Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T15:50:36.904130Z
Paper Citation Record · LEDGER
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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T15:50:36.904130Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-20T17:20:29.589792Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z
59 of 59 outbound references displayed
External citation measurements
0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z
Observation 67a2cf31-4244-49ce-87ff-91f4dbe2b03d · outbound
Sum of Squares Submodularity DC decomposition of nonconvex polynomials with algebraic techniques
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4e301bda-eeeb-46c2-84a9-6111e0bb8544 · outbound
Sum of Squares Submodularity A complete characterization of the gap between convexity and sos-convexity
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6e27fa3e-f142-4dbe-ba63-cd0d9144f078 · outbound
Sum of Squares Submodularity NP -hardness of deciding convexity of quartic polynomials and related problems
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation da87a7e9-678d-41c1-8c5f-d3c0ef8477c8 · outbound
Sum of Squares Submodularity Submodularity in conic quadratic mixed 0--1 optimization
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cf28e3e4-0361-47f5-a5c3-9c12ba1071f9 · outbound
Sum of Squares Submodularity Submodular functions: from discrete to continuous domains
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2173671a-27f6-4c50-bd64-57379f0358e1 · outbound
Sum of Squares Submodularity Learning with submodular functions: A convex optimization perspective
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3addf231-14e2-4919-ab04-f419b36fa971 · outbound
Sum of Squares Submodularity Learning submodular functions
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ab3cb0b6-6a4e-4a69-852e-29ede35c40d3 · outbound
Sum of Squares Submodularity Submodular functions: Learnability, structure, and optimization
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 85c82a29-32de-4fff-b519-d0fcb1a3646d · outbound
Sum of Squares Submodularity Guarantees for greedy maximization of non-submodular functions with applications
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f98f231e-c29c-4775-8d59-89d8d0a6d118 · outbound
Sum of Squares Submodularity Continuous Submodular Function Maximization
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f9ac604b-f6d9-49ba-95d2-f4ab3c94d237 · outbound
Sum of Squares Submodularity Maximizing a supermodular pseudoboolean function: A polynomial algorithm for supermodular cubic functions
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2f38a1b3-e5de-4eeb-b647-e0abf2c7d355 · outbound
Sum of Squares Submodularity Submodularity In Machine Learning and Artificial Intelligence
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5ba048c5-dac0-404c-a1c0-5a46caecb269 · outbound
Sum of Squares Submodularity Semidefinite O ptimization and C onvex A lgebraic G eometry
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8243abff-4279-4a02-bc6f-8a3c316019c7 · outbound
Sum of Squares Submodularity Undominated DC decompositions of quadratic functions and applications to branch-and-bound approaches
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5af7183a-16b7-4c83-ba70-77b7aeda26ad · outbound
Sum of Squares Submodularity Convex O ptimization
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c3a65b5e-f47f-4218-bea1-94c72a86b26c · outbound
Sum of Squares Submodularity Decomposition Polyhedra of Piecewise Linear Functions
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d305c51f-a8ef-4c6f-ba8e-f09589e2b577 · outbound
Sum of Squares Submodularity On the Semidefinite Representability of Continuous Quadratic Submodular Minimization With Applications to Moment Problems
Reference 17
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3f4a6ff3-9a9f-470b-a701-8fe1e014e3a9 · outbound
Sum of Squares Submodularity Recognition problems for special classes of polynomials in 0--1 variables
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a917c30c-0540-4d5f-9572-b14b8404810a · outbound
Sum of Squares Submodularity Boolean F unctions: T heory, A lgorithms, and A pplications
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 117ef802-76ae-4ce7-8673-f051e06174c2 · outbound
Sum of Squares Submodularity Shape-constrained regression using sum of squares polynomials
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation acebe48a-2bae-460d-810d-48e5e1ee31d7 · outbound
Sum of Squares Submodularity Approximate submodularity and its applications: Subset selection, sparse approximation and dictionary selection
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f4bddf59-3190-4065-b2f5-f9b4f9f375f2 · outbound
Sum of Squares Submodularity Neural estimation of submodular functions with applications to differentiable subset selection
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cc4901a6-18fe-43a3-ab56-979e39fbb83b · outbound
Sum of Squares Submodularity Deep submodular functions: Definitions and learning
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e98b4fa8-354f-4950-9d6d-27f5142a3930 · outbound
Sum of Squares Submodularity Submodular functions, matroids, and certain polyhedra
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d00a3f1d-c65f-4c8f-935f-87872ccdee74 · outbound
Sum of Squares Submodularity Difference of submodular minimization via DC programming
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8369e0e9-940e-4dd5-8507-1add430d1db2 · outbound
Sum of Squares Submodularity Sparse sum-of-squares certificates on finite abelian groups
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 096bb0ac-bd73-4a49-a341-78f4376fe570 · outbound
Sum of Squares Submodularity Optimal bounds on approximation of submodular and xos functions by juntas
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f276d24f-1470-4f30-9574-a2b1aac0c91b · outbound
Sum of Squares Submodularity Representation, approximation and learning of submodular functions using low-rank decision trees
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation dfbf3625-794c-4b8e-a602-7849f4780abb · outbound
Sum of Squares Submodularity Submodular functions in graph theory
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 67a419c5-a7d3-4c2e-817f-ac499f9c433b · outbound
Sum of Squares Submodularity Submodular F unctions and O ptimization , volume 58
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a8ab76d3-b3e0-45a2-87e4-12816663a5cc · outbound
Sum of Squares Submodularity On the supermodular knapsack problem
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2f5be08c-c125-4523-892a-84ff54bfbf91 · outbound
Sum of Squares Submodularity Approximating submodular functions everywhere
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 452272b9-0ae1-44ce-ae0f-12e71dc040d0 · outbound
Sum of Squares Submodularity PEP it: computer-assisted worst-case analyses of first-order optimization methods in python
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8507be87-9b75-4640-a898-6a051c28fbeb · outbound
Sum of Squares Submodularity Equivalent representations of set functions
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1474a413-99d9-49fc-959c-968402d709bc · outbound
Sum of Squares Submodularity Semidefinite representation of convex sets
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 43e06e57-1cd8-4b7c-8dbe-13c9ca5cc335 · outbound
Sum of Squares Submodularity Maximization of approximately submodular functions
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 24ac79ac-af82-424b-be73-0c92395ba9cb · outbound
Sum of Squares Submodularity Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 687ebf45-243d-4ced-bf4b-15867895c9b0 · outbound
Sum of Squares Submodularity Submodularity beyond submodular energies: coupling edges in graph cuts
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 929c236f-0399-444f-a440-55a86b70b03b · outbound
Sum of Squares Submodularity Near-optimal sensor placements in gaussian processes: Theory, efficient algorithms and empirical studies
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation baf9fcaf-5a1e-48c9-99e3-ecac918491f5 · outbound
Sum of Squares Submodularity Lower bound for the number of iterations in semidefinite hierarchies for the cut polytope
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e674f7a5-271a-449b-8ea6-0d75121d21ac · outbound
Sum of Squares Submodularity Sums of squares, moment matrices and optimization over polynomials
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 54368282-315d-4dc0-95dc-20b04713aadf · outbound
Sum of Squares Submodularity Learning Mixtures of Submodular Shells with Application to Document Summarization
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f348769c-4603-4841-9d8f-1d5f913827d2 · outbound
Sum of Squares Submodularity A submodular-supermodular procedure with applications to discriminative structure learning
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cd49fc29-ecb1-4396-8c11-8068061ef436 · outbound
Sum of Squares Submodularity Submodular F unctions and E lectrical N etworks , volume 54
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1cf7aaf5-ecc6-4481-bcc8-50a74ebc5704 · outbound
Sum of Squares Submodularity An analysis of approximations for maximizing submodular set functions—i
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 38545426-8fd0-4b80-a411-ece50900fd84 · outbound
Sum of Squares Submodularity Multilinear extensions of games
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2ba6ac69-6e1d-4afa-b702-c94f29d8a81d · outbound
Sum of Squares Submodularity Selecting a monomial basis for sums of squares programming over a quotient ring
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e11c2c24-6d61-4867-951b-e442ffee75e3 · outbound
Sum of Squares Submodularity The quadratic unconstrained binary optimization problem
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4129fdc0-d8fc-426d-9e3f-fcd44bb71b6d · outbound
Sum of Squares Submodularity Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 41785ef7-0df2-47fe-a56f-5f8171a0ac57 · outbound
Sum of Squares Submodularity Exact sdp relaxations with truncated moment matrix for binary polynomial optimization problems
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ea867ab6-02a6-4e4f-8220-fe5d49f084b1 · outbound
Sum of Squares Submodularity A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b4a18369-47e0-44cc-996c-03d46c716f51 · outbound
Sum of Squares Submodularity Is submodularity testable? Algorithmica, 69 0 (1): 0 1--25, 2014
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 857665f8-06f0-4f98-a4a5-a881110c7ed0 · outbound
Sum of Squares Submodularity Large-margin learning of submodular summarization models
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2c42ba12-3bb1-4a43-a517-669a06e64fca · outbound
Sum of Squares Submodularity Introduction to the T heory of C omputation
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2658cb85-959d-47b9-9dc4-584d765c6c68 · outbound
Sum of Squares Submodularity Learning F ourier sparse set functions
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9fbf0e44-414e-4331-837d-ea505a824dfc · outbound
Sum of Squares Submodularity Minimizing a submodular function on a lattice
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a6414b66-17c2-4f50-a201-8c6c8af34c2d · outbound
Sum of Squares Submodularity Supermodularity and C omplementarity
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7a57e04e-2542-4db1-9ddd-9842a6e346b2 · outbound
Sum of Squares Submodularity Learning mixtures of submodular functions for image collection summarization
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation de62ea74-d44a-4011-9ba6-41868b0ccb00 · outbound
Sum of Squares Submodularity The concave-convex procedure
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4279d50b-ca15-4792-8ca4-1abefb09ec75 · inbound
Copositive Matrices with Ordered Off-Diagonal Entries Sum of Squares Submodularity
Reference 72
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.