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We focus on numerical techniques for expanding 3-loop Feynman integrals with respect to the dimensional regularization parameter $\varepsilon,$ which is related to the space-time dimension as $\nu = 4-2\varepsilon,$ and describes underlying UV singularities located at the boundaries of the integration domain. As a function of the squared momentum $s,$ the expansion coefficients exhibit thresholds that generally delineate regions for their computational techniques. For the problem at hand, a sequence of integrations with a linear extrapolation as $\varepsilon\rightarrow 0$ may be performed to determine leading coefficients of the $\varepsilon$-expansion numerically. For the "baseball" Feynman diagram, we have used extrapolation with respect to an additional parameter to improve the accuracy of the $\varepsilon$-expansion coefficients in case of singularities internal to the domain., Comment: 6 pages, 2 figures, Proceedings submission to ACAT 2024

In recent years, the use of data-driven methods has provided insights into underlying patterns and principles behind culinary recipes. In this exploratory work, we introduce the use of topological data analysis, especially persistent homology, in order to study the space of culinary recipes. In particular, persistent homology analysis provides a set of recipes surrounding the multiscale "holes" in the space of existing recipes. We then propose a method to generate novel ingredient combinations using combinatorial optimization on this topological information. We made biscuits using the novel ingredient combinations, which were confirmed to be acceptable enough by a sensory evaluation study. Our findings indicate that topological data analysis has the potential for providing new tools and insights in the study of culinary recipes., Comment: 21 pages

Centaurs, distinguished by their volatile-rich compositions, play a pivotal role in understanding the formation and evolution of the early solar system, as they represent remnants of the primordial material that populated the outer regions. Stellar occultations offer a means to investigate their physical properties, including shape, rotational state, or the potential presence of satellites and rings. This work aims to conduct a detailed study of the centaur (54598) Bienor through stellar occultations and rotational light curves from photometric data collected during recent years. We successfully predicted three stellar occultations by Bienor, which were observed from Japan, Eastern Europe, and the USA. In addition, we organized observational campaigns from Spain to obtain rotational light curves. At the same time, we develop software to generate synthetic light curves from three-dimensional shape models, enabling us to validate the outcomes through computer simulations. We resolve Bienor's projected ellipse for December 26, 2022, determine a prograde sense of rotation, and confirm an asymmetric rotational light curve. We also retrieve the axes of its triaxial ellipsoid shape as a = (127 $\pm$ 5) km, b = (55 $\pm$ 4) km, and c = (45 $\pm$ 4) km. Moreover, we refine the rotation period to 9.1736 $\pm$ 0.0002 hours and determine a geometric albedo of (6.5 $\pm$ 0.5) %, higher than previously determined by other methods. Finally, by comparing our findings with previous results and simulated rotational light curves, we analyze whether an irregular or contact-binary shape, the presence of an additional element such as a satellite, or significant albedo variations on Bienor's surface, may be present.

Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are computed numerically. The energy dependence of the integrals is shown explicitly, and a discussion of its behavior is presented., Comment: 14 pages

Understanding the high-frequency transport characteristics of magnetic tunnel junctions (MTJs) is crucial for the development of fast-operating spintronics memories and radio frequency devices. Here, we present the study of frequency-dependent capacitive current effect in CoFeB/MgO-based MTJs and its influence on magnetization dynamics using time-resolved magneto-optical Kerr effect technique. In our device operating at gigahertz frequencies, we find a large displacement current of the order of mA's, which does not break the tunnel barrier of the MTJ. Importantly, this current generates an Oersted field and spin-orbit torque, inducing magnetization dynamics. Our discovery holds promise for building robust MTJ devices operating under high current conditions, also highlighting the significance of capacitive impedance in high frequency magnetotransport techniques.

Employing spins in quantum dots for fault-tolerant quantum computing in large-scale qubit arrays with on-chip control electronics requires high-fidelity qubit operation at elevated temperature. This poses a challenge for single spin initialization and readout. Existing schemes rely on Zeeman splitting or Pauli spin blockade with typical energy scales of 0.1 or 1 meV for electron-based qubits, so that sufficient fidelity is obtained only at temperatures around or below 0.1 or 1 K, respectively. Here we describe a method to achieve high temperature spin selectivity in a quantum dot using a reservoir with a spin accumulation, which deterministically sets the spin of a single electron on the dot. Since spin accumulation as large as 10 meV is achievable in silicon, spin selection with electrically adjustable error rates below $10^{-4}$ is possible even in a liquid He bath at 4 K. Via the reservoir spin accumulation, induced and controlled by a nearby ferromagnet, classical information (magnetization direction) is mapped onto a spin qubit. These features provide the prospect of spin qubit operation at elevated temperatures and connect the worlds of quantum computing and spintronics., Comment: Supplementary material available via the journal reference

The product of two unitaries can normally be expressed as a single exponential through the famous Baker-Campbell-Hausdorff formula. We present here a counterexample in quantum optics, by showing that an expression in terms of a single exponential is possible only at the expense of the introduction of a new element (a central extension of the algebra), implying that there will be unitaries, generated by a sequence of gates, that cannot be generated by any time-independent quadratic Hamiltonian. A quantum-optical experiment is proposed that brings to light this phenomenon., Comment: 12 pages, 7 figures

Efficient error estimates for the Trotter product formula are central in quantum computing, mathematical physics, and numerical simulations. However, the Trotter error's dependency on the input state and its application to unbounded operators remains unclear. Here, we present a general theory for error estimation, including higher-order product formulas, with explicit input state dependency. Our approach overcomes two limitations of the existing operator-norm estimates in the literature. First, previous bounds are too pessimistic as they quantify the worst-case scenario. Second, previous bounds become trivial for unbounded operators and cannot be applied to a wide class of Trotter scenarios, including atomic and molecular Hamiltonians. Our method enables analytical treatment of Trotter errors in chemistry simulations, illustrated through a case study on the hydrogen atom. Our findings reveal: (i) for states with fat-tailed energy distribution, such as low-angular-momentum states of the hydrogen atom, the Trotter error scales worse than expected (sublinearly) in the number of Trotter steps; (ii) certain states do not admit an advantage in the scaling from higher-order Trotterization, and thus, the higher-order Trotter hierarchy breaks down for these states, including the hydrogen atom's ground state; (iii) the scaling of higher-order Trotter bounds might depend on the order of the Hamiltonians in the Trotter product for states with fat-tailed energy distribution. Physically, the enlarged Trotter error is caused by the atom's ionization due to the Trotter dynamics. Mathematically, we find that certain domain conditions are not satisfied by some states so higher moments of the potential and kinetic energies diverge. Our analytical error analysis agrees with numerical simulations, indicating that we can estimate the state-dependent Trotter error scaling genuinely., Comment: 49 pages, 8 figures

We present a new hydrodynamic scheme named Godunov Density-Independent Smoothed Particle Hydrodynamics (GDISPH), that can accurately handle shock waves and contact discontinuities without any manually tuned parameters. This is in contrast to the standard formulation of smoothed particle hydrodynamics (SSPH), which requires the parameters for an artificial viscosity term to handle the shocks and struggles to accurately handle the contact discontinuities due to unphysical repulsive forces, resulting in surface tension that disrupts pressure equilibrium and suppresses fluid instabilities. While Godunov SPH (GSPH) can handle the shocks without the parameters by using solutions from a Riemann solver, it still cannot fully handle the contact discontinuities. Density-Independent Smoothed Particle Hydrodynamics (DISPH), one of several schemes proposed to handle contact discontinuities more effectively than SSPH, demonstrates superior performance in our tests involving strong shocks and contact discontinuities. However, DISPH still requires the artificial viscosity term. We integrate the Riemann solver into DISPH in several ways, yielding some patterns of GDISPH. The results of standard tests such as the one-dimensional Riemann problem, pressure equilibrium, Sedov-Taylor, and Kelvin-Helmholtz tests are favourable to GDISPH Case 1 and GDISPH Case 2, as well as DISPH. We conclude that GDISPH Case 1 has an advantage over GDISPH Case 2, effectively handling shocks and contact discontinuities without the need for specific parameters or introducing any additional numerical diffusion., Comment: Accepted for publication in New Astronomy, 34 pages, 19 pages. Updated February 5, 2024 to correct minor errors in the explanations in the text and added detailed explanations in Section 2.2

We propose a skein model for the quantum cluster algebras of surface type with coefficients. We introduce a skein algebra $\mathscr{S}_{\Sigma,\mathbb{W}}^{A}$ of a walled surface $(\Sigma,\mathbb{W})$, and prove that it has a quantum cluster structure. The walled surfaces naturally generalize the marked surfaces with multi-laminations, which have been used to describe the quantum cluster algebras of geometric type for marked surfaces by Fomin--Thurston [FT18]. Moreover, we give skein theoretic interpretation for some of quasi-homomorphisms [Fra16] between these quantum cluster algebras., Comment: 43 pages; v2: Major revision, introduction refreshed, arguments concerning the minimal position moved to Section 5, the Fomin--Thurston's description of the normalized cluster algebras moved to Section 4.2, Examples 2.13 and 2.14 added

Understanding a \textit{reinforcement learning} policy, which guides state-to-action mappings to maximize rewards, necessitates an accompanying explanation for human comprehension. In this paper, we introduce a set of \textit{linear temporal logic} (LTL) formulae designed to provide explanations for policies, and an algorithm for searching through those formulae for the one that best explains a given policy. Our focus is on crafting explanations that elucidate both the ultimate objectives accomplished by the policy and the prerequisite conditions it upholds throughout its execution. These LTL-based explanations feature a structured representation, which is particularly well-suited for local-search techniques. The effectiveness of our proposed approach is illustrated through a simulated game of capture the flag and a car-parking environment. The paper concludes with suggested directions for future, Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

We investigated the effect of Fe segregated from partially Fe-substituted MgO (MgFeO) on the magnetic properties of CoFeB/MgFeO multilayers. X-ray photoelectron spectroscopy (XPS) as well as magnetic measurements revealed that the segregated Fe was reduced to metal and exhibited ferromagnetism at the CoFeB/MgFeO interface. The CoFeB/MgFeO multilayer showed more than 2-fold enhancement in perpendicular magnetic anisotropy (PMA) energy density compared with a standard CoFeB/MgO multilayer. The PMA energy density was further enhanced by inserting an ultrathin MgO layer in between CoFeB and MgFeO layers. Ferromagnetic resonance measurement also revealed a remarkable reduction of magnetic damping in the CoFeB/MgFeO multilayers., Comment: 15 pages, 5 figures

Multiple neuromorphic applications require the tuning of two or more devices to a common signal. Various types of neuromorphic computation can be realized using spintronic oscillators, where the DC current induces magnetization precession, which turns into an AC voltage generator. However, in spintronics, synchronization of two oscillators using a DC signal is still a challenging problem because it requires a certain degree of similarity between devices that are to be synchronized, which may be difficult to achieve due to device parameter distribution during the fabrication process. In this work, we present experimental results on the mechanisms of synchronization of spin-torque oscillators. Devices are based on magnetic tunnel junction with a perpendicularly magnetized free layer and take advantage of a uniform magnetization precision in the presence of the magnetic field and a DC bias. By using an external microwave source, we show the optimal condition for the synchronization of the magnetic tunnel junctions. Finally, we present results on the in-series connection of two junctions and discuss the possible path towards improving oscillation power and linewidth. In addition, using numerical simulations of the coupled oscillators model, we aim to reproduce the conditions of the experiments and determine the tolerance for achieving synchronization.

Voltage-controlled magnetoresistive random access memory (VC-MRAM) based on voltage-induced dynamic switching in magnetic tunnel junctions (MTJs) is a promising ultimate non-volatile memory with ultralow power consumption. However, the dynamic switching in a conventional MTJ is accompanied by a relatively high write error rate (WER), hindering the reliable operation of VC-MRAM. Here, we propose a reliable writing scheme using the in-plane demagnetizing field (IDF) and voltage-induced negative out-of-plane anisotropy field (NOAF). Numerical simulations based on macrospin model demonstrate that the voltage-induced NOAF modifies the switching dynamics and increases the torque due to the IDF, thereby reducing the switching time. The IDF and voltage-induced NOAF also reduce the mean energy difference between the magnetization direction at the end of the pulse and the equilibrium direction. As a result, an appropriate combination of the IDF and voltage-induced NOAF reduces the WER by one order of magnitude compared with that of the dynamic switching in a conventional MTJ.

Representing text into a multidimensional space can be done with sentence embedding models such as Sentence-BERT (SBERT). However, training these models when the data has a complex multilevel structure requires individually trained class-specific models, which increases time and computing costs. We propose a two step approach which enables us to map sentences according to their hierarchical memberships and polarity. At first we teach the upper level sentence space through an AdaCos loss function and then finetune with a novel loss function mainly based on the cosine similarity of intra-level pairs. We apply this method to three different datasets: two weakly supervised Big Five personality dataset obtained from English and Japanese Twitter data and the benchmark MNLI dataset. We show that our single model approach performs better than multiple class-specific classification models., Comment: Copyright is owned by JSAI

The probability of a given candidate winning a future election is worked out in closed form as a function of (i) the current support rates for each candidate, (ii) the relative positioning of the candidates within the political spectrum, (iii) the time left to the election, and (iv) the rate at which noisy information is revealed to the electorate from now to the election day, when there are three or more candidates. It is shown, in particular, that the optimal strategy for controlling information can be intricate and nontrivial, in contrast to a two-candidate race. A surprising finding is that for a candidate taking the centre ground in an electoral competition among a polarised electorate, certain strategies are fatal in that the resulting winning probability for that candidate vanishes identically., Comment: 17 pages, 6 figures, version to appear in the Royal Society Open Science

Highly periodic structures are often said to convey the beauty of nature. However, most material properties are strongly influenced by the defects they contain. On the mesoscopic scale, molecular self-assembly exemplifies this interplay; thermodynamic principles determine short-range order, but long-range order is mainly impeded by the kinetic history of the material and by thermal fluctuations. For the development of self-assembly technologies, it is imperative to characterise and understand the interplay between self-assembled order and defect-induced disorder. Here we used synchrotron-based hard X-ray nanotomography to reveal a pair of extended topological defects within a self-assembled single-diamond network morphology. These defects are morphologically similar to the comet and trefoil patterns of equal and opposite half-integer topological charges observed in liquid crystals and appear to maintain a constant separation across the thickness of the sample, resembling pairs of full vortices in superconductors and other hard condensed matter systems. These results are expected to open new windows to study defect formation in soft condensed matter, particularly in biological systems where most structures are formed by self-assembly., Comment: Nat. Nanotechnol. (2024)

Block copolymers are recognised as a valuable platform for creating nanostructured materials with unique properties. Morphologies formed by block copolymer self-assembly can be transferred into a wide range of inorganic materials, enabling applications including energy storage and metamaterials. However, imaging of the underlying, often complex, nanostructures in large volumes has remained a challenge, limiting progress in materials development. Taking advantage of recent advances in X-ray nanotomography, we non-invasively imaged exceptionally large volumes of nanostructured soft materials at high resolution, revealing a single diamond morphology in a triblock terpolymer composite network. This morphology, which is ubiquitous in nature, has so far remained elusive in block copolymers, despite its potential to create materials with large photonic bandgaps. The discovery was made possible by the precise analysis of distortions in a large volume of the self-assembled diamond network, which are difficult to unambiguously assess using traditional characterisation tools. We anticipate that high-resolution X-ray nanotomography, which allows imaging of much larger sample volumes than electron-based tomography, will become a powerful tool for the quantitative analysis of complex nanostructures and that structures such as the triblock terpolymer-directed single diamond will enable the generation of advanced multicomponent composites with hitherto unknown property profiles., Comment: updated reference 38; added reference 40; corrected name of one author; corrected one affiliation; corrected legend in Extended Data Fig. 3

We study the energy extraction from and charging to a finite-dimensional quantum system by general quantum operations. We prove that the changes in energy induced by unital quantum operations are limited by the ergotropy/charging bound for unitary quantum operations. This implies that, in order to break the ergotropy/charging bound for unitary quantum operations, one needs to perform a quantum operation with feedback control. We also show that the ergotropy/charging bound for unital quantum operations, applied to initial thermal equilibrium states, is tighter than the inequality representing the standard second law of thermodynamics without feedback control., Comment: 11 pages, 7 figures

We developed a cryogenic temperature deposition process for high-performance CoFeB/MgO/CoFeB magnetic tunnel junctions (MTJs) on 300 mm thermally oxidized silicon wafers. The effect of the deposition temperature of the CoFeB layers on the nanostructure, magnetic and magneto-transport properties of the MTJs were investigated in detail. When CoFeB was deposited at 100 K, the MTJs exhibited a perpendicular magnetic anisotropy (PMA) of 214 uJ/m2 and a voltage-controlled magnetic anisotropy (VCMA) coefficient of -45 fJ/Vm, corresponding to 1.4- and 1.7-fold enhancements in PMA and VCMA, respectively, compared to the case of room-temperature deposition of CoFeB. The improvement in the MTJ properties was not simply due to the morphology of the MTJ films. The interface-sensitive magneto-transport properties indicated that interfacial qualities such as intermixing and oxidation states at the MgO/CoFeB interfaces were improved by the cryogenic temperature deposition. Cryogenic-temperature sputtering deposition is expected to be a standard manufacturing process for next-generation magnetoresistive random-access memory., Comment: Submitted to ACS Applied Materials and Interfaces