text:
// Generated by the protocol buffer compiler.  DO NOT EDIT!
// source: google/rpc/error_details.proto

package com.google.rpc;

public interface QuotaFailureOrBuilder extends
    // @@protoc_insertion_point(interface_extends:google.rpc.QuotaFailure)
    com.google.protobuf.MessageOrBuilder {

  /**
   *

   * Describes all quota violations.
   *

   *
   * repeated .google.rpc.QuotaFailure.Violation violations = 1;
   */
  java.util.List<com.google.rpc.QuotaFailure.Violation>
      getViolationsList();
  /**
   *

   * Describes all quota violations.
   *

   *
   * repeated .google.rpc.QuotaFailure.Violation violations = 1;
   */
  com.google.rpc.QuotaFailure.Violation getViolations(int index);
  /**
   *

   * Describes all quota violations.
   *

   *
   * repeated .google.rpc.QuotaFailure.Violation violations = 1;
   */
  int getViolationsCount();
  /**
   *

   * Describes all quota violations.
   *

   *
   * repeated .google.rpc.QuotaFailure.Violation violations = 1;
   */
  java.util.List<? extends com.google.rpc.QuotaFailure.ViolationOrBuilder>
      getViolationsOrBuilderList();
  /**
   *

   * Describes all quota violations.
   *

   *
   * repeated .google.rpc.QuotaFailure.Violation violations = 1;
   */
  com.google.rpc.QuotaFailure.ViolationOrBuilder getViolationsOrBuilder(
      int index);
}

redpajama_set_name: RedPajamaGithub


Starting my New Year off covering New Edition is not a bad start to 2017! The group gained major popularity in the 80's and continue to sell out concert worldwide. Now they've teamed up with BET to document it all in "The New Edition Story".
Bobby Brown, Luke James & producer Jesse Collins kicked off the nationwide fan screening tour. Lucky listeners tuned into partnered radio stations to win tickets to see a sneak preview of the 3-part, six hour series that airs January 24th, 25th & 26th.
I had a chance to chat with the cast & crew about The New Edition Story.
For more information on THE NEW EDITION STORY log on to BET.com and join the conversation on social media using the hashtag #NewEditionBET.


La Fête by Falz Afrimma Awards Best Male Artist For West Africa Falz the Bahd Guy blows in heavily on New Project labelled "La Fête" right after bagging an Endorsement Deal with Hennessy.
The "La Fête", Falz delivers the hook on French, La Fête was performed at the just concluded Afrimma Awards in Dallas, He premieres the fire tune along with Visuals today, The new tune was produced by Demsa & video shot by Clarence A Peters.
Download & Share "La Fête" by Falz Below, Drop your comments behind.


Ever thought of enhancing the beauty of your outdoor landscape? And at the same time reducing the maintenance of the same? With the right installation of hardscape and lighting, you can work on your already existing landscape design for the better. Or create a new landscape design altogether.
Why do we always look for the facilities and maintenance more than the beautification of anything and everything? Isn't it possible to achieve both? Yes, it is possible in case of landscapes – you can have the best mandatory landscape services without ignoring the ornamentation of the same. Los Angeles Hardscapes are there to help you enjoy and decorate your outdoor spaces throughout the year.
Hardscaping is the process of designing and installation of beautifying and utility features such as fireplaces, hot tub surrounds, water features, walkways, retaining walls, and more. Hardscapes change the entire outlook of the landscaping or the backyard design, improve drainage and bring out the best of the property. The additional outdoor lighting makes you utilize the space even in the evening and ensures safety as well.
Hardscape designs like patios, pergolas, arbors, pathways, benches, fire pits, and ponds are in much demand as they add to the beauty and entertainment of the outdoor living spaces. If you want to add on a wow-factor at low maintenance, go for a paver patio instead of the typical concrete patio. Walkways, pathways, stairways, and terraces are few of the other elements that help you utilize the maximum of your outdoor unit.
For an additional decoration, you may go for pergolas, sitting walls, benches, and water features that doubles up the style of the landscape. The best of all, add an outdoor fireplace to beat the chilly nights while enjoying the outdoor space to the fullest.
All these features would make you friends and family long for for your invitation for a get-together at your landscape soon.
Rainforest LA provides hardscape of the best quality. They would guide you through the requirement and what's suited for your landscape. They specialize in a broad range of LA hardscape styles and work with definite schematics, budget and timeline. If you want to opt for a revamped hardscape, contact http://rainforestla.com/ now.


text:
Book Review: America's Other Audubon
Reader Contribution by Christian Williams
Tags: Book Reviews, Illustration, Nature,
America's Other Audubon
By Joy M. Kiser
Published in 2012 and available through Princeton Architectural Press
For bird lovers, the exquisite paintings of John James Audubon's Birds of America stand not only as beautiful art, but as valuable references of ornithology from early America. Undoubtedly, Audubon's work has influenced countless artists and naturalists alike to produce their own memorable work or research, but perhaps none more so than the book produced by one ambitious young woman and her family.
It's unlikely you've heard of Genevieve Jones' Illustrations of the Nests and Eggs of Birds of Ohio, published in 1886. Limited to a print run of only 100, the book has only been known to natural history museum librarians and rare book collectors. But for one librarian, Joy M. Kiser, the few known details of its author and the circumstances surrounding the book's creation were tantalizing and demanded further research. Furthermore, it seemed to her that a book that rivals the beauty and scientific value of Audubon's work should be made more accessible to the public. The result is a story within a story—America's Other Audubon—which combines the original panels produced by Jones and her family with Kiser's own research into a tragic but inspiring family story.
Upon viewing Audubon's color plates in an exhibition at the 1876 World's Fair in Philadelphia, Jones was inspired to take his work a step further. Where Audubon focused on the beauty and characteristics of the birds themselves, Jones realized that no one had focused on the various nests and eggs of birds—information she recognized as being even more valuable in the pursuit of identification than Audubon's work. Having collected bird nests and eggs with her father since childhood, Jones realized it'd be up to her to create that reference book, and her family and friends enthusiastically supported the endeavor. An indicator of her incredible ambition, Jones' original plan was to illustrate the nests and eggs of all 320 known bird species in America at that time, but was talked down by her father to focus on a more reasonable goal of illustration the 130 known species of Ohio. Despite Jones' lack of formal art training, the initial paintings were met with an enthusiastic reception, and orders for the hand painted book exceeded expectations. Good fortune wasn't to last, though, as Jones succumbed to typhoid fever in 1879 at the age of 32, the book just barely begun. While most families would have grieved and moved on, Kiser's research revealed a family galvanized in the effort to see Genevieve's book completed. They grieved by continuing her work, enduring further setbacks and difficulties to finish the book seven years later.
Kiser's success in reprinting Illustrations of the Nests and Eggs of Birds of Ohio is reason enough to check out America's Other Audubon. Whether you're a bird lover or not, it's hard not to appreciate nature's beauty illustrated in the color plates. But Kiser's research puts the Jones' work in context, and makes the color panels that follow her account of the family's story even more beautiful and special. Altogether, it's a moving tribute to one woman's love for birds, and her family's love for her.
How to Find That Book You've Spent Years Looking For
Fish To Eat Always, Never, and Sometimes
Ten Things to Do When You're Feeling Hopeless
The Dark Side of Soy
Organic Body Care Recipes
When Technology Fails
Natural & Herbal Family Remedies E-Handbook
Vegan Lifestyle: The Seed
Taking a Stance on Food Waste
By the Way, Your House is On Fire
Back to the Kitchen: Escaping Processed Food
Hi, thanks for stopping by. Like to read more content, Join the Utne Community Today!

redpajama_set_name: RedPajamaCommonCrawl


175 15th St is a Multi-Family building located in Park Slope, Brooklyn constructed in 1925. This 4-story building has 8 units. The building is within Community District 306 and zoned for the following school - P.S. 124 Silas B. Dutcher. Nearby transportation include the D, F, G, N, R subway lines.


We at Backtime smelt this comeback coming even while #7 was still serving 2-to-3.
There was too much ability and too much game to count him out. His time as a guest of the federal government gave him pay his debt to society, and emerge like so many others, with a second chance...to play the game that he redefined.
And the other thing that nobody talks about - he didn't take a hit in 3 years. He's still only 30 years old with a football age of 27. And now we see a new piece to the Vicksaw puzzle: poise.
Not only has he become a pass-first Quarterback, but he's playing now with a serenity to go with his sizzle. And you can make the argument that he's playing with the type of speedy skill players that Donovan McNabb never had (the Eagles ironically take on McNabb and the Skins this weekend).
With LeSean McCoy, DeSean Jackson, and Jeremy Maclin to complement him, Vick doesn't have to do things on his own the way he did his early days in Atlanta (or McNabb throughout his career in Philly). Vick can trust the guys around him, and if he can trust himself, he may just have a season for the ages.
Just as we forecast over a year ago.
July 27, 2009 - The Trick for Vick: Gotta be like "Mike"


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Bǎotíng Li and Miao Autonomous County, (along the centre line), is one of six autonomous counties in Hainan and it's famous for having the most perfectly preserved primal tropic rain forest in all of China. It's an area of outstanding natural beauty that has yet to be discovered by western tourists. The old growth forest is one of the most biologically diverse areas in all of China and home to numerous species of plants and animals under state protection. Bǎotíng is an area steeped in ancient culture and traditions, from food & drink to music & dancing to clothing & lifestyle of the local people and it is first on our list of places not to miss in Hainan.
Yanoda Rainforest Tourism Zone, Baoting Li and Miao Autonomous County is 18 kilometers from Baoting along the Central Line and 35 kilometers from Sanya City. The government invested nearly RMB 4 billion in the park (45 square km) and Cultural Tourist Zone, the whole area of protected forest is 123 square km. In 2012, the Tourism Zone was rated a AAAAA-scenic spot. There's rock climbing, up the waterfall, (so expect to get wet), but in the tropical temperatures it's not a problem, there's a zip line which is quite high, but fun and there are tour packages to climb the mountain, again you're going to get wet, reports on the food are quite good. There's also a 5 star hotel with prices from $150 - 300 for standard rooms if you're looking for more than just a day trip.
At peak season it can get very, very busy so it's recommended to go during quieter periods, it is also quite commercial.
Hainan Bing Lang Valley Tourist Area and resort, founded in 1998, is a nature reserve that borders Sanya. Located a mere 26 kilometers from the city (Sanya) center, Bing Lang Valley is a massive area of over 5000 acres.
Historical records dating back 2000 years to the Han Dynasty mention the linen cloth made by Li women. With hundreds of patterns and designs all inspired from nature and their daily lives Li cloth is instantly recognisable and internationally acclaimed.
The majority of Li are fond of drinking Shanlan rice wine, which is a mild sweet homemade wine, they also brew sweet potato wine and cassava wine. They also like to chew betelnuts.
For centuries the tattoos of Li women were used to identify not only their tribe, family and social status but they also allowed them to be recognised by their ancestors after their death.
Hainan is not really equipped for family camping, there are no campsites as you would recognise them in Europe, with showers, hot water and in some cases even kitchens, although this is set to change in the very near future with a large campsite being built close to Sanya. This didn't stop us (or many others) however, having a fantastic week camping in Jian Feng Ling National Park in Ledong, along the centre of line of Hainan.


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text:
Schaer taking on gangs & social media
Assemblyman Gary Schaer (D-Passaic) will announce his plan to crack down on street gags at a news conference on Tuesday. Schaer is expected to unveil comprehensive legislation that will challenge a street gang's ability to recruit minors through social media...
Morris Freeholder faces GOP battle
January 19, 2018 12:06 am March 30, 2018 1:29 am
Morris County Freeholder John Cesaro is going to have a rough time winning a Republican primary this year, as some GOP leaders look to settle some deep grudges. Cesaro challenged Assemblywoman Betty Lou DeCroce (R-Parsippany) in the 2017 Republican primary. ...
Timberlake headed to Assembly
Sheila Oliver's successor in the State Assembly will be Britnee Timberlake, an Essex County Freeholder from East Orange. Passaic County Democrats signed off on her candidacy tonight, which means she'll likely be unopposed in a special election convention for the...
In show of force, Ramos runs
Councilman Anibal Ramos Jr. announced his re-election bid for a fourth term on the Newark City Council Thursday to a packed crowd at the Waterfront, a gleaming new recreation facility that he helped bring to fruition. Essex County Executive Joseph DiVincenzo, Sheriff...
Report: Gusciora may run for mayor
Assemblyman Reed Gusciora is mulling a bid for Mayor of Trenton this spring, if incumbent Eric Jackson declines to seek re-election. The Trentonian was the first to break this story. There has been speculation for weeks that Jackson doesn't want...
ELEC will push changes in campaign finance laws
The New Jersey Election Law Enforcement Commission wants to strengthen political party committees as a way of curbing the influence of spending in state elections. ELEC has proposed a series of changes to New Jersey campaign finance laws, including raising...
Independent spending topped parties by $30 million
The gubernatorial and legislative campaign committees spent $13.3 million in 2017, and independent groups spent an additional $45.4 million. "Party committees are now regularly out-gunned by independent groups during New Jersey's statewide elections," said Jeff Brindle, the Executive Director of...


This engaging role requires a senior software engineer with an architect's mindset, and an interest in client contact, to design, develop and deliver high end IoT / RTLS software solutions to advanced industries. These are "mission critical" systems for clients, non-trivial and tailored for their specific needs.
You will work with clients and your fellow developers to establish requirements and capabilities, and ultimately to deliver robust, tested solutions. The company you will join has a portfolio of specialised technology which will be at your disposal – this is not "run of the mill" CRM software, but high-tech systems used in cutting edge manufacturing and other such demanding applications. Whilst powerful, these solutions need significant tailoring to meet a client's exacting needs, and some applications may require significant bespoke work.
Your CV will show your strong technical degree and relevant career history. Commercial experience in C#, preferably with additional languages, and clear capability to work with heavily data-driven systems are all required. Oracle or other relational SQL database experience is also necessary, as is full existing permission to live and work in the UK without time limit, restriction or sponsorship.
Strong candidates will exhibit excellent written (as in your CV) and verbal communication skills. Evidence of ability to precisely describe complex scenarios, in a manner understandable to clients, is favoured. Work can be fast paced; a calm and critical thinking candidate can do well.
Expenses-paid travel is likely to be required within the UK and Western Europe for approximately 6-10 working days per month.


text:
1987 - Woody Pop: Shinjinrui no Block Kuzugi is released for the Sega Mark III in Japan.
1991 - Head Buster is released for the Game Gear in Japan.
1995 - Parasquad is launched in Japan for the Sega 32X.
1996 - The Sega Saturn receives Brain Battle Q, Doraemon: Nobita to Fukkatsu no Hoshi, FIFA Soccer 96, Fishing Koushien, Game no Tatsujin 2, GunGriffon: The Eurasian Conflict, Idol Mahjong Final Romance R, Linkle Liver Story, Mainichi Kawaru Quiz Bangumi Quiz 365, Street Fighter II Movie, Virtual Casino, World Advanced Daisenryaku: Sakusen File and Zork I: The Great Underground Empire in Japan. Encyclopédie des Codes Secrets is published in France.
1997 - Independence Day is released for the Saturn in North America, while Jissen Pachi-Slot Hisshouhou! 4 and J. League Victory Goal '97 launch for the console in Japan. GameWorks Seattle, the first ever GameWorks, opens to the public.
1998 - Burning Rangers is released for the Saturn in North America.
2001 - Battle Beaster and Le Mans 24 Hours are released for the Dreamcast in Japan.
2002 - Space Channel 5 is released for the PlayStation 2 in Europe. Doubutsu Pico: Hamster Land is released for the Japanese Pico.
2005 - Super Monkey Ball Deluxe and Worms Forts: Under Siege are released in North America.
2007 - Sonic and the Secret Rings launches for the Wii in Japan. Sega the Best re-releases of Guilty Gear XX Slash, Standard Daisenryaku: Dengekisen, Standard Daisenryaku: Ushinawareta Shouri and Tenka-bito arrive on Japanese PlayStation 2s, while the Platinum re-release of Chromehounds comes to the Xbox 360. Oshare Majo Love and Berry: 2007 Spring & Summer Song Collection is released in Japan.
2011 - Yakuza 4 is released in North America for the PlayStation 3, while Sega Genesis Classic Collection Gold Edition is released in that region for Windows PCs. Shogun 2: Total War debuts on Steam.
2012 - Yakuza: Dead Souls is released for the PlayStation 3 in Australia. The PlayStation Portable game Shining Blade and its pre-order bonus Shining Blade Haru no Shin Seikatsu Ouen Fan Disc are released in Japan, while Shining Force Cross Elysion debuts in Japanese arcades. The Mega Drive version of Strider is released for the Wii's Virtual Console service in Europe, while the Game Gear games Dragon Crystal, The GG Shinobi and Sonic the Hedgehog Triple Trouble are released for the Nintendo 3DS Virtual Console in North America.
2015 - Squads: Saikyou no Kizuna launches for Android devices in Japan.


The task from a client was complex: to unite in a single corporate style an updated positioning of gaming department + customize a solution for a by-product – embedded mini-games under the same name.
Having cast aside over two dozen options, the client's team settled upon an ambitious version of the world as a game cube with the slogan "Let's play the world!". Based on the given direction we designed a pool of required elements: an animated version, envelopes, business cards, dozens of printed documents, presentation, distribution and design for social networks.


text:
Isabela Moner Shares That Her Mom Has Cancer
Actress Isabela Moner opened her heart and revealed the bad news she recently received, ones that have tested her faith. The protagonist of the film Dora and the Lost City of Gold shared with her followers on social networks that her mother suffers from breast cancer.
In his networks, the 18-year-old is optimistic and sends a positive message to his followers.
"My mom did it!" She wrote, along with a photo of her mother in a hospital bed, from where she would be waging her battle against the disease. "I don't usually post about private matters, but I've never been so happy and wanted to share it."
Moner revealed that the day he found out about his mom's illness, everything that was happening in his life seemed insignificant to him - and facing his condition put her to the test.
"It could have put me off, I could have become a bitter person … but I have never felt so faithful," he said. "I am so happy that we managed to overcome it. Although I never had the doubt that she would make it. It is an ongoing battle, but I think she will be fine because she is the strongest human being I know."
The young woman appreciated the support she has received from her family and friends and assured that this experience left her with a lesson in love.
"I don't know why these things happen. So much love has come out of that and there is no way it can be more than a blessing,"he added. "Go and celebrate that you have another day with your loved ones."
Although she has shared family moments on her social networks, the actress had kept her mother's health condition a secret, whom she has classified as "the sweetest woman" in the world.
Mom Of 3 Learns She Has Breast Cancer After Doctors Dismiss Lump As 'Pregnancy Changes
Isabela Moner New JcPenney Clothing Collection
The young Peruvian is already in the big leagues in Hollywood
Eva Mendes Shares Her Beauty Secret After Being A Mom
Actress Eva Mendes reveals her favorite product from her brand Circa and shares her beauty secret after becoming a mother
MIchelle Obama Shares Her Mom's Grammy Messages
The former first lady exposed the messages that her mother sent her, claiming that she did not warn her about her performance in the Grammy awards
Chelsea Clinton Shares Her Routines As Mom Of Her Baby Charlot
Chelsea Clinton shares her routine as a mom with Elmo (VIDEO)


Copyright © 2015 Mauricio Tejo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We propose a stochastic nonlinear system to model the gating activity coupled with the membrane potential for a typical neuron. It distinguishes two different levels: a macroscopic one, for the membrane potential, and a mesoscopic one, for the gating process through the movement of its voltage sensors. Such a nonlinear system can be handled to form a Hodgkin-Huxley-like model, which links those two levels unlike the original deterministic Hodgkin-Huxley model which is positioned at a macroscopic scale only. Also, we show that an interacting particle system can be used to approximate our model, which is an approximation technique similar to the jump Markov processes, used to approximate the original Hodgkin-Huxley model.
In 1952, Hodgkin and Huxley proposed their famous model for the membrane potential dynamic of a typical neuron through observations made in the squid giant axon. Basically, the model is based on the mean behavior of the potassium () and sodium () ion channels, whose states (open/closed) are determined by a gating process acting inside those channels. The proposed system is 4-dimensional nonlinear equations, fully coupled through the membrane potential (or voltage) and the probability that a representative gate/ion channel of each species is open (see ). As it describes deterministically the general membrane potential through such a mean field approach, it might be indicated as a macroscopic process with respect to all the processes involved in the internal neuronal process.
In order to explain the internal fluctuations or its channel noise in a neuron (see ), stochastic versions of the original Hodgkin-Huxley model have been suggested. A bunch of them are based on taking into account the underlying stochasticity in the gating activity, by describing the open/closed processes as jump voltage-coupled Markov processes and by using empirical measures instead of probability measures of the corresponding open times (see [3–6]). In a certain way, such methods are consistent because when the number of channels or gates goes towards infinity the original deterministic Hodgkin-Huxley equations are recovered (see [5, 6]).
In this work, beyond considering the inherent stochasticity of such phenomena, we want to include a continuous dynamical model for the gating activity, because the discrete two-state (open/closed) point of view of its modeling is just an approximation of the corresponding metastable states of the continuous movement of the proteins involved.
The voltage sensors are proteins whose conformational positions are responsible for the states of the gating activity (see ). This internal process is known as the voltage-gated ion channel process. A continuous state space stochastic process seems to be suitable to describe the position of such proteins, and it is what we are going to propose. Due to the nature and scale on which we will tackle this, we say that the dynamics representing such voltage sensors are located at a mesoscopic scale or level. Thus, our proposed system will consider two different levels, the macroscopic and the mesoscopic one, which are fully coupled through a link voltage-dependent function. We will call our model Hodgkin-Huxley-like model, which will conserve the main structural characteristics of the original voltage equation. Thus, placing the gating phenomenon from a continuous point of view is basically the main motivation for conducting this work.
Our model is a stochastic nonlinear system, where its nonlinearity is due to the intervention of the probability law of the stochastic process in its dynamic (see [8–12]). In our case, such a probability will represent the probability that a representative voltage sensor of any species "pulls up" its corresponding gate, which is equivalent to the probability that the corresponding channel is open in the original or classical model.
The mathematical consistence of our proposal is evaluated by means of the approximation via a particle system, that is, a system with several interacting voltage sensors. It means that our model will meet with features similar to those of the original macroscopic case, with respect to the convergence of empirical measures to the corresponding probability law. In our case, this convergence property by using empirical measures from a stochastic particle system approximating our ideal system is known as propagation of chaos.
Specifically, our propagation of chaos result is as follows: consider the voltage equation depending on empirical measures instead of the probability that the (potassium, sodium) ion channels are in an open state, as in the original Hodgkin-Huxley equations. Suppose that those empirical measures depend on the behavior of certain continuous state space stochastic processes representing the interacting voltage sensors of typical (potassium, sodium) ion channels. Then, when the number of sensors (or channels) goes towards infinity, we will recover a Hodgkin-Huxley-like system which has two remarkable fully coupled components: the voltage equation depending on the probability laws of the corresponding voltage sensor positions (macroscopic part) and the stochastic equations for the position of those voltage sensors (mesoscopic part).
This result extends earlier ideas for the description of the ion channel dynamic: from a discrete space state of open/closed gates to a continuous state space of the position of the voltage sensors. Our extension makes the introduction of the propagation of chaos property necessary, which comes to replace the approximation via jump voltage-coupled Markov processes.
Another nice property of our model is the recurrence, which has a biological interpretation. Also, this work generalizes the ideas in .
In Section 2, an introduction of those stochastic nonlinear processes, our model, and its main features are set.
In Section 3, the connection of our model with the original Hodgkin-Huxley model is given, as well as its mathematical justification.
We are going to introduce some basic facts about a certain class of nonlinear stochastic differential equations which are useful to describe situations where individuals (particles, components of a system, etc.) are interacting with each other through a mean field force. Let be a continuous-time -valued stochastic process defined on some complete probability space satisfyingwhere is a -Brownian motion and . This kind of systems has been widely studied under different forms of and under extensions of the diffusion part (see, e.g., [8–12, 14]). As example, (1) is a special case of the nonlinear system considered in  and the existence and uniqueness of a solution of (1) are proved when (i.e., , where is the set of probability measures on satisfying , for ) and Lipschitz condition on (see Theorem 2.2 therein, which states the existence and uniqueness of a solution in law sense, although a stronger result is proved). That analysis is based on the contraction of the Wasserstein metric on , which is defined aswhere is the set of probability measures on such that the marginal law with respect to is and the marginal law with respect to is . The nice feature of this metric is that the metric space is complete and separable (see ). Here we say that (1) has a unique solution pathwise and in law, which for a usual Itô diffusion is analogous to saying that it has a unique strong solution.
The probability law of (1) follows a special parametrization of the McKean-Vlasov equation. This is a nonlinear equation whose general form is given bywhere is a measure on and is a test function with compact support and with derivatives of any order. In this case, it describes the Fokker-Planck equation for the temporal evolution of the law of (1) (also called Fokker-Planck McKean-Vlasov equation), where we have thatOther interesting examples arising in possibly singular cases of can be found in .
The law is considered to describe a mean field force. That is, two individuals from (1), and driven by independent and identically distributed (iid, for short) Brownian motions and , are "interacting" through its common law . But it is an ideal situation because, probabilistically, they are not interacting ( and are iid). It is a well-known fact that, under some conditions, we can approximate the law of (1) on bounded intervals of time by the interacting particle systemwhere the Brownian motions are iid. Here, the main result is as follows: for some fixed, if solves (1) driven by and , then uniformly on any finite time horizon (see, e.g., Theorem 2.3 in ). This property is known as propagation of chaos, term attributed to Kac ().
In this work and under the reference of the Hodgkin-Huxley model (), we are going to suggest that when the gating process in a typical potassium or sodium ion channel is seen as a continuous-space stochastic process describing the movement of a representative voltage sensor, the law of the opening times can be approximated via interacting particle systems as in (5). This comes to replace the classical view of the two-state jump voltage-coupled Markov process for the gating activity (see [3–6]). Due to the dimensional change, we say that the interacting particle system is located at a lower level than the general membrane potential. If the membrane potential is considered as a macroscopic process, which is natural since the voltage equation is describing the deterministic and general membrane potential through a mean field approach, the voltage sensor dynamic will be seen as a mesoscopic process (where for us, the ion dynamics are at microscopic scale).
To describe the coupled evolution of the membrane potential and the voltage-gated process through the position of the voltage sensors, we distinguish two different scales according to its nature: the first one follows a deterministic general dynamic (macroscopic), and the second one follows a stochastic local dynamic in a continuous state space (mesoscopic). The classical Hodgkin-Huxley equations explicitly describe the mean performance of the and channels depending on the voltage evolution. The paradigm is that each channel contains 4 gates, which can be in one of the two states: open or closed. A channel is in an open state (conductance) if all its gates are open. Otherwise, the channel is in a closed state (nonconductance).
Such gates and its corresponding voltage sensors are proteins and together they form the so-called voltage-gated process. A channel has its 4 gates of the same type and a channel has 3 of one type and 1 of another. Although all of this comes from the classical formulation of Hodgkin-Huxley model, as technology advances (see ), more precise descriptions about how those proteins operate have been given (see, e.g., ).
For our mathematical treatment, it is enough to consider only a simple system with 1 gate (voltage sensor) type (extension arises naturally as we will see later). A simple scheme for the states of an ion channel is depicted in Figure 1.
Figure 1: A simple schematic view of the parts forming a voltage-dependent ion channel (taken from ). So far, this is a way at which those proteins called voltage sensors apparently act to yield the gating mechanism (see ).
The voltage sensors are responsible of the opening/closing times of its associated gates, therefore, the conformational state of those sensors determines the channel state. The movement of a representative voltage sensor can be seen as a double-well potential diffusion, where one well represents the open state and the other represents the closed state (see Figure 2).
Figure 2: A symmetric double-well potential. The main idea is that one well is representing the open or "up" state of a typical voltage sensor and the other well is the closed or "down" state ("up" and "down" according to Figure 1). For our model, symmetry means the absence of a voltage-dependent force. Thus, this symmetry is broken (and possibly the existence of a double-well at all times) when an additive force is considered.
A typical symmetric double-well potential as in Figure 2 is given bywhere , is a Brownian motion, and . (Just for simplicity, we chose the double-well potential centered at zero where its minimum is located at .) To use this kind of process for the position of a voltage sensor, we need to add a continuous voltage-dependent force, say , where is the membrane potential or the voltage evolution. That function is the force responsible for the depth variation of the basins of : according to the values of , there are periods where the voltage sensor tends to open (or "to go up") and others where it tends to close (or "to go down"). For example, when takes positive values the depth of the basin of the right-hand side becomes deeper than the left-hand side one. Just the opposite occurs when takes negative values. Thus, the position of the voltage sensor will be described by the coupled process , where satisfiesNote that the new potential is now given by . It is a double-well potential if and only if .
To complete our model, we need to provide the dynamical behavior of . As the general voltage evolution of a neuron is usually modeled via a mean field approach of the gating activity, following the Hodgkin-Huxley paradigm we need to introduce the law of . Thus, our ideal complete system will be given bywhere is an appropriate function describing the voltage evolution. Here, (8) combines two processes at different levels: the membrane potential or general voltage at a macroscopic level and the voltage sensor dynamic at a mesoscopic level. The function plays the role of connecting those two scales. In the next section we are going to relate (8) with the Hodgkin-Huxley model in a more precise way.
Now, we are going to impose some assumptions to ensure the existence and uniqueness of a solution of (8). These are as follows.(A.1) and , where is the set of bounded probability measures.(A.2) is a Lipschitz function on with constant .(A.3) is a Lipschitz function where there exists such thatBefore showing that, under (A.1)–(A.3), (8) has a unique solution pathwise and in law, we are going to show that (8) can be written as in (1).
Let , where is the matrix/vector transposition. Consider the following applications:By denoting and , we have that (8) can be written aswhere and then .
The function is locally Lipschitz since is locally Lipschitz. Thus, the usual globally Lipschitz assumption for the existence and uniqueness of a solution of (11) is not satisfied. Nevertheless, we can use a stopping argument to ensure that. First, consider, for any , , where by (A.3) it is clear that and . Then, (7) is equivalent toTherefore, , where each interval limit solveswith and where the Brownian motions involved are indistinguishable from each other. The last two processes are well defined, as is shown in the following proposition.
Proposition 1. Let , , and . Let be a real-valued stochastic process defined on some complete probability space and assume that it is given bywhere , is a Brownian motion, and . Then, there exists a unique strong solution for the above equation with second moment, , for any .
Clearly, the processes can be identified with a special case of (14).
Proof. The drift part is locally Lipschitz because is polynomial. Then, by  (Chapter 2, Theorem 3.5), it is enough to show thatfor some .
We haveTaking we obtain the result.
Comment 1. In  (Chapter 2, Theorem 3.5) a stopping procedure based on a special growth condition, as the one displayed in the preceding proof, is used in order to demonstrate the existence and uniqueness of a strong solution. Nevertheless, we are going to use additionally another stopping argument which arises from condition (A.1) and regularity, which is property defined below and part of the recurrence property.
Recurrence of (14) is an interesting feature from a biological standpoint. It means that the process representing the voltage sensor is always operating, unless the heat transference between the cell and its environment or reservoir is lost ( in (11)).
Definition 2. Let be a continuous-time real-valued stochastic process. Denote . For any integer , consider the sets and define the following increasing sequence of stopping times:and its limit . (i)A process is said to be regular if, for all , (ii)Let , where is the Borel algebra on . A process is said to be recurrent relative to (-recurrence) if it is regular and for every , where is the first exit time from starting at .
A process is said to be recurrent if it is recurrent relative to any segment containing the origin.
Comment 2. This last definition has been inspired from .
Before showing the recurrence of (14), note that the Fokker-Planck equation associated with the law of such a stochastic differential equation is given bywhose stationary probability measure is equal towhere . By continuity, it will imply that the expected proportion of time that spends in each well (if ) can be bounded by the stationary probability that and spend in those wells.
Proof. Note that the corresponding generator is given byConsider the functionIt is easily seen that and when . To conclude, we recall Lemma 3.9 from .
Lemma 4. Suppose that a process almost surely exits from each bounded domain in a finite time. Then a sufficient condition for -recurrence is that there exists a nonnegative function in the domain such thatThe existence comes from Proposition 1. Thus, the function satisfies the assumptions of the previous lemma for every segment containing the origin, and hence, proposition holds.
Mathematically speaking, one of the consequences of recurrence is that the solution of the corresponding system does not explode or escape towards infinity: if we define, for any and , , then . Indeed, if not, there exists such that . Thus, the event has a positive probability, which contradicts regularity of . Another consequence is that the corresponding solution is almost surely always visiting the segments containing the origin, which within our biological setting will imply that the voltage sensor described by (7) will never be stuck in one of the wells of . That is, the states "up" and "down" will always be visited, which is one of the characteristics of the two-state gating approach.
Theorem 5. Under (A.1)–(A.3) system (8) (or (11)) has a unique solution pathwise and in law.
For convenience, we are going to use both notations (8) and (11).
Proof. Consider the processes and :By (A.1), there exists such that . For any , define and . Let . By assuming and , consider and . Then, according to Theorem 2.2 in  (or Theorem 1.1 in ), there exists a unique solution pathwise and in law to the equation:since by (A.2) and (A.3) on the set is bounded Lipschitz. But it is almost surely bounded Lipschitz on any finite time horizon, since regularity of and implies that, for any , . Thus, theorem holds.
It can be easily verified that the voltage sensor represented by (7) is also recurrent since it is continuous and is in between two recurrent processes (called above ).
From a macroscopic perspective, we can find that in some situations it is possible to justify the presence of different time scales involved in a membrane potential/gating model, as in the Hodgkin-Huxley model (see, e.g., ) and in the FitzHugh-Nagumo model (see ). What could happen is that works faster than since they are positioned at different levels. In such a case, we may homogenize time scales.
Consider a small parameter, say (), which acts in the following way:where , and under the time-change we getwhere . Dependence of on is due to time acting in the second moment of the Brownian motion. If we might expect that , and then, under the standpoint of the faster dynamic , is near to being a constant ( varies slowly, to be more precise). Thus, this could tempt us to regard (7) as an equation of the form of (14) by freezing the activity of at some point .
Following this idea, let be a solution of (14) with , that is, by considering that the double-well structure holds. Replace therein by and consider . The corresponding deterministic solution (i.e., when ) has three fixed points: , where and are stable points and is an unstable point. Define the quasi-potentials:Consider the basins of attraction and , and let and be the first exit times from and , respectively. If , then for any we haveif , andif . This is a result from  (Chapter 4, Theorem 4.2) in which the authors used large deviations to argue the classical Kramers' time for the expected time between transitions from one well to another in the small noise limit. It was also applied within the neuroscience context in the mentioned work  for the FitzHugh-Nagumo model, using a similar procedure but having a different time scale perspective.
In this remark we wanted to point out that when different time scales are involved, approximated methods can be used to obtain some interesting results, which can be difficult to obtain when such different time scales are not present or their existence cannot be justified. Indeed, more detailed results can be obtained for our model under this situation, but it would mean moving away from the main aims of this work.
The original Hodgkin-Huxley model (1952) describes the membrane potential or voltage under the following scheme:where is the membrane capacitance and (A) represents the external stimulus which will be seen here as a given parameter; () represents the maximum conductance; and , , and are the Nernst potassium, sodium, and leak equilibrium potentials. The leakage current is an Ohmic current representing mostly the chloride () one. Processes , , and represent the corresponding probability that a representative gate is in an open state. As we mentioned before, in the case of potassium channels 4 gates are of the same type () and in the case of sodium channels there are 3 gates of the same type () and 1 of another type () (do not be confused with the function defined in (7)). The probability that a typical potassium and sodium ion channel is open is given by and , respectively, where the iid assumption for the behavior of each corresponding gate is adopted. The explicit values for the transition rates , as well as the typical values for the involved constants can be found in .
The master equations for , , and also suggest that each gate works according to the following transitional scheme:that is, a two-state jump voltage-coupled Markov regime. Because of independence between ionic species and according to the mathematical treatment that we want to do, it is enough to consider the law of one gate of any type and a generic function . Such a reduction is given bywith . System (34) together with the stochastic regime of the gating transitional scheme described above forms a particular example of a piecewise deterministic Markov process (PDMP), which corresponds to a general class of nondiffusion stochastic models introduced by  in 1984. Its construction can be easily described as follows (see [6, 25] for a further development of such a regime in this context). For all , let be the solution of the voltage equation (34) at time starting at . Let be the first time that the gate gets closed and let be the first time after that the gate opens. Then,where in this case . Analogously, let be the first time after that the gate gets closed. Then,where now and so on. All this leads us to the conclusion that the classical Hodgkin-Huxley model, together with its corresponding gating regimes, can be clearly identified with a PDMP.
(a) is a continuous function such that for any the equationis linear, and, for any , is polynomial in .
We can identify such properties with those of the Hodgkin-Huxley model, where its generalization to three gate types (i.e., , , and types) is straightforward: Just consider instead of , where . We are going to identify those characteristics with our macroscopic/mesoscopic approach and show that, despite the scale reduction for the gating activity, it conserves a similar structure for the voltage equation as in the classical Hodgkin-Huxley model.
Let be an increasing Lipschitz function and consider , such that is continuous and, for any , is linear in and polynomial in . Define the stochastic process by . Following the mean field approach of the Hodgkin-Huxley process, as , we can define , where clearly satisfies (a). So, from now on, assume that, for all , . Call this last assumption Assumption (A.2′).
With all those ingredients, we say that our system (8) satisfies a Hodgkin-Huxley-like model. Here, represents a cumulative distribution function such that is the probability that a typical voltage sensor is in the open or "up" state (thus, it plays the role of in the macroscopic case (34)). As example, we have the Laplace cumulative distribution function:where . As is increasing, it can be convenient to think that the open or "up" state is located at the right-hand side of the potential , that is, . Note that our proposal enlarges the state space of the dynamic of the gating activity: from a discrete two-state space dynamic to a continuous real state space dynamic. So, it is such enlargement which causes a change in the reference level: from the macroscopic 0-1 gating dynamic to the mesoscopic scale reduction regarding the continuous movement of the voltage sensor.
Comment 3. In  we suggested the function , which arises as a limit point of the degenerated case in the previous Laplace cumulative distribution function. So, this work extends the mentioned one by considering a class of smooth functions for picturing the probability that a typical voltage sensor is in the open or "up" state.
As we mentioned in Section 2.3, processes (8) and (34) are in an ideal situation due to the determinism of and the absence of probabilistic interaction among all the voltage sensors. The more realistic situation is when (8) and (34) are just limiting cases, which is the topic that comes next.
To be realistic, we cannot ignore the inherent stochasticity of the voltage evolution. With respect to (34), some authors have proposed to use an empirical stochastic measure instead of ([3–6], among others). The basic idea is to consider a stochastic sequence , with representing the state of the th gate: 1 if the gate is open and 0 if not. Hence, if we take into account gates, we can replace by . Thus, system (34) is replaced bywith , where the expression is defined between jumps of . Specifically, forms a sequence of jump voltage-coupled Markov process, characterized by (i)its state space ,(ii)its intensity ,(iii)its jump law (see ).
In [5, 6] the convergence uniformly on any bounded time horizon, where satisfies (34), is proved under smoothness and Lipschitz conditions on , , and , the boundedness of on any finite time horizon and the uniformly boundedness of in , on any finite time horizon. Thus, stochastic hybrid system (39) forms a PDMP where the jumps of go to zero when , thereby raising the paradigm that the Hodgkin-Huxley equations arise as a limit of infinity gates.
Further results were also obtained in . For example, a Central Limit Theorem for was provided, which allows us to justify mathematically the following diffusion approximation:where is a Brownian motion.
In  we proposed the following voltage dynamic, in the ideal case:where is a the voltage sensor dynamic and represents the "open region." The problem is that it allows just the function as integrand in the mean field approach, trying to emulate the classical 0-1 gating process, which can be recovered by a degenerate limit of a suitable smooth function (see the previous comment). Thus, in this work a variety of smooth functions can be considered as integrand in the mean field approach in order to describe the probability of the open gate state, or the "up" voltage sensor state. Also, the smoothness of sets our model in a more familiar structure, as pictured in (11), with respect to the nonlinear stochastic differential equations as (1).
Under this nonideal setting, in  a propagation of chaos result was proposed, but just locally in time. In this work, we can develop a propagation of chaos result in a very classical way (see, e.g., Theorem 1.4 in  and Theorem 2.3 in ) due to the smoothness of , although an additional step is needed in order to overcome the problem that our drift part is locally Lipschitz and not globally, as assumed in the above references (see Theorem 7 below).
For our model, systems as (5) arise in order to approximate nonlinear equations as (11). Thus, our paradigm is that we can recover a Hodgkin-Huxley-like model when propagation of chaos holds. That is the main difference between the setting of PDMPs approximating the classical Hodgkin-Huxley equations and the proposed setting of an interacting particle system approximating a Hodgkin-Huxley-like, as defined by us in the previous subsection: propagation of chaos is the tool that we have to use in order to show consistency.
So, consider gates and let be a stochastic sequence where each element satisfieswhere the Brownian motions are iid. Here, each represents the voltage sensor associated with the th gate being dependent on each other through the interaction function . Thus, propagation of chaos will ensure us that the voltage sensors become independent of each other, implying that all its gates become independent of each other as in the macroscopic case. Note that our approximating system is in and the ideal system is in . That is because in the limit of infinity gates it is sufficient to consider only one representative ideal gate (voltage sensor) to describe the law . Before setting this fact, we have to show that our approximating system is well posed.
Theorem 6. Under (A.1)–(A.3) and (A.2′) system (43) has a unique strong solution with second moment.
Proof. In this proof we are going to proceed similarly as in Proposition 1 because our definition of recurrence was set for one dimension only.
Let , where . We have . Consider the application:where is representing the drift part of (43).
By (A.2), (A.3) and due to being polynomial, is locally Lipschitz, and then, again by Theorem 3.5 in  it is enough to show thatfor some positive .
We haveOn one hand, by (A.3) and as a straightforward generalization of the proof of Proposition 1, we getOn the other hand, consider . Thenby (A.2) and (A.2′); there exist , , and , such that . Define and .
Then we getDefining we obtainLet . Thenwhere we have used . By Jensen's inequality we obtainFinally, putting all together we getThe result holds by taking .
To show our propagation of chaos result, for convenience, instead of (43) we are going to considerwhere and . Thus, we will show the convergence of (54) towards (11).
Theorem 7. For any fixed , let be a component from (54) and assume that solves (11), with , where they are driven by indistinguishable Brownian motions. Then, under (A.1)–(A.3) and (A.2′)on any finite time horizon , when goes to infinity.
Comment 4. Actually, (A.2′) is not used here. It was set only by formalism due to Theorem 6.
Proof. Assume for now that is Lipschitz of constant . Then,by Jensen's inequality. Using Lipschitz property of and we getNow, consider an iid sequence such that each element solves (11) where and are driven by indistinguishable Brownian motions and . ThenLet . By taking expectations we obtainNote that , because are iid. Hence, . On the other hand, have the same distribution and hence using again , . ThereforeLet and consider, for any , , which satisfiesand using Gronwall's inequality we obtainThus, , which proves the theorem but under the assumption that is Lipschitz. Since is locally Lipschitz, is locally Lipschitz as well, and the above inequality holds just locally in time (i.e., stopped by means of a suitable stopping time with respect to ), where the constant (and then ) will depend on the bound at which the process is stopped. To show that for any finite time horizon there exists a finite constant such that the above inequality still holds (almost surely) in our case, we are going to proceed under a similar stopping method to that used in the proof of Theorem 5.
Consider the processes:As there exists such that , for any , define , , and . Thus, we have thatfor , where whenever . But regularity of and implies that is finite almost surely. Therefore, for any there exists a finite constant , almost surely, such that the following inequality holds:Hence, the proof is finished.
This last result gives us the consistency result. So, we can set a Hodgkin-Huxley-like model, which preserves similar characteristics and properties as in the macroscopic case (see Section 3.1). It should be noted that we could theoretically recover some macroscopic features from the mesoscopic system. From (43), using the preceding theorem and Doob's inequality we obtainon any finite time horizon . That is, the macroscopic link can be estimated by observing the mesoscopic situation.
We saw that it is possible to obtain similar equations to those of Hodgkin-Huxley equations through a stochastic nonlinear system, which links two different levels: the macroscopic one, represented by the membrane potential, and the mesoscopic one, represented by the gating process through the movement of its voltage sensors. The advantage of our model in the mathematical description is that it precisely includes such a second level in the neuronal modeling, giving a more accurate description of the gating process in the sense that the state space of the position of a voltage sensor enlarges the earlier two-state descriptions. As an analogy, these two states in the gating activity correspond to the two metastable states of our proposed stochastic continuous voltage sensor model.
Also, in our continuous state space model, the recurrence property of the dynamic of the voltage sensors is in agreement with the biological mechanism of those proteins, because there is no absorbent state: gates pass from one metastate to the other (open/closed or "up"/"down" for voltage sensors) recurrently.
In this biological context, propagation of chaos plays the role of approximating a Hodgkin-Huxley-like model, as the PDMPs do for the classical Hodgkin-Huxley equations. This means that an interacting particle system is a nice way to include a process in a lower level than the macroscopic one, preserving similar characteristics and properties to those within the macroscopic setting.
The author was supported by FONDECYT 3140613 postdoctorate grant and kindly acknowledges the partial support by Instituto de Ecología y Biodiversidad (IEB), Departamento de Ecología at Pontificia Universidad Católica de Chile, Grant PIA-CONICYT ACT 1112 "Stochastic Analysis Research Network," and VRI-PUC Grant "Biostochastic Program." The author's thanks go to Professor Etienne Tanré (INRIA, Sophia-Antipolis), Professor Rolando Rebolledo (Centro de Análisis Estocástico, Pontificia Universidad Católica de Chile), Professor Michèle Thieullen (Laboratoire de Probabilités et Modeles Aléatoires, Université Pierre et Marie Curie, Paris 6), and Professor Pablo Marquet (Departamento de Ecología, Pontificia Universidad Católica de Chile) for their valuable advice.
M. Kac, "Foundation of kinetic theory," in Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability, vol. 3, pp. 171–197, Berkeley, Calif, USA, 1956.


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Trevor Williams (born Trevor Leslie Williams; 19 January 1945) is a bass guitarist, vocalist and lyricist known primarily for his work with Audience, British art rock band which ran from 1969 to 1972 and from 2004 -2013.

Williams was born in Hereford, Herefordshire. Beginning his musical career on lead guitar and accordion, he switched to bass in 1964, playing in numerous line-ups and backing chart artistes of the day such as Vince Taylor and Bert Weedon before joining soul band Lloyd Alexander Real Estate, which contained, or was associated with, the future members of Audience.  When Audience folded, Williams went on to play sessions for numerous artistes, also joining The Nashville Teens and Jonathan Kelly's Outside before retiring from the music business in 1975 to pursue interests in animal welfare, ultimately founding The Fox Project, a wildlife charity.

Williams reformed Audience in 2004 with other co-founders Howard Werth and Keith Gemmell, plus new drummer John Fisher, who died in 2008 and was subsequently replaced by Simon Jeffrey.  Audience finally folded in 2013 due to Gemmell's declining health and Williams' reluctance to continue with substitute musicians.

In 2009, Williams joined Blue Pulse, releasing, in May 2012, an album entitled Trams, largely featuring his own material.  The band has also served as backing band for vintage UK rock star, Terry Dene.

External links
Interview on The Marquee Club
Interview with Progsheet
Overview and Discography on AllMusic

1945 births
Living people
People from Hereford
English rock bass guitarists
Male bass guitarists

redpajama_set_name: RedPajamaWikipedia


A lot of things have happened over the past few weeks since the last TY Thursday and since I have a Halloween midterm, I thought I would tell you whats been going on!
If you don't live in Ireland you may not have heard of this story. In 2013, Donal Walsh, a 16 year old wrote a letter to the editor in the Irish Independent talking about how pointless it was for young people to kill themselves when they have their whole lives ahead of them but he didn't have this luxury as he had terminal cancer. He than started talking out about it and also his life with cancer.
His father Fionnbar Walsh came to talk to 6th years and TYs about his son and the charity Donal Walsh Live Life Foundation. It was very interesting but really sad as I remember when RTÉ had made a documentary about Donal and I cried through parts of it. His message was live your life and if you need help, get help.
In Ireland, you have to be 16 before you can do your theory test, so I did it last Saturday and I PASSED!!!! I was so happy as I thought I had failed it (you have to have at least 35/40 questions right to pass). The only thing is I'll have to wait until next April (that's when I turn 17) to get my learners permit but I don't really mind as I'm really busy doing other things but I'm nearly on the way there!
This was a 7km obstacle course through a forest and a bog and is supposed to be a team building sort of thing. I really enjoy things like this as there are various obstacles you have to go over, under, through and around. I would not recommend jumping into a bog hole as I did that and I got stuck and had to be dragged out of it by 2 guys in my year. The only thing that wasn't the best was that you got absolutely covered in muck and trying to wash that off (ugh!) especially when it gets in your hair but all and all it was so enjoyable and I would definitely do it again!
My school were holding a business expo and they asked TY mini companies to take a table or two at the school stall. I decided to do it and I'm so glad I did as it was a great learning experience and I got a few orders for what I am selling. I'll go into more detail at the end of this post. A dew teachers were even at the expo with their kids which was weird as personally you think teachers are teachers and not parents. The day was kinda long (11am-3pm) but I knew everyone on the school stand.
Also, I was fortunate to win hamper from Oriflame Sweden. I'm going to do a first impressions/ review on all the products I got in on 14th November (as I still haven't tried everything out yet).
I have finished my work experience with a local graphic design and printers company. I really enjoyed it and I was kinda sad to be leaving the last time as all the people they were so kind to me and nothing was a problem also I got to try out tasks that graphic designers actually do. Even if I don't go down this road in the future I think it will help me when I'm designing posters, projects etc. as I learned about the importance of not putting things too close to the edge. I think it will also help since I will be one of the editors of the yearbook (that company actually prints the yearbook) and I got to create a logo and business card for my mini company!
Every year since the school I go to has been open, the day before we finish up for Halloween everyone (well nearly everyone) dress up, including the teachers. It is that one day of the year where everyone goes slightly mad and comes in, in character. There are also prizes for the best costumes, somebody dressed up as Joy from Inside Out, my friend Isabelle dressed up as a Starbucks cup and someone even dressed up as one of the teachers! I decided to dress up as a CSI agent and went sneaking around the school for mot of the day. It was an easy costume as my dad has an old CSI jumper he got and then I wore jeans and boots, I had a gun and a warrant as well just to add more realism to the outfit.
This year for TY students, we have to have a profolio with everything that we have done this year in it. So far mine is jam packed with stuff like evaluation sheets (I have to do one of them up on anything that is done, I hate them!), work experience diary, print outs from work experience, samples from different subjects and ticket stubs. I think I may have to upgrade to a bigger folder as I have my one half full already.
This is a mock up of my art portrait.
KCK Creations business card and sample of business card.
All I can say is I'm busy, busy, busy!


2.0, 3.5, 4.0... What Does it Mean?
You'll often hear pickleball players describe themselves with a number. These numbers indicate a player's current skill level, and are based on the International Federation of Pickleball's (IFP) rating system. Ratings are on a scale of 1.0 to 5.0, with half point increments. If you plan on playing in tournaments, you will need to assess your rating so that you can enter the appropriate bracket.
Ratings are self-assigned, until you've played in enough tournaments then USAPA will start calculating your rating for you based on your wins and losses. You can start by asking other experienced players around you what they think your rating should be. Use the links below to learn about the rating system and determine which rating describes you best.
Occasionally you may have the opportunity to be professionally rated. A ratings clinic is where, for a fee, a ratings expert will run you through various games and drills in order to assess your skill level. Keep an eye out for rating clinics that may be happening locally at venues listed on our Places to Play page.


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'The Voice' Stars Have Literally Grown Up Before Our Eyes [Pictures]
Frederick M. Brown / Ethan Miller, Getty Images
Eight years (and counting) made a huge difference for many of the most popular stars of The Voice. Blake Shelton looks noticeably different, but so do some of country music's most memorable performers.
Winners like Cassadee Pope and Danielle Bradbery wore baby faces when they auditioned during their respective seasons. The same can be said for Morgan Wallen, a forgotten castmember from the show who's transformed more than anyone else on this list of The Voice stars then and now.
Since premiering in April 2011, NBC's hit reality show has featured dozens, if not hundreds, of singers but these are the faces we still see today, including the first cast of judges and host Carson Daly.
Daly and Shelton are the only two to make all 17 seasons of the show (Season 17 ran in Sept. 2019), but Adam Levine — who was much skinnier in 2011 — and Christina Aguilera — who was much sassier — were familiar faces throughout most of the show's early run. Also find a baby-faced RaeLynn and a very Euro version of the Swon Brothers.
See The Voice Stars, Then and Now:
Who is your all-time favorite country singer from The Voice? The show has produced several big winners, including Craig Wayne Boyd and Sundance Head. Hit songwriter Nicolle Galyon was also an early contestant on the show — in fact, she's arguably the most successful contestant to date.
Here Are the 10 Most Successful Country Singers from The Voice:
Source: 'The Voice' Stars Have Literally Grown Up Before Our Eyes [Pictures]
Filed Under: blake shelton, cassadee pope, danielle bradbery, raelynn, the voice


Asociación de Amigos del Órgano de Palencia | Fundada en 1992, la Asociación de Amigos del Órgano de Palencia tiene como principal objetivo estudiar, investigar y divulgar la música de órgano en cualquiera de sus aspectos.
The Asociación de Amigos del Órgano de Palencia was founded in 1992, its main goal being the study, the research and the information about organ music in all its aspects. That is why this association felt the need for organising and providing formative activities addressed to organists and scholars, who could also experience the magnificent historic organs from Palencia, everything supported by prestigious professors.
San Hipólito el Real Organ Church – Támara de Campos.
And this is how the 1st Academia de Órgano Fray Joseph de Echevarria took place in the summer 1997. Its name pays homage to the celebrated Basque organ builder, who conceived the organ of Palencia cathedral, so representative for the Castilian "organería" in past times.
The Academia is financially supported by the Excelentísima Diputación Provincial de Palencia and they both cooperate in the organization of the International Music Festival of Palencia with regards to organs. They also provide the participation of national and international important artists as well as the maintenance of the historic organs where recitals are given.
This association also wants to thank those who have generously contributed with their effort and encouragement to recover the heritage of the organ building and its music. Special thanks to the first members who started the Academia and to the priests who open the gates of their churches so generously year after year.
Órgano de la Iglesia de San Hipólito el Real – Támara de Campos.


text:
Q: Regular expression for name with spaces allowed in between the text and avoid spaces when there is no text Hello I'm trying to write a regular expression for user name in my form.
The regular expression should allow spaces and . when the text is written
Ex : S. Harish Kumar
Check the regEx that I have written so far
^[a-zA-Z\s\.]*$

The above regEx also accepts any string with just spaces and . which I don't want.  Can you help me with the perfect regEx which doesn't accept spaces and . when no text is entered?
Thanks in advance :)

A: Just disallow a string that only consists of whitespaces/dots:
^(?![\s.]+$)[a-zA-Z\s.]*$
 ^^^^^^^^^^^

See the regex demo.
The (?![\s.]+$) is a negative lookahead that fails the match if the whole string contains whitespace or dot chars only.

A: You could use ^[a-zA-Z].*[\s\.]*$

*

*^[a-zA-Z] asserts string starts with a char (a-zA-Z)

*.*[\s\.]*$ followed by any char dot and spaces included

See following example:

var regex = /^[a-zA-Z].*[\s\.]*$/g;

function check(par){
  console.log(par.value + " match: " + regex.test(par.value));
}
Name <input type="text" id="test" value="" onchange="javascript:check(this)">

A: I would say a name is a sequence of alphabetic chars delimited by spaces or dots, which can be defined by the following regex:
^[a-zA-Z]+(?:[\s.]+[a-zA-Z]+)*$

Demo: https://regex101.com/r/rH5jtc/2

redpajama_set_name: RedPajamaStackExchange


text:
Poll: With What Family Would You LEAST Like to Spend the Holidays?
Vote here Thanksgiving, Christmas, Milad un Nabi, Chanukah, Kwanzaa: Whatever you celebrate, spending holidays with families that sometimes drive you crazy is universal. With which of these families would you least like to celebrate the holidays? Vote in Part 2 of Poll here Vote in Part 3 here Commiserate here
Poll by: rubyfruit76
Created Nov 27 2014
Jane Fonda, Jason Bateman, Connie Britton, Rose Byrne, Tina Fey, Corey Stoll, Kathryn Hahn, and Adam Driver in This Is Where I Leave You (2014)
The Altmans
The Squid and the Whale (2005)
The Berkmans
Debra Winger, Anne Hathaway, and Rosemarie DeWitt in Rachel Getting Married (2008)
The Buchmans
"Parenthood" Cast
The Buckmans (from Parenthood, 1989)
Rob Reiner, Sally Struthers, Carroll O'Connor, and Jean Stapleton in All in the Family (1971)
The Bunkers
The Burnhams (in American Beauty, 1999)
Robert De Niro, Dustin Hoffman, Barbra Streisand, Blythe Danner, Teri Polo, and Ben Stiller in Meet the Fockers (2004)
The Byrnes / Focker Family
Buddy Ebsen, Max Baer Jr., Donna Douglas, and Irene Ryan in The Beverly Hillbillies (1962)
The Clampetts
The Corleones
Death at a Funeral (2007)
Daniel's Family
Louise Fletcher, Kristy Swanson, Jeb Stuart Adams, Ben Ryan Ganger, and Lindsay Parker in Flowers in the Attic (1987)
The Dollangangers
Gwyneth Paltrow, Jill Clayburgh, Brian Cox, and Evan Rachel Wood in Running with Scissors (2006)
The Finch and Burroughs Families
Lauren Ambrose, Freddy Rodríguez, Frances Conroy, Rachel Griffiths, Michael C. Hall, Richard Jenkins, Peter Krause, and Mathew St. Patrick in Six Feet Under (2001)
The Fishers
Setsuko Hara, Kyôko Kagawa, Shirô Ôsaka, Chishû Ryû, Haruko Sugimura, and Sô Yamamura in Tokyo Story (1953)
The Hirayamas
Kevin Kline and Joan Allen in The Ice Storm (1997)
The Hoods (and Carvers) (from The Ice Storm, 1997)
Alan Arkin, Toni Collette, Greg Kinnear, Steve Carell, Paul Dano, and Abigail Breslin in Little Miss Sunshine (2006)
The Hoovers
Timothy Hutton and Mary Tyler Moore in Ordinary People (1980)
The Jarretts
Philip Seymour Hoffman and Lara Flynn Boyle in Happiness (1998)
The Jordan / Maplewood Clan
The Larsons
Kirsten Dunst, A.J. Cook, Hanna Hall, Leslie Hayman, and Chelse Swain in The Virgin Suicides (1999)
The Lisbons
Crimes of the Heart (1986)
The Magraths
Beau Bridges, Will Arnett, Margo Martindale, Jayma Mays, Nelson Franklin, and Lulu Wilson in The Millers (2013)
Julie Benz, Michael C. Hall, C.S. Lee, David Zayas, Jennifer Carpenter, and Lauren Valez in Dexter (2006)
The Morgans
Yvonne De Carlo, Fred Gwynne, Al Lewis, Butch Patrick, and Pat Priest in The Munsters (1964)
Parker Posey, Tori Spelling, Freddie Prinze Jr., and Josh Hamilton in The House of Yes (1997)
The Pascal Family
Sofía Vergara, Julie Bowen, Ty Burrell, Jesse Tyler Ferguson, Sarah Hyland, Ed O'Neill, Eric Stonestreet, Ariel Winter, Nolan Gould, Rico Rodriguez, Aubrey Anderson-Emmons, and Jeremy Maguire in Modern Family (2009)
The Pritchett / Dunphy Family
The Sawyer Family
Danny Glover, Gene Hackman, Gwyneth Paltrow, Anjelica Huston, Ben Stiller, Luke Wilson, Jonah Meyerson, Kumar Pallana, and Grant Rosenmeyer in The Royal Tenenbaums (2001)
The Tenenbaums
Ewan McGregor, Julia Roberts, Juliette Lewis, Dermot Mulroney, Meryl Streep, Chris Cooper, and Margo Martindale in August: Osage County (2013)
The Weston / Aiken Family
See results without voting


text:
Headline, Health, OPINION, Politics
Trump's actions against the WHO put U.S. national security, public health at risk
May 1, 2020 4:28 pm by Frank F. Islam
The last thing that Trump should do in the middle of a planetary pandemic is to threaten to deprive the WHO of the funding that it needs to be the first line of defense.
Follow @ambazaarmag
On April 25, a bevy of world leaders met virtually to discuss the development and production of vaccines and other critical tools to combat Covid-19. Global leaders who participated in the event, hosted by French President Emmanuel Macron, among others, included the heads of state of Spain, South Africa, Germany, Vietnam, and Costa Rica,
Representatives of one nation were conspicuous by their absence. The United States – the country that's been ravaged most by the pandemic, accounting for nearly a third of all the confirmed global Covid-19 cases and more than a fourth of the total fatalities worldwide – did not participate.
The United States wasn't at the event because one of the co-hosts was the World Health Organization (WHO). Other co-hosts, in addition to Macron, were the President of the European Commission and the Bill & Melinda Gates Foundation.
Unfortunately, the WHO, which is responsible for monitoring global public health and overseeing pandemic responses, is the latest multilateral entity to be in President Donald Trump's purgatory. The president announced on April 15 that he was halting funding for the UN agency for 60 days, pending an investigation into the organization's handling of the coronavirus pandemic. The United States is the WHO's largest funder contributing $400 million last year.
Trump's action will impact not only WHO. It will also have an effect on the U.S. scientists and doctors working round the clock to develop vaccines to slow down Covid-19. Their heroic efforts will be hamstrung by Trump's decision to halt funding for WHO, which is a UN agency.
RELATED: American Bazaar's Covid-19 coverage
For more than seven decades, this UN agency has led humanity's fight against epidemics and pandemics. It successfully coordinated the global fight against a number of diseases ranging from smallpox and polio to HIV/AIDS, Ebola and malaria. It has also helped contain many deadly diseases from entering the U.S. mainland. Among the many important roles WHO performs is preparing countries for health emergencies and when such emergencies occur, detect and respond to them.
At a time when the United States is losing, on an average, more than 2,000 Americans a day to the Coronavirus, squeezing an organization that is spearheading the fight against the disease and to not be a part of the process to speed up and deploy vaccines to tackle the deadly virus is reckless. It puts U.S. public health and national security at additional unnecessary risk.
As of April 28, the number of Americans tested positive for Coronavirus crossed 1 million and U.S. fatalities topped 57,000. Soon, the total the American lives lost to Covid-19 will outnumber total U.S. deaths in the Vietnam War: 58,209. The United States lost more men and women in only three wars: The Civil War and the two World Wars.
This is an enormous human cost. The Coronavirus should teach America and other nations around the world two cardinal lessons.
First, that public health is a vital part of national security. A pathogen originating in a distant corner of earth can destroy economies and ravage communities. Second, we were and are ill-prepared to tackle a pandemic like the coronavirus.
On October 24, 2019, roughly two months before the coronavirus began its deadly dance in the central Chinese city of Wuhan, three highly regarded organizations released a Global Health Security Index (GHSI or index) in Washington, DC, ranking countries based on their preparedness to face a pandemic.
Read more columns by Frank F. Islam
The index, a joint project of the Nuclear Threat Initiative, the Johns Hopkins Center for Health Security and the Economist Intelligence Unit, all highly reputable organizations, examined the health security capabilities of 195 countries worldwide. These groups issued a stern warning pointing out there are "severe weaknesses in countries abilities to prevent, detect, and respond to significant disease outbreaks" and stating unequivocally "health security is fundamentally weak around the world, and no country is fully prepared to handle an epidemic or pandemic."
The United States ranked first on the GHSI with an overall value of 83.5. It fell short, however, in some critical indicator areas including: access to health care where it ranked 175 out of 195, socio-economic resilience with a ranking of 59; and exercising response plans with a ranking of 54.
The deficiencies in these areas, in conjunction with the lack of presidential and federal leadership, help to explain why the U.S. has stumbled in responding to the Covid-19 onslaught. Now nearly 120 days into the onslaught of the pandemic, no country in the world has suffered from the disease worse than the United States.
Trump's temporary suspension of WHO funding indicates that the president is more interested in scoring political points and running for re-election than serving U.S. national interests and the larger public health.
This should not be the case. The last thing that the United States should do in the middle of a planetary pandemic is to threaten to deprive the WHO of the funding that it needs to be the first line of defense and the world's go-to resource for combating this pandemic.
This should not be a time for the United States to go AWOL. This should be a time for the U.S. to stand and deliver. It should be a time for the U.S. to commit additional support to WHO and the countries that have been the hardest hit by the pandemic. It should be a time for the U.S. to resume its status as a global leader and to serve as a role model by joining with and uniting the nations of the world to win the Covid-19 war.
Author: Frank F. IslamFrank F. Islam is an entrepreneur, civic leader, and thought leader based in Washington, DC. An author of two books, he is a contributor for the American Bazaar, as well as several publications in the United States and India. His website is www.frankislam.com.


Well taken class notes can be a great resource when it comes to reviewing and preparing for an exam. To ensure your child is taking useful notes, encourage them to use the following techniques.
Even if your child takes clear and concise notes, if their handwriting is not legible their notes will not be useful. While their notes don't have be written down in perfect handwriting, your child should at least be able to decipher what it is they wrote. If you notice your child struggles to read their notes at home, have them complete extra handwriting practice or remind them to slow down as they jot down their notes.
When taking notes in class, it's important that your child understands that they don't have to write down every single thing the teacher says or every single word that appears in a presentation. They should focus on important items and ideas that get the idea across. To help hem accomplish this, they should learn to read cues during a lecture. For example, if their teacher writes a few things on the board, these are likely important items that should be noted. Similarly, if the teacher stops to discuss a point in more detail, it is likely that this is an important point that should be noted.
Keeping notes organised and clearly divided will help when it comes time to study. Encourage your child to label their notes with the date they were written down and a heading that defines the topic discussed. Using dividers in between notes regarding different items will also help keep things sorted. Using resources like bullet point and numbered lists will also help keep things organized and in order.
If your child can use some extra help developing better study habits, The Tutoring Center, Powder Springs GA can help. Contact The Tutoring Center, Powder Springs GA at (770)222-7133 to find out more about the academic programs they offer or to schedule your free consultation.


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text:
Don't Wake Me Up Jonas Blue feat. Why Don't We
TV & Film Home
The Kissing Booth
Sabrina The Teenage Witch: What Do The Original Cast Look Like Now?
25 October 2018, 13:09 | Updated: 25 October 2018, 14:23
What do the cast of Sabrina the Teenage Witch look like now? Picture: Getty
The Chilling Adventures of Sabrina is coming but the original Sabrina the Teenage Witch first aired in 1996 – so what do the cast look like now, in 2018?
Prepare to feel old - Sabrina the Teenage Witch first aired in 1996; 22 years ago. It hurts, doesn't it?
So, before The Chilling Adventures of Sabrina airs on Netflix, we wanted to see exactly what the original cast of Sabrina the Teenage Witch are up to now.
> Want Tickets To Capital's Jingle Bell Ball Before Anyone Else? Download Our App Now To Access Pre-Sale!
Melissa Joan Hart
If you don't remember Melissa Joan Hart as Sabrina the Teenage Witch, did you even have a childhood at all?
Melissa first earned the role of Sabrina in 1996, but has since gone on to appear in several films, as well as Dancing with the Stars and now stars in her own sitcom, Melissa & Joey.
She is also married to a musician, called Mark Wilkerson, and together they have three sons.
Sabrina Spellman will be played by young actress Kiernan Shipka in the new Netflix series.
A post shared by Melissa Joan Hart (@melissajoanhart) on May 18, 2018 at 6:01am PDT
Caroline began her career as a stand-up comedian, performing alongside the likes of Chris Rock and Louis C.K., before landing her role as Hilda Spellman, Sabrina's impulsive aunt.
She is now known as the voice of Linda Flynn-Fletcher on Disney Channel's Phineas and Ferb, and regularly appears on Hollywood Squares, alongside her friend Whoopi Goldberg.
A post shared by Caroline Rhea (@carolinerhea4real) on Nov 8, 2017 at 6:09pm PST
You may remember Beth Broderick as Sabrina's other aunt, Zelda, but did you know she also starred as Diane Janssen in Lost, and as Rose Twitchell in Under the Dome.
Not only is she an actress, but Beth also directed three episodes of Sabrina the Teenage Witch; 'Guilty!', 'Cloud Ten' and 'Making the Grade'.
A post shared by Beth Broderick (@bethabroderick) on Aug 28, 2017 at 3:49pm PDT
Nate Richert
Nate played Sabrina's on-off boyfriend, Harvey Kinkle, for seven years on the show, and has had four smaller TV roles since.
A post shared by Nate Richert (@nate.richert) on Sep 10, 2018 at 12:30pm PDT
Jenna Leigh Green
Jenna Leigh Green played Libby Chessler, Sabrina's arch-enemy in Sabrina the Teenage Witch, but she is actually a well-known name on Broadway.
Her theatre experience includes The Wizard of Oz, Romeo and Juliet and West Side Story. She became a cast member of Wicked, playing the role of Elphaba over 40 times.
A post shared by jennaleighgreen (@jennaleighgreen) on Aug 6, 2018 at 9:01am PDT
While Paul Feig only appeared as Mr Pool, Sabrina's favourite teacher, for one season, you may recognise him as the director of Bridesmaids. No. Really.
He went on to direct huge Hollywood movies, such as Spy and the Ghostbusters reboot, as well as episodes of Parks and Recreation, 30 Rock and The Office.
A post shared by Paul Feig (@paulfeig) on Sep 18, 2018 at 3:48am PDT
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Visit Maui's newest luau, held every Wednesday at the Ka'anapali Beach Club. Experience Momi 'O Ka Pakipika, Hawaii – the pearl of the Pacific – through the music and story of Huaka'i, Journey Through Polynesia.
Huaka'i Luau invites you to experience the culture of the Polynesian islands brought to life through musical entertainment, dances and traditional luau-style food.
**Menu is subject to change without notice.
Gluten Free - Anything on the menu with a **. There are several Gluten Free options.
Please note, in the event of inclement weather, the luau will be moved to an indoors venue.


Chelsea have offered £10m for Benfica's Brazilian defender David Luiz. Manchester City and Real Madrid are also interested in the 23-year-old.
Newcastle have made a surprise move to sign Bolton left-back Jlloyd Samuel as they look to strengthen their side for the Premier League next season.
Newcastle manager Chris Hughton is set to make a £1m bid for Algeria goalkeeper Rais M'Bolhi.
Brazil striker Robinho, whose loan agreement between Manchester City and Santos ends in August, will be told on Wednesday he can leave the Eastlands club.
Birmingham manager Alex McLeish has ruled himself out of the running to sign Rangers striker Kris Boyd and Celtic winger Aiden McGeady.
Birmingham and Fulham are both interested in Ivory Coast midfielder Cheik Tiote.
South Africa striker Katlego Mphela is wanted by Birmingham.
Tottenham winger Giovani dos Santos is a target for Italian side Genoa.
Everton are eyeing up a £5m deal for Italy Under-21 defender Angelo Ogbonna, who plays for Torino.
Blackpool are set to pull out of a permanent move for striker Stephen Dobbie, who has been on loan from Swansea, as they are not happy with the £500,000 asking price.
Fulham will turn to former Manchester City manager Sven-Goran Eriksson if boss Roy Hodgson leaves for Liverpool or England.
Former Celtic boss Tony Mowbray and ex Wales midfielder Gary Speed are in line for the vacant manager's job at Hull. The club have cooled their interest in former Portsmouth manager Paul Hart.
Stoke are chasing NEC Nijmegen left-back Youssef El Akchaoui.
QPR have pulled out of a deal for Crystal Palace winger Darren Ambrose.
Middlesbrough look set to win the race to sign Scunthorpe striker Gary Hooper for around £2.5million.
Manchester City are after Palermo midfielder Edinson Cavani, who is rated in the £20million bracket.
Billy Sharp is on his way to Burnley in a £1million deal.
Barcelona are determined to sign Fernando Torres from Liverpool but say they will not pay more than £38m for the Spain striker.
Liverpool managing director Christian Purslow says no players will be allowed to leave Anfield until a new manager is appointed and gives the go-ahead.
Serbia striker Milan Jovanovic has hinted that he might pull out of his move to Liverpool and follow former Reds boss Rafael Benitez to Inter Milan. Jovanovic, whose contract with Standard Liege ended this summer, signed a pre-contract deal with the Anfield club in February.
Heard a rumour? There's no secrets amongst friends so tell us in the comment box.


We spend hundreds of pounds on feeding the fish but seem to neglect our own feeding requirements!
The ridgemonkey sandwich toaster completely changes that. My own cooking on the bank has changed hugely. This toaster has seen me through the Winter time which has been invaluable. Particularly during those long periods when you are not catching. I've not yet figured out why these are called deep fill sandwich toasters as they are so much more versatile than that!
HERE ARE SOME RIDGEMONKEY SANDWICH TOASTER RECIPE IDEAS AND YOU WILL SEE WHAT I MEAN.
The ridgemonkey sandwich toaster is light and easy to store in your tackle bag. It comes in three variations and there is also a utensil set available. The deep fill sandwich toaster is nonstick so cooks everything from a toasty to a fried egg. It can be used as a frying pan, a normal pan and can even be treated as a small oven when the lids are closed. This opens up options which include Pasties, pizzas and even bread and butter pudding. Another feature I particularly enjoy is the ability to drain fluid quickly. If you open up the lids very slightly of the ridgemonkey toaster any fluid inside, such as water or oil, can easily be drained away. The ridgemonkey toaster is also extremely easy to clean, a quick wipe with a damp cloth piece of kitchen towel does the job.
This was the first release from ridgemonkey. It is broadly the same size as a slice of bread. This making it perfect for toasties. It can also handle a slice of bacon, sausage and an egg so easily provides a full English for one!
Then came the ridgemonkey XL sandwich toaster which significantly stepped up the ability to pretty much cook up whatever takes your fancy. I have tried spaghetti Bolognese, chilli and rice, Thai curry, roast dinners and good old steak and chips. All of which have turned out very well and well worth the extra ingredients in your cool bag. This has the same nonstick coating as the original ridgemonkey sandwich toaster. It has to be said that the nonstick coating is very good. I have dry fried an egg without any issues. So the opportunity to have fried eggs on the without having to take a bottle of oil fishing is a welcomed one!
The newest model on the market, which is slightly bigger than an original and XL ridgemonkey, has some special features which provide an upgrade as well assome new features too. New features include the ability to take the two sides apart which effectively gives you the use of 2 pans. Beyond this, the most obvious change is that one side has been split into four sections. This now gives you the option to keep your liquid-based food separate from other foods while you are cooking. The perfect example would be your full English breakfast. Your bacon and sausages in one section, with egg, baked beans and mushrooms having their own section. This ensures the flavours of your food stay separate and you don't end up with soggy food! Another improvement on this model is the removable handle which makes storage even easier than before.
All the ridge monkey toasters have an amazing nonstick surface. As a result, you need to ensure you use the right utensils when cooking to make sure you don't scratch the nonstick off. Ridgemonkey has thought of everything and has produced this ridgemonkey utensil set. It includes a spoon, a spoon with the drainer, a flat spatula, and a forked spatula. Specially designed to be stored inside the ridge monkey toaster (when cool!) the utensils are made from a heat resistant nylon which will withstand all you can ask of them. There are two sizes available one for the original ridgemonkey and the other for the deep full extra large.
Buying a deep filled sandwich toaster now is better than ever. I'm not sure whether it's a limited offer but you can currently get a choice of colours between silver and black and you also get a free utensil set with every purchase.
Using a ridgemonkey sandwich toaster on the bank has completely changed my fishing experience and I can highly recommend this product. It is one product you will never regret buying.