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With the growing popularity of generative AI for images, video, and music, we witnessed models rapidly improve in quality and performance. However, not much attention is paid towards enabling AI's ability to "be creative". In this study, we implemented and simulated the systems model of creativity (proposed by Csikszentmihalyi) using virtual agents utilizing large language models (LLMs) and text prompts. For comparison, the simulations were conducted with the "virtual artists" being: 1)isolated and 2)placed in a multi-agent system. Both scenarios were compared by analyzing the variations and overall "creativity" in the generated artifacts (measured via a user study and LLM). Our results suggest that the generative agents may perform better in the framework of the systems model of creativity.

We proved that the boundary Dehn twist on the Milnor fiber $M_c(2, q, r)$ is an exotic diffeomorphism relative to the boundary if $q, r$ are odd, coprime integers bigger than $3$ and $(q-1)(r-1)/4$ is an odd number. The proof is given by comparing the family relative Bauer--Furuta invariants of the mapping torus., Comment: 12 pages

Consider a one-dimensional diffusion process which has state-dependent drift and deviation and is reflected at the origin, which is called a one-side reflected diffusion or simply reflected diffusion. We are particularly interested in the case that its drift and deviation are discontinuous. We define this reflected diffusion as the solution of a stochastic integral equation, and find conditions for its positive recurrence, We then derive its stationary distribution under these conditions. As a related problem, we also consider the case that it is reflected at two sides, which is called a two-sides reflected diffusion. Its existence, positive recurrence and stationary distribution are similarly studied. In the literature, these problems are studied through a state-dependent diffusion on the whole line particularly when the drift and deviation are discontinuous. However, the reflected process itself is not defined in such a study. Thus, the stationary distribution has not been fully studied for a general state-dependent reflected diffusion. We aim to fills this insufficiency and to make the stationary distributions of reflected diffusions widely available in application., Comment: Submitted for publication

We propose ratio divergence (RD) learning for discrete energy-based models, a method that utilizes both training data and a tractable target energy function. We apply RD learning to restricted Boltzmann machines (RBMs), which are a minimal model that satisfies the universal approximation theorem for discrete distributions. RD learning combines the strength of both forward and reverse Kullback-Leibler divergence (KLD) learning, effectively addressing the "notorious" issues of underfitting with the forward KLD and mode-collapse with the reverse KLD. Since the summation of forward and reverse KLD seems to be sufficient to combine the strength of both approaches, we include this learning method as a direct baseline in numerical experiments to evaluate its effectiveness. Numerical experiments demonstrate that RD learning significantly outperforms other learning methods in terms of energy function fitting, mode-covering, and learning stability across various discrete energy-based models. Moreover, the performance gaps between RD learning and the other learning methods become more pronounced as the dimensions of target models increase., Comment: 14 pages, 19 figures

There are several challenges in developing a model for multi-tasking humanoid control. Reinforcement learning and imitation learning approaches are quite popular in this domain. However, there is a trade-off between the two. Reinforcement learning is not the best option for training a humanoid to perform multiple behaviors due to training time and model size, and imitation learning using kinematics data alone is not appropriate to realize the actual physics of the motion. Training models to perform multiple complex tasks take long training time due to high DoF and complexities of the movements. Although training models offline would be beneficial, another issue is the size of the dataset, usually being quite large to encapsulate multiple movements. There are few implementations of transformer-based models to control humanoid characters and predict their motion based on a large dataset of recorded/reference motion. In this paper, we train a GPT on a large dataset of noisy expert policy rollout observations from a humanoid motion dataset as a pre-trained model and fine tune that model on a smaller dataset of noisy expert policy rollout observations and actions to autoregressively generate physically plausible motion trajectories. We show that it is possible to train a GPT-based foundation model on a smaller dataset in shorter training time to control a humanoid in a realistic physics environment to perform human-like movements.

A semi-martingale reflecting Brownian motion is a popular process for diffusion approximations of queueing models including their networks. In this paper, we are concerned with the case that it lives on the nonnegative half-line, but the drift and variance of its Brownian component discontinuously change at its finitely many states. This reflecting diffusion process naturally arises from a state-dependent single server queue, studied by the author (2024). Our main interest is in its stationary distribution, which is important for application. We define this reflecting diffusion process as the solution of a stochastic integral equation, and show that it uniquely exists in the weak sense. This result is also proved in a different way by Atar, Castiel and Reiman (2022,2023). In this paper, we consider its Harris irreducibility and stability, that is, positive recurrence, and derive its stationary distribution under this stability condition. The stationary distribution has a simple analytic expression, likely extendable to a more general state-dependent SRBM. Our proofs rely on the generalized Ito formula for a convex function and local time., Comment: This paper is accepted for publication by Journal of the Indian Society for Probability and Statistics

We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile framework for designing efficient approximation schemes for classic geometric packing problems. The framework effectively addresses problems such as the multiple knapsack, bin packing, multiple strip packing, and multiple minimum container problems. Furthermore, the framework handles additional problem features, including item multiplicity, item rotation, and additional constraints on the items commonly encountered in packing contexts. The core of our framework lies in formulating the problems as integer programs with a nearly decomposable structure. This approach enables us to obtain well-behaved fractional solutions, which can then be efficiently rounded. By modeling the problems in this manner, our framework offers significant flexibility, allowing it to address a wide range of problems and incorporate additional features. To the best of our knowledge, prior to this work, the known results on approximation algorithms for packing problems were either highly fixed for one problem or restricted to one class of objects, mainly polygons and hypercubes. In this sense, our framework is the first result with a general toolbox flavor in the context of approximation algorithms for geometric packing problems. Thus, we believe that our technique is of independent interest, being possible to inspire further work on geometric packing.

In the classic realm of impact mitigation, targeting different impact scenarios with a universally designed device still remains an unassailable challenge. In this study, we delve into the untapped potential of Resch-patterned origami for impact mitigation, specifically considering the adaptively reconfigurable nature of the Resch origami structure. Our unit-cell-level analyses reveal two distinctive modes of deformation, each characterized by contrasting mechanical responses: the folding mode that displays monostability coupled with strain-hardening, and the unfolding mode that manifests bistability, facilitating energy absorption through snap-through dynamics. Drop tests further unveil a novel dynamic bifurcation phenomenon, where the origami switches between folding and unfolding depending on impact speed, thereby showcasing its innate self-reconfigurability in a wide range of dynamic events. The tessellated meter-scale Resch structure mimicking an automotive bumper inherits this dynamically bifurcating behavior, demonstrating the instantaneous morphing into favorable deformation mode to minimize the peak acceleration upon impact. This suggests a self-adaptive and universally applicable impact-absorbing nature of the Resch-patterned origami system. We believe that our findings pave the way for developing smart, origami-inspired impact mitigation devices capable of real-time response and adaptation to external stimuli, offering insights into designing universally protective structures with enhanced performance in response to various impact scenarios.

In Braverman et al. (2024), the authors prove that the stationary distribution of a multiclass queueing network converges to the stationary distribution of a semimartingale reflecting Brownian motion (SRBM) in heavy traffic. Among the sufficient conditions for the convergence is that the reflection matrix $R$ of the SRBM is "tight". In this paper, we study how we can verify this tightness of $R$. For a $2$-dimensional SRBM, we give necessary and sufficient conditions for $R$ to be tight, while, for a general dimension, we only give sufficient conditions. We then apply these results to the SRBMs arising from the diffusion approximations of multiclass queueing networks with static buffer priority service disciplines that are studied in Braverman et al. (2024). It is shown that $R$ is always tight for this network with two stations if $R$ is defined and completely-S. For the case of more than two stations, it is shown that $R$ is tight for reentrant lines with last-buffer-first-service (LBFS) discipline, but it is not always tight for reentrant line with first-buffer-first-service (FBFS) discipline.

How are emotions formed? Through extensive debate and the promulgation of diverse theories , the theory of constructed emotion has become prevalent in recent research on emotions. According to this theory, an emotion concept refers to a category formed by interoceptive and exteroceptive information associated with a specific emotion. An emotion concept stores past experiences as knowledge and can predict unobserved information from acquired information. Therefore, in this study, we attempted to model the formation of emotion concepts using a constructionist approach from the perspective of the constructed emotion theory. Particularly, we constructed a model using multilayered multimodal latent Dirichlet allocation , which is a probabilistic generative model. We then trained the model for each subject using vision, physiology, and word information obtained from multiple people who experienced different visual emotion-evoking stimuli. To evaluate the model, we verified whether the formed categories matched human subjectivity and determined whether unobserved information could be predicted via categories. The verification results exceeded chance level, suggesting that emotion concept formation can be explained by the proposed model., Comment: This work has been submitted to the IEEE for possible publication. We would like to thank Professor Takayuki Nagai for useful discussions

XL-Calibur is a balloon-borne Compton polarimeter for X-rays in the $\sim$15-80 keV range. Using an X-ray mirror with a 12 m focal length for collecting photons onto a beryllium scattering rod surrounded by CZT detectors, a minimum-detectable polarization as low as $\sim$3% is expected during a 24-hour on-target observation of a 1 Crab source at 45$^{\circ}$ elevation. Systematic effects alter the reconstructed polarization as the mirror focal spot moves across the beryllium scatterer, due to pointing offsets, mechanical misalignment or deformation of the carbon-fiber truss supporting the mirror and the polarimeter. Unaddressed, this can give rise to a spurious polarization signal for an unpolarized flux, or a change in reconstructed polarization fraction and angle for a polarized flux. Using bench-marked Monte-Carlo simulations and an accurate mirror point-spread function characterized at synchrotron beam-lines, systematic effects are quantified, and mitigation strategies discussed. By recalculating the scattering site for a shifted beam, systematic errors can be reduced from several tens of percent to the few-percent level for any shift within the scattering element. The treatment of these systematic effects will be important for any polarimetric instrument where a focused X-ray beam is impinging on a scattering element surrounded by counting detectors., Comment: Submitted to Astroparticle Physics

We investigate edge and bulk states in Weyl-orbit based quantum Hall effect by measuring a Corbino-type device fabricated from a topological Dirac semimetal (Cd1-xZnx)3As2 film. Clear quantum Hall plateaus are observed when measuring one-sided terminals of the Corbino-type device. This indicates that edge states of the Weyl-orbit quantum Hall effect form closed trajectories consisting of Fermi arcs and chiral zero modes independently on inner and outer sides. On the other hand, the bulk resistance does not diverge at fields where the quantum Hall plateau appears, suggesting that the Weyl orbits in the bulk region are not completely localized when applying electric current through the bulk region.

We consider a single server queue which has a threshold to change its arrival process and service speed by its queue length, which is referred to as a two-level single server queue. This model is motivated by an energy saving problem for a single server queue whose arrival process and service speed are controlled. To get its performance in tractable form, we study the limit of the stationary distribution of the queue length in this two-level queue under scaling in heavy traffic. Except for a special case, this limit corresponds to its diffusion approximation. It is shown that this limiting distribution is truncated exponential (or uniform if the drift is null) below the threshold level and exponential above it under suitably chosen system parameters and generally distributed inter-arrival times and workloads brought by customers. This result is proved under a mild limitation on arrival parameters using the so called BAR approach studied in Braverman, Dai and Miyazawa (2017, 2023) and Miyazawa (2017, 2023). We also intuitively discuss about a diffusion process corresponding to the limit of the stationary distribution under scaling., Comment: 40 pages, 2 figure, submitted for publication. This paper will appear in Advances in Applied Probability 57.4 (December 2025)

We give an infinite family of embeddings of $\mathbb{R} P^2$ to $S^4$ such that they are mutually topologically isotopic however are not smoothly isotopic to each other. Moreover, they are topologically isotopic to the standard $P^2$-knot. To prove that these $P^2$-knots are not smoothly isotopic to each other, we construct a gauge theoretic invariant of embedded surfaces in $4$-manifolds using a variant of the Seiberg--Witten theory, which is called the Real Seiberg--Witten theory., Comment: 45 pages

We consider Palm distributions arising in a Markov process with time homogeneous transitions which is jointly stationary with multiple point processes. Motivated by a BAR approach studied in the recent paper Braverman, Dai and Miyazawa (2023}, we are interested in two problems; when this Markov process inherits the same Markov structure under the Palm distributions, and how the state changes at counting instants of the point processes can be handled to derive stationary equations when there are simultaneous counts and each of them influences the state changes. We affirmatively answer to the first problem, and propose a framework for resolving the second problem. We also discuss how those results can be applied in deriving BAR's for the diffusion approximation of queueing models in heavy traffic. In particular, as their new application, the heavy traffic limit of the stationary distribution is derived for a single server queue with a finite waiting room. Those examples show how the BAR approach is useful under the proposed framework., Comment: Submitted for publication, revised

This paper presents theoretical and practical results for the bin packing problem with scenarios, a generalization of the classical bin packing problem which considers the presence of uncertain scenarios, of which only one is realized. For this problem, we propose an absolute approximation algorithm whose ratio is bounded by the square root of the number of scenarios times the approximation ratio for an algorithm for the vector bin packing problem. We also show how an asymptotic polynomial-time approximation scheme is derived when the number of scenarios is constant. As a practical study of the problem, we present a branch-and-price algorithm to solve an exponential model and a variable neighborhood search heuristic. To speed up the convergence of the exact algorithm, we also consider lower bounds based on dual feasible functions. Results of these algorithms show the competence of the branch-and-price in obtaining optimal solutions for about 59% of the instances considered, while the combined heuristic and branch-and-price optimally solved 62% of the instances considered.

This paper focuses on exact approaches for the Colored Bin Packing Problem (CBPP), a generalization of the classical one-dimensional Bin Packing Problem in which each item has, in addition to its length, a color, and no two items of the same color can appear consecutively in the same bin. To simplify modeling, we present a characterization of any feasible packing of this problem in a way that does not depend on its ordering. Furthermore, we present four exact algorithms for the CBPP. First, we propose a generalization of Val\'erio de Carvalho's arc flow formulation for the CBPP using a graph with multiple layers, each representing a color. Second, we present an improved arc flow formulation that uses a more compact graph and has the same linear relaxation bound as the first formulation. And finally, we design two exponential set-partition models based on reductions to a generalized vehicle routing problem, which are solved by a branch-cut-and-price algorithm through VRPSolver. To compare the proposed algorithms, a varied benchmark set with 574 instances of the CBPP is presented. Results show that the best model, our improved arc flow formulation, was able to solve over 62% of the proposed instances to optimality, the largest of which with 500 items and 37 colors. While being able to solve fewer instances in total, the set-partition models exceeded their arc flow counterparts in instances with a very small number of colors.

We develop a version of Seiberg--Witten Floer cohomology/homotopy type for a spin$^c$ 4-manifold with boundary and with an involution which reverses the spin$^c$ structure, as well as a version of Floer cohomology/homotopy type for oriented links with non-zero determinant. This framework generalizes the previous work of the authors regarding Floer homotopy type for spin 3-manifolds with involutions and for knots. Based on this Floer cohomological setting, we prove Fr{\o}yshov-type inequalities which relate topological quantities of 4-manifolds with certain equivariant homology cobordism invariants. The inequalities and homology cobordism invariants have applications to the topology of unoriented surfaces, Nielsen realization problem for non-spin 4-manifolds, and non-smoothable unoriented surfaces in 4-manifolds., Comment: 43 pages, Added Remark 1.19 to mention upcoming work by Arabadji and Baykur on the Nielsen realization problem for non-spin 4-manifolds. Fixed typo in Theorem 1.6

Origami structures often serve as the building block of mechanical systems due to their rich static and dynamic behaviors. Experimental observation and theoretical modeling of origami dynamics have been reported extensively, whereas the data-driven modeling of origami dynamics is still challenging due to the intrinsic nonlinearity of the system. In this study, we show how the dynamic mode decomposition (DMD) method can be enhanced by integrating geometry information of the origami structure to model origami dynamics in an efficient and accurate manner. In particular, an improved version of DMD with control, that we term geometry-informed dynamic mode decomposition~(giDMD), is developed and evaluated on the origami chain and dual Kresling origami structure to reveal the efficacy and interpretability. We show that giDMD can accurately predict the dynamics of an origami chain across frequencies, where the topological boundary state can be identified by the characteristics of giDMD. Moreover, the periodic intrawell motion can be accurately predicted in the dual origami structure. The type of dynamics in the dual origami structure can also be identified. The model learned by the giDMD also reveals the influential geometrical parameters in the origami dynamics, indicating the interpretability of this method. The accurate prediction of chaotic dynamics remains a challenge for the method. Nevertheless, we expect that the proposed giDMD approach will be helpful towards the prediction and identification of dynamics in complex origami structures, while paving the way to the application to a wider variety of lightweight and deployable structures., Comment: 11 pages, 7 figures

The basic adjoint relationship (BAR) approach is an analysis technique based on the stationary equation of a Markov process. This approach was introduced to study heavy-traffic, steady-state convergence of generalized Jackson networks in which each service station has a single job class. We extend it to multiclass queueing networks operating under static-buffer-priority (SBP) service disciplines. Our extension makes a connection with Palm distributions that allows one to attack a difficulty arising from queue-length truncation, which appears to be unavoidable in the multiclass setting. For multiclass queueing networks operating under SBP service disciplines, our BAR approach provides an alternative to the "interchange of limits" approach that has dominated the literature in the last twenty years. The BAR approach can produce sharp results and allows one to establish steady-state convergence under three additional conditions: stability, state space collapse (SSC) and a certain matrix being "tight." These three conditions do not appear to depend on the interarrival and service-time distributions beyond their means, and their verification can be studied as three separate modules. In particular, they can be studied in a simpler, continuous-time Markov chain setting when all distributions are exponential. As an example, these three conditions are shown to hold in reentrant lines operating under last-buffer-first-serve discipline. In a two-station, five-class reentrant line, under the heavy-traffic condition, the tight-matrix condition implies both the stability condition and the SSC condition. Whether such a relationship holds generally is an open problem.

The XL-Calibur balloon-borne hard X-ray polarimetry mission comprises a Compton-scattering polarimeter placed at the focal point of an X-ray mirror. The polarimeter is housed within a BGO anticoincidence shield, which is needed to mitigate the considerable background radiation present at the observation altitude of ~40 km. This paper details the design, construction and testing of the anticoincidence shield, as well as the performance measured during the week-long maiden flight from Esrange Space Centre to the Canadian Northwest Territories in July 2022. The in-flight performance of the shield followed design expectations, with a veto threshold <100 keV and a measured background rate of ~0.5 Hz (20-40 keV). This is compatible with the scientific goals of the mission, where %-level minimum detectable polarisation is sought for a Hz-level source rate., Comment: Submitted to Nuclear Instruments and Methods A

Joyce, Tanaka, and Upmeier give an orientation of the $G$-instanton moduli spaces on a closed four manifolds which is canonically defined using the the $\mathrm{Spin}^c$ structure on the $4$-manifold. In this note, we describe the relation between the orientations given by other choices of the $\mathrm{Spin}^c$ structures, in a slightly more general setting. Furthermore, we give an alternative proof of the orientability of the instanton moduli spaces and an alternative construction of the orientation by Joyce, Tanaka and Upmeier, by using Witten localization of the index of a Dirac type operator., Comment: 11pages

The short-term sensitivity of a kilometer-long fiber-optic gyroscope is limited mainly by thermal phase noise and relative intensity noise. Increasing the phase modulation frequency decreases the thermal phase noise but not the relative intensity noise since it behaves as white noise. Here, we propose and experimentally demonstrate that the angular random walk can be effectively decreased by suppressing relative intensity noise at the modulation frequency and its third-order harmonic using direct feedback to the drive current of a superluminescent diode. Our simultaneous suppression of thermal phase noise and relative intensity noise yields an angular random walk of $15\,\mu\mathrm{deg}/\sqrt{\mathrm{h}}$ and a bias instability of $33\,\mu\mathrm{deg}/\mathrm{h}$ using a fiber coil with a length of $5\,$km and an effective area of $280\,\mathrm{m^2}$ for a measurement time of 40 hours., Comment: 7 pages, 6 figures, 1 table

We report the realization of a Bose-Einstein condensate of europium atoms, which is a strongly dipolar species with unique properties, a highly symmetric $[\mathrm{Xe}]\ 4f^7 6s^2\ {}^8\mathrm{S}_{7/2}$ electronic ground state and a hyperfine structure. By means of evaporative cooling in a crossed optical dipole trap, we produced a condensate of ${}^{151}$Eu containing up to $5\times 10^4$ atoms. The scattering length of ${}^{151}$Eu was estimated to be $a_s = 110(4)\, a_\mathrm{B}$ by comparing the velocities of expansion of condensates with different orientations of the atomic magnetic moments. We observed deformation of the condensate in the vicinity of the Feshbach resonance at $1.32\,\mathrm{G}$ with a width of $10\,\mathrm{mG}$., Comment: 5 pages, 4 figures

Label-free metabolic imaging of non-alcoholic fatty liver disease (NAFLD) mouse liver is demonstrated ex vivo by dynamic optical coherence tomography (OCT). The NAFLD mouse is a methionine choline-deficient (MCD)-diet model, and two mice fed MCD diet for 1 and 2 weeks are involved in addition to a normal-diet mouse. The dynamic OCT is based on repeating raster scan and logarithmic intensity variance (LIV) analysis which enables volumetric metabolic imaging with a standard-speed (50,000 A-lines/s) OCT system. Metabolic domains associated with lipid droplet accumulation and inflammation are clearly visualized three-dimensionally. Particularly, the normal-diet liver exhibits highly metabolic vessel-like structures of peri-vascular hepatic zones. The 1-week MCD-diet liver shows ring-shaped highly metabolic structures formed with lipid droplets. The 2-week MCD-diet liver exhibits fragmented vessel-like structures associated with inflammation. These results imply that volumetric LIV imaging is useful for visualizing and assessing NAFLD abnormalities.

We consider a two station cascade system in which waiting or externally arriving customers at station $1$ move to the station $2$ if the queue size of station $1$ including a customer being served is greater than a given threshold level $C_{1} \ge 1$ and if station $2$ is empty. Assuming that external arrivals are subject to independent renewal processes satisfying certain regularity conditions and service times are $i.i.d.$ at each station, we derive necessary and sufficient conditions for a Markov process describing this system to be positive recurrent in the sense of Harris. This result is extended to the cascade system with a general number $k$ of stations in series. This extension requires the actual traffic intensities of stations $2,3,\ldots, k-1$ for $k \ge 3$. We finally note that the modeling assumptions on the renewal arrivals and $i.i.d.$ service times are not essential if the notion of the stability is replaced by a certain sample path condition. This stability notion is identical with the standard stability if the whole system is described by the Markov process which is a Harris irreducible $T$-process., Comment: Accepted for publication in Queueing Systems

Topological mechanical metamaterials have been widely explored for their boundary states, which can be robustly isolated or transported in a controlled manner. However, such systems often require pre-configured design or complex active actuation for wave manipulation. Here, we present the possibility of in-situ transfer of topological boundary modes by leveraging the reconfigurability intrinsic in twisted origami lattices. In particular, we employ a dimer Kresling origami system consisting of unit cells with opposite chirality, which couples longitudinal and rotational degrees of freedom in elastic waves. The quasi-static twist imposed on the lattice alters the strain landscape of the lattice, thus significantly affecting the wave dispersion relations and the topology of the underling bands. This in turn facilitates an efficient topological state transfer from one edge to the other. This simple and practical approach of energy transfer in origami-inspired lattices can thus inspire a new class of efficient energy manipulation devices., Comment: 24 pages, 5 figures

Our objective is to stabilise and accelerate the time-domain boundary element method (TDBEM) for the three-dimensional wave equation. To overcome the potential time instability, we considered using the Burton--Miller-type boundary integral equation (BMBIE) instead of the ordinary boundary integral equation (OBIE), which consists of the single- and double-layer potentials. In addition, we introduced a smooth temporal basis, i.e. the B-spline temporal basis of order $d$, whereas $d=1$ was used together with the OBIE in a previous study [Takahashi 2014]. Corresponding to these new techniques, we generalised the interpolation-based fast multipole method that was developed in \cite{takahashi2014}. In particular, we constructed the multipole-to-local formula (M2L) so that even for $d\ge 2$ we can maintain the computational complexity of the entire algorithm, i.e. $O(N_{\rm s}^{1+\delta} N_{\rm t})$, where $N_{\rm s}$ and $N_{\rm t}$ denote the number of boundary elements and the number of time steps, respectively, and $\delta$ is theoretically estimated as $1/3$ or $1/2$. The numerical examples indicated that the BMBIE is indispensable for solving the homogeneous Dirichlet problem, but the order $d$ cannot exceed 1 owing to the doubtful cancellation of significant digits when calculating the corresponding layer potentials. In regard to the homogeneous Neumann problem, the previous TDBEM based on the OBIE with $d=1$ can be unstable, whereas it was found that the BMBIE with $d=2$ can be stable and accurate. The present study will enhance the usefulness of the TDBEM for 3D scalar wave problems.

We establish a version of Seiberg--Witten Floer $K$-theory for knots, as well as a version of Seiberg-Witten Floer $K$-theory for 3-manifolds with involution. The main theorems are 10/8-type inequalities for knots and for involutions. The 10/8-inequality for knots yields numerous applications to knots, such as lower bounds on stabilizing numbers and relative genera. We also give obstructions to extending involutions on 3-manifolds to 4-manifolds, and detect non-smoothable involutions on 4-manifolds with boundary., Comment: 69 pages, 1 figure, 5 tables. Many applications and calculations were added. Some properties of the kappa invariant were added

It is known that the Dirac index of a $Spin^c$ structure is localized to the characteristic submanifold. We introduce the notion of $G^{\pm}(n,s^+,s^-)$ structure on a manifold as a common generalization of the $Spin^c$ structure and the $H_n(s)$ structure defined by D.~Freed--M.~Hopkins, and formulate a version of characteristic submanifold for the $G^{\pm}(n,s^+,s^-)$ structure. We show that the $KO^*(pt)$-valued index associated with the $G^{\pm}(n,s^+,s^-)$ structure is localized to the characteristic submanifold. As an application, we give a topological sufficient condition for the moduli space of $Pin^-(2)$ monopoles to be orientable., Comment: 27 pages

In the $d$-dimensional hypercube bin packing problem, a given list of $d$-dimensional hypercubes must be packed into the smallest number of hypercube bins. Epstein and van Stee [SIAM J. Comput. 35 (2005)] showed that the asymptotic performance ratio $\rho$ of the online bounded space variant is $\Omega(\log d)$ and $O(d/\log d)$, and conjectured that it is $\Theta(\log d)$. We show that $\rho$ is in fact $\Theta(d/\log d)$, using probabilistic arguments., Comment: This manuscript is derived from arXiv:1712.06763, where further material is presented and the proofs are formulated a little differently

In this work we present an analytical and numerical study of rogue and solitary waves in a coupled one-dimensional nonlinear lattice that involves both axial and rotational degrees of freedom. Using a multiple-scale analysis we derive a system of coupled nonlinear Schr\"odinger type equations in order to approximate solitary waves and rogue waves of the coupled lattice model. Numerical simulations are found to agree with the analytical approximations. We also consider generic initialization data in the form of a Gaussian profile and observe that they can result in the spontaneous formation of rogue wave-like patterns in the lattice. The solitary and rogue waves in the lattice demonstrate both energy isolation and exchange between the axial and rotational degrees of freedom of the system. This suggests that the studied coupled lattice has the potential to be an efficient energy isolation, transfer, and focusing medium., Comment: 11 pages, 6 figures

We address the solution of Mixed Integer Linear Programming (MILP) models with strong relaxations that are derived from Dantzig-Wolfe decompositions and allow a pseudo-polynomial pricing algorithm. We exploit their network-flow characterization and provide a framework based on column generation, reduced-cost variable-fixing, and a highly asymmetric branching scheme that allows us to take advantage of the potential of the current MILP solvers. We apply our framework to a variety of cutting and packing problems from the literature. The efficiency of the framework is proved by extensive computational experiments, in which a significant number of open instances could be solved to proven optimality for the first time.

To realize autonomous collaborative robots, it is important to increase the trust that users have in them. Toward this goal, this paper proposes an algorithm which endows an autonomous agent with the ability to explain the transition from the current state to the target state in a Markov decision process (MDP). According to cognitive science, to generate an explanation that is acceptable to humans, it is important to present the minimum information necessary to sufficiently understand an event. To meet this requirement, this study proposes a framework for identifying important elements in the decision-making process using a prediction model for the world and generating explanations based on these elements. To verify the ability of the proposed method to generate explanations, we conducted an experiment using a grid environment. It was inferred from the result of a simulation experiment that the explanation generated using the proposed method was composed of the minimum elements important for understanding the transition from the current state to the target state. Furthermore, subject experiments showed that the generated explanation was a good summary of the process of state transition, and that a high evaluation was obtained for the explanation of the reason for an action.

We report the measurement of one-body loss rates for magnetically trapped metastable europium atoms and the study of their loss mechanism. The loss of atoms observed in a magneto-optical trap is not fully understood because of the indivisibility of the loss regarding optical pumpings due to the presence of cooling laser beams. We magnetically trapped the atoms by directly loading from the magneto-optical trap and observed almost identical one-body loss rates of approximately $2.6\,\mathrm{s^{-1}}$ for two isotopes: $\mathrm{{}^{151}Eu}$ and $\mathrm{{}^{153}Eu}$. Our rate-equation-based model, combined with loss rate measurements carried out with repumpers, shows that blackbody radiation at room temperature drives E1 transitions and induces the observed losses., Comment: 6 pages, 4 figures, 1 table

We report on the realization of a magneto-optical trap (MOT) for europium atoms using a narrow-line cooling transition with a natural linewidth of 97 kHz. Our starting point is continuous capturing and cooling of optically pumped metastable europium atoms. We have employed simultaneous MOT for the metastable and ground-state atoms. The trapped metastable atoms are successively pumped back to the ground state and then continuously loaded to the narrow-line MOT, where up to $4.7\times10^7$ atoms are captured. A spin-polarized sample at a temperature of $6\,\mathrm{\mu K}$ and with a peak number density of $2.2\times10^{11}\,\mathrm{cm^{-3}}$ is obtained through the compression process, resulting in a phase space density of $3\times10^{-5}$., Comment: 5 pages, 4 figures, 2 tables

Glass nanopipettes are widely used for various applications in nanosciences. In most of the applications, it is important to characterize their geometrical parameters, such as the aperture size and the inner cone angle at the tip region. For nanopipettes with sub-10 nm aperture and thin wall thickness, transmission electron microscopy (TEM) must be most instrumental in their precise geometrical measurement. However, this measurement has remained a challenge because heat generated by electron beam irradiation would largely deform sub-10-nm nanopipettes. Here we provide methods for preparing TEM specimens that do not cause deformation of such tiny nanopipettes., Comment: 8 pages, 4 figures

XL-Calibur is a hard X-ray (15-80 keV) polarimetry mission operating from a stabilised balloon-borne platform in the stratosphere. It builds on heritage from the X-Calibur mission, which observed the accreting neutron star GX 301-2 from Antarctica, between December 29th 2018 and January 1st 2019. The XL-Calibur design incorporates an X-ray mirror, which focusses X-rays onto a polarimeter comprising a beryllium rod surrounded by Cadmium Zinc Telluride (CZT) detectors. The polarimeter is housed in an anticoincidence shield to mitigate background from particles present in the stratosphere. The mirror and polarimeter-shield assembly are mounted at opposite ends of a 12 m long lightweight truss, which is pointed with arcsecond precision by WASP - the Wallops Arc Second Pointer. The XL-Calibur mission will achieve a substantially improved sensitivity over X-Calibur by using a larger effective area X-ray mirror, reducing background through thinner CZT detectors, and improved anticoincidence shielding. When observing a 1 Crab source for $t_{\rm day}$ days, the Minimum Detectable Polarisation (at 99% confidence level) is $\sim$2$\%\cdot t_{\rm day}^{-1/2}$. The energy resolution at 40 keV is $\sim$5.9 keV. The aim of this paper is to describe the design and performance of the XL-Calibur mission, as well as the foreseen science programme., Comment: 19 pages, 17 figures. Accepted for publication in Astroparticle Physics

In this paper, we analyze a transportation game first introduced by Fotakis, Gourv\`es, and Monnot in 2017, where players want to be transported to a common destination as quickly as possible and, in order to achieve this goal, they have to choose one of the available buses. We introduce a sequential version of this game and provide bounds for the Sequential Price of Stability and the Sequential Price of Anarchy in both metric and non-metric instances, considering three social cost functions: the total traveled distance by all buses, the maximum distance traveled by a bus, and the sum of the distances traveled by all players (a new social cost function that we introduce). Finally, we analyze the Price of Stability and the Price of Anarchy for this new function in simultaneous transportation games.

Dabkowski and Sahi defined an invariant of a link in the $3$-sphere, which is preserved under $4$-moves. This invariant is a quotient of the fundamental group of the complement of the link. It is generally difficult to distinguish the Dabkowski-Sahi invariants of given links. In this paper, we give a necessary condition for the existence of an isomorphism between the Dabkowski-Sahi invariant of a link and that of the corresponding trivial link. Using this condition, we provide a practical obstruction to a link to be trivial up to $4$-moves., Comment: 9 pages

We survey the main formulations and solution methods for two-dimensional orthogonal cutting and packing problems, where both items and bins are rectangles. We focus on exact methods and relaxations for the four main problems from the literature: finding a packing with minimum height, packing the items into the minimum number of bins, finding a packing of maximum value, and determining the existence of a feasible packing.

Recently, the bidirectional encoder representations from transformers (BERT) model has attracted much attention in the field of natural language processing, owing to its high performance in language understanding-related tasks. The BERT model learns language representation that can be adapted to various tasks via pre-training using a large corpus in an unsupervised manner. This study proposes the language and action learning using multimodal BERT (lamBERT) model that enables the learning of language and actions by 1) extending the BERT model to multimodal representation and 2) integrating it with reinforcement learning. To verify the proposed model, an experiment is conducted in a grid environment that requires language understanding for the agent to act properly. As a result, the lamBERT model obtained higher rewards in multitask settings and transfer settings when compared to other models, such as the convolutional neural network-based model and the lamBERT model without pre-training., Comment: 8 pages, 9 figures

Although common in nature, the self-assembly of small molecules at sold-liquid interfaces is difficult to control in artificial systems. The high mobility of dissolved small molecules limits their residence at the interface, typically restricting the self-assembly to systems under confinement or with mobile tethers between the molecules and the surface. Small hydrogen-bonding molecules can overcome these issues by exploiting group-effect stabilization to achieve non-tethered self-assembly at hydrophobic interfaces. Significantly, the weak molecular interactions with the solid makes it possible to influence the interfacial hydrogen bond network, potentially creating a wide variety of supramolecular structures. Here we investigate the nanoscale details of water and alcohols mixtures self-assembling at the interface with graphite through group effect. We explore the interplay between inter-molecular and surface interactions by adding small amounts of foreign molecules able to interfere with the hydrogen bond network and systematically varying the length of the alcohol hydrocarbon chain. The resulting supramolecular structures forming at room temperature are then examined using atomic force microscopy with insights from computer simulations. We show that the group-based self-assembly approach investigated here is general and can be reproduced on other substrates such as molybdenum disulphide and graphene oxide, potentially making it relevant for a wide variety of systems., Comment: 6 figures, Supporting Information files are available upon request to the authors

For a classical link, Milnor defined a family of isotopy invariants, called Milnor $\overline{\mu}$-invariants. Recently, Chrisman extended Milnor $\overline{\mu}$-invariants to welded links by a topological approach. The aim of this paper is to show that Milnor $\overline{\mu}$-invariants can be extended to welded links by a combinatorial approach. The proof contains an alternative proof for the invariance of the original $\overline{\mu}$-invariants of classical links., Comment: 25 pages; v2: the title changed, Section 1 rewritten, remarks and references added; to appear in Michigan Mathematical Journal

Advances in machine learning have revolutionized capabilities in applications ranging from natural language processing to marketing to health care. Here, we demonstrate the efficacy of machine learning in predicting chaotic behavior in complex nonlinear mechanical systems. Specifically, we use quasi-recurrent neural networks to predict extremely chaotic time series data obtained from multistable origami systems. Additionally, while machine learning is often viewed as a "black box", in this study we conduct hidden layer analysis to understand how the neural network can process not only periodic, but also chaotic data in an accurate manner. Also, our approach shows its effectiveness in characterizing and predicting chaotic dynamics in a noisy environment of vibrations without relying on a mathematical model of origami systems. Therefore, our method is fully data-driven and has the potential to be used for complex scenarios, such as the nonlinear dynamics of thin-walled structures and biological membrane systems.

We consider a Markov modulated fluid network with a finite number of stations. We are interested in the tail asymptotics behavior of the stationary distribution of its buffer content process. Using two different approaches, we derive upper and lower bounds for the stationary tail decay rate in various directions. Both approaches are based on a well-known time-evolution formula of a Markov process, so-called Dynkin's formula, where a key ingredient is a suitable choice of test functions. Those results show how multidimensional tail asymptotics can be studied for the more than two-dimensional case, which is known as a hard problem., Comment: 2nd revised version, submitted for publication

We address the problem of partitioning a vertex-weighted connected graph into $k$ connected subgraphs that have similar weights, for a fixed integer $k\geq 2$. This problem, known as the \emph{balanced connected $k$-partition problem} ($BCP_k$), is defined as follows. Given a connected graph $G$ with nonnegative weights on the vertices, find a partition $\{V_i\}_{i=1}^k$ of $V(G)$ such that each class $V_i$ induces a connected subgraph of $G$, and the weight of a class with the minimum weight is as large as possible. It is known that $BCP_k$ is $NP$-hard even on bipartite graphs and on interval graphs. It has been largely investigated under different approaches and perspectives. On the practical side, $BCP_k$ is used to model many applications arising in police patrolling, image processing, cluster analysis, operating systems and robotics. We propose three integer linear programming formulations for the balanced connected $k$-partition problem. The first one contains only binary variables and a potentially large number of constraints that are separable in polynomial time. Some polyhedral results on this formulation, when all vertices have unit weight, are also presented. The other formulations are based on flows and have a polynomial number of constraints and variables. Preliminary computational experiments have shown that the proposed formulations outperform the other formulations presented in the literature.

The inverse Potts problem to infer a Boltzmann distribution for homologous protein sequences from their single-site and pairwise amino acid frequencies recently attracts a great deal of attention in the studies of protein structure and evolution. We study regularization and learning methods and how to tune regularization parameters to correctly infer interactions in Boltzmann machine learning. Using $L_2$ regularization for fields, group $L_1$ for couplings is shown to be very effective for sparse couplings in comparison with $L_2$ and $L_1$. Two regularization parameters are tuned to yield equal values for both the sample and ensemble averages of evolutionary energy. Both averages smoothly change and converge, but their learning profiles are very different between learning methods. The Adam method is modified to make stepsize proportional to the gradient for sparse couplings. It is shown by first inferring interactions from protein sequences and then from Monte Carlo samples that the fields and couplings can be well recovered, but that recovering the pairwise correlations in the resolution of a total energy is harder for the natural proteins than for the protein-like sequences. Selective temperature for folding/structural constrains in protein evolution is also estimated., Comment: In arXiv:1909.05006v3 the values of selective temperature for protein PF00153, $T_s$ in Table 5 and in the section 2.8, and folding free energy for PF00595, and in the v4 the method for soft-thresholding were corrected; shown in red. The v2 was published in the IEEE/ACM Transactions on Computational Biology and Bioinformatics. The program is available from https://gitlab.com/sanzo.miyazawa/BM/

In a previous paper, the authors proved that Milnor link-homotopy invariants modulo $n$ classify classical string links up to $2n$-move and link-homotopy. As analogues to the welded case, in terms of Milnor invariants, we give here two classifications of welded string links up to $2n$-move and self-crossing virtualization, and up to $V^{n}$-move and self-crossing virtualization, respectively., Comment: 16 pages, 18 figures. arXiv admin note: text overlap with arXiv:1902.06079

Two string links are equivalent up to $2n$-moves and link-homotopy if and only if their all Milnor link-homotopy invariants are congruent modulo $n$. Moreover, the set of the equivalence classes forms a finite group generated by elements of order $n$. The classification induces that if two string links are equivalent up to $2n$-moves for every $n>0$, then they are link-homotopic., Comment: 16 pages, 8 figures