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The symmetry of the superconducting order parameter, or simply the ``gap'', provides certain constraints on the actual mechanism that gives rise to pairing and ultimately to superconductivity. In this work we continue to investigate the possible symmetries that can arise, particularly below $T_c$, for a generic tight-binding model. We first examine the 1D case to better illustrate the prevalence of symmetry-breaking transitions below $T_c$, and then the more realistic 2D case. In both cases we illustrate the implication for spectroscopic investigations of the energy gap by calculating the density of states for different temperatures below $T_c$. The result is a very different signature near $T_c$ compared to that near $T=0$. A complete picture of the superconducting symmetry can only be attained if measurements are made over the entire temperature range., Comment: 15 pages, 17 figures. We wish to acknowledge the memory of Jan Zaanen with this manuscript. His animated discussion of a multitude of topics at conferences and accompanying meals will always be remembered. His enthusiasm for discovery and for "new ways of thinking about things'' remain an inspiration for those who knew him

Dipolar supersolids--quantum states which are simultaneously superfluid and solid--have had their superfluid nature rigorously tested, while its solid nature remains uncharted. Arguably, the defining characteristic of a solid is the existence of elastic shear waves. In this work, we investigate transverse wave packet propagation in dipolar supersolids with triangular and honeycomb structure. Remarkably, the honeycomb supersolid displays anomalous dispersion, supporting waves traveling faster than the transverse speed of sound: a supersonic shear wave. For both supersolid phases, we calculate the shear modulus, a key parameter that quantifies the material's rigidity. Our findings are pertinent to current experimental efforts scrutinizing the fundamental properties of supersolids., Comment: 9 pages, 6 figures

In open quantum many-body systems, the theoretical description of resonant states of many particles strongly coupled to the continuum can be challenging. Such states are commonplace in, for example, exotic nuclei and hadrons, and can reveal important information about the underlying forces at play in these systems. In this work, we demonstrate that the complex-augmented eigenvector continuation (CA-EC) method, originally formulated for the two-body problem with uniform complex scaling, can reliably perform bound-to-resonance extrapolations for genuine three-body resonances having no bound subsystems. We first establish that three-body bound-to-resonance extrapolations are possible by benchmarking different few-body approaches, and we provide arguments to explain how the extrapolation works in the many-body case. We furthermore pave the way towards scalable resonance extrapolations in many-body systems by showing that the CA-EC method also works in the Berggren basis, studying a realistic application using the Gamow shell model., Comment: 11 pages, 6 figures

Users of decentralized finance (DeFi) applications face significant risks from adversarial actions that manipulate the order of transactions to extract value from users. Such actions -- an adversarial form of what is called maximal-extractable value (MEV) -- impact both individual outcomes and the stability of the DeFi ecosystem. MEV exploitation, moreover, is being institutionalized through an architectural paradigm known Proposer-Builder Separation (PBS). This work introduces a system called PROF (PRotected Order Flow) that is designed to limit harmful forms of MEV in existing PBS systems. PROF aims at this goal using two ideas. First, PROF imposes an ordering on a set ("bundle") of privately input transactions and enforces that ordering all the way through to block production -- preventing transaction-order manipulation. Second, PROF creates bundles whose inclusion is profitable to block producers, thereby ensuring that bundles see timely inclusion in blocks. PROF is backward-compatible, meaning that it works with existing and future PBS designs. PROF is also compatible with any desired algorithm for ordering transactions within a PROF bundle (e.g., first-come, first-serve, fee-based, etc.). It executes efficiently, i.e., with low latency, and requires no additional trust assumptions among PBS entities. We quantitatively and qualitatively analyze incentive structure of PROF, and its utility to users compared with existing solutions. We also report on inclusion likelihood of PROF transactions, and concrete latency numbers through our end-to-end implementation., Comment: 21 pages, 14 figures

Over the past year, the field of Natural Language Generation (NLG) has experienced an exponential surge, largely due to the introduction of Large Language Models (LLMs). These models have exhibited the most effective performance in a range of domains within the Natural Language Processing and Generation domains. However, their application in domain-specific tasks, such as paraphrasing, presents significant challenges. The extensive number of parameters makes them difficult to operate on commercial hardware, and they require substantial time for inference, leading to high costs in a production setting. In this study, we tackle these obstacles by employing LLMs to develop three distinct models for the paraphrasing field, applying a method referred to as sequence-level knowledge distillation. These distilled models are capable of maintaining the quality of paraphrases generated by the LLM. They demonstrate faster inference times and the ability to generate diverse paraphrases of comparable quality. A notable characteristic of these models is their ability to exhibit syntactic diversity while also preserving lexical diversity, features previously uncommon due to existing data quality issues in datasets and not typically observed in neural-based approaches. Human evaluation of our models shows that there is only a 4% drop in performance compared to the LLM teacher model used in the distillation process, despite being 1000 times smaller. This research provides a significant contribution to the NLG field, offering a more efficient and cost-effective solution for paraphrasing tasks., Comment: Published in: 2024 5th International Conference on Advancements in Computational Sciences (ICACS) with IEEE

Paraphrase generation is a pivotal task in natural language processing (NLP). Existing datasets in the domain lack syntactic and lexical diversity, resulting in paraphrases that closely resemble the source sentences. Moreover, these datasets often contain hate speech and noise, and may unintentionally include non-English language sentences. This research introduces ParaFusion, a large-scale, high-quality English paraphrase dataset developed using Large Language Models (LLM) to address these challenges. ParaFusion augments existing datasets with high-quality data, significantly enhancing both lexical and syntactic diversity while maintaining close semantic similarity. It also mitigates the presence of hate speech and reduces noise, ensuring a cleaner and more focused English dataset. Results show that ParaFusion offers at least a 25% improvement in both syntactic and lexical diversity, measured across several metrics for each data source. The paper also aims to set a gold standard for paraphrase evaluation as it contains one of the most comprehensive evaluation strategies to date. The results underscore the potential of ParaFusion as a valuable resource for improving NLP applications.

Quantum resonances, i.e., metastable states with a finite lifetime, play an important role in nuclear physics and other domains. Describing this phenomenon theoretically is generally a challenging task. In this work, we combine two established techniques to address this challenge. Complex scaling makes it possible to calculate resonances with bound-state-like methods. Finite-volume simulations exploit the fact that the infinite-volume properties of quantum systems are encoded in how discrete energy levels change as one varies the size of the volume. We apply complex scaling to systems in finite periodic boxes and derive the volume dependence of states in this scenario, demonstrating with explicit examples how one can use these relations to infer infinite-volume resonance energies and lifetimes., Comment: 13 pages, 7 figures, matched published version

The global pandemic situation has severely affected all countries. As a result, almost all countries had to adjust to online technologies to continue their processes. In addition, Sri Lanka is yearly spending ten billion on elections. We have examined a proper way of minimizing the cost of hosting these events online. To solve the existing problems and increase the time potency and cost reduction we have used IoT and ML-based technologies. IoT-based data will identify, register, and be used to secure from fraud, while ML algorithms manipulate the election data and produce winning predictions, weather-based voters attendance, and election violence. All the data will be saved in cloud computing and a standard database to store and access the data. This study mainly focuses on four aspects of an E-voting system. The most frequent problems across the world in E-voting are the security, accuracy, and reliability of the systems. E-government systems must be secured against various cyber-attacks and ensure that only authorized users can access valuable, and sometimes sensitive information. Being able to access a system without passwords but using biometric details has been there for a while now, however, our proposed system has a different approach to taking the credentials, processing, and combining the images, reformatting and producing the output, and tracking. In addition, we ensure to enhance e-voting safety. While ML-based algorithms use different data sets and provide predictions in advance.

The study of open quantum systems (OQSs), i.e., systems interacting with an environment, impacts our understanding of exotic nuclei in low-energy nuclear physics, hadrons, cold-atom systems, or even noisy intermediate-scale quantum computers. Such systems often exhibit resonance states characterized by energy positions and dispersions (or decay widths), the properties of which can be difficult to predict theoretically due to their coupling to the continuum of scattering states. Dealing with this phenomenon poses challenges both conceptually and numerically. For that reason, we investigate how the reduced basis method known as eigenvector continuation (EC), which has emerged as a powerful tool to emulate bound and scattering states in closed quantum systems, can be used to study resonance properties. In particular, we present a generalization of EC that we call conjugate-augmented eigenvector continuation, which is based on the complex-scaling method and designed to predict Gamow-Siegert states, and thus resonant properties of OQSs, using only bound-state wave functions as input., Comment: 12 pages, 10 figures, published version, Python code provided as ancillary files

We analyse the Coulomb breakup of 19C measured at 67A MeV at RIKEN. We use the Coulomb-Corrected Eikonal (CCE) approximation to model the reaction and describe the one-neutron halo nucleus 19C within Halo Effective Field Theory (EFT). At leading order we obtain a fair reproduction of the measured cross section as a function of energy and angle. The description is insensitive to the choice of optical potential, as long as it accurately represents the size of 18C. It is also insensitive to the interior of the 19C wave function. Comparison between theory and experiment thus enables us to infer asymptotic properties of the ground state of 19C: these data put constraints on the one-neutron separation energy of this nucleus and, for a given binding energy, can be used to extract an asymptotic normalisation coefficient (ANC). These results are confirmed by CCE calculations employing next-to-leading order Halo EFT descriptions of 19C: at this order the results for the Coulomb breakup cross section are completely insensitive to the choice of the regulator. Accordingly, this reaction can be used to constrain the one-neutron separation energy and ANC of 19C., Comment: Resubmitted version accepted for publication within the European Physical Journal A

We develop an extension of eigenvector continuation (EC) that makes it possible to extrapolate simulations of quantum systems in finite periodic boxes across large ranges of box sizes. The formal justification for this approach, which we call finite-volume eigenvector continuation (FVEC), is provided by matching periodic functions at different box sizes. As concrete FVEC implementation we use a discrete variable representation based on plane-wave states and present several applications calculated within this framework., Comment: 7 pages, 4 figures, published version

Domain walls in superfluid 3He-B have gained renewed interest in light of experimental progress on confining helium in nanofabricated geometries. Here, we study the effect of strong-coupling corrections on domain wall width and interfacial tension by determining self-consistent solutions to spatially-dependent Ginzburg-Landau equations. We find that the formation of domain walls is generally energetically favored in strong coupling over weak coupling. Calculations were performed over a wide range of temperatures and pressures, showing decreasing interface energy with increasing temperature and pressure. This has implications for the observability of such domain walls in 3He-B, which are of both fundamental interest and form the basis for spatially-modulated pair-density wave states, when stabilized by strong confinement., Comment: 9 pages, 6 figures, accepted version, includes appendix with alternative Wiman beta parameters

Recent advances in experiment and theory suggest that superfluid $^3$He under planar confinement may form a pair density wave (PDW) whereby superfluid and crystalline orders coexist. While a natural candidate for this phase is a unidirectional stripe phase predicted by Vorontsov and Sauls in 2007, recent nuclear magnetic resonance measurements of the superfluid order parameter rather suggest a two-dimensional PDW with noncollinear wavevectors, of possibly square or hexagonal symmetry. In this Letter, we present a general mechanism by which a PDW with the symmetry of a triangular lattice can be stabilized, based on a superfluid generalization of Landau's theory of the liquid-solid transition. A soft-mode instability at finite wavevector within the translationally invariant planar-distorted B phase triggers a transition from uniform superfluid to PDW that is first order due to a cubic term generally present in the PDW free-energy functional. This cubic term also lifts the degeneracy of possible PDW states in favor of those for which wavevectors add to zero in triangles, which in two dimensions uniquely selects the triangular lattice., Comment: main text: 6 pages, 4 figures; supplemental material: 17 pages, 1 figure, 9 animated plots (see ancillary files). v2: published version