function $Q_{\pi}(s,a)=\mathbb{E}\left [ R_1 + R_2 + ... \:|\: S_0=s, A_0=a, \pi \right ]$ that represents the expected (possibly discounted) cumulative reward at state $s$ if action $a$ is taken, if policy $\pi$ is followed afterwards. The optimal value function $Q^*$ is such that $Q^*(s,a) = \textup{max}_{\pi}Q_{\pi}(s,a)$ for all state and action pairs, and obtaining a decision policy from a value function simply consists in acting greedily with regard to action values : $A_{\pi}(s)=\textup{argmax}_{a}Q_{\pi}(s,a)$.

In Q-learning \citep{Watkins1989LearningRewards}, the value function is iteratively updated by sampling based on the Bellman equation: $Q(S_t,A_t) \leftarrow Q(S_t,A_t) + \alpha [ R + \gamma \: \textup{max}_{a}Q(S_{t+1}, a) - Q(S_t, A_t)]$, so the update uses the received reward and the current estimate of the next state value (bootstrap) as its target. Importantly, for convergence to optimality, the Q-learning agent needs to correctly learn the values of its actions (exploitation) while trying new actions, possibly more promising (exploration). This trade-off is central to any RL method, and here we will consider an $\epsilon$-greedy selection rule for this purpose ($\epsilon$ \% of the time, the greedy action is selected, otherwise a random action is taken).

Even if our state space has a small number of dimensions and the number of actions is also small, calculating the value function individually for every state-action pair with a tabular method would be out of reach considering the exponential number of combinations. Instead, Deep Q-learning uses a neural network (NN) as a function approximator that takes the state features as inputs and outputs the estimated values for each possible action \citep{Mnih2015}. Using function approximators allows to escape the curse of dimensionality by leveraging information about similar states and by generalising to unseen state-action pairs using only a limited number of parameters. Let us denote by $\mathbf{w_t}$ the current parameters, weights, of the neural network function approximator and by $Q(s, a, \mathbf{w_t})$ the value of state $s$ - action $a$ estimated by this neural network. Because a neural network is differentiable, we can minimise the square loss error between the current estimate value and the target by taking a step in the opposite direction of the value function's gradient: $\mathbf{w_{t+1}} \leftarrow \mathbf{w_t} + \alpha [R_{t+1} + \gamma \: \textup{max}_{a} Q(S_{t+1}, a, \mathbf{w_t}) - Q(S_t, A_t,\mathbf{w_t})]\nabla Q(S_t, A_t, \mathbf{w_t})$.

In the case of an infinite time horizon system, such as ours where retrieval tasks never end, rewards cannot simply be accumulated because the state values would never converge but rather would diverge to infinity. The most common solution is to apply a discount factor $\gamma$ in the Bellman equations, such that for a given policy $\pi$ we have: $Q_{\pi}(s)=\mathbb{E}_{\pi}[R_{t+1} + \gamma \: Q_{\pi}(S_{t+1}) \:|\: S_t=s]$, with $0 < \gamma < 1$. The justification for using a discount factor is first for the mathematical convenience of convergence of the cumulative finite rewards. Also, in some systems, a discount factor can represent an economical discount rate, or at least the idea that rewards received now are worth more than they would be later. Yet in our case, no incentive should be given for early performance since operations throughout the day have equal importance and no termination occurs. An alternative to discounted rewards is what is called \emph{differential returns} or \emph{average rewards} \citep{Sutton2018ReinforcementIntroduction}. Introduced in Dynamic Programming \citep{BERTSEKAS1976DynamicControl} and later in Reinforcement Learning (R-Learning in \cite{Watkins1989LearningRewards}), the idea is to optimise the average sum of reward $\lim_{n \to \infty}\frac{\sum_{t=1}^{n} R_t}{n}$ by considering return values equal to $R_t -\bar{R}$, with $\bar{R}$ the average reward of policy $\pi$. This setting has the interesting property of having the sum of returns converging (to 0) while maximising the average reward in the process. When action $A_t$ of policy $\pi$ is taken, the state-action value update rule becomes $Q(S_t,A_t) \leftarrow Q(S_t,A_t) + \alpha [ R - \bar{R} + \textup{max}_{a}Q(S_{t+1}, a) - Q(S_t, A_t)]$.

Q-learning is known to suffer from an overestimation of actions' values. Two main reasons explain this phenomenon. First, in its update mechanism, the maximum value of the next state-action pair is used as an approximation for the maximum expected value. Second, both the action selection and value estimation come from the same maximum operator that suffers from estimation errors, and thus favours overestimated values. To answer this problem, \cite{VanHasselt2010DoubleQ-learning} proposes a Double Q-learning method in the tabular case, which was later extended to Deep Q-learning in \cite{vanHasselt2016DeepQ-Learning}. For Deep Q-learning, the general idea is to separate the action selection from the value estimation using two neural networks, the online NN and the target NN. The authors demonstrate that this approach eliminates the positive bias on the action values and results, in general, in better performance. The online NN is updated as before, but the target NN is not. Instead, it receives a copy of the weights of the online NN every $K$ iterations.

Algorithm \ref{alg:algo1} combines the different elements presented above into one agent, denoted as \emph{Double Differential Deep Q-Learning}. Step 1 initialises a starting state, the average reward (arbitrarily set, for instance, to 0) and the weights of both the online and target neural networks, equal to each other. For every iteration, Step 3 selects an action, greedily or not, takes it, and observes the reward and the next state. Step 4 calculates the target value for state $S_t$ - action $A_t$ pair. Step 5 does the gradient descent to update the online network. If the action selected $A_t$ was greedy with respect to the online network, Steps 6 to 8 update the average reward $\bar{R}$. Finally, every $K$ iterations, the target network receives a copy of the online network weights (Steps 9 to 11).

\begin{algorithm}
\begin{algorithmic}[1]
\small
\STATE initialise state $S_{0}, \bar{R}, \mathbf{w_t} = \mathbf{w^{-}_{t}}$
\FOR{$t = 0$ to $\infty$}
    \STATE{take action $A_{t}$ ($\epsilon\text{-greedy}$ wrt $Q(S_{t}, ., \mathbf{w_{t}})$), observe $R_{t+1}$, $S_{t+1}$}
    \STATE{$Y_{t} \leftarrow R_{t+1} - \bar{R} + Q(S_{t+1},\argmax_a Q(S_{t+1}, a, \mathbf{w_{t}}), \mathbf{w^{-}_{t}})$}
    \STATE{$\mathbf{w_{t+1}} \leftarrow \mathbf{w_t} + \alpha [Y_{t}-Q(S_t, A_t,\mathbf{w_t})]\nabla Q(S_t, A_t, \mathbf{w_t})$}
    \IF{$A_t==\argmax _a Q(S_{t}, a, \mathbf{w_{t}})$}
        \STATE {$\bar{R}\leftarrow \bar{R} + \beta [Y_{t}-Q(S_t, A_t,\mathbf{w_t})]$}
    \ENDIF
    \IF{$t \: \text{mod} \: K == 0$}
        \STATE {$\mathbf{w^{-}_{t}} \leftarrow \mathbf{w_t}$}
    \ENDIF
\ENDFOR

\end{algorithmic}
\caption{Double Differential Deep Q-Learning}
\label{alg:algo1}
\end{algorithm}

\subsection{Implementation details}
\label{sec:imple_details}

In our experiments, we use a fully connected feed-forward neural network as a function approximator. While the neural network has one output per storage zone, which represents the expected cumulative cycle times onwards (relative to the average cycle time), if the storage zone is selected, some zones may not be selected if they are currently full. For this reason, when we select an action based on its value out of the neural network, we first need to filter out full zones.

Another point worth mentioning deals with backpropagation when an opportunistic task is performed. Such a task is enforced when possible, which occurs when the next retrieval zone is not a zone but the picking station (encoded in the features extraction). Even though the agent does not require any action to be taken, it is essential to backpropagate the observed reward in the neural network for all of the actions. The reason for that is bootstrapping. If a non-opportunistic task transitions to a state that will enforce an opportunistic task, the state-action value update in Q-learning uses the observed cycle time as well as the estimated value of the future state, which, in this case, requires an opportunistic task. The neural network must then be accurate for such a state and learn that the values of all the storage zones are to be equal to the value of an opportunistic task.

As in \cite{Mnih2015}, we use experience replay. It consists in storing simulation experiences (vector $S_t, A_t, R_{t+1}, S_{t+1}$) into a fixed size replay memory. Instead of training after each observed experience, we wait for some iterations before sampling a batch of experiences from the replay memory and then train the neural networks with mini-batches. This batch training affords more training stability, allows the reuse of past experiences, and speeds up the training step.

Finally, to make better use of available information, particularly requests that are already revealed at a given time step, we propose an extension to using only Q-values. A look-ahead rollout strategy is proposed. We present this method in Section \ref{sec:rollout} and the results of our Q-learning application with and without rollouts is presented in Section \ref{sec:simulation_study}.

\subsection{Look-ahead rollout strategy}
\label{sec:rollout}

Monte Carlo Tree Search (MCTS) methods are exploration techniques to improve policies, based on previous work on Monte Carlo methods. \cite{coulom2007} first describes a tree search method applied to games. Several variants have been adapted for numerous applications, such as the famous AlphaGo Zero from \cite{Silver2017}. The general idea behind MCTS is to explore the action space by simulations following a tree structure, further exploring the promising areas of the tree.

For the RMFS real-time storage assignment, the objective of a look-ahead search is twofold. First, as in other applications, it helps the agent take better actions by exploring numerous possible scenarios. Second, and more specific to our application, the look-ahead can leverage information that is already revealed but not necessarily given in the state representation. This is the case of future orders. So far, in Section \ref{system_representation}, only information about the next order the robot needs to retrieve is included in the state features. However, at a given time step, while not all future orders have been revealed, some have. The look-ahead can then use \emph{only} those already-revealed orders (even if the real future sequence will differ) to take a better informed first action.

Figure \ref{fig:mcts_revealed} illustrates this point. The orders $o_i$ are sorted according to the sequence in which they will actually be processed, but at time $t_0$ only the \emph{green} orders $\{o_1, \: o_2, \: o_4, \: o_5\}$ are known. The \emph{orange} orders $\{o_3, \: o_6, \: o_8\}$ will be revealed later at time $t_1>t_0$, for instance by the time order $o_2$ will have been processed. In this case, order $o_3$ is be inserted before $o_4$, for priority reasons. In this case, even if new orders will later be inserted into the list, at time $t_0$ only requests $\{o_1, \: o_2, \: o_4, \: o_5\}$ are used in the rollout, the only exceptions being potential other \emph{green} requests not depicted on Figure \ref{fig:mcts_revealed}.

\begin{figure}
\centering
\includegraphics[width=60mm]{figures/mcts_revealed_requests.png}
\caption{Revealed orders at decision time}
\label{fig:mcts_revealed}
\end{figure}

\cite{Bertsekas2019ReinforcementControl} presents different approaches for MCTS implementation. One of these approaches is a single-step look-ahead with truncated rollout and cost approximation. Figure \ref{fig:mcts} presents the implementation of this type of rollout adapted to our problem. At first, all feasible actions at a given state $S_0$ (time $t_0$) are considered and their values $V(S_0, A_i)$ and visit counts $n_{A_i}$ are set to $0$. At each iteration, an action is randomly selected (action $A_1$ in Figure \ref{fig:mcts}) and a simulation of $h$ (horizon) consecutive storage tasks is run. This finite simulation uses orders revealed by time $t_0$. The action selection in the simulation uses the agent's current policy. The sum of reward along the simulation is computed, and the value of the last state $S_h$ is, by bootstrapping, set as the Q-value of the agent. Then, the value of the selected action is updated to its experienced average, and the visit counter is incremented. The process is repeated for a given number of iterations, and finally, the action presenting the best (min) value is selected. Note that in our specific usage of this look-ahead rollout strategy, each feasible action needs to be selected only once. Indeed, both the policy and the transitions within the rollout are deterministic because of the Q-learning agent's policy and because we do not simulate unknown future orders.

\begin{figure}
\centering
\includegraphics[width=110mm]{figures/mcts.png}
\caption{Look-ahead rollout strategy}
\label{fig:mcts}
\end{figure}

\section{Simulation study}
\label{sec:simulation_study}

In this section, we present a simulation study comparing our proposed methods to typical storage policies found in the literature. We start by defining the framework of the study, before presenting our results.

\subsection{Parameters}
\label{sec:parameters}

Kiva and Amazon have claimed travel speeds up to 3 to 4 miles per hour; however, to account for turns and congestion, we assume that the robots travel at a constant speed of 1.4 miles per hour (about 0.6 m/s). In our experiments, we assume an average picking time by the human operators of 8 sec and a loading and unloading time by the robots of 3 sec. Our study considers a relatively small storage area, with 36 storage locations (6 zones of size 2 by 3 shelves) for 34 shelves, 5 automated robots and one picking station.

Incoming orders in warehousing systems are typically skewed, with a small percentage of the items representing the vast majority of the orders and the others qualified as slow movers. \cite{Hausman1976OptimalSystems} propose modelling such a demand distribution with the definition of an \emph{ABC} curve: $G(x)=x^s \quad \text{for } 0 < s \leq 1$, which represents the proportion of cumulative demand (\%) of the first $x\%$ of the shelves. The smaller the skewness parameter $s$, the more skewed the demand distribution. We follow this suggestion by associating with every item type $i$ (equivalent to the corresponding shelf), at every discretised period, a Poisson distribution of average $\lambda _i = \left (\left ( \frac{i}{m} \right )^s - \left ( \frac{i-1}{m} \right )^s \right) \times \frac{n}{N}$, where $m$ is the number of item types, $n$ the total number of orders in the time horizon, and $N$ the number of discretised periods. Then, for every generated order $k$, a completion time $\delta_k$ is randomly drawn from a uniform distribution of interval $[1; \alpha \times T]$ where $\alpha$ defines the tightness of the completion times. Note that in the case where a drawn demand for a given item type is greater than one, the resulting orders are automatically grouped, corresponding to an opportunistic task of type 2 in \cite{Rimele2020RoboticApplications}. The values used here are: $m=34$, $n=30000$, $N=1440$ (corresponding to discretised periods every 1 min) for a time horizon of 24h, and $\alpha=0.4$. The values of the skewness parameters will be varied to study their impact on the different storage policies.

\begin{figure}
\centering
\includegraphics[width=80mm]{figures/ScatterPlot.png}
\caption{Simulation study - Plan view of the storage area}
\label{fig:plan_view}
\end{figure}

After some trial and error, we set the parameter values for the RL agent as follows. Each training phase is conducted over 10000 episodes, corresponding to 24h of simulated incoming orders. Each of these training episodes uses its own generated instance of demand, while the comparisons between the baselines and the test of the RL policy are made on another shared instance. The exploration rate $\epsilon$ is kept constant at $0.1$. The neural networks are created using the Keras library. We use the mean square error loss function and the Adam optimiser for gradient descent. Both neural networks are feed-forward, fully connected with 3 inner layers of 32 neurons each and Relu activation functions. The output layer presents one neuron per zone of storage (6), and these neurons are linearly activated. The learning rate is set to $0.00025$, the replay memory has a capacity of $1000$, and batch training is performed every $100$ iterations. This batch consists of $256$ experiences sampled from the replay memory, and they are fitted to the model in mini-batches of $64$. The target network's weights are updated every $500$ iterations.

\subsection{Results}
\label{results}

This section presents results obtained by the proposed approach and the standard baselines. First, experiments were run using the method presented in Section \ref{sec:rl_method} on different instances corresponding to different values of demand skewness parameter $s$. Then, the rollout strategy presented in Section \ref{sec:rollout} was applied on both the Q-learning agent and the best-performing baseline, and gains that can be obtained by using additional available information were observed. The three baselines tested were the following: \emph{Random} storage policy, \emph{Class-based} and \emph{Shortest Leg}.

The \emph{Class-based} storage policy uses the concentric classes definition, depicted in Figure \ref{fig:class_zone_layouts} (left) and conventionally described in the literature. Since our method allocates shelves to zones instead of exact locations, the \emph{Shortest Leg} storage policy is implemented similarly. When a storage task needs to be performed and the location of the next retrieval is known, the exact potential location within each zone can be identified because of the arbitrary choice of selecting the location closest to the picking station. Knowing the candidate location from each zone (if any), the \emph{leg} distance can be computed as being the distance from the picking station to the storage location plus the distance from the storage location to the next retrieval. The selected zone corresponds to the smallest leg value. This policy results in greedily minimising the immediate cycle times.

Table \ref{table:1} presents the average travelling times, $t(s)$, obtained from the three baselines and the RL agent, without rollouts, for several skewness parameter values ranging from $s=0.4$ (very skewed) to $s=1$ (flat distribution). For each storage policy, the corresponding performance gain, g(\%), compared to the \emph{Random} storage policy is also computed; this represents the percentage decrease in travelling time. As expected, the performance of the \emph{Class-based} policy increases when the skewness parameter value $s$ decreases. In concordance with the literature, we observe the good performance of the \emph{Shortest Leg} policy, which remains rather constant, between 10 and 11\% of improvement, depending on the skewness parameter values. In fact, it is only surpassed once by the \emph{Class-based} policy for the most skewed distribution $s=0.4$, but it offers the net advantage of being independent of the distribution pattern. The Q-learning agent consistently performs better than the baselines, between 3.21\% and 4.83\% of additional gain compared to the baselines relative to \emph{Random} storage. Similar to the SL policy, its performance remains rather independent of the skewness of the distribution. Figure \ref{fig:learning_curve} presents a typical training curve, here for parameter $s=0.6$. The \emph{x} axis shows the number of training episodes ranging from 0 to 10000 and \emph{y} corresponds to the relative gain in travelling time compared to the \emph{Random} storage policy. The horizontal dashed lines in the graph represent the performance of the three baseline policies. The test policy curve represents the performance of the RL policy in training, which is tested every 100 training episodes. With our training settings, we notice the non-linear evolution of the test policy curve until it reaches some plateau value around 5000 episodes.

\begin{table}
\centering
\small
\begin{tabular}{ |m{1.0cm}||m{0.9cm}|m{0.5cm}|m{0.9cm}|m{0.9cm}|m{0.9cm}|m{0.9cm}|m{0.9cm}|m{0.9cm}|  }
 \hline
 \multirow{2}{*}{\shortstack{Storage \\ policy}} & \multicolumn{2}{c|}{Random} & \multicolumn{2}{c|}{Class-based} & \multicolumn{2}{c|}{SL} & \multicolumn{2}{c|}{Agent} \\

            & t(s)       & g(\%)                       & t(s)       & g(\%)     & t(s)       & g(\%)   & t(s)   & g(\%) \\
\hline
 s=0.4      & 37.97      & \multicolumn{1}{c|}{-}      & 33.41      & 12.01      & 33.61      & 11.48   & 32.19  & 15.22 \\
 s=0.5      & 38.62      & \multicolumn{1}{c|}{-}      & 34.65      & 10.27      & 34.18      & 11.48   & 32.90  & 14.79 \\
 s=0.6      & 38.69      & \multicolumn{1}{c|}{-}      & 35.34      & 8.65      & 34.79      & 10.09   & 32.92  & 14.92 \\
 s=0.7      & 38.73      & \multicolumn{1}{c|}{-}      & 36.01      & 7.02      & 34.70      & 10.39   & 32.91  & 15.02 \\
 s=0.8      & 38.94      & \multicolumn{1}{c|}{-}      & 36.48      & 6.30      & 34.76      & 10.73   & 33.04  & 15.15 \\
 s=0.9      & 38.98      & \multicolumn{1}{c|}{-}      & 37.41      & 4.03      & 34.53      & 11.42   & 33.03  & 15.27 \\
 s=1.0      & 39.06      & \multicolumn{1}{c|}{-}      & 38.26      & 2.05      & 34.76      & 11.01   & 33.4  & 14.48 \\
 \hline
\end{tabular}
\caption{Average travelling times t(s) and performance gains g(\%) depending on distribution skewness parameter value s - without rollouts}
\label{table:1}
\end{table}

\begin{figure}
\centering
\includegraphics[width=90mm]{figures/training_curve_inverse.png}
\caption{Typical instance of a training curve (here for s=0.6)}
\label{fig:learning_curve}
\end{figure}

Over a second phase, we retained the overall best performing-baseline (SL) and our Q-learning agent to enhance them using the look-ahead rollout strategy presented in Section \ref{sec:rollout}. Again, we tested the resulting policies on different skewness parameter $s$ values, but we also considered different horizon values $h$, which define how far ahead the rollout is run. The only difference in the application of the rollout strategy to the SL baseline compared to the Q-learning agent is the absence of a Q-value at the last step of the rollout. In this case, the SL policy is run over the next $h$ already-revealed orders, and the average of the resulting cycle times is computed, for each first feasible action. Table \ref{table:2} presents the obtained results in terms of performance gains (\%) compared to \emph{Random} storage. First, we notice that for all parameter values, the performance is significantly improved. We can see that for both policies, the performance varies depending on the horizon of the rollout that is considered. As a general statement, it appears that horizon values 20 and 30 give the best results, with some exceptions. The fact that the performance increases with the horizon value before decreasing again is not too surprising. While using revealed orders in the rollouts is beneficial to making better-informed decisions, the longer the rollout, the more likely it is that new, unknown orders will be later inserted between the orders considered in the rollout. When this phenomenon starts to occur too often, it deteriorates the insight of the rollout and results in worse policies. The values in bold in the table designate the best results for each parameter $s$ for both policies. For the SL storage policy, the application of the rollout strategy increases its performance gains between 5.26\% ($s=1.0$) and 7.11\% ($s=0.7$). For the Q-learning agent, the performance gains range between 2.78\% ($s=0.8$) and 4.54\% ($s=0.4$). It appears that using rollouts benefits strongly skewed distributions slightly more than less skewed ones, which is most likely explained by more opportunities associated with fast and slow-moving shelves. Also, the rollout strategy benefits the SL policy more so than the agent. The differences in performance gains between the two policies with rollouts are now 2.29, 0.83, 1.47, 1.07, 1.55, 2.2 and 1.29\% for increasing $s$ values. Using rollouts gives a policy insights about future behaviours by simulating possible trajectories. While the Q-learning agent still benefits from this insight, with the Bellman equation it is, by design, already taking into account future impacts of a decision. On the other hand, the SL policy acts perfectly greedily; it has more to gain by looking into possible future outcomes. While the combination of the Q-learning agent with rollouts still performs best with an average of 1.53\% of performance gain compared to SL with rollouts, this assessment has interesting practical value because of the relative simplicity of implementation of SL with rollouts and its highly competitive performance. Finally, when comparing the results of the complete method with the best baseline commonly used from the literature (SL without rollouts), an average performance gain of 7.58\% is found.

\begin{table}
\centering
\footnotesize
\begin{tabular}{ |m{1cm}||m{0.6cm}|m{0.6cm}|m{0.65cm}|m{0.65cm}|m{0.65cm}|m{0.6cm}|m{0.6cm}|m{0.65cm}|m{0.65cm}|m{0.65cm}|  }
 \hline
  & \multicolumn{5}{c|}{SL + rollouts} & \multicolumn{5}{c|}{Agent + rollouts} \\

 h value    & \multicolumn{1}{c|}{5}     & \multicolumn{1}{c|}{10}    & \multicolumn{1}{c|}{20}    & \multicolumn{1}{c|}{30}    & \multicolumn{1}{c|}{40}    & \multicolumn{1}{c|}{5}     & \multicolumn{1}{c|}{10}    & \multicolumn{1}{c|}{20}    & \multicolumn{1}{c|}{30}    & \multicolumn{1}{c|}{40} \\
\hline
 s=0.4      & 14.01 & 16.83 & \textbf{17.47} & 17.07 & 17.22 & 16.26 & 17.01 & \textbf{19.76} & 18.84 & 18.80 \\
 s=0.5      & 14.91 & 16.03 & 17.57 & \textbf{17.65} & 16.00 & 15.17 & 17.14 & \textbf{18.48} & 18.41 & 17.89 \\
 s=0.6      & 14.97 & 15.47 & 16.06 & \textbf{16.92} & 16.05 & 15.71 & 17.45 & \textbf{18.39} & 17.99 & 18.16 \\
 s=0.7      & 14.41 & 15.45 & \textbf{17.50} & 16.22 & 15.85 & 14.96 & 16.82 & 18.13 & \textbf{18.57} & 18.11 \\
 s=0.8      & 14.23 & 15.51 & \textbf{16.38} & 15.42 & 15.46 & 15.13 & 16.32 & 17.23 & \textbf{17.93} & 16.96 \\
 s=0.9      & 14.22 & 15.49 & 16.34 & \textbf{16.79} & 16.52 & 15.11 & 17.04 & 17.83 & 18.95 & \textbf{18.99} \\
 s=1.0      & 15.15 & 15.60 & \textbf{16.27} & 15.64 & 15.61 & 15.27 & 16.81 & 17.34 & \textbf{17.56} & 17.17 \\
 \hline
\end{tabular}
\caption{Performance gains g(\%) depending on distribution skewness parameter value s and horizon h - with look-ahead rollouts}
\label{table:2}
\end{table}

\section{Conclusions}
\label{conclusions}

This work tackles the problem of dynamically allocating shelves to storage locations within a Robotic Mobile Fulfillment System. Because of the very nature of the e-commerce market, new orders need to be considered, if not fulfilled, as soon as they are revealed, which limits opportunities for batching. Typical methods from the literature correspond to decision rules which rely either on the distinct turnover rates of the containers or on minimising immediate cycles greedily. After making several assumptions about other operational decision rules in such warehouses, as well as the physical characteristics of the warehouse, we propose defining a storage policy using a POMDP and a Q-learning agent from Reinforcement Learning, to minimise the average travelling cycle time. This agent learns from repeated experiences which storage decision should be made based on a set of features representing the current state of the warehouse. Using zone-based storage allocation, we compared our method to decision rule baselines, including the \emph{Class-based} storage policy and \emph{Shortest Leg} storage policy. A performance gain between 3.5\% and 5\% higher than the best baseline relative to \emph{Random} storage was observed. In a second phase, the objective was to leverage additional information regarding orders that are already revealed at a given time step. While new orders will later appear and be inserted between those revealed orders, the latter can still be used in a look-ahead rollout strategy applied at the decision-making step. This rollout simulates finite horizon trajectories using the storage policy at hand for action selection within the trajectory, as well as a Q-value estimation at the last step, acting as an estimation of future expected objective value. Such a rollout strategy has the benefit of being applicable to any storage policy, which allowed us to make fair comparisons between the Q-learning agent and the \emph{Shortest Leg} policy, both using rollouts. After selecting the proper horizon length, using look-ahead rollouts increased the performance gains of the SL and Q-learning policies by about 6 and 4\%, respectively. Even though the Q-learning with rollouts policy gave the best results, the higher positive impact of rollouts on the SL policy makes it an interesting contender, due to its relative simplicity of application. Comparing the policy obtained from Q-learning with rollouts to the best baseline, we observed an average performance gain of 7.5\%, which, we think, demonstrates the potential for more research in this direction.

Future research may build on this work to extend it further. First, storage allocation could select exact open locations instead of using the notion of zones as described here. Instead of using single-step look-ahead rollouts, one could implement a complete Monte Carlo Tree Search algorithm to better explore action selection. The expensive computational cost of such an approach may limit online deployment but, coupled with a policy gradient agent instead of a Q-learning one, the tree search could be used extensively in the training phase only for fast future deployment. Another aspect worth looking into would be the waiting time of robots at the picking stations. In this work, we only consider the travelling time, which is a lower bound to the full cycle time. Aiming at minimising the travelling time along with implementing a distributed arrival of robots at the picking stations could result in higher throughput, but how to do that exactly appears to be quite challenging.

\section*{Acknowledgements}

We are grateful to the Mitacs Accelerate Program for providing funding for this project. We also wish to gratefully acknowledge the support and valuable insights of our industrial partners, JDA Software and Element AI.

redpajama_set_name: RedPajamaArXiv


text:
TTRPG writeups: Madcap Redcap Recap #1
I don't know what happened to October either, aside from the roleplaying games continued (I have this vague idea that I will write about how roleplaying games are good for maths, drama and general language development one day). I think we may have also started more hardcore development of my dice system. 12yo has been making suggestions and helping test mechanics. October may have also been the month where I found out that 16yo was doing more algebra, because apparently he thinks he needs algebra for the TAFE course he's thinking of enrolling in. Not sure how much he's done as I think he's gotten himself a new Khan Academy account instead of resetting the password for his existing one so I'll have to try to remember to check that up when I'm compiling the report for the moderator meeting.
September was States month and it felt unusually close to Regionals because it was (we had the slightly awkward situation of that we needed to put people forward for states before we had the results from regionals to make sure they'd actually qualified, and to add chaos to the confusion, because it had been another unprecedented year, people were allowed to apply for states if they hadn't done regionals (there were a number of people that missed out due to being sick or having to quarantine).
I forgot to mention, over badge test and regionals, 16yo learned how to make chips in a commercial deep fryer from one of the people he would accept chips from and helped out on regionals and states weekends. He makes a great bucket of chips. Below is one he handed me during a break. We hung out at the door I guard before he headed back to the canteen to get ready for the between-round rush.
TTRPG writeups: WoD Modern 2 - Mercenaries #1
Mild content warning: occasional swearing and mild adult themes
We had a slight derailment right at the outset as S was unable to make the session. I only do character driven stories so players not being able to make sessions can make things fall apart, so normally we would just skip (I had previously tried to encourage the kids to make Redcaps that we could use in a casual drop-in/out filler game as a Redcap gang lends itself well to that, plus they could get any murderhobo/random dickishness/silly out, but the older boys had decided "Changeling is cringe"). However in this case seeing as it was early on, I managed to restructure stuff in my head (and later on in my notes) enough to postpone S to the next session.
System: World of Darkness (edition uncertain as the sourcebooks are all over the joint and also I fudge and homebrew a lot)
August Homeschool Miscellany
I did not forget July, apparently we didn't do anything at all.
Or at least we didn't do anything that I took photos of. The boys had random conversations with me and 16yo with his friends at gym about astrophysics, philosophy, life, the universe and everything and I really wish they would write this stuff down so I had proof. 14yo has been out and about with her boyfriend including going to AQWA. I'm trying really hard to pressure them harder into writing down stuff and basically doing their own reports especially as they're doing so much stuff on their own now but still having zero luck with that.
12yo had homeschool group where he's made a couple of friends and is doing science and drama classes, and I won't usually use any photos I take there (which is not many at all) as it's hard not to get someone else in the shot.
May/June Homeschool Miscellany
During May, 12yo decided to get into fruit sculpture, and made a ridiculous amount of stuff out of bananas. Because I was really preoccupied with I can't remember what at the time, the only thing I caught a photo of was this "sword".
I did have time to make a trip to Spotlight to pick up some elastic and some fabric for 14yo to make a blanket thing that apparently only needs tying together.
April Homeschool Miscellany
April was a bit of a blur of late nights and continued chaos. When the budget cycle rolled around we did manage a zoo trip. 16yo refused to wake up, and 14yo, 12yo and 14yo's SO and I were literally just about to walk out of the house when the outlaws arrived with my 4yo nephew. We told them we were just heading out to the zoo and they were welcome to come along if they wanted, so we all ended up piling back into their car and heading on over.
We used to have zoo passes so our trips to the zoo always started off with deciding what each person wanted to study and then checking out the map to work out the most efficient paths between what everyone wanted and then make up anything else in between or afterwards, so there was an automatic gravitation to the map to do this.
I would love to say things are picking up but they're really not. Issues are abounding, some of them standard teenage ones, some of them teenage politics I thought we might have a prayer of avoiding if we avoided using the school system (very naive thought there, because to completely avoid it I guess we'd have to exist in an insular community with only mostly like-minded individuals), a lot probably stemming from the other thing even though we're trying to both ignore it and deal with it as much as possible.
The smalls had a bit of an arty month. 12yo actually sat still long enough to twine a piece of blutack around a skewer (in fairness there was some mild distraction as he was watching Youtube at the same time and just wanted to do something with his hands while doing so) and in a completely separate session also started drawing DnD item and magic cards while waiting for a box that he'd bought to arrive.
At the end of January Homeschool Miscellany we were re-establishing routines and trying to get into good habits and making new plans.
Two of those things are somewhat working out for us.
I'm still struggling to go to bed on time x_x
There were a few unexpected shenanigans quite close together which have thrown me right off with AER and hive and training which is about normal, and in way too many cases excursion days were postponed as well.