@inproceedings{17634, abstract = {System behaviors are traditionally evaluated through binary classifications of correctness, which do not suffice for properties involving quantitative aspects of systems and executions. Quantitative automata offer a more nuanced approach, mapping each execution to a real number by incorporating weighted transitions and value functions generalizing acceptance conditions. In this paper, we introduce QuAK, the first tool designed to automate the analysis of quantitative automata. QuAK currently supports a variety of quantitative automaton types, including Inf, Sup, LimInf, LimSup, LimInfAvg, and LimSupAvg automata, and implements decision procedures for problems such as emptiness, universality, inclusion, equivalence, as well as for checking whether an automaton is safe, live, or constant. Additionally, QuAK is able to compute extremal values when possible, construct safety-liveness decompositions, and monitor system behaviors. We demonstrate the effectiveness of QuAK through experiments focusing on the inclusion, constant-function check, and monitoring problems.}, author = {Chalupa, Marek and Henzinger, Thomas A and Mazzocchi, Nicolas Adrien and Sarac, Naci E}, booktitle = {12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation}, isbn = {9783031753862}, issn = {1611-3349}, location = {Crete, Greece}, pages = {3--20}, publisher = {Springer Nature}, title = {{QuAK: Quantitative Automata Kit}}, doi = {10.1007/978-3-031-75387-9_1}, volume = {15222}, year = {2024}, } @inproceedings{18121, abstract = {It is known that sparsity can improve interpretability for deep neural networks. However, existing methods in the area either require networks that are pre-trained with sparsity constraints, or impose sparsity after the fact, altering the network’s general behavior. In this paper, we demonstrate, for the first time, that sparsity can instead be incorporated into the interpretation process itself, as a sample-specific preprocessing step. Unlike previous work, this approach, which we call SPADE, does not place constraints on the trained model and does not affect its behavior during inference on the sample. Given a trained model and a target sample, SPADE uses sample-targeted pruning to provide a "trace" of the network’s execution on the sample, reducing the network to the most important connections prior to computing an interpretation. We demonstrate that preprocessing with SPADE significantly increases the accuracy of image saliency maps across several interpretability methods. Additionally, SPADE improves the usefulness of neuron visualizations, aiding humans in reasoning about network behavior. Our code is available at https://github.com/IST-DASLab/SPADE.}, author = {Moakhar, Arshia Soltani and Iofinova, Eugenia B and Frantar, Elias and Alistarh, Dan-Adrian}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, issn = {2640-3498}, location = {Vienna, Austria}, pages = {45955--45987}, publisher = {ML Research Press}, title = {{SPADE: Sparsity-guided debugging for deep neural networks}}, volume = {235}, year = {2024}, } @article{15297, abstract = {Populations evolve by accumulating advantageous mutations. Every population has some spatial structure that can be modeled by an underlying network. The network then influences the probability that new advantageous mutations fixate. Amplifiers of selection are networks that increase the fixation probability of advantageous mutants, as compared to the unstructured fully-connected network. Whether or not a network is an amplifier depends on the choice of the random process that governs the evolutionary dynamics. Two popular choices are Moran process with Birth-death updating and Moran process with death-Birth updating. Interestingly, while some networks are amplifiers under Birth-death updating and other networks are amplifiers under death-Birth updating, so far no spatial structures have been found that function as an amplifier under both types of updating simultaneously. In this work, we identify networks that act as amplifiers of selection under both versions of the Moran process. The amplifiers are robust, modular, and increase fixation probability for any mutant fitness advantage in a range r ∈ (1, 1.2). To complement this positive result, we also prove that for certain quantities closely related to fixation probability, it is impossible to improve them simultaneously for both versions of the Moran process. Together, our results highlight how the two versions of the Moran process differ and what they have in common.}, author = {Svoboda, Jakub and Joshi, Soham Shrikant and Tkadlec, Josef and Chatterjee, Krishnendu}, issn = {1553-7358}, journal = {PLoS Computational Biology}, number = {3}, publisher = {Public Library of Science}, title = {{Amplifiers of selection for the Moran process with both Birth-death and death-Birth updating}}, doi = {10.1371/journal.pcbi.1012008}, volume = {20}, year = {2024}, } @article{18703, abstract = {Spatial games provide a simple and elegant mathematical model to study the evolution of cooperation in networks. In spatial games, individuals reside in vertices, adopt simple strategies, and interact with neighbors to receive a payoff. Depending on their own and neighbors’ payoffs, individuals can change their strategy. The payoff is determined by the Prisoners’ Dilemma, a classical matrix game, where players cooperate or defect. While cooperation is the desired behavior, defection provides a higher payoff for a selfish individual. There are many theoretical and empirical studies related to the role of the network in the evolution of cooperation. However, the fundamental question of whether there exist networks that for low initial cooperation rate ensure a high chance of fixation, i.e., cooperation spreads across the whole population, has remained elusive for spatial games with strong selection. In this work, we answer this fundamental question in the affirmative by presenting network structures that ensure high fixation probability for cooperators in the strong selection regime. Besides, our structures have many desirable properties: (a) they ensure the spread of cooperation even for a low initial density of cooperation and high temptation of defection, (b) they have constant degrees, and (c) the number of steps, until cooperation spreads, is at most quadratic in the size of the network.}, author = {Svoboda, Jakub and Chatterjee, Krishnendu}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {50}, publisher = {National Academy of Sciences}, title = {{Density amplifiers of cooperation for spatial games}}, doi = {10.1073/pnas.2405605121}, volume = {121}, year = {2024}, } @unpublished{18689, abstract = {Multiplexed fluorescence microscopy imaging is widely used in biomedical applications. However, simultaneous imaging of multiple fluorophores can result in spectral leaks and overlapping, which greatly degrades image quality and subsequent analysis. Existing popular spectral unmixing methods are mainly based on computational intensive linear models and the performance is heavily dependent on the reference spectra, which may greatly preclude its further applications. In this paper, we propose a deep learning-based blindly spectral unmixing method, termed AutoUnmix, to imitate the physical spectral mixing process. A tranfer learning framework is further devised to allow our AutoUnmix adapting to a variety of imaging systems without retraining the network. Our proposed method has demonstrated real-time unmixing capabilities, surpassing existing methods by up to 100-fold in terms of unmixing speed. We further validate the reconstruction performance on both synthetic datasets and biological samples. The unmixing results of AutoUnmix achieve a highest SSIM of 0.99 in both three- and four-color imaging, with nearly up to 20% higher than other popular unmixing methods. Due to the desirable property of data independency and superior blind unmixing performance, we believe AutoUnmix is a powerful tool to study the interaction process of different organelles labeled by multiple fluorophores.}, author = {Gallei, Michelle C and Truckenbrodt, Sven M and Kreuzinger, Caroline and Inumella, Syamala and Vistunou, Vitali and Sommer, Christoph M and Tavakoli, Mojtaba and Agudelo Duenas, Nathalie and Vorlaufer, Jakob and Jahr, Wiebke and Randuch, Marek and Johnson, Alexander J and Benková, Eva and Friml, Jiří and Danzl, Johann G}, booktitle = {bioRxiv}, title = {{Super-resolution expansion microscopy in plant roots}}, doi = {10.1101/2024.02.21.581330}, year = {2024}, } @unpublished{18688, abstract = {The human brain has remarkable computational power. It generates sophisticated behavioral sequences, stores engrams over an individual’s lifetime, and produces higher cognitive functions up to the level of consciousness. However, so little of our neuroscience knowledge covers the human brain, and it remains unknown whether this organ is truly unique, or is a scaled version of the extensively studied rodent brain. To address this fundamental question, we determined the cellular, synaptic, and connectivity rules of the hippocampal CA3 recurrent circuit using multicellular patch clamp-recording. This circuit is the largest autoassociative network in the brain, and plays a key role in memory and higher-order computations such as pattern separation and pattern completion. We demonstrate that human hippocampal CA3 employs sparse connectivity, in stark contrast to neocortical recurrent networks. Connectivity sparsifies from rodents to humans, providing a circuit architecture that maximizes associational power. Unitary synaptic events at human CA3–CA3 synapses showed both distinct species-specific and circuit-dependent properties, with high reliability, unique amplitude precision, and long integration times. We also identify differential scaling rules between hippocampal pathways from rodents to humans, with a moderate increase in the convergence of CA3 inputs per cell, but a marked increase in human mossy fiber innervation. Anatomically guided full-scale modeling suggests that the human brain’s sparse connectivity, expanded neuronal number, and reliable synaptic signaling combine to enhance the associative memory storage capacity of CA3. Together, our results reveal unique rules of connectivity and synaptic signaling in the human hippocampus, demonstrating the absolute necessity of human brain research and beginning to unravel the remarkable performance of our autoassociative memory circuits.}, author = {Watson, Jake F. and Vargas-Barroso, Victor and Morse-Mora, Rebecca J. and Navas-Olive, Andrea and Tavakoli, Mojtaba and Danzl, Johann G and Tomschik, Matthias and Rössler, Karl and Jonas, Peter M}, booktitle = {bioRxiv}, title = {{Human hippocampal CA3 uses specific functional connectivity rules for efficient associative memory}}, doi = {10.1101/2024.05.02.592169}, year = {2024}, } @phdthesis{18681, author = {Tavakoli, Mojtaba}, isbn = {978-3-99078-048-0}, issn = {2663-337X}, pages = {230}, publisher = {Institute of Science and Technology Austria}, title = {{Developing molecular and structural tools for studying brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics reconstruction with light microscopy}}, doi = {10.15479/at:ista:18681}, year = {2024}, } @unpublished{18677, abstract = {The information-processing capability of the brain’s cellular network depends on the physical wiring pattern between neurons and their molecular and functional characteristics. Mapping neurons and resolving their individual synaptic connections can be achieved by volumetric imaging at nanoscale resolution with dense cellular labeling. Light microscopy is uniquely positioned to visualize specific molecules but dense, synapse-level circuit reconstruction by light microscopy has been out of reach due to limitations in resolution, contrast, and volumetric imaging capability. Here we developed light-microscopy based connectomics (LICONN). We integrated specifically engineered hydrogel embedding and expansion with comprehensive deep-learning based segmentation and analysis of connectivity, thus directly incorporating molecular information in synapse-level brain tissue reconstructions. LICONN will allow synapse-level brain tissue phenotyping in biological experiments in a readily adoptable manner.}, author = {Tavakoli, Mojtaba and Lyudchik, Julia and Januszewski, Michał and Vistunou, Vitali and Agudelo Duenas, Nathalie and Vorlaufer, Jakob and Sommer, Christoph M and Kreuzinger, Caroline and Oliveira, Bárbara and Cenameri, Alban and Novarino, Gaia and Jain, Viren and Danzl, Johann G}, booktitle = {bioRxiv}, title = {{Light-microscopy based dense connectomic reconstruction of mammalian brain tissue}}, doi = {10.1101/2024.03.01.582884}, year = {2024}, } @article{14793, abstract = {Superconductor/semiconductor hybrid devices have attracted increasing interest in the past years. Superconducting electronics aims to complement semiconductor technology, while hybrid architectures are at the forefront of new ideas such as topological superconductivity and protected qubits. In this work, we engineer the induced superconductivity in two-dimensional germanium hole gas by varying the distance between the quantum well and the aluminum. We demonstrate a hard superconducting gap and realize an electrically and flux tunable superconducting diode using a superconducting quantum interference device (SQUID). This allows to tune the current phase relation (CPR), to a regime where single Cooper pair tunneling is suppressed, creating a sin(2y) CPR. Shapiro experiments complement this interpretation and the microwave drive allows to create a diode with ≈ 100% efficiency. The reported results open up the path towards integration of spin qubit devices, microwave resonators and (protected) superconducting qubits on the same silicon technology compatible platform.}, author = {Valentini, Marco and Sagi, Oliver and Baghumyan, Levon and de Gijsel, Thijs and Jung, Jason and Calcaterra, Stefano and Ballabio, Andrea and Aguilera Servin, Juan L and Aggarwal, Kushagra and Janik, Marian and Adletzberger, Thomas and Seoane Souto, Rubén and Leijnse, Martin and Danon, Jeroen and Schrade, Constantin and Bakkers, Erik and Chrastina, Daniel and Isella, Giovanni and Katsaros, Georgios}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Parity-conserving Cooper-pair transport and ideal superconducting diode in planar germanium}}, doi = {10.1038/s41467-023-44114-0}, volume = {15}, year = {2024}, } @article{12312, abstract = {Let $\ell$ be a prime number. We classify the subgroups $G$ of $\operatorname{Sp}_4(\mathbb{F}_\ell)$ and $\operatorname{GSp}_4(\mathbb{F}_\ell)$ that act irreducibly on $\mathbb{F}_\ell^4$, but such that every element of $G$ fixes an $\mathbb{F}_\ell$-vector subspace of dimension 1. We use this classification to prove that the local-global principle for isogenies of degree $\ell$ between abelian surfaces over number fields holds in many cases -- in particular, whenever the abelian surface has non-trivial endomorphisms and $\ell$ is large enough with respect to the field of definition. Finally, we prove that there exist arbitrarily large primes $\ell$ for which some abelian surface $A/\mathbb{Q}$ fails the local-global principle for isogenies of degree $\ell$.}, author = {Lombardo, Davide and Verzobio, Matteo}, issn = {1420-9020}, journal = {Selecta Mathematica}, number = {2}, publisher = {Springer Nature}, title = {{On the local-global principle for isogenies of abelian surfaces}}, doi = {10.1007/s00029-023-00908-0}, volume = {30}, year = {2024}, } @unpublished{19425, abstract = {We demonstrate that periodically driven quantum rotors provide a promising and broadly applicable platform to implement multi-gap topological phases, where groups of bands can acquire topological invariants due to non-Abelian braiding of band degeneracies. By adiabatically varying the periodic kicks to the rotor we find nodal-line braiding, which causes sign flips of topological charges of band nodes and can prevent them from annihilating, indicated by non-zero values of the %non-Abelian patch Euler class. In particular, we report on the emergence of an anomalous Dirac string phase arising in the strongly driven regime, a truly out-of-equilibrium phase of the quantum rotor. This phase emanates from braiding processes involving all (quasienergy) gaps and manifests itself with edge states at zero angular momentum. Our results reveal direct applications in state-of-the-art experiments of quantum rotors, such as linear molecules driven by periodic far-off-resonant laser pulses or artificial quantum rotors in optical lattices, whose extensive versatility offers precise modification and observation of novel non-Abelian topological properties. }, author = {Karle, Volker and Lemeshko, Mikhail and Bouhon, Adrien and Slager, Robert-Jan and Ünal, F. Nur}, booktitle = {arXiv}, title = {{Anomalous multi-gap topological phases in periodically driven quantum rotors}}, doi = {10.48550/arXiv.2408.16848}, year = {2024}, } @article{17127, abstract = {Let P(x)∈Z[x] be a polynomial with at least two distinct complex roots. We prove that the number of solutions (x1,…,xk,y1,…,yk)∈[N]2k to the equation ∏1≤i≤kP(xi)=∏1≤j≤kP(yj)≠0 (for any k≥1 ) is asymptotically k!Nk as N→+∞. This solves a question first proposed and studied by Najnudel. The result can also be interpreted as saying that all even moments of random partial sums 1N√∑n≤Nf(P(n)) match standard complex Gaussian moments as N→+∞ , where f is the Steinhaus random multiplicative function.}, author = {Wang, Victor and Xu, Max Wenqiang}, issn = {1469-2120}, journal = {Bulletin of the London Mathematical Society}, number = {8}, pages = {2718--2726}, publisher = {London Mathematical Society}, title = {{Paucity phenomena for polynomial products}}, doi = {10.1112/blms.13095}, volume = {56}, year = {2024}, } @article{15338, abstract = {We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version of the Hardy–Littlewood circle method over number fields.}, author = {Browning, Timothy D and Pierce, Lillian B. and Schindler, Damaris}, issn = {1475-3030}, journal = {Journal of the Institute of Mathematics of Jussieu}, number = {6}, pages = {2859--2912}, publisher = {Cambridge University Press}, title = {{Generalised quadratic forms over totally real number fields}}, doi = {10.1017/S1474748024000161}, volume = {23}, year = {2024}, } @article{15337, abstract = {We prove the Manin–Peyre conjecture for the number of rational points of bounded height outside of a thin subset on a family of Fano threefolds of bidegree (1, 2).}, author = {Bonolis, Dante and Browning, Timothy D and Huang, Zhizhong}, issn = {1432-1807}, journal = {Mathematische Annalen}, pages = {4123--4207}, publisher = {Springer Nature}, title = {{Density of rational points on some quadric bundle threefolds}}, doi = {10.1007/s00208-024-02854-4}, volume = {390}, year = {2024}, } @article{18930, abstract = {We study sumsets 𝒜 + ℬ in the set of squares 𝒮 (and, more generally, in the set of kth powers 𝒮k, where k ≥2 is an integer). It is known by a result of Gyarmati that 𝒜 + ℬ ⊂ 𝒮k ∩[1,N] implies that min(|𝒜|,|ℬ|) =Ok(logN). Here, we study how the upper bound on |ℬ| decreases, when the size of |𝒜| increases (or vice versa). In particular, if |𝒜| ≥ Ck1m m(logN)1m , then |ℬ| = Ok(m2logN), for sufficiently large N, a positive integer m and an explicit constant C > 0. For example, with m ∼ loglogN this gives: If |𝒜| ≥ CkloglogN,then |ℬ| = Ok(logN(loglogN)2).}, author = {Elsholtz, Christian and Wurzinger, Lena}, issn = {1464-3847}, journal = {The Quarterly Journal of Mathematics}, number = {4}, pages = {1243--1254}, publisher = {Oxford University Press}, title = {{Sumsets in the set of squares}}, doi = {10.1093/qmath/haae044}, volume = {75}, year = {2024}, } @article{15312, abstract = {The question of whether or not a given integral polynomial takes infinitely many square-free values has only been addressed unconditionally for polynomials of degree at most 3. We address this question, on average, for polynomials of arbitrary degree.}, author = {Browning, Timothy D and Shparlinski, Igor E.}, issn = {0022-314X}, journal = {Journal of Number Theory}, pages = {220--240}, publisher = {Elsevier}, title = {{Square-free values of random polynomials}}, doi = {10.1016/j.jnt.2024.02.013}, volume = {261}, year = {2024}, } @article{19051, abstract = {This paper corrects an error in an earlier work of the author.}, author = {Browning, Timothy D}, issn = {1687-0247}, journal = {International Mathematics Research Notices}, number = {13}, pages = {10165--10168}, publisher = {Oxford University Press}, title = {{The polynomial sieve and equal sums of like polynomials}}, doi = {10.1093/imrn/rnae066}, volume = {2024}, year = {2024}, } @article{10018, abstract = {In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type A1 + A3 and prove an analogue of Manin's conjecture for integral points with respect to its singularities and its lines.}, author = {Derenthal, Ulrich and Wilsch, Florian Alexander}, issn = {1475-3030 }, journal = {Journal of the Institute of Mathematics of Jussieu}, keywords = {Integral points, del Pezzo surface, universal torsor, Manin’s conjecture}, number = {3}, pages = {1259--1294}, publisher = {Cambridge University Press}, title = {{Integral points on singular del Pezzo surfaces}}, doi = {10.1017/S1474748022000482}, volume = {23}, year = {2024}, } @article{17447, abstract = {Let F be a diagonal cubic form over Z in six variables. From the dual variety in the delta method of Duke–Friedlander–Iwaniec and Heath‐Brown, we unconditionally extract a weighted count of certain special integral zeros of F in regions of diameter X - 8 . Heath‐Brown did the same in four variables, but our analysis differs and captures some novel features. We also put forth an axiomatic framework for more general F.}, author = {Wang, Victor}, issn = {1469-7750}, journal = {Journal of the London Mathematical Society}, number = {3}, publisher = {Wiley}, title = {{Special cubic zeros and the dual variety}}, doi = {10.1112/jlms.12975}, volume = {110}, year = {2024}, } @article{17323, abstract = {We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence that only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods. At the end of the paper, there is an appendix by Sandro Bettin on divisor closed sets that we use to study the density of prime terms that appear in strong divisibility sequences.}, author = {Browning, Timothy D and Verzobio, Matteo}, issn = {2041-7942}, journal = {Mathematika}, number = {4}, publisher = {London Mathematical Society}, title = {{Strong divisibility sequences and sieve methods}}, doi = {10.1112/mtk.12269}, volume = {70}, year = {2024}, }