An approximation theory for Markov chain compression | Paper Citation Record

Observation a10e7f85-2a01-4ee5-bb82-c04e176a01ed · outbound

This paper cites Inequalities for rare events in time-reversible Markov chains I.

An approximation theory for Markov chain compression Inequalities for rare events in time-reversible Markov chains I

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:04.862118Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 91a966ed-d54f-4db9-aa5e-a3e9ce7cbb1a · outbound

This paper cites Aldous and J.

An approximation theory for Markov chain compression Aldous and J

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:05.047097Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5d72fd31-d322-4e80-9885-9ea833547d3d · outbound

This paper cites Spectral methods in machine learning and new strategies for very large datasets.

An approximation theory for Markov chain compression Spectral methods in machine learning and new strategies for very large datasets

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:05.184072Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2499db87-958a-432b-be77-12c7b81a46be · outbound

This paper cites Committors, first-passage times, fluxes, Markov states, milestones, and all that.

An approximation theory for Markov chain compression Committors, first-passage times, fluxes, Markov states, milestones, and all that

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:05.320249Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd65dbb4-13f1-4972-938e-ae02b99b946d · outbound

This paper cites An Improved Approximation Algorithm for the Column Subset Selection Problem.

An approximation theory for Markov chain compression An Improved Approximation Algorithm for the Column Subset Selection Problem

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:05.504983Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc582da5-4bbe-447f-a581-612cced4566e · outbound

This paper cites Approximating IMRL distributions by exponential distributions, with appli- cations to first passage times.

An approximation theory for Markov chain compression Approximating IMRL distributions by exponential distributions, with appli- cations to first passage times

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:05.651750Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6b1decc-4490-4bdb-921b-142effabea54 · outbound

This paper cites Uncertainty in a Markov state model with missing states and rates: Application to a room temperature kinetic model obtained using high temperature molecular dynamics.

An approximation theory for Markov chain compression Uncertainty in a Markov state model with missing states and rates: Application to a room temperature kinetic model obtained using high temperature molecular dynamics

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:05.762063Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 992ae344-78a7-49a0-b63e-f031df825e0a · outbound

This paper cites Nonlinear model reduction via discrete empirical interpolation.

An approximation theory for Markov chain compression Nonlinear model reduction via discrete empirical interpolation

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:05.886950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5f5e9ce-b8bd-4feb-a3ec-b2c254e4daae · outbound

This paper cites RCHOL: Randomized Cholesky Factorization for Solving SDD Linear Systems.

An approximation theory for Markov chain compression RCHOL: Randomized Cholesky Factorization for Solving SDD Linear Systems

Reference 9

Resolution: verified exact; doi, observed 2026-08-06T22:03:14.602447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 7f9f734c-1e1d-4bae-8374-ff753dbc45e5 · outbound

This paper cites Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations.

An approximation theory for Markov chain compression Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:06.185718Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 13cc4eed-1d0c-4bf9-a68b-10fe5ca03d22 · outbound

This paper cites Markov state models of biomolecular conformational dynamics.

An approximation theory for Markov chain compression Markov state models of biomolecular conformational dynamics

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:06.306111Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2ccaca33-0688-4d4b-8172-94945f028fca · outbound

This paper cites Discrete Green’s functions.

An approximation theory for Markov chain compression Discrete Green’s functions

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:06.444804Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ae574ff-1680-4b2e-b875-8db19df8f734 · outbound

This paper cites On selecting a maximum volume sub-matrix of a matrix and related problems.

An approximation theory for Markov chain compression On selecting a maximum volume sub-matrix of a matrix and related problems

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:06.578405Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59f8a054-b6b4-46a6-84c4-c24fa61f279f · outbound

This paper cites Adaptive randomized pivoting for column subset selection, DEIM, and low-rank approximation.

An approximation theory for Markov chain compression Adaptive randomized pivoting for column subset selection, DEIM, and low-rank approximation

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:27.891357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c302c891-a47e-4914-8704-7d09e6f1775e · outbound

This paper cites Determinantal point processes in randomized nu- merical linear algebra.

An approximation theory for Markov chain compression Determinantal point processes in randomized nu- merical linear algebra

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:27.715102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ea27d0e7-473c-4e1f-9734-fc28a4fb52ec · outbound

This paper cites Optimal state-space lumping in Markov chains.

An approximation theory for Markov chain compression Optimal state-space lumping in Markov chains

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:27.523399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 83050046-8a4a-4faf-b3c4-b11299ae2d8f · outbound

This paper cites Efficient volume sampling for row/column subset selection.

An approximation theory for Markov chain compression Efficient volume sampling for row/column subset selection

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:27.390087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d5be9d44-53d8-456a-bf79-1c2e58da913f · outbound

This paper cites Adaptive sampling and fast low-rank matrix approxima- tion.

An approximation theory for Markov chain compression Adaptive sampling and fast low-rank matrix approxima- tion

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:27.164040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4540d240-fc61-4536-b10c-6912feb2b63a · outbound

This paper cites Estimating the eigenvalue error of Markov state models.

An approximation theory for Markov chain compression Estimating the eigenvalue error of Markov state models

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:26.977098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0a5905b7-d622-4d4c-9469-98fdebb27483 · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:26.755648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6d6c9e63-ad11-467a-84de-770721f06ffb · outbound

This paper cites On the Nystr¨ om method for approximating a Gram matrix for improved kernel-based learning.

An approximation theory for Markov chain compression On the Nystr¨ om method for approximating a Gram matrix for improved kernel-based learning

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:26.586832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2e5b972e-f684-45ae-b291-080a25fff50e · outbound

This paper cites Lattice QCD at the physical point: simulation and analysis details.

An approximation theory for Markov chain compression Lattice QCD at the physical point: simulation and analysis details

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:26.390381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a2a3787f-076d-4e82-97e8-58f024d52fe1 · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:26.221979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 57e5b5be-4234-4238-b1ba-2ab23d9ed5dc · outbound

This paper cites Modeling molecular kinetics with Milestoning.

An approximation theory for Markov chain compression Modeling molecular kinetics with Milestoning

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:26.037895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a3eed962-4f87-44a5-8ba7-3bed3c0e418e · outbound

This paper cites Computing time scales from reaction coordinates by mileston- ing.

An approximation theory for Markov chain compression Computing time scales from reaction coordinates by mileston- ing

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:25.875416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 19617fbc-fbe0-4a7d-a881-a1ec9d7cd319 · outbound

This paper cites RNA folding at elementary step resolution.

An approximation theory for Markov chain compression RNA folding at elementary step resolution

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:25.677157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 28c4933a-c971-4354-a931-ffe82dfcb03f · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:25.467597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6e04c5b3-f2a4-488d-8217-e63d5b0f9f1b · outbound

This paper cites Column and row subset selection using nuclear scores: algorithms and theory for Nystr\"{o}m approximation, CUR decomposition, and graph Laplacian reduction.

An approximation theory for Markov chain compression Column and row subset selection using nuclear scores: algorithms and theory for Nystr\"{o}m approximation, CUR decomposition, and graph Laplacian reduction

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:03:14.783224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ac6b6ff2-86d0-4f7e-a353-a0b537b09ca4 · outbound

This paper cites A Unified Dynamic Programming Frame- work for the Analysis of Interacting Nucleic Acid Strands: Enhanced Models, Scalability, and Speed.

An approximation theory for Markov chain compression A Unified Dynamic Programming Frame- work for the Analysis of Interacting Nucleic Acid Strands: Enhanced Models, Scalability, and Speed

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:25.274457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b5c1affa-40a7-423e-850b-b1cdb30af8ae · outbound

This paper cites NUPACK: Analysis and Design of Nucleic Acid Structures, Devices, and Systems.

An approximation theory for Markov chain compression NUPACK: Analysis and Design of Nucleic Acid Structures, Devices, and Systems

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:25.119852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a713f0d7-dd90-4952-98a2-8fea24b005d3 · outbound

This paper cites Computational methods for simulating and parameterizing nucleic acid secondary structure thermodynamics and kinetics.

An approximation theory for Markov chain compression Computational methods for simulating and parameterizing nucleic acid secondary structure thermodynamics and kinetics

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:24.975002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e287866c-5381-4bd9-8a14-2a8f5a2e088b · outbound

This paper cites Frenkel and B.

An approximation theory for Markov chain compression Frenkel and B

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:24.787457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation fb9b7213-e985-478a-8c59-b68258553e49 · outbound

This paper cites Robust and Practical Solution of Laplacian Equations by Approximate Elimination.

An approximation theory for Markov chain compression Robust and Practical Solution of Laplacian Equations by Approximate Elimination

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T22:03:08.883092Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53587b3e-c8b6-4cc5-badc-5a354132e977 · outbound

This paper cites Strong rank revealing Cholesky factorization.

An approximation theory for Markov chain compression Strong rank revealing Cholesky factorization

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:24.611233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c0d796ac-c56e-42e1-9fe3-588e20df1017 · outbound

This paper cites Optimal Column-Based Low-Rank Matrix Reconstruc- tion.

An approximation theory for Markov chain compression Optimal Column-Based Low-Rank Matrix Reconstruc- tion

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:24.433912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cc57531c-2be8-4836-b9dd-3b2d15c601dc · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 36

Resolution: malformed identifier; no resolver link, observed 2026-08-06T22:03:09.205014Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c227c4c2-5118-4c3b-9b25-d2832e53fdcf · outbound

This paper cites Optimal dimensionality reduction of multistate kinetic and Markov-state models.

An approximation theory for Markov chain compression Optimal dimensionality reduction of multistate kinetic and Markov-state models

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:24.266466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cf25c5f1-5d07-4f94-b048-3d9db984c348 · outbound

This paper cites Markov State Models: From an Art to a Science.

An approximation theory for Markov chain compression Markov State Models: From an Art to a Science

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:24.100239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d4d513b4-f224-4649-a1fe-3872a8550725 · outbound

This paper cites Jacobsen.

An approximation theory for Markov chain compression Jacobsen

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:23.967519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 48f72cc5-96f4-4aa7-8d65-8719b6cae82d · outbound

This paper cites Markov State Models of Molecular Simulations to Study Protein Folding and Dynamics.

An approximation theory for Markov chain compression Markov State Models of Molecular Simulations to Study Protein Folding and Dynamics

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:23.778279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 314b3c6d-0ac8-40ca-b834-0970ee622555 · outbound

This paper cites Rarity and Exponentiality.

An approximation theory for Markov chain compression Rarity and Exponentiality

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:23.587776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 697bf21b-face-41db-8877-52bd2ea30854 · outbound

This paper cites Correlation functions, mean first passage times, and the Kemeny constant.

An approximation theory for Markov chain compression Correlation functions, mean first passage times, and the Kemeny constant

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:23.356789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 137add2f-1d92-478a-887d-08c8babc7bbe · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:23.140779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 46952170-4540-4c65-bf14-9026405d0b73 · outbound

This paper cites Approximate Gaussian elimination for Laplacians - fast, sparse, and simple.

An approximation theory for Markov chain compression Approximate Gaussian elimination for Laplacians - fast, sparse, and simple

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:22.876792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d892db38-b72c-492f-b505-5d9137f7581f · outbound

This paper cites Leskovec and A.

An approximation theory for Markov chain compression Leskovec and A

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:22.657981Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5c53d178-db7a-46a1-b746-fd971d447d34 · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:22.470165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 886c4f8c-f411-4007-9825-2de2739035a0 · outbound

This paper cites A mathematical theory of optimal milestoning (with a detour via exact milestoning).

An approximation theory for Markov chain compression A mathematical theory of optimal milestoning (with a detour via exact milestoning)

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:22.289909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c48c2128-8b88-4b41-bc6c-1193b4f0859c · outbound

This paper cites Integrated variational approach to conformational dynamics: a robust strategy for identifying eigenfunctions of dynamical operators.

An approximation theory for Markov chain compression Integrated variational approach to conformational dynamics: a robust strategy for identifying eigenfunctions of dynamical operators

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:22.084537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 57cd2216-9354-449e-aa31-ccaa2058784f · outbound

This paper cites CUR matrix decompositions for improved data analysis.

An approximation theory for Markov chain compression CUR matrix decompositions for improved data analysis

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:21.946993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 734cac52-6b4b-41c7-b93c-1387cff71315 · outbound

This paper cites Variational cross-validation of slow dynamical modes in molecular kinetics.

An approximation theory for Markov chain compression Variational cross-validation of slow dynamical modes in molecular kinetics

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:21.742644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 77961ee2-7f48-451e-8dff-8474c4e54340 · outbound

This paper cites Hutch++: Optimal Stochastic Trace Estimation.

An approximation theory for Markov chain compression Hutch++: Optimal Stochastic Trace Estimation

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:21.601201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8fd1e3c0-df81-498c-bd28-9adcfe63df9a · outbound

This paper cites Everything you wanted to know about Markov State Models but were afraid to ask.

An approximation theory for Markov chain compression Everything you wanted to know about Markov State Models but were afraid to ask

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:21.339951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b9f2ac5b-a946-48a5-8b0f-da3264db5826 · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 53

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:21.087695Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cd3f87f1-5bd6-4882-a476-5479701ab47b · outbound

This paper cites Validation of Markov state models using Shannon’s entropy.

An approximation theory for Markov chain compression Validation of Markov state models using Shannon’s entropy

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:20.783124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 17601ef2-f994-44f6-b0ad-5850d2fa539c · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 55

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:20.461408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 73db206b-488c-4a02-985b-87966d846b04 · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 56

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:20.230650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cf8b8f37-31e7-49a4-8358-1bd9f9ff0d85 · outbound

This paper cites Multi-Scale attributed node embedding.

An approximation theory for Markov chain compression Multi-Scale attributed node embedding

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:20.069494Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 78f1ebd8-2f91-4c15-95c4-aea60a3f89ba · outbound

This paper cites Armadillo: a template-based C++ library for linear algebra.

An approximation theory for Markov chain compression Armadillo: a template-based C++ library for linear algebra

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:19.981072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6c9f4b02-72f2-4745-ac28-4822e05ead0b · outbound

This paper cites Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation.

An approximation theory for Markov chain compression Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:19.900013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 390b0aeb-dcab-4f83-b464-71d1a768d984 · outbound

This paper cites On the approximation quality of Markov state models.

An approximation theory for Markov chain compression On the approximation quality of Markov state models

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:19.806525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6b292366-414e-4edc-be66-ae870f6f3f3d · outbound

This paper cites Stochastic simulation of the kinetics of multiple interacting nucleic acid strands.

An approximation theory for Markov chain compression Stochastic simulation of the kinetics of multiple interacting nucleic acid strands

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:19.697193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5050dd6c-c52d-40f5-b046-892710270fd8 · outbound

This paper cites Uber eine Klasse von Mittelbildungen mit Anwendungen auf die Determinanten- theorie.

An approximation theory for Markov chain compression Uber eine Klasse von Mittelbildungen mit Anwendungen auf die Determinanten- theorie

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:19.593316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0e8c935b-8d1b-44e1-b01d-c780a4693cf7 · outbound

This paper cites Markov state models based on milestoning.

An approximation theory for Markov chain compression Markov state models based on milestoning

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:19.442536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ba48a197-d802-4a67-a672-aaf727af7f4a · outbound

This paper cites Improvements in Markov State Model Construction Reveal Many Non-Native Interactions in the Folding of NTL9.

An approximation theory for Markov chain compression Improvements in Markov State Model Construction Reveal Many Non-Native Interactions in the Folding of NTL9

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:19.315860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a0cd784f-7977-4390-bb76-aafe593a688e · outbound

This paper cites Column subset selection is NP-complete.

An approximation theory for Markov chain compression Column subset selection is NP-complete

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:19.223182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 52437a24-b6f3-43b6-94bc-64984d2b785d · outbound

This paper cites Markov state models provide insights into dynamic modulation of protein function.

An approximation theory for Markov chain compression Markov state models provide insights into dynamic modulation of protein function

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:19.083849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2cf43ac0-ff45-4bbf-99f1-3d0bc8e35eb5 · outbound

This paper cites A family of face products of matrices and its properties.

An approximation theory for Markov chain compression A family of face products of matrices and its properties

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:18.935911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 663dbef3-e65f-4822-833c-56927a170f21 · outbound

This paper cites Randomly Pivoted Partial Cholesky: Random How?.

An approximation theory for Markov chain compression Randomly Pivoted Partial Cholesky: Random How?

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:18.833153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c8553f30-8a69-4bfd-af16-a65632f1cc6f · outbound

This paper cites Stochastic simulation in systems biology.

An approximation theory for Markov chain compression Stochastic simulation in systems biology

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:18.658292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8bdc4243-c92b-46bd-9f7c-58676e4e08bf · outbound

This paper cites Galerkin approximation of dynamical quantities using trajectory data.

An approximation theory for Markov chain compression Galerkin approximation of dynamical quantities using trajectory data

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:18.470356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c3ae34ad-f207-4647-8b52-0660015e1755 · outbound

This paper cites Simple O(m log n) time Markov chain lumping.

An approximation theory for Markov chain compression Simple O(m log n) time Markov chain lumping

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:18.326902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0bea6325-c0e0-452c-994f-e678dfa58896 · outbound

This paper cites On the assumptions underlying milestoning.

An approximation theory for Markov chain compression On the assumptions underlying milestoning

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:18.111475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 121def1c-7d7c-47db-821e-1edc074d814f · outbound

This paper cites Error bounds for dynamical spectral estimation.

An approximation theory for Markov chain compression Error bounds for dynamical spectral estimation

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:17.943361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 17e9bbb5-06fb-451d-af7c-0684855838a6 · outbound

This paper cites Using the Nystr¨ om method to speed up kernel machines.

An approximation theory for Markov chain compression Using the Nystr¨ om method to speed up kernel machines

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:17.791180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2b905d0a-5d61-41b3-bdff-7df9acd6a5a7 · outbound

This paper cites Hierarchical Nystr¨ om methods for constructing Markov state models for conformational dynamics.

An approximation theory for Markov chain compression Hierarchical Nystr¨ om methods for constructing Markov state models for conformational dynamics

Reference 75

Resolution: verified exact; doi, observed 2026-08-06T22:03:14.322911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 81dc9855-996e-4747-8c79-c8bc5c08e158 · outbound

This paper cites Fast and accurate interpolative decompositions for general, sparse, and structured tensors.

An approximation theory for Markov chain compression Fast and accurate interpolative decompositions for general, sparse, and structured tensors

Reference 76

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:17.606482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f17dd0a8-54ce-4325-8397-9a4906b03425 · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 77

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:17.470378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ef818bab-bef0-418a-8723-e25bd989f0fd · outbound

This paper cites the first return to j after hitting any one of I.

An approximation theory for Markov chain compression the first return to j after hitting any one of I

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:17.343191Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 225616b8-1757-4eb6-af34-15ebe816a84f · outbound

This paper cites More precisely, − ˆR−1 i,i = E(τ I \{i} | X0 = i).

An approximation theory for Markov chain compression More precisely, − ˆR−1 i,i = E(τ I \{i} | X0 = i)

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:17.126162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 1ea7f8f3-adf9-411a-bc9e-5d9b069fbfa7 · outbound

This paper cites More precisely, − ˆRi,j/ ˆRi,i = P(Xτ I \{i} = j | X0 = i).

An approximation theory for Markov chain compression More precisely, − ˆRi,j/ ˆRi,i = P(Xτ I \{i} = j | X0 = i)

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:16.992685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8731a07f-0c26-48c1-a662-94b5ec98a969 · outbound

This paper cites More precisely, ˆπi = P(Xτ I = i).

An approximation theory for Markov chain compression More precisely, ˆπi = P(Xτ I = i)

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:16.834773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 10503313-c44b-4f65-8cc5-eff9ab6f5435 · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 82

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:16.693215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 156ea42c-f61d-4677-92bd-60d6f70bdf55 · outbound

This paper cites Given this approach, the probability 50 of the chain not having reached I \{i} at time t is: P(τI \{i} > t| X0 = i) = lim β→0 lim α→∞ Ii,: exp (R − β1π⊤ − αI:,I \{i}I⊤ :,I \{i})t.

An approximation theory for Markov chain compression Given this approach, the probability 50 of the chain not having reached I \{i} at time t is: P(τI \{i} > t| X0 = i) = lim β→0 lim α→∞ Ii,: exp (R − β1π⊤ − αI:,I \{i}I⊤ :,I \{i})t

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:16.515908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6d40481e-59c1-49e0-9242-6bca43a3a6af · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 84

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:16.370690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 05219ef3-9d90-4d7f-ad18-03365d79fcb6 · outbound

This paper cites The rates between marked states ( i, i) → (i′, i′) are inherited from the rates i → i′ in the original chain M.

An approximation theory for Markov chain compression The rates between marked states ( i, i) → (i′, i′) are inherited from the rates i → i′ in the original chain M

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:16.213858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c7a05a3e-716f-45cb-9b78-4777f9ce624a · outbound

This paper cites The rates between unmarked states (i, j) → (i′, j′) are inherited from the rates j → j′ in the original chain M when i = i′, otherwise they are zero.

An approximation theory for Markov chain compression The rates between unmarked states (i, j) → (i′, j′) are inherited from the rates j → j′ in the original chain M when i = i′, otherwise they are zero

Reference 86

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:16.005937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 21b5241f-e950-48c2-8303-1816c7c86dff · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 87

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:15.850246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b58dee61-386a-4c77-bae2-96a7736c67f6 · outbound

This paper cites Any unmarked state ( i, j) is allowed to transition to any marked state ( k, k), with a rate inherited from the rate j → k in the original chain M.

An approximation theory for Markov chain compression Any unmarked state ( i, j) is allowed to transition to any marked state ( k, k), with a rate inherited from the rate j → k in the original chain M

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:15.658737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b15f4b05-cdf3-46dc-9b7c-cb370019ce46 · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 89

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:15.455180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 43194737-6001-4a9d-94ca-b30ca69fd7b9 · outbound

This paper cites an unresolved cited work.

An approximation theory for Markov chain compression Unresolved cited work

Reference 90

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:03:15.241550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f51b95f9-de98-492e-8b12-20bf823b2ac1 · outbound

This paper cites killed Laplace equation.

An approximation theory for Markov chain compression killed Laplace equation

Reference 91

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:03:14.995087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Coverage vector

Reference resolution

Outbound references

Pith citing papers