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Port-based teleportation is a variant of quantum teleportation, where the receiver can choose one of the ports in his part of the entangled state shared with the sender, but cannot apply other recovery operations. We show that the optimal fidelity of deterministic port-based teleportation (dPBT) using $N=n+1$ ports to teleport a $d$-dimensional state is equivalent to the optimal fidelity of $d$-dimensional unitary estimation using $n$ calls of the input unitary operation. From any given dPBT, we can explicitly construct the corresponding unitary estimation protocol achieving the same optimal fidelity, and vice versa. Using the obtained one-to-one correspondence between dPBT and unitary estimation, we derive the asymptotic optimal fidelity of port-based teleportation given by $F = 1-\Theta(d^4 N^{-2})$, which improves the previously known result given by $1-O(d^5 N^{-2}) \leq F \leq 1-\Omega(d^2 N^{-2})$. We also show that the optimal fidelity of unitary estimation for the case $n\leq d-1$ is $F = {n+1 \over d^2}$, and this fidelity is equal to the optimal fidelity of unitary inversion with $n\leq d-1$ calls of the input unitary operation even if we allow indefinite causal order among the calls., Comment: 7+22 pages, 1+1 figures

This paper introduces FLEURS-R, a speech restoration applied version of the Few-shot Learning Evaluation of Universal Representations of Speech (FLEURS) corpus. FLEURS-R maintains an N-way parallel speech corpus in 102 languages as FLEURS, with improved audio quality and fidelity by applying the speech restoration model Miipher. The aim of FLEURS-R is to advance speech technology in more languages and catalyze research including text-to-speech (TTS) and other speech generation tasks in low-resource languages. Comprehensive evaluations with the restored speech and TTS baseline models trained from the new corpus show that the new corpus obtained significantly improved speech quality while maintaining the semantic contents of the speech. The corpus is publicly released via Hugging Face.

Morton and Vivaldi defined the polynomials whose roots are parabolic parameters for a one-parameter family of polynomial maps. We call these polynomials delta factors. They conjectured that delta factors are irreducible for the family $z\mapsto z^2+c$. One can easily show the irreducibility for periods $1$ and $2$ by reducing it to the irreducibility of cyclotomic polynomials. However, for periods $3$ and beyond, this becomes a challenging problem. This paper proves the irreducibility of delta factors for the period $3$ and demonstrates the existence of infinitely many irreducible delta factors for periods greater than $3$., Comment: 12 pages, 4 figures, 2 tables

An iterated circumcenter sequence (ICS) in dimension $d$ is a sequence of points in $\mathbb{R}^d$ where each point is the circumcenter of the preceding $d+1$ points. The purpose of this paper is to completely determine the parameter space of ICSs and its subspace consisting of periodic ICSs. In particular, we prove Goddyn's conjecture on periodic ICSs, which was independently proven recently by Ardanuy. We also prove the existence of a periodic ICS in any dimension., Comment: 13 pages. Comments welcome!

In the trend towards the globalization of football and the increasing commercialization of professional football clubs, a methodology for calculating the firm value of clubs in non-western countries has yet to be established. This study reviews the valuation methods for the club firm values in Europe and North America and how values are calculated at the time of changing ownership of Japanese clubs and develops regression models with higher explanatory power than before to estimate the more accurate firm value of Japanese football clubs. A review of the existing literature on methods for calculating the firm value of professional sports clubs in Europe and North America, as well as financial statements and registers relating to changes of ownership of Japanese clubs, was conducted. After that, multiple regression analyses were conducted using the firm value of European clubs as the explained variable. From the literature review and the Japanese case studies, it has become clear that European clubs' standard valuation methods are based on revenue and other factors, while in Japan, valuation is based solely on the par value of stocks or net assets. Multiple regression analysis revealed that the firm value of European clubs over the past three years is best explained by revenue or player market value and the number of SNS followers. Two models with high explanatory power were developed. The estimated firm value using the revenue-based formula was higher than the one based on player market value. However, in the J.League, the former was more than three times higher than the latter, while the former was only 1.2 times higher for European clubs. The discrepancy relates to differences in European and J.League clubs' revenues and asset structures. In either formula, the firm value of J.League clubs exceeded the actual transaction price when the change of ownership occurred in the past.

In recent years, quantum Ising machines have drawn a lot of attention, but due to physical implementation constraints, it has been difficult to achieve dense coupling, such as full coupling with sufficient spins to handle practical large-scale applications. Consequently, classically computable equations have been derived from quantum master equations for these quantum Ising machines. Parallel implementations of these algorithms using FPGAs have been used to rapidly find solutions to these problems on a scale that is difficult to achieve in physical systems. We have developed an FPGA implemented cyber coherent Ising machine (cyber CIM) that is much more versatile than previous implementations using FPGAs. Our architecture is versatile since it can be applied to the open-loop CIM, which was proposed when CIM research began, to the closed-loop CIM, which has been used recently, as well as to Jacobi successive over-relaxation method. By modifying the sequence control code for the calculation control module, other algorithms such as Simulated Bifurcation (SB) can also be implemented. Earlier research on large-scale FPGA implementations of SB and CIM used binary or ternary discrete values for connections, whereas the cyber CIM used FP32 values. Also, the cyber CIM utilized Zeeman terms that were represented as FP32, which were not present in other large-scale FPGA systems. Our implementation with continuous interaction realizes N=4096 on a single FPGA, comparable to the single-FPGA implementation of SB with binary interactions, with N=4096. The cyber CIM enables applications such as CDMA multi-user detector and L0 compressed sensing which were not possible with earlier FPGA systems, while enabling superior calculation speeds, more than ten times faster than a GPU implementation. The calculation speed can be further improved by increasing parallelism, such as through clustering., Comment: 20 pages, 9 figures

The integration of artificial intelligence (AI) into military capabilities has become a norm for major military power across the globe. Understanding how these AI models operate is essential for maintaining strategic advantages and ensuring security. This paper demonstrates an open-source methodology for analyzing military AI models through a detailed examination of the Zhousidun dataset, a Chinese-originated dataset that exhaustively labels critical components on American and Allied destroyers. By demonstrating the replication of a state-of-the-art computer vision model on this dataset, we illustrate how open-source tools can be leveraged to assess and understand key military AI capabilities. This methodology offers a robust framework for evaluating the performance and potential of AI-enabled military capabilities, thus enhancing the accuracy and reliability of strategic assessments.

We consider the forces acting on electrons in magnetic field including the constraints and a condition arising from quantum mechanics. The force is calculated as the electron mass, $m_e$, multiplied by the total time-derivative of the velocity field evaluated using the quantum mechanical many-electron wave function. The velocity field includes a term of the Berry connection from the many-body wave function; thereby, quantum mechanical effects are included. It is shown that additional important forces besides the Lorentz force exist; they include the gradient of the electron velocity field kinetic energy, the gradient of the chemical potential, and the `force' for producing topologically protected loop currents. These additional forces are shown to be important in superconductivity, electric current in metallic wires, and charging of capacitors.

A theory for cuprate superconductivity predicts the existence of nano-sized loop currents called, `` spin-vortex-induced loop currents (SVILCs)''. We calculate magnetic fields produced by them for a model of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) thin films composed of one surface and two bulk CuO$_2$ bilayers. In this model, bulk CuO$_2$ layers host stable spin-vortices around small polarons formed from doped holes; they give rise to a $U(1)$ gauge field described by the Berry connection from many-body wave functions, and generates the SVILCs. The effect of the gauge field is taken into account by the particle-number conserving Bogoliubov-de Gennes (PNC-BdG) formalism. The magnitude of the calculated magnetic field produced by the SVILCs in the vicinity of the surface ($10a \approx 4$ nm, where $a$ is the lattice constant of the CuO$_2$ plane) is in the order of mT; thus, may be detectable by currently available detection methods. The detection of the SVILCs by the magnetic field measurement may bring about the elucidation of the cuprate superconductivity, and may also lead to their quantum device applications, including qubits.

Recently, a new theory of superconductivity has been put forward that attributes the origin of superconductivity to the appearance of a non-trivial Berry connection from many-electron wave functions. This theory reproduces the major results of the BCS theory with conserving the particle number, and predicts the single-electron supercurrent tunneling across the Josephson junction with keeping the correct Josephson relation. We re-examine the quantization of superconducting qubit circuits by taking into account the above development, and show that the dynamical variables used in the standard theory, the flux nodes relating to the voltage, should be replaced by those relating to the electromagnetic vector potential. The fact that the Josephson junction tunneling allows the single-electron supercurrent tunneling is the reason for the existence of excited single electrons in superconducting qubits with Josephson junctions. We predict that it will be avoided by weakening the coupling between two superconductors in the Josephson junction.

In this report, we introduce the Gemini 1.5 family of models, representing the next generation of highly compute-efficient multimodal models capable of recalling and reasoning over fine-grained information from millions of tokens of context, including multiple long documents and hours of video and audio. The family includes two new models: (1) an updated Gemini 1.5 Pro, which exceeds the February version on the great majority of capabilities and benchmarks; (2) Gemini 1.5 Flash, a more lightweight variant designed for efficiency with minimal regression in quality. Gemini 1.5 models achieve near-perfect recall on long-context retrieval tasks across modalities, improve the state-of-the-art in long-document QA, long-video QA and long-context ASR, and match or surpass Gemini 1.0 Ultra's state-of-the-art performance across a broad set of benchmarks. Studying the limits of Gemini 1.5's long-context ability, we find continued improvement in next-token prediction and near-perfect retrieval (>99%) up to at least 10M tokens, a generational leap over existing models such as Claude 3.0 (200k) and GPT-4 Turbo (128k). Finally, we highlight real-world use cases, such as Gemini 1.5 collaborating with professionals on completing their tasks achieving 26 to 75% time savings across 10 different job categories, as well as surprising new capabilities of large language models at the frontier; when given a grammar manual for Kalamang, a language with fewer than 200 speakers worldwide, the model learns to translate English to Kalamang at a similar level to a person who learned from the same content.

The kinetics of interfaces in alloy solidification pose a classic free boundary problem. This paper introduces an approach that amalgamates the distinctive characteristics of sharp and diffuse interface models. The motion of the diffuse interface is governed by the phase-field equation featuring a traveling wave function [I. Steinbach, Modell. Simul. Mater. Sci. Eng. 17(7), 073001 (2009)]. To emulate solute rejection in the sharp interface model, the concept of the middle-obstacle and the casting operation are employed. Moreover, the undercooling along the interface normal is flattened to minimize the impact of bulk undercooling in the interface and the associated effects, such as stretching and arc-length diffusion. Notably, the results for interface kinetics under both equilibrium and non-equilibrium conditions closely approximate their analytical solutions, all achieved with artificially wide interfaces and comparatively low computational cost.

The electronic states and topological properties of the biphenylene network (BPN) are analyzed using a tight-binding model based on the $\pi$-electron network. It is shown that tuning the hopping parameters induces topological phase transitions, leading to the emergence of edge states owing to the nontrivial topological Zak phase of the bulk BPN. Elementary band analysis clearly gives the number of edge states, which are associated with the location of Wannier centers. In addition, we have presented the conditions for the emergence of corner states owing to the higher-order topological nature of BPN., Comment: 11 pages, 10 figures

The biphenylene network (BPN) has a unique two-dimensional atomic structure, where hexagonal unit cells are arranged on a square lattice. Inspired by such a BPN structure, we design a counterpart in the fashion of photonic crystals (PhCs), which we refer to as the BPN PhC. We study the photonic band structure using the finite element method and characterize the topological properties of the BPN PhC through the use of the Wilson loop. Our findings reveal the emergence of topological edge states in the BPN PhC, specifically in the zigzag edge and the chiral edge, as a consequence of the nontrivial Zak phase in the corresponding directions. In addition, we find the localization of electromagnetic waves at the corners formed by the chiral edges, which can be considered as second-order topological states, i.e., topological corner states., Comment: 13 pages, 7 figures

The formula for the number of domino tilings due to Kasteleyn and Temperley-Fisher is strikingly similar to Eisenstein's formula for the Legendre symbol. We study the connection between these two concepts and prove a formula which expresses the Jacobi symbol in terms of domino tilings., Comment: 15 Pages. A combinatorial proof has been included

The temperature measurement of material inside of an object is one of the key technologies for control of dynamical processes. For this purpose, various techniques such as laser-based thermography and phase-contrast imaging thermography have been studied. However, it is, in principle, impossible to measure the temperature of an element inside of an object using these techniques. One of the possible solutions is measurements of Doppler brooding effect in neutron resonance absorption (NRA). Here we present a method to measure the temperature of an element or an isotope inside of an object using NRA with a single neutron pulse of approximately 100 ns width provided from a high-power laser. We demonstrate temperature measurements of a tantalum (Ta) metallic foil heated from the room temperature up to 617 K. Although the neutron energy resolution is fluctuated from shot to shot, we obtain exactly the temperature using a reference of a silver (Ag) foil kept to the room temperature. A free gas model well reproduces the results. This method enables element(isotope)-sensitive thermometry to detect the instantaneous temperature rise in dynamical processes.

A new diffuse interface model has been proposed in this study for simulating binary alloy solidification under universal cooling conditions, involving both equilibrium and non-equilibrium solute partitioning. Starting from the Gibbs-Thomson equation, which is the classical theory that describes the dynamics of a sharp interface, the phase-field equation is derived using a traveling wave solution that represents a diffuse interface. To tackle the spurious effects caused by the variation of liquid concentration within the diffuse interface with artificial width, a middle obstacle is introduced to sharpen the diffuse interface and an invariant liquid concentration can be found for determining a constant undercooling in the interface normal direction. For slow solidification under equilibrium conditions, the convergence performance of the dendrite tip shows superior invulnerability to the width effect of the diffuse interface. For rapid solidification under non-equilibrium conditions, the output partition coefficients obtained from the steady-state concentration profiles agree with the input velocity-dependent function. The proposed model is promising to be an indispensable tool for the development of advanced alloy materials through the microstructure control of solidification under a wide range of cooling conditions.

The velocity field composed of the Berry connection from many-body wave functions and electromagnetic vector potential explains the energy-momentum balance during the reversible superconducting-normal phase transition in the presence of an externally applied magnetic field. In this formalism, forces acting on electrons are the Lorentz force and force expressed as the gradient of the kinetic energy. In the stationary situation, they balance; however, an infinitesimal imbalance of them causes a phase boundary shift. In order to explain the energy balance during this phase boundary shift, the electromotive force of the Faraday's magnetic induction type is considered for the Berry connection. This theory assumes that supercurrent exists as a collection of stable quantized loop currents, and the transition from the superconducting to normal phase is due to the loss of their stabilizations through the thermal fluctuation of the winding numbers of the loop currents. We argue that an abrupt change of loop current states with integral quantum numbers should be treated as a quantum transition; then, the direct conversion of the quantized loop currents to the magnetic field occurs; consequently, the Joule heat generation does not occur during the phase transition.

Morphogenesis of living systems involves topological shape transformations which are highly unusual in the inanimate world. Here we demonstrate that a droplet of a nematic liquid crystal changes its equilibrium shape from a simply-connected tactoid, which is topologically equivalent to a sphere, to a torus, which is not simply-connected. The topological shape transformation is caused by the interplay of nematic elastic constants, which facilitates splay and bend of molecular orientations in tactoids but hinders splay in the toroids. The elastic anisotropy mechanism might be helpful in understanding topology transformations in morphogenesis and paves the way to control and transform shapes of droplets of liquid crystals and related soft materials., Comment: 28 pages, 12 figures