It is shown that if a triple of distinct positive integers ( a,b,c) were to exist such that a n + b n = c n for some odd integer n≥3, then it must be Pythagorean, i.e. a 2 + b 2 = c 2 must hold too, from which a contradiction arises since this is possible only if either a or b are zero. We arrive at this conclusion by investigating the (partial) trace of a model hamiltonian operator whose energy levels correspond to those of the so-called Hückel hamiltonian applied to rings containing an odd number of atoms lying on a Möbius strip rather than a planar topology. Furthermore, the contradictory nature of our result implies the correctness of the associated statement contained in the famous Fermat’s Last Theorem. Given the use of concepts from quantum mechanics and matrix algebra unknown at his time, and the fact that the essence of the present proof may not fit within a margin of a typical book, mystery still remains over Pierre de Fermat’s demonstrationem mirabilem.

A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the first step towards constructing a useful quantum computer. There are currently three approaches for exhibiting proofs of quantumness: (i) Inverting a classically-hard one-way function (e.g. using Shor’s algorithm). This seems technologically out of reach. (ii) Sampling from a classically-hard-to-sample distribution (e.g. BosonSampling). This may be within reach of near-term experiments, but for all such tasks known verification requires exponential time. (iii) Interactive protocols based on cryptographic assumptions. The use of a trapdoor scheme allows for efficient verification, and implementation seems to require much less resources than (i), yet still more than (ii). In this work we propose a significant simplification to approach (iii) by employing the random oracle heuristic. (We note that we do not apply the Fiat-Shamir paradigm.) We give a two-message (challenge-response) proof of quantumness based on any trapdoor claw-free function. In contrast to earlier proposals we do not need an adaptive hard-core bit property. This allows the use of smaller security parameters and more diverse computational assumptions (such as Ring Learning with Errors), significantly reducing the quantum computational effort required for a successful demonstration.

Metabolic reprogramming is a hallmark of cancer, yet how oncogenic drivers shape tumor metabolism across disease progression remains incompletely understood. In this study, we present iMSEA (in silico Metabolic State and Enrichment Analysis), a computational framework that infers flux-based metabolic states from omics profiles. Applying iMSEA to isogenic BRCA1-mutant and BRCA1-wild-type ovarian cancer cells, we identified a shift toward glycolysis, nucleotide biosynthesis, and redox imbalance, coupled with impaired oxidative phosphorylation. These predictions were validated with metabolomics, Seahorse, and SCENITH assays, demonstrating the accuracy of our approach. Extending the analysis to homologous recombination deficient patient tumors at single-cell resolution, we found that BRCA1-deficient cancers display heightened metabolic activity and site-specific adaptations, including altered central carbon fluxes, mitochondrial function, nucleotide biosynthesis, and lipid metabolism. By linking transcriptional programs to functional metabolic states, iMSEA reveals hidden metabolic liabilities in BRCA1-deficient ovarian cancer and provides a broadly applicable strategy for dissecting metabolic heterogeneity and therapeutic vulnerabilities in cancer.

We introduce a protocol between a classical polynomial-Time verifier and a quantum polynomial-Time prover that allows the verifier to securely delegate to the prover the preparation of certain single-qubit quantum states The prover is unaware of which state he received and moreover, the verifier can check with high confidence whether the preparation was successful. The delegated preparation of single-qubit states is an elementary building block in many quantum cryptographic protocols. We expect our implementation of 'random remote state preparation with verification', a functionality first defined in (Dunjko and Kashefi 2014), to be useful for removing the need for quantum communication in such protocols while keeping functionality. The main application that we detail is to a protocol for blind and verifiable delegated quantum computation (DQC) that builds on the work of (Fitzsimons and Kashefi 2018), who provided such a protocol with quantum communication. Recently, both blind an verifiable DQC were shown to be possible, under computational assumptions, with a classical polynomial-Time client (Mahadev 2017, Mahadev 2018). Compared to the work of Mahadev, our protocol is more modular, applies to the measurement-based model of computation (instead of the Hamiltonian model) and is composable. Our proof of security builds on ideas introduced in (Brakerski et al. 2018).

A non-interactive zero-knowledge (NIZK) proof system for a language (Formula Presented) allows a prover (who is provided with an instance (Formula Presented), and a witness w for x) to compute a classical certificate π for the claim that (Formula Presented) such that π has the following properties: 1) π can be verified efficiently, and 2) π does not reveal any information about w, besides the fact that it exists (i.e. that (Formula Presented)). NIZK proof systems have recently been shown to exist for all languages in NP in the common reference string (CRS) model and under the learning with errors (LWE) assumption. We initiate the study of NIZK arguments for languages in QMA. An argument system differs from a proof system in that the honest prover must be efficient, and that it is only sound against (quantum) polynomial-time provers. Our first main result is the following: if LWE is hard for quantum computers, then any language in QMA has an NIZK argument with preprocessing. The preprocessing in our argument system consists of (i) the generation of a CRS and (ii) a single (instance-independent) quantum message from verifier to prover. The instance-dependent phase of our argument system, meanwhile, involves only a single classical message from prover to verifier. Importantly, verification in our protocol is entirely classical, and the verifier needs not have quantum memory; its only quantum actions are in the preprocessing phase. NIZK proofs of (classical) knowledge are widely used in the construction of more advanced cryptographic protocols, and we expect the quantum analogue to likewise find a broad range of applications. In this respect, the fact that our protocol has an entirely classical verification phase is particularly appealing. Our second contribution is to extend the notion of a classical proof of knowledge to the quantum setting. We introduce the notions of arguments and proofs of quantum knowledge (AoQK/PoQK), and we show that our non-interactive argument system satisfies the definition of an AoQK, which extends its domain of usefulness with respect to cryptographic applications. In particular, we explicitly construct an extractor which can recover a quantum witness from any prover who is successful in our protocol. We also show that any language in QMA has an (interactive) proof of quantum knowledge, again by exhibiting a particular proof system for all languages in QMA and constructing an extractor for it.

This thesis addresses the challenge of the culturally dormant long tail in television archives. It argues that the issue lies not only in access, but also in the mismatch between a dynamic media and a static archival paradigm, which often overlooks the experiential value for the public, especially non-specialist and casual audiences. My research activates a fluid mode for archival practices by reframing television archives through a conceptual lens called Personal Memories of the Everyday, and unlocks new forms of resonance beyond traditional notions of their historical and cultural significance. This activation unfolds in two stages. First, the encoding stage transforms archival content into representations of memories made through watching using a novel computational pipeline. It puts forward a memory-based video representation through text-video joint embeddings, with the guidance of a phenomenology-focused meta-happening description. These embeddings aim to link sensory richness with nuanced human interpretation in a latent, open-ended form that resists static meaning. Second, the decoding stage reimagines the engagement with archives as mediated memory practices. To demonstrate the conceptual and computational propositions, two demonstrative interfaces were developed and evaluated with the archive of Radio Télévision Suisse (RTS) through the mechanism of emergent narrative and serendipitous discovery. As a result, users can form dynamic, universal, yet deeply personal connections with archival content, bridging and negotiating the private and the public, the present and the past, the embedded and the embodied. In culmination, this research lays the groundwork for a profound transformation in the future of television archives through computational mediation, reimagining archival engagement not as static retrieval but as an ongoing, inclusive, dialogical co-creation of meaning. It offers a tangible path forward for cultural heritage to evolve into vibrant, human-centred memory ecosystems, ensuring enduring relevance for our shared televisual past across time and culture.

X-ray free-electron lasers (XFELs) provide highly intense, femtosecond X-ray pulses that are ideal for the study of photoionization dynamics in atoms and molecules. This thesis aims to follow and understand the X-ray induced fragmentation dynamics of molecules on the ultrafast timescale. It comprises two main bodies of work: first, the commissioning of a Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) experimental setup at the Maloja endstation of SwissFEL; and second, the investigation of ultrafast dynamics in ethanol following core ionization above the oxygen K-edge, with focus on the intramolecular hydrogen transfer and roaming mechanisms.

The COLTRIMS spectrometer resolution was characterized with the recoil momentum of He+ ions upon X-ray ionization. The resolution of the COLTRIMS spectrometer was determined to be < 1 a.u. The capability of ion coincidence spectroscopy was demonstrated with the resonant photofragmentation of CO2, showing evidence that the bent Renner-Teller state was populated after ionization at the O 1s â Ï â resonance. More complex molecular dynamics was observed in the fragmentation of ethanol upon ionization in the O K-edge region. The kinetic energy release spectra of the coincident channels containing H2+ and H3+ ions suggested that the ethanol dication decays into the roaming intermediate (H2 â C2H4O)2+. Experimental evidence of the roaming mechanism formed the basis for a time-resolved study on ethanol.

For the second work, the dynamics of H+, H2+ and H3+ ions that were formed after the core ionization of ethanol were studied using time-resolved ion time-of-flight spectroscopy, employing an X-ray pump/near-infrared (NIR) laser probe scheme. The formation of H3+ ions from the roaming mechanism is consistent with previous studies, but with a faster timescale of 145 ± 40 fs. Unlike H3+ ions, H2+ ions are formed from the molecular rearrangement of highly excited doubly charged ethanol cations within 81 ± 12 fs. Lastly, H+ ions are formed from the progressive fragmentation of the destabilized ethanol dication. They exhibit interesting dynamics that suggest the coupling of electronic states of the excited dication. These results reveal dynamics that shed light on the effect of core ionization in populating excited cationic states, resulting in phenomena such as a faster roaming time and an increase in kinetic energy of the ejected fragment ions. Future work will be directed towards molecular dynamics simulations to support the current interpretations and investigation of hydrogen transfer in other molecules. In summary, by studying ultrafast X-ray induced dynamics, this thesis provides insights into fundamental processes in nature such as radiation damage and the formation of simple molecules in interstellar medium.

Diseases, including those related to aging and cancer, often begin with genetic mutations, which can be caused by damage to the genome. Our genome is constantly exposed to sources of damage which may be endogenous, e.g., replication errors, or exogenous, e.g., radiation exposure. Proper identification and repair of DNA damage is therefore essential for cellular health and thus for preventing disease. To help prevent the propagation of mutations, cells have evolved surveillance systems throughout the cell cycle. These surveillance systems, known as checkpoints, arrest the cell cycle when certain conditions are met, such as in the presence of genomic damage. However, after prolonged arrest, many of these checkpoints are overridden, and the cell begins the next cell cycle despite the presence of genomic damage, thus propagating damage to the daughter cell. The choice between staying arrested at checkpoints and allowing time for repair or overriding checkpoints and dividing determines the cell's fate: cells that override checkpoints have a different chance of survival as cells unable to do so. Yet, the biological reasons behind this distinction remain unclear.

To better understand this survival difference and its biological significance, we investigated the consequences of checkpoint override on cellular survival. We used yeast as a model organism, allowing simple genetic manipulations to precisely induce DNA damage and control the cell cycle. By additionally using optogenetics to induce override at different time points after checkpoint arrest, the biological importance of override timing was observed: cell survival rates peaked around the same time as the wild-type override time and slowly decreased when override took place earlier or later.

Subsequently, we studied the mechanism behind the difference in survival of overriding and non-overriding cells. This mechanism could be a purely statistical argument, as at the checkpoint there is only one cell and after override there are two, the mother cell and the new daughter cell, thus increasing the chances of survival. We tested this mechanism by adding a fluorescent tag and following the location of the broken DNA fragments after override. In the majority of cases, we observed that the DNA fragments did not segregate symmetrically between the two cells post-override, and thus, there was only one cell that had all the DNA fragments needed for repair.

Alternatively, the mechanism behind the difference in survival could be due to a new accessibility of various repair pathways after override, thereby increasing the chance of repair. We tested this by using the auxin-inducible degron system to knock down key repair proteins during and after override to determine if that repair protein was required post-override for survival. A dependency on Rad1 and a partial dependence on Dnl4 and Nej1 in overriding cells was observed, suggesting that during or after override, cells rely on microhomology-mediated end joining, an error-prone repair pathway, for repair. \newline \newline Overall, these findings shed light on the biological significance of checkpoint override and uncover a new role for microhomology-mediated end joining, both of which we expect to be highly relevant to expand our knowledge of disease, as malfunctioning checkpoints and erroneous repair can lead to genomic instability.

Audiovisual (AV) archives constitute the mnemonic record of the 20th and 21st centuries, capturing everyday life, historical events, and culturally significant moments through their rich multimodality. While large-scale digitisation efforts and the increasing production of born-digital materials have expanded these collections, access for the general public remains limited due to multiple barriers. First, a structural access gap remains, as legal and institutional constraints continue to restrict public dissemination despite widespread digitisation. Second, a representational gap stems from the limitations of metadata-driven interfaces in capturing the multimodal and exploratory nature of AV archives. Third, a participatory gap emerges when immersive technologies favour visual spectacle over performative potential.

This inquiry addresses the challenge of enhancing access to digital AV archives through situated, embodied experiences tailored to diverse museum-going audiences. It investigates how interactive and immersive installations can support situated encounters with AV archives, through a transdisciplinary approach that integrates theoretical inquiry, technical development, and empirical evaluation. The research engages with collections spanning dance performances, sports events, television broadcasts, concert recordings, and early silent cinema, exploring how each may be experienced anew through computational and spatial reconfigurations.

The dissertation is structured around two interrelated perspectives. First, it investigates how visitors engage with AV archives in embodied ways through interactive technologies that spatialise archival content as an architecture of participation. Visitors co-construct archival paths through their interactions, shaping both their own experience and that of other spectators. To capture this process, a five-dimensional embodied framework is proposed. Second, the dissertation examines how computational methods are employed to sculpt AV archives for embodied exploration. This includes processes of datafication and vectorisation, forms of algorithmic vision that transform audiovisual content into feature spaces, and computational mappings that render these spaces navigable within immersive systems.

In conclusion, the dissertation reflects on the transformation of AV archives into situated, interactive experiences as a practice of experimental museology. It offers both practical insights for cultural heritage stakeholders and a conceptual framing informed by the theories of Deleuze's virtuality and Simondon's transduction. Through these lenses, the research conceptualises the archive's transformation, from a digital repository to an architecture of participation and, ultimately, to emergent archival paths, as a creative process enacted by both designers and visitors.

This thesis investigates structure and computation in high-dimensional complex systems, with a focus on dynamical processes on graphs and learning in neural networks. Both settings involve many interacting variables coupled through disorder, that give rise to rich emergent phenomena. A central objective is to understand how microscopic interactions give rise to macroscopic behavior, and how phase transitions delineate qualitatively distinct regimes. In the first part, we extend methods from statistical physics to study dynamical processes on graphs. We develop the backtracking dynamical cavity method, which characterizes attractors by tracing dynamics backward from final states. This approach gives new insights into quenches in spin glasses and dynamical phase transitions in cellular automata and opinion dynamics on random graphs. In the second part, we turn to neural networks and examine how learning dynamics shape internal representations and mechanisms. We focus on sequence models and analyse them using solvable toy models, controlled experiments, and interpretability tools. We identify a phase transition between positional and semantic learning in attention models, characterize distinct counting strategies in small transformers, and show soft labels can reveal information about held-out samples in dataset distillation. With these insights, this thesis contributes new analytical methods for graph dynamics and theoretical insights into neural network internals.