@phdthesis{9022,
abstract = {In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime.
In the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time
(up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions.
In the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result
improves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices.},
author = {Cipolloni, Giorgio},
issn = {2663-337X},
pages = {380},
publisher = {IST Austria},
title = {{Fluctuations in the spectrum of random matrices}},
doi = {10.15479/AT:ISTA:9022},
year = {2021},
}
@article{10222,
abstract = {Consider a random set of points on the unit sphere in ℝd, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the case d = 3, for which there are elementary proofs and fascinating formulas for metric properties. In particular, we study the fraction of acute facets, the expected intrinsic volumes, the total edge length, and the distance to a fixed point. Finally we generalize the results to the ellipsoid with homeoid density.},
author = {Akopyan, Arseniy and Edelsbrunner, Herbert and Nikitenko, Anton},
issn = {1944950X},
journal = {Experimental Mathematics},
pages = {1--15},
publisher = {Taylor and Francis},
title = {{The beauty of random polytopes inscribed in the 2-sphere}},
doi = {10.1080/10586458.2021.1980459},
year = {2021},
}
@article{10202,
abstract = {Zygotic genome activation (ZGA) initiates regionalized transcription underlying distinct cellular identities. ZGA is dependent upon dynamic chromatin architecture sculpted by conserved DNA-binding proteins. However, the direct mechanistic link between the onset of ZGA and the tissue-specific transcription remains unclear. Here, we have addressed the involvement of chromatin organizer Satb2 in orchestrating both processes during zebrafish embryogenesis. Integrative analysis of transcriptome, genome-wide occupancy and chromatin accessibility reveals contrasting molecular activities of maternally deposited and zygotically synthesized Satb2. Maternal Satb2 prevents premature transcription of zygotic genes by influencing the interplay between the pluripotency factors. By contrast, zygotic Satb2 activates transcription of the same group of genes during neural crest development and organogenesis. Thus, our comparative analysis of maternal versus zygotic function of Satb2 underscores how these antithetical activities are temporally coordinated and functionally implemented highlighting the evolutionary implications of the biphasic and bimodal regulation of landmark developmental transitions by a single determinant.},
author = {Pradhan, Saurabh J. and Reddy, Puli Chandramouli and Smutny, Michael and Sharma, Ankita and Sako, Keisuke and Oak, Meghana S. and Shah, Rini and Pal, Mrinmoy and Deshpande, Ojas and Dsilva, Greg and Tang, Yin and Mishra, Rakesh and Deshpande, Girish and Giraldez, Antonio J. and Sonawane, Mahendra and Heisenberg, Carl-Philipp J and Galande, Sanjeev},
issn = {20411723},
journal = {Nature Communications},
number = {1},
publisher = {Springer Nature},
title = {{Satb2 acts as a gatekeeper for major developmental transitions during early vertebrate embryogenesis}},
doi = {10.1038/s41467-021-26234-7},
volume = {12},
year = {2021},
}
@article{10271,
abstract = {Understanding interactions between antibiotics used in combination is an important theme in microbiology. Using the interactions between the antifolate drug trimethoprim and the ribosome-targeting antibiotic erythromycin in Escherichia coli as a model, we applied a transcriptomic approach for dissecting interactions between two antibiotics with different modes of action. When trimethoprim and erythromycin were combined, the transcriptional response of genes from the sulfate reduction pathway deviated from the dominant effect of trimethoprim on the transcriptome. We successfully altered the drug interaction from additivity to suppression by increasing the sulfate level in the growth environment and identified sulfate reduction as an important metabolic determinant that shapes the interaction between the two drugs. Our work highlights the potential of using prioritization of gene expression patterns as a tool for identifying key metabolic determinants that shape drug-drug interactions. We further demonstrated that the sigma factor-binding protein gene crl shapes the interactions between the two antibiotics, which provides a rare example of how naturally occurring variations between strains of the same bacterial species can sometimes generate very different drug interactions.},
author = {Qi, Qin and Angermayr, S. Andreas and Bollenbach, Mark Tobias},
issn = {1664-302X},
journal = {Frontiers in Microbiology},
keywords = {microbiology},
publisher = {Frontiers Media SA},
title = {{Uncovering Key Metabolic Determinants of the Drug Interactions Between Trimethoprim and Erythromycin in Escherichia coli}},
doi = {10.3389/fmicb.2021.760017},
volume = {12},
year = {2021},
}
@article{9287,
abstract = {The phytohormone auxin and its directional transport through tissues are intensively studied. However, a mechanistic understanding of auxin-mediated feedback on endocytosis and polar distribution of PIN auxin transporters remains limited due to contradictory observations and interpretations. Here, we used state-of-the-art methods to reexamine the
auxin effects on PIN endocytic trafficking. We used high auxin concentrations or longer treatments versus lower concentrations and shorter treatments of natural (IAA) and synthetic (NAA) auxins to distinguish between specific and nonspecific effects. Longer treatments of both auxins interfere with Brefeldin A-mediated intracellular PIN2 accumulation and also with general aggregation of endomembrane compartments. NAA treatment decreased the internalization of the endocytic tracer dye, FM4-64; however, NAA treatment also affected the number, distribution, and compartment identity of the early endosome/trans-Golgi network (EE/TGN), rendering the FM4-64 endocytic assays at high NAA concentrations unreliable. To circumvent these nonspecific effects of NAA and IAA affecting the endomembrane system, we opted for alternative approaches visualizing the endocytic events directly at the plasma membrane (PM). Using Total Internal Reflection Fluorescence (TIRF) microscopy, we saw no significant effects of IAA or NAA treatments on the incidence and dynamics of clathrin foci, implying that these treatments do not affect the overall endocytosis rate. However, both NAA and IAA at low concentrations rapidly and specifically promoted endocytosis of photo-converted PIN2 from the PM. These analyses identify a specific effect of NAA and IAA on PIN2 endocytosis, thus contributing to its
polarity maintenance and furthermore illustrate that high auxin levels have nonspecific effects on trafficking and endomembrane compartments. },
author = {Narasimhan, Madhumitha and Gallei, Michelle C and Tan, Shutang and Johnson, Alexander J and Verstraeten, Inge and Li, Lanxin and Rodriguez Solovey, Lesia and Han, Huibin and Himschoot, E and Wang, R and Vanneste, S and Sánchez-Simarro, J and Aniento, F and Adamowski, Maciek and Friml, Jiří},
issn = {1532-2548},
journal = {Plant Physiology},
number = {2},
pages = {1122–1142},
publisher = {Oxford University Press},
title = {{Systematic analysis of specific and nonspecific auxin effects on endocytosis and trafficking}},
doi = {10.1093/plphys/kiab134},
volume = {186},
year = {2021},
}
@phdthesis{10083,
abstract = {Plant motions occur across a wide spectrum of timescales, ranging from seed dispersal through bursting (milliseconds) and stomatal opening (minutes) to long-term adaptation of gross architecture. Relatively fast motions include water-driven growth as exemplified by root cell expansion under abiotic/biotic stresses or during gravitropism. A showcase is a root growth inhibition in 30 seconds triggered by the phytohormone auxin. However, the cellular and molecular mechanisms are still largely unknown. This thesis covers the studies about this topic as follows. By taking advantage of microfluidics combined with live imaging, pharmaceutical tools, and transgenic lines, we examined the kinetics of and causal relationship among various auxininduced rapid cellular changes in root growth, apoplastic pH, cytosolic Ca2+, cortical microtubule (CMT) orientation, and vacuolar morphology. We revealed that CMT reorientation and vacuolar constriction are the consequence of growth itself instead of responding directly to auxin. In contrast, auxin induces apoplast alkalinization to rapidly inhibit root growth in 30 seconds. This auxin-triggered apoplast alkalinization results from rapid H+- influx that is contributed by Ca2+ inward channel CYCLIC NUCLEOTIDE-GATED CHANNEL 14 (CNGC14)-dependent Ca2+ signaling. To dissect which auxin signaling mediates the rapid apoplast alkalinization, we
combined microfluidics and genetic engineering to verify that TIR1/AFB receptors conduct a non-transcriptional regulation on Ca2+ and H+ -influx. This non-canonical pathway is mostly mediated by the cytosolic portion of TIR1/AFB. On the other hand, we uncovered, using biochemical and phospho-proteomic analysis, that auxin cell surface signaling component TRANSMEMBRANE KINASE 1 (TMK1) plays a negative role during auxin-trigger apoplast
alkalinization and root growth inhibition through directly activating PM H+ -ATPases. Therefore, we discovered that PM H+ -ATPases counteract instead of mediate the auxintriggered rapid H+ -influx, and that TIR1/AFB and TMK1 regulate root growth antagonistically. This opposite effect of TIR1/AFB and TMK1 is consistent during auxin-induced hypocotyl elongation, leading us to explore the relation of two signaling pathways. Assisted with biochemistry and fluorescent imaging, we verified for the first time that TIR1/AFB and TMK1 can interact with each other. The ability of TIR1/AFB binding to membrane lipid provides a basis for the interaction of plasma membrane- and cytosol-localized proteins.
Besides, transgenic analysis combined with genetic engineering and biochemistry showed that vi
they do function in the same pathway. Particularly, auxin-induced TMK1 increase is TIR1/AFB dependent, suggesting TIR1/AFB regulation on TMK1. Conversely, TMK1 also regulates TIR1/AFB protein levels and thus auxin canonical signaling. To follow the study of rapid growth regulation, we analyzed another rapid growth regulator, signaling peptide RALF1. We showed that RALF1 also triggers a rapid and reversible growth inhibition caused by H + influx, highly resembling but not dependent on auxin. Besides, RALF1 promotes auxin biosynthesis by increasing expression of auxin biosynthesis enzyme YUCCAs and thus induces auxin signaling in ca. 1 hour, contributing to the sustained RALF1-triggered growth inhibition. These studies collectively contribute to understanding rapid regulation on plant cell
growth, novel auxin signaling pathway as well as auxin-peptide crosstalk. },
author = {Li, Lanxin},
issn = {2663-337X},
publisher = {IST Austria},
title = {{Rapid cell growth regulation in Arabidopsis}},
doi = {10.15479/at:ista:10083},
year = {2021},
}
@article{10220,
abstract = {We study conditions under which a finite simplicial complex K can be mapped to ℝd without higher-multiplicity intersections. An almost r-embedding is a map f: K → ℝd such that the images of any r pairwise disjoint simplices of K do not have a common point. We show that if r is not a prime power and d ≥ 2r + 1, then there is a counterexample to the topological Tverberg conjecture, i.e., there is an almost r-embedding of the (d +1)(r − 1)-simplex in ℝd. This improves on previous constructions of counterexamples (for d ≥ 3r) based on a series of papers by M. Özaydin, M. Gromov, P. Blagojević, F. Frick, G. Ziegler, and the second and fourth present authors.
The counterexamples are obtained by proving the following algebraic criterion in codimension 2: If r ≥ 3 and if K is a finite 2(r − 1)-complex, then there exists an almost r-embedding K → ℝ2r if and only if there exists a general position PL map f: K → ℝ2r such that the algebraic intersection number of the f-images of any r pairwise disjoint simplices of K is zero. This result can be restated in terms of a cohomological obstruction and extends an analogous codimension 3 criterion by the second and fourth authors. As another application, we classify ornaments f: S3 ⊔ S3 ⊔ S3 → ℝ5 up to ornament concordance.
It follows from work of M. Freedman, V. Krushkal and P. Teichner that the analogous criterion for r = 2 is false. We prove a lemma on singular higher-dimensional Borromean rings, yielding an elementary proof of the counterexample.},
author = {Avvakumov, Sergey and Mabillard, Isaac and Skopenkov, Arkadiy B. and Wagner, Uli},
issn = {15658511},
journal = {Israel Journal of Mathematics},
pages = {1--34},
publisher = {Springer Nature},
title = {{Eliminating higher-multiplicity intersections. III. Codimension 2}},
doi = {10.1007/s11856-021-2216-z},
year = {2021},
}
@inproceedings{10218,
abstract = {Let G be a graph on n nodes. In the stochastic population protocol model, a collection of n indistinguishable, resource-limited nodes collectively solve tasks via pairwise interactions. In each interaction, two randomly chosen neighbors first read each other’s states, and then update their local states. A rich line of research has established tight upper and lower bounds on the complexity of fundamental tasks, such as majority and leader election, in this model, when G is a clique. Specifically, in the clique, these tasks can be solved fast, i.e., in n polylog n pairwise interactions, with high probability, using at most polylog n states per node. In this work, we consider the more general setting where G is an arbitrary graph, and present a technique for simulating protocols designed for fully-connected networks in any connected regular graph. Our main result is a simulation that is efficient on many interesting graph families: roughly, the simulation overhead is polylogarithmic in the number of nodes, and quadratic in the conductance of the graph. As an example, this implies that, in any regular graph with conductance φ, both leader election and exact majority can be solved in φ^{-2} ⋅ n polylog n pairwise interactions, with high probability, using at most φ^{-2} ⋅ polylog n states per node. This shows that there are fast and space-efficient population protocols for leader election and exact majority on graphs with good expansion properties.},
author = {Alistarh, Dan-Adrian and Gelashvili, Rati and Rybicki, Joel},
booktitle = {35th International Symposium on Distributed Computing},
isbn = {9-783-9597-7210-5},
issn = {1868-8969},
location = {Freiburg, Germany},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Brief announcement: Fast graphical population protocols}},
doi = {10.4230/LIPIcs.DISC.2021.43},
volume = {209},
year = {2021},
}
@inproceedings{10219,
abstract = {We show that any algorithm that solves the sinkless orientation problem in the supported LOCAL model requires Ω(log n) rounds, and this is tight. The supported LOCAL is at least as strong as the usual LOCAL model, and as a corollary this also gives a new, short and elementary proof that shows that the round complexity of the sinkless orientation problem in the deterministic LOCAL model is Ω(log n).},
author = {Korhonen, Janne and Paz, Ami and Rybicki, Joel and Schmid, Stefan and Suomela, Jukka},
booktitle = {35th International Symposium on Distributed Computing},
isbn = {9-783-9597-7210-5},
issn = {1868-8969},
location = {Freiburg, Germany},
publisher = {Schloss Dagstuhl - Leibniz Zentrum für Informatik},
title = {{Brief announcement: Sinkless orientation is hard also in the supported LOCAL model}},
doi = {10.4230/LIPIcs.DISC.2021.58},
volume = {209},
year = {2021},
}
@inproceedings{10216,
abstract = {This paper reports a new concurrent graph data structure that supports updates of both edges and vertices and queries: Breadth-first search, Single-source shortest-path, and Betweenness centrality. The operations are provably linearizable and non-blocking.},
author = {Chatterjee, Bapi and Peri, Sathya and Sa, Muktikanta},
booktitle = {35th International Symposium on Distributed Computing},
isbn = {9-783-9597-7210-5},
issn = {1868-8969},
location = {Freiburg, Germany},
publisher = {Schloss Dagstuhl - Leibniz Zentrum für Informatik},
title = {{Brief announcement: Non-blocking dynamic unbounded graphs with worst-case amortized bounds}},
doi = {10.4230/LIPIcs.DISC.2021.52},
volume = {209},
year = {2021},
}