@article{19493,
  abstract     = {In 2016, Balakrishnan, Ho, Kaplan, Spicer, Stein and Weigandt produced a database of elliptic curves over Q ordered by height in which they computed the rank, the size of the 2-Selmer group, and other arithmetic invariants. They observed that after a certain point, the average rank seemed to decrease as the height increased. Here we consider the family of elliptic curves over 
Q whose rational torsion subgroup is isomorphic to Z∕2Z×Z∕8Z. Conditional on GRH and BSD, we compute the rank of 92% of the 202,461 curves with parameter height less than 103. We also compute the size of the 2-Selmer group and the Tamagawa product, and prove that their averages tend to infinity for this family.},
  author       = {Chan, Yik Tung and Hanselman, Jeroen and Li, Wanlin},
  issn         = {2329-907X},
  journal      = {The Open Book Series},
  pages        = {173--189},
  publisher    = {Mathematical Sciences Publishers},
  title        = {{Ranks, 2-Selmer groups, and Tamagawa numbers of elliptic curves with ℤ∕2ℤ × ℤ∕8ℤ-torsion}},
  doi          = {10.2140/obs.2019.2.173},
  volume       = {2},
  year         = {2019},
}

@article{196,
  abstract     = {The abelian sandpile serves as a model to study self-organized criticality, a phenomenon occurring in biological, physical and social processes. The identity of the abelian group is a fractal composed of self-similar patches, and its limit is subject of extensive collaborative research. Here, we analyze the evolution of the sandpile identity under harmonic fields of different orders. We show that this evolution corresponds to periodic cycles through the abelian group characterized by the smooth transformation and apparent conservation of the patches constituting the identity. The dynamics induced by second and third order harmonics resemble smooth stretchings, respectively translations, of the identity, while the ones induced by fourth order harmonics resemble magnifications and rotations. Starting with order three, the dynamics pass through extended regions of seemingly random configurations which spontaneously reassemble into accentuated patterns. We show that the space of harmonic functions projects to the extended analogue of the sandpile group, thus providing a set of universal coordinates identifying configurations between different domains. Since the original sandpile group is a subgroup of the extended one, this directly implies that it admits a natural renormalization. Furthermore, we show that the harmonic fields can be induced by simple Markov processes, and that the corresponding stochastic dynamics show remarkable robustness over hundreds of periods. Finally, we encode information into seemingly random configurations, and decode this information with an algorithm requiring minimal prior knowledge. Our results suggest that harmonic fields might split the sandpile group into sub-sets showing different critical coefficients, and that it might be possible to extend the fractal structure of the identity beyond the boundaries of its domain. },
  author       = {Lang, Moritz and Shkolnikov, Mikhail},
  issn         = {1091-6490},
  journal      = {Proceedings of the National Academy of Sciences of the United States of America},
  number       = {8},
  pages        = {2821--2830},
  publisher    = {National Academy of Sciences},
  title        = {{Harmonic dynamics of the Abelian sandpile}},
  doi          = {10.1073/pnas.1812015116},
  volume       = {116},
  year         = {2019},
}

@article{151,
  abstract     = {We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function f∈Lp with p>1. More precisely, for any 1<q<(p+1)/2 we construct W1,q-bi-Sobolev maps with identity boundary conditions; for f∈L∞, we provide bi-Lipschitz maps. The basic building block of our construction are bi-Lipschitz maps which stretch a given compact subset of the unit square by a given factor while preserving the boundary. The construction of these stretching maps relies on a slight strengthening of the celebrated covering result of Alberti, Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We apply our result to a model functional in nonlinear elasticity, the integrand of which features fast blowup as the Jacobian determinant of the deformation becomes small. For such functionals, the derivation of the equilibrium equations for minimizers requires an additional regularization of test functions, which our maps provide.},
  author       = {Fischer, Julian L and Kneuss, Olivier},
  journal      = {Journal of Differential Equations},
  number       = {1},
  pages        = {257 -- 311},
  publisher    = {Elsevier},
  title        = {{Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with L p data and applications to nonlinear elasticity}},
  doi          = {10.1016/j.jde.2018.07.045},
  volume       = {266},
  year         = {2019},
}

@unpublished{15147,
  abstract     = {Circadian rhythms are generated by a transcription-based feedback loop where CLOCK:BMAL1 drive transcription of their repressors (PER1/2, CRY1/2), which bind to CLOCK:BMAL1 to close the feedback loop with ~24-hour periodicity. Here we identify a key biochemical and structural difference between CRY1 and CRY2 that underlies their differential strengths as transcriptional repressors. While both cryptochromes bind the BMAL1 transactivation domain with similar affinity to sequester it from coactivators, CRY1 is recruited with much higher affinity to the PAS domain core of CLOCK:BMAL1, allowing it to serve as a stronger repressor that lengthens circadian period. We identify a dynamic loop in the secondary pocket that regulates differential binding of cryptochromes to the PAS domain core. Notably, PER2 binding remodels this loop in CRY2 to enhance its affinity for CLOCK:BMAL1, explaining why CRY2 forms an obligate heterodimer with PER2, while CRY1 is capable of repressing CLOCK:BMAL1 both with and without PER2.},
  author       = {Fribourgh, Jennifer L. and Srivastava, Ashutosh and Sandate, Colby R. and Michael, Alicia and Hsu, Peter L. and Rakers, Christin and Nguyen, Leslee T. and Torgrimson, Megan R. and Parico, Gian Carlo G. and Tripathi, Sarvind and Zheng, Ning and Lander, Gabriel C. and Hirota, Tsuyoshi and Tama, Florence and Partch, Carrie L.},
  booktitle    = {bioRxiv},
  title        = {{Protein dynamics regulate distinct biochemical properties of cryptochromes in mammalian circadian rhythms}},
  doi          = {10.1101/740464},
  year         = {2019},
}

@article{15230,
  abstract     = {We have searched the Gaia DR2 catalog for previously unknown hot white dwarfs in the direction of young open star clusters. The aim of this experiment was to try and extend the initial–final mass relation (IFMR) to somewhat higher masses, potentially challenging the Chandrasekhar limit currently thought to be around 1.38 M⊙. We discovered a particularly interesting white dwarf in the direction of the young ∼150 Myr old cluster Messier 47 (NGC 2422). All Gaia indicators (proper motion, parallax, location in the Gaia color–magnitude diagram) suggest that it is a cluster member. Its spectrum, obtained from Gemini-South, yields a number of anomalies: it is a DB (helium-rich atmosphere) white dwarf, it has a large magnetic field (2.5 MG), is of high mass (∼1.06 M⊙), and its colors are very peculiar—particularly the redder ones (r, i, z and y), which suggests that it may have a late-type companion. This may be the only magnetized, detached binary white dwarf with a non-degenerate companion of any spectral type known in or out of a star cluster. If the white dwarf is a cluster member, as all indicators suggest, its progenitor had a mass just over 6 M⊙. It may, however, be telling an even more interesting story than the one related to the IFMR, one about the origin of stellar magnetic fields, SNe I, and gravitational waves from low-mass stellar systems.},
  author       = {Richer, Harvey B. and Kerr, Ronan and Heyl, Jeremy and Caiazzo, Ilaria and Cummings, Jeffrey and Bergeron, Pierre and Dufour, Patrick},
  issn         = {1538-4357},
  journal      = {The Astrophysical Journal},
  keywords     = {Space and Planetary Science, Astronomy and Astrophysics},
  number       = {2},
  publisher    = {American Astronomical Society},
  title        = {{A massive magnetic helium atmosphere white dwarf binary in a young star cluster}},
  doi          = {10.3847/1538-4357/ab2874},
  volume       = {880},
  year         = {2019},
}

@article{15231,
  abstract     = {In this paper, we analyze stellar proper motions in the core of the globular cluster 47 Tucanae to explore the possibility of an intermediate-mass black hole (IMBH) influence on the stellar dynamics. Our use of short-wavelength photometry affords us an exceedingly clear view of stellar motions into the very center of the crowded core, yielding proper motions for >50,000 stars in the central 2′. We model the velocity dispersion profile of the cluster using an isotropic Jeans model. The density distribution is taken as a central IMBH point mass added to a combination of King templates. We individually model the general low-mass cluster objects (main sequence/giant stars), as well as the concentrated populations of heavy binary systems and dark stellar remnants. Using unbinned likelihood model fitting, we find that the inclusion of the concentrated populations in our model plays a crucial role in fitting for an IMBH mass. The concentrated binaries and stellar-mass black holes (BHs) produce a sufficient velocity dispersion signal in the core so as to make an IMBH unnecessary to fit the observations. We additionally determine that a stellar-mass BH retention fraction of 8.5% becomes incompatible with our observed velocities in the core.},
  author       = {Mann, Christopher R. and Richer, Harvey and Heyl, Jeremy and Anderson, Jay and Kalirai, Jason and Caiazzo, Ilaria and Möhle, Swantje D. and Knee, Alan and Baumgardt, Holger},
  issn         = {1538-4357},
  journal      = {The Astrophysical Journal},
  keywords     = {Space and Planetary Science, Astronomy and Astrophysics},
  number       = {1},
  publisher    = {American Astronomical Society},
  title        = {{A multimass velocity dispersion model of 47 Tucanae indicates no evidence for an intermediate-mass black hole}},
  doi          = {10.3847/1538-4357/ab0e6d},
  volume       = {875},
  year         = {2019},
}

@article{10619,
  abstract     = {The quantum anomalous Hall (QAH) effect combines topology and magnetism to produce precisely quantized Hall resistance at zero magnetic field. We report the observation of a QAH effect in twisted bilayer graphene aligned to hexagonal boron nitride. The effect is driven by intrinsic strong interactions, which polarize the electrons into a single spin- and valley-resolved moiré miniband with Chern number C = 1. In contrast to magnetically doped systems, the measured transport energy gap is larger than the Curie temperature for magnetic ordering, and quantization to within 0.1% of the von Klitzing constant persists to temperatures of several kelvin at zero magnetic field. Electrical currents as small as 1 nanoampere controllably switch the magnetic order between states of opposite polarization, forming an electrically rewritable magnetic memory.},
  author       = {Serlin, M. and Tschirhart, C. L. and Polshyn, Hryhoriy and Zhang, Y. and Zhu, J. and Watanabe, K. and Taniguchi, T. and Balents, L. and Young, A. F.},
  issn         = {1095-9203},
  journal      = {Science},
  keywords     = {multidisciplinary},
  number       = {6480},
  pages        = {900--903},
  publisher    = {American Association for the Advancement of Science},
  title        = {{Intrinsic quantized anomalous Hall effect in a moiré heterostructure}},
  doi          = {10.1126/science.aay5533},
  volume       = {367},
  year         = {2019},
}

@article{10620,
  abstract     = {Partially filled Landau levels host competing electronic orders. For example, electron solids may prevail close to integer filling of the Landau levels before giving way to fractional quantum Hall liquids at higher carrier density1,2. Here, we report the observation of an electron solid with non-collinear spin texture in monolayer graphene, consistent with solidification of skyrmions3—topological spin textures characterized by quantized electrical charge4,5. We probe the spin texture of the solids using a modified Corbino geometry that allows ferromagnetic magnons to be launched and detected6,7. We find that magnon transport is highly efficient when one Landau level is filled (ν=1), consistent with quantum Hall ferromagnetic spin polarization. However, even minimal doping immediately quenches the magnon signal while leaving the vanishing low-temperature charge conductivity unchanged. Our results can be understood by the formation of a solid of charged skyrmions near ν=1, whose non-collinear spin texture leads to rapid magnon decay. Data near fractional fillings show evidence of several fractional skyrmion solids, suggesting that graphene hosts a highly tunable landscape of coupled spin and charge orders.},
  author       = {Zhou, H. and Polshyn, Hryhoriy and Taniguchi, T. and Watanabe, K. and Young, A. F.},
  issn         = {1745-2481},
  journal      = {Nature Physics},
  keywords     = {General Physics and Astronomy},
  number       = {2},
  pages        = {154--158},
  publisher    = {Springer Nature},
  title        = {{Solids of quantum Hall skyrmions in graphene}},
  doi          = {10.1038/s41567-019-0729-8},
  volume       = {16},
  year         = {2019},
}

@article{10621,
  abstract     = {Twisted bilayer graphene has recently emerged as a platform for hosting correlated phenomena. For twist angles near θ ≈ 1.1°, the low-energy electronic structure of twisted bilayer graphene features isolated bands with a flat dispersion1,2. Recent experiments have observed a variety of low-temperature phases that appear to be driven by electron interactions, including insulating states, superconductivity and magnetism3,4,5,6. Here we report electrical transport measurements up to room temperature for twist angles varying between 0.75° and 2°. We find that the resistivity, ρ, scales linearly with temperature, T, over a wide range of T before falling again owing to interband activation. The T-linear response is much larger than observed in monolayer graphene for all measured devices, and in particular increases by more than three orders of magnitude in the range where the flat band exists. Our results point to the dominant role of electron–phonon scattering in twisted bilayer graphene, with possible implications for the origin of the observed superconductivity.},
  author       = {Polshyn, Hryhoriy and Yankowitz, Matthew and Chen, Shaowen and Zhang, Yuxuan and Watanabe, K. and Taniguchi, T. and Dean, Cory R. and Young, Andrea F.},
  issn         = {1745-2481},
  journal      = {Nature Physics},
  keywords     = {general physics and astronomy},
  number       = {10},
  pages        = {1011--1016},
  publisher    = {Springer Nature},
  title        = {{Large linear-in-temperature resistivity in twisted bilayer graphene}},
  doi          = {10.1038/s41567-019-0596-3},
  volume       = {15},
  year         = {2019},
}

@article{10622,
  abstract     = {We demonstrate a method for manipulating small ensembles of vortices in multiply connected superconducting structures. A micron-size magnetic particle attached to the tip of a silicon cantilever is used to locally apply magnetic flux through the superconducting structure. By scanning the tip over the surface of the device and by utilizing the dynamical coupling between the vortices and the cantilever, a high-resolution spatial map of the different vortex configurations is obtained. Moving the tip to a particular location in the map stabilizes a distinct multivortex configuration. Thus, the scanning of the tip over a particular trajectory in space permits nontrivial operations to be performed, such as braiding of individual vortices within a larger vortex ensemble—a key capability required by many proposals for topological quantum computing.},
  author       = {Polshyn, Hryhoriy and Naibert, Tyler and Budakian, Raffi},
  issn         = {1530-6992},
  journal      = {Nano Letters},
  keywords     = {mechanical engineering, condensed matter physics, general materials science, general chemistry, bioengineering},
  number       = {8},
  pages        = {5476--5482},
  publisher    = {American Chemical Society},
  title        = {{Manipulating multivortex states in superconducting structures}},
  doi          = {10.1021/acs.nanolett.9b01983},
  volume       = {19},
  year         = {2019},
}

@article{10625,
  abstract     = {The discovery of superconductivity and exotic insulating phases in twisted bilayer graphene has established this material as a model system of strongly correlated electrons. To achieve superconductivity, the two layers of graphene need to be at a very precise angle with respect to each other. Yankowitz et al. now show that another experimental knob, hydrostatic pressure, can be used to tune the phase diagram of twisted bilayer graphene (see the Perspective by Feldman). Applying pressure increased the coupling between the layers, which shifted the superconducting transition to higher angles and somewhat higher temperatures.},
  author       = {Yankowitz, Matthew and Chen, Shaowen and Polshyn, Hryhoriy and Zhang, Yuxuan and Watanabe, K. and Taniguchi, T. and Graf, David and Young, Andrea F. and Dean, Cory R.},
  issn         = {1095-9203},
  journal      = {Science},
  keywords     = {multidisciplinary},
  number       = {6431},
  pages        = {1059--1064},
  publisher    = {American Association for the Advancement of Science (AAAS)},
  title        = {{Tuning superconductivity in twisted bilayer graphene}},
  doi          = {10.1126/science.aav1910},
  volume       = {363},
  year         = {2019},
}

@article{10664,
  abstract     = {Since the discovery of correlated insulators and superconductivity in magic-angle twisted bilayer graphene (tBLG) ([1, 2], JCCM April 2018), theorists have been excitedly pursuing the alluring mix of band topology, symmetry breaking, Mott insulators and superconductivity at play, as well as the potential relation (if any) to high-Tc physics. Now a new stream
of experimental work is arriving which further enriches the story. To briefly recap Episodes 1 and 2 (JCCM April and November 2018), when two graphene layers are stacked with a small rotational mismatch θ, the resulting long-wavelength moire pattern leads to a superlattice potential which reconstructs the low energy band structure. When θ approaches the “magic-angle” θM ∼ 1 ◦, the band structure features eight nearly-flat bands which fill when the electron number per moire unit cell, n/n0, lies between −4 < n/n0 < 4. The bands can be counted as 8 = 2 × 2 × 2: for each spin (2×) and valley (2×) characteristic of monolayergraphene, tBLG has has 2× flat bands which cross at mini-Dirac points.},
  author       = {Yankowitz, Mathew and Chen, Shaowen and Polshyn, Hryhoriy and Watanabe, K. and Taniguchi, T. and Graf, David and Young, Andrea F. and Dean, Cory R. and Sharpe, Aaron L. and Fox, E.J. and Barnard, A.W. and Finney, Joe},
  journal      = {Journal Club for Condensed Matter Physics},
  publisher    = {Simons Foundation ; University of California, Riverside},
  title        = {{New correlated phenomena in magic-angle twisted bilayer graphene/s}},
  doi          = {10.36471/jccm_february_2019_03},
  volume       = {03},
  year         = {2019},
}

@inproceedings{10722,
  abstract     = {Bilayer graphene, rotationally faulted to ~1.1 degree misalignment, has recently been shown to host superconducting and resistive states associated with the formation of a flat electronic band. While numerous theories exist for the origins of both states, direct validation of these theories remains an outstanding experimental problem. Here, we focus on the resistive states occurring at commensurate filling (1/2, 1/4, and 3/4) of the two lowest superlattice bands. We test theoretical proposals that these states arise due to broken spin—and/or valley—symmetry by performing direct magnetic imaging with nanoscale SQUID-on-tip microscopy. This technique provides single-spin resolved magnetometry on sub-100nm length scales. I will present imaging data from our 4.2K nSOT microscope on graphite-gated twisted bilayers near the flat band condition and discuss the implications for the physics of the commensurate resistive states.},
  author       = {Serlin, Marec and Tschirhart, Charles and Polshyn, Hryhoriy and Zhu, Jiacheng and Huber, Martin E. and Young, Andrea},
  booktitle    = {APS March Meeting 2019},
  issn         = {0003-0503},
  location     = {Boston, MA, United States},
  number       = {2},
  publisher    = {American Physical Society},
  title        = {{Direct Imaging of magnetic structure in twisted bilayer graphene with scanning nanoSQUID-On-Tip microscopy}},
  volume       = {64},
  year         = {2019},
}

@inproceedings{10723,
  abstract     = {In monolayer graphene, the interplay of electronic correlations with the internal spin- and valley- degrees of freedom leads to a complex phase diagram of isospin symmetry breaking at high magnetic fields. Recently, Wei et al. (Science (2018)) demonstrated that spin waves can be electrically generated and detected in graphene heterojunctions, allowing direct experiment access to the spin degree of freedom. Here, we apply this technique to high quality graphite-gated graphene devices showing robust fractional quantum Hall phases and isospin phase transitions. We use an edgeless Corbino geometry to eliminate the contributions of edge states to the spin-wave mediated nonlocal voltage, allowing unambiguous identification of spin wave transport signatures. Our data reveal two phases within the ν = 1 plateau. For exactly ν=1, charge is localized but spin waves propagate freely while small carrier doping completely quenches the low-energy spin-wave transport, even as those charges remain localized. We identify this new phase as a spin textured electron solid. We also find that spin-wave transport is modulated by phase transitions in the valley order that preserve spin polarization, suggesting that this technique is sensitive to both spin and valley order.},
  author       = {Zhou, Haoxin and Polshyn, Hryhoriy and Tanaguchi, Takashi and Watanabe, Kenji and Young, Andrea},
  booktitle    = {APS March Meeting 2019},
  issn         = {0003-0503},
  location     = {Boston, MA, United States},
  number       = {2},
  publisher    = {American Physical Society},
  title        = {{Spin wave transport through electron solids and fractional quantum Hall liquids in graphene}},
  volume       = {64},
  year         = {2019},
}

@inproceedings{10724,
  abstract     = {Twisted bilayer graphene (tBLG) near the flat band condition is a versatile new platform for the study of correlated physics in 2D. Resistive states have been observed at several commensurate fillings of the flat miniband, along with superconducting states near half filling. To better understand the electronic structure of this system, we study electronic transport of graphite gated superconducting tBLG devices in the normal regime. At high magnetic fields, we observe full lifting of the spin and valley degeneracy. The transitions in the splitting of this four-fold degeneracy as a function of carrier density indicate Landau level (LL) crossings, which tilted field measurements show occur between LLs with different valley polarization. Similar LL structure measured in two devices, one with twist angle θ=1.08° at ambient pressure and one at θ=1.27° and 1.33GPa, suggests that the dimensionless combination of twist angle and interlayer coupling controls the relevant details of the band structure. In addition, we find that the temperature dependence of the resistance at B=0 shows linear growth at several hundred Ohm/K in a broad range of temperatures. We discuss the implications for modeling the scattering processes in this system.},
  author       = {Polshyn, Hryhoriy and Zhang, Yuxuan and Yankowitz, Matthew and Chen, Shaowen and Taniguchi, Takashi and Watanabe, Kenji and Graf, David E. and Dean, Cory R. and Young, Andrea},
  booktitle    = {APS March Meeting 2019},
  issn         = {0003-0503},
  location     = {Boston, MA, United States},
  number       = {2},
  publisher    = {American Physical Society},
  title        = {{Normal state transport in superconducting twisted bilayer graphene}},
  volume       = {64},
  year         = {2019},
}

@inproceedings{10725,
  abstract     = {Bilayer graphene with ~ 1.1 degrees twist mismatch between the layers hosts a low energy flat band in which the Coulomb interaction is large relative to the bandwidth, promoting correlated insulating states at half band filling, and superconducting (SC) phases with dome-like structure neighboring correlated insulating states. Here we show measurements of a dual-graphite-gated twisted bilayer graphene device, which minimizes charge inhomogeneity. We observe new correlated phases, including for the first time a SC pocket near half-filling of the electron-doped band and resistive states at quarter-filling of both bands that emerge in a magnetic field. Changing the layer polarization with vertical electric field reveals an unexpected competition between SC and correlated insulator phases, which we interpret to result from differences in disorder of each graphene layer and underscores the spatial inhomogeneity like twist angle as a significant source of disorder in these devices [1].},
  author       = {Chen, Shaowen and Yankowitz, Matthew and Polshyn, Hryhoriy and Watanabe, Kenji and Taniguchi, Takashi and Graf, David E. and Young, Andrea and Dean, Cory R.},
  booktitle    = {APS March Meeting 2019},
  issn         = {0003-0503},
  location     = {Boston, MA, United States},
  number       = {2},
  publisher    = {American Physical Society},
  title        = {{Correlated insulating and superconducting phases in twisted bilayer graphene}},
  volume       = {64},
  year         = {2019},
}

@article{10874,
  abstract     = {In this article we prove an analogue of a theorem of Lachaud, Ritzenthaler, and Zykin, which allows us to connect invariants of binary octics to Siegel modular forms of genus 3. We use this connection to show that certain modular functions, when restricted to the hyperelliptic locus, assume values whose denominators are products of powers of primes of bad reduction for the associated hyperelliptic curves. We illustrate our theorem with explicit computations. This work is motivated by the study of the values of these modular functions at CM points of the Siegel upper half-space, which, if their denominators are known, can be used to effectively compute models of (hyperelliptic, in our case) curves with CM.},
  author       = {Ionica, Sorina and Kılıçer, Pınar and Lauter, Kristin and Lorenzo García, Elisa and Manzateanu, Maria-Adelina and Massierer, Maike and Vincent, Christelle},
  issn         = {2363-9555},
  journal      = {Research in Number Theory},
  keywords     = {Algebra and Number Theory},
  publisher    = {Springer Nature},
  title        = {{Modular invariants for genus 3 hyperelliptic curves}},
  doi          = {10.1007/s40993-018-0146-6},
  volume       = {5},
  year         = {2019},
}

@inproceedings{10877,
  abstract     = {This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with piecewise constant dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2019. In this third edition, six tools have been applied to solve five different benchmark problems in the category for piecewise constant dynamics: BACH, Lyse, Hy- COMP, PHAVer/SX, PHAVerLite, and VeriSiMPL. Compared to last year, a new tool has participated (HyCOMP) and PHAVerLite has replaced PHAVer-lite. The result is a snap- shot of the current landscape of tools and the types of benchmarks they are particularly suited for. Due to the diversity of problems, we are not ranking tools, yet the presented results probably provide the most complete assessment of tools for the safety verification of continuous and hybrid systems with piecewise constant dynamics up to this date.},
  author       = {Frehse, Goran and Abate, Alessandro and Adzkiya, Dieky and Becchi, Anna and Bu, Lei and Cimatti, Alessandro and Giacobbe, Mirco and Griggio, Alberto and Mover, Sergio and Mufid, Muhammad Syifa'ul and Riouak, Idriss and Tonetta, Stefano and Zaffanella, Enea},
  booktitle    = {ARCH19. 6th International Workshop on Applied Verification of Continuous and Hybrid Systems},
  editor       = {Frehse, Goran and Althoff, Matthias},
  issn         = {2398-7340},
  location     = {Montreal, Canada},
  pages        = {1--13},
  publisher    = {EasyChair},
  title        = {{ARCH-COMP19 Category Report: Hybrid systems with piecewise constant dynamics}},
  doi          = {10.29007/rjwn},
  volume       = {61},
  year         = {2019},
}

@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},
}

@article{10879,
  abstract     = {We study effects of a bounded and compactly supported perturbation on multidimensional continuum random Schrödinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schrödinger operators. Among others, we prove that Anderson orthogonality does occur for Fermi energies in the region of complete localisation with a non-zero probability. This partially confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015), 560–565]. The spectral shift function plays an important role in our analysis of Anderson orthogonality. We identify it with the index of the corresponding pair of spectral projections and explore the consequences thereof. All our results rely on the main technical estimate of this paper which guarantees separate exponential decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b. Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication operator corresponding to the indicator function of a unit cube centred about a∈Rd, and f is in a suitable class of functions of bounded variation with distributional derivative supported in the region of complete localisation for H.},
  author       = {Dietlein, Adrian M and Gebert, Martin and Müller, Peter},
  issn         = {1664-039X},
  journal      = {Journal of Spectral Theory},
  keywords     = {Random Schrödinger operators, spectral shift function, Anderson orthogonality},
  number       = {3},
  pages        = {921--965},
  publisher    = {European Mathematical Society},
  title        = {{Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function}},
  doi          = {10.4171/jst/267},
  volume       = {9},
  year         = {2019},
}