TY - THES
AB - This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.
For triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.
In the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars.
AU - Masárová, Zuzana
ID - 7944
KW - reconfiguration
KW - reconfiguration graph
KW - triangulations
KW - flip
KW - constrained triangulations
KW - shellability
KW - piecewise-linear balls
KW - token swapping
KW - trees
KW - coloured weighted token swapping
SN - 978-3-99078-005-3
TI - Reconfiguration problems
ER -
TY - JOUR
AB - In agricultural systems, nitrate is the main source of nitrogen available for plants. Besides its role as a nutrient, nitrate has been shown to act as a signal molecule for plant growth, development and stress responses. In Arabidopsis, the NRT1.1 nitrate transceptor represses lateral root (LR) development at low nitrate availability by promoting auxin basipetal transport out of the LR primordia (LRPs). In addition, our present study shows that NRT1.1 acts as a negative regulator of the TAR2 auxin biosynthetic gene expression in the root stele. This is expected to repress local auxin biosynthesis and thus to reduce acropetal auxin supply to the LRPs. Moreover, NRT1.1 also negatively affects expression of the LAX3 auxin influx carrier, thus preventing cell wall remodeling required for overlying tissues separation during LRP emergence. Both NRT1.1-mediated repression of TAR2 and LAX3 are suppressed at high nitrate availability, resulting in the nitrate induction of TAR2 and LAX3 expression that is required for optimal stimulation of LR development by nitrate. Altogether, our results indicate that the NRT1.1 transceptor coordinately controls several crucial auxin-associated processes required for LRP development, and as a consequence that NRT1.1 plays a much more integrated role than previously anticipated in regulating the nitrate response of root system architecture.
AU - Maghiaoui, A
AU - Bouguyon, E
AU - Cuesta, Candela
AU - Perrine-Walker, F
AU - Alcon, C
AU - Krouk, G
AU - Benková, Eva
AU - Nacry, P
AU - Gojon, A
AU - Bach, L
ID - 7948
JF - Journal of Experimental Botany
SN - 0022-0957
TI - The Arabidopsis NRT1.1 transceptor coordinately controls auxin biosynthesis and transport to regulate root branching in response to nitrate
ER -
TY - JOUR
AB - Peptides derived from non-functional precursors play important roles in various developmental processes, but also in (a)biotic stress signaling. Our (phospho)proteome-wide analyses of C-terminally encoded peptide 5 (CEP5)-mediated changes revealed an impact on abiotic stress-related processes. Drought has a dramatic impact on plant growth, development and reproduction, and the plant hormone auxin plays a role in drought responses. Our genetic, physiological, biochemical and pharmacological results demonstrated that CEP5-mediated signaling is relevant for osmotic and drought stress tolerance in Arabidopsis, and that CEP5 specifically counteracts auxin effects. Specifically, we found that CEP5 signaling stabilizes AUX/IAA transcriptional repressors, suggesting the existence of a novel peptide-dependent control mechanism that tunes auxin signaling. These observations align with the recently described role of AUX/IAAs in stress tolerance and provide a novel role for CEP5 in osmotic and drought stress tolerance.
AU - Smith, S
AU - Zhu, S
AU - Joos, L
AU - Roberts, I
AU - Nikonorova, N
AU - Vu, LD
AU - Stes, E
AU - Cho, H
AU - Larrieu, A
AU - Xuan, W
AU - Goodall, B
AU - van de Cotte, B
AU - Waite, JM
AU - Rigal, A
AU - R Harborough, SR
AU - Persiau, G
AU - Vanneste, S
AU - Kirschner, GK
AU - Vandermarliere, E
AU - Martens, L
AU - Stahl, Y
AU - Audenaert, D
AU - Friml, Jiří
AU - Felix, G
AU - Simon, R
AU - Bennett, M
AU - Bishopp, A
AU - De Jaeger, G
AU - Ljung, K
AU - Kepinski, S
AU - Robert, S
AU - Nemhauser, J
AU - Hwang, I
AU - Gevaert, K
AU - Beeckman, T
AU - De Smet, I
ID - 7949
IS - 8
JF - Molecular & Cellular Proteomics
SN - 1535-9476
TI - The CEP5 peptide promotes abiotic stress tolerance, as revealed by quantitative proteomics, and attenuates the AUX/IAA equilibrium in Arabidopsis
VL - 19
ER -
TY - CONF
AB - Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently fine triangulation 𝒯. This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary.
AU - Boissonnat, Jean-Daniel
AU - Wintraecken, Mathijs
ID - 7952
SN - 1868-8969
T2 - 36th International Symposium on Computational Geometry
TI - The topological correctness of PL-approximations of isomanifolds
VL - 164
ER -
TY - CONF
AB - Simple stochastic games are turn-based 2½-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a conjunction of such conditions as objective. Despite a plethora of recent results on the analysis of systems with multiple objectives, the decidability of this basic problem remains open. In this paper, we present an algorithm approximating the Pareto frontier of the achievable values to a given precision. Moreover, it is an anytime algorithm, meaning it can be stopped at any time returning the current approximation and its error bound.
AU - Ashok, Pranav
AU - Chatterjee, Krishnendu
AU - Kretinsky, Jan
AU - Weininger, Maximilian
AU - Winkler, Tobias
ID - 7955
SN - 9781450371049
T2 - Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science
TI - Approximating values of generalized-reachability stochastic games
ER -
TY - JOUR
AB - We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.
AU - Alt, Johannes
AU - Erdös, László
AU - Krüger, Torben H
AU - Schröder, Dominik J
ID - 6184
IS - 2
JF - Annals of Probability
TI - Correlated random matrices: Band rigidity and edge universality
VL - 48
ER -
TY - JOUR
AB - For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969).
AU - Erdös, László
AU - Krüger, Torben H
AU - Schröder, Dominik J
ID - 6185
JF - Communications in Mathematical Physics
SN - 0010-3616
TI - Cusp universality for random matrices I: Local law and the complex hermitian case
ER -
TY - JOUR
AB - We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates.
AU - Carlen, Eric A.
AU - Maas, Jan
ID - 6358
IS - 2
JF - Journal of Statistical Physics
SN - 00224715
TI - Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
VL - 178
ER -
TY - JOUR
AB - This paper presents two algorithms. The first decides the existence of a pointed homotopy between given simplicial maps 𝑓,𝑔:𝑋→𝑌, and the second computes the group [𝛴𝑋,𝑌]∗ of pointed homotopy classes of maps from a suspension; in both cases, the target Y is assumed simply connected. More generally, these algorithms work relative to 𝐴⊆𝑋.
AU - Filakovský, Marek
AU - Vokřínek, Lukas
ID - 6563
JF - Foundations of Computational Mathematics
SN - 16153375
TI - Are two given maps homotopic? An algorithmic viewpoint
VL - 20
ER -
TY - JOUR
AB - We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising.
AU - Shehu, Yekini
AU - Li, Xiao-Huan
AU - Dong, Qiao-Li
ID - 6593
JF - Numerical Algorithms
SN - 1017-1398
TI - An efficient projection-type method for monotone variational inequalities in Hilbert spaces
VL - 84
ER -
TY - JOUR
AB - While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.
AU - Benedikter, Niels P
AU - Nam, Phan Thành
AU - Porta, Marcello
AU - Schlein, Benjamin
AU - Seiringer, Robert
ID - 6649
JF - Communications in Mathematical Physics
SN - 0010-3616
TI - Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime
VL - 374
ER -
TY - JOUR
AB - In resource allocation games, selfish players share resources that are needed in order to fulfill their objectives. The cost of using a resource depends on the load on it. In the traditional setting, the players make their choices concurrently and in one-shot. That is, a strategy for a player is a subset of the resources. We introduce and study dynamic resource allocation games. In this setting, the game proceeds in phases. In each phase each player chooses one resource. A scheduler dictates the order in which the players proceed in a phase, possibly scheduling several players to proceed concurrently. The game ends when each player has collected a set of resources that fulfills his objective. The cost for each player then depends on this set as well as on the load on the resources in it – we consider both congestion and cost-sharing games. We argue that the dynamic setting is the suitable setting for many applications in practice. We study the stability of dynamic resource allocation games, where the appropriate notion of stability is that of subgame perfect equilibrium, study the inefficiency incurred due to selfish behavior, and also study problems that are particular to the dynamic setting, like constraints on the order in which resources can be chosen or the problem of finding a scheduler that achieves stability.
AU - Avni, Guy
AU - Henzinger, Thomas A
AU - Kupferman, Orna
ID - 6761
JF - Theoretical Computer Science
SN - 03043975
TI - Dynamic resource allocation games
VL - 807
ER -
TY - JOUR
AB - Nearby grid cells have been observed to express a remarkable degree of long-rangeorder, which is often idealized as extending potentially to infinity. Yet their strict peri-odic firing and ensemble coherence are theoretically possible only in flat environments, much unlike the burrows which rodents usually live in. Are the symmetrical, coherent grid maps inferred in the lab relevant to chart their way in their natural habitat? We consider spheres as simple models of curved environments and waiting for the appropriate experiments to be performed, we use our adaptation model to predict what grid maps would emerge in a network with the same type of recurrent connections, which on the plane produce coherence among the units. We find that on the sphere such connections distort the maps that single grid units would express on their own, and aggregate them into clusters. When remapping to a different spherical environment, units in each cluster maintain only partial coherence, similar to what is observed in disordered materials, such as spin glasses.
AU - Stella, Federico
AU - Urdapilleta, Eugenio
AU - Luo, Yifan
AU - Treves, Alessandro
ID - 6796
IS - 4
JF - Hippocampus
SN - 10509631
TI - Partial coherence and frustration in self-organizing spherical grids
VL - 30
ER -
TY - JOUR
AB - Super-resolution fluorescence microscopy has become an important catalyst for discovery in the life sciences. In STimulated Emission Depletion (STED) microscopy, a pattern of light drives fluorophores from a signal-emitting on-state to a non-signalling off-state. Only emitters residing in a sub-diffraction volume around an intensity minimum are allowed to fluoresce, rendering them distinguishable from the nearby, but dark fluorophores. STED routinely achieves resolution in the few tens of nanometers range in biological samples and is suitable for live imaging. Here, we review the working principle of STED and provide general guidelines for successful STED imaging. The strive for ever higher resolution comes at the cost of increased light burden. We discuss techniques to reduce light exposure and mitigate its detrimental effects on the specimen. These include specialized illumination strategies as well as protecting fluorophores from photobleaching mediated by high-intensity STED light. This opens up the prospect of volumetric imaging in living cells and tissues with diffraction-unlimited resolution in all three spatial dimensions.
AU - Jahr, Wiebke
AU - Velicky, Philipp
AU - Danzl, Johann G
ID - 6808
IS - 3
JF - Methods
SN - 1046-2023
TI - Strategies to maximize performance in STimulated Emission Depletion (STED) nanoscopy of biological specimens
VL - 174
ER -
TY - JOUR
AB - We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge of the network is operable with its associated probability and the problem is to determine the probability of having at least one source-to-target path that is entirely composed of operable edges. This problem is known to be NP-hard.
We provide a novel scalable algorithm to solve the Network Reliability problem when the treewidth of the underlying network is small. We also show our algorithm’s applicability for real-world transit networks that have small treewidth, including the metro networks of major cities, such as London and Tokyo. Our algorithm leverages tree decompositions to shrink the original graph into much smaller graphs, for which reliability can be efficiently and exactly computed using a brute force method. To the best of our knowledge, this is the first exact algorithm for Network Reliability that can scale to handle real-world instances of the problem.
AU - Goharshady, Amir Kafshdar
AU - Mohammadi, Fatemeh
ID - 6918
JF - Reliability Engineering and System Safety
SN - 09518320
TI - An efficient algorithm for computing network reliability in small treewidth
VL - 193
ER -
TY - JOUR
AB - Origami is rapidly transforming the design of robots1,2, deployable structures3,4,5,6 and metamaterials7,8,9,10,11,12,13,14. However, as foldability requires a large number of complex compatibility conditions that are difficult to satisfy, the design of crease patterns is limited to heuristics and computer optimization. Here we introduce a systematic strategy that enables intuitive and effective design of complex crease patterns that are guaranteed to fold. First, we exploit symmetries to construct 140 distinct foldable motifs, and represent these as jigsaw puzzle pieces. We then show that when these pieces are fitted together they encode foldable crease patterns. This maps origami design to solving combinatorial problems, which allows us to systematically create, count and classify a vast number of crease patterns. We show that all of these crease patterns are pluripotent—capable of folding into multiple shapes—and solve exactly for the number of possible shapes for each pattern. Finally, we employ our framework to rationally design a crease pattern that folds into two independently defined target shapes, and fabricate such pluripotent origami. Our results provide physicists, mathematicians and engineers with a powerful new design strategy.
AU - Dieleman, Peter
AU - Vasmel, Niek
AU - Waitukaitis, Scott R
AU - van Hecke, Martin
ID - 6976
IS - 1
JF - Nature Physics
SN - 1745-2473
TI - Jigsaw puzzle design of pluripotent origami
VL - 16
ER -
TY - JOUR
AU - Zhang, Yuzhou
AU - Friml, Jiří
ID - 6997
IS - 3
JF - New Phytologist
SN - 0028-646x
TI - Auxin guides roots to avoid obstacles during gravitropic growth
VL - 225
ER -
TY - JOUR
AB - When short-range attractions are combined with long-range repulsions in colloidal particle systems, complex microphases can emerge. Here, we study a system of isotropic particles, which can form lamellar structures or a disordered fluid phase when temperature is varied. We show that, at equilibrium, the lamellar structure crystallizes, while out of equilibrium, the system forms a variety of structures at different shear rates and temperatures above melting. The shear-induced ordering is analyzed by means of principal component analysis and artificial neural networks, which are applied to data of reduced dimensionality. Our results reveal the possibility of inducing ordering by shear, potentially providing a feasible route to the fabrication of ordered lamellar structures from isotropic particles.
AU - Pȩkalski, J.
AU - Rzadkowski, Wojciech
AU - Panagiotopoulos, A. Z.
ID - 7956
IS - 20
JF - The Journal of chemical physics
TI - Shear-induced ordering in systems with competing interactions: A machine learning study
VL - 152
ER -
TY - JOUR
AU - Parenti, Ilaria
AU - Garcia Rabaneda, Luis E
AU - Schön, Hanna
AU - Novarino, Gaia
ID - 7957
JF - Trends in Neurosciences
SN - 01662236
TI - Neurodevelopmental disorders: From genetics to functional pathways
ER -
TY - JOUR
AB - Let A={A1,…,An} be a family of sets in the plane. For 0≤i2b be integers. We prove that if each k-wise or (k+1)-wise intersection of sets from A has at most b path-connected components, which all are open, then fk+1=0 implies fk≤cfk−1 for some positive constant c depending only on b and k. These results also extend to two-dimensional compact surfaces.
AU - Kalai, Gil
AU - Patakova, Zuzana
ID - 7960
JF - Discrete and Computational Geometry
SN - 01795376
TI - Intersection patterns of planar sets
ER -