@misc{9814, abstract = {Data and mathematica notebooks for plotting figures from Language learning with communication between learners}, author = {Ibsen-Jensen, Rasmus and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin}, publisher = {Royal Society}, title = {{Data and mathematica notebooks for plotting figures from language learning with communication between learners from language acquisition with communication between learners}}, doi = {10.6084/m9.figshare.5973013.v1}, year = {2020}, } @misc{9878, author = {Gupta, Chitrak and Khaniya, Umesh and Chan, Chun Kit and Dehez, Francois and Shekhar, Mrinal and Gunner, M.R. and Sazanov, Leonid A and Chipot, Christophe and Singharoy, Abhishek}, publisher = {American Chemical Society}, title = {{Movies}}, doi = {10.1021/jacs.9b13450.s002}, year = {2020}, } @misc{9885, abstract = {Data obtained from the fine-grained simulations used in Figures 2-5, data obtained from the coarse-grained numerical calculations used in Figure 6, and a sample script for the fine-grained simulation as a Jupyter notebook (ZIP)}, author = {Ucar, Mehmet C and Lipowsky, Reinhard}, publisher = {American Chemical Society }, title = {{MURL_Dataz}}, doi = {10.1021/acs.nanolett.9b04445.s002}, year = {2020}, } @article{27, abstract = {The cerebral cortex is composed of a large variety of distinct cell-types including projection neurons, interneurons and glial cells which emerge from distinct neural stem cell (NSC) lineages. The vast majority of cortical projection neurons and certain classes of glial cells are generated by radial glial progenitor cells (RGPs) in a highly orchestrated manner. Recent studies employing single cell analysis and clonal lineage tracing suggest that NSC and RGP lineage progression are regulated in a profound deterministic manner. In this review we focus on recent advances based mainly on correlative phenotypic data emerging from functional genetic studies in mice. We establish hypotheses to test in future research and outline a conceptual framework how epigenetic cues modulate the generation of cell-type diversity during cortical development. This article is protected by copyright. All rights reserved.}, author = {Amberg, Nicole and Laukoter, Susanne and Hippenmeyer, Simon}, journal = {Journal of Neurochemistry}, number = {1}, pages = {12--26}, publisher = {Wiley}, title = {{Epigenetic cues modulating the generation of cell type diversity in the cerebral cortex}}, doi = {10.1111/jnc.14601}, volume = {149}, year = {2019}, } @article{301, abstract = {A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that appear in the usual formulation are not even defined in the Itô sense.}, author = {Gerencser, Mate and Gyöngy, István}, journal = {Stochastic Processes and their Applications}, number = {3}, pages = {995--1012}, publisher = {Elsevier}, title = {{A Feynman–Kac formula for stochastic Dirichlet problems}}, doi = {10.1016/j.spa.2018.04.003}, volume = {129}, year = {2019}, } @article{319, abstract = {We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is sufficiently large to cover in particular the Dirichlet and Neumann heat kernels. These results are then used to provide solution theories for the KPZ equation with Dirichlet and Neumann boundary conditions and for the 2D generalised parabolic Anderson model with Dirichlet boundary conditions. In the case of the KPZ equation with Neumann boundary conditions, we show that, depending on the class of mollifiers one considers, a “boundary renormalisation” takes place. In other words, there are situations in which a certain boundary condition is applied to an approximation to the KPZ equation, but the limiting process is the Hopf–Cole solution to the KPZ equation with a different boundary condition.}, author = {Gerencser, Mate and Hairer, Martin}, issn = {14322064}, journal = {Probability Theory and Related Fields}, number = {3-4}, pages = {697–758}, publisher = {Springer}, title = {{Singular SPDEs in domains with boundaries}}, doi = {10.1007/s00440-018-0841-1}, volume = {173}, 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}, } @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 Publishing House}, 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}, } @inproceedings{11222, author = {Kim, Olena and Borges Merjane, Carolina and Jonas, Peter M}, booktitle = {Intrinsic Activity}, issn = {2309-8503}, keywords = {hippocampus, mossy fibers, readily releasable pool, electron microscopy}, location = {Innsbruck, Austria}, number = {Suppl. 1}, publisher = {Austrian Pharmacological Society}, title = {{Functional analysis of the docked vesicle pool in hippocampal mossy fiber terminals by electron microscopy}}, doi = {10.25006/ia.7.s1-a3.27}, volume = {7}, year = {2019}, } @unpublished{7950, abstract = {The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results: 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.}, author = {Biniaz, Ahmad and Jain, Kshitij and Lubiw, Anna and Masárová, Zuzana and Miltzow, Tillmann and Mondal, Debajyoti and Naredla, Anurag Murty and Tkadlec, Josef and Turcotte, Alexi}, booktitle = {arXiv}, title = {{Token swapping on trees}}, year = {2019}, } @article{8, abstract = {Despite their different origins, Drosophila glia and hemocytes are related cell populations that provide an immune function. Drosophila hemocytes patrol the body cavity and act as macrophages outside the nervous system whereas glia originate from the neuroepithelium and provide the scavenger population of the nervous system. Drosophila glia are hence the functional orthologs of vertebrate microglia, even though the latter are cells of immune origin that subsequently move into the brain during development. Interestingly, the Drosophila immune cells within (glia) and outside the nervous system (hemocytes) require the same transcription factor Glide/Gcm for their development. This raises the issue of how do glia specifically differentiate in the nervous system and hemocytes in the procephalic mesoderm. The Repo homeodomain transcription factor and pan-glial direct target of Glide/Gcm is known to ensure glial terminal differentiation. Here we show that Repo also takes center stage in the process that discriminates between glia and hemocytes. First, Repo expression is repressed in the hemocyte anlagen by mesoderm-specific factors. Second, Repo ectopic activation in the procephalic mesoderm is sufficient to repress the expression of hemocyte-specific genes. Third, the lack of Repo triggers the expression of hemocyte markers in glia. Thus, a complex network of tissue-specific cues biases the potential of Glide/Gcm. These data allow us to revise the concept of fate determinants and help us understand the bases of cell specification. Both sexes were analyzed.SIGNIFICANCE STATEMENTDistinct cell types often require the same pioneer transcription factor, raising the issue of how does one factor trigger different fates. In Drosophila, glia and hemocytes provide a scavenger activity within and outside the nervous system, respectively. While they both require the Glide/Gcm transcription factor, glia originate from the ectoderm, hemocytes from the mesoderm. Here we show that tissue-specific factors inhibit the gliogenic potential of Glide/Gcm in the mesoderm by repressing the expression of the homeodomain protein Repo, a major glial-specific target of Glide/Gcm. Repo expression in turn inhibits the expression of hemocyte-specific genes in the nervous system. These cell-specific networks secure the establishment of the glial fate only in the nervous system and allow cell diversification.}, author = {Trébuchet, Guillaume and Cattenoz, Pierre B and Zsámboki, János and Mazaud, David and Siekhaus, Daria E and Fanto, Manolis and Giangrande, Angela}, journal = {Journal of Neuroscience}, number = {2}, pages = {238--255}, publisher = {Society for Neuroscience}, title = {{The Repo homeodomain transcription factor suppresses hematopoiesis in Drosophila and preserves the glial fate}}, doi = {10.1523/JNEUROSCI.1059-18.2018}, volume = {39}, year = {2019}, } @article{80, abstract = {We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose–Einstein condensation in the following sense: The one-particle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer.}, author = {Deuchert, Andreas and Seiringer, Robert and Yngvason, Jakob}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {723--776}, publisher = {Springer}, title = {{Bose–Einstein condensation in a dilute, trapped gas at positive temperature}}, doi = {10.1007/s00220-018-3239-0}, volume = {368}, year = {2019}, } @inproceedings{8175, abstract = {We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's problem on longest increasing subsequences of random permutations and the last passage percolation (corner growth) discrete versions thereof. Moreover they interpolate between said measures and the uniform measure on partitions. In the new KPZ-like 1/3 exponent edge scaling limit with logarithmic corrections, we find new probability distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions from the theory of random matrices.}, author = {Betea, Dan and Bouttier, Jérémie and Nejjar, Peter and Vuletíc, Mirjana}, booktitle = {Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics}, location = {Ljubljana, Slovenia}, publisher = {Formal Power Series and Algebraic Combinatorics}, title = {{New edge asymptotics of skew Young diagrams via free boundaries}}, year = {2019}, } @unpublished{8182, abstract = {Suppose that $n\neq p^k$ and $n\neq 2p^k$ for all $k$ and all primes $p$. We prove that for any Hausdorff compactum $X$ with a free action of the symmetric group $\mathfrak S_n$ there exists an $\mathfrak S_n$-equivariant map $X \to {\mathbb R}^n$ whose image avoids the diagonal $\{(x,x\dots,x)\in {\mathbb R}^n|x\in {\mathbb R}\}$. Previously, the special cases of this statement for certain $X$ were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We take a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of $\mathfrak S_n$-equivariant maps from the boundary $\partial\Delta^{n-1}$ of $(n-1)$-simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser's conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem.}, author = {Avvakumov, Sergey and Kudrya, Sergey}, booktitle = {arXiv}, publisher = {arXiv}, title = {{Vanishing of all equivariant obstructions and the mapping degree}}, year = {2019}, } @unpublished{8184, abstract = {Denote by ∆N the N-dimensional simplex. A map f : ∆N → Rd is an almost r-embedding if fσ1∩. . .∩fσr = ∅ whenever σ1, . . . , σr are pairwise disjoint faces. A counterexample to the topological Tverberg conjecture asserts that if r is not a prime power and d ≥ 2r + 1, then there is an almost r-embedding ∆(d+1)(r−1) → Rd. This was improved by Blagojevi´c–Frick–Ziegler using a simple construction of higher-dimensional counterexamples by taking k-fold join power of lower-dimensional ones. We improve this further (for d large compared to r): If r is not a prime power and N := (d+ 1)r−r l d + 2 r + 1 m−2, then there is an almost r-embedding ∆N → Rd. For the r-fold van Kampen–Flores conjecture we also produce counterexamples which are stronger than previously known. Our proof is based on generalizations of the Mabillard–Wagner theorem on construction of almost r-embeddings from equivariant maps, and of the Ozaydin theorem on existence of equivariant maps. }, author = {Avvakumov, Sergey and Karasev, R. and Skopenkov, A.}, booktitle = {arXiv}, publisher = {arXiv}, title = {{Stronger counterexamples to the topological Tverberg conjecture}}, year = {2019}, } @unpublished{8185, abstract = {In this paper we study envy-free division problems. The classical approach to some of such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and finding sufficient conditions when this map hits the center of the simplex. The mere continuity is not sufficient for such a conclusion, the usual assumption (for example, in the Knaster--Kuratowski--Mazurkiewicz and the Gale theorem) is a certain boundary condition. We follow Erel Segal-Halevi, Fr\'ed\'eric Meunier, and Shira Zerbib, and replace the boundary condition by another assumption, which has the economic meaning of possibility for a player to prefer an empty part in the segment partition problem. We solve the problem positively when $n$, the number of players that divide the segment, is a prime power, and we provide counterexamples for every $n$ which is not a prime power. We also provide counterexamples relevant to a wider class of fair or envy-free partition problems when $n$ is odd and not a prime power.}, author = {Avvakumov, Sergey and Karasev, Roman}, booktitle = {arXiv}, title = {{Envy-free division using mapping degree}}, doi = {10.48550/arXiv.1907.11183}, year = {2019}, } @inbook{8281, abstract = {We review the history of population genetics, starting with its origins a century ago from the synthesis between Mendel and Darwin's ideas, through to the recent development of sophisticated schemes of inference from sequence data, based on the coalescent. We explain the close relation between the coalescent and a diffusion process, which we illustrate by their application to understand spatial structure. We summarise the powerful methods available for analysis of multiple loci, when linkage equilibrium can be assumed, and then discuss approaches to the more challenging case, where associations between alleles require that we follow genotype, rather than allele, frequencies. Though we can hardly cover the whole of population genetics, we give an overview of the current state of the subject, and future challenges to it.}, author = {Barton, Nicholas H and Etheridge, Alison}, booktitle = {Handbook of statistical genomics}, editor = {Balding, David and Moltke, Ida and Marioni, John}, isbn = {9781119429142}, pages = {115--144}, publisher = {Wiley}, title = {{Mathematical models in population genetics}}, doi = {10.1002/9781119487845.ch4}, year = {2019}, }