Pith. sign in

Paper Citation Record · LEDGER

Sum of Squares Submodularity

As of 16 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 1 inbound Pith citation observation for arXiv:2510.24550.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2510.24550 v2

Coverage vector

measured 59 of 59 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:50:36.904130Z

measured 60 of 60 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-20T17:20:29.589792Z

measured 1 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

59 of 59 outbound references displayed

  • verified exact1
  • verified fuzzy50
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 67a2cf31-4244-49ce-87ff-91f4dbe2b03d · outbound

This paper cites DC decomposition of nonconvex polynomials with algebraic techniques.

Sum of Squares Submodularity DC decomposition of nonconvex polynomials with algebraic techniques

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.584910Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.698659Z digest=sha256:d5d05dd5cc5e31cc4cf4ebebbb0ea44cbac38ee68104c74ab998758296ff9065

Observation 4e301bda-eeeb-46c2-84a9-6111e0bb8544 · outbound

This paper cites A complete characterization of the gap between convexity and sos-convexity.

Sum of Squares Submodularity A complete characterization of the gap between convexity and sos-convexity

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.573721Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.703537Z digest=sha256:9f1058e5a14d8d072c92c98e636d24423e88a8904522c5f4a055186f38b73f6d

Observation 6e27fa3e-f142-4dbe-ba63-cd0d9144f078 · outbound

This paper cites NP -hardness of deciding convexity of quartic polynomials and related problems.

Sum of Squares Submodularity NP -hardness of deciding convexity of quartic polynomials and related problems

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.562710Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.707298Z digest=sha256:cc47f918191eafb8ba4bc7057805c0443152dc3fdabdddb76d056e8eacff0a15

Observation da87a7e9-678d-41c1-8c5f-d3c0ef8477c8 · outbound

This paper cites Submodularity in conic quadratic mixed 0--1 optimization.

Sum of Squares Submodularity Submodularity in conic quadratic mixed 0--1 optimization

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.551563Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.711662Z digest=sha256:68e23797212046e12c8f9eb6774d550e3b7f3624a1c5e9b0e1e287ff2644c8cf

Observation cf28e3e4-0361-47f5-a5c3-9c12ba1071f9 · outbound

This paper cites Submodular functions: from discrete to continuous domains.

Sum of Squares Submodularity Submodular functions: from discrete to continuous domains

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.539875Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.715460Z digest=sha256:6e9902485b89664e9147c7687b04da1b5b1e3417b88a905c64df78dedbac5149

Observation 2173671a-27f6-4c50-bd64-57379f0358e1 · outbound

This paper cites Learning with submodular functions: A convex optimization perspective.

Sum of Squares Submodularity Learning with submodular functions: A convex optimization perspective

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.528536Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.718918Z digest=sha256:148f802c65a7605b67347d35ccf57c1f343a708e22f981c3060a96ef98653986

Observation 3addf231-14e2-4919-ab04-f419b36fa971 · outbound

This paper cites Learning submodular functions.

Sum of Squares Submodularity Learning submodular functions

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.516441Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.723043Z digest=sha256:f6c489229dc60a236daf431742ca440a959858af15c0ccdf0167e6205468f6f1

Observation ab3cb0b6-6a4e-4a69-852e-29ede35c40d3 · outbound

This paper cites Submodular functions: Learnability, structure, and optimization.

Sum of Squares Submodularity Submodular functions: Learnability, structure, and optimization

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.504236Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.726505Z digest=sha256:998b2f5c077f06f26db5f4b4cdada80906d9411817d97e88c0b02994d20e02c5

Observation 85c82a29-32de-4fff-b519-d0fcb1a3646d · outbound

This paper cites Guarantees for greedy maximization of non-submodular functions with applications.

Sum of Squares Submodularity Guarantees for greedy maximization of non-submodular functions with applications

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.493629Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.730117Z digest=sha256:54835e7a3ffaee961d8a6fd58ef56ca642d253592e28bb147577df02b09090a0

Observation f98f231e-c29c-4775-8d59-89d8d0a6d118 · outbound

This paper cites Continuous Submodular Function Maximization.

Sum of Squares Submodularity Continuous Submodular Function Maximization

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.733820Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.733820Z digest=sha256:637a4e56ad9bafff722d938d8bd1cc44dca6ea136d38eb71d6e4dc4fa0098cef

Observation f9ac604b-f6d9-49ba-95d2-f4ab3c94d237 · outbound

This paper cites Maximizing a supermodular pseudoboolean function: A polynomial algorithm for supermodular cubic functions.

Sum of Squares Submodularity Maximizing a supermodular pseudoboolean function: A polynomial algorithm for supermodular cubic functions

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.481144Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.738113Z digest=sha256:4c17c5796918d3e4d50597d680aa94cff0b105877b88f019de3a21e631e02eca

Observation 2f38a1b3-e5de-4eeb-b647-e0abf2c7d355 · outbound

This paper cites Submodularity In Machine Learning and Artificial Intelligence.

Sum of Squares Submodularity Submodularity In Machine Learning and Artificial Intelligence

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.741798Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.741798Z digest=sha256:14a5d129720b516b512c6f2db6dccf24aee63969298cb849c9881c5759675904

Observation 5ba048c5-dac0-404c-a1c0-5a46caecb269 · outbound

This paper cites Semidefinite O ptimization and C onvex A lgebraic G eometry.

Sum of Squares Submodularity Semidefinite O ptimization and C onvex A lgebraic G eometry

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.469076Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.745041Z digest=sha256:e79775d5269205e651bdd72dcabffcc2f9957216923476fc78f9325d905e95f0

Observation 8243abff-4279-4a02-bc6f-8a3c316019c7 · outbound

This paper cites Undominated DC decompositions of quadratic functions and applications to branch-and-bound approaches.

Sum of Squares Submodularity Undominated DC decompositions of quadratic functions and applications to branch-and-bound approaches

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.456844Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.748227Z digest=sha256:f5891e2b06dd0dc94cdeee69aae9ae5d394f7ddb8a79c18a1ca975a270591a71

Observation 5af7183a-16b7-4c83-ba70-77b7aeda26ad · outbound

This paper cites Convex O ptimization.

Sum of Squares Submodularity Convex O ptimization

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.445714Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.751265Z digest=sha256:4013cb8205f047ffdaa954fb703e5c742ae6fd53013a28626da5e979ecb5f754

Observation c3a65b5e-f47f-4218-bea1-94c72a86b26c · outbound

This paper cites Decomposition Polyhedra of Piecewise Linear Functions.

Sum of Squares Submodularity Decomposition Polyhedra of Piecewise Linear Functions

Reference 16

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.754438Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.754438Z digest=sha256:65105abd032598ac8d2bb9a1c8c0aa7f7003b41913db9166d6f7a6e487c517ed

Observation d305c51f-a8ef-4c6f-ba8e-f09589e2b577 · outbound

This paper cites On the Semidefinite Representability of Continuous Quadratic Submodular Minimization With Applications to Moment Problems.

Sum of Squares Submodularity On the Semidefinite Representability of Continuous Quadratic Submodular Minimization With Applications to Moment Problems

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.758276Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.758276Z digest=sha256:b2819c56dfd90ea15804e5881a81a1005b078a21d18e10588244404e377dbbd3

Observation 3f4a6ff3-9a9f-470b-a701-8fe1e014e3a9 · outbound

This paper cites Recognition problems for special classes of polynomials in 0--1 variables.

Sum of Squares Submodularity Recognition problems for special classes of polynomials in 0--1 variables

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.434783Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.762052Z digest=sha256:b42b595004d7387575952efcd40cf5e6bcd5b310b5363084a1e30b368537cac0

Observation a917c30c-0540-4d5f-9572-b14b8404810a · outbound

This paper cites Boolean F unctions: T heory, A lgorithms, and A pplications.

Sum of Squares Submodularity Boolean F unctions: T heory, A lgorithms, and A pplications

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.423603Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.765701Z digest=sha256:19b4693e4087ef5113890670a0fad177755a5426aa3a29616fdc9af30f8a6b09

Observation 117ef802-76ae-4ce7-8673-f051e06174c2 · outbound

This paper cites Shape-constrained regression using sum of squares polynomials.

Sum of Squares Submodularity Shape-constrained regression using sum of squares polynomials

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.411615Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.769311Z digest=sha256:13b36e5df17feac76945ae331b13846728ab45bec932ecc87787510852adc3fc

Observation acebe48a-2bae-460d-810d-48e5e1ee31d7 · outbound

This paper cites Approximate submodularity and its applications: Subset selection, sparse approximation and dictionary selection.

Sum of Squares Submodularity Approximate submodularity and its applications: Subset selection, sparse approximation and dictionary selection

Reference 21

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.772714Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.772714Z digest=sha256:f5fcf1388e7aa9ba6c853423c7f3fdcae3801e14be40bc7887859cca16d0ee6e

Observation f4bddf59-3190-4065-b2f5-f9b4f9f375f2 · outbound

This paper cites Neural estimation of submodular functions with applications to differentiable subset selection.

Sum of Squares Submodularity Neural estimation of submodular functions with applications to differentiable subset selection

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.394521Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.776136Z digest=sha256:92589466a9edc412c074a9e4fab9c55d03ae9534aede05a0da1e8553590cdcd9

Observation cc4901a6-18fe-43a3-ab56-979e39fbb83b · outbound

This paper cites Deep submodular functions: Definitions and learning.

Sum of Squares Submodularity Deep submodular functions: Definitions and learning

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.385543Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.779558Z digest=sha256:95e3cb556f691f72f1d84226c7f8a8a2beb5633a7fa96c04990cd4a50be73e6d

Observation e98b4fa8-354f-4950-9d6d-27f5142a3930 · outbound

This paper cites Submodular functions, matroids, and certain polyhedra.

Sum of Squares Submodularity Submodular functions, matroids, and certain polyhedra

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.375539Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.783156Z digest=sha256:b5f0806f27f8c03b904c15849de4a7b23c649026ada68182882f9090f47c84ae

Observation d00a3f1d-c65f-4c8f-935f-87872ccdee74 · outbound

This paper cites Difference of submodular minimization via DC programming.

Sum of Squares Submodularity Difference of submodular minimization via DC programming

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.364552Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.786630Z digest=sha256:6fcb2f3cee4e09f2bdc9ff0e01fabee2837a0a701f9d4e1f78f0faef6cd53000

Observation 8369e0e9-940e-4dd5-8507-1add430d1db2 · outbound

This paper cites Sparse sum-of-squares certificates on finite abelian groups.

Sum of Squares Submodularity Sparse sum-of-squares certificates on finite abelian groups

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.354249Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.790361Z digest=sha256:e4b8d92c648bae34e41268c517b06948c8aea84410d57157f2d6fbb56050a6b7

Observation 096bb0ac-bd73-4a49-a341-78f4376fe570 · outbound

This paper cites Optimal bounds on approximation of submodular and xos functions by juntas.

Sum of Squares Submodularity Optimal bounds on approximation of submodular and xos functions by juntas

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.343433Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.793956Z digest=sha256:84b748a27ce26a10caefb8f78044be0d636098932ee22a8f9e9ab3c8cd7b24ed

Observation f276d24f-1470-4f30-9574-a2b1aac0c91b · outbound

This paper cites Representation, approximation and learning of submodular functions using low-rank decision trees.

Sum of Squares Submodularity Representation, approximation and learning of submodular functions using low-rank decision trees

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.331082Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.797724Z digest=sha256:e2ec6186196bb7c206d1b86cc8c60f42913c9a9f62249aaf1482b963178d097a

Observation dfbf3625-794c-4b8e-a602-7849f4780abb · outbound

This paper cites Submodular functions in graph theory.

Sum of Squares Submodularity Submodular functions in graph theory

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.319253Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.801047Z digest=sha256:e3d95cefb5e4e45c4411046349796462ff4aaf47a83498cc428522aa624b2d39

Observation 67a419c5-a7d3-4c2e-817f-ac499f9c433b · outbound

This paper cites Submodular F unctions and O ptimization , volume 58.

Sum of Squares Submodularity Submodular F unctions and O ptimization , volume 58

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.307560Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.804835Z digest=sha256:4ef2e2e03a606d89ba8e80017f05a84a4c0b35b0f8ebf7329852f2c61aa5b234

Observation a8ab76d3-b3e0-45a2-87e4-12816663a5cc · outbound

This paper cites On the supermodular knapsack problem.

Sum of Squares Submodularity On the supermodular knapsack problem

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.296838Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.807760Z digest=sha256:939bf171a23ff6369c8040f2dd960e78c62d154fa81fedddedaa7da803205bb7

Observation 2f5be08c-c125-4523-892a-84ff54bfbf91 · outbound

This paper cites Approximating submodular functions everywhere.

Sum of Squares Submodularity Approximating submodular functions everywhere

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.285899Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.811230Z digest=sha256:5668a3306dff83d6ab780d29b13a6af0c566a6f1818c702603f5c01d1041222d

Observation 452272b9-0ae1-44ce-ae0f-12e71dc040d0 · outbound

This paper cites PEP it: computer-assisted worst-case analyses of first-order optimization methods in python.

Sum of Squares Submodularity PEP it: computer-assisted worst-case analyses of first-order optimization methods in python

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.273897Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.814805Z digest=sha256:9819342221f4c0d02a25385ad4962a06d2f997408c89570ad53f7d0f77999baa

Observation 8507be87-9b75-4640-a898-6a051c28fbeb · outbound

This paper cites Equivalent representations of set functions.

Sum of Squares Submodularity Equivalent representations of set functions

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.262712Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.818265Z digest=sha256:bdc5effe64f428a76facefc5ebe02621f0f3a3d74a6ce89fbe219f00bae7022a

Observation 1474a413-99d9-49fc-959c-968402d709bc · outbound

This paper cites Semidefinite representation of convex sets.

Sum of Squares Submodularity Semidefinite representation of convex sets

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.251588Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.821239Z digest=sha256:ba8cfd65ade25beb0b2698cfbfe7859c58c2a7bcddb1feb8c8cd8deccb4837c5

Observation 43e06e57-1cd8-4b7c-8dbe-13c9ca5cc335 · outbound

This paper cites Maximization of approximately submodular functions.

Sum of Squares Submodularity Maximization of approximately submodular functions

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.240548Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.824836Z digest=sha256:5206f318179657036b6b0a9c83a93ea1c3a28289c57bf0a5969a9e4a11966a1e

Observation 24ac79ac-af82-424b-be73-0c92395ba9cb · outbound

This paper cites Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications.

Sum of Squares Submodularity Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications

Reference 37

Resolution
verified exact
local_arxiv, observed 2026-08-15T15:50:36.952171Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.828440Z digest=sha256:e1add2e9fac34c7bf7f406b952d947b8622706d6fda0534747384123193edb5d

Observation 687ebf45-243d-4ced-bf4b-15867895c9b0 · outbound

This paper cites Submodularity beyond submodular energies: coupling edges in graph cuts.

Sum of Squares Submodularity Submodularity beyond submodular energies: coupling edges in graph cuts

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.229907Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.832308Z digest=sha256:b510899f467b53d856fb1289a1ab808ce0252eefa81d3b64665f4bc52140dbef

Observation 929c236f-0399-444f-a440-55a86b70b03b · outbound

This paper cites Near-optimal sensor placements in gaussian processes: Theory, efficient algorithms and empirical studies.

Sum of Squares Submodularity Near-optimal sensor placements in gaussian processes: Theory, efficient algorithms and empirical studies

Reference 39

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.836305Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.836305Z digest=sha256:f8184d209e052bb36bbdfb36a84084823e4c038174c4ca4fd91cc465c2f4e5f0

Observation baf9fcaf-5a1e-48c9-99e3-ecac918491f5 · outbound

This paper cites Lower bound for the number of iterations in semidefinite hierarchies for the cut polytope.

Sum of Squares Submodularity Lower bound for the number of iterations in semidefinite hierarchies for the cut polytope

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.210036Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.840058Z digest=sha256:45129f4680bea21110dc22b69ec98fd7367fd4a209ad86c308ea0fd187104a2a

Observation e674f7a5-271a-449b-8ea6-0d75121d21ac · outbound

This paper cites Sums of squares, moment matrices and optimization over polynomials.

Sum of Squares Submodularity Sums of squares, moment matrices and optimization over polynomials

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.199005Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.843880Z digest=sha256:278b7d3cd9186cffd3434abe1364e988b1041e65db911fb9ec087de990ecc45c

Observation 54368282-315d-4dc0-95dc-20b04713aadf · outbound

This paper cites Learning Mixtures of Submodular Shells with Application to Document Summarization.

Sum of Squares Submodularity Learning Mixtures of Submodular Shells with Application to Document Summarization

Reference 42

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.847568Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.847568Z digest=sha256:0abd8a5f37ba19a7ffaae0aae1e496cc4104e4e680dba6286d0f91e28fda7daf

Observation f348769c-4603-4841-9d8f-1d5f913827d2 · outbound

This paper cites A submodular-supermodular procedure with applications to discriminative structure learning.

Sum of Squares Submodularity A submodular-supermodular procedure with applications to discriminative structure learning

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.188004Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.851886Z digest=sha256:fc0b8748780e6a3210487a8b6afa79fb8ed4c7bb26382b82622f8c682b6891d5

Observation cd49fc29-ecb1-4396-8c11-8068061ef436 · outbound

This paper cites Submodular F unctions and E lectrical N etworks , volume 54.

Sum of Squares Submodularity Submodular F unctions and E lectrical N etworks , volume 54

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.177613Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.855785Z digest=sha256:f9ed9a70102652d744e996524a3f3803c13b51767d115bead6b8a45cb1211c9a

Observation 1cf7aaf5-ecc6-4481-bcc8-50a74ebc5704 · outbound

This paper cites An analysis of approximations for maximizing submodular set functions—i.

Sum of Squares Submodularity An analysis of approximations for maximizing submodular set functions—i

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.166360Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.859409Z digest=sha256:65ca959bbfcdf7b250ca16868d5de56f9926dd6f87d11f237cc42b76bc8329f9

Observation 38545426-8fd0-4b80-a411-ece50900fd84 · outbound

This paper cites Multilinear extensions of games.

Sum of Squares Submodularity Multilinear extensions of games

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.862728Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.862728Z digest=sha256:7d6722130cf145eddd22d3e2ac10a039add24fbe5e20956aad2725b3a1f05cc1

Observation 2ba6ac69-6e1d-4afa-b702-c94f29d8a81d · outbound

This paper cites Selecting a monomial basis for sums of squares programming over a quotient ring.

Sum of Squares Submodularity Selecting a monomial basis for sums of squares programming over a quotient ring

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.149097Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.865935Z digest=sha256:23d01d331df96aa300d725a6fcababc083b27be2425a83ae723f36d459ca12ea

Observation e11c2c24-6d61-4867-951b-e442ffee75e3 · outbound

This paper cites The quadratic unconstrained binary optimization problem.

Sum of Squares Submodularity The quadratic unconstrained binary optimization problem

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.138791Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.869745Z digest=sha256:926e92d080d8a6a6864ae35cde8b456fa9b6d25c79ea97e9d116647955f3d11c

Observation 4129fdc0-d8fc-426d-9e3f-fcd44bb71b6d · outbound

This paper cites Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds.

Sum of Squares Submodularity Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.126995Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.873132Z digest=sha256:4752d772d84014b075600b4aa86a25f8a34e0a0a05fffccf552ec342ed3aa42d

Observation 41785ef7-0df2-47fe-a56f-5f8171a0ac57 · outbound

This paper cites Exact sdp relaxations with truncated moment matrix for binary polynomial optimization problems.

Sum of Squares Submodularity Exact sdp relaxations with truncated moment matrix for binary polynomial optimization problems

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.113891Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.876231Z digest=sha256:de86cb2e4d3006dd0b5a970c729949086dec20f79f19e6ecb9fb07ff2f421a1d

Observation ea867ab6-02a6-4e4f-8220-fe5d49f084b1 · outbound

This paper cites A combinatorial algorithm minimizing submodular functions in strongly polynomial time.

Sum of Squares Submodularity A combinatorial algorithm minimizing submodular functions in strongly polynomial time

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.101705Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.879495Z digest=sha256:b95f39c0f01f2a1028d78b72be43b027c22fedc3e7be7a166d0995fefa2984cb

Observation b4a18369-47e0-44cc-996c-03d46c716f51 · outbound

This paper cites Is submodularity testable? Algorithmica, 69 0 (1): 0 1--25, 2014.

Sum of Squares Submodularity Is submodularity testable? Algorithmica, 69 0 (1): 0 1--25, 2014

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.090970Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.883109Z digest=sha256:55c0f7ef242debed3da401589532484d28a8c12866aa37481549e07fc45e1af7

Observation 857665f8-06f0-4f98-a4a5-a881110c7ed0 · outbound

This paper cites Large-margin learning of submodular summarization models.

Sum of Squares Submodularity Large-margin learning of submodular summarization models

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.081250Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.886611Z digest=sha256:02a7a8981413a2415c84dc5b62f0ed16510905524086ea930db23753105b531a

Observation 2c42ba12-3bb1-4a43-a517-669a06e64fca · outbound

This paper cites Introduction to the T heory of C omputation.

Sum of Squares Submodularity Introduction to the T heory of C omputation

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.069813Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.889492Z digest=sha256:739a1feaf58feef9af4e2f55dc73f52e86357d646f56cdb8a623399cdea6a021

Observation 2658cb85-959d-47b9-9dc4-584d765c6c68 · outbound

This paper cites Learning F ourier sparse set functions.

Sum of Squares Submodularity Learning F ourier sparse set functions

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.057555Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.892331Z digest=sha256:c7d10841441ad0f21d731dd08d58dfbac6d3e3be525d61e8177234a07a0a503a

Observation 9fbf0e44-414e-4331-837d-ea505a824dfc · outbound

This paper cites Minimizing a submodular function on a lattice.

Sum of Squares Submodularity Minimizing a submodular function on a lattice

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.045627Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.895057Z digest=sha256:827251ab591a02b76526a77a418da8f639a8715015941afb9f5c44dda0eb258b

Observation a6414b66-17c2-4f50-a201-8c6c8af34c2d · outbound

This paper cites Supermodularity and C omplementarity.

Sum of Squares Submodularity Supermodularity and C omplementarity

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.033408Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.898041Z digest=sha256:d2911be49faacd7034f03226d55cac88b40366dcfdcc919fb08162493fb862b9

Observation 7a57e04e-2542-4db1-9ddd-9842a6e346b2 · outbound

This paper cites Learning mixtures of submodular functions for image collection summarization.

Sum of Squares Submodularity Learning mixtures of submodular functions for image collection summarization

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.021959Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.900978Z digest=sha256:50c21e9f162e16ace01e24198c0508d6d96c8746247c544523d086bec70025ea

Observation de62ea74-d44a-4011-9ba6-41868b0ccb00 · outbound

This paper cites The concave-convex procedure.

Sum of Squares Submodularity The concave-convex procedure

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.010256Z

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.

source=arxiv_source observed=2026-08-15T15:50:36.904130Z digest=sha256:a28153d802c61d8b022e4cb5b10075efa82e11ea57b72e45f254801f61564a36

Pith citing papers

Observation 4279d50b-ca15-4792-8ca4-1abefb09ec75 · inbound

Copositive Matrices with Ordered Off-Diagonal Entries cites this paper.

Copositive Matrices with Ordered Off-Diagonal Entries Sum of Squares Submodularity

Reference 72

Resolution
verified exact
arxiv_id, observed 2026-06-29T02:14:52.228958Z

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.

source=arxiv_source observed=2026-05-20T17:20:29.589792Z digest=sha256:2a04e70c7edd47bcca6ea339103a17713b2720118f9ae1478e935c3d8fe5b94e