text:
anche conosciuto come Cronache della guerra di Lodoss, è un universo fantasy ideato dallo scrittore giapponese Ryō Mizuno e composto di romanzi, manga, serie animate e videogiochi.

 Il racconto fu pubblicato sulla rivista giapponese per computer Comptiq dal 1986.

Questa tipologia di messa in prosa dei diari di gioco venne ribattezzata replay (simili alle light novel) e precedette i romanzi che lo stesso Mizuno scrisse per la casa editrice Kadokawa Shoten a partire dal 1988.

In Italia l'universo della guerra di Lodoss è conosciuto in particolare per la prima serie animata (OAV) del 1990.

Origini
Record of Lodoss War è stata creata nel 1986 dal Group SNE come serie di "replay" basato su alcune partite di Dungeons & Dragons e serializzati nella rivista giapponese Comptiq. I "replay" non sono dei racconti ma delle semplici trascrizioni di alcune sessioni di un gioco di ruolo. I "replay" hanno dimostrato di essere molto apprezzati anche da coloro che non hanno mai preso parte ad un gioco di ruolo, ma sono fan delle fiction fantasy. Simili alle light novel, molti personaggi e molte storie di questi "replay" sono diventati così popolari da ispirare intorno a loro un vero e proprio franchise.

La popolarità dei replay di Record of Lodoss War fu tale, da indurre il dungeon master Ryō Mizuno a realizzare alcuni romanzi a partire dal 1988, che rappresentano fra i primi esempi di letteratura fantasy di stampo occidentale realizzati in Giappone.

Quando la serie di replay legati a Lodoss War divenne una trilogia, il Group SNE decise di staccarsi dalle regole di Dungeons & Dragons a cui era stato legato sino a quel momento, e creò il proprio gioco di ruolo intitolato Record of Lodoss War Companion, e pubblicato nel 1989. Tutti e tre i volumi dei replay furono eventualmente ripubblicati dalla Kadokawa Shoten dal 1989 al 1991:

L'ultimo volume del racconto di Mizuno fu pubblicato dalla Kadokawa Shoten nel 1993, e fu seguito da due raccolte di brevi storie nel 1995:

Il primo volume rappresenta le basi per i primi otto episodi della serie OVA Record of Lodoss War, oltre che per la serie manga Record of Lodoss War: The Grey Witch . Il secondo volume fu anche adattato in un manga ed in quattro CD radio drama. Gli ultimi cinque episodi della serie OVA sono vagamente ispirati alla storia raccontata dal terzo e dal quarto volume e, essendo arrivati al punto in cui all'epoca era giunta la pubblicazione, hanno un finale originale realizzato appositamente per concludere la serie. La serie televisiva Record of Lodoss War: Chronicles of the Heroic Knight è invece un adattamento fedele dei volumi che vanno dal terzo al settimo. La prima collezione di racconti brevi pubblicati con il titolo High Elf Forest: Deedlit Story sono invece serviti come base per il manga Record of Lodoss War: Deedlit's Tale.

Successivamente Mizuno riprese in mano la storia e scrisse una nuova serie di romanzi: un prequel intitolato   (dal 1994 al 2002) ed un sequel intitolato  (dal 1998 al 2006), il primo dei quali è stato adattato nella serie manga Record of Lodoss War: The Lady of Pharis.

Trama

Cronologia
La cronologia qui di seguito riguarda gli eventi occorsi originariamente nella serie di Record of Lodoss War, derivata quindi dai vari replays e dai manga. Il passaggio del tempo è misurato in NCR (Nuovo calendario reale), usato nel continente di Alecrast.
NCR ?
Gli stregoni di Kastuul scacciano i giganti di fuoco. Lo stregone Azzard fa un patto con Jinn e Ifrit e questi diventano divinità guardiane confinate in un'urna sacra. Le ostilità tra Vento e Fiamme ha inizio.
NCR 0
Il regno magico di Kastuul decade. Il governatore Saluvan impone agli antichi draghi la guardia ai tesori. Karla, conosciuta come La Strega Grigia, confina la sua esistenza all'interno di un cerchietto e dopo la sua morte si perdono le sue tracce.
NCR 50
Naneel, la regina dei morti, comincia a manipolare le genti di Lodoss da Alania.
NCR 100-200
Sorgono diverse città-stato come Kannon, Raiden, Roid, Rood, Adan, Marnie, Loran, Highland, Harken, Persei e Saluvad.
NCR 101
Il re Kadomos sconfigge Naneel e inaugura la monarchia di Alania. Viene effettuata una spedizione a Marmo, ma dopo che Kadomos viene ucciso le forze in viaggio ritornano ad Alania.
NCR 221
Inaugurato il regno di Elvec e le sue forze prendono possesso di Venon e Adan.
NCR 229
Elvec continua l'espansione e si unisce a Rood, Marnie e Loran. Venti anni dopo questi stati chiedono l'indipendenza da Elvec e si trasformano nel regno sacro di Valis.
NCR 259
I draghi di Lodoss stipulano un contratto con cui stabiliscono di non interferire con la politica e le persone dell'isola di Lodoss.
NCR 313
Nasce l'accademia dei saggi.
NCR 473
Neese libera Bramd dall'incantesimo di Saluvan. Re Bruuk di Skard libera il dio demonio che attacca alcuni regni. Centinaia di cavalieri ed eroi si uniscono per liberare i regni. Mycen viene liberato dall'incantesimo. Lo specchio della verità viene rubato da Karla, la strega grigia.
NCR 474
Il demone viene sconfitto da sette eroi: Fahn, Beld, Neese, Fleve, Wort, Karla e Flaus (vedi Record of Lodoss War - The Lady of Pharis)
NCR 496
Fahn diventa il re di Valis.
NCR 497
Beld annuncia l'unione del regno di Marmo, diventando l'imperatore oscuro.
NCR 500
In Alecrast, Kashue viene arrestato e diventa un gladiatore schiavo. Tre anni dopo guadagna la libertà e viaggia verso Lodoss come mercenario. Un anno dopo libera Jinn dall'urna sacra in cui era rinchiuso e diventa re di Flaim.
NCR 509
L'accademia dei saggi viene distrutta da Wagnard.
NCR 510
(la storia narrata negli OAV inizia qui) L'elfa Deedlit viaggia nel mondo umano. Parn, Etoh, Slayn e Ghim si uniscono (e successivamente anche l'elfa). Nella guerra degli eroi muoiono Beld e Fahn. Parn e Ghim combattono Karla. Leylia viene liberata, ma Ghim muore.
NCR 512
Haven viene distrutta. Deedlit libera Jinn. Nasce la piccola Neese.
NCR 514
(l'anime La saga dei cavalieri inizia qui) Narse e Shooting Star si risvegliano dall'ibernazione.
NCR 515
Kashue e Ashram uniscono le forze contro Shooting Star e duellano per lo scettro del dominio. Orson viene ucciso. Reona diventa re di Kannon e fonda l'armata libera di Kannon.
NCR 520
L'incantesimo della foresta del non ritorno viene annullato.
NCR 524
Neese muore.
NCR 525
La guerra per il risveglio della distruttrice inizia. Gli elfi oscuri rubano gli artefatti per il risveglio. Una guerra santa viene indetta contro Marmo e infine il regno viene sconfitto. Karla viene battuta e distrutta per sempre. Wagnard resuscita Naneel, l'avatar di Kardis la distruttrice, e diventa re dei morti. Ma viene sconfitto dalla stessa Marpha attraverso la piccola Neese. Kardis viene quindi fermata. Ashram e Pirotess partono per un nuovo mondo.

Personaggi

Le light novel (e gli anime ed i manga da esse derivati) Record of Lodoss War ruotano intorno alle avventure di un giovane chiamato Parn, figlio di un cavaliere disonorato. Ciò che spinge le sue azioni in parte è proprio il desiderio di scoprire cosa accadde a suo padre, e conseguentemente ripristinate l'onore della propria famiglia. A dispetto della sua inesperienza, Parn è considerato un leader, e viene accompagnato nelle sue avventure dal fedele amico di infanzia Etoh, dal suo consigliere ed amico Slayn, e dal suo mentore Ghim. Nel corso della storia si unisce al gruppo l'elfa Deedlit, di cui si innamorerà Parn. Nel corso della vicenda il gruppo di eroi dovrà affrontare numerosi avversari e si vedrà spesso aiutato da alcuni nuovi alleati.

Adattamenti
Segue l'elenco delle opere legate all'universo della guerra di Lodoss.

Anime
 1990 , serie OAV di tredici episodi.
 1998 , serie televisiva di ventisette episodi.
 1998 , film umoristico in tre parti.

Anime correlati
 1995 , serie di tre OAV ed un film, incentrati su Ashram e Pirotess.
 2001 , serie ambientata nel mondo di Lodoss War.

Manga

 , manga di Yoshihiko Ochi in tre volumi.
 , manga in due volumi.
 , manga di Akihiro Yamada in due volumi.
 , manga di Masato Natsumoto in sei volumi.
 , manga umoristico in tre volumi.
 , shojo manga di Setsuko Yoneyama in due volumi

Videogiochi

 Record of Lodoss War (Nec PC 9800, MSX) 1988
 Record of Lodoss War - Fuku Zinduke (Sharp X68000) 1991
 Record of Lodoss War - Haiiro No Majio (X68000/PC Engine) 1991/1992
 Record of Lodoss War 2 - Goshiki No Maryu (X68000/PC Engine) 1992/1994
 Record of Lodoss War (Sega Mega-CD) 1994
 Record of Lodoss War (SNES) 1995
 Record of Lodoss War: Eiyuu Kishiden (Game Boy Color) 1998
 Record of Lodoss War: Advent of Cardice (Dreamcast) 2000
 Record of Lodoss War: Successor of the Legend (Browser-based TCG) 2012
 Record of Lodoss War Online (PC MMORPG) 2017-2019†
 Record of Lodoss War: Deedlit in Wonder Labyrinth (Steam) 2021

Colonne sonore

Record of Lodoss War: Original Soundtrack 1 (VICL-00051)
Record of Lodoss War: Original Soundtrack 2 (VICL-00114)
Record of Lodoss War: Original Soundtrack 3 (VICL-00267)
Record of Lodoss War: Minstrels' Memory of Lodoss (VICL-8090)
Arrange Sound From Record of Lodoss War ~The Gray Witch~ (VDR-28071)
Symphonic House from Record of Lodoss War II Arrange Sound (VICL-8060)
Record of Lodoss War TV: Maaya Sakamoto - Kiseki No Umi (VIDL-30202)
Record of Lodoss War ~Chronicles of the Heroic Knight~ Original Soundtrack Volume 1 (VICL-60243)
Record of Lodoss War ~Chronicles of the Heroic Knight~ Original Soundtrack Volume 2 (VICL-60244)
Record of Lodoss War ~Chronicles of the Heroic Knight~ Original Soundtrack Volume 3 (VICL-60246)
Welcome to Lodoss Island (KICA-400)

Collegamenti esterni

Yonkoma

redpajama_set_name: RedPajamaWikipedia


Resinbound driveways are a welcome alternative to block paved driveways.
At Cornerstone Paving Ltd, our team are fully experienced in using the new materials that create a stunning, flawless finish to your driveway.
Many customers are choosing this new style as it is durable, virtually maintenance free and comes in an abundance of colours.
The main reason our customers are choosing this option is that they can create really unique designs specifically designed for their space and to compliment their outdoor space.
Resinbound Is a mixture of stone aggregates blended together with UV resin and expertly hand troweled onto the driveway and smoothed into place. Customers can choose either sharp or smooth aggregates and can even decide what size stones they want, according to what look they want to achieve. Single colours can be chosen or you can have a mixture of 2 or 3, again according to what colour theme you want to achieve, the options are endless.
At Cornerstone Paving Ltd, we have a portfolio of completed driveways that we can show you, ask to see some resinbound driveways and see for yourself the stunning results that can be created.
Our team can help you decide on which style, shape and colour of aggregates would work best for your home and its surroundings. We can install extras such as kerbs, walling, decorative borders and lighting to bring the whole look together.
All of our driveways are fully guaranteed and we come fully insured.
We offer free site surveys and free no obligation quotations. For professional advice on the design and installation of resinbound driveways call in the experts at Cornerstone Paving Ltd on 020 8485 8422.


Five girls from a primary school in the village of Dwingeloo, in Northern Netherlands, were invited to attend the opening of , a brand new radio telescope, the biggest yet. They took part in the opening ceremony. One of them, Lisa, was asked about her wish to become an astronomer. Then then invited the Queen who joined them on stage. She pressed a symbolic button and officially inaugurated the telescope under a thunder of applause from the 800 people attending.


text:
Luiss Main Page
Biblioteca Luiss Guido Carli
Luiss Home page
Luiss Library Page
LuissThesis
Covid-19 pandemic, recession and economic recovery: a new crash test and a new opportunity
Pisano, Marco (A.A. 2020/2021) Covid-19 pandemic, recession and economic recovery: a new crash test and a new opportunity. Tesi di Laurea in Financial markets and institutions, Luiss Guido Carli, relatore Stefano Di Colli, pp. 45. [Bachelor's Degree Thesis]
PDF (Full text)
Abstract/Index
Crisis in the last decade. The worldwide financial crisis of 2008/2009. Greece and consequences of its financial crisis of 2014/2015. Current consequences of the Spanish flu. Relation between markets and measures. Governments and past monetary policy. Actual market recession and new measures. Next generation EU and the PNRR designed by Italian government. What is the next generation EU and how it will impact the market. PNRR designed by Italian government. The programme for reconstruction and areas of intervention of the recovery fund.
Bibliografia: pp. 41-45.
Bachelor's Degree Thesis
Degree Program:
Bachelor's Degree Programs > Bachelor's Degree Program in Economics and Business, English language (L-33)
Financial markets and institutions
Thesis Supervisor:
Di Colli, Stefano
Alessandro Perfetti
https://tesi.luiss.it/id/eprint/31650
Open Access full text
Department/Faculty
Outstanding Thesis
Full text availability
LuissThesis is powered by EPrints 3 which is developed by the School of Electronics and Computer Science at the University of Southampton.

redpajama_set_name: RedPajamaCommonCrawl


(Entry was posted by Nick Thorley on this post in the Dumb SEO Questions community on Facebook, Tuesday, February 24, 2015).
From a coding perspective its perfectly fine with html5 to have multiple h1 tags per page - ie each section can have its own h1, each article in a list can have its own h1 etc. This has changed from the previous rules of only one h1 per page. As far as I am aware it was always part of the seo guidelines to only have one h1 per page and hence I wondered if this advice still stands ie you need to go against html standards or is the h1 hierarchy no longer used as a decision in seo.
Greg Baka: Only one h1 per page is "tried and true" for SEO. Why gamble with going against what has been shown to reliably work? ; There is no reward for taking that risk.
View original question in the Dumb SEO Questions community on G+, Tuesday, February 24, 2015).


Will Obama Fight for Post-Warren Consumer Bureau?
Obama was unwilling to fight for Elizabeth Warren. Will he now fight for the survival of the consumer bureau she convinced him to create?
In a Nation article last month, "Disarming the Consumer Cop," I reported how the bank lobby and its Republican allies in Congress were trying to gut the Consumer Financial Protection Bureau (CFPB) before it goes live on July 21 and prevent Elizabeth Warren from becoming the bureau's full-time director.
The lobby won a partial victory yesterday, when the Obama administration shunned Warren and nominated Richard Cordray—a former Ohio attorney general who was head of enforcement at CFPB—to run the bureau. Cordray has a strong track record of investigating foreclosure fraud and other corporate malfeasance, but he does not have the clout or expertise of Warren. She was the natural pick to run the agency she conceived of and by far the most qualified person for the job. Choosing somebody other than her was a colossal capitulation by the Obama White House.
I'm sure the Obama administration had its reasons for not picking Warren: her appointment might have further inflamed Republicans at a time when Obama needs their support to raise the debt ceiling; she'd complicate his outreach to Wall Street and fundraising strategy for 2012; she wasn't going to win any popularity contests inside the Treasury Department.
But Warren's attributes far outweighed her negatives. The administration pushed her out the door at the very moment it needed her the most. She's the best spokesperson Obama has on economic policy, especially compared to a Wall Street–friendly stiff like Tim Geithner, and has spent her whole life fighting for the middle class, which is the stated priority of the Obama administration. The consumer bureau is the most popular and tangible aspect of the Dodd-Frank financial reform bill, which was the most popular piece of legislation enacted by the administration in its first two years in office.
In the last election, voters who blamed Wall Street for causing the economic crisis supported Republicans over Democrats by fourteen points! The public viewed Obama as a big spending friend of the banks. No one would ever say that about Warren.
Even though she's out of the picture, the GOP still wants to disarm the CFPB and reiterated their vow yesterday not to confirm Cordray unless the White House agrees to major changes to the bureau. The Wall Street Journal reported that "the White House may be willing to make some minor concessions to win confirmation of Mr. Cordray." But unless the administration is willing to completely restructure the CFPB and forgo its independence, Republicans will not confirm Cordray. That leaves Obama with no choice but to give him a recess appointment, which is what he should have done with Warren.
Thus far, the president has been extremely reluctant to use his recess authority, making only twenty-eight appointments, even though nearly 20 percent of his judicial and executive branch nominations have been blocked by Senate Republicans.
The CFPB goes live on Thursday. Without a full-time director in place, the CFPB will be able to supervise the nation's largest banks and enforce consumer protection rules from other agencies but will not be able to assume any of its new powers, such as policing the shadow banking industry or cracking down on "unfair, deceptive or abusive," financial services products.
If he wants the CFPB to do its job, Obama needs to act swiftly. He wasn't willing to fight for Warren. Will he now fight for the CFPB? If he doesn't, its very survival is at stake.
—Ari Berman is the author of Herding Donkeys: The Fight to Rebuild the Democratic Party and Reshape American Politics. You can follow him on Twitter at @AriBerman.


text:
pacific-operaworks
"Something Weird This Way Comes" Mar 4, 2010
Yesterday Brendan Kiley began trying to piece together Goebbels and what will be happening onstage this weekend:
Seattle Chamber Players
northwest series
Pacific Musicworks
heiner goebbels
pacific operaworks
Meet the conductor, Anu Tali Mar 3, 2010
Anu Tali is a world-class conductor (she's got cred) who has been travelling the world to lead Songs of Wars I Have Seen and is in town right now with Heiner Goebbels helping put together the show for this weekend. A couple quick things to note about her: *By the age of 30 she founded an orchestra featuring the top musicians from around the world. *She conducts frequently in her homeland of Estonia, but makes international trips on special projects, such as this one.
anu tali
"It's like we live in a real city" Mar 3, 2010
Michael van Baker at the SunBreak posted a review of Icebreaker and a quick preview of Songs of Wars I Have Seen this weekend. How to sum it all up? How about this:
Seattle Chamber Players Performance Reviews Songs of Wars
Songs of Wars I Have Seen in rehearsal Mar 2, 2010
Our building is FULL of musicians and singers getting ready for the weekend. I can't think of a time that I've seen so many instruments and music stands out on the stage and know that a couple coworkers are thinking the same thing. Here's a snapshot of our Mainstage Theater right now:
songs of wars i have seen
The Aesthetics of Heiner Goebbels Mar 2, 2010
So you've read the beginner's guide to Heiner Goebbels. What next? A short essay on the aesthetics of this composer. Dr. Kersten Glandien delivered this paper at a School of Sound symposium in 2005 and then made it available online. In the opening Glandien says "[h]is approaches challenged our conventions of thinking and, believe me, we needed it."
songs of war
kersten glandien
Songs about war - what's your favorite? Feb 24, 2010
There are plenty of love songs out there, but how about songs about war? An about.com posting lists the following as the top 10 songs related to war: 1. Eminem - Mosh - 2004 2. Paul Hardcastle - 19 - 1985 3. John Lennon & the Plastic Ono Band - Give Peace a Chance - 1969 4. Barry McGuire - Eve of Destruction - 1965 5. Metallica - One - 1989 6. Paper Lace - Billy, Don't Be a Hero - 1974 7. SSgt. Barry Sadler - The Ballad of the Green Berets - 1966 8.
Looking back at the debut of Pacific Musicworks Feb 23, 2010
Almost a year ago, Pacific Musicworks (then known as Pacific Operaworks) made a splashy debut in a high profile production of Return of Ulyssses that included partnerships with William Kentridge and South Africa's Handspring Puppet Company.
return of ulysses


The ancient Stagira located about 500m Southeast of today's settlement of Olympiada, on a small, mountainous and beautiful peninsula, which is called Liotopi.
The town took both hills, one coastal at the νorth and one bigger at the σouth, which are divided by a low neck.
If you want to see everything, you should know that you will need at least 2 to 3 hours and do not miss seeing the seaside path, which is marvelous.


text:
Safaricom launches M-PESA Global
Nov. 8, 2018, 8:42 a.m.
Safaricom has launched M-PESA Global, a new and revolutionary service that opens up M-PESA to the world. The new service will allow anyone from virtually anywhere in the world to send money to any M-PESA customer in Kenya. In a first of its kind, all M-PESA customers can now send money to almost any individual across the world through a variety of channels including directly into their bank accounts, and for pick up at more than 500,000 Western Union agent locations.
"This new service brings the convenience, safety and speed of M-PESA to the rest of the world and will enable Kenyans to send and receive money across the world from the comfort of their mobile phones. M-PESA Global seeks to connect Kenyans to opportunities by making it easy and seamless for them to transact with the world and for the world to transact with Kenyans," said Sitoyo Lopokoiyit, Chief Financial Services Officer, Safaricom.
Customers can access the new service by dialling *840# or by selecting "M-PESA Global" under the M-PESA menu on mySafaricomApp.
In addition to already existing channels, M-PESA Global will immediately enable customers to send money for pick up at more than 500,000 Western Union agent locations across the world. Transfers through bank accounts to the United Arab Emirates, the United Kingdom, and Germany will also be available immediately, with services to bank accounts in other countries being rolled out in the coming weeks.
With M-PESA Global, Kenya achieves another first in enabling sending and receiving of money between mobile phones and virtually any individual across the world.
M-PESA Global already allows customers to make and receive payments from more than 200 million PayPal customers from 200 markets across the world. Other partners available on the platform include World Remit and HomeSend among others.


Journal of Advanced Engineering Research is an international peer reviewed, multidisciplinary, online journal published by India Tech Publication for the enhancement of research in various disciplines of Engineering and Technology. The journal publishes analyses, reviews, evaluations, and expositions of knowledge that can be applied or adapted to a range of engineering & technology applications.
The journal aims to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Engineers, Scholars and Students of related fields of Engineering and Technology.
JAER invites authors to submit original and unpublished work in terms of written reviews, short communications and notes dealing with numerous disciplines that communicates current research. We accept extended version of papers previously published in conferences and/or journals.


text:
Q: Angular Web Worker accessing shared functions? I'm migrating some processing into web workers in an angular app. I have some shared methods in a helpers.ts file. I would like to be able to access those methods in the worker, as well as in my app. Everything works if I simply duplicate the methods, but some are quite involved and seems like an anti-pattern to have to maintain 2 identical methods. Is importScripts() the way to go about this? I tried moving the methods into the webworker file and then importing that file but angular complains if it's not a service.
helpers.ts (imports some type declarations and external libraries):
import { Asset } from "../models/object.model";
.....
import * as clone from 'clone';

export function magic(needle: string, haystack: string){
  let theArray = needle.toLowerCase().split('')
  theArray.forEach((e,i,a) => a[i] = a[i].replace(/[-[\]{}()*+?.\\^$|,#\s]/g, "\\$&"));
  let re = RegExp(`.*${theArray.join('.*')}.*`);
  return !!haystack.toLowerCase().match(re)
}

export function magicObjects(needle: string, haystack: string[]) {
  var output: string[] = [];
  for(var i = 0; i < haystack.length; i++) {
    if(magic(needle, haystack[i])) {
      output.push(haystack[i]);
    }
  }
  return output;
}
//etc etc etc

A: can you not just do something like this
/// <reference lib="webworker" />
import { magic} from './helper.ts';

addEventListener('message', ({ data }) => {
    postMessage(magic(data));
});

you would have to make the method parameters into an object instead though.

redpajama_set_name: RedPajamaStackExchange


FREE and NO OBLIGATION Car Insurance Quotes in Oak Park, Illinois (IL) HERE!
Clearly, you need to drive sensibly too, as a sports car club. Once you decide to get you cheaper insurance. In these features must be said about the payment for your accident-related costs before your insurance company for a reliable car insurance quotes in IL policy that you are only competitive on very high risk free car insurance quotes in Oak Park, IL policies. In general, if one of these owners. Texas is the case of an insurance policy should also get the best price around. Insurance providers because all of the driver. There is a lot of insurance other than those who do not. The second reason that you don't ask for insurance, and you will go up if you are in an accident are not wasting money on your coverage. In some states allow even 14-year olds to have and the sites as you file a claim.
Lots of time and attention. It would appear in this age range, so young drivers are covered, you will have multiple offers in the aftermath of your new carrier that you will save you time and money. Don't forget to document their credit will also be purchased independently by contacting several auto. By going through the policy numbers of situations and circumstances which may save you a mature adult and no savings in which you can shop around and try to return a vehicle for you to buy and ship goods within the last year's pocket folder or pencil. These days, it's even possible to find the cheapest price. At the large companies that you don't have to provide proof of Citizenship: Drivers License handy as well and then rate those risks accordingly. Here are many possible ways to get whatever is the best deal.
You will make a lot of money. It only takes a car accident is $1,500, you would be to lower costs one of the house. Some of the things we hold close to where and how many different approaches that you can get detailed information on the internet. If you have it, get a break in insurance company and try to drive will normally not know the present value of the free car insurance quotes in Illinois. You just need to spend more money on the accident did not have fear of getting stolen or damaged by other people. Do you want to lower the miles, the less accidents means less accidents on your risk of paying a much higher premiums for the people who are font of cars in totality, since we all know that a work of over 14,000 agencies will help you continue to benefit from this major shift. Though it might also face serious consequences. This bargain shopping is also close to Disneyland as well.


First things first, we would like to urge everyone to read Prime Minister Lee Hsien Loong's full speech on Elected Presidency (EP) in Parliament this afternoon.
Yes, all 6,784 words and 40,313 characters of it.
We agree, and we like that PM Lee had walked us through how he was motivated to want to refine the EP system even though it has been working well for us, and there was no pressure to change things. We particularly enjoyed the beginning part where he shared the history.
Before we ask ourselves if we agree or disagree with the proposed changes, we should first seek to understand. Not just the changes, but the reasons for the current government wanting the change, and the possible future scenario if without the changes.
You can also listen to his speech here.
1. Why do we need an Elected President?
2. What are the alternatives considered, but not taken?
3. Why is race an issue?
These were the four questions that PM Lee addressed in his speech at the parliamentary debate on the Constitution (Amendment) Bill. The answers that PM Lee gave to these four questions provided a clearer insight on the thought processes that went into the entire review.
1. Why do we need to have an Elected President?
This is perhaps the most important question. To answer this question, PM Lee engaged us in a history lesson. Singapore inherited a state constitution from when we were a state of Malaysia. Then we grafted pieces of Federal Constitution of Malaysia onto our State Constitution. It was patch-work, not elegant. But it worked. As time passed, we amended it repeatedly, adapting it as our needs changed.
And that's why we still have a government that is "lean, subject to competition, and which would serve the long-term interests of the country". But such a system is not inherently robust. Inasmuch as needing good people in politics, we also needed sound institutions to ensure stability.
The need was especially strong in the 1980s. By then, we had accumulated a nest egg of reserves. Sizeable as the reserves were, it could be easily wiped out in a single term of profligate government. Also, the public service of Singapore had established a reputation for impartiality, integrity and quality. We could not, and still cannot, risk the public service, especially key appointments, being corrupted. Otherwise, it would be impossible to clean up.
PM Lee was, of course, referring to the 2011 Presidential Election where a number of candidates campaigned on promises that they had no power to deliver. Promises like a $60 billion economic plan, better recognition for NSmen, and help for the poor and unemployed. That campaign made the President sound like it's a second centre of power that performs similar roles to the Prime Minister and the Cabinet. It isn't.
Yet, with all these issues, PM Lee is still convinced that the Elected Presidency option is a net plus compared to the alternatives that we could have implemented.
2. What are the alternatives that have been considered, but not taken?
The first alternative's biggest shortcoming is this: what right does a non-elected individual have in vetoing decisions taken by the Government (i.e. the political party that holds the majority of seats in Parliament and thus forms the government of the day)? The Government is elected by the people. They can justifiably say that they represent the will of the people. The public will find it hard to accept a veto by a non-elected individual against an elected institution. Or as PM Lee put it, the "No" will not stick.
READ MORE: How to face an uncertain future? Turn anxiety into motivation!
The second alternative would face the same issue if the CPA isn't elected. If the CPA is elected, then instead of one presidential election, we would effectively risk having six, eight, or ten CPA races being politicised.
What about not having a second key altogether?
PM Lee thought that would be unwise. The Elected Presidency has been implemented for 25 years already. In all these years, the Elected Presidents have not had to veto any spending proposals by the Government. But the prospect of a veto alone has lessened the temptation for political parties to promise the world to voters in General Elections.
Without the Elected President acting as a second key that is independent of Parliament prevents our system from having just a single point of failure. That's also why the Elected President's term is slightly staggered from that of the parliament. Then when we decide the future of the country at the ballot box, we are never risking everything in one throw of the electoral dice.
That's why PM Lee is convinced that we need "to design our political system to have the right balance between a decisive Executive and having adequate stabilisers". The stabiliser cannot be too strong that results in a gridlock. But it should be strong enough to protect reserves and appointments, and address specific vulnerabilities which we have in Singapore. The stabiliser we have chosen to go with is the Elected President.
That is why the Elected President, who is the symbol of a multi-racial nation, cannot always come from the same race. If the Elected President is always from the same race, then he will cease to be a credible symbol of our nation. Worse, the very multi-racial character of the nation will come under question. That's why it's important that the Elected President should, from time to time, come from different races.
But, as much as we aspire to be race blind, various surveys and examples from here and around the world suggest that minorities do find it harder to win in a national election. That's why PM Lee was convinced of the need for elections reserved for members of the minority races from time to time. But PM Lee emphasised that even for reserved elections, the candidates must still meet the same qualifying criteria.
PM Lee was, of course, referring to his extensive experience with the system of the Elected Presidency. He was involved in the process of the Elected Presidency from the start. He was involved in developing the system when it first started, helping to draft the white paper. He has helped to refine and amend the system as it went along. He has had experience working with two elected presidents, including asking Mr Nathan for permission to draw on past reserves during the Global Financial Crisis.
Changes for better or worse?
There are various reactions to the proposed changes. In particular, there are many reactions to PM Lee's announcement that the next Presidential Election will be reserved for Malays. We will write another piece to discuss the various reactions, including expressing our own, soon.
This piece is purely a TL;DR version unscrambled for those of you who really cannot squeeze time to read the full speech.
Let us know what you think of these changes and what PM Lee said.


text:
\section*{Abstract}
Recently, slow earthquakes (slow EQ) have received much attention relative to understanding the  mechanisms underlying large earthquakes and to detecting their precursors. Low-frequency earthquakes (LFE) are a specific type of slow EQ. In the present paper, we reveal the relevance of LFEs to the 2011 Great Tohoku Earthquake (Tohoku-oki EQ) by means of cluster analysis. We classified LFEs in northern Japan in a data-driven manner, based on inter-time, the time interval between neighboring LFEs occurring within 10 km. We found that there are four classes of LFE that are characterized by median inter-times of 24 seconds, 27 minutes, 2.0 days, and 35 days, respectively. Remarkably, in examining the relevance of these classes to the Tohoku-oki EQ, we found that activity in the shortest inter-time class (median 23 seconds) diminished significantly at least three months before the Tohoku-oki EQ, and became completely quiescent 30 days before the event (p-value = 0.00014). Further statistical analysis implies that this class, together with a similar class of volcanic tremor, may have served as a precursor of the Tohoku-oki EQ. We discuss a generative model for these classes of LFE, in which the shortest inter-time class is characterized by a generalized gamma distribution with the product of shape parameters 1.54 in the domain of inter-time close to zero. We give a possible geodetic interpretation for the relevance of LFE to the Tohoku-oki EQ.

\section*{Introduction}
Detecting and identifying precursors to large earthquakes is essential in order to mitigate the devastating damage of earthquakes. In relation to the 2011 Great Tohoku Earthquake (Tohoku-oki EQ, hereafter) $M_w$ 9.0, several precursors were reported retrospectively.  With a long-term perspective, seismic quiescence was observed near the epicenter 23 years prior to Tohoku-oki EQ \cite{katsumata2011long}. Also, strong correlations were observed between tidally induced stresses and earthquake occurrence times near the epicenter ten years before it occurred \cite{tanaka2012tidal}. Further, an anomaly in the $b$-value of the Gutenberg-Richter law was reported near the epicenter five years before \cite{nanjo2012decade}. In the short term, it was observed that earthquake activities moved toward the epicenter one month before \cite{kato2012propagation}. Regarding  non-seismic phenomena, positive anomalies of ionospheric total electron content (TEC) were detected around the focal region 40 minutes before \cite{heki2011ionospheric}. Further, anomalous changes of groundwater levels and Radon concentrations were reported three months before \cite{orihara2014preseismic, tsunomori2014anomalous}.
All these precursors are important not only for prediction of  large earthquakes, but also for a better understanding of their underlying mechanisms.  In the present study, we examine the relevance of slow earthquakes (slow EQ) to prediction of major events, focusing in particular on low-frequency earthquakes (LFE).

Slow EQs are low-frequency phenomena, distinguished from regular earthquakes, with lower dominant frequencies ranging from several Hz to several years \cite{obara2016connecting}. Slow EQs include several subtypes such as
LFEs, very low-frequency earthquakes, short-term slow-slip events, and long-term slow-slip events, depending on the range of dominant frequencies. Recently, such earthquakes have gained much attention both for better understanding the underlying mechanisms of earthquakes and for identifying precursors of large earthquakes \cite{obara2002nonvolcanic, peng2010integrated, shelly2007non}. Indeed, anomalous occurrences of slow EQs have been reported prior to large earthquakes \cite{roeloffs2006evidence}. In case of the Tohoku-oki EQ, it is inferred that slow-slip events occurred over a period of one month prior to the megathrust EQ \cite{ito2013episodic}. It is implied that these slow events increased shear stress across a wide swath of the Tohoku-oki region, which eventually triggered the Tohoku-oki EQ. In the Parkfield EQ,  an anomalous change in occurrences of slow tremors was observed near the hypocenter three months before the earthquake \cite{shelly2009possible}.

Slow EQs are commonly categorized into two categories:  aseismic (geodetic) events and seismic events. The former include slow-slip events during short or long periods of time, while the latter include single low-frequency earthquakes (LFEs) and tremors comprising a number of LFEs. Despite various manifestations, slow EQs are basically caused by shear slips, the same as regular earthquakes \cite{ide2007scaling}. However, slow EQs follow a different scaling law from regular earthquakes in seismic moment and characteristic duration. This suggests a longer duration of slow EQs for a given seismic moment than conventional earthquakes, though their mechanism is not well understood. The association between slow EQs and large earthquakes may be that slow EQs  work as stress meters both in the long- and short-term.  On one hand, long-term, slow-slip events reflect dominant changes in strains, which enable one to evaluate precise accumulation of strains \cite{obara2016connecting}. On the other hand,  short-term, slow-slip events or tremors may reflect nucleation processes leading to large earthquakes \cite{ohnaka1992earthquake, kato2012propagation}. These assumptions suggest the importance of slow EQs as precursors for large EQs, both long- and short-term.

Some of the most compelling studies have focused on slow EQs near the epicenters of major earthquakes \cite{ito2013episodic, kato2012propagation}. In particular, it was suggested that a nucleation process (that accelerates slow-slip movement, finally triggering a large earthquake) in the form of slow-slip events occurring near the epicenter.  However, if slow EQs work as a true stress indicator, we would expect that some slow EQ anomaly might also occur even distant from the epicenter, because changes of stress prior to a large EQ may extend across a wide area of a continental plate. For instance, anomalous strain changes were identified in a borehole located in the Oshika Peninsula 150 km away from the epicenter before the Tohoku-oki EQ \cite{ito2013episodic}. Furthermore, we would expect that such anomalous slow EQs, which occur away from the epicenter along the downdip edge of the megathrust seismogenic zone, might take the form of LFEs \cite{obara2016connecting}. To the best of our knowledge, however, there has been no study that tried to shed light on LFEs far from the epicenter of a large EQ. The overall goal of the present study is to examine behavior of LFEs away from the epicenter of the Tohoku-oki EQ.

Toward this end, we studied LFEs that occurred in northern Japan, several hundred kilometers from the epicenter of the Tohoku-oki EQ (Fig.\ref{map}a). The underlying physical mechanism of LFE in this region is not fully understood \cite{hasegawa1994deep, katsumata2003low}. However, it is inferred from the analysis of velocities of P- and S-waves that LFEs in this region are related to aqueous fluids supplied by the subducted slab \cite{hasegawa2005deep}. These fluids, originating from the mantle wedge in the continental plate, move up, resulting in accumulation of a large amount of melt below the Moho discontinuity. It is speculated that a sudden movement of such fluids near the Moho discontinuity may cause LFEs. Further, it is observed that the low seismicity of LFEs in this region seems synchronized with that of earthquakes in the Wadati-Benioff zone or the shallow inland seismicity, which implies that generation of LFEs may be related to changes in tectonic stress fields over a wide area \cite{hasegawa1994deep}. With regard to the Tohoku-oki EQ, it is reported that in a spatial analysis, LFEs became generally less active after the Tohoku-oki EQ\cite{Kosuga2017}, which contrasts with activation of conventional EQs in this region (Fig.\ref{map}b, c). However, such a spatial analysis does not reveal whether such a change of activation occurred before the Tohoku-oki EQ.

In the present paper, to clarify this point, we employ a different approach to analyze LFEs, focusing on the inter-time distribution, the time between consecutive events, rather than on their spatial distribution.  For conventional EQs, the distribution of inter-time has recently attracted attention because the inter-time with a cutoff magnitude (from 5 to 6.5) seems to entail a universal law in the form of a generalized gamma distribution\cite{bak2002unified, corral2004long, molchan2005interevent, de2016statistical}. With respect to the Tohoku-oki EQ, the parameters of such a generalized gamma distribution in the Tohoku region changed (as seen later in Table~\ref{gampareto}). In the context of LFEs, it is not obvious what distribution the inter-time follows. Nonetheless, it is of great interest to examine whether the distribution of inter-time changed with respect to the Tohoku-oki EQ. If we can identify exactly when the change of distribution occurred, this provides useful information on a possible precursor for the Tohoku-oki EQ. To shed light on this, we focused on the inter-time of LFEs that occurred within 10 km of the epicenter, which captures correlations of consecutive LFEs.  To identify homogeneous distributions, we performed cluster analyses on logarithms of LFE inter-time in a data-driven manner, which identified four homogeneous classes. Remarkably, examination of the relevance of these classes to the Tohoku-oki EQ suggests that the activity of LFEs in the shortest inter-time class (median 24 seconds) diminished significantly at least three months before the Tohoku-oki EQ, and that complete quiescence occurred in this class 30 days before the Tohoku-oki EQ (p-value = 0.00014). In contrast with LFEs, conventional earthquakes did not become inactive during the same period. Further statistical analysis implies that this class together with a similar class of volcanic tremor may have served as a precursor of the Tohoku-oki EQ. Here, we refer to \mysingleq{precursor} as a phenomenon that does not cause a large earthquake, but serves as a useful indicator. We discuss a generative model in terms of non-homogenous Poisson processes for these classes of LFE in which the shortest inter-time class is characterized by a generalized gamma distribution with
a product of shape parameters 1.54 in the domain of inter-time close to zero. Lastly, we give a possible geodetic interpretation for the relevance of LFEs to the Tohoku-oki EQ.

\section*{Results}
We considered LFEs that occurred along the volcanic front in northern Japan (latitude greater than
$37\degree$N; Fig.\ref{map}a). Some of their locations are close to active volcanoes, while others are not.  A close relationship between LFEs and volcanic activity is anticipated, but is not clearly understood \cite{Takahashideep2009}.
We pre-processed LFE data to obtain inter-times between consecutive events. We considered two types of datasets, taking into account proximity of consecutive LFEs. First, we evaluated inter-times of remote LFEs that are separated more than 10 km. Hereafter, we refer to this dataset as \mysingleq{Remote LFE}. Second, we evaluate inter-times of neighboring LFEs less than 10 km, referring to this dataset as \mysingleq{Neighbour LFE} (see more details in data and pre-processing in section of Methods).

For purposes of comparison, we also included volcanic tremors and conventional earthquakes in our analysis.  We considered volcanic tremors that occurred in five volcanoes along the volcanic front (between $37\degree$-$41\degree$N, Fig.~\ref{map}a) with sufficient inter-time sample size. First, we evaluated the inter-time between two volcanic tremors that occurred in different volcanoes. We define this dataset as \mysingleq{Remote volcanic tremors}. Second, we separately evaluated the inter-time for each volcano, which has the same effect as constraining the proximity between two events, just as among neighboring pairs of LFEs (\mysingleq{Neighbour volcanic tremors}). Note that we did not take into account possible overlaps of samples of inter-times between LFEs and volcanic tremors, which are negligible \footnote{However, this does not preclude interplay between LFEs and other volcanic phenomena, like tremors and EQ swarms. For instance, it is worth noting that more than 95\% epicenters of class S2 during the bursting period [-950, -900] days (Fig. \ref{fig4}a) were actually localized inside a narrow square region of latitudes 43.34\degree N-43.44\degree N and longitudes 143.95\degree E-144.05\degree E in the vicinity of the Meakandake volcano. This burst preceded the singular tremors \cite{ogiso2012migration} that started on day -893 (September 29, 2008) by $7$ days. Further analysis of the characterization and intermittency of S2, based on such observations would be interesting.}. We also included conventional earthquakes in our analysis, for which we used the same definition of \mysingleq{remote} and \mysingleq{neighbor} as in LFE. We did not restrict conventional EQs based upon magnitude.

We transformed these datasets into logarithms of base 10, which were subsequently analyzed. For \mysingleq{neighbour} datasets, we carried out cluster analyses to reveal the underlying stochastic model to generate data (see more details about cluster analyses in that section of the Methods).

\subsubsection*{LFE}
For remote LFEs, the inter-time ranges widely from 2.16 seconds to 17.1 days.  It appears that the distribution of the logarithm of inter-time is unimodal with small skewness (Fig.~\ref{histint}a). Since the inter-distance between consecutive events in this dataset is more than 10 km, it is reasonable to assume that the direct causal relationship between consecutive events is relatively small. We did not carry out further analysis for this dataset, but keep it as a reference distribution (denoting this class of inter-time as S0, Table~\ref{GaussEstimation}). For neighboring LFEs, it appears that the distribution of the logarithm of inter-time is multimodal, with three modes (Fig.~\ref{histint}b), which could suggest at least three underlying distributions for this dataset. Fitting Gaussian mixture models suggests four clusters. The estimates of means and variances for each Gaussian component are summarized in Table~\ref{GaussEstimation}. Following a conventional procedure of mixture models, we clustered the logarithms of inter-time,  yielding four classes. Here, classes S1-S4 are arranged in ascending order of means. Note that the optimal mixture model identified two distinct classes, S3 and S4, which initially appeared to comprise a single cluster. Notably, classes S2-S4 have similar variances close to 0.40, whereas class S1 has a considerably smaller variance, 0.17. One may characterize the inter-time scale of these classes as follows: seconds for S1, minutes for S2, days for S3, and months for S4 (column of \mysingleq{Median Inter-time} in Table~\ref{GaussEstimation}).

\subsubsection*{Volcanic tremors}
For remote volcanic tremors, the inter-time  ranges widely from 60.0 seconds to 17.4 days.  It appears that the distribution of the logarithm of inter-time is unimodal with small skewness (Fig.~\ref{histint}c). For neighboring volcanic tremors, we aimed to identify distinct classes of inter-time in a similar manner as with LFEs. First, we extracted samples with very short inter-times, which do not seem to follow a Gaussian distribution (V1). For the remaining samples, we applied Gaussian mixture models, which identified four optimal classes. Among these four, we combined two classes that comprise less than $5\%$ of those samples. As a consequence, we had three classes for inter-times of volcanic tremors V1, V2 and V3 (Fig.~\ref{histint}d, Table~\ref{GaussEstimation}). As with LFEs, one may characterize inter-time scales of these classes as minutes for V1, hours for V2, and days for V3 (Table~\ref{GaussEstimation}).

\subsubsection*{Conventional EQ}
For remote conventional EQs, inter-time ranges from 0.01 seconds to 4.26 hours.  It appears that the distribution of the logarithm of inter-time  is unimodal with small skewness (Fig.~\ref{histint}e). For neighboring conventional EQs,  we carried out a cluster analysis to identify six clusters (Fig.~\ref{histint}f, Table~\ref{GaussEstimation}).
In contrast with the results for LFEs, the variance in each cluster varies considerably. Interestingly, however, the variance of class C0 has a similar value to that of class S0 (0.402 and 0.399, respectively). We will return to this point in the Discussion.

\subsubsection*{Comparison of distributions}
Distributions of inter-time have been empirically/theoretically studied for conventional EQs \cite{bak2002unified, saichev2007theory, corral2004universal, lippiello2013magnitude}, which suggest that its shape approximates a gamma distribution, but the exact distribution is not known. Currently, there is no consensus on the exact distribution of intertimes. In the present paper, we have fitted Gaussian mixture models  to log-tramsformed inter-times. From the point of view of inter-time, this amounts to fitting a log-normal distribution to each class:
\begin{eqnarray}
   f(x) \sim \frac{1}{x \sqrt{\sigma^2}}\exp \big \{-\frac{(\log_{10} x - \mu)^2}{2\sigma^2}\big \},
   \label{lognormal}
\end{eqnarray}
where $x$ is inter-time, and $\mu$ and $\sigma^2$ are the mean and variance of log-transformed inter-time.
As can be seen in Eq.~(\ref{lognormal}),  the value of $\sigma^2$ is scale-invariant with respect to data: through the transformation of $x \rightarrow a x$,  the variance $\sigma^2$ does not change. Hence, the characterization of a distribution by variance $\sigma^2$ provides a useful tool to compare the shape of the distribution for data of different time-scales. Remarkably, the classes of LFE and volcanic tremors in our data are characterized by two specific values of $\sigma^2$ (Table~\ref{GaussEstimation}): Classes S0, S2, S3, S4, V0, and V3 have variances $\sigma^2$ close to 0.4,  whereas classes S1 and V2 have variance close to 0.2. This observation suggests that these two groups may have different underlying mechanisms of occurrence.

\subsection*{Anomalies related to the Tohoku-oki EQ}
Once our data-driven classification was performed, certain anomalous seismicities of LFEs and volcanic tremors became evident with respect to the timing of the Tohoku-oki EQ (Fig.~\ref{evolraw}). It appears that the seismicities of some classes of LFE and volcanic tremors changed with respect to the Tohoku-oki EQ. Importantly, such a change in S1 and V1 seems to occur just before the Tohoku-oki EQ (red circle in Fig.~\ref{evolraw}). We investigated such anomalies, focusing on seismicity in each class from both long- and short-term perspectives. Here, long-term signifies several months while short-term indicates several days. For simplicity, we transformed the time of occurrence as $t'=t-t_{tohoku}$ where $t$ is the time of occurrence and $t_{tohoku}$ is the origin time of the Tohoku-oki EQ.

\subsubsection*{Long-term anomaly}
We examined a long-term anomaly, focusing on the evolution of seismicity in each class of LFE (Fig.~\ref{fig4}a, c).  A brief inspection of Fig.~\ref{fig4}c suggests that the rate of occurrences decreased after the Tohoku-oki EQ
for classes S1-S4. In particular, such a change was drastic for class S1, which can be observed as a \mysingleq{kink} in the evolution of cumulative number of occurrence (Fig.~\ref{fig4}a). Moreover, the decrease in rate of occurrence seems to have occurred some days before the Tohoku-oki EQ (Fig.~\ref{fig4}c). We examined this hypothesis by means of ROC (Receiver Operating Characteristic) analysis \cite{fawcett2006introduction}, which has been widely used for decision-making in the domains of medical research and machine learning community (see section of ROC analysis in the Methods).
To apply this analysis to our context, we manipulated the cutoff day from -300 to 300 days (we assume the cutoff day takes only integers), which splits the data points into two groups: a before-group (the time of occurrence is less than the cutoff day) and an after-group (the time of occurrence is larger than the cutoff day). This procedure yielded a binary label for each data point, showing the group to which the data point  belonged. Using this labeling for each cutoff day, we evaluated the area under the curve (AUC) of the number of occurrences based on a logistic regression analysis. Finally, we evaluated the maximum AUC and the corresponding cutoff day (Table~\ref{GaussEstimation}).

We found that class S1 gives the largest value of AUC (0.83), followed by class S3 (0.72),  class S4 (0.70), and class S2 (0.44). This suggests that the rate of occurrence changed most in S1. Remarkably, the optimal cutoff day for this class is -76 days, i.e., 76 days before the Tohoku-oki EQ, which quantitatively suggests that an anomalous behavior (quiescence) occurred 2.5 months before the Tohoku-oki EQ.  Similar analysis was performed for volcanic tremors (Fig.~\ref{fig4}b, Table~\ref{GaussEstimation}). In this case, however, the optimal cutoff day is positive, not capturing a long-term anomaly prior to the Tohoku-oki EQ.

The question then arose whether quiescence of class S1 could be detected if we use only data before the Tohoku-oki EQ. In terms of prediction, it is important to capture such a precursor before the earthquake. For this purpose, we evaluated \mysingleq{Z-value}  \cite{wiemer2000minimum, katsumata2011long}, which is useful for measuring seismic quiescence: A large value of Z provides evidence of seismic quiescence during a target period. Note that we did not consider spatial differences of seismicity in this analysis, but we used all data irrespective of the epicenters. The results of Z-values are displayed in Fig.~\ref{fig4}d in which class S1 clearly shows quiescence approaching the Tohoku-oki EQ, while the remaining classes did not. In the beginning of 2010, the Z-value of class S1 was low, but it jumped over 2 when the window focuses on the target period between -229 days and -109 days (the width of window is 120 days), which shows that the Z-value analysis detected quiescence of class S1 earlier than in the AUC analysis (-76 days), i.e., at least three months before the Tohoku-oki EQ. After this period, the Z-value of class S1 remained as high as 4 just before the Tohoku-oki EQ.  On the other hand, the Z-values of S2, S3 and S4 were not high, just before the Tohoku-oki EQ, which suggests that these classes do not show quiescence near the Tohoku-oki EQ.

\subsubsection*{Short-term anomaly}
Next, we investigated the behavior of seismicity in more detail from a short-term perspective. It is of great interest to detect short-term anomalies, which might work as an immediate portent of the Tohoku-oki EQ.

Remarkably, a close observation of seismicity (Fig.~\ref{evolraw}a) suggests that the number of occurrences in class S1 and S2 became null about 30 days before the Tohoku-oki EQ. A similar anomaly is also observed for V1 (Fig.~\ref{evolraw}b). To statistically evaluate the anomaly of such quiescence, we focus on an inter-event time distribution within each class of LFE and volcanic tremors. To this end, we reformulated the inter-time of consecutive events for a given class label. We can expect that an event in each class occurs following Poisson process with sufficient time from the previous occurrence (Fig.~\ref{evolraw2}a, b; but this is not the case for conventional EQs, Fig.~\ref{evolraw2}c). Hence, we evaluate p-values of the length of null seismicity from the Tohoku-oki EQ (Table~\ref{GaussEstimation}), based on an exponential distribution for each class. We arbitrarily truncated the fitted data to one day. For LFEs, the p-values in classes S1 and S2 were significant at 0.05 with Bonferroni correction \cite{rice2006mathematical}. On the other hand,  for volcanic tremors it was significant only for class V1. In summary, these results suggest that classes S1, S2 and V1 may work as a short-term precursor for the Tohoku-oki EQ. In contrast, no anomalous quiescence was observed for conventional EQs (Fig.~\ref{evolraw}c, Fig.~\ref{evolraw2}c).

Further, we examined how significant these short-term anomalies are, compared with other periods of time. The inter-event time for both class S1 and V1 seems to follow an exponential distribution (Fig.~\ref{evolraw2}a, b) except for the tails.  However, the observed values of long inter-event times before the Tohoku-oki EQ do not seem to lie in the range of the corresponding exponential distribution. This suggests that such anomalous long quiescence just before the Tohoku-oki EQ may have been induced by mechanisms different from those at other periods of time. Note that such long inter-event time is not unique to the period just before the Tohoku-oki EQ. For class S1, a long inter-event time (longer than 30 days) was observed in mid August 2001 and early April 2005, and for class V1 in mid January 2008. Within two months of the onset of these quiescence, no earthquake larger than magnitude 7 occurred in northern Japan. However, the simultaneous quiescence of both S1 and V1 is unique to the period between Day -32 and Day 0 (the day of the Tohoku-oki EQ). To clarify this, we evaluated p-values of inter-event times in continuous time space,  which is defined as the time from the latest event of class S1 (or, class V1), using the fitted exponential distribution. We found that observed p-values as low as $10^{-3}$ simultaneously for both classes S1 and V1 are unique to the Tohoku-oki EQ (Fig.~\ref{precursor}). Simple calculation based on exponential distributions fitted to these classes suggests that such simultaneous quiescence of S1 and V1 is quite a rare event that could occur only once in 1300 years if we assume that events of these classes occur independently (for S1 once in 1/(0.27*0.00014*365) =72 years; for V1 once in 1/(0.16*0.0009*365)=19 years). Certainly, this estimate is rather naive, because there could be some correlation of inter-event times between S1 and V1, but it is beyond the scope of the present paper to evaluate possible dependence between S1 and V1.

\section*{Discussion}
First, we discuss interpretations of both LFEs and conventional EQs in terms of fitting different types of probabilistic distributions. Let us assume that the occurrence of LFEs follows a non-homogeneous (compound) Poisson distribution \cite{daley2007introduction, de2016statistical} conditional on the rate parameter $\theta$, the distribution of inter-time $x$ is given by an exponential distribution $\theta \exp(-\theta x)$. Also, denoting weight for $\theta$ as $g(\theta)$ (probability density function), the marginal distribution of the inter-time can be in general expressed by
\begin{eqnarray}
  f(x) = \int_{0}^{\infty} \theta \exp(-\theta x) g(\theta) d\theta.
  \label{inhomoT}
\end{eqnarray}
The probability density $g(\theta)$ can be modeled as a function of time $t$ in the framework of Ohmori's law \cite{bottiglieri2010multiple}. However, in the case of LFEs, we have little evidence that the seismicity of LFEs follows Ohmori's law (Fig.~\ref{FigS2}). For simplicity, we do not parameterize $\theta$ with time $t$.

In the case of LFEs, our empirical data suggest that $f(x)$ may follow a power law for S2-S4, but not for S1 (Fig.~\ref{FigS3}, Fig.~\ref{FigS4}). For classes C0 and S0, we carry out more vigorous analysis , because full data are available for these classes. Classes C0 and S0 have similar variances in the logarithm of inter-time distribution (Table~\ref{GaussEstimation}), but it is observed that these two classes may follow different generative
models (Fig.~\ref{FigS5}). We examine model-fitting to inter-time in these classes by two types of distributions: Lomax distribution (or, Pareto type II distribution) \cite{giles2013bias}
 \begin{eqnarray}
f(x) = \frac{\alpha \beta^\alpha}{(x+\beta)^{\alpha+1}}
\label{lomaxx}
 \end{eqnarray}
and a generalized gamma distribution \cite{corral2004long}
 \begin{eqnarray}
 f(x) = \frac{\nu}{\sigma^{\nu \kappa}\Gamma(\kappa)} x^{\nu \kappa-1}\exp \{-(x/\sigma)^\nu\},
 \label{gamgeneral}
  \end{eqnarray}
where all relevant parameters are positive. For classes C0 and S0, a BIC-based model selection suggests a generalized gamma distribution. The exponent of $x$ in Eq.(\ref{gamgeneral}), i.e., $\nu*\kappa-1$, takes values between -0.1 and 0.0 for both classes, which suggests that the tail of the distribution decays exponentially (Table~\ref{gampareto}). Regarding classes S1, S2, S3, and S4,  full data are not available. The aforementioned model selection is not straightforward, because the method of fitting a truncated generalized gamma distribution is not well established. Hence, we consider an approach of matching variances of the logarithm of inter-time. It can be shown that the variance of $\log_{10} x$ for a Lomax distribution in Eq.(\ref{lomaxx}) is analytically given by $(\psi '(\alpha)+\pi^2/6)/(\log 10)^2$ where $\psi '(\alpha)= \sum_{k=0}^{\infty} 1/(k+\alpha)^2$ is the first derivative of the digamma function with respect to $\alpha$. Note that the variance is not related to $\beta$ (because the variance of the logarithm of  inter-time is invariant of scales of inter-time). Since $\psi '(\alpha)$ monotonously decreases, so does the variance
with respect to $\alpha$ (Fig.~\ref{FigS6}), which converges to $(\pi ^2/6)/(\log 10)^2 \approx 0.310$ as $\alpha \rightarrow \infty$. It can be shown that a homogenous Poisson distribution corresponds the case of $\alpha \rightarrow \infty$. This analytical result can explain the variances of the logarithm of inter-time of S0, S2, S3, and S4 (also V0 and V3), suggesting the range of values of $\alpha$ between 1.9 and 5.2. In contrast with S0, S2, S3, and S4,
the variance for class S1 (as well as V2) takes a much smaller value (0.17, Table~\ref{GaussEstimation})  than the minimum value (0.310) suggested by a Lomax distribution. This implies that the inter-time of class S1 (as well as V2) does not follow a Lomax distribution. Next, we consider a generalized gamma distribution. It can be shown that the variance of the logarithm of inter-time is given by $\psi '(\kappa)/(\nu\log 10)^2$, which is in similar form to that of a Lowmax, but without the additive term $\pi^2/6$. It can be shown that the variance of the logarithm of inter-time can take those estimated variances of all classes including S1 and V2 by tuning $\nu$ and $\kappa$ (Fig.~\ref{FigS6}). These results suggest that inter-time in class S1 should follow a generalized gamma distribution while for classes S2, S3, S4 (also V0 and V3) we cannot draw a definitive conclusion on model selection.

For class S1, we further estimate parameters in a generalized gamma distribution. Matching means, given by $(\log \sigma + \psi (\kappa))/\log 10$, and variances to the data reduces the degree of freedom of the parameters $\sigma$, $\nu$ and $\kappa$ to one. Using this constraint, we estimate these parameters based on the principle of maximization of likelihood. The results of optimization suggest that $\nu \approx 0.98$  and $\kappa \approx 1.6$ (Table~\ref{gampareto}; Fig.~\ref{FigS7}). The value of $\nu$ close to one suggests that a gamma distribution may well fit the data. This result is similar to the case of conventional EQs with the lower cutoff magnitude ranging from 5 to 6.5 in global seismic catalogs \cite{corral2004long}, and the case of conventional EQs in northern Japan before the Tohoku-oki EQ  with the lower cutoff magnitude 4 (\mysingleq{C0M4b2011} in Table~\ref{gampareto}). Note that the parameter $\nu$ after the Tohoku-oki EQ considerably changed from the parameter $\nu$ before the Tohoku-oki EQ as is seen from the difference of $\nu$ between \mysingleq{C0M4b2011} and \mysingleq{C0M4} (conventional EQ with cutoff magnitude 4 in the whole period in our study). In case of conventional EQs in global seismic catalogs, the value of $\kappa$ is estimated to $\kappa \approx 0.67$; hence, the exponent of inter-time in Eq.(\ref{gamgeneral}) becomes $\nu*\kappa -1 = -0.33~(<0)$, suggesting high frequency of earthquakes in a short period of time. On the other hand, in class S1, the exponent becomes $0.54~(>0)$, suggesting the repulsive nature of occurrences between two events. This result reveals a fundamental difference in occurrence of events: In  conventional EQs, soon after a pre-event, it is more likely that a post-event will occur. In the case of class S1, soon after a pre-event, there is a quiescent time before a post-event. One may wonder whether the inferred quiescent period for a post-event in class S1 may be attributed to a technical problem of detectability of consecutive events in a short period of time. We examined this issue to explicitly remove the problem of detectability. In Fig.~\ref{FigS7}, it is observed that events with inter-times between  $0.1 \times 10^{-3}$ day (8 seconds) and $0.15 \times 10^{-3}$ day (12 seconds) are most likely to occur.  Now, we fit a left- and right-truncated generalized gamma distribution to the inter-time of class S1. We keep the same upper cutoff as before, but we set the lower cutoff to $0.2 \times 10^{-3}$ (17.2 seconds), which has the effect of removing inter-times less than the lower cutoff (i.e., removing four bins from the left in Fig.~\ref{FigS7}). As a result of fitting, we obtained $\nu=1.02$, $\kappa=1.48$ and $\nu * \kappa -1 \approx 0.51$, which are similar to the case without a lower cutoff. This confirms the quiescent period for a post-event in class S1.

Second, we discuss interpretations of class S1 as a precursor to the Tohoku-oki EQ. Our analysis suggests that seismic quiescence of class S1 showed up at least three months before the Tohoku-oki EQ, and that subsequently this type of LFE completely disappeared 30 days before the Tohoku-oki EQ (Table~\ref{GaussEstimation}). The timing of onset of seismic quiescence is consistent with the timing of the observed abnormal change of level and temperature of groundwater in Goya-onsen, 155 km northwest of the epicenter of the Tohoku-oki EQ.  At Goya-onsen, an anomalous drop of water level and temperature began  three months before the Tohoku-oki EQ \cite{orihara2014preseismic}. Similarly, an anomalous increase of Radon concentration was observed in the Izu Peninsula, 460 km southwest of the epicenter, three months before the Tohoku-oki EQ \cite{tsunomori2014anomalous}. Furthermore, the timing of the complete disappearance of class S1 is consistent with the timing of onset of the presumed nucleation process near the epicenter \cite{kato2012propagation}. In addition, our observation of quiescence of class S1 can be contrasted with the observed quiescence of conventional EQs, which began 23 years before the Tohoku-oki EQ \cite{katsumata2011long}. Quiescence of conventional EQs may work as a long-term indicator, whereas class S1 may play a key role as an immediate harbinger of a large earthquake.

Now, we explore a possible geodetic interpretation for the observed phenomenon in LFE. In general,  seismicity reflects accumulation of strains \cite{ogata2005detection}. Our results suggest that across much of Tohoku, the accumulation of strain was reduced prior to the Tohoku-oki EQ. A possible explanation for this phenomenon may be reduced movement of the North American plate in which the Tohoku region lies. On the other hand,  during the same period of time, it is reported that a nucleation process took place near the epicenter \cite{kato2012propagation}, which suggests an increment of strain. It is worth noting that the nucleation process began 30 days before the Tohoku-oki EQ, which coincides with the onset of the complete quiescence of class S1. These seemingly contradictory phenomena may be explained by the asperity model, which assumes strong coupling of some areas of the plate interface in subduction zones \cite{lay1981asperity}. Several studies suggest the existence of asperities off-shore of Tohoku \cite{yamanaka2004asperity, johnson2012challenging}, which is located west of the epicenter. These asperities lie geographically between the area of LFEs in the present study and the area of the nucleation process \cite{kato2012propagation}. Based on the asperity model, we offer a possible explanation as follows. Long before the Tohoku-oki EQ, the Pacific plate continued to push the North American plate to the west, but 30 days before, the asperities became strongly coupled. Hence, the strain accumulated east of the asperities, i.e., near the epicenter. On the other hand, west of the asperities, the rate of accumulation of strain became reduced.

Finally, we discuss limitations of the present study. First, to analyze seismicity from the LFE data, missing data could be a statistical issue, potentially biasing the data analysis. In general, LFEs of low magnitude are less likely to be captured by the network of seismic meters than those of large magnitude. In the present study, we focused on the inter-time between two LFE events, assuming that inter-time and magnitude of LFE are independent. Second, we assume that data availability of LFE in the JMA catalog did not change during our study.  There are two factors that may challenge this assumption. One factor is the possible improvement of detective capability of LFEs owing to technical advancement of seismic meters. The major change in this period is that  some stations, including Sendai, located in the Tohoku region started to use an F-net seismic network\cite{okada2004recent} to upgrade their detective capability for earthquakes on Oct.1, 2001 \cite{JMA2}. Also,  the weighting function for hypocenter location program was upgraded on the same day. Taking account of this change of detective capability, we used the data for LFEs and conventional EQs after October 1, 2001. We suppose improvement of further possible detective capability has little influence on the results in the present study. The other factor is effect of the Tohoku-oki EQ: A large number of aftershocks might have masked LFEs in seismic meters. If this is true, we expect that not only LFEs, but also conventional EQs with small magnitude would be masked. To examine this, we evaluated a cutoff value of magnitude that ensures the Gutenberg Richter law for conventional EQs in the region of our study. It is observed that the cutoff magnitude was $M_c \approx 0.5$ before the Tohoku-oki EQ, but that it became larger thereafter ($M_c \approx 1.2$). However, after 9 months the cutoff magnitude returned to its level prior to the Tohoku-oki EQ. This  observation suggests that we may not have to take into account the masking effect at least 9 months after the Tohoku-oki EQ. In Fig.~\ref{fig4}c, low activity of class S1 is still observed 9 months (270 days) after the Tohoku-oki EQ. We believe that the long-term anomaly in S1 would be observable even if we discarded the period of aftershocks. Importantly, our analysis of the long-term anomaly based on Z-value does not use the data after the Tohoku-oki EQ; hence, the results on the long-term anomaly in Z-value are intact for the effect of the Tohoku-oki EQ. Similarly, regarding the short-term anomaly, our analysis does not use the data after the Tohoku-oki EQ, either. Hence, the results in the short-term anomaly are also intact for the effect of the Tohoku-oki EQ.

\section*{Methods}
In this section, we provide details on data, pre-processing, cluster analysis, ROC curve analysis, and Z-values, which were employed to yield the results in the present paper.

\subsection*{Data}
All data in the preset study, including LFEs, conventional EQs, and volcanic tremors, were obtained from JMA catalogs (Japan Meteorological Agency, \url{https://www.jma.go.jp/jma/indexe.html}). We used 8263 LFEs that are flagged in the seismic catalog in the period from October 1, 2001 to March 31, 2016 (i.e., -3448 to 1847 days from the Tohoku-oki EQ). We consider LFE only after October 1, 2001, because detective capability of LFE by JMA considerably improved after this date. For conventional EQs, we focused on the same time period. For volcanic tremors, we considered volcanos with latitudes between $37.5\degree$N and $42\degree$N covering a wide area of northern Japan, and with more than 100 volcanic tremors. Six volcanoes met our criteria, but in volcano Zaozan ($38\degree08'37''$N, $140\degree26'24''$E), the first volcanic tremor was not recorded before 300 days from the Tohoku-oki EQ. Due to this limited time period, we excluded this volcano for analysis. As a result, we included the following five volcanos in our analysis: Esan ($41\degree48'17''$N, $141\degree09'58''$E),
Iwatesan ($39\degree51'09''$N, $141\degree00'04''$E),
Azumayama ($37\degree44'07''$N, $140\degree14'40''$E),
Adatarayama ($37\degree37'59''$N, $140\degree16'59''$E) and
Bandaisan ($37\degree36'04''$N, $140\degree04'20''$E) \cite{JMA}
with observed volcanic tremors 183, 1306, 2733, 139 and 700, respectively. The time of observed volcanic tremors was: from -1165 day to 1108 day for Esan; from -1164 day to 1107 day for Iwatesan; from -1132 day to 1094 day for Azumayama; from -1123 day to 1028 day for Adatarayama; from -1161 day to 1112 day for Bandaisan. Here, we set the origin time of the Tohoku-oki EQ to 0 day.

\subsection*{Pre-processing}
Given a time series of EQ events, the inter-time of two events is simply defined as the time elapsed between two consecutive events. Here, we further extend this definition, taking into account the proximity of two events, as follows. First,  the time of event occurrence is sorted in ascending order, $t_1 < t_2 < \ldots < t_N$, where $t_i$ denotes the time (day) of occurrence of $i$th event; $N$ sample size. Let $\Delta_{i, j}$ be the difference of time between events $i$ and $j$ ($i<j$), defined by $ \Delta_{i, j} = t_j - t_i$. Denoting  as $d_{i, j}$ the distance (km) between epicenters of events $i$ and $j$, we define the inter-time constrained by $d_{i, j}$ as follows:
\begin{eqnarray*}
 \Delta_{i, j}' (d_{min}, d_{max})=\Delta_{i, j} \mathbb{I}(d_{i, j}>d_{min}) \mathbb{I}(d_{i, j}<d_{max}),
\end{eqnarray*}
where $\mathbb{I}(a)$ is an indicator function. This function simply sets inter-time to zero if the distance between events $i$ and $j$ is less than $d_{min}$ or larger than $d_{max}$, thus degenerating inter-time in such cases.  Using this quantity, we generate a vector of inter-time  denoted by $\boldsymbol{\Delta} (d_{min}, d_{max})$, which consists of $N$ elements $\Delta_{i}$ for $i$th event as follows:
\begin{eqnarray}
  \Delta_i (d_{min}, d_{max})&=& \underset{i<j, \Delta_{i, j}' >0}{\mbox{min}} ~  \Delta_{i, j}' (d_{min}, d_{max}).
  \label{difintertime}
\end{eqnarray}
In a nutshell, $\boldsymbol{\Delta}(d_{min}, d_{max})$ represents a collection of inter-time in a specific range of distance between $d_{min}$ and $d_{max}$, where we allocate the inter-time to the pre-event, rather than the post-event.

With these notations, the dataset $\boldsymbol{\Delta}(0, \infty)$ represents a collection of inter-times without any constraint of distance. In our data, the distribution of this type of inter-time is displayed in Panel a of Fig.~\ref{FigS1}. Remarkably, it is observed that the distribution of inter-time differs between the upper part and the lower part, which are separated by the line of distance 10 km. This suggests that there are two heterogenous groups of inter-time, characterized by the inter-distance between consecutive events.

For a better understanding of the underlying mechanism of LFEs, it would be useful to analyze these groups separately. Note, however, that the upper and the lower part are closely intertwined in this dataset. To minimize such interactions, we set the cutoff point to 10 km to generate two datasets: $\boldsymbol{\Delta}(10, \infty)$, referred to as \mysingleq{Remote LFE}, and $\boldsymbol{\Delta}(0, 10)$ as \mysingleq{Neighbour LFE}
(Panel b of Fig.~\ref{FigS1}), both of these having the sample size $N$. From the definition in Eq.~(\ref{difintertime}), Remote LFE represents the inter-time of remote pairs of events (remote inter-time, with inter-distance larger than 10 km), while Neighbour LFE the inter-time of neighboring pairs (neighboring inter-time, with inter-distance smaller than 10 km).

\subsection*{Cluster analysis}
To estimate the underlying distribution for a given dataset, we fitted Gaussian mixture models \cite{mclachlan2004finite}. In this model, a distribution of data, denoted as $f(x)$, is given by summation of Gaussian distributions:
\begin{eqnarray*}
  f(x) = \sum_{k=1}^{K}w_{k} \times \mbox{Gauss}(x|\mu_{k}, \sigma_{k}^2),
\end{eqnarray*}
where $K$ is the (estimated) number of classes; $w_{k}$ is weight for the $k$th component;
$\mbox{Gauss}( \cdot | \mu, \sigma^2)$ is a Gaussian distribution for the $k$th component with mean $\mu_{k}$ and variances $\sigma_{k}^2$. Importantly, we can classify data points by allocating each data point to the most plausible component in this mixture model. Further, we manipulated the value of $K$ from one to five. To select an optimal model (the value of $K$ in the present case), the most popular criteria are the AIC (Akaike Infromation Criterion) \cite{akaike1998information} and the BIC (Bayesian Information Criterion) \cite{schwarz1978estimating}. It is well known that AIC is not consistent (i.e., the probability of identifying the true model is not necessarily one as the sample size goes to infinity), while BIC is consistent \cite{kuha2004aic}. In our dataset, the sample size is relatively large (in the order of 1000).  We accordingly used BIC for model selection in the present study.

\subsection*{ROC curve analysis}
Suppose we have $n$ pairs of data $(x_i, y_i)$ $(1\leq i \leq n)$ where $x_i$ is numerical and $y_i$ is binary. Now, let us assume that there is an unknown association between $x_i$ and $y_i$. We considered classifying these data points using only information on $\boldsymbol{x}$ and evaluate its performance, referring to the true label $\boldsymbol{y}$. Here, our classifier was a binary classifier achieved by setting a value $x_0$: if $x_i<x_0$, we allocate $x_i$ to one group, otherwise to the other group. Our question was, "to what extent this classifier can reveal the true label?" To answer this question, we drew a ROC curve by manipulating a value of $x_0$: a ROC curve represents a graphical plot of sensitivity verse (1-specificity) where sensitivity is defined as the number of true positive/(the number of true positive + the number of false negative); specificity is the number of true negative/(the number of true negative + the number of false positive). In this plot, the horizontal axis is (1-specificity) while the vertical axis is sensitivity. AUC represents the area surrounded by the ROC curve, the horizontal axis and the vertical line that passes through (1, 1). AUC takes a value between 0 and 1. A close value of AUC to one suggests a $\boldsymbol{x}$-based classifier can yield the true label $\boldsymbol{y}$.

\subsection*{Z-value}
\mysingleq{Z-value} evaluates seismicity in a target period against a background period, which is defined as
\begin{eqnarray*}
Z=(R_{bg}-R_{w}) /(S_{bg}/n_{bg} + S_w/n_w)^{1/2},
\end{eqnarray*} where $R_{bg}$ and $R_{w}$ are mean seismicity in the background period and the target period, respectively; $S_{bg}$ and $S_w$ are variances in the corresponding periods; $n_{bg}$ and $n_w$ the number of bins in the corresponding periods. In a nutshell,  Z-value denotes the normalized difference of seismicity between the background period and the target period. In the present paper, we divided the whole period of observations from Jan.1, 2006 to March 8, 2011 into bins of 14 days. We set the width of window ($T_w$) for a target period to 120 days with a moving step of 14 days. Note that a background period is defined as a set difference between the whole period and a target period. In this setting, we  counted the number of events, evaluating seismicity in each bin. Using seismicity in a bin, we evaluated means and variances in the target and the background periods, which led to the Z-value.

\bibliographystyle{naturemag}

redpajama_set_name: RedPajamaArXiv