@unpublished{10065, abstract = {We study double quantum dots in a Ge/SiGe heterostructure and test their maturity towards singlet-triplet ($S-T_0$) qubits. We demonstrate a large range of tunability, from two single quantum dots to a double quantum dot. We measure Pauli spin blockade and study the anisotropy of the $g$-factor. We use an adjacent quantum dot for sensing charge transitions in the double quantum dot at interest. In conclusion, Ge/SiGe possesses all ingredients necessary for building a singlet-triplet qubit.}, author = {Hofmann, Andrea C and Jirovec, Daniel and Borovkov, Maxim and Prieto Gonzalez, Ivan and Ballabio, Andrea and Frigerio, Jacopo and Chrastina, Daniel and Isella, Giovanni and Katsaros, Georgios}, booktitle = {arXiv}, title = {{Assessing the potential of Ge/SiGe quantum dots as hosts for singlet-triplet qubits}}, doi = {10.48550/arXiv.1910.05841}, year = {2019}, } @inproceedings{10190, abstract = {The verification of concurrent programs remains an open challenge, as thread interaction has to be accounted for, which leads to state-space explosion. Stateless model checking battles this problem by exploring traces rather than states of the program. As there are exponentially many traces, dynamic partial-order reduction (DPOR) techniques are used to partition the trace space into equivalence classes, and explore a few representatives from each class. The standard equivalence that underlies most DPOR techniques is the happens-before equivalence, however recent works have spawned a vivid interest towards coarser equivalences. The efficiency of such approaches is a product of two parameters: (i) the size of the partitioning induced by the equivalence, and (ii) the time spent by the exploration algorithm in each class of the partitioning. In this work, we present a new equivalence, called value-happens-before and show that it has two appealing features. First, value-happens-before is always at least as coarse as the happens-before equivalence, and can be even exponentially coarser. Second, the value-happens-before partitioning is efficiently explorable when the number of threads is bounded. We present an algorithm called value-centric DPOR (VCDPOR), which explores the underlying partitioning using polynomial time per class. Finally, we perform an experimental evaluation of VCDPOR on various benchmarks, and compare it against other state-of-the-art approaches. Our results show that value-happens-before typically induces a significant reduction in the size of the underlying partitioning, which leads to a considerable reduction in the running time for exploring the whole partitioning.}, author = {Chatterjee, Krishnendu and Pavlogiannis, Andreas and Toman, Viktor}, booktitle = {Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications}, issn = {2475-1421}, keywords = {safety, risk, reliability and quality, software}, location = {Athens, Greece}, publisher = {ACM}, title = {{Value-centric dynamic partial order reduction}}, doi = {10.1145/3360550}, volume = {3}, year = {2019}, } @article{10354, abstract = {Background ESCRT-III is a membrane remodelling filament with the unique ability to cut membranes from the inside of the membrane neck. It is essential for the final stage of cell division, the formation of vesicles, the release of viruses, and membrane repair. Distinct from other cytoskeletal filaments, ESCRT-III filaments do not consume energy themselves, but work in conjunction with another ATP-consuming complex. Despite rapid progress in describing the cell biology of ESCRT-III, we lack an understanding of the physical mechanisms behind its force production and membrane remodelling. Results Here we present a minimal coarse-grained model that captures all the experimentally reported cases of ESCRT-III driven membrane sculpting, including the formation of downward and upward cones and tubules. This model suggests that a change in the geometry of membrane bound ESCRT-III filaments—from a flat spiral to a 3D helix—drives membrane deformation. We then show that such repetitive filament geometry transitions can induce the fission of cargo-containing vesicles. Conclusions Our model provides a general physical mechanism that explains the full range of ESCRT-III-dependent membrane remodelling and scission events observed in cells. This mechanism for filament force production is distinct from the mechanisms described for other cytoskeletal elements discovered so far. The mechanistic principles revealed here suggest new ways of manipulating ESCRT-III-driven processes in cells and could be used to guide the engineering of synthetic membrane-sculpting systems.}, author = {Harker-Kirschneck, Lena and Baum, Buzz and Šarić, Anđela}, issn = {1741-7007}, journal = {BMC Biology}, keywords = {cell biology}, number = {1}, publisher = {Springer Nature}, title = {{Changes in ESCRT-III filament geometry drive membrane remodelling and fission in silico}}, doi = {10.1186/s12915-019-0700-2}, volume = {17}, year = {2019}, } @article{10355, abstract = {The molecular machinery of life is largely created via self-organisation of individual molecules into functional assemblies. Minimal coarse-grained models, in which a whole macromolecule is represented by a small number of particles, can be of great value in identifying the main driving forces behind self-organisation in cell biology. Such models can incorporate data from both molecular and continuum scales, and their results can be directly compared to experiments. Here we review the state of the art of models for studying the formation and biological function of macromolecular assemblies in living organisms. We outline the key ingredients of each model and their main findings. We illustrate the contribution of this class of simulations to identifying the physical mechanisms behind life and diseases, and discuss their future developments.}, author = {Hafner, Anne E and Krausser, Johannes and Šarić, Anđela}, issn = {0959-440X}, journal = {Current Opinion in Structural Biology}, keywords = {molecular biology, structural biology}, pages = {43--52}, publisher = {Elsevier}, title = {{Minimal coarse-grained models for molecular self-organisation in biology}}, doi = {10.1016/j.sbi.2019.05.018}, volume = {58}, year = {2019}, } @article{105, abstract = {Clinical Utility Gene Card. 1. Name of Disease (Synonyms): Pontocerebellar hypoplasia type 9 (PCH9) and spastic paraplegia-63 (SPG63). 2. OMIM# of the Disease: 615809 and 615686. 3. Name of the Analysed Genes or DNA/Chromosome Segments: AMPD2 at 1p13.3. 4. OMIM# of the Gene(s): 102771.}, author = {Marsh, Ashley and Novarino, Gaia and Lockhart, Paul and Leventer, Richard}, journal = {European Journal of Human Genetics}, pages = {161--166}, publisher = {Springer Nature}, title = {{CUGC for pontocerebellar hypoplasia type 9 and spastic paraplegia-63}}, doi = {10.1038/s41431-018-0231-2}, volume = {27}, 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{9460, abstract = {Epigenetic reprogramming is required for proper regulation of gene expression in eukaryotic organisms. In Arabidopsis, active DNA demethylation is crucial for seed viability, pollen function, and successful reproduction. The DEMETER (DME) DNA glycosylase initiates localized DNA demethylation in vegetative and central cells, so-called companion cells that are adjacent to sperm and egg gametes, respectively. In rice, the central cell genome displays local DNA hypomethylation, suggesting that active DNA demethylation also occurs in rice; however, the enzyme responsible for this process is unknown. One candidate is the rice REPRESSOR OF SILENCING 1a (ROS1a) gene, which is related to DME and is essential for rice seed viability and pollen function. Here, we report genome-wide analyses of DNA methylation in wild-type and ros1a mutant sperm and vegetative cells. We find that the rice vegetative cell genome is locally hypomethylated compared with sperm by a process that requires ROS1a activity. We show that many ROS1a target sequences in the vegetative cell are hypomethylated in the rice central cell, suggesting that ROS1a also demethylates the central cell genome. Similar to Arabidopsis, we show that sperm non-CG methylation is indirectly promoted by DNA demethylation in the vegetative cell. These results reveal that DNA glycosylase-mediated DNA demethylation processes are conserved in Arabidopsis and rice, plant species that diverged 150 million years ago. Finally, although global non-CG methylation levels of sperm and egg differ, the maternal and paternal embryo genomes show similar non-CG methylation levels, suggesting that rice gamete genomes undergo dynamic DNA methylation reprogramming after cell fusion.}, author = {Kim, M. Yvonne and Ono, Akemi and Scholten, Stefan and Kinoshita, Tetsu and Zilberman, Daniel and Okamoto, Takashi and Fischer, Robert L.}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, keywords = {Multidisciplinary}, number = {19}, pages = {9652--9657}, publisher = {National Academy of Sciences}, title = {{DNA demethylation by ROS1a in rice vegetative cells promotes methylation in sperm}}, doi = {10.1073/pnas.1821435116}, volume = {116}, year = {2019}, } @article{9530, abstract = {Background DNA methylation of active genes, also known as gene body methylation, is found in many animal and plant genomes. Despite this, the transcriptional and developmental role of such methylation remains poorly understood. Here, we explore the dynamic range of DNA methylation in honey bee, a model organism for gene body methylation. Results Our data show that CG methylation in gene bodies globally fluctuates during honey bee development. However, these changes cause no gene expression alterations. Intriguingly, despite the global alterations, tissue-specific CG methylation patterns of complete genes or exons are rare, implying robust maintenance of genic methylation during development. Additionally, we show that CG methylation maintenance fluctuates in somatic cells, while reaching maximum fidelity in sperm cells. Finally, unlike universally present CG methylation, we discovered non-CG methylation specifically in bee heads that resembles such methylation in mammalian brain tissue. Conclusions Based on these results, we propose that gene body CG methylation can oscillate during development if it is kept to a level adequate to preserve function. Additionally, our data suggest that heightened non-CG methylation is a conserved regulator of animal nervous systems.}, author = {Harris, Keith D. and Lloyd, James P. B. and Domb, Katherine and Zilberman, Daniel and Zemach, Assaf}, issn = {1756-8935}, journal = {Epigenetics and Chromatin}, publisher = {Springer Nature}, title = {{DNA methylation is maintained with high fidelity in the honey bee germline and exhibits global non-functional fluctuations during somatic development}}, doi = {10.1186/s13072-019-0307-4}, volume = {12}, year = {2019}, } @article{9580, abstract = {An r-cut of a k-uniform hypergraph H is a partition of the vertex set of H into r parts and the size of the cut is the number of edges which have a vertex in each part. A classical result of Edwards says that every m-edge graph has a 2-cut of size m/2+Ω)(m−−√) and this is best possible. That is, there exist cuts which exceed the expected size of a random cut by some multiple of the standard deviation. We study analogues of this and related results in hypergraphs. First, we observe that similarly to graphs, every m-edge k-uniform hypergraph has an r-cut whose size is Ω(m−−√) larger than the expected size of a random r-cut. Moreover, in the case where k = 3 and r = 2 this bound is best possible and is attained by Steiner triple systems. Surprisingly, for all other cases (that is, if k ≥ 4 or r ≥ 3), we show that every m-edge k-uniform hypergraph has an r-cut whose size is Ω(m5/9) larger than the expected size of a random r-cut. This is a significant difference in behaviour, since the amount by which the size of the largest cut exceeds the expected size of a random cut is now considerably larger than the standard deviation.}, author = {Conlon, David and Fox, Jacob and Kwan, Matthew Alan and Sudakov, Benny}, issn = {1565-8511}, journal = {Israel Journal of Mathematics}, number = {1}, pages = {67--111}, publisher = {Springer}, title = {{Hypergraph cuts above the average}}, doi = {10.1007/s11856-019-1897-z}, volume = {233}, year = {2019}, } @article{9585, abstract = {An n-vertex graph is called C-Ramsey if it has no clique or independent set of size C log n. All known constructions of Ramsey graphs involve randomness in an essential way, and there is an ongoing line of research towards showing that in fact all Ramsey graphs must obey certain “richness” properties characteristic of random graphs. More than 25 years ago, Erdős, Faudree and Sós conjectured that in any C-Ramsey graph there are Ω(n^5/2) induced subgraphs, no pair of which have the same numbers of vertices and edges. Improving on earlier results of Alon, Balogh, Kostochka and Samotij, in this paper we prove this conjecture.}, author = {Kwan, Matthew Alan and Sudakov, Benny}, issn = {1088-6850}, journal = {Transactions of the American Mathematical Society}, number = {8}, pages = {5571--5594}, publisher = {American Mathematical Society}, title = {{Proof of a conjecture on induced subgraphs of Ramsey graphs}}, doi = {10.1090/tran/7729}, volume = {372}, year = {2019}, } @article{9586, abstract = {Consider integers 𝑘,ℓ such that 0⩽ℓ⩽(𝑘2) . Given a large graph 𝐺 , what is the fraction of 𝑘 -vertex subsets of 𝐺 which span exactly ℓ edges? When 𝐺 is empty or complete, and ℓ is zero or (𝑘2) , this fraction can be exactly 1. On the other hand, if ℓ is far from these extreme values, one might expect that this fraction is substantially smaller than 1. This was recently proved by Alon, Hefetz, Krivelevich, and Tyomkyn who initiated the systematic study of this question and proposed several natural conjectures. Let ℓ∗=min{ℓ,(𝑘2)−ℓ} . Our main result is that for any 𝑘 and ℓ , the fraction of 𝑘 -vertex subsets that span ℓ edges is at most log𝑂(1)(ℓ∗/𝑘)√ 𝑘/ℓ∗, which is best-possible up to the logarithmic factor. This improves on multiple results of Alon, Hefetz, Krivelevich, and Tyomkyn, and resolves one of their conjectures. In addition, we also make some first steps towards some analogous questions for hypergraphs. Our proofs involve some Ramsey-type arguments, and a number of different probabilistic tools, such as polynomial anticoncentration inequalities, hypercontractivity, and a coupling trick for random variables defined on a ‘slice’ of the Boolean hypercube.}, author = {Kwan, Matthew Alan and Sudakov, Benny and Tran, Tuan}, issn = {1469-7750}, journal = {Journal of the London Mathematical Society}, number = {3}, pages = {757--777}, publisher = {Wiley}, title = {{Anticoncentration for subgraph statistics}}, doi = {10.1112/jlms.12192}, volume = {99}, year = {2019}, }