TY - JOUR AB - The order-k Voronoi tessellation of a locally finite set 𝑋⊆ℝ𝑛 decomposes ℝ𝑛 into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold. AU - Edelsbrunner, Herbert AU - Nikitenko, Anton ID - 5678 IS - 4 JF - Discrete and Computational Geometry SN - 01795376 TI - Poisson–Delaunay Mosaics of Order k VL - 62 ER - TY - JOUR AB - Hippocampus is needed for both spatial working and reference memories. Here, using a radial eight-arm maze, we examined how the combined demand on these memories influenced CA1 place cell assemblies while reference memories were partially updated. This was contrasted with control tasks requiring only working memory or the update of reference memory. Reference memory update led to the reward-directed place field shifts at newly rewarded arms and to the gradual strengthening of firing in passes between newly rewarded arms but not between those passes that included a familiar-rewarded arm. At the maze center, transient network synchronization periods preferentially replayed trajectories of the next chosen arm in reference memory tasks but the previously visited arm in the working memory task. Hence, reference memory demand was uniquely associated with a gradual, goal novelty-related reorganization of place cell assemblies and with trajectory replay that reflected the animal's decision of which arm to visit next. AU - Xu, Haibing AU - Baracskay, Peter AU - O'Neill, Joseph AU - Csicsvari, Jozsef L ID - 5828 IS - 1 JF - Neuron SN - 10974199 TI - Assembly responses of hippocampal CA1 place cells predict learned behavior in goal-directed spatial tasks on the radial eight-arm maze VL - 101 ER - TY - JOUR AB - We give a bound on the ground-state energy of a system of N non-interacting fermions in a three-dimensional cubic box interacting with an impurity particle via point interactions. We show that the change in energy compared to the system in the absence of the impurity is bounded in terms of the gas density and the scattering length of the interaction, independently of N. Our bound holds as long as the ratio of the mass of the impurity to the one of the gas particles is larger than a critical value m∗ ∗≈ 0.36 , which is the same regime for which we recently showed stability of the system. AU - Moser, Thomas AU - Seiringer, Robert ID - 5856 IS - 4 JF - Annales Henri Poincare SN - 14240637 TI - Energy contribution of a point-interacting impurity in a Fermi gas VL - 20 ER - TY - THES AB - In many shear flows like pipe flow, plane Couette flow, plane Poiseuille flow, etc. turbulence emerges subcritically. Here, when subjected to strong enough perturbations, the flow becomes turbulent in spite of the laminar base flow being linearly stable. The nature of this instability has puzzled the scientific community for decades. At onset, turbulence appears in localized patches and flows are spatio-temporally intermittent. In pipe flow the localized turbulent structures are referred to as puffs and in planar flows like plane Couette and channel flow, patches arise in the form of localized oblique bands. In this thesis, we study the onset of turbulence in channel flow in direct numerical simulations from a dynamical system theory perspective, as well as by performing experiments in a large aspect ratio channel. The aim of the experimental work is to determine the critical Reynolds number where turbulence first becomes sustained. Recently, the onset of turbulence has been described in analogy to absorbing state phase transition (i.e. directed percolation). In particular, it has been shown that the critical point can be estimated from the competition between spreading and decay processes. Here, by performing experiments, we identify the mechanisms underlying turbulence proliferation in channel flow and find the critical Reynolds number, above which turbulence becomes sustained. Above the critical point, the continuous growth at the tip of the stripes outweighs the stochastic shedding of turbulent patches at the tail and the stripes expand. For growing stripes, the probability to decay decreases while the probability of stripe splitting increases. Consequently, and unlike for the puffs in pipe flow, neither of these two processes is time-independent i.e. memoryless. Coupling between stripe expansion and creation of new stripes via splitting leads to a significantly lower critical point ($Re_c=670+/-10$) than most earlier studies suggest. While the above approach sheds light on how turbulence first becomes sustained, it provides no insight into the origin of the stripes themselves. In the numerical part of the thesis we investigate how turbulent stripes form from invariant solutions of the Navier-Stokes equations. The origin of these turbulent stripes can be identified by applying concepts from the dynamical system theory. In doing so, we identify the exact coherent structures underlying stripes and their bifurcations and how they give rise to the turbulent attractor in phase space. We first report a family of localized nonlinear traveling wave solutions of the Navier-Stokes equations in channel flow. These solutions show structural similarities with turbulent stripes in experiments like obliqueness, quasi-streamwise streaks and vortices, etc. A parametric study of these traveling wave solution is performed, with parameters like Reynolds number, stripe tilt angle and domain size, including the stability of the solutions. These solutions emerge through saddle-node bifurcations and form a phase space skeleton for the turbulent stripes observed in the experiments. The lower branches of these TW solutions at different tilt angles undergo Hopf bifurcation and new solutions branches of relative periodic orbits emerge. These RPO solutions do not belong to the same family and therefore the routes to chaos for different angles are different. In shear flows, turbulence at onset is transient in nature. Consequently,turbulence can not be tracked to lower Reynolds numbers, where the dynamics may simplify. Before this happens, turbulence becomes short-lived and laminarizes. In the last part of the thesis, we show that using numerical simulations we can continue turbulent stripes in channel flow past the 'relaminarization barrier' all the way to their origin. Here, turbulent stripe dynamics simplifies and the fluctuations are no longer stochastic and the stripe settles down to a relative periodic orbit. This relative periodic orbit originates from the aforementioned traveling wave solutions. Starting from the relative periodic orbit, a small increase in speed i.e. Reynolds number gives rise to chaos and the attractor dimension sharply increases in contrast to the classical transition scenario where the instabilities affect the flow globally and give rise to much more gradual route to turbulence. AU - Paranjape, Chaitanya S ID - 6957 KW - Instabilities KW - Turbulence KW - Nonlinear dynamics TI - Onset of turbulence in plane Poiseuille flow ER - TY - JOUR AB - We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion. AU - Erdös, LĂĄszlĂł AU - KrĂŒger, Torben H AU - Schröder, Dominik J ID - 6182 JF - Forum of Mathematics, Sigma TI - Random matrices with slow correlation decay VL - 7 ER - TY - JOUR AB - We prove that the local eigenvalue statistics of real symmetric Wigner-type matrices near the cusp points of the eigenvalue density are universal. Together with the companion paper [arXiv:1809.03971], which proves the same result for the complex Hermitian symmetry class, this completes the last remaining case of the Wigner-Dyson-Mehta universality conjecture after bulk and edge universalities have been established in the last years. We extend the recent Dyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp regime using the optimal local law from [arXiv:1809.03971] and the accurate local shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752]. We also present a PDE-based method to improve the estimate on eigenvalue rigidity via the maximum principle of the heat flow related to the Dyson Brownian motion. AU - Cipolloni, Giorgio AU - Erdös, LĂĄszlĂł AU - KrĂŒger, Torben H AU - Schröder, Dominik J ID - 6186 IS - 4 JF - Pure and Applied Analysis SN - 2578-5893 TI - Cusp universality for random matrices, II: The real symmetric case VL - 1 ER - TY - JOUR AB - Across diverse biological systems—ranging from neural networks to intracellular signaling and genetic regulatory networks—the information about changes in the environment is frequently encoded in the full temporal dynamics of the network nodes. A pressing data-analysis challenge has thus been to efficiently estimate the amount of information that these dynamics convey from experimental data. Here we develop and evaluate decoding-based estimation methods to lower bound the mutual information about a finite set of inputs, encoded in single-cell high-dimensional time series data. For biological reaction networks governed by the chemical Master equation, we derive model-based information approximations and analytical upper bounds, against which we benchmark our proposed model-free decoding estimators. In contrast to the frequently-used k-nearest-neighbor estimator, decoding-based estimators robustly extract a large fraction of the available information from high-dimensional trajectories with a realistic number of data samples. We apply these estimators to previously published data on Erk and Ca2+ signaling in mammalian cells and to yeast stress-response, and find that substantial amount of information about environmental state can be encoded by non-trivial response statistics even in stationary signals. We argue that these single-cell, decoding-based information estimates, rather than the commonly-used tests for significant differences between selected population response statistics, provide a proper and unbiased measure for the performance of biological signaling networks. AU - Cepeda Humerez, Sarah A AU - Ruess, Jakob AU - Tkačik, GaĆĄper ID - 6900 IS - 9 JF - PLoS computational biology TI - Estimating information in time-varying signals VL - 15 ER - TY - JOUR AB - Clathrin-mediated endocytosis (CME) is a highly conserved and essential cellular process in eukaryotic cells, but its dynamic and vital nature makes it challenging to study using classical genetics tools. In contrast, although small molecules can acutely and reversibly perturb CME, the few chemical CME inhibitors that have been applied to plants are either ineffective or show undesirable side effects. Here, we identify the previously described endosidin9 (ES9) as an inhibitor of clathrin heavy chain (CHC) function in both Arabidopsis and human cells through affinity-based target isolation, in vitro binding studies and X-ray crystallography. Moreover, we present a chemically improved ES9 analog, ES9-17, which lacks the undesirable side effects of ES9 while retaining the ability to target CHC. ES9 and ES9-17 have expanded the chemical toolbox used to probe CHC function, and present chemical scaffolds for further design of more specific and potent CHC inhibitors across different systems. AU - Dejonghe, Wim AU - Sharma, Isha AU - Denoo, Bram AU - De Munck, Steven AU - Lu, Qing AU - Mishev, Kiril AU - Bulut, Haydar AU - Mylle, Evelien AU - De Rycke, Riet AU - Vasileva, Mina K AU - Savatin, Daniel V. AU - Nerinckx, Wim AU - Staes, An AU - Drozdzecki, Andrzej AU - Audenaert, Dominique AU - Yperman, Klaas AU - Madder, Annemieke AU - Friml, Jiƙí AU - Van Damme, DaniĂ«l AU - Gevaert, Kris AU - Haucke, Volker AU - Savvides, Savvas N. AU - Winne, Johan AU - Russinova, Eugenia ID - 6377 IS - 6 JF - Nature Chemical Biology SN - 15524450 TI - Disruption of endocytosis through chemical inhibition of clathrin heavy chain function VL - 15 ER - TY - THES AB - Tissue morphogenesis in developmental or physiological processes is regulated by molecular and mechanical signals. While the molecular signaling cascades are increasingly well described, the mechanical signals affecting tissue shape changes have only recently been studied in greater detail. To gain more insight into the mechanochemical and biophysical basis of an epithelial spreading process (epiboly) in early zebrafish development, we studied cell-cell junction formation and actomyosin network dynamics at the boundary between surface layer epithelial cells (EVL) and the yolk syncytial layer (YSL). During zebrafish epiboly, the cell mass sitting on top of the yolk cell spreads to engulf the yolk cell by the end of gastrulation. It has been previously shown that an actomyosin ring residing within the YSL pulls on the EVL tissue through a cable-constriction and a flow-friction motor, thereby dragging the tissue vegetal wards. Pulling forces are likely transmitted from the YSL actomyosin ring to EVL cells; however, the nature and formation of the junctional structure mediating this process has not been well described so far. Therefore, our main aim was to determine the nature, dynamics and potential function of the EVL-YSL junction during this epithelial tissue spreading. Specifically, we show that the EVL-YSL junction is a mechanosensitive structure, predominantly made of tight junction (TJ) proteins. The process of TJ mechanosensation depends on the retrograde flow of non-junctional, phase-separated Zonula Occludens-1 (ZO-1) protein clusters towards the EVL-YSL boundary. Interestingly, we could demonstrate that ZO-1 is present in a non-junctional pool on the surface of the yolk cell, and ZO-1 undergoes a phase separation process that likely renders the protein responsive to flows. These flows are directed towards the junction and mediate proper tension-dependent recruitment of ZO-1. Upon reaching the EVL-YSL junction ZO-1 gets incorporated into the junctional pool mediated through its direct actin-binding domain. When the non-junctional pool and/or ZO-1 direct actin binding is absent, TJs fail in their proper mechanosensitive responses resulting in slower tissue spreading. We could further demonstrate that depletion of ZO proteins within the YSL results in diminished actomyosin ring formation. This suggests that a mechanochemical feedback loop is at work during zebrafish epiboly: ZO proteins help in proper actomyosin ring formation and actomyosin contractility and flows positively influence ZO-1 junctional recruitment. Finally, such a mesoscale polarization process mediated through the flow of phase-separated protein clusters might have implications for other processes such as immunological synapse formation, C. elegans zygote polarization and wound healing. AU - Schwayer, Cornelia ID - 7186 SN - 2663-337X TI - Mechanosensation of tight junctions depends on ZO-1 phase separation and flow ER - TY - THES AB - The first part of the thesis considers the computational aspects of the homotopy groups πd(X) of a topological space X. It is well known that there is no algorithm to decide whether the fundamental group π1(X) of a given finite simplicial complex X is trivial. On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with π1(X) trivial), compute the higher homotopy group πd(X) for any given d ≄ 2. However, these algorithms come with a caveat: They compute the isomorphism type of πd(X), d ≄ 2 as an abstract finitely generated abelian group given by generators and relations, but they work with very implicit representations of the elements of πd(X). We present an algorithm that, given a simply connected space X, computes πd(X) and represents its elements as simplicial maps from suitable triangulations of the d-sphere Sd to X. For fixed d, the algorithm runs in time exponential in size(X), the number of simplices of X. Moreover, we prove that this is optimal: For every fixed d ≄ 2, we construct a family of simply connected spaces X such that for any simplicial map representing a generator of πd(X), the size of the triangulation of S d on which the map is defined, is exponential in size(X). In the second part of the thesis, we prove that the following question is algorithmically undecidable for d < ⌊3(k+1)/2⌋, k ≄ 5 and (k, d) Ìž= (5, 7), which covers essentially everything outside the meta-stable range: Given a finite simplicial complex K of dimension k, decide whether there exists a piecewise-linear (i.e., linear on an arbitrarily fine subdivision of K) embedding f : K â†Ș→ Rd of K into a d-dimensional Euclidean space. AU - Zhechev, Stephan Y ID - 6681 SN - 2663-337X TI - Algorithmic aspects of homotopy theory and embeddability ER - TY - GEN AB - 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. AU - Avvakumov, Sergey AU - Kudrya, Sergey ID - 8182 T2 - arXiv TI - Vanishing of all equivariant obstructions and the mapping degree ER - TY - GEN AB - 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. AU - Avvakumov, Sergey AU - Karasev, Roman ID - 8185 T2 - arXiv TI - Envy-free division using mapping degree ER - TY - GEN AB - We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\rho$ and inverse temperature $\beta$ differs from the one of the non-interacting system by the correction term $4 \pi \rho^2 |\ln a^2 \rho|^{-1} (2 - [1 - \beta_{\mathrm{c}}/\beta]_+^2)$. Here $a$ is the scattering length of the interaction potential, $[\cdot]_+ = \max\{ 0, \cdot \}$ and $\beta_{\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. The result is valid in the dilute limit $a^2\rho \ll 1$ and if $\beta \rho \gtrsim 1$. AU - Deuchert, Andreas AU - Mayer, Simon AU - Seiringer, Robert ID - 7524 T2 - arXiv:1910.03372 TI - The free energy of the two-dimensional dilute Bose gas. I. Lower bound ER - TY - JOUR AB - We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha complex, and we use the persistence diagram of the distance function to guide the hole opening and closing operations. The dependences between the holes define a partial order on the cells in K that characterizes what can and what cannot be constructed using the operations. The relations in this partial order reveal structural information about the underlying filtration of complexes beyond what is expressed by the persistence diagram. AU - Edelsbrunner, Herbert AU - Ölsböck, Katharina ID - 6608 JF - Computer Aided Geometric Design TI - Holes and dependences in an ordered complex VL - 73 ER - TY - CONF AB - The Fiat-Shamir heuristic transforms a public-coin interactive proof into a non-interactive argument, by replacing the verifier with a cryptographic hash function that is applied to the protocol’s transcript. Constructing hash functions for which this transformation is sound is a central and long-standing open question in cryptography. We show that solving the END−OF−METERED−LINE problem is no easier than breaking the soundness of the Fiat-Shamir transformation when applied to the sumcheck protocol. In particular, if the transformed protocol is sound, then any hard problem in #P gives rise to a hard distribution in the class CLS, which is contained in PPAD. Our result opens up the possibility of sampling moderately-sized games for which it is hard to find a Nash equilibrium, by reducing the inversion of appropriately chosen one-way functions to #SAT. Our main technical contribution is a stateful incrementally verifiable procedure that, given a SAT instance over n variables, counts the number of satisfying assignments. This is accomplished via an exponential sequence of small steps, each computable in time poly(n). Incremental verifiability means that each intermediate state includes a sumcheck-based proof of its correctness, and the proof can be updated and verified in time poly(n). AU - Choudhuri, Arka Rai AU - Hubáček, Pavel AU - Kamath Hosdurg, Chethan AU - Pietrzak, Krzysztof Z AU - Rosen, Alon AU - Rothblum, Guy N. ID - 6677 SN - 9781450367059 T2 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019 TI - Finding a Nash equilibrium is no easier than breaking Fiat-Shamir ER - TY - JOUR AB - Given a triangulation of a point set in the plane, a flip deletes an edge e whose removal leaves a convex quadrilateral, and replaces e by the opposite diagonal of the quadrilateral. It is well known that any triangulation of a point set can be reconfigured to any other triangulation by some sequence of flips. We explore this question in the setting where each edge of a triangulation has a label, and a flip transfers the label of the removed edge to the new edge. It is not true that every labelled triangulation of a point set can be reconfigured to every other labelled triangulation via a sequence of flips, but we characterize when this is possible. There is an obvious necessary condition: for each label l, if edge e has label l in the first triangulation and edge f has label l in the second triangulation, then there must be some sequence of flips that moves label l from e to f, ignoring all other labels. Bose, Lubiw, Pathak and Verdonschot formulated the Orbit Conjecture, which states that this necessary condition is also sufficient, i.e. that all labels can be simultaneously mapped to their destination if and only if each label individually can be mapped to its destination. We prove this conjecture. Furthermore, we give a polynomial-time algorithm (with 𝑂(𝑛8) being a crude bound on the run-time) to find a sequence of flips to reconfigure one labelled triangulation to another, if such a sequence exists, and we prove an upper bound of 𝑂(𝑛7) on the length of the flip sequence. Our proof uses the topological result that the sets of pairwise non-crossing edges on a planar point set form a simplicial complex that is homeomorphic to a high-dimensional ball (this follows from a result of Orden and Santos; we give a different proof based on a shelling argument). The dual cell complex of this simplicial ball, called the flip complex, has the usual flip graph as its 1-skeleton. We use properties of the 2-skeleton of the flip complex to prove the Orbit Conjecture. AU - Lubiw, Anna AU - MasĂĄrovĂĄ, Zuzana AU - Wagner, Uli ID - 5986 IS - 4 JF - Discrete & Computational Geometry SN - 0179-5376 TI - A proof of the orbit conjecture for flipping edge-labelled triangulations VL - 61 ER - TY - JOUR AB - Problems involving quantum impurities, in which one or a few particles are interacting with a macroscopic environment, represent a pervasive paradigm, spanning across atomic, molecular, and condensed-matter physics. In this paper we introduce new variational approaches to quantum impurities and apply them to the Fröhlich polaron–a quasiparticle formed out of an electron (or other point-like impurity) in a polar medium, and to the angulon–a quasiparticle formed out of a rotating molecule in a bosonic bath. We benchmark these approaches against established theories, evaluating their accuracy as a function of the impurity-bath coupling. AU - Li, Xiang AU - Bighin, Giacomo AU - Yakaboylu, Enderalp AU - Lemeshko, Mikhail ID - 5886 JF - Molecular Physics SN - 00268976 TI - Variational approaches to quantum impurities: from the Fröhlich polaron to the angulon ER - TY - CONF AB - Motivated by fixed-parameter tractable (FPT) problems in computational topology, we consider the treewidth tw(M) of a compact, connected 3-manifold M, defined to be the minimum treewidth of the face pairing graph of any triangulation T of M. In this setting the relationship between the topology of a 3-manifold and its treewidth is of particular interest. First, as a corollary of work of Jaco and Rubinstein, we prove that for any closed, orientable 3-manifold M the treewidth tw(M) is at most 4g(M)-2, where g(M) denotes Heegaard genus of M. In combination with our earlier work with Wagner, this yields that for non-Haken manifolds the Heegaard genus and the treewidth are within a constant factor. Second, we characterize all 3-manifolds of treewidth one: These are precisely the lens spaces and a single other Seifert fibered space. Furthermore, we show that all remaining orientable Seifert fibered spaces over the 2-sphere or a non-orientable surface have treewidth two. In particular, for every spherical 3-manifold we exhibit a triangulation of treewidth at most two. Our results further validate the parameter of treewidth (and other related parameters such as cutwidth or congestion) to be useful for topological computing, and also shed more light on the scope of existing FPT-algorithms in the field. AU - HuszĂĄr, KristĂłf AU - Spreer, Jonathan ID - 6556 KW - computational 3-manifold topology KW - fixed-parameter tractability KW - layered triangulations KW - structural graph theory KW - treewidth KW - cutwidth KW - Heegaard genus SN - 1868-8969 T2 - 35th International Symposium on Computational Geometry TI - 3-manifold triangulations with small treewidth VL - 129 ER - TY - JOUR AB - In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is a variety of problems in computational 3-manifold topology - some of them known to be computationally hard in general - that become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded treewidth. In view of these algorithmic results, it is natural to ask whether every 3-manifold admits a triangulation of bounded treewidth. We show that this is not the case, i.e., that there exists an infinite family of closed 3-manifolds not admitting triangulations of bounded pathwidth or treewidth (the latter implies the former, but we present two separate proofs). We derive these results from work of Agol, of Scharlemann and Thompson, and of Scharlemann, Schultens and Saito by exhibiting explicit connections between the topology of a 3-manifold M on the one hand and width-type parameters of the dual graphs of triangulations of M on the other hand, answering a question that had been raised repeatedly by researchers in computational 3-manifold topology. In particular, we show that if a closed, orientable, irreducible, non-Haken 3-manifold M has a triangulation of treewidth (resp. pathwidth) k then the Heegaard genus of M is at most 18(k+1) (resp. 4(3k+1)). AU - HuszĂĄr, KristĂłf AU - Spreer, Jonathan AU - Wagner, Uli ID - 7093 IS - 2 JF - Journal of Computational Geometry SN - 1920-180X TI - On the treewidth of triangulated 3-manifolds VL - 10 ER - TY - JOUR AB - During bacterial cell division, the tubulin-homolog FtsZ forms a ring-like structure at the center of the cell. This Z-ring not only organizes the division machinery, but treadmilling of FtsZ filaments was also found to play a key role in distributing proteins at the division site. What regulates the architecture, dynamics and stability of the Z-ring is currently unknown, but FtsZ-associated proteins are known to play an important role. Here, using an in vitro reconstitution approach, we studied how the well-conserved protein ZapA affects FtsZ treadmilling and filament organization into large-scale patterns. Using high-resolution fluorescence microscopy and quantitative image analysis, we found that ZapA cooperatively increases the spatial order of the filament network, but binds only transiently to FtsZ filaments and has no effect on filament length and treadmilling velocity. Together, our data provides a model for how FtsZ-associated proteins can increase the precision and stability of the bacterial cell division machinery in a switch-like manner. AU - Dos Santos Caldas, Paulo R AU - Lopez Pelegrin, Maria D AU - Pearce, Daniel J. G. AU - Budanur, Nazmi B AU - BruguĂ©s, Jan AU - Loose, Martin ID - 7197 JF - Nature Communications SN - 2041-1723 TI - Cooperative ordering of treadmilling filaments in cytoskeletal networks of FtsZ and its crosslinker ZapA VL - 10 ER -