@article{7472,
author = {Käfer, Karola and Nardin, Michele and Blahna, Karel and Csicsvari, Jozsef L},
issn = {0896-6273},
journal = {Neuron},
number = {1},
pages = {154--165.e6},
publisher = {Elsevier},
title = {{Replay of behavioral sequences in the medial prefrontal cortex during rule switching}},
doi = {10.1016/j.neuron.2020.01.015},
volume = {106},
year = {2020},
}
@phdthesis{7629,
abstract = {This thesis is based on three main topics: In the first part, we study convergence of discrete gradient flow structures associated with regular finite-volume discretisations of Fokker-Planck equations. We show evolutionary I convergence of the discrete gradient flows to the L2-Wasserstein gradient flow corresponding to the solution of a Fokker-Planck
equation in arbitrary dimension d >= 1. Along the argument, we prove Mosco- and I-convergence results for discrete energy functionals, which are of independent interest for convergence of equivalent gradient flow structures in Hilbert spaces.
The second part investigates L2-Wasserstein flows on metric graph. The starting point is a Benamou-Brenier formula for the L2-Wasserstein distance, which is proved via a regularisation scheme for solutions of the continuity equation, adapted to the peculiar geometric structure of metric graphs. Based on those results, we show that the L2-Wasserstein space over a metric graph admits a gradient flow which may be identified as a solution of a Fokker-Planck equation.
In the third part, we focus again on the discrete gradient flows, already encountered in the first part. We propose a variational structure which extends the gradient flow structure to Markov chains violating the detailed-balance conditions. Using this structure, we characterise contraction estimates for the discrete heat flow in terms of convexity of
corresponding path-dependent energy functionals. In addition, we use this approach to derive several functional inequalities for said functionals.},
author = {Forkert, Dominik L},
issn = {2663-337X},
pages = {154},
publisher = {IST Austria},
title = {{Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains}},
doi = {10.15479/AT:ISTA:7629},
year = {2020},
}
@article{7686,
abstract = {The agricultural green revolution spectacularly enhanced crop yield and lodging resistance with modified DELLA-mediated gibberellin signaling. However, this was achieved at the expense of reduced nitrogen-use efficiency (NUE). Recently, Wu et al. revealed novel gibberellin signaling that provides a blueprint for improving tillering and NUE in Green Revolution varieties (GRVs). },
author = {Xue, Huidan and Zhang, Yuzhou and Xiao, Guanghui},
issn = {13601385},
journal = {Trends in Plant Science},
publisher = {Elsevier},
title = {{Neo-gibberellin signaling: Guiding the next generation of the green revolution}},
doi = {10.1016/j.tplants.2020.04.001},
year = {2020},
}
@inproceedings{7802,
abstract = {The Massively Parallel Computation (MPC) model is an emerging model which distills core aspects of distributed and parallel computation. It has been developed as a tool to solve (typically graph) problems in systems where the input is distributed over many machines with limited space.
Recent work has focused on the regime in which machines have sublinear (in $n$, the number of nodes in the input graph) space, with randomized algorithms presented for fundamental graph problems of Maximal Matching and Maximal Independent Set. However, there have been no prior corresponding deterministic algorithms.
A major challenge underlying the sublinear space setting is that the local space of each machine might be too small to store all the edges incident to a single node. This poses a considerable obstacle compared to the classical models in which each node is assumed to know and have easy access to its incident edges. To overcome this barrier we introduce a new graph sparsification technique that deterministically computes a low-degree subgraph with additional desired properties. The degree of the nodes in this subgraph is small in the sense that the edges of each node can be now stored on a single machine. This low-degree subgraph also has the property that solving the problem on this subgraph provides \emph{significant} global progress, i.e., progress towards solving the problem for the original input graph.
Using this framework to derandomize the well-known randomized algorithm of Luby [SICOMP'86], we obtain $O(\log \Delta+\log\log n)$-round deterministic MPC algorithms for solving the fundamental problems of Maximal Matching and Maximal Independent Set with $O(n^{\epsilon})$ space on each machine for any constant $\epsilon > 0$. Based on the recent work of Ghaffari et al. [FOCS'18], this additive $O(\log\log n)$ factor is conditionally essential. These algorithms can also be shown to run in $O(\log \Delta)$ rounds in the closely related model of CONGESTED CLIQUE, improving upon the state-of-the-art bound of $O(\log^2 \Delta)$ rounds by Censor-Hillel et al. [DISC'17].},
author = {Czumaj, Artur and Davies, Peter and Parter, Merav},
booktitle = {Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2020)},
location = {Philadelphia, PA, United States},
publisher = {Association for Computing Machinery},
title = {{Graph sparsification for derandomizing massively parallel computation with low space}},
year = {2020},
}
@inproceedings{7807,
abstract = {In a straight-line embedded triangulation of a point set P in the plane, removing an inner edge and—provided the resulting quadrilateral is convex—adding the other diagonal is called an edge flip. The (edge) flip graph has all triangulations as vertices, and a pair of triangulations is adjacent if they can be obtained from each other by an edge flip. The goal of this paper is to contribute to a better understanding of the flip graph, with an emphasis on its connectivity.
For sets in general position, it is known that every triangulation allows at least edge flips (a tight bound) which gives the minimum degree of any flip graph for n points. We show that for every point set P in general position, the flip graph is at least -vertex connected. Somewhat more strongly, we show that the vertex connectivity equals the minimum degree occurring in the flip graph, i.e. the minimum number of flippable edges in any triangulation of P, provided P is large enough. Finally, we exhibit some of the geometry of the flip graph by showing that the flip graph can be covered by 1-skeletons of polytopes of dimension (products of associahedra).
A corresponding result ((n – 3)-vertex connectedness) can be shown for the bistellar flip graph of partial triangulations, i.e. the set of all triangulations of subsets of P which contain all extreme points of P. This will be treated separately in a second part.},
author = {Wagner, Uli and Welzl, Emo},
booktitle = {Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms},
isbn = {9781611975994},
location = {Salt Lake City, UT, United States},
pages = {2823--2841},
publisher = {SIAM},
title = {{Connectivity of triangulation flip graphs in the plane (Part I: Edge flips)}},
doi = {10.1137/1.9781611975994.172},
volume = {2020-January},
year = {2020},
}
@article{7814,
abstract = {Scientific research is to date largely restricted to wealthy laboratories in developed nations due to the necessity of complex and expensive equipment. This inequality limits the capacity of science to be used as a diplomatic channel. Maker movements use open-source technologies including additive manufacturing (3D printing) and laser cutting, together with low-cost computers for developing novel products. This movement is setting the groundwork for a revolution, allowing scientific equipment to be sourced at a fraction of the cost and has the potential to increase the availability of equipment for scientists around the world. Science education is increasingly recognized as another channel for science diplomacy. In this perspective, we introduce the idea that the Maker movement and open-source technologies have the potential to revolutionize science, technology, engineering and mathematics (STEM) education worldwide. We present an open-source STEM didactic tool called SCOPES (Sparking Curiosity through Open-source Platforms in Education and Science). SCOPES is self-contained, independent of local resources, and cost-effective. SCOPES can be adapted to communicate complex subjects from genetics to neurobiology, perform real-world biological experiments and explore digitized scientific samples. We envision such platforms will enhance science diplomacy by providing a means for scientists to share their findings with classrooms and for educators to incorporate didactic concepts into STEM lessons. By providing students the opportunity to design, perform, and share scientific experiments, students also experience firsthand the benefits of a multinational scientific community. We provide instructions on how to build and use SCOPES on our webpage: http://scopeseducation.org.},
author = {Beattie, Robert J and Hippenmeyer, Simon and Pauler, Florian},
issn = {2504-284X},
journal = {Frontiers in Education},
publisher = {Frontiers Media},
title = {{SCOPES: Sparking curiosity through Open-Source platforms in education and science}},
doi = {10.3389/feduc.2020.00048},
volume = {5},
year = {2020},
}
@article{6563,
abstract = {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.},
author = {Filakovský, Marek and Vokřínek, Lukas},
issn = {16153383},
journal = {Foundations of Computational Mathematics},
pages = {311--330},
publisher = {Springer Nature},
title = {{Are two given maps homotopic? An algorithmic viewpoint}},
doi = {10.1007/s10208-019-09419-x},
volume = {20},
year = {2020},
}
@article{6796,
abstract = {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.},
author = {Stella, Federico and Urdapilleta, Eugenio and Luo, Yifan and Treves, Alessandro},
issn = {10981063},
journal = {Hippocampus},
number = {4},
pages = {302--313},
publisher = {Wiley},
title = {{Partial coherence and frustration in self-organizing spherical grids}},
doi = {10.1002/hipo.23144},
volume = {30},
year = {2020},
}
@article{7888,
abstract = {Embryonic stem cell cultures are thought to self-organize into embryoid bodies, able to undergo symmetry-breaking, germ layer specification and even morphogenesis. Yet, it is unclear how to reconcile this remarkable self-organization capacity with classical experiments demonstrating key roles for extrinsic biases by maternal factors and/or extraembryonic tissues in embryogenesis. Here, we show that zebrafish embryonic tissue explants, prepared prior to germ layer induction and lacking extraembryonic tissues, can specify all germ layers and form a seemingly complete mesendoderm anlage. Importantly, explant organization requires polarized inheritance of maternal factors from dorsal-marginal regions of the blastoderm. Moreover, induction of endoderm and head-mesoderm, which require peak Nodal-signaling levels, is highly variable in explants, reminiscent of embryos with reduced Nodal signals from the extraembryonic tissues. Together, these data suggest that zebrafish explants do not undergo bona fide self-organization, but rather display features of genetically encoded self-assembly, where intrinsic genetic programs control the emergence of order.},
author = {Schauer, Alexandra and Nunes Pinheiro, Diana C and Hauschild, Robert and Heisenberg, Carl-Philipp J},
issn = {2050-084X},
journal = {eLife},
publisher = {eLife Sciences Publications},
title = {{Zebrafish embryonic explants undergo genetically encoded self-assembly}},
doi = {10.7554/elife.55190},
volume = {9},
year = {2020},
}
@article{7876,
abstract = {In contrast to lymph nodes, the lymphoid regions of the spleen—the white pulp—are located deep within the organ, yielding the trafficking paths of T cells in the white pulp largely invisible. In an intravital microscopy tour de force reported in this issue of Immunity, Chauveau et al. show that T cells perform unidirectional, perivascular migration through the enigmatic marginal zone bridging channels. },
author = {Sixt, Michael K and Lämmermann, Tim},
issn = {10974180},
journal = {Immunity},
number = {5},
pages = {721--723},
publisher = {Elsevier},
title = {{T cells: Bridge-and-channel commute to the white pulp}},
doi = {10.1016/j.immuni.2020.04.020},
volume = {52},
year = {2020},
}
@article{7864,
abstract = {Purpose of review: Cancer is one of the leading causes of death and the incidence rates are constantly rising. The heterogeneity of tumors poses a big challenge for the treatment of the disease and natural antibodies additionally affect disease progression. The introduction of engineered mAbs for anticancer immunotherapies has substantially improved progression-free and overall survival of cancer patients, but little efforts have been made to exploit other antibody isotypes than IgG.
Recent findings: In order to improve these therapies, ‘next-generation antibodies’ were engineered to enhance a specific feature of classical antibodies and form a group of highly effective and precise therapy compounds. Advanced antibody approaches include among others antibody-drug conjugates, glyco-engineered and Fc-engineered antibodies, antibody fragments, radioimmunotherapy compounds, bispecific antibodies and alternative (non-IgG) immunoglobulin classes, especially IgE.
Summary: The current review describes solutions for the needs of next-generation antibody therapies through different approaches. Careful selection of the best-suited engineering methodology is a key factor in developing personalized, more specific and more efficient mAbs against cancer to improve the outcomes of cancer patients. We highlight here the large evidence of IgE exploiting a highly cytotoxic effector arm as potential next-generation anticancer immunotherapy.},
author = {Singer, Judit and Singer, Josef and Jensen-Jarolim, Erika},
issn = {14736322},
journal = {Current opinion in allergy and clinical immunology},
number = {3},
pages = {282--289},
publisher = {Wolters Kluwer},
title = {{Precision medicine in clinical oncology: the journey from IgG antibody to IgE}},
doi = {10.1097/ACI.0000000000000637},
volume = {20},
year = {2020},
}
@article{7908,
abstract = {Volatile anesthetics are widely used for surgery, but neuronal mechanisms of anesthesia remain unidentified. At the calyx of Held in brainstem slices from rats of either sex, isoflurane at clinical doses attenuated EPSCs by decreasing the release probability and the number of readily releasable vesicles. In presynaptic recordings of Ca2+ currents and exocytic capacitance changes, isoflurane attenuated exocytosis by inhibiting Ca2+ currents evoked by a short presynaptic depolarization, whereas it inhibited exocytosis evoked by a prolonged depolarization via directly blocking exocytic machinery downstream of Ca2+ influx. Since the length of presynaptic depolarization can simulate the frequency of synaptic inputs, isoflurane anesthesia is likely mediated by distinct dual mechanisms, depending on input frequencies. In simultaneous presynaptic and postsynaptic action potential recordings, isoflurane impaired the fidelity of repetitive spike transmission, more strongly at higher frequencies. Furthermore, in the cerebrum of adult mice, isoflurane inhibited monosynaptic corticocortical spike transmission, preferentially at a higher frequency. We conclude that dual presynaptic mechanisms operate for the anesthetic action of isoflurane, of which direct inhibition of exocytic machinery plays a low-pass filtering role in spike transmission at central excitatory synapses.},
author = {Wang, Han Ying and Eguchi, Kohgaku and Yamashita, Takayuki and Takahashi, Tomoyuki},
issn = {15292401},
journal = {The Journal of neuroscience},
number = {21},
pages = {4103--4115},
publisher = {Society for Neuroscience},
title = {{Frequency-dependent block of excitatory neurotransmission by isoflurane via dual presynaptic mechanisms}},
doi = {10.1523/JNEUROSCI.2946-19.2020},
volume = {40},
year = {2020},
}
@inbook{7941,
abstract = {Expansion microscopy is a recently developed super-resolution imaging technique, which provides an alternative to optics-based methods such as deterministic approaches (e.g. STED) or stochastic approaches (e.g. PALM/STORM). The idea behind expansion microscopy is to embed the biological sample in a swellable gel, and then to expand it isotropically, thereby increasing the distance between the fluorophores. This approach breaks the diffraction barrier by simply separating the emission point-spread-functions of the fluorophores. The resolution attainable in expansion microscopy is thus directly dependent on the separation that can be achieved, i.e. on the expansion factor. The original implementation of the technique achieved an expansion factor of fourfold, for a resolution of 70–80 nm. The subsequently developed X10 method achieves an expansion factor of 10-fold, for a resolution of 25–30 nm. This technique can be implemented with minimal technical requirements on any standard fluorescence microscope, and is more easily applied for multi-color imaging than either deterministic or stochastic super-resolution approaches. This renders X10 expansion microscopy a highly promising tool for new biological discoveries, as discussed here, and as demonstrated by several recent applications.},
author = {Truckenbrodt, Sven M and Rizzoli, Silvio O.},
booktitle = {Methods in Cell Biology},
issn = {0091679X},
publisher = {Elsevier},
title = {{Simple multi-color super-resolution by X10 microscopy}},
doi = {10.1016/bs.mcb.2020.04.016},
year = {2020},
}
@article{7960,
abstract = {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.},
author = {Kalai, Gil and Patakova, Zuzana},
issn = {14320444},
journal = {Discrete and Computational Geometry},
publisher = {Springer Nature},
title = {{Intersection patterns of planar sets}},
doi = {10.1007/s00454-020-00205-z},
year = {2020},
}
@article{7600,
abstract = {Directional intercellular transport of the phytohormone auxin mediated by PIN FORMED (PIN) efflux carriers plays essential roles in both coordinating patterning processes and integrating multiple external cues by rapidly redirecting auxin fluxes. Multilevel regulations of PIN activity under internal and external cues are complicated; however, the underlying molecular mechanism remains elusive. Here we demonstrate that 3’-Phosphoinositide-Dependent Protein Kinase1 (PDK1), which is conserved in plants and mammals, functions as a molecular hub integrating the upstream lipid signalling and the downstream substrate activity through phosphorylation. Genetic analysis uncovers that loss-of-function Arabidopsis mutant pdk1.1 pdk1.2 exhibits a plethora of abnormalities in organogenesis and growth, due to the defective PIN-dependent auxin transport. Further cellular and biochemical analyses reveal that PDK1 phosphorylates D6 Protein Kinase to facilitate its activity towards PIN proteins. Our studies establish a lipid-dependent phosphorylation cascade connecting membrane composition-based cellular signalling with plant growth and patterning by regulating morphogenetic auxin fluxes.},
author = {Tan, Shutang and Zhang, Xixi and Kong, Wei and Yang, Xiao-Li and Molnar, Gergely and Vondráková, Zuzana and Filepová, Roberta and Petrášek, Jan and Friml, Jiří and Xue, Hong-Wei},
issn = {20550278},
journal = {Nature Plants},
pages = {556--569},
publisher = {Springer Nature},
title = {{The lipid code-dependent phosphoswitch PDK1–D6PK activates PIN-mediated auxin efflux in Arabidopsis}},
doi = {10.1038/s41477-020-0648-9},
volume = {6},
year = {2020},
}
@phdthesis{7996,
abstract = {Quantum computation enables the execution of algorithms that have exponential complexity. This might open the path towards the synthesis of new materials or medical drugs, optimization of transport or financial strategies etc., intractable on even the fastest classical computers. A quantum computer consists of interconnected two level quantum systems, called qubits, that satisfy DiVincezo’s criteria. Worldwide, there are ongoing efforts to find the qubit architecture which will unite quantum error correction compatible single and two qubit fidelities, long distance qubit to qubit coupling and
calability. Superconducting qubits have gone the furthest in this race, demonstrating an algorithm running on 53 coupled qubits, but still the fidelities are not even close to those required for realizing a single logical qubit. emiconductor qubits offer extremely good characteristics, but they are currently investigated across different platforms. Uniting those good characteristics into a single platform might be a big step towards the quantum computer realization.
Here we describe the implementation of a hole spin qubit hosted in a Ge hut wire double quantum dot. The high and tunable spin-orbit coupling together with a heavy hole state character is expected to allow fast spin manipulation and long coherence times. Furthermore large lever arms, for hut wire devices, should allow good coupling to superconducting resonators enabling efficient long distance spin to spin coupling and a sensitive gate reflectometry spin readout. The developed cryogenic setup (printed circuit board sample holders, filtering, high-frequency wiring) enabled us to perform low temperature spin dynamics experiments. Indeed, we measured the fastest single spin qubit Rabi frequencies reported so far, reaching 140 MHz, while the dephasing times of 130 ns oppose the long decoherence predictions. In order to further investigate this, a double quantum dot gate was connected directly to a lumped element
resonator which enabled gate reflectometry readout. The vanishing inter-dot transition signal, for increasing external magnetic field, revealed the spin nature of the measured quantity.},
author = {Kukucka, Josip},
issn = {2663-337X},
pages = {178},
publisher = {IST Austria},
title = {{Implementation of a hole spin qubit in Ge hut wires and dispersive spin sensing}},
doi = {10.15479/AT:ISTA:7996},
year = {2020},
}
@article{7580,
abstract = {The eukaryotic endomembrane system is controlled by small GTPases of the Rab family, which are activated at defined times and locations in a switch-like manner. While this switch is well understood for an individual protein, how regulatory networks produce intracellular activity patterns is currently not known. Here, we combine in vitro reconstitution experiments with computational modeling to study a minimal Rab5 activation network. We find that the molecular interactions in this system give rise to a positive feedback and bistable collective switching of Rab5. Furthermore, we find that switching near the critical point is intrinsically stochastic and provide evidence that controlling the inactive population of Rab5 on the membrane can shape the network response. Notably, we demonstrate that collective switching can spread on the membrane surface as a traveling wave of Rab5 activation. Together, our findings reveal how biochemical signaling networks control vesicle trafficking pathways and how their nonequilibrium properties define the spatiotemporal organization of the cell.},
author = {Bezeljak, Urban and Loya, Hrushikesh and Kaczmarek, Beata M and Saunders, Timothy E. and Loose, Martin},
issn = {0027-8424},
journal = {Proceedings of the National Academy of Sciences},
number = {12},
pages = {6504--6549},
publisher = {Proceedings of the National Academy of Sciences},
title = {{Stochastic activation and bistability in a Rab GTPase regulatory network}},
doi = {10.1073/pnas.1921027117},
volume = {117},
year = {2020},
}
@article{7910,
abstract = {Quantum illumination uses entangled signal-idler photon pairs to boost the detection efficiency of low-reflectivity objects in environments with bright thermal noise. Its advantage is particularly evident at low signal powers, a promising feature for applications such as noninvasive biomedical scanning or low-power short-range radar. Here, we experimentally investigate the concept of quantum illumination at microwave frequencies. We generate entangled fields to illuminate a room-temperature object at a distance of 1 m in a free-space detection setup. We implement a digital phase-conjugate receiver based on linear quadrature measurements that outperforms a symmetric classical noise radar in the same conditions, despite the entanglement-breaking signal path. Starting from experimental data, we also simulate the case of perfect idler photon number detection, which results in a quantum advantage compared with the relative classical benchmark. Our results highlight the opportunities and challenges in the way toward a first room-temperature application of microwave quantum circuits.},
author = {Barzanjeh, Shabir and Pirandola, S. and Vitali, D and Fink, Johannes M},
issn = {23752548},
journal = {Science Advances},
number = {19},
publisher = {AAAS},
title = {{Microwave quantum illumination using a digital receiver}},
doi = {10.1126/sciadv.abb0451},
volume = {6},
year = {2020},
}
@misc{7383,
abstract = {Organisms cope with change by employing transcriptional regulators. However, when faced with rare environments, the evolution of transcriptional regulators and their promoters may be too slow. We ask whether the intrinsic instability of gene duplication and amplification provides a generic alternative to canonical gene regulation. By real-time monitoring of gene copy number mutations in E. coli, we show that gene duplications and amplifications enable adaptation to fluctuating environments by rapidly generating copy number, and hence expression level, polymorphism. This ‘amplification-mediated gene expression tuning’ occurs on timescales similar to canonical gene regulation and can deal with rapid environmental changes. Mathematical modeling shows that amplifications also tune gene expression in stochastic environments where transcription factor-based schemes are hard to evolve or maintain. The fleeting nature of gene amplifications gives rise to a generic population-level mechanism that relies on genetic heterogeneity to rapidly tune expression of any gene, without leaving any genomic signature.},
author = {Grah, Rok},
keyword = {Matlab scripts, analysis of microfluidics, mathematical model},
publisher = {IST Austria},
title = {{Matlab scripts for the Paper: Gene Amplification as a Form of Population-Level Gene Expression regulation}},
doi = {10.15479/AT:ISTA:7383},
year = {2020},
}
@inproceedings{7989,
abstract = {We prove general topological Radon-type theorems for sets in ℝ^d, smooth real manifolds or finite dimensional simplicial complexes. Combined with a recent result of Holmsen and Lee, it gives fractional Helly theorem, and consequently the existence of weak ε-nets as well as a (p,q)-theorem. More precisely: Let X be either ℝ^d, smooth real d-manifold, or a finite d-dimensional simplicial complex. Then if F is a finite, intersection-closed family of sets in X such that the ith reduced Betti number (with ℤ₂ coefficients) of any set in F is at most b for every non-negative integer i less or equal to k, then the Radon number of F is bounded in terms of b and X. Here k is the smallest integer larger or equal to d/2 - 1 if X = ℝ^d; k=d-1 if X is a smooth real d-manifold and not a surface, k=0 if X is a surface and k=d if X is a d-dimensional simplicial complex. Using the recent result of the author and Kalai, we manage to prove the following optimal bound on fractional Helly number for families of open sets in a surface: Let F be a finite family of open sets in a surface S such that the intersection of any subfamily of F is either empty, or path-connected. Then the fractional Helly number of F is at most three. This also settles a conjecture of Holmsen, Kim, and Lee about an existence of a (p,q)-theorem for open subsets of a surface.},
author = {Patakova, Zuzana},
booktitle = {36th International Symposium on Computational Geometry},
isbn = {9783959771436},
issn = {18688969},
location = {Zürich, Switzerland},
pages = {61:1--61:13},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Bounding radon number via Betti numbers}},
doi = {10.4230/LIPIcs.SoCG.2020.61},
volume = {164},
year = {2020},
}