path: root/topology.bib

@article{Altieri_2019_Constraint,
 author = {Altieri, Ada and Franz, Silvio},
 title = {Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2019},
 month = {January},
 number = {1},
 volume = {99},
 pages = {010401},
 url = {http://dx.doi.org/10.1103/PhysRevE.99.010401},
 doi = {10.1103/physreve.99.010401},
 issn = {2470-0053}
}

@article{Annesi_2023_Star-shaped,
 author = {Annesi, Brandon Livio and Lauditi, Clarissa and Lucibello, Carlo and Malatesta, Enrico M. and Perugini, Gabriele and Pittorino, Fabrizio and Saglietti, Luca},
 title = {Star-Shaped Space of Solutions of the Spherical Negative Perceptron},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2023},
 month = {11},
 number = {22},
 volume = {131},
 pages = {227301},
 url = {http://dx.doi.org/10.1103/PhysRevLett.131.227301},
 doi = {10.1103/physrevlett.131.227301},
 issn = {1079-7114}
}

@article{Annibale_2003_Supersymmetric,
 author = {Annibale, Alessia and Cavagna, Andrea and Giardina, Irene and Parisi, Giorgio},
 title = {Supersymmetric complexity in the {Sherrington}-{Kirkpatrick} model},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2003},
 month = {12},
 number = {6},
 volume = {68},
 pages = {061103},
 url = {https://doi.org/10.1103%2Fphysreve.68.061103},
 doi = {10.1103/physreve.68.061103}
}

@article{Annibale_2003_The,
 author = {Annibale, Alessia and Cavagna, Andrea and Giardina, Irene and Parisi, Giorgio and Trevigne, Elisa},
 title = {The role of the {Becchi}--{Rouet}--{Stora}--{Tyutin} supersymmetry in the calculation of the complexity for the {Sherrington}--{Kirkpatrick} model},
 journal = {Journal of Physics A: Mathematical and General},
 publisher = {IOP Publishing},
 year = {2003},
 month = {10},
 number = {43},
 volume = {36},
 pages = {10937--10953},
 url = {https://doi.org/10.1088%2F0305-4470%2F36%2F43%2F018},
 doi = {10.1088/0305-4470/36/43/018}
}

@article{Annibale_2004_Coexistence,
 author = {Annibale, Alessia and Gualdi, Giulia and Cavagna, Andrea},
 title = {Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses},
 journal = {Journal of Physics A: Mathematical and General},
 publisher = {IOP Publishing},
 year = {2004},
 month = {11},
 number = {47},
 volume = {37},
 pages = {11311--11320},
 url = {https://doi.org/10.1088%2F0305-4470%2F37%2F47%2F001},
 doi = {10.1088/0305-4470/37/47/001}
}

@book{Audin_2014_Morse,
 author = {Audin, Michèle and Damian, Mihai},
 title = {Morse theory and {Floer} homology},
 publisher = {Springer},
 year = {2014},
 address = {London},
 isbn = {9781447154952},
 series = {Universitext},
 translator = {Erné, Reinie}
}

@unpublished{Auffinger_2022_The,
 author = {Auffinger, Antonio and Zhou, Yuxin},
 title = {The Spherical $p+s$ Spin Glass At Zero Temperature},
 year = {2022},
 month = {9},
 url = {http://arxiv.org/abs/2209.03866v1},
 doi = {10.48550/arXiv.2209.03866},
 note = {arXiv preprint},
 date = {2022-09-08T15:08:26Z},
 eprint = {2209.03866v1},
 eprintclass = {math.PR},
 eprinttype = {arxiv}
}

@article{Baldassi_2016_Unreasonable,
 author = {Baldassi, Carlo and Borgs, Christian and Chayes, Jennifer T. and Ingrosso, Alessandro and Lucibello, Carlo and Saglietti, Luca and Zecchina, Riccardo},
 title = {Unreasonable effectiveness of learning neural networks: From accessible states and robust ensembles to basic algorithmic schemes},
 journal = {Proceedings of the National Academy of Sciences},
 publisher = {Proceedings of the National Academy of Sciences},
 year = {2016},
 month = {11},
 number = {48},
 volume = {113},
 pages = {E7655--E7662},
 url = {http://dx.doi.org/10.1073/pnas.1608103113},
 doi = {10.1073/pnas.1608103113},
 issn = {1091-6490}
}

@article{Baldassi_2019_Properties,
 author = {Baldassi, Carlo and Malatesta, Enrico M. and Zecchina, Riccardo},
 title = {Properties of the Geometry of Solutions and Capacity of Multilayer Neural Networks with Rectified Linear Unit Activations},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2019},
 month = {10},
 number = {17},
 volume = {123},
 pages = {170602},
 url = {https://doi.org/10.1103%2Fphysrevlett.123.170602},
 doi = {10.1103/physrevlett.123.170602}
}

@article{Baldassi_2023_Typical,
 author = {Baldassi, Carlo and Malatesta, Enrico M. and Perugini, Gabriele and Zecchina, Riccardo},
 title = {Typical and atypical solutions in nonconvex neural networks with discrete and continuous weights},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2023},
 month = {August},
 number = {2},
 volume = {108},
 pages = {024310},
 url = {http://dx.doi.org/10.1103/PhysRevE.108.024310},
 doi = {10.1103/physreve.108.024310},
 issn = {2470-0053}
}

@unpublished{Beneventano_2023_On,
 author = {Beneventano, Pierfrancesco},
 title = {On the Trajectories of {SGD} Without Replacement},
 year = {2023},
 month = {dec},
 url = {http://arxiv.org/abs/2312.16143v2},
 archiveprefix = {arXiv},
 eprint = {2312.16143v2},
 eprintclass = {cs.LG},
 eprinttype = {arxiv}
}

@article{Castellani_2005_Spin-glass,
 author = {Castellani, Tommaso and Cavagna, Andrea},
 title = {Spin-glass theory for pedestrians},
 journal = {Journal of Statistical Mechanics: Theory and Experiment},
 publisher = {IOP Publishing},
 year = {2005},
 month = {5},
 number = {05},
 volume = {2005},
 pages = {P05012},
 url = {https://doi.org/10.1088%2F1742-5468%2F2005%2F05%2Fp05012},
 doi = {10.1088/1742-5468/2005/05/p05012}
}

@article{Crisanti_1992_The,
 author = {Crisanti, A. and Sommers, H.-J.},
 title = {The spherical $p$-spin interaction spin glass model: the statics},
 journal = {Zeitschrift für Physik B Condensed Matter},
 publisher = {Springer Science and Business Media LLC},
 year = {1992},
 month = {10},
 number = {3},
 volume = {87},
 pages = {341--354},
 url = {https://doi.org/10.1007%2Fbf01309287},
 doi = {10.1007/bf01309287}
}

@article{Crisanti_2004_Spherical,
 author = {Crisanti, A. and Leuzzi, L.},
 title = {Spherical $2+p$ Spin-Glass Model: An Exactly Solvable Model for Glass to Spin-Glass Transition},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2004},
 month = {11},
 number = {21},
 volume = {93},
 pages = {217203},
 url = {https://doi.org/10.1103%2Fphysrevlett.93.217203},
 doi = {10.1103/physrevlett.93.217203}
}

@article{Crisanti_2006_Spherical,
 author = {Crisanti, A. and Leuzzi, L.},
 title = {Spherical $2+p$ spin-glass model: An analytically solvable model with a glass-to-glass transition},
 journal = {Physical Review B},
 publisher = {American Physical Society (APS)},
 year = {2006},
 month = {1},
 number = {1},
 volume = {73},
 pages = {014412},
 url = {https://doi.org/10.1103%2Fphysrevb.73.014412},
 doi = {10.1103/physrevb.73.014412}
}

@book{DeWitt_1992_Supermanifolds,
 author = {DeWitt, Bryce S.},
 title = {Supermanifolds},
 publisher = {Cambridge University Press},
 year = {1992},
 address = {Cambridge ; New York},
 edition = {2nd ed},
 isbn = {9780521413206 9780521423779},
 keyword = {Supermanifolds (Mathematics), Mathematical physics},
 series = {Cambridge monographs on mathematical physics}
}

@article{Erba_2024_Quenches,
 author = {Erba, Vittorio and Behrens, Freya and Krzakala, Florent and Zdeborová, Lenka},
 title = {Quenches in the {Sherrington}–{Kirkpatrick} model},
 journal = {Journal of Statistical Mechanics: Theory and Experiment},
 publisher = {IOP Publishing},
 year = {2024},
 month = {August},
 number = {8},
 volume = {2024},
 pages = {083302},
 url = {http://dx.doi.org/10.1088/1742-5468/ad685a},
 doi = {10.1088/1742-5468/ad685a},
 issn = {1742-5468}
}

@article{Folena_2020_Rethinking,
 author = {Folena, Giampaolo and Franz, Silvio and Ricci-Tersenghi, Federico},
 title = {Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed $p$-Spin Model},
 journal = {Physical Review X},
 publisher = {American Physical Society},
 year = {2020},
 month = {8},
 volume = {10},
 pages = {031045},
 url = {https://link.aps.org/doi/10.1103/PhysRevX.10.031045},
 doi = {10.1103/PhysRevX.10.031045},
 issue = {3},
 numpages = {26}
}

@article{Folena_2021_Gradient,
 author = {Folena, Giampaolo and Franz, Silvio and Ricci-Tersenghi, Federico},
 title = {Gradient descent dynamics in the mixed $p$-spin spherical model: finite-size simulations and comparison with mean-field integration},
 journal = {Journal of Statistical Mechanics: Theory and Experiment},
 publisher = {IOP Publishing},
 year = {2021},
 month = {3},
 number = {3},
 volume = {2021},
 pages = {033302},
 url = {https://doi.org/10.1088%2F1742-5468%2Fabe29f},
 doi = {10.1088/1742-5468/abe29f}
}

@article{Folena_2023_On,
 author = {Folena, Giampaolo and Zamponi, Francesco},
 title = {On weak ergodicity breaking in mean-field spin glasses},
 journal = {SciPost Physics},
 publisher = {Stichting SciPost},
 year = {2023},
 month = {9},
 number = {3},
 volume = {15},
 pages = {109},
 url = {https://doi.org/10.21468%2Fscipostphys.15.3.109},
 doi = {10.21468/scipostphys.15.3.109}
}

@article{Franz_2016_The,
 author = {Franz, Silvio and Parisi, Giorgio},
 title = {The simplest model of jamming},
 journal = {Journal of Physics A: Mathematical and Theoretical},
 publisher = {IOP Publishing},
 year = {2016},
 month = {February},
 number = {14},
 volume = {49},
 pages = {145001},
 url = {http://dx.doi.org/10.1088/1751-8113/49/14/145001},
 doi = {10.1088/1751-8113/49/14/145001},
 issn = {1751-8121}
}

@article{Franz_2017_Universality,
 author = {Franz, Silvio and Parisi, Giorgio and Sevelev, Maxime and Urbani, Pierfrancesco and Zamponi, Francesco},
 title = {Universality of the {SAT-UNSAT} (jamming) threshold in non-convex continuous constraint satisfaction problems},
 journal = {SciPost Physics},
 publisher = {Stichting SciPost},
 year = {2017},
 month = {June},
 number = {3},
 volume = {2},
 pages = {019},
 url = {http://dx.doi.org/10.21468/SciPostPhys.2.3.019},
 doi = {10.21468/scipostphys.2.3.019},
 issn = {2542-4653}
}

@article{Franz_2019_Critical,
 author = {Franz, Silvio and Sclocchi, Antonio and Urbani, Pierfrancesco},
 title = {Critical Jammed Phase of the Linear Perceptron},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2019},
 month = {September},
 number = {11},
 volume = {123},
 pages = {115702},
 url = {http://dx.doi.org/10.1103/PhysRevLett.123.115702},
 doi = {10.1103/physrevlett.123.115702},
 issn = {1079-7114}
}

@article{Fyodorov_2004_Complexity,
 author = {Fyodorov, Yan V.},
 title = {Complexity of Random Energy Landscapes, Glass Transition, and Absolute Value of the Spectral Determinant of Random Matrices},
 journal = {Physical Review Letters},
 publisher = {American Physical Society (APS)},
 year = {2004},
 month = {6},
 number = {24},
 volume = {92},
 pages = {240601},
 url = {https://doi.org/10.1103%2Fphysrevlett.92.240601},
 doi = {10.1103/physrevlett.92.240601}
}

@article{Fyodorov_2019_A,
 author = {Fyodorov, Yan V.},
 title = {A Spin Glass Model for Reconstructing Nonlinearly Encrypted Signals Corrupted by Noise},
 journal = {Journal of Statistical Physics},
 publisher = {Springer Science and Business Media LLC},
 year = {2019},
 month = {1},
 number = {5},
 volume = {175},
 pages = {789--818},
 url = {https://doi.org/10.1007%2Fs10955-018-02217-9},
 doi = {10.1007/s10955-018-02217-9}
}

@article{Fyodorov_2020_Counting,
 author = {Fyodorov, Y. V. and Tublin, R.},
 title = {Counting Stationary Points of the Loss Function in the Simplest Constrained Least-square Optimization},
 journal = {Acta Physica Polonica B},
 publisher = {Jagiellonian University},
 year = {2020},
 number = {7},
 volume = {51},
 pages = {1663},
 url = {http://dx.doi.org/10.5506/APhysPolB.51.1663},
 doi = {10.5506/aphyspolb.51.1663},
 issn = {1509-5770}
}

@article{Fyodorov_2022_Optimization,
 author = {Fyodorov, Yan V and Tublin, Rashel},
 title = {Optimization landscape in the simplest constrained random least-square problem},
 journal = {Journal of Physics A: Mathematical and Theoretical},
 publisher = {IOP Publishing},
 year = {2022},
 month = {May},
 number = {24},
 volume = {55},
 pages = {244008},
 url = {http://dx.doi.org/10.1088/1751-8121/ac6d8e},
 doi = {10.1088/1751-8121/ac6d8e},
 issn = {1751-8121}
}

@book{Hatcher_2002_Algebraic,
 author = {Hatcher, Allen},
 title = {Algebraic topology},
 publisher = {Cambridge University Press},
 year = {2002},
 address = {Cambridge ; New York},
 isbn = {9780521791601 9780521795401},
 keyword = {Algebraic topology}
}

@article{Kac_1943_On,
 author = {Kac, M.},
 title = {On the average number of real roots of a random algebraic equation},
 journal = {Bulletin of the American Mathematical Society},
 publisher = {American Mathematical Society},
 year = {1943},
 month = {4},
 number = {4},
 volume = {49},
 pages = {314--320},
 url = {https://projecteuclid.org:443/euclid.bams/1183505112}
}

@article{Kamali_2023_Dynamical,
 author = {Kamali, Persia Jana and Urbani, Pierfrancesco},
 title = {Dynamical mean field theory for models of confluent tissues and beyond},
 journal = {SciPost Physics},
 publisher = {Stichting SciPost},
 year = {2023},
 month = {November},
 number = {5},
 volume = {15},
 pages = {219},
 url = {http://dx.doi.org/10.21468/SciPostPhys.15.5.219},
 doi = {10.21468/scipostphys.15.5.219},
 issn = {2542-4653}
}

@unpublished{Kamali_2023_Stochastic,
 author = {Kamali, Persia Jana and Urbani, Pierfrancesco},
 title = {Stochastic Gradient Descent outperforms Gradient Descent in recovering a high-dimensional signal in a glassy energy landscape},
 year = {2023},
 month = {sep},
 url = {http://arxiv.org/abs/2309.04788v2},
 note = {},
 archiveprefix = {arXiv},
 eprint = {2309.04788v2},
 eprintclass = {cs.LG},
 eprinttype = {arxiv}
}

@article{Kent-Dobias_2023_How,
 author = {Kent-Dobias, Jaron and Kurchan, Jorge},
 title = {How to count in hierarchical landscapes: a full solution to mean-field complexity},
 journal = {Physical Review E},
 publisher = {American Physical Society (APS)},
 year = {2023},
 month = {6},
 number = {6},
 volume = {107},
 pages = {064111},
 url = {https://doi.org/10.1103/PhysRevE.107.064111},
 doi = {10.1103/PhysRevE.107.064111}
}

@article{Kent-Dobias_2023_When,
 author = {Kent-Dobias, Jaron},
 title = {When is the average number of saddle points typical?},
 journal = {Europhysics Letters},
 publisher = {IOP Publishing},
 year = {2023},
 month = {8},
 number = {6},
 volume = {143},
 pages = {61003},
 url = {https://doi.org/10.1209%2F0295-5075%2Facf521},
 doi = {10.1209/0295-5075/acf521}
}

@unpublished{Kent-Dobias_2024_Algorithm-independent,
 author = {Kent-Dobias, Jaron},
 title = {Algorithm-independent bounds on complex optimization through the statistics of marginal optima},
 year = {2024},
 url = {https://arxiv.org/abs/2407.02092},
 archiveprefix = {arXiv},
 eprint = {2407.02092},
 primaryclass = {cond-mat.dis-nn}
}

@unpublished{Kent-Dobias_2024_Conditioning,
 author = {Kent-Dobias, Jaron},
 title = {Conditioning the complexity of random landscapes on marginal optima},
 year = {2024},
 url = {https://arxiv.org/abs/2407.02082},
 archiveprefix = {arXiv},
 eprint = {2407.02082},
 primaryclass = {cond-mat.dis-nn}
}

@article{Mezard_2009_Constraint,
 author = {Mézard, Marc and Mora, Thierry},
 title = {Constraint satisfaction problems and neural networks: A statistical physics perspective},
 journal = {Journal of Physiology-Paris},
 publisher = {Elsevier BV},
 year = {2009},
 month = {January},
 number = {1–2},
 volume = {103},
 pages = {107--113},
 url = {http://dx.doi.org/10.1016/j.jphysparis.2009.05.013},
 doi = {10.1016/j.jphysparis.2009.05.013},
 issn = {0928-4257}
}

@unpublished{Montanari_2023_Solving,
 author = {Montanari, Andrea and Subag, Eliran},
 title = {Solving overparametrized systems of random equations: I. Model and algorithms for approximate solutions},
 year = {2023},
 month = {jun},
 url = {http://arxiv.org/abs/2306.13326v1},
 note = {},
 archiveprefix = {arXiv},
 eprint = {2306.13326v1},
 eprintclass = {math.PR},
 eprinttype = {arxiv}
}

@unpublished{Montanari_2024_On,
 author = {Montanari, Andrea and Subag, Eliran},
 title = {On {Smale}'s 17th problem over the reals},
 year = {2024},
 month = {may},
 url = {http://arxiv.org/abs/2405.01735v1},
 note = {},
 archiveprefix = {arXiv},
 eprint = {2405.01735v1},
 eprintclass = {cs.DS},
 eprinttype = {arxiv}
}

@article{Rice_1939_The,
 author = {Rice, S. O.},
 title = {The Distribution of the Maxima of a Random Curve},
 journal = {American Journal of Mathematics},
 publisher = {JSTOR},
 year = {1939},
 month = {4},
 number = {2},
 volume = {61},
 pages = {409},
 url = {https://doi.org/10.2307%2F2371510},
 doi = {10.2307/2371510}
}

@phdthesis{Tublin_2022_A,
 author = {Tublin, Rashel},
 title = {A Few Results in Random Matrix Theory and Random Optimization},
 year = {2022},
 month = {September},
 url = {https://kclpure.kcl.ac.uk/portal/en/studentTheses/a-few-results-in-random-matrix-theory-and-random-optimization},
 school = {King's College London}
}

@article{Urbani_2023_A,
 author = {Urbani, Pierfrancesco},
 title = {A continuous constraint satisfaction problem for the rigidity transition in confluent tissues},
 journal = {Journal of Physics A: Mathematical and Theoretical},
 publisher = {IOP Publishing},
 year = {2023},
 month = {February},
 number = {11},
 volume = {56},
 pages = {115003},
 url = {http://dx.doi.org/10.1088/1751-8121/acb742},
 doi = {10.1088/1751-8121/acb742},
 issn = {1751-8121}
}

@article{Urbani_2024_Quantum,
 author = {Urbani, Pierfrancesco},
 title = {Quantum exploration of high-dimensional canyon landscapes},
 journal = {Journal of Statistical Mechanics: Theory and Experiment},
 publisher = {IOP Publishing},
 year = {2024},
 month = {August},
 number = {8},
 volume = {2024},
 pages = {083301},
 url = {http://dx.doi.org/10.1088/1742-5468/ad0635},
 doi = {10.1088/1742-5468/ad0635},
 issn = {1742-5468}
}

@unpublished{Urbani_2024_Statistical,
 author = {Urbani, Pierfrancesco},
 title = {Statistical physics of complex systems: glasses, spin glasses, continuous constraint satisfaction problems, high-dimensional inference and neural networks},
 year = {2024},
 month = {may},
 url = {http://arxiv.org/abs/2405.06384v1},
 note = {},
 archiveprefix = {arXiv},
 eprint = {2405.06384v1},
 eprintclass = {cond-mat.dis-nn},
 eprinttype = {arxiv}
}

@unpublished{Vivo_2024_Random,
 author = {Vivo, Pierpaolo},
 title = {Random Linear Systems with Quadratic Constraints: from Random Matrix Theory to replicas and back},
 year = {2024},
 month = {jan},
 url = {http://arxiv.org/abs/2401.03209v2},
 archiveprefix = {arXiv},
 eprint = {2401.03209v2},
 eprintclass = {cond-mat.stat-mech},
 eprinttype = {arxiv}
}