Search

We study the concept of (generalized) $p$-th variation of a real-valued continuous function along a general class of refining sequence of partitions. We show that the finiteness of the $p$-th variation of a given function is closely related to the finiteness of $\ell^p$-norm of the coefficients along a Schauder basis, similar to the fact that H\"older coefficient of the function is connected to $\ell^{\infty}$-norm of the Schauder coefficients. This result provides an isomorphism between the space of $\alpha$-H\"older continuous functions with finite (generalized) $p$-th variation along a given partition sequence and a subclass of infinite-dimensional matrices equipped with an appropriate norm, in the spirit of Ciesielski.

Recent research on mobile robot navigation has focused on socially aware navigation in crowded environments. However, existing methods do not adequately account for human robot interactions and demand accurate location information from omnidirectional sensors, rendering them unsuitable for practical applications. In response to this need, this study introduces a novel algorithm, BNBRL+, predicated on the partially observable Markov decision process framework to assess risks in unobservable areas and formulate movement strategies under uncertainty. BNBRL+ consolidates belief algorithms with Bayesian neural networks to probabilistically infer beliefs based on the positional data of humans. It further integrates the dynamics between the robot, humans, and inferred beliefs to determine the navigation paths and embeds social norms within the reward function, thereby facilitating socially aware navigation. Through experiments in various risk laden scenarios, this study validates the effectiveness of BNBRL+ in navigating crowded environments with blind spots. The model's ability to navigate effectively in spaces with limited visibility and avoid obstacles dynamically can significantly improve the safety and reliability of autonomous vehicles., Comment: 8 pages, 4 figures

Quantum emitters in solid-state materials are highly promising building blocks for quantum information processing and communication science. Recently, single-photon emission from van der Waals materials has been reported in transition metal dichalcogenides and hexagonal boron nitride, exhibiting the potential to realize photonic quantum technologies in two-dimensional materials. Here, we report the observation of single-photon generation from exfoliated and thermally annealed single crystals of van der Waals {\alpha}-MoO3. The second-order correlation function measurement displays a clear photon antibunching, while the luminescence intensity exceeds 100 kcounts/s and remains stable under laser excitation. Also, the zero-phonon lines of these emitters are distributed in a spectrally narrow energy range. The theoretical calculation suggests that an oxygen vacancy defect is a possible candidate for the observed emitters. Together with photostability and brightness, quantum emitters in {\alpha}-MoO3 provide a new avenue to realize photon-based quantum information science in van der Waals materials., Comment: 20 pages, 4 figures

Quantum phases of matter such as superconducting, ferromagnetic and Wigner crystal states are often driven by the two-dimensionality (2D) of correlated systems. Meanwhile, spin-orbit coupling (SOC) is a fundamental element leading to nontrivial topology which gives rise to quantum phenomena such as the large anomalous Hall effect and nontrivial superconductivity. However, the search for controllable platforms with both 2D and SOC has been relatively overlooked so far. Here, we control and study the electronic ground states of iridate ultrathin films having both 2D and SOC by angle-resolved photoemission spectroscopy (ARPES) and dynamical mean field theory (DMFT) calculations. The metallicity of SrIrO$_3$ ultrathin films is controlled down to a monolayer by dimensional and strain manipulation. Our results suggest that the iridate ultrathin films can be a controllable 2D SOC platform exhibiting a variety of phenomena for future functional devices., Comment: 7 pages, 4 figures

Robot navigation has transitioned from prioritizing obstacle avoidance to adopting socially aware navigation strategies that accommodate human presence. As a result, the recognition of socially aware navigation within dynamic human-centric environments has gained prominence in the field of robotics. Although reinforcement learning technique has fostered the advancement of socially aware navigation, defining appropriate reward functions, especially in congested environments, has posed a significant challenge. These rewards, crucial in guiding robot actions, demand intricate human-crafted design due to their complex nature and inability to be automatically set. The multitude of manually designed rewards poses issues with hyperparameter redundancy, imbalance, and inadequate representation of unique object characteristics. To address these challenges, we introduce a transformable gaussian reward function (TGRF). The TGRF significantly reduces the burden of hyperparameter tuning, displays adaptability across various reward functions, and demonstrates accelerated learning rates, particularly excelling in crowded environments utilizing deep reinforcement learning (DRL). We introduce and validate TGRF through sections highlighting its conceptual background, characteristics, experiments, and real-world application, paving the way for a more effective and adaptable approach in robotics.The complete source code is available on https://github.com/JinnnK/TGRF, Comment: 22 pages, 9 figures

Mobile robots often rely on pre-existing maps for effective path planning and navigation. However, when these maps are unavailable, particularly in unfamiliar environments, a different approach become essential. This paper introduces DynaCon, a novel system designed to provide mobile robots with contextual awareness and dynamic adaptability during navigation, eliminating the reliance of traditional maps. DynaCon integrates real-time feedback with an object server, prompt engineering, and navigation modules. By harnessing the capabilities of Large Language Models (LLMs), DynaCon not only understands patterns within given numeric series but also excels at categorizing objects into matched spaces. This facilitates dynamic path planner imbued with contextual awareness. We validated the effectiveness of DynaCon through an experiment where a robot successfully navigated to its goal using reasoning. Source code and experiment videos for this work can be found at: https://sites.google.com/view/dynacon., Comment: Submitted to ICRA 2024

Altermagnetism is a newly identified fundamental class of magnetism with vanishing net magnetization and time-reversal symmetry broken electronic structure. Probing the unusual electronic structure with nonrelativistic spin splitting would be a direct experimental verification of altermagnetic phase. By combining high-quality film growth and $in~situ$ angle-resolved photoemission spectroscopy, we report the electronic structure of an altermagnetic candidate, $\alpha$-MnTe. Temperature dependent study reveals the lifting of Kramers{\textquoteright} degeneracy accompanied by a magnetic phase transition at $T_N=267\text{ K}$ with spin splitting of up to $370\text{ meV}$, providing direct spectroscopic evidence for altermagnetism in MnTe.

Identifying ordered phases and their underlying symmetries is the first and most important step toward understanding the mechanism of high-temperature superconductivity; critical behaviors of ordered phases are expected to be correlated with superconductivity. Efforts to find such ordered phases have been focused on symmetry breaking in the pseudogap region while the Fermi liquid-like metal region beyond the so-called critical doping $p_{c}$ has been regarded as a trivial disordered state. Here, we used rotational anisotropy second harmonic generation and uncovered a broken mirror symmetry in the Fermi liquid-like phase in (Bi,Pb)$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ with $p = 0.205 > p_{c}$. By tracking the temperature evolution of the symmetry-breaking response, we verify an order parameter-like behavior with the onset temperature $T_{up}$ at which the strange metal to Fermi liquid-like-metal crossover takes place. Complementary angle-resolved photoemission study showed that the quasiparticle coherence between $\mathrm{CuO_{2}}$ bilayers is enhanced in proportion to the symmetry-breaking response as a function of temperature, indicating that the change in metallicity and symmetry breaking are linked. These observations contradict the conventional quantum disordered scenario for over-critical-doped cuprates and provide new insight into the nature of the quantum critical point in cuprates., Comment: 8 pages, 4 figures

We study how to construct a stochastic process on a finite interval with given `roughness' and finite joint moments of marginal distributions. We first extend Ciesielski's isomorphism along a general sequence of partitions, and provide a characterization of H\"older regularity of a function in terms of its Schauder coefficients. Using this characterization we provide a better (pathwise) estimator of H\"older exponent. As an additional application, we construct fake (fractional) Brownian motions with some path properties and finite moments of marginal distributions same as (fractional) Brownian motions. These belong to non-Gaussian families of stochastic processes which are statistically difficult to distinguish from real (fractional) Brownian motions., Comment: Accepted for publication at Bernoulli

In this paper, we develop the theory of functional generation of portfolios in an equity market with changing dimension. By introducing dimensional jumps in the market, as well as jumps in stock capitalization between the dimensional jumps, we construct different types of self-financing stock portfolios (additive, multiplicative, and rank-based) in a very general setting. Our study explains how a dimensional change caused by a listing or delisting event of a stock, and unexpected shocks in the market, affect portfolio return. We also provide empirical analyses of some classical portfolios, quantifying the impact of dimensional change in portfolio performance relative to the market., Comment: 41 pages, 4 figures

Divergent density of states (DOS) can induce extraordinary phenomena such as significant enhancement of superconductivity and unexpected phase transitions. Moreover, van Hove singularities (VHSs) are known to lead to divergent DOS in two-dimensional (2D) systems. Despite the recent interest in VHSs, only a few controllable cases have been reported to date. In this work, we investigate the electronic band structures of a 2D VHS with angle-resolved photoemission spectroscopy and control transport properties by utilizing an atomically ultrathin SrRuO$_3$ film. By applying electric fields with alkali metal deposition and ionic-liquid gating methods, we precisely control the 2D VHS, and the sign of the charge carrier. Use of a tunable 2D VHS in an atomically flat oxide film could serve as a new strategy to realize infinite DOS near the Fermi level, thereby allowing efficient tuning of electric properties., Comment: 7 pages, 4 figures

This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements: (i) there exists a supermartingale num\'eraire portfolio; (ii) each dissected market, which is of a fixed dimension between dimensional jumps, has locally finite growth; (iii) there is no arbitrage of the first kind; (iv) there exists a local martingale deflator; (v) the market is viable. We also present the optional decomposition theorem, which characterizes a given nonnegative process as the wealth process of some investment-consumption strategy. Furthermore, similar results still hold in an open market embedded in the entire market of stochastic dimension, where investors can only invest in a fixed number of large capitalization stocks. These results are developed in an equity market model where the price process is given by a piecewise continuous semimartingale of stochastic dimension. Without the continuity assumption on the price process, we present similar results but without explicit characterization of the num\'eraire portfolio.

We consider degenerate diffusion equations of the form $\partial_tp_t = \Delta f(p_t)$ on a bounded domain and subject to no-flux boundary conditions, for a class of nonlinearities $f$ that includes the porous medium equation. We derive for them a trajectorial analogue of the entropy dissipation identity, which describes the rate of entropy dissipation along every path of the diffusion. Our approach is based on applying stochastic calculus to the underlying probabilistic representations, which in our context are stochastic differential equations with normal reflection on the boundary. This trajectorial approach also leads to a new derivation of the Wasserstein gradient flow property for nonlinear diffusions, as well as to a simple proof of the HWI inequality in the present context.

Hund's rule coupling ($\textit{J}$) has attracted much attention recently for its role in the description of the novel quantum phases of multi orbital materials. Depending on the orbital occupancy, $\textit{J}$ can lead to various intriguing phases. However, experimental confirmation of the orbital occupancy dependency has been difficult as controlling the orbital degrees of freedom normally accompanies chemical inhomogeneities. Here, we demonstrate a method to investigate the role of orbital occupancy in $\textit{J}$ related phenomena without inducing inhomogeneities. By growing SrRuO$_3$ monolayers on various substrates with symmetry-preserving interlayers, we gradually tune the crystal field splitting and thus the orbital degeneracy of the Ru $\textit{t$_2$$_g$}$ orbitals. It effectively varies the orbital occupancies of two-dimensional (2D) ruthenates. Via in-situ angle-resolved photoemission spectroscopy, we observe a progressive metal-insulator transition (MIT). It is found that the MIT occurs with orbital differentiation: concurrent opening of a band insulating gap in the $\textit{d$_x$$_y$}$ band and a Mott gap in the $\textit{d$_x$$_z$$_/$$_y$$_z$}$ bands. Our study provides an effective experimental method for investigation of orbital-selective phenomena in multi-orbital materials.

We study market-to-book ratios of stocks in the context of Stochastic Portfolio Theory. Functionally generated portfolios that depend on auxiliary economic variables other than relative capitalizations ("sizes") are developed in two ways, together with their relative returns with respect to the market. This enables us to identify the value factor (i.e., market-to-book ratio) in returns of such generated portfolios when the auxiliary variables are stocks' book values. Examples of portfolios, as well as their empirical results, are given, with the evidence that, in addition to size, the value factor does affect the performance of the portfolio., Comment: 3 Figures

We study heterogeneously interacting diffusive particle systems with mean-field type interaction characterized by an underlying graphon and their finite particle approximations. Under suitable conditions, we obtain exponential concentration estimates over a finite time horizon for both 1 and 2 Wasserstein distances between the empirical measures of the finite particle systems and the averaged law of the graphon system, extending the work of Bayraktar-Wu.

Interfaces between dissimilar correlated oxides can offer devices with versatile functionalities. In that respect, manipulating and measuring novel physical properties of oxide heterointerfaces are highly desired. Yet, despite extensive studies, obtaining direct information on their momentum-resolved electronic structure remains a great challenge. This is because most correlated interfacial phenomena appear within a few atomic layers from the interface, thus limiting the application of available experimental probes. Here, we utilize atomic-scale epitaxy and photoemission spectroscopy to demonstrate the interface control of correlated electronic phases in atomic-scale ruthenate--titanate heterostructures. While bulk SrRuO$_3$ is a ferromagnetic metal, the heterointerfaces exclusively realize three distinct correlated phases in the single-atomic-layer limit. Our theory reveals that atomic-scale structural proximity effects lead to the emergence of Fermi liquid, Hund metal, and Mott insulator phases in the quantum-confined SrRuO$_3$. These results highlight the extensive interfacial tunability of electronic phases, hitherto hidden in the atomically thin correlated heterostructure., Comment: 25 pages, 5 main figures, 16 supplementary figures

We performed in-situ angle-resolved photoemission spectroscopy (ARPES) and spin-resolved ARPES (SARPES) experiments to investigate the relationship between electronic band structures and ferromagnetism in SrRuO$_3$ (SRO) thin films. Our high-quality ARPES and SARPES results show clear spin-lifted band structures. The spin polarization is strongly dependent on momentum around the Fermi level, whereas it becomes less dependent at high-binding energies. This experimental observation matches our dynamical mean-field theory (DMFT) results very well. As temperature increases from low to the Curie temperature, spin-splitting gap decreases and band dispersions become incoherent. Based on the ARPES study and theoretical calculation results, we found that SRO possesses spin-dependent electron correlations in which majority and minority spins are localized and itinerant, respectively. Our finding explains how ferromagnetism and electronic structure are connected, which has been under debate for decades in SRO., Comment: 6 pages, 4 figures

Using angle-resolved photoemission spectroscopy (ARPES), we studied the evolution of the electronic structure of Fe1-xCuxSe from x = 0 to 0.10. We found that the Cu dopant introduces extra electron carriers. The hole bands near the gamma point are observed to steadily shift downward with increasing doping and completely sink down below the Fermi level (EF) for x > 0.05. Meanwhile, the electron pocket near the M point becomes larger but loses the spectral weight near EF. We also observed that effective mass of the electron band near the M point increases with doping. Our result explains why superconductivity disappears and metal insulator transition (MIT) like behavior occurs upon Cu doping in terms of electronic structure, and provide insight into emergent magnetic fluctuation in Fe1-xCuxSe.

Correlated electrons in transition metal oxides (TMOs) exhibit a variety of emergent phases. When TMOs are confined to a single-atomic-layer thickness, experiments so far have shown that they usually lose diverse properties and become insulators. In an attempt to extend the range of electronic phases of the single-atomic-layer oxide, we search for a metallic phase in a monolayer-thick epitaxial SrRuO$_3$ film. Combining atomic-scale epitaxy and angle-resolved photoemission measurements, we show that the monolayer SrRuO$_3$ is a strongly correlated metal. Systematic investigation reveals that the interplay between dimensionality and electronic correlation makes the monolayer SrRuO$_3$ an incoherent metal with orbital-selective correlation. Furthermore, the unique electronic phase of the monolayer SrRuO$_3$ is found to be highly tunable, as charge modulation demonstrates an incoherent-to-coherent crossover of the two-dimensional metal. Our work emphasizes the potentially rich phases of single-atomic-layer oxides and provides a guide to the manipulation of their two-dimensional correlated electron systems.

In spectroscopic experiments, data acquisition in multi-dimensional phase space may require long acquisition time, owing to the large phase space volume to be covered. In such case, the limited time available for data acquisition can be a serious constraint for experiments in which multidimensional spectral data are acquired. Here, taking angle-resolved photoemission spectroscopy (ARPES) as an example, we demonstrate a denoising method that utilizes deep learning as an intelligent way to overcome the constraint. With readily available ARPES data and random generation of training data set, we successfully trained the denoising neural network without overfitting. The denoising neural network can remove the noise in the data while preserving its intrinsic information. We show that the denoising neural network allows us to perform similar level of second-derivative and line shape analysis on data taken with two orders of magnitude less acquisition time. The importance of our method lies in its applicability to any multidimensional spectral data that are susceptible to statistical noise., Comment: 8 pages, 8 figures

Ferromagnetism and exotic topological structures in SrRuO$_3$ (SRO) induce sign-changing anomalous Hall effect (AHE). Recently, hump structures have been reported in the Hall resistivity of SRO thin films, especially in the ultra-thin regime. We investigate the AHE and hump structure in the Hall resistivity of SRO ultra-thin films with an SrTiO$_3$ (STO) capping layer and ionic liquid gating. STO capping results in sign changes in the AHE and modulation of the hump structure. In particular, the hump structure in the Hall resistivity is strongly modulated and even vanishes in STO-capped 4 unit cell (uc) films. In addition, the conductivity of STO-capped SRO ultra-thin films is greatly enhanced with restored ferromagnetism. We also performed ionic liquid gating to modulate the electric field at SRO/STO interface. Drastic changes in the AHE and hump structure are observed with different gate voltages. Our study shows that the hump structure as well as the AHE can be controlled by tuning inversion symmetry and the electric field at the interface., Comment: 5 pages, 5 figures

We studied the electronic band structure of pulsed laser deposition (PLD) grown (111)-oriented SrRuO$_3$ (SRO) thin films using \textit{in situ} angle-resolved photoemission spectroscopy (ARPES) technique. We observed previously unreported, light bands with a renormalized quasiparticle effective mass of about 0.8$m_{e}$. The electron-phonon coupling underlying this mass renormalization yields a characteristic "kink" in the band dispersion. The self-energy analysis using the Einstein model suggests five optical phonon modes covering an energy range 44 to 90 meV contribute to the coupling. Besides, we show that the quasiparticle spectral intensity at the Fermi level is considerably suppressed, and two prominent peaks appear in the valance band spectrum at binding energies of 0.8 eV and 1.4 eV, respectively. We discuss the possible implications of these observations. Overall, our work demonstrates that high-quality thin films of oxides with large spin-orbit coupling can be grown along the polar (111) orientation by the PLD technique, enabling \textit{in situ} electronic band structure study. This could allow for characterizing the thickness-dependent evolution of band structure of (111) heterostructures$-$a prerequisite for exploring possible topological quantum states in the bilayer limit.

An open market is a subset of an entire equity market composed of a certain fixed number of top capitalization stocks. Though the number of stocks in the open market is fixed, the constituents of the market change over time as each company's rank by its market capitalization fluctuates. When one is allowed to invest also in the money market, the open market resembles the entire 'closed' equity market in the sense that the equivalence of market viability (lack of arbitrage) and the existence of numeraire portfolio (portfolio which cannot be outperformed) holds. When access to the money market is prohibited, some topics such as Capital Asset Pricing Model (CAPM), construction of functionally generated portfolios, and the concept of the universal portfolio are presented in the open market setting., Comment: 47 pages

Magnetism and spin-orbit coupling (SOC) are two quintessential ingredients underlying novel topological transport phenomena in itinerant ferromagnets. When spin-polarized bands support nodal points/lines with band degeneracy that can be lifted by SOC, the nodal structures become a source of Berry curvature; this leads to a large anomalous Hall effect (AHE). Contrary to three-dimensional systems that naturally host nodal points/lines, two-dimensional (2D) systems can possess stable nodal structures only when proper crystalline symmetry exists. Here we show that 2D spin-polarized band structures of perovskite oxides generally support symmetry-protected nodal lines and points that govern both the sign and the magnitude of the AHE. To demonstrate this, we performed angle-resolved photoemission studies of ultrathin films of SrRuO$_3$, a representative metallic ferromagnet with SOC. We show that the sign-changing AHE upon variation in the film thickness, magnetization, and chemical potential can be well explained by theoretical models. Our study is the first to directly characterize the topological band structure of 2D spin-polarized bands and the corresponding AHE, which could facilitate new switchable devices based on ferromagnetic ultrathin films.

We studied surface and electronic structures of barium stannate (BaSnO$_3$) thin-film by low energy electron diffraction (LEED), and angle-resolved photoemission spectroscopy (ARPES) techniques. BaSnO$_3$/Ba$_{0.96}$La$_{0.04}$SnO$_3$/SrTiO$_3$ (10 nm/100 nm/0.5 mm) samples were grown using pulsed-laser deposition (PLD) method and were \emph{ex-situ} transferred from PLD chamber to ultra-high vacuum (UHV) chambers for annealing, LEED and ARPES studies. UHV annealing starting from 300$^{\circ}$C up to 550$^{\circ}$C, followed by LEED and ARPES measurements show 1$\times$1 surfaces with non-dispersive energy-momentum bands. The 1$\times$1 surface reconstructs into a $\sqrt{2}$$\times$$\sqrt{2}R45^\circ$ one at the annealing temperature of 700$^{\circ}$C where the ARPES data shows clear dispersive bands with valence band maximum located around 3.3 eV below Fermi level. While the $\sqrt{2}$$\times$$\sqrt{2}R45^\circ$ surface reconstruction is stable under further UHV annealing, it is reversed to 1$\times$1 surface by annealing the sample in 400 mTorr oxygen at 600$^{\circ}$C. Another UHV annealing at 600$^{\circ}$C followed by LEED and ARPES measurements, suggests that LEED $\sqrt{2}$$\times$$\sqrt{2}R45^\circ$ surface reconstruction and ARPES dispersive bands are reproduced. Our results provide a better picture of electronic structure of BaSnO$_3$ surface and are suggestive of role of oxygen vacancies in the reversible $\sqrt{2}$$\times$$\sqrt{2}R45^\circ$ surface reconstruction., Comment: 7 pages, 4 figures, Journal

We study a continuous pathwise local time of order p for continuous functions with finite p-th variation along a sequence of time partitions, for even integers p >= 2. With this notion, we establish a Tanaka-type change of variable formula, as well as Tanaka-Meyer formulae. We also derive some identities involving this high-order pathwise local time, each of which generalizes a corresponding identity from semimartingale theory. We then use collision local times between multiple functions of arbitrary regularity, to study the dynamics of ranked continuous functions of arbitrary regularity. We present also another definition of pathwise local time which is more natural for fractional Brownian Motions, and give a connection with the previous notion of local time., Comment: 29 pages

Almost twenty years ago, E.R. Fernholz introduced portfolio generating functions which can be used to construct a variety of portfolios, solely in the terms of the individual companies' market weights. I. Karatzas and J. Ruf recently developed another methodology for the functional construction of portfolios, which leads to very simple conditions for strong relative arbitrage with respect to the market. In this paper, both of these notions of functional portfolio generation are generalized in a pathwise, probability-free setting; portfolio generating functions are substituted by path-dependent functionals, which involve the current market weights, as well as additional bounded-variation functions of past and present market weights. This generalization leads to a wider class of functionally-generated portfolios than was heretofore possible, and yields improved conditions for outperforming the market portfolio over suitable time-horizons., Comment: 45 pages, 3 figures