Discrete analytical objects in the body-centered cubic grid - Čomić, Lidija; Largeteau-Skapin, Gaëlle; Zrour, Rita; Biswas, Ranita; Andres, Eric (Pattern Recognition)
We propose a characterization of discrete analytical spheres, planes and lines in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently proposed alternative compact coordinate system, in which each integer triplet addresses some voxel in the grid. We define spheres and planes through double Diophantine inequalities and investigate their relevant topological features, such as functionality or the interrelation between the thickness of the objects and their connectivity and separation properties. We define lines as the intersection of planes. The number of the planes (up to six) is equal to the number of the pairs of faces of a BCC voxel that are parallel to the line.

Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity - Agresti, Antonio; Veraar, Mark (Journal of Differential Equations)
In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model.

Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain - Orlov, Pavel; Tiutiakina, Anastasiia; Sharipov, Rustem; Petrova, Elena; Gritsev, Vladimir; Kurlov, Denis V. (Physical Review B)
We consider the spin- 1 2 Heisenberg chain (XXX model) weakly perturbed away from integrability by an isotropic next-to-nearest neighbor exchange interaction. Recently, it was conjectured that this model possesses an infinite tower of quasiconserved integrals of motion (charges) [D. Kurlov et al., Phys. Rev. B 105, 104302 (2022)]. In this work we first test this conjecture by investigating how the norm of the adiabatic gauge potential (AGP) scales with the system size, which is known to be a remarkably accurate measure of chaos. We find that for the perturbed XXX chain the behavior of the AGP norm corresponds to neither an integrable nor a chaotic regime, which supports the conjectured quasi-integrability of the model. We then prove the conjecture and explicitly construct the infinite set of quasiconserved charges. Our proof relies on the fact that the XXX chain perturbed by next-to-nearest exchange interaction can be viewed as a truncation of an integrable long-range deformation of the Heisenberg spin chain.

Correct approximation of stationary distributions - Meggendorfer, Tobias (TACAS 2023: Tools and Algorithms for the Construction and Analysis of Systems)
A classical problem for Markov chains is determining their stationary (or steady-state) distribution. This problem has an equally classical solution based on eigenvectors and linear equation systems. However, this approach does not scale to large instances, and iterative solutions are desirable. It turns out that a naive approach, as used by current model checkers, may yield completely wrong results. We present a new approach, which utilizes recent advances in partial exploration and mean payoff computation to obtain a correct, converging approximation.

Computing adequately permissive assumptions for synthesis - Anand, Ashwani; Mallik, Kaushik; Nayak, Satya Prakash; Schmuck, Anne Kathrin (TACAS 2023: Tools and Algorithms for the Construction and Analysis of Systems)
We automatically compute a new class of environment assumptions in two-player turn-based finite graph games which characterize an “adequate cooperation” needed from the environment to allow the system player to win. Given an ω-regular winning condition Φ for the system player, we compute an ω-regular assumption Ψ for the environment player, such that (i) every environment strategy compliant with Ψ allows the system to fulfill Φ (sufficiency), (ii) Ψ can be fulfilled by the environment for every strategy of the system (implementability), and (iii) Ψ does not prevent any cooperative strategy choice (permissiveness). For parity games, which are canonical representations of ω-regular games, we present a polynomial-time algorithm for the symbolic computation of adequately permissive assumptions and show that our algorithm runs faster and produces better assumptions than existing approaches—both theoretically and empirically. To the best of our knowledge, for ω -regular games, we provide the first algorithm to compute sufficient and implementable environment assumptions that are also permissive.

A learner-verifier framework for neural network controllers and certificates of stochastic systems - Chatterjee, Krishnendu; Henzinger, Thomas A; Lechner, Mathias; Zikelic, Dorde (Tools and Algorithms for the Construction and Analysis of Systems)
Reinforcement learning has received much attention for learning controllers of deterministic systems. We consider a learner-verifier framework for stochastic control systems and survey recent methods that formally guarantee a conjunction of reachability and safety properties. Given a property and a lower bound on the probability of the property being satisfied, our framework jointly learns a control policy and a formal certificate to ensure the satisfaction of the property with a desired probability threshold. Both the control policy and the formal certificate are continuous functions from states to reals, which are learned as parameterized neural networks. While in the deterministic case, the certificates are invariant and barrier functions for safety, or Lyapunov and ranking functions for liveness, in the stochastic case the certificates are supermartingales. For certificate verification, we use interval arithmetic abstract interpretation to bound the expected values of neural network functions.

Certifying giant nonprimes - Hoffmann, Charlotte; Hubáček, Pavel; Kamath, Chethan; Pietrzak, Krzysztof Z (Public-Key Cryptography - PKC 2023)
GIMPS and PrimeGrid are large-scale distributed projects dedicated to searching giant prime numbers, usually of special forms like Mersenne and Proth primes. The numbers in the current search-space are millions of digits large and the participating volunteers need to run resource-consuming primality tests. Once a candidate prime N has been found, the only way for another party to independently verify the primality of N used to be by repeating the expensive primality test. To avoid the need for second recomputation of each primality test, these projects have recently adopted certifying mechanisms that enable efficient verification of performed tests. However, the mechanisms presently in place only detect benign errors and there is no guarantee against adversarial behavior: a malicious volunteer can mislead the project to reject a giant prime as being non-prime. In this paper, we propose a practical, cryptographically-sound mechanism for certifying the non-primality of Proth numbers. That is, a volunteer can – parallel to running the primality test for N – generate an efficiently verifiable proof at a little extra cost certifying that N is not prime. The interactive protocol has statistical soundness and can be made non-interactive using the Fiat-Shamir heuristic. Our approach is based on a cryptographic primitive called Proof of Exponentiation (PoE) which, for a group G, certifies that a tuple (x,y,T)∈G2×N satisfies x2T=y (Pietrzak, ITCS 2019 and Wesolowski, J. Cryptol. 2020). In particular, we show how to adapt Pietrzak’s PoE at a moderate additional cost to make it a cryptographically-sound certificate of non-primality.

A Mecke-type characterization of the Dirichlet–Ferguson measure - Dello Schiavo, Lorenzo; Lytvynov, Eugene (Electronic Communications in Probability)
We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes.

Running Windows-applications on a Linux HPC cluster using WINE - Schlögl, Alois; Elefante, Stefano; Hodirnau, Victor-Valentin (ASHPC23 - Austrian-Slovenian HPC Meeting 2023)

Cryo-EM software packages: A sys-admins point of view - Elefante, Stefano; Stadlbauer, Stephan; Alexander, Michael F; Schlögl, Alois (ASHPC23 - Austrian-Slovenian HPC Meeting 2023)

Divergent molecular signatures in fish Bouncer proteins define cross-fertilization boundaries - Gert, Krista R.B.; Panser, Karin; Surm, Joachim; Steinmetz, Benjamin S.; Schleiffer, Alexander; Jovine, Luca; Moran, Yehu; Kondrashov, Fyodor; Pauli, Andrea (Nature Communications)
Molecular compatibility between gametes is a prerequisite for successful fertilization. As long as a sperm and egg can recognize and bind each other via their surface proteins, gamete fusion may occur even between members of separate species, resulting in hybrids that can impact speciation. The egg membrane protein Bouncer confers species specificity to gamete interactions between medaka and zebrafish, preventing their cross-fertilization. Here, we leverage this specificity to uncover distinct amino acid residues and N-glycosylation patterns that differentially influence the function of medaka and zebrafish Bouncer and contribute to cross-species incompatibility. Curiously, in contrast to the specificity observed for medaka and zebrafish Bouncer, seahorse and fugu Bouncer are compatible with both zebrafish and medaka sperm, in line with the pervasive purifying selection that dominates Bouncer’s evolution. The Bouncer-sperm interaction is therefore the product of seemingly opposing evolutionary forces that, for some species, restrict fertilization to closely related fish, and for others, allow broad gamete compatibility that enables hybridization.

Successive vertex orderings of fully regular graphs - Fang, Lixing; Huang, Hao; Pach, János; Tardos, Gábor; Zuo, Junchi (Journal of Combinatorial Theory. Series A)
A graph G=(V, E) is called fully regular if for every independent set I c V, the number of vertices in V\I that are not connected to any element of I depends only on the size of I. A linear ordering of the vertices of G is called successive if for every i, the first i vertices induce a connected subgraph of G. We give an explicit formula for the number of successive vertex orderings of a fully regular graph. As an application of our results, we give alternative proofs of two theorems of Stanley and Gao & Peng, determining the number of linear edge orderings of complete graphs and complete bipartite graphs, respectively, with the property that the first i edges induce a connected subgraph. As another application, we give a simple product formula for the number of linear orderings of the hyperedges of a complete 3-partite 3-uniform hypergraph such that, for every i, the first i hyperedges induce a connected subgraph. We found similar formulas for complete (non-partite) 3-uniform hypergraphs and in another closely related case, but we managed to verify them only when the number of vertices is small.

The evolutionary history of Brachyury genes in Hydrozoa involves duplications, divergence, and neofunctionalization - Vetrova, Alexandra A.; Kupaeva, Daria M.; Kizenko, Alena; Lebedeva, Tatiana S.; Walentek, Peter; Tsikolia, Nikoloz; Kremnyov, Stanislav V. (Scientific Reports)
Brachyury, a member of T-box gene family, is widely known for its major role in mesoderm specification in bilaterians. It is also present in non-bilaterian metazoans, such as cnidarians, where it acts as a component of an axial patterning system. In this study, we present a phylogenetic analysis of Brachyury genes within phylum Cnidaria, investigate differential expression and address a functional framework of Brachyury paralogs in hydrozoan Dynamena pumila. Our analysis indicates two duplication events of Brachyury within the cnidarian lineage. The first duplication likely appeared in the medusozoan ancestor, resulting in two copies in medusozoans, while the second duplication arose in the hydrozoan ancestor, resulting in three copies in hydrozoans. Brachyury1 and 2 display a conservative expression pattern marking the oral pole of the body axis in D. pumila. On the contrary, Brachyury3 expression was detected in scattered presumably nerve cells of the D. pumila larva. Pharmacological modulations indicated that Brachyury3 is not under regulation of cWnt signaling in contrast to the other two Brachyury genes. Divergence in expression patterns and regulation suggest neofunctionalization of Brachyury3 in hydrozoans.

Effects of urban living environments on mental health in adults - Xu, Jiayuan; Liu, Nana; Polemiti, Elli; Garcia-Mondragon, Liliana; Tang, Jie; Liu, Xiaoxuan; Lett, Tristram; Yu, Le; Nöthen, Markus M.; Feng, Jianfeng; Yu, Chunshui; Marquand, Andre; et al. (Nature Medicine)
Urban-living individuals are exposed to many environmental factors that may combine and interact to influence mental health. While individual factors of an urban environment have been investigated in isolation, no attempt has been made to model how complex, real-life exposure to living in the city relates to brain and mental health, and how this is moderated by genetic factors. Using the data of 156,075 participants from the UK Biobank, we carried out sparse canonical correlation analyses to investigate the relationships between urban environments and psychiatric symptoms. We found an environmental profile of social deprivation, air pollution, street network and urban land-use density that was positively correlated with an affective symptom group (r = 0.22, Pperm < 0.001), mediated by brain volume differences consistent with reward processing, and moderated by genes enriched for stress response, including CRHR1, explaining 2.01% of the variance in brain volume differences. Protective factors such as greenness and generous destination accessibility were negatively correlated with an anxiety symptom group (r = 0.10, Pperm < 0.001), mediated by brain regions necessary for emotion regulation and moderated by EXD3, explaining 1.65% of the variance. The third urban environmental profile was correlated with an emotional instability symptom group (r = 0.03, Pperm < 0.001). Our findings suggest that different environmental profiles of urban living may influence specific psychiatric symptom groups through distinct neurobiological pathways.

Transition from tonic to phasic neurotransmitter release by presynaptic GABAB receptor activation in medial habenula terminals - Shigemoto, Ryuichi
GABAB receptor (GBR) activation inhibits neurotransmitter release in axon terminals in the brain, except in medial habenula (MHb) terminals, which show robust potentiation. However, mechanisms underlying this enigmatic potentiation remain elusive. Here, we report that GBR activation on MHb terminals induces an activity-dependent transition from a facilitating, tonic to a depressing, phasic neurotransmitter release mode. This transition is accompanied by a 4.1-fold increase in readily releasable vesicle pool (RRP) size and a 3.5-fold increase of docked synaptic vesicles at the presynaptic active zone (AZ). Strikingly, tonic and phasic release exhibit distinct coupling distances and are selectively affected by deletion of synaptoporin (SPO) and Ca2+-dependent activator protein for secretion 2 (CAPS2), respectively. SPO modulates augmentation, the short-term plasticity associated with tonic release, and CAPS2 retains the increased RRP for initial responses in phasic response trains. Double pre-embedding immunolabeling confirmed the co-localization of CAPS2 and SPO inside the same terminal. The cytosolic protein CAPS2 showed a synaptic vesicle (SV)-associated distribution similar to the vesicular transmembrane protein SPO. A newly developed “Flash and Freeze-fracture” method revealed the release of SPO-associated vesicles in both tonic and phasic modes and activity-dependent recruitment of CAPS2 to the AZ during phasic release, which lasted several minutes. Overall, these results indicate that GBR activation translocates CAPS2 to the AZ along with the fusion of CAPS2-associated SVs, contributing to a persistent RRP increase. Thus, we discovered structural and molecular mechanisms underlying tonic and phasic neurotransmitter release and their transition by GBR activation in MHb terminals.
Keywords: medial habenula; GABAB receptor; vesicle release; Flash and Freeze; Flash and Freeze-fracture

Cavity quantum electrooptics - Sahu, Rishabh
About a 100 years ago, we discovered that our universe is inherently noisy, that is, measuring any physical quantity with a precision beyond a certain point is not possible because of an omnipresent inherent noise. We call this - the quantum noise. Certain physical processes allow this quantum noise to get correlated in conjugate physical variables. These quantum correlations can be used to go beyond the potential of our inherently noisy universe and obtain a quantum advantage over the classical applications. Quantum noise being inherent also means that, at the fundamental level, the physical quantities are not well defined and therefore, objects can stay in multiple states at the same time. For example, the position of a particle not being well defined means that the particle is in multiple positions at the same time. About 4 decades ago, we started exploring the possibility of using objects which can be in multiple states at the same time to increase the dimensionality in computation. Thus, the field of quantum computing was born. We discovered that using quantum entanglement, a property closely related to quantum correlations, can be used to speed up computation of certain problems, such as factorisation of large numbers, faster than any known classical algorithm. Thus began the pursuit to make quantum computers a reality. Till date, we have explored quantum control over many physical systems including photons, spins, atoms, ions and even simple circuits made up of superconducting material. However, there persists one ubiquitous theme. The more readily a system interacts with an external field or matter, the more easily we can control it. But this also means that such a system can easily interact with a noisy environment and quickly lose its coherence. Consequently, such systems like electron spins need to be protected from the environment to ensure the longevity of their coherence. Other systems like nuclear spins are naturally protected as they do not interact easily with the environment. But, due to the same reason, it is harder to interact with such systems. After decades of experimentation with various systems, we are convinced that no one type of quantum system would be the best for all the quantum applications. We would need hybrid systems which are all interconnected - much like the current internet where all sorts of devices can all talk to each other - but now for quantum devices. A quantum internet. Optical photons are the best contenders to carry information for the quantum internet. They can carry quantum information cheaply and without much loss - the same reasons which has made them the backbone of our current internet. Following this direction, many systems, like trapped ions, have already demonstrated successful quantum links over a large distances using optical photons. However, some of the most promising contenders for quantum computing which are based on microwave frequencies have been left behind. This is because high energy optical photons can adversely affect fragile low-energy microwave systems. In this thesis, we present substantial progress on this missing quantum link between microwave and optics using electrooptical nonlinearities in lithium niobate. The nonlinearities are enhanced by using resonant cavities for all the involved modes leading to observation of strong direct coupling between optical and microwave frequencies. With this strong coupling we are not only able to achieve almost 100% internal conversion efficiency with low added noise, thus presenting a quantum-enabled transducer, but also we are able to observe novel effects such as cooling of a microwave mode using optics. The strong coupling regime also leads to direct observation of dynamical backaction effect between microwave and optical frequencies which are studied in detail here. Finally, we also report first observation of microwave-optics entanglement in form of two-mode squeezed vacuum squeezed 0.7dB below vacuum level. With this new bridge between microwave and optics, the microwave-based quantum technologies can finally be a part of a quantum network which is based on optical photons - putting us one step closer to a future with quantum internet.
Keywords: quantum optics; electrooptics; quantum networks; quantum communication; transduction

Sobolev-type inequalities and eigenvalue growth on graphs with finite measure - Hua, Bobo; Keller, Matthias; Schwarz, Michael; Wirth, Melchior (Proceedings of the American Mathematical Society)
In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established.

Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron - Mitrouskas, David Johannes; Mysliwy, Krzysztof; Seiringer, Robert (Forum of Mathematics)
We consider the large polaron described by the Fröhlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an optimal parabolic upper bound for the energy-momentum relation in the limit of strong coupling. The upper bound consists of a momentum independent term that agrees with the predicted two-term expansion for the ground state energy of the strongly coupled polaron at rest and a term that is quadratic in the momentum with coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar.

CQS: A formally-verified framework for fair and abortable synchronization - Koval, Nikita; Khalanskiy, Dmitry; Alistarh, Dan-Adrian (Proceedings of the ACM on Programming Languages)
Writing concurrent code that is both correct and efficient is notoriously difficult. Thus, programmers often prefer to use synchronization abstractions, which render code simpler and easier to reason about. Despite a wealth of work on this topic, there is still a gap between the rich semantics provided by synchronization abstractions in modern programming languages—specifically, fair FIFO ordering of synchronization requests and support for abortable operations—and frameworks for implementing it correctly and efficiently. Supporting such semantics is critical given the rising popularity of constructs for asynchronous programming, such as coroutines, which abort frequently and are cheaper to suspend and resume compared to native threads. This paper introduces a new framework called CancellableQueueSynchronizer (CQS), which enables simple yet efficient implementations of a wide range of fair and abortable synchronization primitives: mutexes, semaphores, barriers, count-down latches, and blocking pools. Our main contribution is algorithmic, as implementing both fairness and abortability efficiently at this level of generality is non-trivial. Importantly, all our algorithms, including the CQS framework and the primitives built on top of it, come with formal proofs in the Iris framework for Coq for many of their properties. These proofs are modular, so it is easy to show correctness for new primitives implemented on top of CQS. From a practical perspective, implementation of CQS for native threads on the JVM improves throughput by up to two orders of magnitude over Java’s AbstractQueuedSynchronizer, the only practical abstraction offering similar semantics. Further, we successfully integrated CQS as a core component of the popular Kotlin Coroutines library, validating the framework’s practical impact and expressiveness in a real-world environment. In sum, CancellableQueueSynchronizer is the first framework to combine expressiveness with formal guarantees and solid practical performance. Our approach should be extensible to other languages and families of synchronization primitives.

Local solubility for a family of quadrics over a split quadric surface - Browning, Timothy D; Lyczak, Julian; Sarapin, Roman (Involve)
We study the density of everywhere locally soluble diagonal quadric surfaces, parameterised by rational points that lie on a split quadric surface