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Resolving knowledge conflicts is a crucial challenge in Question Answering (QA) tasks, as the internet contains numerous conflicting facts and opinions. While some research has made progress in tackling ambiguous settings where multiple valid answers exist, these approaches often neglect to provide source citations, leaving users to evaluate the factuality of each answer. On the other hand, existing work on citation generation has focused on unambiguous settings with single answers, failing to address the complexity of real-world scenarios. Despite the importance of both aspects, no prior research has combined them, leaving a significant gap in the development of QA systems. In this work, we bridge this gap by proposing the novel task of QA with source citation in ambiguous settings, where multiple valid answers exist. To facilitate research in this area, we create a comprehensive framework consisting of: (1) five novel datasets, obtained by augmenting three existing reading comprehension datasets with citation meta-data across various ambiguous settings, such as distractors and paraphrasing; (2) the first ambiguous multi-hop QA dataset featuring real-world, naturally occurring contexts; (3) two new metrics to evaluate models' performances; and (4) several strong baselines using rule-based, prompting, and finetuning approaches over five large language models. We hope that this new task, datasets, metrics, and baselines will inspire the community to push the boundaries of QA research and develop more trustworthy and interpretable systems., Comment: Accepted to EMNLP 2024

Manipulating the dispersive characteristics of vibrational waves is beneficial for many applications, e.g., high-precision instruments. architected hierarchical phononic materials have sparked promise tunability of elastodynamic waves and vibrations over multiple frequency ranges. In this article, hierarchical unit-cells are obtained, where features at each length scale result in a band gap within a targeted frequency range. Our novel approach, the ``hierarchical unit-cell template method,'' is an interpretable machine-learning approach that uncovers global unit-cell shape/topology patterns corresponding to predefined band-gap objectives. A scale-separation effect is observed where the coarse-scale band-gap objective is mostly unaffected by the fine-scale features despite the closeness of their length scales, thus enabling an efficient hierarchical algorithm. Moreover, the hierarchical patterns revealed are not predefined or self-similar hierarchies as common in current hierarchical phononic materials. Thus, our approach offers a flexible and efficient method for the exploration of new regions in the hierarchical design space, extracting minimal effective patterns for inverse design in applications targeting multiple frequency ranges.

We consider a "symmetric" quantum droplet in two spatial dimensions, which rotates in a harmonic potential, focusing mostly on the limit of "rapid" rotation. We examine this problem using a purely numerical approach, as well as a semi-analytic Wigner-Seitz approximation (first developed by Baym, Pethick et al.) for the description of the state with a vortex lattice. Within this approximation we assume that each vortex occupies a cylindrical cell, with the vortex-core size treated as a variational parameter. Working with a fixed angular momentum, as the angular momentum increases and depending on the atom number, the droplet accommodates none, few, or many vortices, before it turns to center-of-mass excitation. For the case of a "large" droplet, working with a fixed rotational frequency of the trap $\Omega$, as $\Omega$ approaches the trap frequency $\omega$, a vortex lattice forms, the number of vortices increases, the mean spacing between them decreases, while the "size" of each vortex increases as compared to the size of each cell. In contrast to the well-known problem of contact interactions, where we have melting of the vortex lattice and highly-correlated many-body states, here no melting of the vortex lattice is present, even when $\Omega = \omega$. This difference is due to the fact that the droplet is self-bound. Actually, for $\Omega = \omega$, the "smoothed" density distribution becomes a flat top, very much like the static droplet. When $\Omega$ exceeds $\omega$, the droplet maintains its shape and escapes to infinity, via center-of-mass motion., Comment: 11 pages, 11 figures

We investigate the rotational properties of quantum droplets, which form in a mixture of two Bose-Einstein condensates, in the presence of an anharmonic trapping potential. We identify various phases as the atom number and the angular momentum/angular velocity of the trap vary. These phases include center-of-mass-like excitation (without, or with vortices), vortices of single and multiple quantization, etc. Finally, we compare our results with those of the single-component problem., Comment: 11 pages, 7 figures

The evolution of vector solitons under nonlinearity management is studied. The averaged over strong and rapid modulations in time of the inter-species interactions vector Gross-Pitaevskii equation (GPE) is derived. The averaging gives the appearance of the effective nonlinear quantum pressure depending on the population of the other component. Using this system of equations, the existence and stability of the vector solitons under the action of the strong nonlinearity management (NM) is investigated. Using a variational approach the parameters of NM vector solitons are found. The numerical simulations of the full time-dependent coupled GPE confirms the theoretical predictions.

We evaluate the tendency for different voting methods to promote political compromise and reduce tensions in a society by using computer simulations to determine which voters candidates are incentivized to appeal to. We find that Instant Runoff Voting incentivizes candidates to appeal to a wider range of voters than Plurality Voting, but that it leaves candidates far more strongly incentivized to appeal to their base than to voters in opposing factions. In contrast, we find that Condorcet methods and STAR (Score Then Automatic Runoff) Voting provide the most balanced incentives; these differences between voting methods become more pronounced with more candidates are in the race and less pronounced in the presence of strategic voting. We find that the incentives provided by Single Transferable Vote to appeal to opposing voters are negligible, but that a tweak to the tabulation algorithm makes them substantial.

We investigate the rotational properties of a two-component, two-dimensional self-bound quantum droplet, which is confined in a harmonic potential and compare them with the well-known problem of a single-component atomic gas with contact interactions. For a fixed value of the trap frequency, choosing some representative values of the atom number, we determine the lowest-energy state, as the angular momentum increases. For a sufficiently small number of atoms, the angular momentum is carried via center-of-mass excitation. For larger values, when the angular momentum is sufficiently small, we observe vortex excitation instead. Depending on the actual atom number, one or more vortices enter the droplet. Beyond some critical value of the angular momentum, however, the droplet does not accommodate more vortices and the additional angular momentum is carried via center-of-mass excitation in a "mixed" state. Finally, the excitation spectrum is also briefly discussed., Comment: 11 pages, 7 figures, changes in v2: the title was updated, the overall readability was improved, an error in the unit of $N$ was corrected, a few references were added

For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems (MBPs) with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front, giving a direct estimate on the service life of the material. In this paper, we propose a random walk algorithm able to lead to good numerical approximations of both the concentration profile and the location of the sharp front. Essentially, the proposed scheme decouples the target evolution system in two steps: (i) the ordinary differential equation corresponding to the evaluation of the speed of the moving boundary is solved via an explicit Euler method, and (ii) the associated diffusion problem is solved by a random walk method. To verify the correctness of our random walk algorithm we compare the resulting approximations to results based on a finite element approach with a controlled convergence rate. Our numerical experiments recover well penetration depth measurements of an experimental setup targeting dense rubbers., Comment: 15 pages, 10 figures, 2 tables

The Gaussian phase-space representation can be used to implement quantum dynamics for fermionic particles numerically. To improve numerical results, we explore the use of dynamical diffusion gauges in such implementations. This is achieved by benchmarking quantum dynamics of few-body systems against independent exact solutions. A diffusion gauge is implemented here as a so-called noise-matrix, which satisfies a matrix equation defined by the corresponding Fokker--Planck equation of the phase-space representation. For the physical systems with fermionic particles considered here, the numerical evaluation of the new diffusion gauges allows us to double the practical simulation time, compared with hitherto known analytic noise-matrices. This development may have far reaching consequences for future quantum dynamical simulations of many-body systems.

In stochastic modeling of infectious diseases, it has been established that variations in infectivity affect the probability of a major outbreak, but not the shape of the curves during a major outbreak, which is predicted by deterministic models [Diekmann et al., 2012]. However, such conclusions are derived under idealized assumptions such as the population size tending to infinity, and the individual degree of infectivity only depending on variations in the infectiousness period. In this paper we show that the same conclusions hold true in a finite population representing a medium size city, where the degree of infectivity is determined by the offspring distribution, which we try to make as realistic as possible for SARS-CoV-2. In particular, we consider distributions with fat tails, to incorporate the existence of super-spreaders. We also provide new theoretical results on convergence of stochastic models which allows to incorporate any offspring distribution with a finite variance.

Phase-space representations are a family of methods for dynamics of both bosonic and fermionic systems, that work by mapping the system's density matrix to a quasi-probability density and the Liouville-von Neumann equation of the Hamiltonian to a corresponding density differential equation for the probability. We investigate here the accuracy and the computational efficiency of one approximate phase-space representation, called the fermionic Truncated Wigner Approximation (fTWA), applied to the Fermi-Hubbard model. On a many-body 2D system, with hopping strength and Coulomb $U$ tuned to represent the electronic structure of graphene, the method is found to be able to capture the time evolution of first-order (site occupation) and second-order (correlation functions) moments significantly better than the mean-field, Hartree-Fock method. The fTWA was also compared to results from the exact diagonalization method for smaller systems, and in general the agreement was found to be good. The fully parallel computational requirement of fTWA scales in the same order as the Hartree-Fock method, and the largest system considered here contained 198 lattice sites.

Management of solitons in media with competing quadratic and cubic nonlinearities is investigated. Two schemes, using rapid modulations of a mismatch parameter, and of the Kerr nonlinearity parameter are studied. For both cases, the averaged in time wave equations are derived. In the case of mismatch management, the region of the parameters where stabilization is possible is found. In the case of Kerr nonlinearity management, it is shown that the effective $\chi^{(2)}$ nonlinearity depends on the intensity imbalance between fundamental (FH) and second (SH) harmonics. Predictions obtained from the averaged equations are confirmed by numerical simulations of the full PDE's.

The High Energy Physics community can benefit from a natural synergy in research activities into next-generation large-scale water and scintillator neutrino detectors, now being studied for remote reactor monitoring, discovery and exclusion applications in cooperative nonproliferation contexts. Since approximately 2010, US nonproliferation researchers, supported by the National Nuclear Security Administration (NNSA), have been studying a range of possible applications of relatively large (100 ton) to very large (hundreds of kiloton) water and scintillator neutrino detectors. In parallel, the fundamental physics community has been developing detectors at similar scales and with similar design features for a range of high-priority physics topics, primarily in fundamental neutrino physics. These topics include neutrino oscillation studies at beams and reactors, solar, and geological neutrino measurements, supernova studies, and others. Examples of ongoing synergistic work at U.S. national laboratories and universities include prototype gadolinium-doped water and water-based and opaque scintillator test-beds and demonstrators, extensive testing and industry partnerships related to large area fast position-sensitive photomultiplier tubes, and the development of concepts for a possible underground kiloton-scale water-based detector for reactor monitoring and technology demonstrations. Some opportunities for engagement between the two communities include bi-annual Applied Antineutrino Physics conferences, collaboration with U.S. National Laboratories engaging in this research, and occasional NNSA funding opportunities supporting a blend of nonproliferation and basic science R&D, directed at the U.S. academic community., Comment: contribution to Snowmass 2021

Machine learning models can assist with metamaterials design by approximating computationally expensive simulators or solving inverse design problems. However, past work has usually relied on black box deep neural networks, whose reasoning processes are opaque and require enormous datasets that are expensive to obtain. In this work, we develop two novel machine learning approaches to metamaterials discovery that have neither of these disadvantages. These approaches, called shape-frequency features and unit-cell templates, can discover 2D metamaterials with user-specified frequency band gaps. Our approaches provide logical rule-based conditions on metamaterial unit-cells that allow for interpretable reasoning processes, and generalize well across design spaces of different resolutions. The templates also provide design flexibility where users can almost freely design the fine resolution features of a unit-cell without affecting the user's desired band gap., Comment: Accepted to Extreme Mechanics Letters, 2022

We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose stationary solution is the solution to the time-independent nonlinear Schr\"odinger equation. Constraints are often considered by projection onto the constraint set, here we include them explicitly into the dynamical system. We show the applicability and efficiency of the methods on examples of relevance in modern physics applications., Comment: Note that Eq. (74) here corrects Eq. (74) in the published version

The dynamics of matter waves in the atomic to molecular condensate transition with a time-modulated atomic scattering length is investigated. Both the cases of rapid and slow modulations are studied. In the case of rapid modulations, the average over oscillations for the system is derived. The corresponding conditions for dynamical suppression of the association of atoms into the molecular field, or of second-harmonic generation in nonlinear optical systems, are obtained. For the case of slow modulations, we find resonant enhancement in the molecular field. We then illustrate chaos in the atomic-molecular BEC system. We suggest a sequential application of the two types of modulations, slow and rapid, when producing molecules.

An object's interior material properties, while invisible to the human eye, determine motion observed on its surface. We propose an approach that estimates heterogeneous material properties of an object from a monocular video of its surface vibrations. Specifically, we show how to estimate Young's modulus and density throughout a 3D object with known geometry. Knowledge of how these values change across the object is useful for simulating its motion and characterizing any defects. Traditional non-destructive testing approaches, which often require expensive instruments, generally estimate only homogenized material properties or simply identify the presence of defects. In contrast, our approach leverages monocular video to (1) identify image-space modes from an object's sub-pixel motion, and (2) directly infer spatially-varying Young's modulus and density values from the observed modes. We demonstrate our approach on both simulated and real videos.

Artificial neural networks can be used for creating surrogate models that can replace computationally expensive simulations. In this paper, a surrogate model was created for a subset of the Compact Linear Collider (CLIC) final-focus system. By training on simulation data, we created a model that maps sextupole offsets to luminosity and beam sizes, thus replacing computationally intensive tracking and beam-beam simulations. This model was then used for optimizing the parameters of a random walk procedure for sextupole alignment., Comment: 18 pages, 10 figures

This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic formulae when they exist, otherwise with numerical solutions from a finite difference method. The innovative part is to model the moving boundary with a random walk method. The results show statistical convergence for many random walkers when $\Delta x \rightarrow 0$. Stochastic methods are very competitive in large domains in higher dimensions and has the advantages of generality and ease of implementation. The stochastic method suffers from that longer execution times are required for increased accuracy. Since the code is easily adapted for parallel computing, it is possible to speed up the calculations. Regarding applications for Stefan problems, they have historically been used to model the dynamics of melting ice, and we give such an example here where the fixed boundary condition follows data from observed day temperatures at \"{O}rebro airport. Nowadays, there are a large range of examples of applications, such as climate models, the diffusion of lithium-ions in lithium-ion batteries and modelling steam chambers for petroleum extraction., Comment: Submitted as Proceedings to Stochastic Processes and Algebraic Structures (SPAS) 2019

This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three qualitative different numerical examples: the radial Schr\"{o}dinger equation for the hydrogen atom; the two-dimensional harmonic oscillator with degenerate excited states; and finally a non-linear Schr\"{o}dinger equation for rotating states. The presented method is intuitive, with analogies in classical mechanics for damped oscillators, and easy to implement, either in own coding, or with software for dynamical systems. Hence, we find it suitable to introduce it in a continuation course in quantum mechanics or generally in applied mathematics courses which contain computational parts., Comment: Final published (Open Access) version, including codes for Matlab or Octave as ancillary files