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On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4
Get PDFA d-dimensional simplex S is called a k-reptile (or a k-reptile simplex) if it can be tiled by k simplices with disjoint interiors that are all mutually congruent and similar to S. For d = 2, triangular k-reptiles exist for all k of the form a^2, 3a^2 or a^2+b^2 and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, the only k-reptile simplices that are known for d ≥ 3, have k = m^d, where m is a positive integer. We substantially simplify the proof by Matoušek and the second author that for d = 3, k-reptile tetrahedra can exist only for k = m^3. We then prove a weaker analogue of this result for d = 4 by showing that four-dimensional k-reptile simplices can exist only for k = m^2
Synaptotagmin 2 Is the Fast Ca^2+ Sensor at a Central Inhibitory Synapse
Get PDFGABAergic synapses in brain circuits generate inhibitory output signals with submillisecond latency and temporal precision. Whether the molecular identity of the release sensor contributes to these signaling properties remains unclear. Here, we examined the Ca^2+ sensor of exocytosis at GABAergic basket cell (BC) to Purkinje cell (PC) synapses in cerebellum. Immunolabeling suggested that BC terminals selectively expressed synaptotagmin 2 (Syt2), whereas synaptotagmin 1 (Syt1) was enriched in excitatory terminals. Genetic elimination of Syt2 reduced action potential-evoked release to ∼10%, identifying Syt2 as the major Ca^2+ sensor at BC-PC synapses. Differential adenovirus-mediated rescue revealed that Syt2 triggered release with shorter latency and higher temporal precision and mediated faster vesicle pool replenishment than Syt1. Furthermore, deletion of Syt2 severely reduced and delayed disynaptic inhibition following parallel fiber stimulation. Thus, the selective use of Syt2 as release sensor at BC-PC synapses ensures fast and efficient feedforward inhibition in cerebellar microcircuits
Spatiotemporal mechanisms of root branching
No full textThe fundamental tasks of the root system are, besides anchoring, mediating interactions between plant and soil and providing the plant with water and nutrients. The architecture of the root system is controlled by endogenous mechanisms that constantly integrate environmental signals, such as availability of nutrients and water. Extremely important for efficient soil exploitation and survival under less favorable conditions is the developmental flexibility of the root system that is largely determined by its postembryonic branching capacity. Modulation of initiation and outgrowth of lateral roots provides roots with an exceptional plasticity, allows optimal adjustment to underground heterogeneity, and enables effective soil exploitation and use of resources. Here we discuss recent advances in understanding the molecular mechanisms that shape the plant root system and integrate external cues to adapt to the changing environment
Subsampling scaling
Get PDFIn real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling. Spatial subsampling can strongly bias inferences about a system's aggregated properties. To overcome the bias, we derive analytically a subsampling scaling framework that is applicable to different observables, including distributions of neuronal avalanches, of number of people infected during an epidemic outbreak, and of node degrees. We demonstrate how to infer the correct distributions of the underlying full system, how to apply it to distinguish critical from subcritical systems, and how to disentangle subsampling and finite size effects. Lastly, we apply subsampling scaling to neuronal avalanche models and to recordings from developing neural networks. We show that only mature, but not young networks follow power-law scaling, indicating self-organization to criticality during development
Brittle fracture simulation with boundary elements for computer graphics
Get PDFThis thesis describes a brittle fracture simulation method for visual effects applications. Building upon a symmetric Galerkin boundary element method, we first compute stress intensity factors following the theory of linear elastic fracture mechanics. We then use these stress intensities to simulate the motion of a propagating crack front at a significantly higher resolution than the overall deformation of the breaking object. Allowing for spatial variations of the material's toughness during crack propagation produces visually realistic, highly-detailed fracture surfaces.
Furthermore, we introduce approximations for stress intensities and crack opening displacements, resulting in both practical speed-up and theoretically superior runtime complexity compared to previous methods. While we choose a quasi-static approach to fracture mechanics, ignoring dynamic deformations, we also couple our fracture simulation framework to a standard rigid-body dynamics solver, enabling visual effects artists to simulate both large scale motion, as well as fracturing due to collision forces in a combined system.
As fractures inside of an object grow, their geometry must be represented both in the coarse boundary element mesh, as well as at the desired fine output resolution. Using a boundary element method, we avoid complicated volumetric meshing operations. Instead we describe a simple set of surface meshing operations that allow us to progressively add cracks to the mesh of an object and still re-use all previously computed entries of the linear boundary element system matrix. On the high resolution level, we opt for an implicit surface representation. We then describe how to capture fracture surfaces during crack propagation, as well as separate the individual fragments resulting from the fracture process, based on this implicit representation.
We show results obtained with our method, either solving the full boundary element system in every time step, or alternatively using our fast approximations. These results demonstrate that both of these methods perform well in basic test cases and produce realistic fracture surfaces. Furthermore we show that our fast approximations substantially out-perform the standard approach in more demanding scenarios. Finally, these two methods naturally combine, using the full solution while the problem size is manageably small and switching to the fast approximations later on. The resulting hybrid method gives the user a direct way to choose between speed and accuracy of the simulation
Timing, variability and cross-protection in bacteria – Insights from dynamic gene expression responses to antibiotics
No full textAntibiotics have diverse effects on bacteria, including massive changes in bacterial gene expression. Whereas the gene expression changes under many antibiotics have been measured, the temporal organization of these responses and their dependence on the bacterial growth rate are unclear. As described in Chapter 1, we quantified the temporal gene expression changes in the bacterium Escherichia coli in response to the sudden exposure to antibiotics using a fluorescent reporter library and a robotic system. Our data show temporally structured gene expression responses, with response times for individual genes ranging from tens of minutes to several hours. We observed that many stress response genes were activated in response to antibiotics. As certain stress responses cross-protect bacteria from other stressors, we then asked whether cellular responses to antibiotics have a similar protective role in Chapter 2. Indeed, we found that the trimethoprim-induced acid stress response protects bacteria from subsequent acid stress. We combined microfluidics with time-lapse imaging to monitor survival, intracellular pH, and acid stress response in single cells. This approach revealed that the variable expression of the acid resistance operon gadBC strongly correlates with single-cell survival time. Cells with higher gadBC expression following trimethoprim maintain higher intracellular pH and survive the acid stress longer. Overall, we provide a way to identify single-cell cross-protection between antibiotics and environmental stressors from temporal gene expression data, and show how antibiotics can increase bacterial fitness in changing environments. While gene expression changes to antibiotics show a clear temporal structure at the population-level, it is unclear whether this clear temporal order is followed by every single cell. Using dual-reporter strains described in Chapter 3, we measured gene expression dynamics of promoter pairs in the same cells using microfluidics and microscopy. Chapter 4 shows that the oxidative stress response and the DNA stress response showed little timing variability and a clear temporal order under the antibiotic nitrofurantoin. In contrast, the acid stress response under trimethoprim ran independently from all other activated response programs including the DNA stress response, which showed particularly high timing variability in this stress condition. In summary, this approach provides insight into the temporal organization of gene expression programs at the single-cell level and suggests dependencies between response programs and the underlying variability-introducing mechanisms. Altogether, this work advances our understanding of the diverse effects that antibiotics have on bacteria. These results were obtained by taking into account gene expression dynamics, which allowed us to identify general principles, molecular mechanisms, and dependencies between genes. Our findings may have implications for infectious disease treatments, and microbial communities in the human body and in nature
Topological data analysis with bregman divergences
Get PDFWe show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory
PirB regulates asymmetries in hippocampal circuitry
Get PDFLeft-right asymmetry is a fundamental feature of higher-order brain structure; however, the molecular basis of brain asymmetry remains unclear. We recently identified structural and functional asymmetries in mouse hippocampal circuitry that result from the asymmetrical distribution of two distinct populations of pyramidal cell synapses that differ in the density of the NMDA receptor subunit GluRε2 (also known as NR2B, GRIN2B or GluN2B). By examining the synaptic distribution of ε2 subunits, we previously found that β2-microglobulin-deficient mice, which lack cell surface expression of the vast majority of major histocompatibility complex class I (MHCI) proteins, do not exhibit circuit asymmetry. In the present study, we conducted electrophysiological and anatomical analyses on the hippocampal circuitry of mice with a knockout of the paired immunoglobulin-like receptor B (PirB), an MHCI receptor. As in β2-microglobulin-deficient mice, the PirB-deficient hippocampus lacked circuit asymmetries. This finding that MHCI loss-of-function mice and PirB knockout mice have identical phenotypes suggests that MHCI signals that produce hippocampal asymmetries are transduced through PirB. Our results provide evidence for a critical role of the MHCI/PirB signaling system in the generation of asymmetries in hippocampal circuitry
Cumulative space in black-white pebbling and resolution
Get PDFWe study space complexity and time-space trade-offs with a focus not on peak memory usage
but on overall memory consumption throughout the computation. Such a cumulative space
measure was introduced for the computational model of parallel black pebbling by [Alwen and
Serbinenko '15] as a tool for obtaining results in cryptography. We consider instead the non-
deterministic black-white pebble game and prove optimal cumulative space lower bounds and
trade-offs, where in order to minimize pebbling time the space has to remain large during a
significant fraction of the pebbling.
We also initiate the study of cumulative space in proof complexity, an area where other
space complexity measures have been extensively studied during the last 10–15 years. Using
and extending the connection between proof complexity and pebble games in [Ben-Sasson and
Nordström '08, '11] we obtain several strong cumulative space results for (even parallel versions
of) the resolution proof system, and outline some possible future directions of study of this, in
our opinion, natural and interesting space measure
Grünlicht-induzierte Rezeptorinaktivierung durch Cobalamin-bindende Domänen
Get PDFOptogenetik und Photopharmakologie ermöglichen präzise räumliche und zeitliche Kontrolle von Proteinwechselwirkung und -funktion in Zellen und Tieren. Optogenetische Methoden, die auf grünes Licht ansprechen und zum Trennen von Proteinkomplexen geeignet sind, sind nichtweitläufig verfügbar,würden jedoch mehrfarbige Experimente zur Beantwortung von biologischen Fragestellungen ermöglichen. Hier demonstrieren wir die Verwendung von Cobalamin(Vitamin B12)-bindenden Domänen von bakteriellen CarH-Transkriptionsfaktoren zur Grünlicht-induzierten Dissoziation von Rezeptoren. Fusioniert mit dem Fibroblasten-Wachstumsfaktor-Rezeptor 1 führten diese im Dunkeln in kultivier ten Zellen zu Signalaktivität durch Oligomerisierung, welche durch Beleuchten umgehend aufgehoben wurde. In Zebrafischembryonen, die einen derartigen Rezeptor exprimieren, ermöglichte grünes Licht die Kontrolle über abnormale Signalaktivität während der Embryonalentwicklung