TY - JOUR
AB - Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the points from a Poisson point process in ℝ n , we study the expected number of simplices in the Delaunay mosaic as well as the expected number of critical simplices and nonsingular intervals in the corresponding generalized discrete gradient. Observing connections with other probabilistic models, we obtain precise expressions for the expected numbers in low dimensions. In particular, we obtain the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions n ≤ 4.
AU - Edelsbrunner, Herbert
AU - Nikitenko, Anton
AU - Reitzner, Matthias
ID - 718
IS - 3
JF - Advances in Applied Probability
SN - 00018678
TI - Expected sizes of poisson Delaunay mosaics and their discrete Morse functions
VL - 49
ER -
TY - JOUR
AB - The ubiquity of computation in modern machines and devices imposes a need to assert the correctness of their behavior. Especially in the case of safety-critical systems, their designers need to take measures that enforce their safe operation. Formal methods has emerged as a research field that addresses this challenge: by rigorously proving that all system executions adhere to their specifications, the correctness of an implementation under concern can be assured. To achieve this goal, a plethora of techniques are nowadays available, all of which are optimized for different system types and application domains.
AU - Chatterjee, Krishnendu
AU - Ehlers, Rüdiger
ID - 719
IS - 6
JF - Acta Informatica
SN - 00015903
TI - Special issue: Synthesis and SYNT 2014
VL - 54
ER -
TY - JOUR
AB - Advances in multi-unit recordings pave the way for statistical modeling of activity patterns in large neural populations. Recent studies have shown that the summed activity of all neurons strongly shapes the population response. A separate recent finding has been that neural populations also exhibit criticality, an anomalously large dynamic range for the probabilities of different population activity patterns. Motivated by these two observations, we introduce a class of probabilistic models which takes into account the prior knowledge that the neural population could be globally coupled and close to critical. These models consist of an energy function which parametrizes interactions between small groups of neurons, and an arbitrary positive, strictly increasing, and twice differentiable function which maps the energy of a population pattern to its probability. We show that: 1) augmenting a pairwise Ising model with a nonlinearity yields an accurate description of the activity of retinal ganglion cells which outperforms previous models based on the summed activity of neurons; 2) prior knowledge that the population is critical translates to prior expectations about the shape of the nonlinearity; 3) the nonlinearity admits an interpretation in terms of a continuous latent variable globally coupling the system whose distribution we can infer from data. Our method is independent of the underlying system’s state space; hence, it can be applied to other systems such as natural scenes or amino acid sequences of proteins which are also known to exhibit criticality.
AU - Humplik, Jan
AU - Tkacik, Gasper
ID - 720
IS - 9
JF - PLoS Computational Biology
SN - 1553734X
TI - Probabilistic models for neural populations that naturally capture global coupling and criticality
VL - 13
ER -
TY - JOUR
AB - Let S be a positivity-preserving symmetric linear operator acting on bounded functions. The nonlinear equation -1/m=z+Sm with a parameter z in the complex upper half-plane ℍ has a unique solution m with values in ℍ. We show that the z-dependence of this solution can be represented as the Stieltjes transforms of a family of probability measures v on ℝ. Under suitable conditions on S, we show that v has a real analytic density apart from finitely many algebraic singularities of degree at most 3. Our motivation comes from large random matrices. The solution m determines the density of eigenvalues of two prominent matrix ensembles: (i) matrices with centered independent entries whose variances are given by S and (ii) matrices with correlated entries with a translation-invariant correlation structure. Our analysis shows that the limiting eigenvalue density has only square root singularities or cubic root cusps; no other singularities occur.
AU - Ajanki, Oskari H
AU - Krüger, Torben H
AU - Erdös, László
ID - 721
IS - 9
JF - Communications on Pure and Applied Mathematics
SN - 00103640
TI - Singularities of solutions to quadratic vector equations on the complex upper half plane
VL - 70
ER -
TY - JOUR
AB - Plants are sessile organisms rooted in one place. The soil resources that plants require are often distributed in a highly heterogeneous pattern. To aid foraging, plants have evolved roots whose growth and development are highly responsive to soil signals. As a result, 3D root architecture is shaped by myriad environmental signals to ensure resource capture is optimised and unfavourable environments are avoided. The first signals sensed by newly germinating seeds — gravity and light — direct root growth into the soil to aid seedling establishment. Heterogeneous soil resources, such as water, nitrogen and phosphate, also act as signals that shape 3D root growth to optimise uptake. Root architecture is also modified through biotic interactions that include soil fungi and neighbouring plants. This developmental plasticity results in a ‘custom-made’ 3D root system that is best adapted to forage for resources in each soil environment that a plant colonises.
AU - Morris, Emily
AU - Griffiths, Marcus
AU - Golebiowska, Agata
AU - Mairhofer, Stefan
AU - Burr Hersey, Jasmine
AU - Goh, Tatsuaki
AU - Von Wangenheim, Daniel
AU - Atkinson, Brian
AU - Sturrock, Craig
AU - Lynch, Jonathan
AU - Vissenberg, Kris
AU - Ritz, Karl
AU - Wells, Darren
AU - Mooney, Sacha
AU - Bennett, Malcolm
ID - 722
IS - 17
JF - Current Biology
SN - 09609822
TI - Shaping 3D root system architecture
VL - 27
ER -
TY - JOUR
AB - We investigate the stationary and dynamical behavior of an Anderson localized chain coupled to a single central bound state. Although this coupling partially dilutes the Anderson localized peaks towards nearly resonant sites, the most weight of the original peaks remains unchanged. This leads to multifractal wave functions with a frozen spectrum of fractal dimensions, which is characteristic for localized phases in models with power-law hopping. Using a perturbative approach we identify two different dynamical regimes. At weak couplings to the central site, the transport of particles and information is logarithmic in time, a feature usually attributed to many-body localization. We connect such transport to the persistence of the Poisson statistics of level spacings in parts of the spectrum. In contrast, at stronger couplings the level repulsion is established in the entire spectrum, the problem can be mapped to the Fano resonance, and the transport is ballistic.
AU - Hetterich, Daniel
AU - Serbyn, Maksym
AU - Domínguez, Fernando
AU - Pollmann, Frank
AU - Trauzettel, Björn
ID - 724
IS - 10
JF - Physical Review B
SN - 24699950
TI - Noninteracting central site model localization and logarithmic entanglement growth
VL - 96
ER -
TY - JOUR
AB - Individual computations and social interactions underlying collective behavior in groups of animals are of great ethological, behavioral, and theoretical interest. While complex individual behaviors have successfully been parsed into small dictionaries of stereotyped behavioral modes, studies of collective behavior largely ignored these findings; instead, their focus was on inferring single, mode-independent social interaction rules that reproduced macroscopic and often qualitative features of group behavior. Here, we bring these two approaches together to predict individual swimming patterns of adult zebrafish in a group. We show that fish alternate between an “active” mode, in which they are sensitive to the swimming patterns of conspecifics, and a “passive” mode, where they ignore them. Using a model that accounts for these two modes explicitly, we predict behaviors of individual fish with high accuracy, outperforming previous approaches that assumed a single continuous computation by individuals and simple metric or topological weighing of neighbors’ behavior. At the group level, switching between active and passive modes is uncorrelated among fish, but correlated directional swimming behavior still emerges. Our quantitative approach for studying complex, multi-modal individual behavior jointly with emergent group behavior is readily extensible to additional behavioral modes and their neural correlates as well as to other species.
AU - Harpaz, Roy
AU - Tkacik, Gasper
AU - Schneidman, Elad
ID - 725
IS - 38
JF - PNAS
SN - 00278424
TI - Discrete modes of social information processing predict individual behavior of fish in a group
VL - 114
ER -
TY - JOUR
AB - The morphogenesis of branched organs remains a subject of abiding interest. Although much is known about the underlying signaling pathways, it remains unclear how macroscopic features of branched organs, including their size, network topology, and spatial patterning, are encoded. Here, we show that, in mouse mammary gland, kidney, and human prostate, these features can be explained quantitatively within a single unifying framework of branching and annihilating random walks. Based on quantitative analyses of large-scale organ reconstructions and proliferation kinetics measurements, we propose that morphogenesis follows from the proliferative activity of equipotent tips that stochastically branch and randomly explore their environment but compete neutrally for space, becoming proliferatively inactive when in proximity with neighboring ducts. These results show that complex branched epithelial structures develop as a self-organized process, reliant upon a strikingly simple but generic rule, without recourse to a rigid and deterministic sequence of genetically programmed events.
AU - Hannezo, Edouard B
AU - Scheele, Colinda
AU - Moad, Mohammad
AU - Drogo, Nicholas
AU - Heer, Rakesh
AU - Sampogna, Rosemary
AU - Van Rheenen, Jacco
AU - Simons, Benjamin
ID - 726
IS - 1
JF - Cell
SN - 00928674
TI - A unifying theory of branching morphogenesis
VL - 171
ER -
TY - JOUR
AB - Actin filaments polymerizing against membranes power endocytosis, vesicular traffic, and cell motility. In vitro reconstitution studies suggest that the structure and the dynamics of actin networks respond to mechanical forces. We demonstrate that lamellipodial actin of migrating cells responds to mechanical load when membrane tension is modulated. In a steady state, migrating cell filaments assume the canonical dendritic geometry, defined by Arp2/3-generated 70° branch points. Increased tension triggers a dense network with a broadened range of angles, whereas decreased tension causes a shift to a sparse configuration dominated by filaments growing perpendicularly to the plasma membrane. We show that these responses emerge from the geometry of branched actin: when load per filament decreases, elongation speed increases and perpendicular filaments gradually outcompete others because they polymerize the shortest distance to the membrane, where they are protected from capping. This network-intrinsic geometrical adaptation mechanism tunes protrusive force in response to mechanical load.
AU - Mueller, Jan
AU - Szep, Gregory
AU - Nemethova, Maria
AU - De Vries, Ingrid
AU - Lieber, Arnon
AU - Winkler, Christoph
AU - Kruse, Karsten
AU - Small, John
AU - Schmeiser, Christian
AU - Keren, Kinneret
AU - Hauschild, Robert
AU - Sixt, Michael K
ID - 727
IS - 1
JF - Cell
SN - 00928674
TI - Load adaptation of lamellipodial actin networks
VL - 171
ER -
TY - JOUR
AB - During animal development, cell-fate-specific changes in gene expression can modify the material properties of a tissue and drive tissue morphogenesis. While mechanistic insights into the genetic control of tissue-shaping events are beginning to emerge, how tissue morphogenesis and mechanics can reciprocally impact cell-fate specification remains relatively unexplored. Here we review recent findings reporting how multicellular morphogenetic events and their underlying mechanical forces can feed back into gene regulatory pathways to specify cell fate. We further discuss emerging techniques that allow for the direct measurement and manipulation of mechanical signals in vivo, offering unprecedented access to study mechanotransduction during development. Examination of the mechanical control of cell fate during tissue morphogenesis will pave the way to an integrated understanding of the design principles that underlie robust tissue patterning in embryonic development.
AU - Chan, Chii
AU - Heisenberg, Carl-Philipp J
AU - Hiiragi, Takashi
ID - 728
IS - 18
JF - Current Biology
SN - 09609822
TI - Coordination of morphogenesis and cell fate specification in development
VL - 27
ER -