The Depth Poset under Transpositions in the Filter

Fuente: arXiv

Enregistré dans:

Détails bibliographiques
Auteurs principaux:	Edelsbrunner, Herbert, Lipiński, Michał, Mrozek, Marian, Soriano-Trigueros, Manuel, Zimin, Fedor
Format:	Preprint
Publié:	2025
Sujets:	Algebraic Topology 55N31
Accès en ligne:	Acceder al recurso
Tags:	Ajouter un tag Pas de tags, Soyez le premier à ajouter un tag!

Documents similaires

Conley-Morse persistence barcode: a homological signature of combinatorial bifurcations
par: Dey, Tamal K., et autres
Publié: (2025)

Topological simplification guided by forbidden regions
par: Leśkiewicz, Jakub, et autres
Publié: (2026)

The poset of cancellations induced by gradient dynamics in a filtered Lefschetz complex
par: Edelsbrunner, Herbert, et autres
Publié: (2023)

The Mid-sphere Cousin of the Medial Axis Transform
par: Edelsbrunner, Herbert, et autres
Publié: (2025)

Chromatic Alpha Complexes
par: di Montesano, Sebastiano Cultrera, et autres
Publié: (2022)

Additive Partial Matchings Induced by Persistence Maps
par: Gonzalez-Diaz, R., et autres
Publié: (2020)

Persistent Cost of Lipschitz Maps
par: Gozzi, Francisco J., et autres
Publié: (2025)

Through the Grapevine: Vineyard Distance as a Measure of Topological Dissimilarity
par: Arulandu, Alvan, et autres
Publié: (2025)

Identifying cobordisms using kernel persistence
par: Bleile, Yossi Bokor, et autres
Publié: (2025)

Notes on abelianity of categories of finitely encoded persistence modules
par: Waas, Lukas
Publié: (2024)

Topological optimization with birth and death cochains
par: Weighill, Thomas, et autres
Publié: (2026)

Algebraic and Topological Persistence
par: Melodia, Luciano
Publié: (2024)

Topological and metric properties of spaces of generalized persistence diagrams
par: Bubenik, Peter, et autres
Publié: (2022)

Notes on Pointwise Finite-Dimensional $2$-Parameter Persistence Modules
par: Li, Wenwen, et autres
Publié: (2024)

Persistent Combinatorial Model of the Restricted Second Configuration Space of Metric Star Graphs
par: Li, Wenwen, et autres
Publié: (2026)

Interleaving Mayer-Vietoris spectral sequences
par: Torras, Álvaro, et autres
Publié: (2021)

Decomposition of Persistent Homology and Spectral Sequences
par: Yang, Peiqi, et autres
Publié: (2024)

Dowker's theorem for higher-order relations
par: de Silva, Vin, et autres
Publié: (2025)

Ephemeral persistence features and the stability of filtered chain complexes
par: Mémoli, Facundo, et autres
Publié: (2022)

Distributed Persistent Homology for 2D Alpha Complexes
par: Jensen, Freya, et autres
Publié: (2024)

Discrete Microlocal Morse Theory
par: Brown, Adam, et autres
Publié: (2022)

Persistent magnitude homology on finite metric space
par: Bi, Wanying, et autres
Publié: (2026)

The Walk-Length Filtration for Persistent Homology on Weighted Directed Graphs
par: Muñoz, David E., et autres
Publié: (2025)

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent
par: Carrière, Mathieu, et autres
Publié: (2024)

Topological feature selection for time series data
par: Bubenik, Peter, et autres
Publié: (2023)

Improving Mapper's Robustness by Varying Resolution According to Lens-Space Density
par: Ruscitti, Kaleb D., et autres
Publié: (2024)

Stabilizing decomposition of multiparameter persistence modules
par: Bjerkevik, Håvard Bakke
Publié: (2023)

Super-Polynomial Growth of the Generalized Persistence Diagram
par: Kim, Donghan, et autres
Publié: (2024)

An axiomatic treatment of Persistent Homology
par: Ura, Sergio Tsuyoshi, et autres
Publié: (2024)

Critical edges in Rips complexes and persistence
par: Goričan, Peter, et autres
Publié: (2023)

Interval-sphere model structures
par: Hess, Kathryn, et autres
Publié: (2025)

Persistent Local Systems of Periodic Spaces
par: Onus, Adam, et autres
Publié: (2025)

Cell decompositions of persistent minimal models
par: Hess, Kathryn, et autres
Publié: (2023)

Persistent cohomology operations and Gromov-Hausdorff estimates
par: Medina-Mardones, Anibal M., et autres
Publié: (2025)

Computing 1-Periodic Persistent Homology with Finite Windows
par: Onus, Adam, et autres
Publié: (2023)

It's All About Covers: Persistent Homology of Cover Refinements
par: Leitão, António
Publié: (2026)

Inferring Ambient Cycles of Point Samples on Manifolds with Universal Coverings
par: Yim, Ka Man
Publié: (2025)

The Dual Degree Cech Bifiltration
par: Brun, Morten
Publié: (2024)

Koszul complexes and relative homological algebra of functors over posets
par: Chacholski, Wojciech, et autres
Publié: (2022)

Harmonic Persistent Homology
par: Basu, Saugata, et autres
Publié: (2021)

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"
language	"fr"
VUFIND_SESSION	"b0c4f6f4315bcd26fc070b3ab940b239"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790808257.4303 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "b0c4f6f4315bcd26fc070b3ab940b239" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

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; language=fr; VUFIND_SESSION=b0c4f6f4315bcd26fc070b3ab940b239"
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	"216.73.216.147"
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	"64433"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2511_21961/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2511_21961/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790808257.4256
REQUEST_TIME	1790808257

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler