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Large Language Models (LLMs) have exhibited remarkable capabilities in many complex tasks including mathematical reasoning. However, traditional approaches heavily rely on ensuring self-consistency within single prompting method, which limits the exploration of diverse problem-solving strategies. This study addresses these limitations by performing an experimental analysis of distinct prompting methods within the domain of mathematical reasoning. Our findings demonstrate that each method explores a distinct search space, and this differentiation becomes more evident with increasing problem complexity. To leverage this phenomenon, we applied efficient sampling process that uniformly combines samples from these diverse methods, which not only expands the maximum search space but achieves higher performance with fewer runs compared to single methods. Especially, within the subset of difficult questions of MATH dataset named MATH-hard, The maximum search space was achieved while utilizing approximately 43% fewer runs than single methods on average. These findings highlight the importance of integrating diverse problem-solving strategies to enhance the reasoning abilities of LLMs., Comment: 6 pages, 4 figures

Spins in solid systems can inherently serve as qubits for quantum simulation or quantum information processing. Spin qubits are usually prone to environmental magnetic field fluctuations; however, a spin qubit encoded in a decoherence-free-subspace (DFS) can be protected from certain degrees of environmental noise depending on the specific structure of the DFS. Here, we derive the "true" DFS from an antiferromagnetic Heisenberg spin-1/2 trimer, which protects the qubit states against both short- and long-wavelength magnetic field fluctuations. We define the spin trimer with three electrons confined in a gate-defined GaAs double quantum dot (DQD) where we exploit Wigner-molecularization in one of the quantum dots. We first utilize the trimer for dynamic nuclear polarization (DNP), which generates a sizable magnetic field difference, $\Delta B_\mathrm{z}$, within the DQD. We show that large $\Delta B_\mathrm{z}$ significantly alters the eigenspectrum of the trimer and results in the "true" DFS in the DQD. Real-time Bayesian estimation of the DFS energy gap explicitly demonstrates protection of the DFS against short-wavelength magnetic field fluctuations in addition to long-wavelength ones. Our findings pave the way toward compact DFS structures for exchange-coupled quantum dot spin chains, the internal structure of which can be coherently controlled completely decoupled from environmental magnetic fields.

Ventilated acoustic resonator(VAR), a type of acoustic metamaterial, emerge as an alternative for sound attenuation in environments that require ventilation, owing to its excellent low-frequency attenuation performance and flexible shape adaptability. However, due to the non-linear acoustic responses of VARs, the VAR designs are generally obtained within a limited parametrized design space, and the design relies on the iteration of the numerical simulation which consumes a considerable amount of computational time and resources. This paper proposes an acoustic response-encoded variational autoencoder (AR-VAE), a novel variational autoencoder-based generative design model for the efficient and accurate inverse design of VAR even with non-parametrized designs. The AR-VAE matches the high-dimensional acoustic response with the VAR cross-section image in the dimension-reduced latent space, which enables the AR-VAE to generate various non-parametrized VAR cross-section images with the target acoustic response. AR-VAE generates non-parameterized VARs from target acoustic responses, which show a 25-fold reduction in mean squared error compared to conventional deep learning-based parameter searching methods while exhibiting lower average mean squared error and peak frequency variance. By combining the inverse-designed VARs by AR-VAE, multi-cavity VAR was devised for broadband and multitarget peak frequency attenuation. The proposed design method presents a new approach for structural inverse-design with a high-dimensional non-linear physical response.

Regionalization of intensive care for premature babies refers to a triage system of mothers with high-risk pregnancies to hospitals of varied capabilities based on risks faced by infants. Due to the limited capacity of high-level hospitals, which are equipped with advanced expertise to provide critical care, understanding the effect of delivering premature babies at such hospitals on infant mortality for different subgroups of high-risk mothers could facilitate the design of an efficient perinatal regionalization system. Towards answering this question, Baiocchi et al. (2010) proposed to strengthen an excess-travel-time-based, continuous instrumental variable (IV) in an IV-based, matched-pair design by switching focus to a smaller cohort amenable to being paired with a larger separation in the IV dose. Three elements changed with the strengthened IV: the study cohort, compliance rate and latent complier subgroup. Here, we introduce a non-bipartite, template matching algorithm that embeds data into a target, pair-randomized encouragement trial which maintains fidelity to the original study cohort while strengthening the IV. We then study randomization-based and IV-dependent, biased-randomization-based inference of partial identification bounds for the sample average treatment effect (SATE) in an IV-based matched pair design, which deviates from the usual effect ratio estimand in that the SATE is agnostic to the IV and who is matched to whom, although a strengthened IV design could narrow the partial identification bounds. Based on our proposed strengthened-IV design, we found that delivering at a high-level NICU reduced preterm babies' mortality rate compared to a low-level NICU for $81,766 \times 2 = 163,532$ mothers and their preterm babies and the effect appeared to be minimal among non-black, low-risk mothers.

Most software applications contain graphics such as charts, diagrams and maps. Currently, these graphics are designed with a ``one size fits all" approach and do not cater to the needs of people with disabilities. Therefore, when using software with graphics, a colour-impaired user may struggle to interpret graphics with certain colours, and a person with dyslexia may struggle to read the text labels in the graphic. Our research addresses this issue by developing a framework that generates adaptive and accessible information graphics for multiple disabilities. Uniquely, the approach also serves people with multiple simultaneous disabilities. To achieve these, we used a case study of public space floorplans presented via a web tool and worked with four disability groups: people with low vision, colour blindness, dyslexia and mobility impairment. Our research involved gathering requirements from 3 accessibility experts and 80 participants with disabilities, developing a system to generate adaptive graphics that address the identified requirements, and conducting an evaluation with 7 participants with disabilities. The evaluation showed that users found our solution easy to use and suitable for most of their requirements. The study also provides recommendations for front-end developers on engineering accessible graphics for their software and discusses the implications of our work on society from the perspective of public space owners and end users.

Resolving single atoms in large-scale volumes has been a goal for atomic resolution microscopy for a long time. Electron microscopy has come close to this goal using a combination of advanced electron optics and computational imaging algorithms. However, atomic-resolution 3D imaging in volumes larger than the depth of field limit of the electron optics has so far been out of reach. Electron ptychography, a computational imaging method allowing to solve the multiple-scattering problem from position- and momentum-resolved measurements, provides the opportunity to surpass this limit. Here, we experimentally demonstrate atomic resolution three-dimensional phase-contrast imaging in a volume surpassing the depth of field limits using multi-slice ptychographic electron tomography. We reconstruct tilt-series 4D-STEM measurements of a Co3O4 nanocube, yielding 1.75 {\AA} resolution in a reconstructed volume of (18.2nm)^3., Comment: 15 pages

Rupture of aortic aneurysms is by far the most fatal heart disease, with a mortality rate exceeding 80%. There are no reliable clinical protocols to predict growth, dissection, and rupture because the fundamental physics driving aneurysm progression is unknown. Here, via in-vitro experiments, we show that a blood-wall, fluttering instability manifests in synthetic arteries under pulsatile forcing. We establish a phase space to prove that the transition from stable flow to unstable aortic flutter is accurately predicted by a flutter instability parameter derived from first principles. Time resolved strain maps of the evolving system reveal the dynamical characteristics of aortic flutter that drive aneurysm progression. We show that low level instability can trigger permanent aortic growth, even in the absence of material remodeling. Sufficiently large flutter beyond a secondary threshold localizes strain in the walls to the length scale clinically observed in aortic dissection. Lastly, significant physical flutter beyond a tertiary threshold can ultimately induce aneurysm rupture via failure modes reported from necropsy. Resolving the fundamental physics of aneurysm progression directly leads to clinical protocols that forecast growth as well as intercept dissection and rupture by pinpointing their physical origin.

Engineered spin-electric coupling enables spin qubits in semiconductor nanostructures to be manipulated efficiently and addressed individually. While synthetic spin-orbit coupling using a micromagnet is widely used for driving qubits based on single spins in silicon, corresponding demonstration for encoded spin qubits is so far limited to natural silicon. Here, we demonstrate fast singlet-triplet qubit oscillation (~100 MHz) in a gate-defined double quantum dot in $^{28}$Si/SiGe with an on-chip micromagnet with which we show the oscillation quality factor of an encoded spin qubit exceeding 580. The coherence time $\textit{T}_{2}$* is analyzed as a function of potential detuning and an external magnetic field. In weak magnetic fields, the coherence is limited by fast noise compared to the data acquisition time, which limits $\textit{T}_{2}$* < 1 ${\mu}$s in the ergodic limit. We present evidence of sizable and coherent coupling of the qubit with the spin states of a nearby quantum dot, demonstrating that appropriate spin-electric coupling may enable a charge-based two-qubit gate in a (1,1) charge configuration.

Measuring the three-dimensional (3D) distribution of chemistry in nanoscale matter is a longstanding challenge for metrological science. The inelastic scattering events required for 3D chemical imaging are too rare, requiring high beam exposure that destroys the specimen before an experiment completes. Even larger doses are required to achieve high resolution. Thus, chemical mapping in 3D has been unachievable except at lower resolution with the most radiation-hard materials. Here, high-resolution 3D chemical imaging is achieved near or below one nanometer resolution in a Au-Fe$_3$O$_4$ metamaterial, Co$_3$O$_4$ - Mn$_3$O$_4$ core-shell nanocrystals, and ZnS-Cu$_{0.64}$S$_{0.36}$ nanomaterial using fused multi-modal electron tomography. Multi-modal data fusion enables high-resolution chemical tomography often with 99\% less dose by linking information encoded within both elastic (HAADF) and inelastic (EDX / EELS) signals. Now sub-nanometer 3D resolution of chemistry is measurable for a broad class of geometrically and compositionally complex materials.

A boundary integral equation method for the 3-D Helmholtz equation in multilayered media with many quasi-periodic layers is presented. Compared with conventional quasi-periodic Green's function method, the new method is robust at all scattering parameters. A periodizing scheme is used to decompose the solution into near- and far-field contributions. The near-field contribution uses the free-space Green's function in an integral equation on the interface in the unit cell and its immediate eight neighbors; the far-field contribution uses proxy point sources that enclose the unit cell. A specialized high-order quadrature is developed to discretize the underlying surface integral operators to keep the number of unknowns per layer small. We achieve overall linear computational complexity in the number of layers by reducing the linear system into block tridiagonal form and then solving the system directly via block LU decomposition. The new solver is capable of handling a 100-interface structure with 961.3k unknowns to $10^{-5}$ accuracy in less than 2 hours on a desktop workstation., Comment: 17 pages, 6 figures, 1 table

In this paper, a Quadrature by Two Expansions (QB2X) numerical integration technique is developed for the single and double layer potentials of the Helmholtz equation in two dimensions. The QB2X method uses both local complex Taylor expansions and plane wave type expansions to achieve a resulting representation which is numerically accurate for all target points (interior, exterior, or exactly on the boundary) inside a leaf box in the fast multipole method (FMM) hierarchical tree structure. Compared to the original Quadrature by Expansion (QBX) method, the QB2X method explicitly includes the nonlinearity from the boundary geometry in the plane wave expansions, thereby providing for higher order representations of both the boundary geometry and density functions in the integrand, with its convergence following standard FMM error analysis. Numerical results are presented to demonstrate the performance of the QB2X method for Helmholtz layer potentials and its comparison with the original QBX method for both flat and curved boundaries with various densities. The QB2X method overcomes the challenges of the original QBX method, and is better suited for efficient solutions of the Helmholtz equation with complex geometries.

Multielectron semiconductor quantum dots (QDs) provide a novel platform to study the role of Coulomb correlations in finite quantum systems and their impact on many-body energy spectra. An example is the formation of interaction-driven, spatially localized electron states of Wigner molecules (WMs). Although Wigner molecularization has been confirmed by real-space imaging and coherent spectroscopy, the open system dynamics of the strongly-correlated states with the environment are not yet well understood. Here, we demonstrate efficient control of spin transfer between an artificial three-electron WM and the nuclear environment in a GaAs double QD. A Landau-Zener sweep-based polarization sequence and low-lying anti-crossings of spin multiplet states enabled by Wigner molecularization are utilized. An efficient polarization rate of 2.58 $h \cdotp kHz \cdotp (g^* \cdotp \mu_B)^{-1}$ per electron spin flip and, consequently, programmable nuclear polarization by controlled single-electron tunneling are achieved. Combined with coherent control of spin states, we achieve control of magnitude, polarity, and site dependence of the nuclear field. It is demonstrated that the same level of control cannot be achieved in the non-interacting regime. Thus, we confirm the multiplet spin structure of a WM, paving the way for active control of newly emerging correlated electron states for application in mesoscopic environment engineering.

We report the simultaneous operation and two-qubit coupling measurement of a pair of two-electron spin qubits that are actively decoupled from quasistatic nuclear noise in a GaAs quadruple quantum dot array. Coherent Rabi oscillations of both qubits (decay time $\approx$2 {\mu}s; frequency few MHz) are achieved by continuously tuning the drive frequency using rapidly converging real-time Hamiltonian estimators. By state conditional exchange oscillation measurements, we also observe strong two-qubit capacitive interaction (> 190 MHz). We show that the scaling of the capacitive interaction with respect to intra-qubit exchange energies is stronger than the bilinear form, consistent with recent theoretical predictions. We observe a high ratio (>16) between coherence and conditional phase-flip time, which supports the possibility of generating high-fidelity and fast quantum entanglement between encoded spin qubits using a simple capacitive interaction., Comment: 30 pages, 7 figures

We report energy selective tunneling readout-based Hamiltonian parameter estimation of a two-electron spin qubit in a GaAs quantum dot array. Optimization of readout fidelity enables a single-shot measurement time of 16 on average, with adaptive initialization and efficient qubit frequency estimation based on real-time Bayesian inference. For qubit operation in a frequency heralded mode, we observe a 40-fold increase in coherence time without resorting to dynamic nuclear polarization. We also demonstrate active frequency feedback with quantum oscillation visibility, single-shot measurement fidelity, and state initialization fidelity up to 97.7%, 99%, and over 99.7%, respectively. By pushing the sensitivity of the energy selective tunneling-based spin to charge conversion to the limit, the technique is useful for advanced quantum control protocols such as error mitigation schemes, where fast qubit parameter calibration with a large signal-to-noise ratio is crucial., Comment: 24 pages, 7 figures, 1 table