@article{17476, abstract = {Lead halide perovskites have recently been reported to demonstrate an exceptionally high nonlinear (Kerr) refractive index n2 of up to 10−8cm2/W in CH3⁢NH3⁢PbBr3. Other researchers, however, observe different, substantially more conservative numbers. In order to resolve this disagreement, the nonlinear Kerr index of a bulk sample of lead halide perovskite was measured directly by means of an interferometer. This approach has many advantages as compared to the more standard z-scan technique. In particular, this method allows studying the induced changes to the refractive index in a time-resolved manner, thus enabling to separate the different contributions to 𝑛2. The extracted 𝑛2 values for CsPbBr3 and MAPbBr3 at 𝜆≈1µ⁢m are 𝑛2=+2.1×10−14cm2/W and 𝑛2=+6×10−15cm2/W, respectively. Hence, these values are substantially lower than what has been indicated in most of the previous reports, implying the latter one should be regarded with great care.}, author = {Lorenc, Dusan and Zhumekenov, Ayan and Bakr, Osman M. and Alpichshev, Zhanybek}, issn = {2475-9953}, journal = {Physical Review Materials}, number = {8}, publisher = {American Physical Society}, title = {{No extraordinary χ(3) in lead-halide perovskites: Placing an upper bound on Kerr nonlinearity by means of time-resolved interferometry}}, doi = {10.1103/PhysRevMaterials.8.085403}, volume = {8}, year = {2024}, } @article{17481, abstract = {Phase-field models such as the Allen–Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen–Cahn equation with a potential with N≥3 distinct minima has been conjectured to describe the evolution of branched interfaces by multiphase mean curvature flow. In the present work, we give a rigorous proof for this statement in two and three ambient dimensions and for a suitable class of potentials: as long as a strong solution to multiphase mean curvature flow exists, solutions to the vectorial Allen–Cahn equation with well-prepared initial data converge towards multiphase mean curvature flow in the limit of vanishing interface width parameter ε↘0. We even establish the rate of convergence O(ε 1/2 ). Our approach is based on the gradient-flow structure of the Allen–Cahn equation and its limiting motion: building on the recent concept of “gradient-flow calibrations” for multiphase mean curvature flow, we introduce a notion of relative entropy for the vectorial Allen–Cahn equation with multi-well potential. This enables us to overcome the limitations of other approaches, e.g. avoiding the need for a stability analysis of the Allen–Cahn operator or additional convergence hypotheses for the energy at positive times.}, author = {Fischer, Julian L and Marveggio, Alice}, issn = {1873-1430}, journal = {Annales de l'Institut Henri Poincare C}, number = {5}, pages = {1117--1178}, publisher = {EMS Press}, title = {{Quantitative convergence of the vectorial Allen–Cahn equation towards multiphase mean curvature flow}}, doi = {10.4171/AIHPC/109}, volume = {41}, year = {2024}, } @phdthesis{17485, abstract = {Large language models (LLMs) have made tremendous progress in the past few years, from being able to generate coherent text to matching or surpassing humans in a wide variety of creative, knowledge or reasoning tasks. Much of this can be attributed to massively increased scale, both in the size of the model as well as the amount of training data, from 100s of millions to 100s of billions, or even trillions. This trend is expected to continue, which, although exciting, also raises major practical concerns. Already today's 100+ billion parameter LLMs require top-of-the-line hardware just to run. Hence, it is clear that sustaining these developments will require significant efficiency advances. Historically, one of the most practical ways of improving model efficiency has been compression, especially in the form of sparsity or quantization. While this has been studied extensively in the past, existing accurate methods are all designed for models around 100 million parameters; scaling them up to ones literally 1000x larger is highly challenging. In this thesis, we introduce a new unified sparsification and quantization approach OBC, which through additional algorithmic enhancements leads to GPTQ and SparseGPT, the first techniques fast and accurate enough to compress 100+ billion parameter models to 4- or even 3-bit precision and 50% weight-sparsity, respectively. Additionally, we show how weight-only quantizion does not just bring space savings but also up to 4.5x faster generation speed, via custom GPU kernels. In fact, we show for the first time that it is possible to develop an FP16 times INT4 mixed-precision matrix multiplication kernel, called Marlin, which comes close to simultaneously maximizing both memory and compute utilization, making weight-only quantization highly practical even for multi-user serving. Further, we demonstrate that GPTQ can be scaled to widely overparametrized trillion-parameter models, where extreme sub-1-bit compression rates can be achieved without any inference slow-down, by co-designing a bespoke entropy coding scheme together with an efficient kernel. Finally, we also study compression from the perspective of someone with access to massive amounts of compute resources for training large models completely from scratch. Here the key questions evolve around the joint scaling behavior between compression, model size, and amount of training data used. Based on extensive experimental results for both vision and text models, we introduce the first scaling law which accurately captures the relationship between weight-sparsity, number of non-zero weights and data. This further allows us to characterize the optimal sparsity, which we find to increase the longer a fixed cost model is being trained. Overall, this thesis presents contributions to three different angles of large model efficiency: affordable but accurate algorithms, highly efficient systems implementations, and fundamental scaling laws for compressed training.}, author = {Frantar, Elias}, issn = {2663-337X}, pages = {129}, publisher = {Institute of Science and Technology Austria}, title = {{Compressing large neural networks : Algorithms, systems and scaling laws}}, doi = {10.15479/at:ista:17485}, year = {2024}, } @article{17535, abstract = {Supermassive black holes (SMBHs) with masses of ∼109 M⊙ within the first billion year of the universe challenge our conventional understanding of black hole formation and growth. One pathway to these SMBHs proposes that supermassive stars born in pristine atomic cooling haloes yield massive seed BHs evolving to these early SMBHs. This scenario leads to an overly massive BH galaxy (OMBG), in which the BH to stellar mass ratio is initially Mbh/M* ≥ 1, well in excess of the typical values of ∼10−3 at low redshifts. Previously, we have investigated two massive seed BH candidates from the Renaissance simulation and found that they remain outliers on the Mbh–M* relation until the OMBG merges with a much more massive halo at z = 8. In this work, we use Monte-Carlo merger trees to investigate the evolution of the Mbh–M* relation for 50 000 protogalaxies hosting massive BH seeds, across 10 000 trees that merge into a 1012 M⊙ halo at z = 6. We find that up to 60 per cent (depending on growth parameters) of these OMBGs remain strong outliers for several 100 Myr, down to redshifts detectable with JWST and with sensitive X-ray telescopes. This represents a way to diagnose the massive-seed formation pathway for early SMBHs. We expect to find ∼0.1–1 of these objects per JWST Near Infrared Camera (NIRCam) field per unit redshift at z ≳ 6. Recently detected SMBHs with masses of ∼107 M⊙ and low-inferred stellar-mass hosts may be examples of this population.}, author = {Scoggins, Matthew T and Haiman, Zoltán}, issn = {0035-8711}, journal = {Monthly Notices of the Royal Astronomical Society}, number = {4}, pages = {4584--4597}, publisher = {Oxford University Press}, title = {{Diagnosing the massive-seed pathway to high-redshift black holes: statistics of the evolving black hole to host galaxy mass ratio}}, doi = {10.1093/mnras/stae1449}, volume = {531}, year = {2024}, } @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}, } @phdthesis{17850, abstract = {Understanding the relationship between a given phenotype and its underlying genotype or genotypes is one of the most pressing challenges of biology, as it lies at the heart of not only basic understanding of evolutionary theory, but also of practical applications in medicine and bioengineering. Understanding this relationship is complicated by the ubiquitous phenomenon of epistasis, wherein mutation effects are dependent on their genetic context. Fitness landscapes — representations of phenotype as a function of genotype — are being increasingly used as a tool to study the effects and interactions of thousands of mutations, but are experimentally limited to exploring a small fraction of a protein’s theoretical sequence space. Furthermore, not all regions of said sequence space are necessarily equally informative. Thus, gene selection for landscape surveys should be carefully considered in order to maximize the usable output of necessarily limited data. In this work, we analyzed the fitness landscapes of orthologous green fluorescent proteins from four different species, by systematically measuring the phenotype, fluorescence, of tens of thousands of mutant genotypes from each protein. These landscapes were highly heterogeneous, with some genes being mutationally robust and displaying epistasis only rarely, and others being highly epistatic and mutationally fragile. We used this data to train machine learning models to predict fluorescence from genotype. Although the training data contained almost exclusively genotypes with less than 3% sequence divergence from the original wild-type sequences, we were able to create novel, functional genotypes with up to 20% sequence divergence. Counterintuitively however, genes with high mutational robustness and rare epistasis were more difficult to introduce large numbers of mutations into, not less. This represents the first study of large-scale fitness landscapes of a protein family, and provides insights into how to approach future landscape surveys and their applications in novel protein design.}, author = {Gonzalez Somermeyer, Louisa}, issn = {2663-337X}, pages = {89}, publisher = {Institute of Science and Technology Austria}, title = {{Fitness landscapes of orthologous green fluorescent proteins}}, doi = {10.15479/at:ista:17850}, year = {2024}, } @article{17852, abstract = {Metal-metal contacts, though not yet widely realized, may provide exciting opportunities to serve as tunable and functional interfaces in single-molecule devices. One of the simplest components which might facilitate such binding interactions is the ferrocene group. Notably, direct bonds between the ferrocene iron center and metals such as Pd or Co have been demonstrated in molecular complexes comprising coordinating ligands attached to the cyclopentadienyl rings. Here, we demonstrate that ferrocene-based single-molecule devices with Fe-Au interfacial contact geometries form at room temperature in the absence of supporting coordinating ligands. Applying a photoredox reaction, we propose that ferrocene only functions effectively as a contact group when oxidized, binding to gold through a formal Fe3+ center. This observation is further supported by a series of control measurements and density functional theory calculations. Our findings extend the scope of junction contact chemistries beyond those involving main group elements, lay the foundation for light switchable ferrocene-based single-molecule devices, and highlight new potential mechanistic function(s) of unsubstituted ferrocenium groups in synthetic processes.}, author = {Lee, Woojung and Li, Liang and Camarasa-Gómez, María and Hernangómez-Pérez, Daniel and Roy, Xavier and Evers, Ferdinand and Inkpen, Michael S. and Venkataraman, Latha}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{Photooxidation driven formation of Fe-Au linked ferrocene-based single-molecule junctions}}, doi = {10.1038/s41467-024-45707-z}, volume = {15}, year = {2024}, } @article{17885, abstract = {The formation of new ribosomes is tightly coordinated with cell growth and proliferation. In eukaryotes, the correct assembly of all ribosomal proteins and RNAs follows an intricate scheme of maturation and rearrangement steps across three cellular compartments: the nucleolus, nucleoplasm, and cytoplasm. We demonstrate that usnic acid, a lichen secondary metabolite, inhibits the maturation of the large ribosomal subunit in yeast. We combine biochemical characterization of pre-ribosomal particles with a quantitative single-particle cryo-EM approach to monitor changes in nucleolar particle populations upon drug treatment. Usnic acid rapidly blocks the transition from nucleolar state B to C of Nsa1-associated pre-ribosomes, depleting key maturation factors such as Dbp10 and hindering pre-rRNA processing. This primary nucleolar block rapidly rebounds on earlier stages of the pathway which highlights the regulatory linkages between different steps. In summary, we provide an in-depth characterization of the effect of usnic acid on ribosome biogenesis, which may have implications for its reported anti-cancer activities.}, author = {Kofler, Lisa and Grundmann, Lorenz and Gerhalter, Magdalena and Prattes, Michael and Merl-Pham, Juliane and Zisser, Gertrude and Grishkovskaya, Irina and Hodirnau, Victor-Valentin and Vareka, Martin and Breinbauer, Rolf and Hauck, Stefanie M. and Haselbach, David and Bergler, Helmut}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{The novel ribosome biogenesis inhibitor usnic acid blocks nucleolar pre-60S maturation}}, doi = {10.1038/s41467-024-51754-3}, volume = {15}, year = {2024}, } @article{17886, abstract = {Thin pancake-like neuronal networks cultured on top of a planar microelectrode array have been extensively tried out in neuroengineering, as a substrate for the mobile robot’s control unit, i.e., as a cyborg’s brain. Most of these attempts failed due to intricate self-organizing dynamics in the neuronal systems. In particular, the networks may exhibit an emergent spatial map of steady nucleation sites (“n-sites”) of spontaneous population spikes. Being unpredictable and independent of the surface electrode locations, the n-sites drastically change local ability of the network to generate spikes. Here, using a spiking neuronal network model with generative spatially-embedded connectome, we systematically show in simulations that the number, location, and relative activity of spontaneously formed n-sites (“the vitals”) crucially depend on the samplings of three distributions: (1) the network distribution of neuronal excitability, (2) the distribution of connections between neurons of the network, and (3) the distribution of maximal amplitudes of a single synaptic current pulse. Moreover, blocking the dynamics of a small fraction (about 4%) of non-pacemaker neurons having the highest excitability was enough to completely suppress the occurrence of population spikes and their n-sites. This key result is explained theoretically. Remarkably, the n-sites occur taking into account only short-term synaptic plasticity, i.e., without a Hebbian-type plasticity. As the spiking network model used in this study is strictly deterministic, all simulation results can be accurately reproduced. The model, which has already demonstrated a very high richness-to-complexity ratio, can also be directly extended into the three-dimensional case, e.g., for targeting peculiarities of spiking dynamics in cerebral (or brain) organoids. We recommend the model as an excellent illustrative tool for teaching network-level computational neuroscience, complementing a few benchmark models.}, author = {Zendrikov, Dmitrii and Paraskevov, Alexander}, issn = {1879-2782}, journal = {Neural Networks}, publisher = {Elsevier}, title = {{The vitals for steady nucleation maps of spontaneous spiking coherence in autonomous two-dimensional neuronal networks}}, doi = {10.1016/j.neunet.2024.106589}, volume = {180}, year = {2024}, } @article{17888, abstract = {Context: Biotic resource exploitation is a critical determinant of species’ distributions. However, quantifying resource exploitation patterns through space and time can be difficult, complicating their incorporation in spatial ecology studies. Therefore, understanding the local drivers of spatial patterns of resource exploitation may contribute to better large-scale species distribution models. Objectives: We investigated (1) how the resource exploitation patterns of two trophic interactions (plant–insect) are explained by insect behaviour, resource aggregation, and potential insect-insect interactions. We also analyzed how (2) resource patch size and (3) resource accessibility in a heterogeneous landscape affected host exploitation patterns. Methods: We quantified nectar robbing by insects in the genus Bombus (bumblebees) and seed predation by Brachypterolus vestitus larvae (Antirrhinum beetle) on Antirrhinum majus L. (wild snapdragons) in the Pyrenees Mountains, Catalonia, Spain. We tested hypotheses about resource exploitation by integrating spatial analyses at multiple scales. Results: Both trophic interactions were aggregated, explained by the aggregation of their resource. At some scales, nectar robbing is more aggregated than the resource. Trophic interaction abundance is proportional to resource patch size, following the ideal free distribution model. Landscape features do not explain the locations exploited. Nectar robbing and seed predation occur together more often than expected. Conclusions: Our findings suggest that multiple biotic and ecological spatial factors may simultaneously affect resource exploitation at a local scale. These findings should be considered when developing agricultural projects, management plans and conservation policies.}, author = {Pocull Belles, Guillem and Baskett, Carina and Barton, Nicholas H}, issn = {1572-9761}, journal = {Landscape Ecology}, number = {9}, publisher = {Springer Nature}, title = {{Multiscale spatial analysis of two plant–insect interactions: Effects of landscape, resource distribution, and other insects}}, doi = {10.1007/s10980-024-01899-9}, volume = {39}, year = {2024}, } @article{17892, abstract = {Enzyme-substrate kinetics form the basis of many biomolecular processes. The interplay between substrate binding and substrate geometry can give rise to long-range interactions between enzyme binding events. Here we study a general model of enzyme-substrate kinetics with restricted long-range interactions described by an exponent −𝛾. We employ a coherent-state path integral and renormalization group approach to calculate the first moment and two-point correlation function of the enzyme-binding profile. We show that starting from an empty substrate the average occupancy follows a power law with an exponent 1/(1−𝛾) over time. The correlation function decays algebraically with two distinct spatial regimes characterized by exponents −𝛾 on short distances and −(2/3)⁢(2−𝛾) on long distances. The crossover between both regimes scales inversely with the average substrate occupancy. Our work allows associating experimental measurements of bound enzyme locations with their binding kinetics and the spatial conformation of the substrate.}, author = {Olmeda, Fabrizio and Rulands, Steffen}, issn = {2470-0053}, journal = {Physical Review E}, number = {2}, publisher = {American Physical Society}, title = {{Field theory of enzyme-substrate systems with restricted long-range interactions}}, doi = {10.1103/PhysRevE.110.024404}, volume = {110}, year = {2024}, } @article{18065, abstract = {We establish a close connection between acceleration and dynamical degree for one-frequency quasi-periodic compact cocycles, by showing that two vectors derived separately from each coincide. Based on this, we provide a dynamical classification of one-frequency quasi-periodic SO(3, R)-cocycles.}, author = {Hou, Xuanji and Pan, Yi and Zhou, Qi}, issn = {1090-2082}, journal = {Advances in Mathematics}, publisher = {Elsevier}, title = {{Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles}}, doi = {10.1016/j.aim.2024.109943}, volume = {457}, year = {2024}, } @inproceedings{18086, abstract = {Abstract. Continuous group key agreement (CGKA) allows a group of users to maintain a continuously updated shared key in an asynchronous setting where parties only come online sporadically and their messages are relayed by an untrusted server. CGKA captures the basic primitive underlying group messaging schemes. Current solutions including TreeKEM (“Messaging Layer Security” (MLS) IETF RFC 9420) cannot handle concurrent requests while retaining low communication complexity. The exception being CoCoA, which is concurrent while having extremely low communication complexity (in groups of size n and for m concurrent updates the communication per user is log(n), i.e., independent of m). The main downside of CoCoA is that in groups of size n, users might have to do up to log(n) update requests to the server to ensure their (potentially corrupted) key material has been refreshed. In this work we present a “fast healing” concurrent CGKA protocol, named DeCAF, where users will heal after at most log(t) requests, with t being the number of corrupted users. While also suitable for the standard central-server setting, our protocol is particularly interesting for realizing decentralized group messaging, where protocol messages (add, remove, update) are being posted on some append-only data structure rather than sent to a server. In this setting, concurrency is crucial once the rate of requests exceeds, say, the rate at which new blocks are added to a blockchain. In the central-server setting, CoCoA (the only alternative with concurrency, sub-linear communication and basic post-compromise security) enjoys much lower download communication. However, in the decentralized setting – where there is no server which can craft specific messages for different users to reduce their download communication – our protocol significantly outperforms CoCoA. DeCAF heals in fewer epochs (log(t) vs. log(n)) while incurring a similar per epoch per user communication cost.}, author = {Alwen, Joel F and Auerbach, Benedikt and Cueto Noval, Miguel and Klein, Karen and Pascual Perez, Guillermo and Pietrzak, Krzysztof Z}, booktitle = {Security and Cryptography for Networks: 14th International Conference}, editor = {Galdi, Clemente and Phan, Duong Hieu}, isbn = {9783031710728}, issn = {1611-3349}, location = {Amalfi, Italy}, pages = {294–313}, publisher = {Springer Nature}, title = {{DeCAF: Decentralizable CGKA with fast healing}}, doi = {10.1007/978-3-031-71073-5_14}, volume = {14974}, year = {2024}, } @inproceedings{18113, abstract = {The emergence of accurate open large language models (LLMs) has led to a race towards performant quantization techniques which can enable their execution on end-user devices. In this paper, we revisit the problem of “extreme” LLM compression—defined as targeting extremely low bit counts, such as 2 to 3 bits per parameter—from the point of view of classic methods in Multi-Codebook Quantization (MCQ). Our algorithm, called AQLM, generalizes the classic Additive Quantization (AQ) approach for information retrieval to advance the state-of-the-art in LLM compression, via two innovations: 1) learned additive quantization of weight matrices in input-adaptive fashion, and 2) joint optimization of codebook parameters across each transformer blocks. Broadly, AQLM is the first scheme that is Pareto optimal in terms of accuracy-vs-model-size when compressing to less than 3 bits per parameter, and significantly improves upon all known schemes in the extreme compression (2bit) regime. In addition, AQLM is practical: we provide fast GPU and CPU implementations of AQLM for token generation, which enable us to match or outperform optimized FP16 implementations for speed, while executing in a much smaller memory footprint.}, author = {Egiazarian, Vage and Panferov, Andrei and Kuznedelev, Denis and Frantar, Elias and Babenko, Artem and Alistarh, Dan-Adrian}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, issn = {2640-3498}, location = {Vienna, Austria}, pages = {12284--12303}, publisher = {ML Research Press}, title = {{Extreme compression of large language models via additive quantization}}, volume = {235}, year = {2024}, } @phdthesis{18132, abstract = {In this thesis, we are dealing with both arithmetic and geometric problems coming from the study of rational points with a particular focus on function fields over finite fields: (1) Using the circle method we produce upper bounds for the number of rational points of bounded height on diagonal cubic surfaces and fourfolds over Fq(t). This is based on joint work with Leonhard Hochfilzer. (2) We study rational points on smooth complete intersections X defined by cubic and quadratic hypersurfaces over Fq(t). We refine the Farey dissection of the “unit square” developed by Vishe [202] and use the circle method with a Kloosterman refinement to establish an asymptotic formula for the number of rational points of bounded height on X when dim(X) ≥ 23. Under the same hypotheses, we also verify weak approximation. (3) In joint work with Hochfilzer, we obtain upper bounds for the number of rational points of bounded height on del Pezzo surfaces of low degree over any global field. Our approach is to take hyperplane sections, which reduces the problem to uniform estimates for the number of rational points on curves. (4) We develop a version of the circle method capable of counting Fq-points on jet schemes of moduli spaces of rational curves on hypersurfaces. Combining this with a spreading out argument and a result of Mustaţă [150], this allows us to show that these moduli spaces only have canonical singularities under suitable assumptions on the degree and the dimension. In addition, we give an overview of guiding questions and conjectures in the field of rational points and explain the basic mechanism underlying the circle method. }, author = {Glas, Jakob}, issn = {2663-337X}, pages = {195}, publisher = {Institute of Science and Technology Austria}, title = {{Counting rational points over function fields}}, doi = {10.15479/at:ista:18132}, year = {2024}, } @phdthesis{18135, abstract = {This thesis consists of two separate parts. In the first part we consider a dilute Fermi gas interacting through a repulsive interaction in dimensions $d=1,2,3$. Our focus is mostly on the physically most relevant dimension $d=3$ and the setting of a spin-polarized (equivalently spinless) gas, where the Pauli exclusion principle plays a key role. We show that, at zero temperature, the ground state energy density of the interacting spin-polarized gas differs (to leading order) from that of the free (i.e. non-interacting) gas by a term of order $a_p^d\rho^{2+2/d}$ with $a_p$ the $p$-wave scattering length of the repulsive interaction and $\rho$ the density. Further, we extend this to positive temperature and show that the pressure of an interacting spin-polarized gas differs from that of the free gas by a now temperature dependent term, again of order $a_p^d\rho^{2+2/d}$. Lastly, we consider the setting of a spin-$\frac{1}{2}$ Fermi gas in $d=3$ dimensions and show that here, as an upper bound, the ground state energy density differs from that of the free system by a term of order $a_s \rho^2$ with an error smaller than $a_s \rho^2 (a_s\rho^{1/3})^{1-\eps}$ for any $\eps > 0$, where $a_s$ is the $s$-wave scattering length of the repulsive interaction. These asymptotic formulas complement the similar formulas in the literature for the dilute Bose and spin-$\frac{1}{2}$ Fermi gas, where the ground state energies or pressures differ from that of the corresponding free systems by a term of order $a_s \rho^2$ in dimension $d=3$. In the spin-polarized setting, the corrections, of order $a_p^3\rho^{8/3}$ in dimension $d=3$, are thus much smaller and requires a more delicate analysis. In the second part of the thesis we consider the Bardeen--Cooper--Schrieffer (BCS) theory of superconductivity and in particular its associated critical temperature and energy gap. We prove that the ratio of the zero-temperature energy gap and critical temperature $\Xi(T=0)/T_c$ approaches a universal constant $\pi e^{-\gamma}\approx 1.76$ in both the limit of high density in dimension $d=3$ and in the limit of weak coupling in dimensions $d=1,2$. This complements the proofs in the literature of this universal behaviour in the limit of weak coupling or low density in dimension $d=3$. Secondly, we prove that the ratio of the energy gap at positive temperature and critical temperature $\Xi(T)/T_c$ approaches a universal function of the relative temperature $T/T_c$ in the limit of weak coupling in dimensions $d=1,2,3$.}, author = {Lauritsen, Asbjørn Bækgaard}, isbn = {978-3-99078-042-8}, issn = {2663-337X}, pages = {353}, publisher = {Institute of Science and Technology Austria}, title = {{Energies of dilute Fermi gases and universalities in BCS theory}}, doi = {10.15479/at:ista:18135}, year = {2024}, } @inproceedings{18155, abstract = {We study the classical problem of verifying programs with respect to formal specifications given in the linear temporal logic (LTL). We first present novel sound and complete witnesses for LTL verification over imperative programs. Our witnesses are applicable to both verification (proving) and refutation (finding bugs) settings. We then consider LTL formulas in which atomic propositions can be polynomial constraints and turn our focus to polynomial arithmetic programs, i.e. programs in which every assignment and guard consists only of polynomial expressions. For this setting, we provide an efficient algorithm to automatically synthesize such LTL witnesses. Our synthesis procedure is both sound and semi-complete. Finally, we present experimental results demonstrating the effectiveness of our approach and that it can handle programs which were beyond the reach of previous state-of-the-art tools.}, author = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Goharshady, Ehsan and Karrabi, Mehrdad and Zikelic, Dorde}, booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}, isbn = {9783031711619}, issn = {1611-3349}, location = {Milan, Italy}, pages = {600--619}, publisher = {Springer Nature}, title = {{Sound and complete witnesses for template-based verification of LTL properties on polynomial programs}}, doi = {10.1007/978-3-031-71162-6_31}, volume = {14933}, year = {2024}, } @article{18173, abstract = {Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over Fq(t), provided char (Fq)>3. Under the same hypotheses, we also verify weak approximation.}, author = {Glas, Jakob}, issn = {1469-7750}, journal = {Journal of the London Mathematical Society}, number = {4}, publisher = {London Mathematical Society}, title = {{Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t)}}, doi = {10.1112/jlms.12991}, volume = {110}, year = {2024}, } @inproceedings{18177, abstract = {Partially Specified Boolean Networks (PSBNs) represent a family of Boolean models resulting from possible interpretations of unknown update logics. Hybrid extension of CTL (HCTL) has the power to express complex dynamical phenomena, such as oscillations or stability. We present BNClassifier to classify Boolean Networks corresponding to a given PSBN according to criteria specified in HCTL. The implementation of the tool is fully symbolic (based on BDDs). The results are visualised using the machine-learning-based technology of decision trees.}, author = {Beneš, Nikola and Brim, Luboš and Huvar, Ondřej and Pastva, Samuel and Šafránek, David}, booktitle = {Computational Methods in Systems Biology}, isbn = {9783031716706}, issn = {1611-3349}, pages = {19--26}, publisher = {Springer Nature}, title = {{BNClassifier: Classifying boolean models by dynamic properties}}, doi = {10.1007/978-3-031-71671-3_2}, volume = {14971}, year = {2024}, } @inproceedings{18206, abstract = {In the context of in vitro fertilization (IVF), selecting embryos for transfer is critical in determining pregnancy outcomes, with implantation as the essential first milestone for a successful pregnancy. This study introduces the Bonna algorithm, an advanced deep-learning framework engineered to predict embryo implantation probabilities. The algorithm employs a sophisticated integration of machine-learning techniques, utilizing MobileNetV2 for pixel and context embedding, a custom Pix2Pix model for precise segmentation, and a Vision Transformer for additional depth in embedding. MobileNetV2 was chosen for its robust feature extraction capabilities, focusing on textures and edges. The custom Pix2Pix model is adapted for precise segmentation of significant biological features such as the zona pellucida and blastocyst cavity. The Vision Transformer adds a global perspective, capturing complex patterns not apparent in local image segments. Tested on a dataset of images of human blastocysts collected from Ukraine, Israel, and Spain, the Bonna algorithm was rigorously validated through 10-fold cross-validation to ensure its robustness and reliability. It demonstrates superior performance with a mean area under the receiver operating characteristic curve (AUC) of 0.754, significantly outperforming existing models. The study not only advances predictive accuracy in embryo selection but also highlights the algorithm’s clinical applicability due to reliable confidence reporting.}, author = {Rave, Gilad and Fordham, Daniel E. and Bronstein, Alexander and Silver, David H.}, booktitle = {First International Conference on Artificial Intelligence in Healthcare}, isbn = {9783031672842}, issn = {1611-3349}, location = {Swansea, United Kingdom}, pages = {160--171}, publisher = {Springer Nature}, title = {{Enhancing predictive accuracy in embryo implantation: The Bonna algorithm and its clinical implications}}, doi = {10.1007/978-3-031-67285-9_12}, volume = {14976}, year = {2024}, }