@article{14739,
  abstract     = {Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods.},
  author       = {Ali, Dashti and Asaad, Aras and Jimenez, Maria-Jose and Nanda, Vidit and Paluzo-Hidalgo, Eduardo and Soriano Trigueros, Manuel},
  issn         = {1939-3539},
  journal      = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
  keywords     = {Applied Mathematics, Artificial Intelligence, Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Software},
  number       = {12},
  pages        = {14069--14080},
  publisher    = {IEEE},
  title        = {{A survey of vectorization methods in topological data analysis}},
  doi          = {10.1109/tpami.2023.3308391},
  volume       = {45},
  year         = {2023},
}

@article{14780,
  abstract     = {In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix.},
  author       = {Ding, Xiucai and Ji, Hong Chang},
  issn         = {1879-209X},
  journal      = {Stochastic Processes and their Applications},
  keywords     = {Applied Mathematics, Modeling and Simulation, Statistics and Probability},
  pages        = {25--60},
  publisher    = {Elsevier},
  title        = {{Spiked multiplicative random matrices and principal components}},
  doi          = {10.1016/j.spa.2023.05.009},
  volume       = {163},
  year         = {2023},
}

@article{12156,
  abstract     = {Models of transcriptional regulation that assume equilibrium binding of transcription factors have been less successful at predicting gene expression from sequence in eukaryotes than in bacteria. This could be due to the non-equilibrium nature of eukaryotic regulation. Unfortunately, the space of possible non-equilibrium mechanisms is vast and predominantly uninteresting. The key question is therefore how this space can be navigated efficiently, to focus on mechanisms and models that are biologically relevant. In this review, we advocate for the normative role of theory—theory that prescribes rather than just describes—in providing such a focus. Theory should expand its remit beyond inferring mechanistic models from data, towards identifying non-equilibrium gene regulatory schemes that may have been evolutionarily selected, despite their energy consumption, because they are precise, reliable, fast, or otherwise outperform regulation at equilibrium. We illustrate our reasoning by toy examples for which we provide simulation code.},
  author       = {Zoller, Benjamin and Gregor, Thomas and Tkačik, Gašper},
  issn         = {2452-3100},
  journal      = {Current Opinion in Systems Biology},
  keywords     = {Applied Mathematics, Computer Science Applications, Drug Discovery, General Biochemistry, Genetics and Molecular Biology, Modeling and Simulation},
  number       = {9},
  publisher    = {Elsevier},
  title        = {{Eukaryotic gene regulation at equilibrium, or non?}},
  doi          = {10.1016/j.coisb.2022.100435},
  volume       = {31},
  year         = {2022},
}

@article{12178,
  abstract     = {In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic partial differential equation are proven using stochastic maximal L² regularity, the theory of critical spaces for stochastic evolution equations, and global a priori bounds. Compared to other results in this direction, we do not need any smallness assumption on the transport noise which acts directly on the velocity field and we also allow rougher noise terms. The adaptation to Stratonovich type noise and, more generally, to variable viscosity and/or conductivity are discussed as well.},
  author       = {Agresti, Antonio and Hieber, Matthias and Hussein, Amru and Saal, Martin},
  issn         = {2194-041X},
  journal      = {Stochastics and Partial Differential Equations: Analysis and Computations},
  keywords     = {Applied Mathematics, Modeling and Simulation, Statistics and Probability},
  publisher    = {Springer Nature},
  title        = {{The stochastic primitive equations with transport noise and turbulent pressure}},
  doi          = {10.1007/s40072-022-00277-3},
  year         = {2022},
}

@article{12259,
  abstract     = {Theoretical foundations of chaos have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world chaotic phenomena, e.g., weather, arise in systems with many (formally infinite) degrees of freedom, which limits direct quantitative analysis of such systems using chaos theory. In the present work, we demonstrate that the hydrodynamic pilot-wave systems offer a bridge between low- and high-dimensional chaotic phenomena by allowing for a systematic study of how the former connects to the latter. Specifically, we present experimental results, which show the formation of low-dimensional chaotic attractors upon destabilization of regular dynamics and a final transition to high-dimensional chaos via the merging of distinct chaotic regions through a crisis bifurcation. Moreover, we show that the post-crisis dynamics of the system can be rationalized as consecutive scatterings from the nonattracting chaotic sets with lifetimes following exponential distributions. },
  author       = {Choueiri, George H and Suri, Balachandra and Merrin, Jack and Serbyn, Maksym and Hof, Björn and Budanur, Nazmi B},
  issn         = {1089-7682},
  journal      = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
  keywords     = {Applied Mathematics, General Physics and Astronomy, Mathematical Physics, Statistical and Nonlinear Physics},
  number       = {9},
  publisher    = {AIP Publishing},
  title        = {{Crises and chaotic scattering in hydrodynamic pilot-wave experiments}},
  doi          = {10.1063/5.0102904},
  volume       = {32},
  year         = {2022},
}

@article{12261,
  abstract     = {Dose–response relationships are a general concept for quantitatively describing biological systems across multiple scales, from the molecular to the whole-cell level. A clinically relevant example is the bacterial growth response to antibiotics, which is routinely characterized by dose–response curves. The shape of the dose–response curve varies drastically between antibiotics and plays a key role in treatment, drug interactions, and resistance evolution. However, the mechanisms shaping the dose–response curve remain largely unclear. Here, we show in Escherichia coli that the distinctively shallow dose–response curve of the antibiotic trimethoprim is caused by a negative growth-mediated feedback loop: Trimethoprim slows growth, which in turn weakens the effect of this antibiotic. At the molecular level, this feedback is caused by the upregulation of the drug target dihydrofolate reductase (FolA/DHFR). We show that this upregulation is not a specific response to trimethoprim but follows a universal trend line that depends primarily on the growth rate, irrespective of its cause. Rewiring the feedback loop alters the dose–response curve in a predictable manner, which we corroborate using a mathematical model of cellular resource allocation and growth. Our results indicate that growth-mediated feedback loops may shape drug responses more generally and could be exploited to design evolutionary traps that enable selection against drug resistance.},
  author       = {Angermayr, Andreas and Pang, Tin Yau and Chevereau, Guillaume and Mitosch, Karin and Lercher, Martin J and Bollenbach, Mark Tobias},
  issn         = {1744-4292},
  journal      = {Molecular Systems Biology},
  keywords     = {Applied Mathematics, Computational Theory and Mathematics, General Agricultural and Biological Sciences, General Immunology and Microbiology, General Biochemistry, Genetics and Molecular Biology, Information Systems},
  number       = {9},
  publisher    = {Embo Press},
  title        = {{Growth‐mediated negative feedback shapes quantitative antibiotic response}},
  doi          = {10.15252/msb.202110490},
  volume       = {18},
  year         = {2022},
}

@article{12286,
  abstract     = {Inspired by the study of loose cycles in hypergraphs, we define the loose core in hypergraphs as a structurewhich mirrors the close relationship between cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial random hypergraph $H^r(n,p)$, the order of the loose core undergoes a phase transition at a certain critical threshold and determine this order, as well as the number of edges, asymptotically in the subcritical and supercritical regimes.
Our main tool is an algorithm called CoreConstruct, which enables us to analyse a peeling process for the loose core. By analysing this algorithm we determine the asymptotic degree distribution of vertices in the loose core and in particular how many vertices and edges the loose core contains. As a corollary we obtain an improved upper bound on the length of the longest loose cycle in $H^r(n,p)$.},
  author       = {Cooley, Oliver and Kang, Mihyun and Zalla, Julian},
  issn         = {1077-8926},
  journal      = {The Electronic Journal of Combinatorics},
  keywords     = {Computational Theory and Mathematics, Geometry and Topology, Theoretical Computer Science, Applied Mathematics, Discrete Mathematics and Combinatorics},
  number       = {4},
  publisher    = {The Electronic Journal of Combinatorics},
  title        = {{Loose cores and cycles in random hypergraphs}},
  doi          = {10.37236/10794},
  volume       = {29},
  year         = {2022},
}

@article{12304,
  abstract     = {We establish sharp criteria for the instantaneous propagation of free boundaries in solutions to the thin-film equation. The criteria are formulated in terms of the initial distribution of mass (as opposed to previous almost-optimal results), reflecting the fact that mass is a locally conserved quantity for the thin-film equation. In the regime of weak slippage, our criteria are at the same time necessary and sufficient. The proof of our upper bounds on free boundary propagation is based on a strategy of “propagation of degeneracy” down to arbitrarily small spatial scales: We combine estimates on the local mass and estimates on energies to show that “degeneracy” on a certain space-time cylinder entails “degeneracy” on a spatially smaller space-time cylinder with the same time horizon. The derivation of our lower bounds on free boundary propagation is based on a combination of a monotone quantity and almost optimal estimates established previously by the second author with a new estimate connecting motion of mass to entropy production.},
  author       = {De Nitti, Nicola and Fischer, Julian L},
  issn         = {1532-4133},
  journal      = {Communications in Partial Differential Equations},
  keywords     = {Applied Mathematics, Analysis},
  number       = {7},
  pages        = {1394--1434},
  publisher    = {Taylor & Francis},
  title        = {{Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation}},
  doi          = {10.1080/03605302.2022.2056702},
  volume       = {47},
  year         = {2022},
}

@article{12305,
  abstract     = {This paper is concerned with the sharp interface limit for the Allen--Cahn equation with a nonlinear Robin boundary condition in a bounded smooth domain Ω⊂\R2. We assume that a diffuse interface already has developed and that it is in contact with the boundary ∂Ω. The boundary condition is designed in such a way that the limit problem is given by the mean curvature flow with constant α-contact angle. For α close to 90° we prove a local in time convergence result for well-prepared initial data for times when a smooth solution to the limit problem exists. Based on the latter we construct a suitable curvilinear coordinate system and carry out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear Robin boundary condition. Moreover, we show a spectral estimate for the corresponding linearized Allen--Cahn operator and with its aid we derive strong norm estimates for the difference of the exact and approximate solutions using a Gronwall-type argument.},
  author       = {Abels, Helmut and Moser, Maximilian},
  issn         = {1095-7154},
  journal      = {SIAM Journal on Mathematical Analysis},
  keywords     = {Applied Mathematics, Computational Mathematics, Analysis},
  number       = {1},
  pages        = {114--172},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°}},
  doi          = {10.1137/21m1424925},
  volume       = {54},
  year         = {2022},
}

@article{10842,
  abstract     = {We determine the unique factorization of some polynomials over a finite local commutative ring with identity explicitly. This solves and generalizes the main conjecture of Qian, Shi and Solé in [13]. We also give some applications to enumeration of certain generalized double circulant self-dual and linear complementary dual (LCD) codes over some finite rings together with an application in asymptotic coding theory.},
  author       = {Köse, Seyda and Özbudak, Ferruh},
  issn         = {1936-2455},
  journal      = {Cryptography and Communications},
  keywords     = {Applied Mathematics, Computational Theory and Mathematics, Computer Networks and Communications},
  number       = {4},
  pages        = {933--948},
  publisher    = {Springer Nature},
  title        = {{Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes}},
  doi          = {10.1007/s12095-022-00557-8},
  volume       = {14},
  year         = {2022},
}

@article{11343,
  abstract     = {Multistable systems are characterized by exhibiting domain coexistence, where each domain accounts for the different equilibrium states. In case these systems are described by vectorial fields, domains can be connected through topological defects. Vortices are one of the most frequent and studied topological defect points. Optical vortices are equally relevant for their fundamental features as beams with topological features and their applications in image processing, telecommunications, optical tweezers, and quantum information. A natural source of optical vortices is the interaction of light beams with matter vortices in liquid crystal cells. The rhythms that govern the emergence of matter vortices due to fluctuations are not established. Here, we investigate the nucleation mechanisms of the matter vortices in liquid crystal cells and establish statistical laws that govern them. Based on a stochastic amplitude equation, the law for the number of nucleated vortices as a function of anisotropy, voltage, and noise level intensity is set. Experimental observations in a nematic liquid crystal cell with homeotropic anchoring and a negative anisotropic dielectric constant under the influence of a transversal electric field show a qualitative agreement with the theoretical findings.},
  author       = {Aguilera, Esteban and Clerc, Marcel G. and Zambra, Valeska},
  issn         = {1573-269X},
  journal      = {Nonlinear Dynamics},
  keywords     = {Electrical and Electronic Engineering, Applied Mathematics, Mechanical Engineering, Ocean Engineering, Aerospace Engineering, Control and Systems Engineering},
  pages        = {3209--3218},
  publisher    = {Springer Nature},
  title        = {{Vortices nucleation by inherent fluctuations in nematic liquid crystal cells}},
  doi          = {10.1007/s11071-022-07396-5},
  volume       = {108},
  year         = {2022},
}

@article{11556,
  abstract     = {We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and compare their performance with efficient deterministic finite-difference method applied to the same model. We validate the stochastic methods on the test problems and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation kinetics recently detected in deterministic simulations. We confirm the emergence of steady oscillations of densities in such systems and prove the stability of the
oscillations with respect to fluctuations and noise.},
  author       = {Kalinov, Aleksei and Osinskiy, A.I. and Matveev, S.A. and Otieno, W. and Brilliantov, N.V.},
  issn         = {0021-9991},
  journal      = {Journal of Computational Physics},
  keywords     = {Computer Science Applications, Physics and Astronomy (miscellaneous), Applied Mathematics, Computational Mathematics, Modeling and Simulation, Numerical Analysis},
  publisher    = {Elsevier},
  title        = {{Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics}},
  doi          = {10.1016/j.jcp.2022.111439},
  volume       = {467},
  year         = {2022},
}

@article{12137,
  abstract     = {We investigate the local self-sustained process underlying spiral turbulence in counter-rotating Taylor–Couette flow using a periodic annular domain, shaped as a parallelogram, two of whose sides are aligned with the cylindrical helix described by the spiral pattern. The primary focus of the study is placed on the emergence of drifting–rotating waves (DRW) that capture, in a relatively small domain, the main features of coherent structures typically observed in developed turbulence. The transitional dynamics of the subcritical region, far below the first instability of the laminar circular Couette flow, is determined by the upper and lower branches of DRW solutions originated at saddle-node bifurcations. The mechanism whereby these solutions self-sustain, and the chaotic dynamics they induce, are conspicuously reminiscent of other subcritical shear flows. Remarkably, the flow properties of DRW persist even as the Reynolds number is increased beyond the linear stability threshold of the base flow. Simulations in a narrow parallelogram domain stretched in the azimuthal direction to revolve around the apparatus a full turn confirm that self-sustained vortices eventually concentrate into a localised pattern. The resulting statistical steady state satisfactorily reproduces qualitatively, and to a certain degree also quantitatively, the topology and properties of spiral turbulence as calculated in a large periodic domain of sufficient aspect ratio that is representative of the real system.},
  author       = {Wang, B. and Ayats López, Roger and Deguchi, K. and Mellibovsky, F. and Meseguer, A.},
  issn         = {1469-7645},
  journal      = {Journal of Fluid Mechanics},
  keywords     = {Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics, Applied Mathematics},
  publisher    = {Cambridge University Press},
  title        = {{Self-sustainment of coherent structures in counter-rotating Taylor–Couette flow}},
  doi          = {10.1017/jfm.2022.828},
  volume       = {951},
  year         = {2022},
}

@article{12145,
  abstract     = {In the class of strictly convex smooth boundaries each of which has no strip around its boundary foliated by invariant curves, we prove that the Taylor coefficients of the “normalized” Mather’s β-function are invariant under C∞-conjugacies. In contrast, we prove that any two elliptic billiard maps are C0-conjugate near their respective boundaries, and C∞-conjugate, near the boundary and away from a line passing through the center of the underlying ellipse. We also prove that, if the billiard maps corresponding to two ellipses are topologically conjugate, then the two ellipses are similar.},
  author       = {Koudjinan, Edmond and Kaloshin, Vadim},
  issn         = {1468-4845},
  journal      = {Regular and Chaotic Dynamics},
  keywords     = {Mechanical Engineering, Applied Mathematics, Mathematical Physics, Modeling and Simulation, Statistical and Nonlinear Physics, Mathematics (miscellaneous)},
  number       = {6},
  pages        = {525--537},
  publisher    = {Springer Nature},
  title        = {{On some invariants of Birkhoff billiards under conjugacy}},
  doi          = {10.1134/S1560354722050021},
  volume       = {27},
  year         = {2022},
}

@article{8773,
  abstract     = {Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell.},
  author       = {Brown, Adam and Romanov, Anna},
  issn         = {1088-6826},
  journal      = {Proceedings of the American Mathematical Society},
  keywords     = {Applied Mathematics, General Mathematics},
  number       = {1},
  pages        = {37--52},
  publisher    = {American Mathematical Society},
  title        = {{Contravariant forms on Whittaker modules}},
  doi          = {10.1090/proc/15205},
  volume       = {149},
  year         = {2021},
}

@article{9387,
  abstract     = {We report the complete analysis of a deterministic model of deleterious mutations and negative selection against them at two haploid loci without recombination. As long as mutation is a weaker force than selection, mutant alleles remain rare at the only stable equilibrium, and otherwise, a variety of dynamics are possible. If the mutation-free genotype is absent, generally the only stable equilibrium is the one that corresponds to fixation of the mutant allele at the locus where it is less deleterious. This result suggests that fixation of a deleterious allele that follows a click of the Muller’s ratchet is governed by natural selection, instead of random drift.},
  author       = {Khudiakova, Kseniia and Neretina, Tatiana Yu. and Kondrashov, Alexey S.},
  issn         = {0022-5193},
  journal      = {Journal of Theoretical Biology},
  keywords     = {General Biochemistry, Genetics and Molecular Biology, Modelling and Simulation, Statistics and Probability, General Immunology and Microbiology, Applied Mathematics, General Agricultural and Biological Sciences, General Medicine},
  publisher    = {Elsevier },
  title        = {{Two linked loci under mutation-selection balance and Muller’s ratchet}},
  doi          = {10.1016/j.jtbi.2021.110729},
  volume       = {524},
  year         = {2021},
}

@article{10211,
  abstract     = {We study the problem of recovering an unknown signal 𝑥𝑥 given measurements obtained from a generalized linear model with a Gaussian sensing matrix. Two popular solutions are based on a linear estimator 𝑥𝑥^L and a spectral estimator 𝑥𝑥^s. The former is a data-dependent linear combination of the columns of the measurement matrix, and its analysis is quite simple. The latter is the principal eigenvector of a data-dependent matrix, and a recent line of work has studied its performance. In this paper, we show how to optimally combine 𝑥𝑥^L and 𝑥𝑥^s. At the heart of our analysis is the exact characterization of the empirical joint distribution of (𝑥𝑥,𝑥𝑥^L,𝑥𝑥^s) in the high-dimensional limit. This allows us to compute the Bayes-optimal combination of 𝑥𝑥^L and 𝑥𝑥^s, given the limiting distribution of the signal 𝑥𝑥. When the distribution of the signal is Gaussian, then the Bayes-optimal combination has the form 𝜃𝑥𝑥^L+𝑥𝑥^s and we derive the optimal combination coefficient. In order to establish the limiting distribution of (𝑥𝑥,𝑥𝑥^L,𝑥𝑥^s), we design and analyze an approximate message passing algorithm whose iterates give 𝑥𝑥^L and approach 𝑥𝑥^s. Numerical simulations demonstrate the improvement of the proposed combination with respect to the two methods considered separately.},
  author       = {Mondelli, Marco and Thrampoulidis, Christos and Venkataramanan, Ramji},
  issn         = {1615-3383},
  journal      = {Foundations of Computational Mathematics},
  keywords     = {Applied Mathematics, Computational Theory and Mathematics, Computational Mathematics, Analysis},
  publisher    = {Springer},
  title        = {{Optimal combination of linear and spectral estimators for generalized linear models}},
  doi          = {10.1007/s10208-021-09531-x},
  year         = {2021},
}

@article{10856,
  abstract     = {We study the properties of the maximal volume k-dimensional sections of the n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a k-dimensional subspace to be a local maximizer of the volume of such sections, which we formulate in a geometric way. We estimate the length of the projection of a vector of the standard basis of Rn onto a k-dimensional subspace that maximizes the volume of the intersection. We nd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2.},
  author       = {Ivanov, Grigory and Tsiutsiurupa, Igor},
  issn         = {2299-3274},
  journal      = {Analysis and Geometry in Metric Spaces},
  keywords     = {Applied Mathematics, Geometry and Topology, Analysis},
  number       = {1},
  pages        = {1--18},
  publisher    = {De Gruyter},
  title        = {{On the volume of sections of the cube}},
  doi          = {10.1515/agms-2020-0103},
  volume       = {9},
  year         = {2021},
}

@article{9781,
  abstract     = {We consider the Pekar functional on a ball in ℝ3. We prove uniqueness of minimizers, and a quadratic lower bound in terms of the distance to the minimizer. The latter follows from nondegeneracy of the Hessian at the minimum.},
  author       = {Feliciangeli, Dario and Seiringer, Robert},
  issn         = {1095-7154},
  journal      = {SIAM Journal on Mathematical Analysis},
  keywords     = {Applied Mathematics, Computational Mathematics, Analysis},
  number       = {1},
  pages        = {605--622},
  publisher    = {Society for Industrial & Applied Mathematics },
  title        = {{Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball}},
  doi          = {10.1137/19m126284x},
  volume       = {52},
  year         = {2020},
}

@article{10878,
  abstract     = {Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with discontinuous coefficients for the action potential of each neuron and takes into account the (random) spatial configuration of neurons allowing the interaction to depend on it. In the limit as the number of particles tends to infinity, we obtain a nonlinear Fokker-Planck type PDE in two variables, with derivatives only with respect to one variable and discontinuous coefficients. We also study strong well-posedness of the system of SDEs and prove the existence and uniqueness of a weak measure-valued solution to the PDE, obtained as the limit of the laws of the empirical measures for the system of particles.},
  author       = {Flandoli, Franco and Priola, Enrico and Zanco, Giovanni A},
  issn         = {1553-5231},
  journal      = {Discrete and Continuous Dynamical Systems},
  keywords     = {Applied Mathematics, Discrete Mathematics and Combinatorics, Analysis},
  number       = {6},
  pages        = {3037--3067},
  publisher    = {American Institute of Mathematical Sciences},
  title        = {{A mean-field model with discontinuous coefficients for neurons with spatial interaction}},
  doi          = {10.3934/dcds.2019126},
  volume       = {39},
  year         = {2019},
}