Percolation and Threshold-like Behavior in Multiple Sclerosis Progression

Fuente: arXiv

Enregistré dans:

Détails bibliographiques
Auteurs principaux:	Mirkov, Nikola, Radivojević, Dušan S., Maletić, Slobodan
Format:	Preprint
Publié:	2026
Sujets:	Disordered Systems and Neural Networks
Accès en ligne:	Acceder al recurso
Tags:	Ajouter un tag Pas de tags, Soyez le premier à ajouter un tag!

_version_	1866910016542343168
author	Mirkov, Nikola Radivojević, Dušan S. Maletić, Slobodan
author_facet	Mirkov, Nikola Radivojević, Dušan S. Maletić, Slobodan
contents	In this study we investigate the Percolation Hypothesis for Multiple Sclerosis Progression. The methodology relies on cross-reference analysis centered around a question: What is the evidence for a Percolation/phase-transition hypothesis in Multiple Sclerosis (MS), especially the idea that the RRMS dynamic balance can abruptly break akin to crossing a percolation threshold into SPMS? We identify theoretical models invoking percolation/critical thresholds, network/connectome studies assessing percolation robustness or threshold-like behavior, clinical markers showing thresholds or early-warning signals, and counter-evidence arguing for gradual/continuum transitions.
format	Preprint
id	arxiv_https___arxiv_org_abs_2602_08576
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	Percolation and Threshold-like Behavior in Multiple Sclerosis Progression Mirkov, Nikola Radivojević, Dušan S. Maletić, Slobodan Disordered Systems and Neural Networks In this study we investigate the Percolation Hypothesis for Multiple Sclerosis Progression. The methodology relies on cross-reference analysis centered around a question: What is the evidence for a Percolation/phase-transition hypothesis in Multiple Sclerosis (MS), especially the idea that the RRMS dynamic balance can abruptly break akin to crossing a percolation threshold into SPMS? We identify theoretical models invoking percolation/critical thresholds, network/connectome studies assessing percolation robustness or threshold-like behavior, clinical markers showing thresholds or early-warning signals, and counter-evidence arguing for gradual/continuum transitions.
title	Percolation and Threshold-like Behavior in Multiple Sclerosis Progression
topic	Disordered Systems and Neural Networks
url	https://arxiv.org/abs/2602.08576

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
VUFIND_SESSION	"483cdd3c7beb746b0e55297779baedcc"
language	"fr"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790979582.8613 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "483cdd3c7beb746b0e55297779baedcc" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1762}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; VUFIND_SESSION=483cdd3c7beb746b0e55297779baedcc; language=fr"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"45233"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2602_08576/Details """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2602_08576/Details"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790979582.8568
REQUEST_TIME	1790979582

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
VUFIND_SESSION	"483cdd3c7beb746b0e55297779baedcc"
language	"fr"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790979582.8613 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "483cdd3c7beb746b0e55297779baedcc" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1762}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; VUFIND_SESSION=483cdd3c7beb746b0e55297779baedcc; language=fr"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"45233"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2602_08576/Details """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2602_08576/Details"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790979582.8568
REQUEST_TIME	1790979582

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Documents similaires

Environment & details:

Environment & details: