@article{12009, abstract = {Changes in the short-term dynamics of excitatory synapses over development have been observed throughout cortex, but their purpose and consequences remain unclear. Here, we propose that developmental changes in synaptic dynamics buffer the effect of slow inhibitory long-term plasticity, allowing for continuously stable neural activity. Using computational modeling we demonstrate that early in development excitatory short-term depression quickly stabilises neural activity, even in the face of strong, unbalanced excitation. We introduce a model of the commonly observed developmental shift from depression to facilitation and show that neural activity remains stable throughout development, while inhibitory synaptic plasticity slowly balances excitation, consistent with experimental observations. Our model predicts changes in the input responses from phasic to phasic-and-tonic and more precise spike timings. We also observe a gradual emergence of short-lasting memory traces governed by short-term plasticity development. We conclude that the developmental depression-to-facilitation shift may control excitation-inhibition balance throughout development with important functional consequences.}, author = {Jia, David W. and Vogels, Tim P and Costa, Rui Ponte}, issn = {2399-3642}, journal = {Communications biology}, publisher = {Springer Nature}, title = {{Developmental depression-to-facilitation shift controls excitation-inhibition balance}}, doi = {10.1038/s42003-022-03801-2}, volume = {5}, year = {2022}, } @inproceedings{12010, abstract = {World models learn behaviors in a latent imagination space to enhance the sample-efficiency of deep reinforcement learning (RL) algorithms. While learning world models for high-dimensional observations (e.g., pixel inputs) has become practicable on standard RL benchmarks and some games, their effectiveness in real-world robotics applications has not been explored. In this paper, we investigate how such agents generalize to real-world autonomous vehicle control tasks, where advanced model-free deep RL algorithms fail. In particular, we set up a series of time-lap tasks for an F1TENTH racing robot, equipped with a high-dimensional LiDAR sensor, on a set of test tracks with a gradual increase in their complexity. In this continuous-control setting, we show that model-based agents capable of learning in imagination substantially outperform model-free agents with respect to performance, sample efficiency, successful task completion, and generalization. Moreover, we show that the generalization ability of model-based agents strongly depends on the choice of their observation model. We provide extensive empirical evidence for the effectiveness of world models provided with long enough memory horizons in sim2real tasks.}, author = {Brunnbauer, Axel and Berducci, Luigi and Brandstatter, Andreas and Lechner, Mathias and Hasani, Ramin and Rus, Daniela and Grosu, Radu}, booktitle = {2022 International Conference on Robotics and Automation}, isbn = {9781728196817}, issn = {1050-4729}, location = {Philadelphia, PA, United States}, pages = {7513--7520}, publisher = {IEEE}, title = {{Latent imagination facilitates zero-shot transfer in autonomous racing}}, doi = {10.1109/ICRA46639.2022.9811650}, year = {2022}, } @inproceedings{12011, abstract = {We characterize the capacity for the discrete-time arbitrarily varying channel with discrete inputs, outputs, and states when (a) the encoder and decoder do not share common randomness, (b) the input and state are subject to cost constraints, (c) the transition matrix of the channel is deterministic given the state, and (d) at each time step the adversary can only observe the current and past channel inputs when choosing the state at that time. The achievable strategy involves stochastic encoding together with list decoding and a disambiguation step. The converse uses a two-phase "babble-and-push" strategy where the adversary chooses the state randomly in the first phase, list decodes the output, and then chooses state inputs to symmetrize the channel in the second phase. These results generalize prior work on specific channels models (additive, erasure) to general discrete alphabets and models.}, author = {Zhang, Yihan and Jaggi, Sidharth and Langberg, Michael and Sarwate, Anand D.}, booktitle = {2022 IEEE International Symposium on Information Theory}, isbn = {9781665421591}, issn = {2157-8095}, location = {Espoo, Finland}, pages = {2523--2528}, publisher = {IEEE}, title = {{The capacity of causal adversarial channels}}, doi = {10.1109/ISIT50566.2022.9834709}, volume = {2022}, year = {2022}, } @inproceedings{12012, abstract = {This paper is eligible for the Jack Keil Wolf ISIT Student Paper Award. We generalize a previous framework for designing utility-optimal differentially private (DP) mechanisms via graphs, where datasets are vertices in the graph and edges represent dataset neighborhood. The boundary set contains datasets where an individual’s response changes the binary-valued query compared to its neighbors. Previous work was limited to the homogeneous case where the privacy parameter ε across all datasets was the same and the mechanism at boundary datasets was identical. In our work, the mechanism can take different distributions at the boundary and the privacy parameter ε is a function of neighboring datasets, which recovers an earlier definition of personalized DP as special case. The problem is how to extend the mechanism, which is only defined at the boundary set, to other datasets in the graph in a computationally efficient and utility optimal manner. Using the concept of strongest induced DP condition we solve this problem efficiently in polynomial time (in the size of the graph).}, author = {Torkamani, Sahel and Ebrahimi, Javad B. and Sadeghi, Parastoo and D'Oliveira, Rafael G.L. and Médard, Muriel}, booktitle = {2022 IEEE International Symposium on Information Theory}, isbn = {9781665421591}, issn = {2157-8095}, location = {Espoo, Finland}, pages = {1623--1628}, publisher = {IEEE}, title = {{Heterogeneous differential privacy via graphs}}, doi = {10.1109/ISIT50566.2022.9834711}, volume = {2022}, year = {2022}, } @inproceedings{12013, abstract = {We consider the problem of communication over adversarial channels with feedback. Two parties comprising sender Alice and receiver Bob seek to communicate reliably. An adversary James observes Alice's channel transmission entirely and chooses, maliciously, its additive channel input or jamming state thereby corrupting Bob's observation. Bob can communicate over a one-way reverse link with Alice; we assume that transmissions over this feedback link cannot be corrupted by James. Our goal in this work is to study the optimum throughput or capacity over such channels with feedback. We first present results for the quadratically-constrained additive channel where communication is known to be impossible when the noise-to-signal (power) ratio (NSR) is at least 1. We present a novel achievability scheme to establish that positive rate communication is possible even when the NSR is as high as 8/9. We also present new converse upper bounds on the capacity of this channel under potentially stochastic encoders and decoders. We also study feedback communication over the more widely studied q-ary alphabet channel under additive noise. For the q -ary channel, where q > 2, it is well known that capacity is positive under full feedback if and only if the adversary can corrupt strictly less than half the transmitted symbols. We generalize this result and show that the same threshold holds for positive rate communication when the noiseless feedback may only be partial; our scheme employs a stochastic decoder. We extend this characterization, albeit partially, to fully deterministic schemes under partial noiseless feedback. We also present new converse upper bounds for q-ary channels under full feedback, where the encoder and/or decoder may privately randomize. Our converse results bring to the fore an interesting alternate expression for the well known converse bound for the q—ary channel under full feedback which, when specialized to the binary channel, also equals its known capacity.}, author = {Joshi, Pranav and Purkayastha, Amritakshya and Zhang, Yihan and Budkuley, Amitalok J. and Jaggi, Sidharth}, booktitle = {2022 IEEE International Symposium on Information Theory}, isbn = {9781665421591}, issn = {2157-8095}, location = {Espoo, Finland}, pages = {504--509}, publisher = {IEEE}, title = {{On the capacity of additive AVCs with feedback}}, doi = {10.1109/ISIT50566.2022.9834850}, volume = {2022}, year = {2022}, } @inproceedings{12014, abstract = {We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let N > 0 and L∈Z≥2. A multiple packing is a set C of points in Rn such that any point in Rn lies in the intersection of at most L – 1 balls of radius nN−−−√ around points in C. Given a well-known connection with coding theory, multiple packings can be viewed as the Euclidean analog of list-decodable codes, which are well-studied for finite fields. In this paper, we exactly pin down the asymptotic density of (expurgated) Poisson Point Processes under a stronger notion called average-radius multiple packing. To this end, we apply tools from high-dimensional geometry and large deviation theory. This gives rise to the best known lower bound on the largest multiple packing density. Our result corrects a mistake in a previous paper by Blinovsky [Bli05].}, author = {Zhang, Yihan and Vatedka, Shashank}, booktitle = {2022 IEEE International Symposium on Information Theory}, isbn = {9781665421591}, issn = {2157-8095}, location = {Espoo, Finland}, pages = {2559--2564}, publisher = {IEEE}, title = {{List-decodability of Poisson Point Processes}}, doi = {10.1109/ISIT50566.2022.9834512}, volume = {2022}, year = {2022}, } @inproceedings{12015, abstract = {We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let P, N > 0 and L∈Z≥2. A multiple packing is a set C of points in Bn(0–,nP−−−√) such that any point in ℝ n lies in the intersection of at most L – 1 balls of radius nN−−−√ around points in C. 1 In this paper, we derive two lower bounds on the largest possible density of a multiple packing. These bounds are obtained through a stronger notion called average-radius multiple packing. Specifically, we exactly pin down the asymptotics of (expurgated) Gaussian codes and (expurgated) spherical codes under average-radius multiple packing. To this end, we apply tools from high-dimensional geometry and large deviation theory. The bound for spherical codes matches the previous best known bound which was obtained for the standard (weaker) notion of multiple packing through a curious connection with error exponents [Bli99], [ZV21]. The bound for Gaussian codes suggests that they are strictly inferior to spherical codes.}, author = {Zhang, Yihan and Vatedka, Shashank}, booktitle = {2022 IEEE International Symposium on Information Theory}, isbn = {9781665421591}, issn = {2157-8095}, location = {Espoo, Finland}, pages = {3085--3090}, publisher = {IEEE}, title = {{Lower bounds for multiple packing}}, doi = {10.1109/ISIT50566.2022.9834443}, volume = {2022}, year = {2022}, } @inproceedings{12016, abstract = {We consider the problem of coded distributed computing using polar codes. The average execution time of a coded computing system is related to the error probability for transmission over the binary erasure channel in recent work by Soleymani, Jamali and Mahdavifar, where the performance of binary linear codes is investigated. In this paper, we focus on polar codes and unveil a connection between the average execution time and the scaling exponent μ of the family of codes. In the finite-length characterization of polar codes, the scaling exponent is a key object capturing the speed of convergence to capacity. In particular, we show that (i) the gap between the normalized average execution time of polar codes and that of optimal MDS codes is O(n –1/μ ), and (ii) this upper bound can be improved to roughly O(n –1/2 ) by considering polar codes with large kernels. We conjecture that these bounds could be improved to O(n –2/μ ) and O(n –1 ), respectively, and provide a heuristic argument as well as numerical evidence supporting this view.}, author = {Fathollahi, Dorsa and Mondelli, Marco}, booktitle = {2022 IEEE International Symposium on Information Theory}, isbn = {9781665421591}, issn = {2157-8095}, location = {Espoo, Finland}, pages = {2154--2159}, publisher = {IEEE}, title = {{Polar coded computing: The role of the scaling exponent}}, doi = {10.1109/ISIT50566.2022.9834712}, volume = {2022}, year = {2022}, } @inproceedings{12017, abstract = {In the classic adversarial communication problem, two parties communicate over a noisy channel in the presence of a malicious jamming adversary. The arbitrarily varying channels (AVCs) offer an elegant framework to study a wide range of interesting adversary models. The optimal throughput or capacity over such AVCs is intimately tied to the underlying adversary model; in some cases, capacity is unknown and the problem is known to be notoriously hard. The omniscient adversary, one which knows the sender’s entire channel transmission a priori, is one of such classic models of interest; the capacity under such an adversary remains an exciting open problem. The myopic adversary is a generalization of that model where the adversary’s observation may be corrupted over a noisy discrete memoryless channel. Through the adversary’s myopicity, one can unify the slew of different adversary models, ranging from the omniscient adversary to one that is completely blind to the transmission (the latter is the well known oblivious model where the capacity is fully characterized).In this work, we present new results on the capacity under both the omniscient and myopic adversary models. We completely characterize the positive capacity threshold over general AVCs with omniscient adversaries. The characterization is in terms of two key combinatorial objects: the set of completely positive distributions and the CP-confusability set. For omniscient AVCs with positive capacity, we present non-trivial lower and upper bounds on the capacity; unlike some of the previous bounds, our bounds hold under fairly general input and jamming constraints. Our lower bound improves upon the generalized Gilbert-Varshamov bound for general AVCs while the upper bound generalizes the well known Elias-Bassalygo bound (known for binary and q-ary alphabets). For the myopic AVCs, we build on prior results known for the so-called sufficiently myopic model, and present new results on the positive rate communication threshold over the so-called insufficiently myopic regime (a completely insufficient myopic adversary specializes to an omniscient adversary). We present interesting examples for the widely studied models of adversarial bit-flip and bit-erasure channels. In fact, for the bit-flip AVC with additive adversarial noise as well as random noise, we completely characterize the omniscient model capacity when the random noise is sufficiently large vis-a-vis the adversary’s budget.}, author = {Yadav, Anuj Kumar and Alimohammadi, Mohammadreza and Zhang, Yihan and Budkuley, Amitalok J. and Jaggi, Sidharth}, booktitle = {2022 IEEE International Symposium on Information Theory}, isbn = {9781665421591}, issn = {2157-8095}, location = {Espoo, Finland}, pages = {2535--2540}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{New results on AVCs with omniscient and myopic adversaries}}, doi = {10.1109/ISIT50566.2022.9834632}, volume = {2022}, year = {2022}, } @inproceedings{12018, abstract = {We study the problem of characterizing the maximal rates of list decoding in Euclidean spaces for finite list sizes. For any positive integer L ≥ 2 and real N > 0, we say that a subset C⊂Rn is an (N,L – 1)-multiple packing or an (N,L– 1)-list decodable code if every Euclidean ball of radius nN−−−√ in ℝ n contains no more than L − 1 points of C. We study this problem with and without ℓ 2 norm constraints on C, and derive the best-known lower bounds on the maximal rate for (N,L−1) multiple packing. Our bounds are obtained via error exponents for list decoding over Additive White Gaussian Noise (AWGN) channels. We establish a curious inequality which relates the error exponent, a quantity of average-case nature, to the list-decoding radius, a quantity of worst-case nature. We derive various bounds on the error exponent for list decoding in both bounded and unbounded settings which could be of independent interest beyond multiple packing.}, author = {Zhang, Yihan and Vatedka, Shashank}, booktitle = {2022 IEEE International Symposium on Information Theory}, isbn = {9781665421591}, issn = {2157-8095}, location = {Espoo, Finland}, pages = {1324--1329}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Lower bounds on list decoding capacity using error exponents}}, doi = {10.1109/ISIT50566.2022.9834815}, volume = {2022}, year = {2022}, } @inproceedings{12019, abstract = {This paper studies combinatorial properties of codes for the Z-channel. A Z-channel with error fraction τ takes as input a length-n binary codeword and injects in an adversarial manner up to nτ asymmetric errors, i.e., errors that only zero out bits but do not flip 0’s to 1’s. It is known that the largest (L − 1)-list-decodable code for the Z-channel with error fraction τ has exponential (in n) size if τ is less than a critical value that we call the Plotkin point and has constant size if τ is larger than the threshold. The (L−1)-list-decoding Plotkin point is known to be L−1L−1−L−LL−1. In this paper, we show that the largest (L−1)-list-decodable code ε-above the Plotkin point has size Θ L (ε −3/2 ) for any L − 1 ≥ 1.}, author = {Polyanskii, Nikita and Zhang, Yihan}, booktitle = {2022 IEEE International Symposium on Information Theory}, isbn = {9781665421591}, issn = {2157-8095}, location = {Espoo, Finland}, pages = {2553--2558}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{List-decodable zero-rate codes for the Z-channel}}, doi = {10.1109/ISIT50566.2022.9834829}, volume = {2022}, year = {2022}, } @article{12051, abstract = {Transcription of the ribosomal RNA precursor by RNA polymerase (Pol) I is a major determinant of cellular growth, and dysregulation is observed in many cancer types. Here, we present the purification of human Pol I from cells carrying a genomic GFP fusion on the largest subunit allowing the structural and functional analysis of the enzyme across species. In contrast to yeast, human Pol I carries a single-subunit stalk, and in vitro transcription indicates a reduced proofreading activity. Determination of the human Pol I cryo-EM reconstruction in a close-to-native state rationalizes the effects of disease-associated mutations and uncovers an additional domain that is built into the sequence of Pol I subunit RPA1. This “dock II” domain resembles a truncated HMG box incapable of DNA binding which may serve as a downstream transcription factor–binding platform in metazoans. Biochemical analysis, in situ modelling, and ChIP data indicate that Topoisomerase 2a can be recruited to Pol I via the domain and cooperates with the HMG box domain–containing factor UBF. These adaptations of the metazoan Pol I transcription system may allow efficient release of positive DNA supercoils accumulating downstream of the transcription bubble.}, author = {Daiß, Julia L and Pilsl, Michael and Straub, Kristina and Bleckmann, Andrea and Höcherl, Mona and Heiss, Florian B and Abascal-Palacios, Guillermo and Ramsay, Ewan P and Tluckova, Katarina and Mars, Jean-Clement and Fürtges, Torben and Bruckmann, Astrid and Rudack, Till and Bernecky, Carrie A and Lamour, Valérie and Panov, Konstantin and Vannini, Alessandro and Moss, Tom and Engel, Christoph}, issn = {2575-1077}, journal = {Life Science Alliance}, keywords = {Health, Toxicology and Mutagenesis, Plant Science, Biochemistry, Genetics and Molecular Biology (miscellaneous), Ecology}, number = {11}, publisher = {Life Science Alliance}, title = {{The human RNA polymerase I structure reveals an HMG-like docking domain specific to metazoans}}, doi = {10.26508/lsa.202201568}, volume = {5}, year = {2022}, } @article{12052, abstract = {Directionality in the intercellular transport of the plant hormone auxin is determined by polar plasma membrane localization of PIN-FORMED (PIN) auxin transport proteins. However, apart from PIN phosphorylation at conserved motifs, no further determinants explicitly controlling polar PIN sorting decisions have been identified. Here we present Arabidopsis WAVY GROWTH 3 (WAV3) and closely related RING-finger E3 ubiquitin ligases, whose loss-of-function mutants show a striking apical-to-basal polarity switch in PIN2 localization in root meristem cells. WAV3 E3 ligases function as essential determinants for PIN polarity, acting independently from PINOID/WAG-dependent PIN phosphorylation. They antagonize ectopic deposition of de novo synthesized PIN proteins already immediately following completion of cell division, presumably via preventing PIN sorting into basal, ARF GEF-mediated trafficking. Our findings reveal an involvement of E3 ligases in the selective targeting of apically localized PINs in higher plants.}, author = {Konstantinova, N and Hörmayer, Lukas and Glanc, Matous and Keshkeih, R and Tan, Shutang and Di Donato, M and Retzer, K and Moulinier-Anzola, J and Schwihla, M and Korbei, B and Geisler, M and Friml, Jiří and Luschnig, C}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{WAVY GROWTH Arabidopsis E3 ubiquitin ligases affect apical PIN sorting decisions}}, doi = {10.1038/s41467-022-32888-8}, volume = {13}, year = {2022}, } @article{12053, abstract = {Strigolactones (SLs) are a class of phytohormones that regulate plant shoot branching and adventitious root development. However, little is known regarding the role of SLs in controlling the behavior of the smallest unit of the organism, the single cell. Here, taking advantage of a classic single-cell model offered by the cotton (Gossypium hirsutum) fiber cell, we show that SLs, whose biosynthesis is fine-tuned by gibberellins (GAs), positively regulate cell elongation and cell wall thickness by promoting the biosynthesis of very-long-chain fatty acids (VLCFAs) and cellulose, respectively. Furthermore, we identified two layers of transcription factors (TFs) involved in the hierarchical regulation of this GA-SL crosstalk. The top-layer TF GROWTH-REGULATING FACTOR 4 (GhGRF4) directly activates expression of the SL biosynthetic gene DWARF27 (D27) to increase SL accumulation in fiber cells and GAs induce GhGRF4 expression. SLs induce the expression of four second-layer TF genes (GhNAC100-2, GhBLH51, GhGT2, and GhB9SHZ1), which transmit SL signals downstream to two ketoacyl-CoA synthase genes (KCS) and three cellulose synthase (CesA) genes by directly activating their transcription. Finally, the KCS and CesA enzymes catalyze the biosynthesis of very long chain fatty acids and cellulose, respectively, to regulate development of high-grade cotton fibers. In addition to providing a theoretical basis for cotton fiber improvement, our results shed light on SL signaling in plant development at the single-cell level.}, author = {Tian, Z and Zhang, Yuzhou and Zhu, L and Jiang, B and Wang, H and Gao, R and Friml, Jiří and Xiao, G}, issn = {1532-298X}, journal = {The Plant Cell}, number = {12}, pages = {4816--4839}, publisher = {Oxford University Press}, title = {{Strigolactones act downstream of gibberellins to regulate fiber cell elongation and cell wall thickness in cotton (Gossypium hirsutum)}}, doi = {10.1093/plcell/koac270}, volume = {34}, year = {2022}, } @article{12054, abstract = {Polar auxin transport is unique to plants and coordinates their growth and development1,2. The PIN-FORMED (PIN) auxin transporters exhibit highly asymmetrical localizations at the plasma membrane and drive polar auxin transport3,4; however, their structures and transport mechanisms remain largely unknown. Here, we report three inward-facing conformation structures of Arabidopsis thaliana PIN1: the apo state, bound to the natural auxin indole-3-acetic acid (IAA), and in complex with the polar auxin transport inhibitor N-1-naphthylphthalamic acid (NPA). The transmembrane domain of PIN1 shares a conserved NhaA fold5. In the substrate-bound structure, IAA is coordinated by both hydrophobic stacking and hydrogen bonding. NPA competes with IAA for the same site at the intracellular pocket, but with a much higher affinity. These findings inform our understanding of the substrate recognition and transport mechanisms of PINs and set up a framework for future research on directional auxin transport, one of the most crucial processes underlying plant development.}, author = {Yang, Z and Xia, J and Hong, J and Zhang, C and Wei, H and Ying, W and Sun, C and Sun, L and Mao, Y and Gao, Y and Tan, S and Friml, Jiří and Li, D and Liu, X and Sun, L}, issn = {1476-4687}, journal = {Nature}, number = {7927}, pages = {611--615}, publisher = {Springer Nature}, title = {{Structural insights into auxin recognition and efflux by Arabidopsis PIN1}}, doi = {10.1038/s41586-022-05143-9}, volume = {609}, year = {2022}, } @article{12065, abstract = {Capacity, rate performance, and cycle life of aprotic Li–O2 batteries critically depend on reversible electrodeposition of Li2O2. Current understanding states surface-adsorbed versus solvated LiO2 controls Li2O2 growth as surface film or as large particles. Herein, we show that Li2O2 forms across a wide range of electrolytes, carbons, and current densities as particles via solution-mediated LiO2 disproportionation, bringing into question the prevalence of any surface growth under practical conditions. We describe a unified O2 reduction mechanism, which can explain all found capacity relations and Li2O2 morphologies with exclusive solution discharge. Determining particle morphology and achievable capacities are species mobilities, true areal rate, and the degree of LiO2 association in solution. Capacity is conclusively limited by mass transport through the tortuous Li2O2 rather than electron transport through a passivating Li2O2 film. Provided that species mobilities and surface growth are high, high capacities are also achieved with weakly solvating electrolytes, which were previously considered prototypical for low capacity via surface growth.}, author = {Prehal, Christian and Mondal, Soumyadip and Lovicar, Ludek and Freunberger, Stefan Alexander}, issn = {2380-8195}, journal = {ACS Energy Letters}, number = {9}, pages = {3112--3119}, publisher = {American Chemical Society}, title = {{Exclusive solution discharge in Li-O₂ batteries?}}, doi = {10.1021/acsenergylett.2c01711}, volume = {7}, year = {2022}, } @phdthesis{12072, abstract = {In this thesis, we study two of the most important questions in Arithmetic geometry: that of the existence and density of solutions to Diophantine equations. In order for a Diophantine equation to have any solutions over the rational numbers, it must have solutions everywhere locally, i.e., over R and over Qp for every prime p. The converse, called the Hasse principle, is known to fail in general. However, it is still a central question in Arithmetic geometry to determine for which varieties the Hasse principle does hold. In this work, we establish the Hasse principle for a wide new family of varieties of the form f(t) = NK/Q(x) ̸= 0, where f is a polynomial with integer coefficients and NK/Q denotes the norm form associated to a number field K. Our results cover products of arbitrarily many linear, quadratic or cubic factors, and generalise an argument of Irving [69], which makes use of the beta sieve of Rosser and Iwaniec. We also demonstrate how our main sieve results can be applied to treat new cases of a conjecture of Harpaz and Wittenberg on locally split values of polynomials over number fields, and discuss consequences for rational points in fibrations. In the second question, about the density of solutions, one defines a height function and seeks to estimate asymptotically the number of points of height bounded by B as B → ∞. Traditionally, one either counts rational points, or integral points with respect to a suitable model. However, in this thesis, we study an emerging area of interest in Arithmetic geometry known as Campana points, which in some sense interpolate between rational and integral points. More precisely, we count the number of nonzero integers z1, z2, z3 such that gcd(z1, z2, z3) = 1, and z1, z2, z3, z1 + z2 + z3 are all squareful and bounded by B. Using the circle method, we obtain an asymptotic formula which agrees in the power of B and log B with a bold new generalisation of Manin’s conjecture to the setting of Campana points, recently formulated by Pieropan, Smeets, Tanimoto and Várilly-Alvarado [96]. However, in this thesis we also provide the first known counterexamples to leading constant predicted by their conjecture. }, author = {Shute, Alec L}, isbn = {978-3-99078-023-7}, issn = {2663-337X}, pages = {208}, publisher = {Institute of Science and Technology Austria}, title = {{Existence and density problems in Diophantine geometry: From norm forms to Campana points}}, doi = {10.15479/at:ista:12072}, year = {2022}, } @article{12079, abstract = {We extend the recent rigorous convergence result of Abels and Moser (SIAM J Math Anal 54(1):114–172, 2022. https://doi.org/10.1137/21M1424925) concerning convergence rates for solutions of the Allen–Cahn equation with a nonlinear Robin boundary condition towards evolution by mean curvature flow with constant contact angle. More precisely, in the present work we manage to remove the perturbative assumption on the contact angle being close to 90∘. We establish under usual double-well type assumptions on the potential and for a certain class of boundary energy densities the sub-optimal convergence rate of order ε12 for general contact angles α∈(0,π). For a very specific form of the boundary energy density, we even obtain from our methods a sharp convergence rate of order ε; again for general contact angles α∈(0,π). Our proof deviates from the popular strategy based on rigorous asymptotic expansions and stability estimates for the linearized Allen–Cahn operator. Instead, we follow the recent approach by Fischer et al. (SIAM J Math Anal 52(6):6222–6233, 2020. https://doi.org/10.1137/20M1322182), thus relying on a relative entropy technique. We develop a careful adaptation of their approach in order to encode the constant contact angle condition. In fact, we perform this task at the level of the notion of gradient flow calibrations. This concept was recently introduced in the context of weak-strong uniqueness for multiphase mean curvature flow by Fischer et al. (arXiv:2003.05478v2).}, author = {Hensel, Sebastian and Moser, Maximilian}, issn = {1432-0835}, journal = {Calculus of Variations and Partial Differential Equations}, number = {6}, publisher = {Springer Nature}, title = {{Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime}}, doi = {10.1007/s00526-022-02307-3}, volume = {61}, year = {2022}, } @article{12080, abstract = {Endocytosis is a multistep process involving the sequential recruitment and action of numerous proteins. This process can be divided into two phases: an early phase, in which sites of endocytosis are formed, and a late phase in which clathrin-coated vesicles are formed and internalized into the cytosol, but how these phases link to each other remains unclear. In this study, we demonstrate that anchoring the yeast Eps15-like protein Pan1p to the peroxisome triggers most of the events occurring during the late phase at the peroxisome. At this ectopic location, Pan1p recruits most proteins that function in the late phases—including actin nucleation promoting factors—and then initiates actin polymerization. Pan1p also recruited Prk1 kinase and actin depolymerizing factors, thereby triggering disassembly immediately after actin assembly and inducing dissociation of endocytic proteins from the peroxisome. These observations suggest that Pan1p is a key regulator for initiating, processing, and completing the late phase of endocytosis.}, author = {Enshoji, Mariko and Miyano, Yoshiko and Yoshida, Nao and Nagano, Makoto and Watanabe, Minami and Kunihiro, Mayumi and Siekhaus, Daria E and Toshima, Junko Y. and Toshima, Jiro}, issn = {1540-8140}, journal = {Journal of Cell Biology}, number = {10}, publisher = {Rockefeller University Press}, title = {{Eps15/Pan1p is a master regulator of the late stages of the endocytic pathway}}, doi = {10.1083/jcb.202112138}, volume = {221}, year = {2022}, } @article{12081, abstract = {Selection accumulates information in the genome—it guides stochastically evolving populations toward states (genotype frequencies) that would be unlikely under neutrality. This can be quantified as the Kullback–Leibler (KL) divergence between the actual distribution of genotype frequencies and the corresponding neutral distribution. First, we show that this population-level information sets an upper bound on the information at the level of genotype and phenotype, limiting how precisely they can be specified by selection. Next, we study how the accumulation and maintenance of information is limited by the cost of selection, measured as the genetic load or the relative fitness variance, both of which we connect to the control-theoretic KL cost of control. The information accumulation rate is upper bounded by the population size times the cost of selection. This bound is very general, and applies across models (Wright–Fisher, Moran, diffusion) and to arbitrary forms of selection, mutation, and recombination. Finally, the cost of maintaining information depends on how it is encoded: Specifying a single allele out of two is expensive, but one bit encoded among many weakly specified loci (as in a polygenic trait) is cheap.}, author = {Hledik, Michal and Barton, Nicholas H and Tkačik, Gašper}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, number = {36}, publisher = {Proceedings of the National Academy of Sciences}, title = {{Accumulation and maintenance of information in evolution}}, doi = {10.1073/pnas.2123152119}, volume = {119}, year = {2022}, }