@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}, } @inproceedings{8570, abstract = {This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with linear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2019. In its third edition, seven tools have been applied to solve six different benchmark problems in the category for linear continuous dynamics (in alphabetical order): CORA, CORA/SX, HyDRA, Hylaa, JuliaReach, SpaceEx, and XSpeed. This report is a snapshot 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 provide one of the most complete assessments of tools for the safety verification of continuous and hybrid systems with linear continuous dynamics up to this date.}, author = {Althoff, Matthias and Bak, Stanley and Forets, Marcelo and Frehse, Goran and Kochdumper, Niklas and Ray, Rajarshi and Schilling, Christian and Schupp, Stefan}, booktitle = {EPiC Series in Computing}, issn = {23987340}, location = {Montreal, Canada}, pages = {14--40}, publisher = {EasyChair}, title = {{ARCH-COMP19 Category Report: Continuous and hybrid systems with linear continuous dynamics}}, doi = {10.29007/bj1w}, volume = {61}, year = {2019}, } @article{175, abstract = {An upper bound sieve for rational points on suitable varieties isdeveloped, together with applications tocounting rational points in thin sets,to local solubility in families, and to the notion of “friable” rational pointswith respect to divisors. In the special case of quadrics, sharper estimates areobtained by developing a version of the Selberg sieve for rational points.}, author = {Browning, Timothy D and Loughran, Daniel}, issn = {10886850}, journal = {Transactions of the American Mathematical Society}, number = {8}, pages = {5757--5785}, publisher = {American Mathematical Society}, title = {{Sieving rational points on varieties}}, doi = {10.1090/tran/7514}, volume = {371}, 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}, 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{6611, abstract = {Cell polarity is crucial for the coordinated development of all multicellular organisms. In plants, this is exemplified by the PIN-FORMED (PIN) efflux carriers of the phytohormone auxin: The polar subcellular localization of the PINs is instructive to the directional intercellular auxin transport, and thus to a plethora of auxin-regulated growth and developmental processes. Despite its importance, the regulation of PIN polar subcellular localization remains poorly understood. Here, we have employed advanced live-cell imaging techniques to study the roles of microtubules and actin microfilaments in the establishment of apical polar localization of PIN2 in the epidermis of the Arabidopsis root meristem. We report that apical PIN2 polarity requires neither intact actin microfilaments nor microtubules, suggesting that the primary spatial cue for polar PIN distribution is likely independent of cytoskeleton-guided endomembrane trafficking.}, author = {Glanc, Matous and Fendrych, Matyas and Friml, Jiří}, journal = {Biomolecules}, number = {6}, publisher = {MDPI}, title = {{PIN2 polarity establishment in arabidopsis in the absence of an intact cytoskeleton}}, doi = {10.3390/biom9060222}, volume = {9}, year = {2019}, } @article{6617, abstract = {The effective large-scale properties of materials with random heterogeneities on a small scale are typically determined by the method of representative volumes: a sample of the random material is chosen—the representative volume—and its effective properties are computed by the cell formula. Intuitively, for a fixed sample size it should be possible to increase the accuracy of the method by choosing a material sample which captures the statistical properties of the material particularly well; for example, for a composite material consisting of two constituents, one would select a representative volume in which the volume fraction of the constituents matches closely with their volume fraction in the overall material. Inspired by similar attempts in materials science, Le Bris, Legoll and Minvielle have designed a selection approach for representative volumes which performs remarkably well in numerical examples of linear materials with moderate contrast. In the present work, we provide a rigorous analysis of this selection approach for representative volumes in the context of stochastic homogenization of linear elliptic equations. In particular, we prove that the method essentially never performs worse than a random selection of the material sample and may perform much better if the selection criterion for the material samples is chosen suitably.}, author = {Fischer, Julian L}, issn = {1432-0673}, journal = {Archive for Rational Mechanics and Analysis}, number = {2}, pages = {635–726}, publisher = {Springer}, title = {{The choice of representative volumes in the approximation of effective properties of random materials}}, doi = {10.1007/s00205-019-01400-w}, volume = {234}, year = {2019}, } @article{6620, abstract = {This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of ℙ3ℚ given by the following equation 𝑥0(𝑥21+𝑥22)−𝑥33=0 in agreement with the Manin-Peyre conjectures. }, author = {De La Bretèche, Régis and Destagnol, Kevin N and Liu, Jianya and Wu, Jie and Zhao, Yongqiang}, issn = {16747283}, journal = {Science China Mathematics}, number = {12}, pages = {2435–2446}, publisher = {Springer}, title = {{On a certain non-split cubic surface}}, doi = {10.1007/s11425-018-9543-8}, volume = {62}, year = {2019}, } @article{6621, abstract = {We read with great interest the recent work in PNAS by Bergero et al. (1) describing differences in male and female recombination patterns on the guppy (Poecilia reticulata) sex chromosome. We fully agree that recombination in males is largely confined to the ends of the sex chromosome. Bergero et al. interpret these results to suggest that our previous findings of population-level variation in the degree of sex chromosome differentiation in this species (2) are incorrect. However, we suggest that their results are entirely consistent with our previous report, and that their interpretation presents a false controversy.}, author = {Wright, Alison E. and Darolti, Iulia and Bloch, Natasha I. and Oostra, Vicencio and Sandkam, Benjamin A. and Buechel, Séverine D. and Kolm, Niclas and Breden, Felix and Vicoso, Beatriz and Mank, Judith E.}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {26}, pages = {12607--12608}, publisher = {Proceedings of the National Academy of Sciences}, title = {{On the power to detect rare recombination events}}, doi = {10.1073/pnas.1905555116}, volume = {116}, year = {2019}, } @article{6627, abstract = {Cortical microtubule arrays in elongating epidermal cells in both the root and stem of plants have the propensity of dynamic reorientations that are correlated with the activation or inhibition of growth. Factors regulating plant growth, among them the hormone auxin, have been recognized as regulators of microtubule array orientations. Some previous work in the field has aimed at elucidating the causal relationship between cell growth, the signaling of auxin or other growth-regulating factors, and microtubule array reorientations, with various conclusions. Here, we revisit this problem of causality with a comprehensive set of experiments in Arabidopsis thaliana, using the now available pharmacological and genetic tools. We use isolated, auxin-depleted hypocotyls, an experimental system allowing for full control of both growth and auxin signaling. We demonstrate that reorientation of microtubules is not directly triggered by an auxin signal during growth activation. Instead, reorientation is triggered by the activation of the growth process itself and is auxin-independent in its nature. We discuss these findings in the context of previous relevant work, including that on the mechanical regulation of microtubule array orientation.}, author = {Adamowski, Maciek and Li, Lanxin and Friml, Jiří}, issn = {1422-0067}, journal = {International Journal of Molecular Sciences}, number = {13}, publisher = {MDPI}, title = {{Reorientation of cortical microtubule arrays in the hypocotyl of arabidopsis thaliana is induced by the cell growth process and independent of auxin signaling}}, doi = {10.3390/ijms20133337}, volume = {20}, year = {2019}, }