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A poverty rate is one of the key economic indicators. It shows the proportion of the population whose income is less than the poverty line in the area. The lower the number is, the more prosperous the life of society is. The current poverty rate in Matawan is 6.5%. In the neighboring cities, this figure is as follows: in Union Beach, 6.7% of the population live below the poverty line, in Monmouth Beach — 6.5%. The poverty rate in New Jersey is 8.16%. Based on such indicators as the poverty rate, we assume that life in Matawan is slightly better than the average for the state.
The median gross rent in Matawan is $1,262 a month (as of 2016). In 2010, this figure was lower — $1,211/mo (-4.2%). Please note, gross rent may include not only the rent payments, but also utility bills and some other building costs. The median gross rent in the state of New Jersey is lower at $1,192 per month (again, data for 2016). The following median gross rent was registered in the neighboring cities: renters in Rahway pay $1,262/mo, in Dunellen — $1,261/mo.
The rent burden in Matawan is 27.9% (2016). Rent burden shows what proportion of the household income is spent on rental housing. This data is useful in estimating the housing affordability in the city. Rent burden in Matawan is lower than in the state of New Jersey, where the rent burden is 32.1%. In neighboring cities, the situation is as follows: rent burden is 28.0% in South Amboy, and in Fords — 26.6%.
36.6% of housing units in Matawan are occupied by renters (2016). A housing unit means a house, an apartment, a mobile home, a room or any other structure that is used for habitation. In 2010, the share of renter-occupied housing units was lower — 36.2%. It seems that now more people live in rented houses in Matawan than before. Neighboring cities have the following shares of renter-occupied housing units: Englishtown (36.9%), Sea Bright (35.9%).
There are 1,362 renter occupied households in Matawan (2016). This is just a rough estimation based on Census and ESRI demographic data. Since 2015, the number of such type of households has increased by 2% (1,362 households in 2016 vs. 1,338 in 2015). Nearby cities have the following renter-occupied housing unit numbers: there are 1,466 households in Middlesex, 1,336 units in Metuchen.
There was 0 eviction reported in Matawan in 2016. Here are how many evictions were made in nearby cities in 2016 : 1 from housing were made in South Plainfield, 1 in Perth Amboy. Reasons for evictions can be different-code violations, violations of the terms of the lease, etc. But often the main reason is the failure to pay the rent on time. That is why a large number of evictions (especially when there is a tendency to increase this number) may indicate a deterioration of the economy.
The total number of eviction cases that were registered in the Matawan in 2016 is 287.00. Please note that some addresses may have multiple eviction cases during the year. Compared to the neighboring cities, Matawan has less eviction cases than Highland Park (298.00 filings in 2016), more eviction cases than Keansburg (224.00 filings).


The Internet of Things (IoT) is seeing the proliferation of smart, networked devices, capable of producing vast amounts of data on aspects of our personal and professional lives. However, it's not so much these smart devices that are adding value, but rather the potential to capture, interpret, analyze and act on the information they collate.
Business Intelligence (BI) technology enables companies – and individuals – to unlock the insights captured and transmitted between objects with Internet connectivity. These prized insights can then be exploited to bring enhanced services to market and improve the performance and efficiency of their business.
BI, in conjunction with IoT, empowers businesses to explore and mine consumer-generated data to better understand and anticipate customer needs. Armed with accurate data on individual customer preferences, businesses can offer highly-tailored marketing and promote products that match individual tastes and lifestyle's thereby improving customer experience and loyalty.
Transport for London is reported to be evaluating how IoT data can help to improve commuters' journeys.
By monitoring passenger behavior, TfL aims to be able to react to passenger needs by, for example, informing people of where congestion is, optimizing traffic lights and ensuring more efficient boarding at tube stations.
The scope for improving business operations, through granular analysis of those operations, is endless and extends across sectors. Manufacturing can use IoT to optimize production and supply chains – taking advantage of connected devices within the production and supply chain processes themselves – in order to monitor efficiencies. Similarly, farmers can use connected sensors to monitor crops and cattle to improve operational efficiencies.
For example, a group of wine producers in Germany are currently trialing IoT technology to optimize the management of wine production and improve the quality of their products.
IoT sensors, deployed throughout the vineyards, measure and record air and soil humidity as well as temperature and solar intensity. Through analysis of the data collated on vineyard conditions, winemakers are empowered with information that enables them to decide when best to fertilize and irrigate the vines to achieve the best quality wine possible.
The vast amount of information produced via smart, connected devices – in terms of both new and rapidly growing data types and sources – means that organizations have the opportunity to use BI to become more profitable. Data-based insights can be used to improve existing products and services.
For example, insurers can analyze data from IoT solutions to give more accurate and personalized quotes and improve marketing through user demographic information and retail spending habits.
BI also enables stakeholders to turn data-based insights into a commodity in itself. These insights, derived from a range of smart connected devices that make-up the IoT phenomenon, can then become entire businesses themselves, with third parties able to sell that information to both consumers and companies.
Businesses can of course sell those insights to individuals directly (aside from using that information to improve products and services), and individuals can sell their personal device-associated usage data back to businesses (often in exchange for various incentives and rewards).
BI represents an opportunity to discover patterns, predict trends and forecast with greater confidence than ever before. BI gives access to these patterns across the entire organizations, meaning that relevant users and departments will be kept in the loop on new trends.
Similarly, by monitoring data streams from connected sensors in complex machinery or systems – such as escalators or airport hardware – it's possible to identify when a component may fail, allowing a business to move to a position of preventative maintenance.
The IoT promises to revolutionize both the workplace and consumers' lifestyles, providing stakeholders with information that enables organizations to be run more efficiently and for businesses to offer products and services tailored to fit their customers' individual needs.
However, any business wishing to reap the benefits of this fast evolving technology will need a solid analytics tool capable of transforming the vast range of data sources into valuable insights that will boost their bottom line.


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2006 Koenigsegg CCX: CCX is the latest and best from Swedish supercarmaker Koenigsegg
Mark Vaughn
If you want to go by sheer speed, the Koenigsegg CCR is officially the fastest production car in the world, having lapped Italy's Nardo test track at 241 mph last year, about 1 mph faster than the McLaren F1. Keep in mind that Nardo is just a big, round circle, meaning the front wheels were slightly turned the whole time and keeping it from hitting an even higher top speed. Find a place where you can straighten the wheels and the number will be even higher. Maybe they need to take one of these to the Bonneville flats.
How do you measure the super in a supercar? Most power? Most expensive? Most impressionable starlets stuffed into the passenger seat in a single sitting?
After the Nardo record, Koenigsegg went to work producing the successor to that car, which you see here and which we recently got to drive, the CCX.
We didn't go 241 mph but only because there wasn't enough room, since we weren't at Nardo. Instead we were at that little-known but very fun road course outside of the Las Vegas Motor Speedway, within sight of the glittering towers of that seminal city.
On hand that day to help out was hired gun Justin Bell, who, among other lifelong accomplishments, drove a McLaren F1 to victory at Le Mans. And since the F1 is so similar to the CCX, who better than Bell to wail on this new car?
After a couple of laps by himself to learn the track and the car, he came into the pits and gave a succinct engineering-minded evaluation of it.
"It's just absolutely f***ing amazing in any gear," said Bell, perhaps waxing a bit more poetic than his race-driver dad might have.
Bell liked the driveability of the car compared to other exotics, citing the Saleen and Mosler in particular as "compromises."
"With this car you don't have to give up as much to get the performance it offers," he said. "It's really the fastest thing on the planet you can take a passenger in."
The Koenigsegg CCX is the third iteration of this quirky Swedish delight, the CCR and CC8S being the first two. Each version has been refined to eke out even more speed and greater stability.
This one was engineered, among other things, to pass both United States and worldwide regulations.
"We wanted to go into the world market, but we couldn't do it with the old car," said development engineer Magnus Jaasund. "We also tried to improve things we thought could be better."
That amounted to 1100 things that are better in the new CCX, from seats to wheels to engine.
Where previous CC engines were based on Ford designs, the new car has an all-Koenigsegg powerplant, including a CCX-specific casting that is stronger and more durable. It's still a 4.7-liter V8 and still puts out 806 hp, "at least the same as before," said Jaasund. The difference is this one
passes not only U.S. but even California emissions and runs on 91 octane. New heads, injectors, camshafts and numerous other improvements make it possible.
Transmission is the same six-speed manual found on the CCR, but you can order your own ratios. It also comes standard with a torque-sensitive limited-slip differential.
Tires are the same Michelin Pilot Sport 2s—255/35s mounted on 19-inch rims in front and 335/30s on 20s rear. Now you can order optional carbon fiber rims and ceramic disc brakes to go with them. The new Sparco carbon fiber seats are padded and also recline.
The genesis of the CCX came when engineers digitally measured the old CCR body, storing the measurements on a computer. Previous CCs were all hand-made. From that data the new car began to take shape.
The CCX is eight inches longer in back to accommodate U.S. rear-impact standards and 50 millimeters higher inside to accommodate U.S. NBA stars.
The carbon fiber frame is largely carryover, but the body panels fixed to it are new. The front end, for instance, accommodates not only the U.S. 2.5-mph bumper standard but holds new fog lights, side marker lamps and allows better brake cooling. New side skirts also increase downforce.
All these features were in play when Bell drove the car, as well as when he rode along with us, as he would be riding along with all the drivers that day. Most of them would be actual rich guys who could conceivably buy one of these with their own money at the car's $695,000 sticker price, as opposed to your reporter, who could conceivably—and, in fact, did—buy a used minivan.
Bell was right about the engine: To a certain extent it almost didn't matter which gear you were in. You could start in third and not worry about stalling, or start in first and light up the tires.
At wide-open throttle the engine has a sonorous throaty wail—if all three of those words can be legally put together in a sentence.
However, braking, turn-in, balance and acceleration were all areas into which we merely dipped a proverbial toe. The car was flawless in every respect as far as we pushed it. The thing was, in only three laps we couldn't push it too far. Given three, or 333, more we would have a sense of the car that came much closer to its limits. As it was, however, this was a fine how-do-you-do.
Steering felt solid and directly coupled to the road without kicking back in the driver's hands. We braked early and probably didn't get any heat in the discs but didn't hear even a squeak of protest from pads. Around the track's sole decreasing-radius turn we did manage to make it understeer each time (who can ever remember which corner is the shrinking one?), but around all the others it balanced perfectly. And under acceleration it simply flew, with no squirrelliness whatsoever coming out of corners.
So yes, it felt pretty close to perfect in all three laps, but we'd have loved to have it for more. Just for scientific research, you understand.
You can have one for as long as you want if you transfer $695,000 to the nice folks at Exotic Cars at Caesars Palace. Yes, the sole Koenigsegg dealer in America is located in the mall at Caesars. It's actually a very interesting place, so interesting that they get 7000 oglers a day.
"We are in the busiest mall in the world," said Exotic Cars CEO Richard Weisman.
Unless you're a true high roller, the typical visitor to the showroom pays a fee and gets to circumnavigate a catwalk that circles the 35,000-square-foot dealership, gazing down upon Ferraris, Lamborghinis and Koenigseggs and those who are about to buy them. You can view the inventory
at www.ecacp.com.

redpajama_set_name: RedPajamaCommonCrawl


Hibiki Tachibana is one of a group of girls able to use Symphogear: a special type of armour that empowers the user as they sing. Alchemist Carol and her group of homunculi are wielding their unknown powers and endangering the world. Their powers have the ability to destroy the Symphogear, and the team find themselves out-matched. In this extremely bleak situation, the battle for the song that will end the world begins.
When I first began watching Symphogear GX, I was a bit overwhelmed with the amount of unexplained things that were going on. Who were these girls? What were they fighting? What on earth is going on? Then I realised that what I was watching was the third season of this anime and, whilst it has been incredibly popular in Japan, it has only just made it to Western screens. With no sign of the first two seasons, it was up to me to fill in the gaps where I could with my extensive knowledge of magical girl canon and tropes.
Essentially, Symphogear is battle armour created from ancient relics, forming when the user harmonises with the relic through song. They battle against the Noise – a dangerous alien race that threatens humanity. Ever since getting caught in Noise crossfire two series ago, Hibiki Tachibana has been protecting the world and saving lives through Symphogear alongside the rest of the team.Now, alchemist Carol Malus Dienheim and her homunculi henchmen are out to destroy everything the Symphogear users have sworn to protect. Carol has the ability to summon a brand new form of augmented Noise known as Alca-Noise, able to to completely destroy Symphogear armour at the slightest touch.
What I like about Symphogear GX is the amount of lore it contains with regard to relics, terminology and alchemic crafts, with the added bonus of most of it being able to be deduced through the show without any prior knowledge (which is good for us Westerners coming in at the third series). Although there are some tensions between Symphogear members which go unexplained because the show assumes we have watched the earlier episodes, on the whole the narrative does a good job of not alienating us newcomers by casually tossing us into the deep end and ploughing ahead regardless of confusion.
Sometimes, magical girl anime tends to take a step back when it comes to fight scenes, but in Symphogear GX they come thick and fast like the proverbial shounen fight-fest. In the first episode we see Hibiki throwing an aircraft caber-style to stop it from crashing into a building. If that is the precedent it sets right off the bat, I'm intrigued as to what's going to go down in the final episodes! The Alca-Noise, as enemies, are a bit faceless and samey, but without them we wouldn't have enough excuse to watch these armoured terrors plough through their number at terrifying speeds.
The action sometimes borders on insane – but that's what I like! When things are a bit out-there and over-the-top, they're at their most entertaining and amusing. It's one of the many things I enjoy about anime on the whole as it's not afraid to put new spins on things and explore some ridiculous situations. For example, the opening sequence of Symphogear GX is a rescue mission rather than a fight, and it still manages to get around to feature the K2 mountain being punched in half. The attacks the Symphogear girls use are the kind that, if I had super powers (one day…), I would be naming my special attacks. You don't want to mess with "Megadeth Party" and "Kill Juliet" and "One Thousand Tears" are pretty clear on their results. Each team member is a different colour and favours a different weapon, as usual and watching them in action, complete with the up-tempo songs they sing, make the battle scenes truly unique.
The only area that Symphogear GX struggles with is the subbing of the lyrics to its musical content. Translating songs in anime without losing too much meaning and content is tricky to begin with and damned challenging when licensing gets involved. To be fair, the translations haven't been too bad in this one, considering its a fast-paced anime that relies heavily on music, however, there are a few noticeable glitches once you start watching. Some songs are completely subtitled, but then you will hear other songs later that have no translation whatsoever – often in the same episode. Knowing the lyrics of the songs isn't mandatory to enjoy the anime, but it does give the sensation that you're missing out on the full experience. The characters are actually singing as they fight, it's not just an opening or ending credits song, and the lyrics often reflect their situation, personalities and fighting style – something which would help Western viewers get up to speed with characters better since they've not watched the first two seasons. Whilst I appreciate the hard work that has gone into all the translations, it sometimes feels like an important element that has been neglected due to time-constraints.
Jumping in at the third series is never going to be an ideal starting point, but if you can get your head around the basics of the Symphogear universe in the first couple of episodes you will discover why this series is so popular in Japan. There's plenty of great characters, action, animation and, better yet, music. Don't be put off by going into Symphogear GX at such a late stage – you will be missing out.


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Commentary: Joan Irvine Smith advocated for responsible development
"Joan Irvine Smith also comprehended the importance of our limited water resources and the responsible management of growth," says commentary writer Peggy V. Palmer.
(Karen Tapia / Los Angeles Times)
By Peggy Palmer
Philanthropist, environmentalist, social and corporate activist were just a few of the adjectives to describe Joan Irvine Smith in her recent obituary.
"A witness to the development of Orange County from citrus groves and lima bean fields to its current population of over three million people, Mrs. Smith was an indomitable advocate for the judicious use of water resources and local government's supervision of land development," according to her obituary in the Orange County Register.
Joan Irvine Smith, philanthropist and major force behind the founding of UCI, dies at 86
She championed the effort to locate the campus on the Irvine Ranch property and persuaded the Irvine Co. to part with 1,000 acres for that purpose for $1.
As the state of California continues to mandate excessive quantities of new housing (only as the state's population stalls), people are being driven to more amicable and affordable states.
We should ask why our water resources are being hijacked to accommodate 4,800 proposed dwellings in Newport Beach alone?
This defies logic and the remnants of the populace are left to discover that California only added residents by a thin 0.35% annual rate over the past 12 months, according to the Los Angeles Times.
Statistically, this is the lowest growth rate since the early 1900s.
Responsible development has to recognize the value of preservation of our harbor, protection of public views, conservation of our land and historical architecture. These priceless and unique components of our coastal towns should not be compromised at the whim of reckless government officials.
The "Plop-Drop and Destroy" development approach is extremely irresponsible and does not consider the unintended consequences or the perverse effect contrary to what was originally intended.
At the beginning of the 20th century, President Teddy Roosevelt ushered in a period of conservation as a major part of his administration.
As the new century began, the frontier was disappearing. Many Americans, including Roosevelt, saw a need to preserve the nation's natural resources. He wanted to protect animals and land from businesses that he saw as a threat.
Smith also comprehended the importance of our limited water resources and the responsible management of growth. She and other activists sought that future developments would compliment existing neighborhoods and would do no harm.
Perhaps, protecting our natural elements and finding common ground for the good of California's coastline, would be a better initiative in 2020.
Peggy V. Palmer lives in Newport Beach.
How to get published: Email us at john.canalis@latimes.com. All correspondence must include full name, hometown and phone number (for verification purposes). The Pilot reserves the right to edit all submissions for clarity and length.
OpinionIrvine
Peggy Palmer
The Crowd: Open your red envelopes at South Coast Plaza
South Coast Plaza will begin its annual Lunar New Year celebration Jan. 23 in Jewel Court.
Mailbag: Landlord should reduce stationery store's rent
Re "Newport Stationers is on the way out after 55 years," (Jan. 10): I am writing to you with the hope that publishing this letter might help put pressure on the Irvine Co. to save Newport Stationers, one of the oldest, core small businesses here in Corona del Mar.
Column: Active shooter drills are another example of how we've failed schoolchildren
My niece was helping her daughter at bath time when the 5-year-old asked, "Mom, what if a bad guy gets a ladder and breaks our class windows that are high up?"
Commentary: New language institute will enrich cultural life in Costa Mesa
At a recent council meeting, I listed Costa Mesa's 2019 highlights, including opening a 50-bed shelter for those experiencing homelessness, transforming Lions Park with our beautiful new Donald Dungan Library and hiring our new city manager, Lori Ann Farrell Harrison, following a nationwide search.
Mailbag: March for Women and equality on Jan. 18 in Santa Ana
As we march toward the 2020 presidential elections, now is the time to speak up loudly for the values that matter to us.
Commentary: Sweeping new laws will provide the gift of 'granny flats'
ADUs, also called "granny flats," offer cities an opportunity to develop new housing units that are not disruptive to the look and feel of single-family neighborhoods.
Commentary: Courage, conviction and character needed to address opioid epidemic in O.C.
Proportionately, opioid overdose deaths in Orange County far outpace those in Los Angeles, Riverside, Santa Barbara, San Bernardino, San Diego and Ventura counties.
Mailbag: A New Year's wish list for Newport Beach
Commentary: Huntington Beach's pension bond proposal feels like déjà vu
The Huntington Beach City Council's recent approval of a resolution to consider pension bonds could put the city at risk of a fiscal wipeout, two Orange County elected officials write.


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TED SWIET
Artist Statement CV Press Release
Ted Swiet is a graduate of San Francisco State University, and was named one of San Francisco's "Top 100 Innovators" by Levi Strauss & Co. His work has been collected all over the world including Japan, London and New York. Swiet's background in arts, graphic design, interior architecture and product design has allowed him to become a versatile, multi-faceted artist who melds elements of fine art, engineering and pop culture to create precise, insightful works. Ted is inspired by artists of many different realms including Rube Goldberg, David Bowie, Stanley Kubrick, David Sadaris, Jasper Johns, Jim Dine, and Steve Jobs.


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LEO CUYPERS
componist, improvised, jazz, piano
As a baby Leo Cuypers (Heemstede, 1 December 1947) lay in his cradle literally under the family's grand piano, as he puts it himself, for his entire family plays the instrument. He grows up in Maastricht and initially wants to be a jazz drummer. At the Maastricht Conservatory, where he ...
componist, piano
1971 Willem Van Manen
1974 Arjen Gorter
1974 Maurice Horsthuis
1974 Rob Verdurmen
1974 Willem Breuker
1975 Harry Miller
Biography Leo Cuypers
As a baby Leo Cuypers (Heemstede, 1 December 1947) lay in his cradle literally under the family's grand piano, as he puts it himself, for his entire family plays the instrument. He grows up in Maastricht and initially wants to be a jazz drummer. At the Maastricht Conservatory, where he drops out before graduating, he eventually opts for piano, however. After an intense period of self-study he wins the 1969 Loosdrecht Jazz Competition with a solo performance. He moves to Amsterdam and joins the Willem Breuker Kollektief on piano. Cuypers stands out for his theatrical contributions and his catchy, often melodious compositions. As a pianist he is controversial, criticized for his technical limitations, but valued for his idiosyncratic style. In 1973 he is awarded the Wessel Ilcken Prijs (the major Dutch jazz award at the time) and in 1974 he and Willem Breuker found the record label BVHaast. Cuypers writes music for theater and film. He also starts forming his own bands. In 1977 his Zeeland Suite is broadcast on TV. Together with writer J. Bernlef he produces musical theater pieces. In the course of the 1980s Cuypers disappears from the music scene. In 1994 he starts performing again as a solo pianist and in 1995 his solo album Songbook is released. His comeback, however, is short-lived. Many of Cuypers' albums have been reissued. His first solo album from 1972 is released on CD for the first time by Music Center the Netherlands in 2011.
Willem Breuker Kollektief piano
Leo Cuypers grows up in family of pianists. Both his parents and all six children play the piano. When he is nine years old the family moves from Heemstede to Maastricht. His oldest brother brings him into contact with jazz. He therefore initially wants to play the drums. In 1962 Cuypers enters the Maastricht Conservatory, where he is taught by a classically trained percussionist. The student prefers the company of arts students at the Jan van Eyck Academie to that of his fellow music students. With them he shares an interest in avant-garde music and freejazz. When he drops out of the conservatory in 1965 his interest has shifted to playing the piano. Through intensive self-study he develops his characteristic solo style in which he improvises between percussive atonality and quiet, melodious passages. Apart from the odd quote from existing music he exclusively plays his own compositions. He doesn't notate his music, however, but learns everything by heart.
In 1969 Cuypers wins the prestigious Loosdrecht Jazz Competition with a solo performance, in which he also uses the piano interior. The jury includes bassist Ruud Jacobs. The prize for Cuypers also includes a TV performance, and his father gives him a grand piano as a present. He will often take the instrument along to gigs. Two weeks later he performs at the Baden-Baden Free Jazz Meeting, at the invitation of reed player Willem Breuker, who had seen Cuypers on TV. In the German town he performs with trombonist Albert Mangelsdorff, bassist Barre Phillips and the Art Ensemble of Chicago. He moves to Amsterdam, where he joins the bands of Willem Breuker and saxophonist Theo Loevendie. Meanwhile he continues to give solo concerts. He makes his recording debut with the album Chess! by the Theo Loevendie Consort, which includes tenor saxophonist Hans Dulfer, trombonist Willem van Manen, bassist Arjen Gorter and drummer Martin van Duynhoven. In 1972 Cuypers records a solo album, which is released as part of the BIM series (1971-'74) of the German BASF label. The LP, produced by Joop Visser, has an edition of only a few hundred copies.
1974 sees the start of the Willem Breuker Kollektief, of which Leo Cuypers is the pianist. The orchestra makes a name for itself with powerful, theatrical performances. In the founding year Cuypers composes the Johnny Rep Suite. This ode to the rebellious (Ajax) soccer player is performed at the Amsterdam Stedelijk Museum, 'with Han Bennink as referee, Willem Breuker in a DWS (Amsterdam soccer club) jersey and I myself in Ajax colors. We also had a tape giving the impression that we were in a huge stadium', is how Cuypers describes the performance in newspaper De Volkskrant – an event at which Rep himself was present. 1974 is also the year Breuker and Cuypers start their own record label, BVHaast. They intend to release their own music and that of likeminded musicians. The first release is Cuypers' Live In Shaffy, featuring a recording of the Johnny Rep Suite, with Breuker, Piet Noordijk and Hans Dulfer in its frontline. The album should not be confused with Live In Shaffy by the Breuker-Cuypers duo, an LP in a large, triangular sleeve, designed by visual artist Ger van Elk.
Cuypers keeps working with the Willem Breuker Kollektief, but also joins the bands of pianist/composer Nedly Elstak and bassist Harry Miller. In 1976 he gives a solo concert at the first North Sea Jazz Festival. He composes music for the theater production Jan Rap En Z'n Maat. For the Festival Nieuwe Muziek Zeeland he writes the Zeeland Suite, for jazz septet. All parts of the suite are dedicated to various towns and villages in the Dutch province. In 1977 these pieces are performed and filmed on location. The NOS broadcasting company airs the registration on Dutch TV and distributes it internationally. 1977 is a busy year for Cuypers: he collaborates with the Scapino Ballet, and the Willem Breuker Kollektief tours the States. 1978 sees the release of live recordings from Berlin and Paris by the Kollektief and the duo Breuker-Cuypers. The Kollektief records soundtracks for filmmaker Johan van der Keuken. In 1979 a solo performance by Cuypers is released on the album In Amsterdam, for which visual artist Jeroen Henneman designs the sleeve. In 1980 Cuypers leaves the Willem Breuker Kollektief.
Cuypers starts his own bands. In 1981 he performs with two different trios, one with Han Bennink and the other with Martin van Duynhoven. With Arjen Gorter and Han Bennink he records two LPs: Heavy Days Are Here Again (which also features Willem Breuker) and Corners. He performs at the 1981 North Sea Jazz Festival with Breuker, Gorter and Bennink. From1982 Cuypers regularly plays with saxophonist Vera Vingerhoeds, in the Leo Cuypers Quartet and other combinations. In 1984 he presents his Leo Cuypers Brull Band, a septet with a frontline featuring Kollektief cohorts Willem van Manen and Maarten van Norden. In 1986 he composes music for Voetnoten, a theater production by writer J. Bernlef about the transience of musical fame. In the years to follow Cuypers does the occasional solo concert, but hardly performs at all. In 1989 he gives a one-off duo concert with Louis van Dijk at the Amsterdam Bimhuis. In the years to follow he quits performing altogether, inhibited by stage fright and an alcohol problem, as he explains in a 1994 interview with newspaper Het Parool. Cuypers moves back to Maastricht.
In 1994 Leo Cuypers makes a comeback with a series of solo concerts where he performs his new, fifty minute suite Hotel Maastricht. In 1995 the solo album Songbook is released, based on a repertoire of brief compositions he has been composing since the 1980s. Shortly after the completion of the studio session he gives a concert on a Bösendorfer grand, and decides to release this registration instead of the studio recordings. The CD release leads to new solo tours. Media reactions to the comeback are generally positive. Cuypers' style is less anarchic than it was back in the 1970s, and more aimed at melodiousness, as he states in an interview with newspaper NRC Handelsblad. In his book New Dutch Swing (1998) Kevin Whitehead draws a comparison between Cuypers' melodious style and the improvisations by the South-African pianist Abdullah Ibrahim (formerly known as Dollar Brand). Songbook ends with the composition Jarrett, a reference to another kindred spirit, Keith Jarrett.
After 1998 little is heard from Leo Cuypers. The Zeeland Suite and Johnny Rep Suite are reissued by BVHaast on one CD. Leo Cuypers' Heavy Days Are Here Again is released on CD in John Corbett's Unheard Music series for the American Atavistic label. In 2011 Cuypers' eponymous solo debut from 1972 is reissued on CD, by Music Center the Netherlands. In addition to the original recordings it features three live bonus tracks from 1973. At the CD launch on 2 October 2011 at the Bimhuis Leo Cuypers' compositions are performed by pianist Guus Janssen.
Discography Leo Cuypers
Act Leo Cuypers
Type and year LP, 1972
Label BASF, 14-25182-9
producer Joop Visser (2)
Details Recorded at Studio André van de Water, Baarn, 6 June & 19 October 1972; released in 2011 on CD by Muziek Centrum Nederland (MCN 1102), containing three extra tracks, recorded at De Brakke Ground, Amsterdam, Augustus 1973 & for VARA Radio, Hilversum, 21 December 1973
Live in Shaffy
Label BVHaast, 001
muzikant Maurice Horsthuis
muzikant Willem Breuker
muzikant Koen van Slogteren
muzikant Piet Noordijk
muzikant Arjen Gorter
muzikant Hans Dulfer
muzikant Ronald Snijders
muzikant Willem van Manen
muzikant Jan Wolff
muzikant Rob Verdurmen
muzikant Martin van Duynhoven
muzikant Bernard Hunnekink
Details Recorded live at the Shaffy Theater, Amsterdam, 24, 25 & 27 September 1974; the Johnny Rep Suite and two other tracks were released in 1993 on BVHaast CD 9307; in 1974 Willem Breuker & Leo Cuypers released an album with the same title
producer Willem Breuker
Details Recorded at the Artisound Studios, Amsterdam, 21 September & 13 October 1977
Zeeland Suite
muzikant Bob Driessen
muzikant Harry Miller
Details Recorded by VARA Radio, Hilversum, 19 September 1977; released in 1993 on BVHaast CD 9307
Willem Breuker / Leo Cuypers - ...Superstars
Label FMP, SAJ-17
Details Recorded live opgenomen at De Brakke Grond, Amsterdam, 19 May 1979
Leo Cuypers Trio - Corners
Label VARA Jazz, 209
muzikant Han Bennink
Details Recorded in VARA Studio 2, Hilversum, 20 July 1981
Leo Cuypers' Heavy Days Are Here Again
Details Recorded at the MCR Studio, Amersfoort, 12 June 1981; rereleased on CD in 2000 in the Unheard Music Series of Atavistic (UMS/ALP207CD)
Leo Cuypers' Brullband
Label VARA Jazz, 5217
muzikant Ernst Glerum
muzikant Maarten van Norden
muzikant Jan Kuiper
Details Recorded at 042, Nijmegen, 21 December 1984
Label BVHaast, CD 9502
Details Recorded live in the garden of the Kloveniersdoelen, Middelburg, 5 August 1995
Nachtrit
Type and year 7", 1979
Label Theaterunie
B-side Drivin' Through The Night
muzikant Kashavan Maslak
Details Recorded in Rotterdam, January 1979; one-sided flexidisc containing the soundtrack of Nachtrit, a theatrical play by J. Bernlef
Label Frascati, 6846 075
muzikant Cor Willemsen
muzikant Dik Baars
muzikant Theo Houtkoop
muzikant Mark Zandveld
Details EP containing 4 tracks, including Mercy Mercy, performed by the Corgelkwartet (featuring Cuypers) and Vivat Frascati, a solo performance by Cuypers
Theo Loevendie Consort	- Chess!
Label BASF, 14 25180-2
muzikant Leo van Oostrom
muzikant Rien de Reede
muzikant Harry Sparnaay
muzikant Leo Cuypers
Willem Breuker	- The European Scene
Label MPS, 68.168
muzikant Boy Raaymakers
Johan van der Keuken / Willem Breuker	- Music For His Films 1967-1978
muzikant Victor Kaihatu
muzikant Maarten Altena
muzikant Gilius van Bergeijk
muzikant Herman de Wit
muzikant Lodewijk de Boer
muzikant Louis Andriessen
Floor van Zutphen	- Play On
Label Frascati, 681 4967
gastmuzikant Peter Guidi
gastmuzikant Hessel de Vries
gastmuzikant Theo de Jong (3)
gastmuzikant Gerhard Jeltes
gastmuzikant Peter Tiehuis
gastmuzikant Martin Oosterwijk
gastmuzikant Machiel Scholder
producer Leo Cuypers
Photos Leo Cuypers
Audio/Video Leo Cuypers


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Mathematics for the Nonmathematician
SKU: 0486248232 Category: Pre-Calculus Books
Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen.
Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.
In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.
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Maryland Major Soccer League
Maryland Majors announces Fortitude FC as expansion team
By MMSL Communications, 12/10/18, 11:00AM EST
The Maryland Major Soccer League is pleased to announce new expansion team Fortitude FC who will begin in the Maryland Majors 2nd Division starting in spring 2019. Hector Monterroso is owner/Head Coach of Fortitude FC. Hector's staff includes Assistant Coach Fudge Ayoub, Marketing Administrator Angelica Ibanez, and Club Administrator Andrew Myers. The club has a solid base of players who have developed playing in competitive youth programs including Pipeline SC, Baltimore Bays, and Soccer Association of Columbia (SAC). Many players possess college experience and the team has competed in the Howard County League but it now looking to take the next step to compete in an elite USASA league to compete against stronger teams and gain more exposure for the club and players.
©2019 Maryland Major Soccer League / SportsEngine. All Rights Reserved.


Language: English . Brand New Book ***** Print on Demand *****. Excerpt from Canadian Immigration in Report: To the Honorable the Minister of Agriculture, Upon the Position and Prospects of Immigration and With Comparative Statements of Emigration From Great Britain During the Past Four Years, 1876 Mr. Doyle having written to the Times an improper letter, which appeared to commit the Local Government Board to a support of his statements, I deemed it to be my duty to use my position in the House of Commons to put a question to the President of the Board, which led to an immediate disclaimer. The Committee in the Canadian House of Parliament, and Miss Rye s letters, together with communications from other persons, have reassured public Opinion, and I believe that, although the emigration through Boards of Guardians may receive a check, the voluntary societies will still continue to carry out a successful deportation of children. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Language: English . Brand New Book ***** Print on Demand *****.Excerpt from Canadian Immigration in Report: To the Honorable the Minister of Agriculture, Upon the Position and Prospects of Immigration and With Comparative Statements of Emigration From Great Britain During the Past Four Years, 1876 Mr. Doyle having written to the Times an improper letter, which appeared to commit the Local Government Board to a support of his statements, I deemed it to be my duty to use my position in the House of Commons to put a question to the President of the Board, which led to an immediate disclaimer. The Committee in the Canadian House of Parliament, and Miss Rye s letters, together with communications from other persons, have reassured public Opinion, and I believe that, although the emigration through Boards of Guardians may receive a check, the voluntary societies will still continue to carry out a successful deportation of children. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Home | Blog | Top 5 Highlights of the West Highland Way
Top 5 Highlights of the West Highland Way
By Mark Wright
The West Highland Way is one of the most iconic trails in the country and something every keen walker should experience. To help whet your appetite here are our top 5 top highlights on the 95 mile trail from Milngavie Fort William.
Between Drymen and Balmaha lies Conic Hill. At just 361m/1148ft it's by no means a giant, however having made the short steep climb to the summit you are rewarded with the most outstanding views of Loch Lomond.
Measuring 23 miles long, Loch Lomond is the largest body of fresh water in Britain. The line of small islands along the loch mark the direction of the Highland Boundary Fault and the start of the Scottish Highlands.
Both Ben Lomond and the Arrochar Alps can be admired from this stunning little viewpoint.
Falls of Falloch
When walking between Inverarnan and Tyndrum, a short detour will reward you with fabulous views of the Falls of Falloch. Easily accessible, it's a popular beauty spot and a great place for walkers to stop and enjoy a snack.
The River Falloch falls in a single 10m drop and despite it's relatively modest size, it's an impressive sight, particularly when in spate. Sit long enough and you might just see a kayaker attempting the descent.
The Woven Sound is a shelter constructed from intricately woven-together steel rods that weaves its way between existing trees and allows a closer view of the falls. The installation features an entry from the diary of Dorothy Wordsworth, sister of William Wordsworth, who visited the falls along with Samuel Taylor Coleridge.
Buachaille Etive Mòr
The magnificent Buachaille Etive Mòr is one of the most recognisable mountains in Scotland. The classic view as seen from the Kings House Hotel is perhaps one of the most photographed sights on the West Highland Way.
The pyramid like shape first comes into view as you cross Rannoch Moor in the direction of Glen Coe, but it's when leaving King's House and heading for the Devil's Staircase that the full majesty of the mountain known to climbers simply as The Buachaille, is truly revealed.
Film fans will recognise this stunning scenery from the 2012 release Skyfall where 007 played by Daniel Craig returns to his Scottish roots.,
The Devil's Staircase
To cross from Kingshouse over to Kinlochleven walkers must climb the Devil's Staircase. Despite its daunting name this is one of the most popular sections of the West Highland Way.
Originally a drove road the Devil's Staircase is part of the Military Road between Tyndrum and Fort William, built in 1752 by General Caulfield. It's believed it was given its name by the soldiers who were part of the road building. At 550m/1804ft it's the highest point on the Way.
When climbing the steep zigzag path take time to savour the views of Rannoch Moor and the surrounding mountains.
Once at the top you're on the edge of the iconic Aonach Eagach Ridge. There are fine views of Glen Coe. On a clear day you can see Ben Nevis and the Mamore mountains.
Glen Nevis
The final stage of the West Highland Way sees walkers journey from Kinlochleven to Fort William through the incredibly picturesque Glen Nevis. The glen has several spectacular waterfalls flowing into the River Nevis, most notably Steall Falls.
At the foot of Ben Nevis, Britain's highest mountain, Glen Nevis is regarded as one of the finest examples of a glaciated valley in Scotland. The scenic beauty of the glen has contributed to Ben Nevis and Glen Coe being recognised as a National Scenic Area. NSAs are generally equivalent to the Areas of Outstanding Natural Beauty found in England, Wales and Northern Ireland.
A number of famous films have used the valley as a filming location, among them Braveheart, Highlander, Rob Roy and even Harry Potter.
Our West Highland Way holidays are already incredibly busy throughout spring 2022, however we do still have availability during summer and autumn months. For more information on our West Highland Way holidays take a look here, email us info@mickledore.co.uk or call us on 017687 72335 to speak with one of our walking holiday experts.
Our first long distance walk and we really felt we were well guided by your information and so well looked after I would most highly recommend you. We had every confidence you had chosen the best accommodations available and everyone was so friendly & welcoming. We would have no hesitation in using Mickledore again most impressed with everything Thank you
Mrs Hudson, Cheshire	 Coast to Coast, May 2021
This is our 4th holiday with you and you have always delivered. This was definitely our toughest walk but we knew it would be. We will definitely come back again.
Mr Kerr, Leicestershire	 Tour of the Lake District, July 2021


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

Although the inflationary paradigm is successful for solving various problems of the Standard cosmology, it has established itself mainly because of providing seeds for the CMB anisotropy~\cite{Lyth2009, Bardeen1980}. Various single field models of inflation have been shown to be compliant to observations, such as those of WMAP and Planck~\cite{Hinshaw2013, Collaboration2014}. But from the model building point of view, multifield models naturally arise in fundamental theories of High Energy physics, such as SUSY or SUGRA in which occurrence of more than one field is the norm rather than a construct~\cite{Halyo1996, Dvali1994}. Power spectrum of multifield models is generally relegated to the $\delta N$ formalism which relies only on the background solution~\cite{Huston2013, Frazer2014, Clesse2014}, instead of direct solution of perturbation equations. Only numerical techniques can explore the full prediction for power spectrum of multifield model by evolving the full set of perturbation and background equations numerically~\cite{Price2015}.

Although sum-separable potentials, such as $N_f$-flation etc., can be handled through the standard numerical techniques~\cite{Huston2013}, however, the situation becomes complicated in the case when there is interaction between the fields, such as hybrid inflation~\cite{Wang1994,Clesse2009}. Interaction between the fields turns the system of differentials equations into stiff and chaotic, \textit{i.e.} sensitive to the initial conditions~\cite{Easther2013}. For example in hybrid model, it is quite difficult to find a successful background trajectory which gives 60 e-folds of inflation, and it is known as initial condition problem in literature~\cite{Clesse2009, Easther2013}. The problem becomes more intricate if one desires to find a power spectrum for a successful background trajectory in the hybrid model. In this paper, we have calculated the power spectrum for a successful background trajectory in the hybrid model by directly evolving perturbation equations.

The paper is organized as follows. In Section~\ref{sec:setup} we review two versions of the potential for hybrid  inflation and provide the relation between them, and its effective one-field dynamics is quickly reviewed. More importantly linear theory for multi-field perturbation and power spectra is introduced.  In Section~\ref{sec:numerics} we describe our numerical results.  In Section~\ref{sec:conclusion} we discuss the implication of our results and identify future lines of enquiry.

\section{Formal set up}\label{sec:setup}

Among many ways to realize hybrid inflation, we focus mainly on the two versions studied in~\cite{Clesse2009}  and~\cite{Easther2013}, and  provide the relations between the parameters of both versions. In the first version~\cite{Easther2013}, the potential in field space $(\psi, \phi)$, where $\phi$ is the inflaton and $\psi$ is the waterfall field, is
\begin{equation}
	\label{eqn:hybridv}
  V(\phi,\psi) = \Lambda^4 \left[\left(1-\frac{\psi^2}{M^2} \right)^2 + \frac{\phi^2}{\mu^2}
  + \frac{\phi^2 \psi^2}{\nu^4} \right],
\end{equation}

with real parameters $\Lambda$, $M$, $\mu$, and $\nu$.

In the second version\cite{Clesse2009}, the potential is

\begin{equation} \label{eqn:potenhyb2d}
V(\phi,\psi) = \frac 1 2 m^2 \phi^2 + \frac \lambda 4 \left(\psi^2
- M^2 \right)^2 +\frac{\lambda'}{2} \phi^2 \psi^2,
\end{equation}
with real parameters $\lambda$, $\lambda'$ $M$, and $m$. The relations between the parameters of the potentials are as follows: To go from the first to the second

\begin{equation}
m= \frac{\sqrt{2} \Lambda ^2}{\mu },\text{$\lambda $}= \frac{2 \Lambda ^4}{\nu ^4},\text{$\lambda' $}= \frac{4 \Lambda
   ^4}{\text{M}^4},
\end{equation}
and to go from the second to the first

\begin{equation}
\Lambda = \frac{\sqrt[4]{\text{$\lambda' $}} \text{M}}{\sqrt{2}},\mu = \frac{\sqrt{\text{$\lambda' $}} \text{M}^2}{\sqrt{2} m},\nu =
   \frac{\sqrt[4]{\text{$\lambda' $}} \text{M}}{\sqrt[4]{2} \sqrt[4]{\text{$\lambda $}}},
\end{equation}
where $M$ is the same in the both the versions.

 \begin{figure}
     \includegraphics{figures/pot}
         \caption{\label{fig:potential} Potential of hybrid inflation with contour in the $(\psi, \phi)$ plane. The  values of the parameters are $\Lambda = 0.1064 \, M_\mathrm{Pl}$, $M=0.1504  \, M_\mathrm{Pl}$, $\mu=3190.4  \, M_\mathrm{Pl}$, and $\nu=0.1265 \, M_\mathrm{Pl}$  with $M_\mathrm{Pl}$ being the reduced Planck mass.}
 \end{figure}

 For convenience, in what follows, we will consider only the first version of the potential~\eqref{eqn:hybridv}.
  The true minima of the potential are located at $\phi=0$ and  $\psi=\pm M$, while the instability point is given by $\psi=0$,
 $\phi=\phi_\mathrm{c}$, where  $\phi_\mathrm{c}= \sqrt{2} \, \nu^2/M$ is the critical point at which the effective mass of $\psi$ becomes complex and inflation is assumed to come to an end. Along the inflationary valley, $\psi \approx 0$, the potential reduces to  $\Lambda^4\left[1+(\phi/\mu)^2\right]$ which shows that, in this  regime, inflation cannot end by violation of the slow-roll
 conditions.

  \begin{figure}[!t]
  \includegraphics{figures/trajinset}
  \includegraphics{figures/trajzoom1arrcopy}

  \caption{\label{fig:background-sol}Exact numerical  solution for a B-type background trajectory. (Top) Evolution of the fields with the number of e-folds realized. The inset clearly shows that this evolution is qualitatively similar to the B-type trajectory. (Bottom) Evolution of fields in configration space. It shows that the trajectory executes a complicated path and even comes out of the waterfall regime --  green in valley and red for waterfall.}
  \end{figure}

\subsection{Multi-field background dynamics}

Before specializing to the hybrid case, we quickly recapitulate the formalism following Ref.~\cite{Price2015}. The Klein-Gordon equations for the homogeneous background fields $\phi_I$ where $\phi_I \, \in \{\psi, \phi, etc.\} $ take the form
\begin{equation}
\ddot{\phi}_I + 3H \dot{\phi}_I + \frac{\partial V}{\partial \phi^I} = 0.
\label{eqn:KGtime}
\end{equation}

Replacing cosmic time $t$ with the number of $e$-folds $N_e \equiv \ln a(t)$, as it is more convenient for inflationary dynamics, gives

\begin{equation}
\frac{\mathrm{d}^2 \phi_I}{\mathrm{d} N_e^2 } + (3 -\epsilon) \frac{\mathrm{d} \phi_I}{\mathrm{d} N_e} + \frac{1}{H^2}\frac{\partial V}{\partial \phi^I} = 0  ,
\label{eqn:back}
\end{equation}
where we have defined the first slow-roll parameter as
\begin{equation}
  \epsilon\equiv-\frac{\dot H}{H^2}
  =\frac{1}{2} \frac{\mathrm{d} \phi_I}{\mathrm{d} N_e} \frac{\mathrm{d} \phi^I}{\mathrm{d} N_e}.
  \label{eqn:eps}
\end{equation}

\subsection{Perturbed equations}
We apply perturbation theory to study the spatially dependent modes, writing
\begin{equation}
\phi_I(t, \vec{x}) \to \phi_I(t) + \delta \phi_I(t, \vec{x})
\end{equation}
where $\phi_I(t)$ is the homogeneous, classical background field. The mode eqaution for the Fourier transformed scalar perturbation in the spatially flat gauge is
\begin{equation}
\frac{\mathrm{d}^2 \delta \phi_I}{\mathrm{d} N_e^2} + (3-\epsilon) \frac{\mathrm{d} \delta \phi_I}{\mathrm{d} N_e} + \frac{k^2}{a^2H^2} \delta \phi_I +  C_{IJ} \delta \phi^J = 0,
\label{eqn:dphi_mode}
\end{equation}
where
\begin{equation}\label{eqn:cij}
C_{IJ} \equiv \frac{\partial_I\partial_J V}{H^2} + \frac{1}{H^2} \left(\frac{\mathrm{d} \phi_I}{\mathrm{d} N_e} \partial_J V  +  \frac{\mathrm{d} \phi_J}{\mathrm{d} N_e} \partial_I V \right)
+ (3-\epsilon) \frac{\mathrm{d} \phi_I}{\mathrm{d} N_e} \frac{\mathrm{d} \phi_J}{\mathrm{d} N_e}
\end{equation}
and $\partial_I \equiv \partial/\partial \phi_I$.
Similarly the evolution equation for the tensor perturbations is written which is identical to the single-field case as tensor perturbation are massless (being non-gauge degrees of freedom) and only minimally coupled to the matter sector.

For convenience, the Mukhanov-Sasaki variable  $u_I \equiv a \delta \phi_I$ is used, and therefore the mode equation for $u_I$ becomes
\begin{equation}
\frac{\mathrm{d}^2 u_I}{\mathrm{d} N_e^2} + (1-\epsilon) \frac{\mathrm{d} u_I}{\mathrm{d} N_e} + \left(\frac{k^2}{a^2H^2} - 2 + \epsilon \right) u_I + C_{IJ} u^J = 0
\label{eqn:ptbmodeeqn}
\end{equation}
with $C_{IJ}$ as in Eq.~\eqref{eqn:cij}.
The perturbation Eqs.~\ref{eqn:ptbmodeeqn} generally mix the annihilation operators for all of the fields as the mass matrix $m^2_{IJ} \equiv \partial_I\partial_J V$ is not necessarily diagonal\cite{Salopek1989}.
Therefore each perturbation mode $u_I({\mathbf{k}})$ and $u_I^\dagger({\mathbf{k}})$ is expanded using $N$ harmonic oscillators $a_J({\mathbf{k}})$:
\begin{equation}
  u_I({\mathbf{k}}, N_e) = \psi_{I}^{\;\; J} ({\mathbf{k}}, N_e) a_J({\mathbf{k}}) \qquad \mathrm{and} \qquad
u_I^\dagger({\mathbf{k}}, N_e) = \psi_{I}^{\;\;J, *}({\mathbf{k}}, N_e) a_J^\dagger({\mathbf{k}}) ,
\end{equation}
where $N$ is the number of fields in the potential and $(\dagger)$ and $(*)$ represent Hermitian and complex conjugation, respectively.
Then one can write canonical commutation relations $ [ a_J({\mathbf{k}}), a^\dagger_I({\mathbf{k}}')] = (2\pi)^3 \delta_{IJ} \delta^{(3)}({\mathbf{k}} - {\mathbf{k}}')$. Finally the mode matrix $\psi_{IJ}$ evolves according to
\begin{equation}
\frac{\mathrm{d}^2 \psi_{IJ}}{\mathrm{d} N_e^2} + (1-\epsilon) \frac{\mathrm{d} \psi_{IJ}}{\mathrm{d} N_e} + \left(\frac{k^2}{a^2H^2} - 2 + \epsilon \right) \psi_{IJ} + C_{IL} \psi^{L}_{\; \, J} = 0 .
\label{eqn:psi}
\end{equation}
We set the Bunch-Davies initial conditions~\cite{Bunch1978} in Eq.~\eqref{eqn:psi} to get the perturbation spectrum. First, the time at which the pivot scale $k_*$ leaves the horizon, $N_*$ $e$-folds before the end of inflation, is found using the background equations~\eqref{eqn:back}. Then the times  $N_{e,\mathbf{k}}$ when other $\mathbf k$ modes leave the horizon are calculated.

The Bunch-Davies state~\cite{Salopek1989a} chooses field bases such that the $\psi_{IJ}$ are originally diagonal and sets the initial condition for Eq.~\eqref{eqn:psi} as if the mode matrix were freely oscillating in Minkowski space. It is to be noted that for a single field, mode evolution is ended when the mode is frozen out of the horizon. On the other hand, to include superhorizon evolution, modes for multifield models are evolved until the end of inflation~\cite{Price2015}.

\subsection{Power spectra}~\label{subsec:powerspectra}

In multifield models, contractions of the mass matrix  are required to obtain the power spectrum.
Using the canonical commutation relations above, the two-point VEV of the field perturbations yields the power spectrum
\begin{equation}
  P_{\delta \phi}^{IJ} (k) = \frac{k^3}{2\pi^2} \left[\frac{1}{a^2}\right] \psi^{I}_{\; L} \; \psi^{J L,*} \, .
  \label{eqn:power}
\end{equation}

To relate this field-space power spectrum to gauge-invariant perturbation variables~\cite{Bardeen1980,Bardeen1983,Nibbelink2002}, the curvature perturbation ${\cal R}$  is defined on comoving hypersurfaces by
\begin{equation}
  {\cal R} \equiv \Psi + \frac{1}{3} \nabla^2 E + aH \left( B + v \right) ,
  \label{eqn:rginvariant}
\end{equation}
where $E$ and $B$ are perturbations to the flat FLRW metric, and
$v$ is given in terms of the momentum density of the stress-energy tensor $T^{\mu}_{\; \; \nu}$ as
\begin{equation}
  T^{i}_{\; \, 0} \equiv \left( \bar \rho + \bar P \right) \delta^{ij} \frac{\partial v}{\partial x^j}  ,
  \label{eqn:XXX}
\end{equation}
where $\bar \rho$ and $\bar P$ are the background energy and pressure densities, respectively.
On evaluating Eq.~\eqref{eqn:rginvariant} on spatially-flat hypersurfaces during inflation, ${\cal R}$ reduces to
\begin{equation}
  {\cal R} = -\frac{H}{\dot \phi_0} \; \omega_I \delta \phi^I  ,
  \label{eqn:rptb}
\end{equation}
where $\omega_I \equiv \dot \phi_I/ \dot \phi_0$ is a basis vector that projects $\delta \phi_I$ along the direction of the classical background trajectory, given by the solutions to Eq.~\eqref{eqn:back}.  The vector $\vec \omega$ and a complementary set of $(N_f-1)$ mutually orthonormal basis vectors $\vec s_K$ form the kinematic basis, where the separation between the adiabatic perturbations in Eq.~\eqref{eqn:rptb} and transverse, isocurvature perturbations is made explicit.  Since $\vec \omega$ depends on the nonlinear background evolution, we find the $\vec s_K$ numerically by Gram--Schmidt orthogonalization.

The \emph{adiabatic curvature power spectrum} ${\mathcal P_\calR}$ is then the projection of ${\mathcal{P}_{\delta \phi}^{IJ}}$ along the field vector $\omega_I$, scaled by the pre-factor in Eq.~\eqref{eqn:rptb}, leaving
\begin{equation}
  {\mathcal P_\calR} (k) = \frac{1}{2 \epsilon} \omega_I  \omega_J {\mathcal{P}_{\delta \phi}^{IJ}}(k)  .
  \label{eqn:pad}
\end{equation}
The gauge-invariant scalar density spectrum in Eq.~\eqref{eqn:pad} is the final result for the adiabatic two-point function to first-order in perturbation theory.

To determine the scalar power spectrum at the end of inflation in hybrid inflation, it is common usage to restrict the dynamics to
the effective one-field potential along the valley $\psi=0$
\begin{equation} \label{eq:potenhybeffectif}
V_{\text eff}(\phi) =  \Lambda^4 \left[1+ \left( \frac{\phi}{\mu}
\right)^2\right],
\end{equation}
and to assume that inflation ends abruptly once the instability
point is reached. Under these hypotheses, the primordial
scalar power spectrum can be easily derived in the
slow-roll approximiation. It is nearly scale invariant,
with a spectral tilt
\begin{equation}
n_\mathrm{s} -1 \equiv \left.\frac{\dd{\mathcal P_\calR}}{\dd \ln k}\right|_{k=k_*} = - 2 \epsilon_{1*} -\epsilon_{2*}~.
\end{equation}
where a star means that the quantity is evaluated when
the pivot mode $k_*$
leaves the Hubble radius, that is when  $k_*=aH$.

\section{Numerical solutions}~\label{sec:numerics}

We stop integrating when  either (a) the orbit achieves more than 60 e-folds during inflation or (b) $\rho < \Lambda^4$ and the trajectory is trapped by the potential wells at $\{\psi,\phi\} = \{\pm M, 0 \}$.

Although there exist other types of trajectories such A, B, C and D as classified in \cite{Clesse2009}, we have focussed only on the B-type trajectory.

 \begin{figure}
 \resizebox{0.5\textwidth}{0.38\textwidth}{\includegraphics{figures/prk_10}}
 \resizebox{0.5\textwidth}{0.4\textwidth}{\includegraphics{figures/amm_prk}}
 \caption{\label{fig:prk-axion-monodromy} Oscillatory features in the power spectra. The spectrum of the hybrid potential (left) contains the drifting oscillatory features which are similar to that in the spectrum of axion  model (right).}
 \end{figure}

Setting $\Lambda = 0.1064 \, M_\mathrm{Pl}$, $M=0.1504  \, M_\mathrm{Pl}$, $\mu=3190.4  \, M_\mathrm{Pl}$, and $\nu=0.1265 \, M_\mathrm{Pl}$ in

 \begin{equation}
   \label{eqn:powerspect}
   A_s \approx \frac{1}{24\pi^2 M_\mathrm{Pl}^4} \left( \frac{V}{\epsilon_V} \right),
 \end{equation}
 %
 where $\epsilon_V = (M_\mathrm{Pl}^2/2)(V_{,\phi}/V)^2$ is the slow-roll parameter, and assuming perturbations are generated when $\psi \approx 0$ and $\phi \approx \phi_c$,  $ A_s$ turns out to be $ \approx 1.2\e{9} \, M_\mathrm{Pl}$.\footnote{Generally the amplitude $A_s$ of the dimensionless power spectrum $\mathcal{P}_\mathcal{R}$ is set to be roughly compatible with the WMAP9 data \cite{Benetti2011,Hinshaw2013}, which fixes the potential energy scale.}  Ref.~\cite{Martin2012} determined that quantum fluctuations dominate the classical field evolution in the inflationary valley when
 %
 \begin{equation}
   \label{eqn:lambdaquant}
   \Lambda > \Lambda_q \text{ where } \Lambda_q^2 \equiv 4 \pi \sqrt{3} M_\mathrm{Pl}^3 \frac{\phi_c}{\mu^2}.
 \end{equation}
 %
 Although, for our parameters $\Lambda_q \simeq 5.7\e{-4} \, M_\mathrm{Pl}$ \textit{i.e.} $\Lambda > \Lambda_q$, perturbations are generated outside the valley \textit{i.e.} when $ |\psi| \simeq 0.075 $. Therefore for the purpose of perturbation spectrum, we will assume that classical equations are self-consistent.

 \subsection{Oscillatory features}

Searching for oscillations is well-motivated, because a discovery would
 imply a very interesting additional structure in the primordial perturbations, and conversely
 a null result can constrain the parameter space in a useful way~\cite{Flauger2014}.
As is clear from Figure~\ref{fig:prk-axion-monodromy}, oscillatory features in ${\mathcal P_\calR}(k)$ for the hybrid inflation potential are qualitatively similar to those of the axion monodromy potential.

 \begin{figure}[!t]
  \resizebox{0.5\textwidth}{!}{\includegraphics{figures/prk_10}}
  \resizebox{0.5\textwidth}{!}{ \includegraphics{figures/pten_10}}
  \caption{\label{fig:k-dependent r}${\mathcal P_\calR}(k)$ versus ${\mathcal P_h}(k)$ in hybrid model. The tensor spectrum varies very little, whereas adiabatic ${\mathcal P_\calR}(k)$ contains oscillations, and thus rendering $r$ strongly $k$-dependent.}
  \end{figure}

 The inflaton potential in the axion monodromy model  motivated by power-law moduli stabilization  is given by
 \begin{equation}
 V(\phi)
 =\lambda\, \left[\phi+\alpha\,\cos\left(\frac{\phi}{\beta}+\delta\right)\right].
 \label{eqn:amm}
 \end{equation}
 Evidently, in this potential, while the parameters~$\alpha$ and
 $\beta$ describe the amplitude and the frequency of the superimposed
 oscillations, the parameter~$\delta$ shifts the oscillations within
 one period. Further the amplitude of the oscillation is fixed in the axion monodromy model and
 the inflaton oscillates as it rolls down this potential, and these
 oscillations persist all the way until the end of inflation~\cite{Hazra2013}.
 Oscillatory contributions to the scalar power spectrum  arise as a direct consequence of the underlying periodicity. However, the oscillatory features  have a model-dependent amplitude, and may be undetectably small: in particular, the amplitude is exponentially suppressed in regimes where the oscillations are generated by instanton
 effects~\cite{Flauger2010, Flauger2014}.

For the inflaton potential (\ref{eqn:amm}), using the same approximations as in \cite{Flauger2010}, the power spectrum can be fitted by a function of the form
 \begin{equation}\label{eq:Ppf}
 \Delta_\mathcal{R}^2(k)=\Delta_\mathcal{R}^2\left(\frac{k}{k_\star}\right)^{n_s-1}\left(1+\delta n_s e^{-C_0\left(\frac{\phi_k}{\phi_0}\right)^{p_\Lambda}}\cos\left[\frac{\phi_0}{f}\left(\frac{\phi_k}{\phi_0}\right)^{p_f+1}+\Delta\varphi\right]\right)\,,
 \end{equation}
 where the amplitude $\delta n_s$ and the phase $\Delta\varphi$ are calculable using the techniques in~\cite{Flauger2010}; $\phi_0$ is some fiducial value for the scalar field to be specified later; and $\phi_k$ represents the scalar field value at the time when the mode with comoving momentum $k$ exits the horizon~\cite{Flauger2014}. Along similar lines, a fitting function for the spectrum of the hybrid potential needs to be developed, which we will undertake in future work.
In Figure~\ref{fig:k-dependent r}, we observe that ${\mathcal P_\calR} (k)$  is highly oscillatory  whereas ${\mathcal P_h} (k)$  is featureless. It implies that tensor-to-scalar ratio $r$ for this model is strongly $k$-dependent.

   \begin{figure}[!t]
   \begin{center}
    \includegraphics{figures/Atype_zoom}

   \caption{\label{fig:A-type}Exact numerical  solution for A-type background trajectory. Respecive zooms in inset clearly show that $\psi$ is nearly stable at $\phi=\phi_{\text valley}\approx3.0464$, whereas $\psi$ oscillates in the narrow band of $\Delta \psi\approx10^14$. }
   \end{center}
   \end{figure}

\subsection{Numerical issues}

 There exists a numerical issue related to calcualting the power spectrum for the A-type trajectory~\cite{Clesse2009}. It is particularly tricky to numerically calculate the spectrum in this case as the oscillations along the $\psi$ direction continue in the narrow band of $\Delta \psi$, whereas  $\psi$ is nearly stable at $\phi=\phi_{\text valley}$ (3.0464 for our choice of parameters). See the zoom of A-type trajectory in Figure~\ref{fig:A-type}.

  \begin{figure*}[!t]
  \begin{center}
  \resizebox{0.45\textwidth}{!}{\includegraphics{figures/ps_10new}}
  \resizebox{0.45\textwidth}{!}{\includegraphics{figures/pdelpnad_10new}}
  \end{center}
  \caption{\footnotesize\label{fig:entropic_mode}  Entropic ${\mathcal P_\calS}(k)$ and non-adiabatic pressure ${\mathcal P_{\delta P, \mathrm{nad}}}$ spectra. Scaled ${\mathcal P_{\delta P, \mathrm{nad}}}$ is similar to  ${\mathcal P_\calR}$.}
  \end{figure*}

\section{Conclusion and discussion}~\label{sec:conclusion}
For the original hybrid inflation model and some of its extensions, Clesse~\cite{Clesse2014} found time evolution of ${\mathcal P_\calR}$ for only the pivot scale $k_*$. On the other hand, we have calculated the complete spectrum ${\mathcal P_\calR} (k)$ for the original hybrid model.
Unlike in the axion model there is no underlying periodicity in the hybrid potential, but the interaction term produces the same kind of oscillatory behaviour in inflaton evolution. Therefore some characterstic features in spectrum of the hybrid potential need to be looked for to distinguish between the axion and hybrid models. It would be interesting to observe how CMB anisotropy spectra will behave for this oscillatory power spectrum. Further it can be explored how the perturbation spectrum will appear if quantum fluctuations are taken into account. Also there exists a need to develop some other theoretical techniques to calculate ${\mathcal P_\calR} (k)$ for other initial conditions where numerical techniques are failing, such as in the case of A-type trajectory. We plan to examine these questions in future work.

\acknowledgments

One of the authors (RK) thanks Layn C. Price, Richard Easther, Sebastian Clesse and Dhiraj Kumar Hazra for many helpful communications.

\bibliographystyle{JHEP}

redpajama_set_name: RedPajamaArXiv


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