@inproceedings{17426, abstract = {The robustness of neural networks against input perturbations with bounded magnitude represents a serious concern in the deployment of deep learning models in safety-critical systems. Recently, the scientific community has focused on enhancing certifiable robustness guarantees by crafting 1-Lipschitz neural networks that leverage Lipschitz bounded dense and convolutional layers. Although different methods have been proposed in the literature to achieve this goal, understanding the performance of such methods is not straightforward, since different metrics can be relevant (e.g., training time, memory usage, accuracy, certifiable robustness) for different applications. For this reason, this work provides a thorough theoretical and empirical comparison between methods by evaluating them in terms of memory usage, speed, and certifiable robust accuracy. The paper also provides some guidelines and recommendations to support the user in selecting the methods that work best depending on the available resources. We provide code at https://github.com/berndprach/1LipschitzLayersCompared.}, author = {Prach, Bernd and Brau, Fabio and Buttazzo, Giorgio and Lampert, Christoph}, booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition}, location = {Seattle, WA, United States}, pages = {24574--24583}, publisher = {Computer Vision Foundation}, title = {{1-Lipschitz layers compared: Memory, speed, and certifiable robustness}}, doi = {10.1109/CVPR52733.2024.02320}, 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}, } @misc{17488, abstract = {Behavioural data for Pokusaeva, Satapathy et al. Relevant information can be found in the 'README.txt' file.}, author = {Satapathy, Roshan K and Jösch, Maximilian A and Symonova, Olga and Pokusaeva, Victoria}, keywords = {drosophila, behaviour, locomotion, gap junctions}, publisher = {Institute of Science and Technology Austria}, title = {{Bilateral interactions of optic-flow sensitive neurons coordinate course control in flies}}, doi = {10.15479/AT:ISTA:17488}, year = {2024}, } @phdthesis{17490, abstract = {Deep learning is essential in numerous applications nowadays, with many recent advancements made possible by training very large models. Despite their broad applicability, training neural networks is often time-intensive, and it is usually impractical to manage large models and datasets on a single machine. To address these issues, distributed deep learning training has become increasingly important. However, distributed training requires synchronization among nodes, and the mini-batch stochastic gradient descent algorithm places a significant load on network connections. A possible solution to tackle the synchronization bottleneck is to reduce a message size by lossy compression. In this thesis, we investigate systems and algorithmic approaches to communication compression during training. From the systems perspective, we demonstrate that a common approach of expensive hardware overprovisioning can be replaced through a thorough system design. We introduce a framework that introduces efficient software support for compressed communication in machine learning applications, applicable to both multi-GPU single-node training and larger-scale multi-node training. Our framework integrates with popular ML frameworks, providing up to 3x speedups for multi-GPU nodes based on commodity hardware and order-of-magnitude improvements in the multi-node setting, with negligible impact on accuracy. Also, we consider an application of our framework to different communication schemes, such as Fully Sharded Data Parallel. We provide strong convergence guarantees for the compression in such a setup. Empirical validation shows that our method preserves model accuracy for GPT-family models with up to 1.3 billion parameters, while completely removing the communication bottlenecks of non-compressed alternatives, providing up to 2.2x speedups end-to-end. From the algorithmic side, we propose a general framework that dynamically adjusts the degree of compression across a model's layers during training. This approach enhances overall compression and results in significant speedups without compromising accuracy. Our algorithm utilizes an adaptive algorithm that automatically selects the optimal compression parameters for model layers, ensuring the best compression ratio while adhering to an error constraint. Our method is effective across all existing families of compression methods. It achieves up to 2.5x faster training and up to a 5x improvement in compression compared to efficient implementations of current approaches. Additionally, LGreCo can complement existing adaptive algorithms. }, author = {Markov, Ilia}, issn = {2663-337X}, pages = {102}, publisher = {Institute of Science and Technology Austria}, title = {{Communication-efficient distributed training of deep neural networks : An algorithms and systems perspective}}, doi = {10.15479/at:ista:17490}, 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}, } @inproceedings{18068, abstract = {We study the following refinement relation between nondeterministic state-transition models: model ℬ strategically dominates model 𝒜 iff every deterministic refinement of 𝒜 is language contained in some deterministic refinement of ℬ. While language containment is trace inclusion, and the (fair) simulation preorder coincides with tree inclusion, strategic dominance falls strictly between the two and can be characterized as "strategy inclusion" between 𝒜 and ℬ: every strategy that resolves the nondeterminism of 𝒜 is dominated by a strategy that resolves the nondeterminism of ℬ. Strategic dominance can be checked in 2-ExpTime by a decidable first-order Presburger logic with quantification over words and strategies, called resolver logic. We give several other applications of resolver logic, including checking the co-safety, co-liveness, and history-determinism of boolean and quantitative automata, and checking the inclusion between hyperproperties that are specified by nondeterministic boolean and quantitative automata.}, author = {Henzinger, Thomas A and Mazzocchi, Nicolas Adrien and Sarac, Naci E}, booktitle = {35th International Conference on Concurrency Theory}, isbn = {9783959773393}, issn = {1868-8969}, location = {Calgary, Canada}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Strategic dominance: A new preorder for nondeterministic processes}}, doi = {10.4230/LIPIcs.CONCUR.2024.29}, volume = {311}, year = {2024}, } @phdthesis{18076, abstract = {The new era of Ge has opened up new possibilities in quantum computing. The maturity of Ge spin qubits is unquestioned, while hybrid semiconductor-superconductor Ge circuits are on track to enter the game. Gate-tunable transmons (gatemons) employing semiconductor Josephson junctions have recently emerged as building blocks for such hybrid quantum circuits. In this thesis, we present a gatemon fabricated in planar Germanium. We induce superconductivity in a two-dimensional hole gas by evaporating aluminum atop a thin spacer, which separates the superconductor from the Ge quantum well. The Josephson junction is then integrated into an Xmon circuit and capacitively coupled to a transmission line resonator. We showcase the qubit tunability in a broad frequency range with resonator and two-tone spectroscopy. Time-domain characterizations reveal energy relaxation and coherence times up to 75 ns. Our results, combined with the recent advances in the spin qubit field, pave the way towards novel hybrid and protected qubits in a group IV, CMOS-compatible material.}, author = {Sagi, Oliver}, issn = {2663-337X}, pages = {111}, publisher = {Institute of Science and Technology Austria}, title = {{Hybrid circuits on planar Germanium}}, doi = {10.15479/at:ista:18076}, 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}, } @article{18087, abstract = {We present a theory describing the interaction of structured light, such as light carrying orbital angular momentum, with molecules. The light-matter interaction Hamiltonian we derive is expressed through couplings between spherical gradients of the electric field and the (transition) electric multipole moments of a particle of any nontrivial rotation point group. Our model can therefore accommodate an arbitrary complexity of the molecular and electric field structure, and it can be straightforwardly extended to atoms or nanostructures. Applying this framework to rovibrational spectroscopy of molecules, we uncover the general mechanism of angular momentum exchange between the spin and orbital angular momenta of light, molecular rotation, and its center-of-mass motion. We show that the nonzero vorticity of Laguerre-Gaussian beams can strongly enhance certain rovibrational transitions that are considered forbidden in the case of nonhelical light. We discuss the experimental requirements for the observation of these forbidden transitions in state-of-the-art spatially resolved spectroscopy measurements.}, author = {Maslov, Mikhail and Koutentakis, Georgios and Hrast, Mateja and Heckl, Oliver H. and Lemeshko, Mikhail}, issn = {2643-1564}, journal = {Physical Review Research}, number = {3}, publisher = {American Physical Society}, title = {{Theory of angular momentum transfer from light to molecules}}, doi = {10.1103/physrevresearch.6.033277}, volume = {6}, year = {2024}, } @phdthesis{18088, abstract = {Instant messaging applications like Whatsapp, Signal or Telegram have become ubiquitous in today's society. Many of them provide not only end-to-end encryption, but also security guarantees even when the key material gets compromised. These are achieved through frequent key update performed by users. In particular, the compromise of a group key should preserve confidentiality of previously exchanged messages (forward secrecy), and a subsequent key update will ensure security for future ones (post-compromise security). Though great protocols for one-on-one communication have been known for some time, the design of ones that scale efficiently for larger groups while achieving akin security guarantees is a hard problem. A great deal of research has been aimed at this topic, much of it under the umbrella of the Messaging Layer Security (MLS) working group at the IETF. Started in 2018, this joint effort by academics and industry culminated in 2023 with the publication of the first standard for secure group messaging [IETF, RFC9420]. At the core of secure group messaging is a cryptographic primitive termed Continuous Group Key Agreement, or CGKA [Alwen et al. 2021], that essentially allows a changing group of users to agree on a common key with the added functionality security against compromises is achieved by users asynchronously issuing a key update. In this thesis we contribute to the understanding of CGKA across different angles. First, we present a new technique to effect dynamic operations in groups, i.e., add or remove members, that can be more efficient that the one employed by MLS in certain settings. Considering the setting of users belonging to multiple overlapping groups, we then show lowerbounds on the communication cost of constructions that leverage said overlap, at the same time showing protocols that are asymptotically optimal and efficient for practical settings, respectively. Along the way, we show that the communication cost of key updates in MLS is average-cost optimal. An important feature in CGKA protocols, particularly for big groups, is the possibility of executing several group operations concurrently. While later versions of MLS support this, they do at the cost of worsening the communication efficiency of future group operations. In this thesis we introduce two new protocols that permit concurrency without any negative effect on efficiency. Our protocols circumvent previously existing lower bounds by satisfying a new notion of post-compromise security that only asks for security to be re-established after a certain number of key updates have taken place. While this can be slower than MLS in terms of rounds of communication, we show that it leads to more efficient overall communication. Additionally, we introduce a new technique that allows group members to decrease the information they need to store and download, which makes one of our protocols enjoy much lower download cost than any other existing CGKA constructions. }, author = {Pascual Perez, Guillermo}, issn = {2663-337X}, pages = {239}, publisher = {Institute of Science and Technology Austria}, title = {{On the efficiency and security of secure group messaging}}, doi = {10.15479/at:ista:18088}, year = {2024}, } @article{18107, abstract = {We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions d∈{1,2,3} . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order adρ2+2/d, where a is the p-wave scattering length of the repulsive interaction and ρ is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260).}, author = {Lauritsen, Asbjørn Bækgaard and Seiringer, Robert}, issn = {2050-5094}, journal = {Forum of Mathematics, Sigma}, publisher = {Cambridge University Press}, title = {{Pressure of a dilute spin-polarized Fermi gas: Lower bound}}, doi = {10.1017/fms.2024.56}, volume = {12}, 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}, } @inproceedings{18117, abstract = {We investigate parameter-efficient fine-tuning (PEFT) methods that can provide good accuracy under limited computational and memory budgets in the context of large language models (LLMs). We present a new PEFT method called Robust Adaptation (RoSA) inspired by robust principal component analysis that jointly trains low-rank and highly-sparse components on top of a set of fixed pretrained weights to efficiently approximate the performance of a full-fine-tuning (FFT) solution. Across a series of challenging generative tasks such as grade-school math and SQL query generation, which require fine-tuning for good performance, we show that RoSA outperforms LoRA, pure sparse fine-tuning, and alternative hybrid methods at the same parameter budget, and can even recover the performance of FFT on some tasks. We provide system support for RoSA to complement the training algorithm, specifically in the form of sparse GPU kernels which enable memory- and computationally-efficient training, and show that it is also compatible with low-precision base weights, resulting in the first joint representation combining quantization, low-rank and sparse approximations. Our code is available at https://github.com/IST-DASLab/RoSA.}, author = {Nikdan, Mahdi and Tabesh, Soroush and Crncevic, Elvir and Alistarh, Dan-Adrian}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, issn = {2640-3498}, location = {Vienna, Austria}, pages = {38187--38206}, publisher = {ML Research Press}, title = {{RoSA: Accurate parameter-efficient fine-tuning via robust adaptation}}, 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}, } @article{18174, abstract = {We investigate the phase ordering (pattern formation) of systems of two-dimensional core–shell particles using Monte Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential having a hard core and a repulsive square shoulder. Our simulations show that on cooling, the liquid state structure becomes increasingly characterized by long wavelength density modulations and on further cooling forms a variety of other phases, including clustered, striped, and other patterned phases. In DFT, the hard core part of the potential is treated using either fundamental measure theory or a simple local density approximation, whereas the soft shoulder is treated using the random phase approximation. The different DFTs are benchmarked using large-scale grand-canonical-MC and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities and shortcomings. We find that having the liquid state static structure factor S(k) for wavenumber k is sufficient to identify the Fourier modes governing both the liquid and solid phases. This allows us to identify from easier-to-obtain liquid state data the wavenumbers relevant to the periodic phases and to predict roughly where in the phase diagram these patterned phases arise.}, author = {Wassermair, Michael and Kahl, Gerhard and Roth, Roland and Archer, Andrew J.}, issn = {1089-7690}, journal = {The Journal of chemical physics}, number = {12}, publisher = {AIP Publishing}, title = {{Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system}}, doi = {10.1063/5.0226954}, volume = {161}, year = {2024}, } @article{18266, abstract = {Matrix games are the most basic model in game theory, and yet robustness with respect to small perturbations of the matrix entries is not fully understood. In this paper, we introduce value positivity and uniform value positivity, two properties that refine the notion of optimality in the context of polynomially perturbed matrix games. The first concept captures how the value depends on the perturbation parameter, and the second consists of the existence of a fixed strategy that guarantees the value of the unperturbed matrix game for every sufficiently small positive parameter. We provide polynomial-time algorithms to check whether a polynomially perturbed matrix game satisfies these properties. We further provide the functional form for a parameterized optimal strategy and the value function. Finally, we translate our results to linear programming and stochastic games, where value positivity is related to the existence of robust solutions.}, author = {Chatterjee, Krishnendu and Oliu-Barton, Miquel and Saona Urmeneta, Raimundo J}, issn = {1526-5471}, journal = {Mathematics of Operations Research}, number = {4}, pages = {2433--3282}, publisher = {Institute for Operations Research and the Management Sciences}, title = {{Value-positivity for matrix games}}, doi = {10.1287/moor.2022.0332}, volume = {50}, year = {2024}, } @phdthesis{18301, abstract = {Physics simulation in computer graphics can bring triangle meshes into topologically invalid states. The method in this thesis contributed to Heiss-Synak* and Kalinov* et al. [2024] who devised a non-manifold hybrid surface tracker—a surface tracker that repairs explicit non-manifold triangle meshes with the help of the implicit domain. Specifically, this thesis provides an algorithm for filling the holes that are left after removing problematic parts of the mesh.}, author = {Etemadihaghighi, Arian}, issn = {2791-4585}, keywords = {surface tracking, non-manifold, hole-filling, topology change, multi-material, solid-modeling}, pages = {39}, publisher = {Institute of Science and Technology Austria}, title = {{Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking}}, doi = {10.15479/at:ista:18301}, year = {2024}, } @phdthesis{18443, abstract = {In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between the hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they conjecture an equivalence between categories of BBB and BAA-branes. At the classical level, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on algebraic integrable systems. In this thesis, we investigate the T-duality relation between hyperkähler structures and the corresponding branes on affine torus bundles. We use the techniques of generalized geometry to show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems. We also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform we upgrade the T-duality between generalized branes to T-duality of submanifolds endowed with U(1)-bundles and connections. This T-duality in the appropriate context specializes to T-duality between BBB and BAA-branes. }, author = {Sisak, Maria A}, issn = {2663-337X}, keywords = {hyperkaehler geometry, branes, mirror symmetry, T-duality}, pages = {178}, publisher = {Institute of Science and Technology Austria}, title = {{T-dual branes on hyperkähler manifolds}}, doi = {10.15479/at:ista:18443}, year = {2024}, }