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A high-quality single-photon blockade system can effectively enhance the quality of single-photon sources. Conventional photon blockade(CPB) suffers from low single-photon purity and high requirements for system nonlinearity, while unconventional photon blockade(UPB) has the disadvantage of low brightness. Recent research by [Laser Photon.Rev 14,1900279,2020] demonstrates that UPB can be used to enhance the strength of CPB, thereby improving the purity of single-photon sources. Research by [Opt. Express 30(12),21787,2022] shows that there is an intersection point between CPB and UPB in certain nonlinear systems, where the performance of single photons is better. In this study, we investigated the phenomenon of photon blockade in a non-degenerate four-wave mixing system, where CPB and UPB can occur simultaneously within the same parameter range. We refer to this phenomenon as composite photon blockade. Particularly, when the system achieves composite photon blockade, the value of g(2)(0) is smaller, and there are more single photons. We conducted analytical analysis and numerical calculations to study the conditions for the realization of CPB, UPB, and 2PB in the system, and discussed in detail the influence of system parameters on various blockade effects.

This paper describes the technical and conceptual development of the LuminLab platform, an online tool that integrates a purpose-fit human-centric AI chatbot and predictive energy model into a streamlined front-end that can rapidly produce and discuss building retrofit plans in natural language. The platform provides users with the ability to engage with a range of possible retrofit pathways tailored to their individual budget and building needs on-demand. Given the complicated and costly nature of building retrofit projects, which rely on a variety of stakeholder groups with differing goals and incentives, we feel that AI-powered tools such as this have the potential to pragmatically de-silo knowledge, improve communication, and empower individual homeowners to undertake incremental retrofit projects that might not happen otherwise.

Building Energy Rating (BER) stands as a pivotal metric, enabling building owners, policymakers, and urban planners to understand the energy-saving potential through improving building energy efficiency. As such, enhancing buildings' BER levels is expected to directly contribute to the reduction of carbon emissions and promote climate improvement. Nonetheless, the BER assessment process is vulnerable to missing and inaccurate measurements. In this study, we introduce \texttt{CLEAR}, a data-driven approach designed to scrutinize the inconsistencies in BER assessments through self-supervised contrastive learning. We validated the effectiveness of \texttt{CLEAR} using a dataset representing Irish building stocks. Our experiments uncovered evidence of inconsistent BER assessments, highlighting measurement data corruption within this real-world dataset.

It has often been observed that the Multifractal Formalism and the Large Deviation Principles are intimately related. In fact, Multifractal Formalism was heuristically derived using the Large Deviations ideas. In numerous examples in which the multifractal results have been rigorously established, the corresponding Large Deviation results are valid as well. Moreover, the proofs of multifractal and large deviations are remarkably similar. The natural question then is whether under which conditions multifractal formalism can be deduced from the corresponding large deviations results. More specifically, given a sequence of random variables $\{ {X_n} \}_{n\in\N}$, satisfying a Large Deviation Principle, what can be said about the multifractal nature of the level sets $K_\alpha=\{\omega: \lim_{n} \frac{X_n(\omega)}{n}=\alpha\}$. Under some technical assumptions, we establish the upper and lower bounds for multifractal spectra in terms of the large deviation rate functions, and show that many known results of multifractal formalism are covered by our setup.

Chiral phases of matter, characterized by a definite handedness, abound in nature, ranging from the crystal structure of quartz to spiraling spin states in helical magnets. In $1T$-TiSe$_2$ a source of chirality has been proposed that stands apart from these classical examples as it arises from combined electronic charge and quantum orbital fluctuations. This may allow its chirality to be accessed and manipulated without imposing either structural or magnetic handedness. However, direct bulk evidence that broken inversion symmetry and chirality are intrinsic to TiSe$_2$ remains elusive. Here, employing resonant elastic scattering of x-rays, we reveal the presence of giant circular dichroism up to $\sim$ 40$\%$ at forbidden Bragg peaks that emerge at the charge and orbital ordering transition. The dichroism varies dramatically with incident energy and azimuthal angle. Comparison to calculated scattering intensities unambiguously traces its origin to bulk chiral electronic order in ${\mathrm{TiSe}}_2$ and establishes resonant elastic x-ray scattering as a sensitive probe to electronic chirality., Comment: 6 pages, 4 figures

Interfacial superconductors have the potential to revolutionize electronics, quantum computing, and fundamental physics due to their enhanced superconducting properties and ability to create new types of superconductors. The emergence of superconductivity at the interface of La$_{2-x}$Sr$_{x}$CuO$_{4}$/La$_{2}$CuO$_{4}$ (LSCO/LCO), with a T$_c$ enhancement of $\sim$ 10 K compared to the La$_{2-x}$Sr$_{x}$CuO$_{4}$ bulk single crystals, provides an exciting opportunity to study quantum phenomena in reduced dimensions. To investigate the carrier distribution and excitations in interfacial superconductors, we combine O K-edge resonant inelastic X-ray scattering and atomic-resolved scanning transmission electron microscopy measurements to study La$_{2-x}$Sr$_{x}$CuO$_{4}$/La$_{2}$CuO$_{4}$ superlattices (x=0.15, 0.45) and bulk La$_{1.55}$Sr$_{0.45}$CuO$_{4}$ films. We find direct evidence of charge redistribution, charge order and plasmon in LSCO/LCO superlattices. Notably, the observed behaviors of charge order and plasmon deviate from the anticipated properties of individual constituents or the average doping level of the superlattice. Instead, they conform harmoniously to the effective doping, a critical parameter governed by the T$_c$ of interfacial superconductors., Comment: 8 pages, 5 figures

The significance of multi-scale features has been gradually recognized by the edge detection community. However, the fusion of multi-scale features increases the complexity of the model, which is not friendly to practical application. In this work, we propose a Compact Twice Fusion Network (CTFN) to fully integrate multi-scale features while maintaining the compactness of the model. CTFN includes two lightweight multi-scale feature fusion modules: a Semantic Enhancement Module (SEM) that can utilize the semantic information contained in coarse-scale features to guide the learning of fine-scale features, and a Pseudo Pixel-level Weighting (PPW) module that aggregate the complementary merits of multi-scale features by assigning weights to all features. Notwithstanding all this, the interference of texture noise makes the correct classification of some pixels still a challenge. For these hard samples, we propose a novel loss function, coined Dynamic Focal Loss, which reshapes the standard cross-entropy loss and dynamically adjusts the weights to correct the distribution of hard samples. We evaluate our method on three datasets, i.e., BSDS500, NYUDv2, and BIPEDv2. Compared with state-of-the-art methods, CTFN achieves competitive accuracy with less parameters and computational cost. Apart from the backbone, CTFN requires only 0.1M additional parameters, which reduces its computation cost to just 60% of other state-of-the-art methods. The codes are available at https://github.com/Li-yachuan/CTFN-pytorch-master., Comment: Manuscript submitted to a Springer journal

24-hour actigraphy data collected by wearable devices offer valuable insights into physical activity types, intensity levels, and rest-activity rhythms (RAR). RARs, or patterns of rest and activity exhibited over a 24-hour period, are regulated by the body's circadian system, synchronizing physiological processes with external cues like the light-dark cycle. Disruptions to these rhythms, such as irregular sleep patterns, daytime drowsiness or shift work, have been linked to adverse health outcomes including metabolic disorders, cardiovascular disease, depression, and even cancer, making RARs a critical area of health research. In this study, we propose a Bayesian Circadian Hidden Markov Model (BCHMM) that explicitly incorporates 24-hour circadian oscillators mirroring human biological rhythms. The model assumes that observed activity counts are conditional on hidden activity states through Gaussian emission densities, with transition probabilities modeled by state-specific sinusoidal functions. Our comprehensive simulation study reveals that BCHMM outperforms frequentist approaches in identifying the underlying hidden states, particularly when the activity states are difficult to separate. BCHMM also excels with smaller Kullback-Leibler divergence on estimated densities. With the Bayesian framework, we address the label-switching problem inherent to hidden Markov models via a positive constraint on mean parameters. From the proposed BCHMM, we can infer the 24-hour rest-activity profile via time-varying state probabilities, to characterize the person-level RAR. We demonstrate the utility of the proposed BCHMM using 2011-2014 National Health and Nutrition Examination Survey (NHANES) data, where worsened RAR, indicated by lower probabilities in low-activity state during the day and higher probabilities in high-activity state at night, is associated with an increased risk of diabetes.

Visual Relation Extraction (VRE) is a powerful means of discovering relationships between entities within visually-rich documents. Existing methods often focus on manipulating entity features to find pairwise relations, yet neglect the more fundamental structural information that links disparate entity pairs together. The absence of global structure information may make the model struggle to learn long-range relations and easily predict conflicted results. To alleviate such limitations, we propose a GlObal Structure knowledge-guided relation Extraction (GOSE) framework. GOSE initiates by generating preliminary relation predictions on entity pairs extracted from a scanned image of the document. Subsequently, global structural knowledge is captured from the preceding iterative predictions, which are then incorporated into the representations of the entities. This "generate-capture-incorporate" cycle is repeated multiple times, allowing entity representations and global structure knowledge to be mutually reinforced. Extensive experiments validate that GOSE not only outperforms existing methods in the standard fine-tuning setting but also reveals superior cross-lingual learning capabilities; indeed, even yields stronger data-efficient performance in the low-resource setting. The code for GOSE will be available at https://github.com/chenxn2020/GOSE., Comment: Accepted by EMNLP 2023 (Findings)

We present a new technique, iterative fluctuation ghost imaging (IFGI) which dramatically enhances the resolution of ghost imaging (GI). It is shown that, by the fluctuation characteristics of the second-order correlation function, the imaging information with the narrower point spread function (PSF) than the original information can be got. The effects arising from the PSF and the iteration times also be discussed.

The Kagome material $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A$ = K, Rb, Cs) with geometry frustration hosts non-trivial topological electronic structures, electronic nematicity, charge density wave (CDW) and superconductivity, providing an ideal platform to study the interplay between these phases. Specifically, in pressurized- or substituted-${\mathrm{CsV}}_3{\mathrm{Sb}}_5$, the relationship between CDW and superconductivity is unusual and remains to be fully understood. Recently, coexisting and competing 2 $\times$ 2 $\times$ 4 and 2 $\times$ 2 $\times$ 2 CDW phases were discovered in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$. To investigate the evolution of the CDW phases with the substitution of V atoms, we performed x-ray diffraction (XRD) experiments on ${\mathrm{Cs(V}}_{1-x}{\mathrm{Ta}}_{x}{\mathrm{)}}_3{\mathrm{Sb}}_5$ and ${\mathrm{Cs(V}}_{1-x}{\mathrm{Nb}}_{x}{\mathrm{)}}_3{\mathrm{Sb}}_5$. Our results indicate that in all substituted samples, the discrete CDW reflection points in pristine ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ change to rod-like structures along the $c^\star$ direction. This suggests that the long-ranged three-dimensional CDW becomes quasi-two-dimensional by the substitution of V by Ta/Nb. Moreover, our temperature-dependent measurements show that there is no hysteresis behavior of CDW signals, indicating that the 2 $\times$ 2 $\times$ 4 CDW phase is easily suppressed by even a slight substitution of V with Nb/Ta. These findings uncover the CDW evolution upon substitution of V atoms in CsV$_3$Sb$_5$, providing insights into the microscopic mechanism of CDW and helping to understand the interplay between intertwined phases and superconductivity., Comment: 7 pages, 6 figures

Recently, an exciting discovery of orientation-dependent superconductivity was made in two-dimensional electron gas (2DEG) at the interfaces of LaAlO$_3$/KTaO$_3$ (LAO/KTO) or EuO/KTaO$_3$ (EuO/KTO). The superconducting transition temperature can reach a $T_c$ of up to $\sim$ 2.2 K, which is significantly higher than its 3$d$ counterpart LaAlO$_3$/SrTiO$_3$ (LAO/STO) with a $T_c$ of $\sim$ 0.2 K. However, the underlying origin remains to be understood. To uncover the nature of electrons in KTO-based interfaces, we employ x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray spectroscopy (RIXS) to study LAO/KTO and EuO/KTO with different orientations. We reveal the absence of $dd$ orbital excitations in all the measured samples. Our RIXS results are well reproduced by calculations that considered itinerant $5d$ electrons hybridized with O $2p$ electrons. This suggests that there is a lack of localized Ta $5d^1$ electrons in KTO interface superconductors, which is consistent with the absence of magnetic hysteresis observed in magneto-resistance (MR) measurements. These findings offer new insights into our understanding of superconductivity in Ta $5d$ interface superconductors and their potential applications., Comment: 8 pages, 6 figures

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results have indicated transport by deep-water breaking waves is enhanced compared to non-breaking waves. To model particle transport in irregular waves, some of which break, we develop a stochastic differential equation describing both mean particle transport and its uncertainty. The equation combines a Brownian motion, which captures non-breaking drift-diffusion effects, and a compound Poisson process, which captures jumps in particle positions due to breaking.We corroborate these predictions with new experiments, in which we track large numbers of particles in irregular breaking waves. For breaking and non-breaking wave fields, our experiments confirm that the variance of the particle position grows linearly with time, in accordance with Taylor's single-particle dispersion theory. For wave fields that include breaking, the compound Poisson process increases the linear growth rate of the mean and variance and introduces a finite skewness of the particle position distribution.

The periodic Gaussian process (PGP) has been increasingly used to model periodic data due to its high accuracy. Yet, computing the likelihood of PGP has a high computational complexity of $\mathcal{O}\left(n^{3}\right)$ ($n$ is the data size), which hinders its wide application. To address this issue, we propose a novel circulant PGP (CPGP) model for large-scale periodic data collected at grids that are commonly seen in signal processing applications. The proposed CPGP decomposes the log-likelihood of PGP into the sum of two computationally scalable composite log-likelihoods, which do not involve any approximations. Computing the likelihood of CPGP requires only $\mathcal{O}\left(p^{2}\right)$ (or $\mathcal{O}\left(p\log p\right)$ in some special cases) time for grid observations, where the segment length $p$ is independent of and much smaller than $n$. Simulations and real case studies are presented to show the superiority of CPGP over some state-of-the-art methods, especially for applications requiring periodicity estimation. This new modeling technique can greatly advance the applicability of PGP in many areas and allow the modeling of many previously intractable problems., Comment: Accepted for publication in Technometrics

A new type of experiment that aims to determine the optimal quantities of a sequence of factors is eliciting considerable attention in medical science, bioengineering, and many other disciplines. Such studies require the simultaneous optimization of both quantities and the sequence orders of several components which are called quantitative-sequence (QS) factors. Given the large and semi-discrete solution spaces in such experiments, efficiently identifying optimal or near-optimal solutions by using a small number of experimental trials is a nontrivial task. To address this challenge, we propose a novel active learning approach, called QS-learning, to enable effective modeling and efficient optimization for experiments with QS factors. QS-learning consists of three parts: a novel mapping-based additive Gaussian process (MaGP) model, an efficient global optimization scheme (QS-EGO), and a new class of optimal designs (QS-design). The theoretical properties of the proposed method are investigated, and optimization techniques using analytical gradients are developed. The performance of the proposed method is demonstrated via a real drug experiment on lymphoma treatment and several simulation studies., Comment: Accepted by Journal of the American Statistical Association

Kagome superconductors AV$_3$Sb$_5$ (A = K, Rb, Cs) provide a fertile playground for studying intriguing phenomena, including non-trivial band topology, superconductivity, giant anomalous Hall effect and charge density wave (CDW). Recently, a $C_2$ symmetric nematic phase prior to the superconducting state in AV$_3$Sb$_5$ drew enormous attention due to its potential inheritance of the symmetry of the unusual superconductivity. However, direct evidence on the rotation symmetry breaking of the electronic structure in the CDW state from the reciprocal space is still rare, and the underlying mechanism remains ambiguous. The observation shows unconventional unidirectionality, indicative of rotation symmetry breaking from six-fold to two-fold. The interlayer coupling between adjacent planes with $\pi$-phase offset in the 2$\times$2$\times$2 CDW phase leads to the preferred two-fold symmetric electronic structure. These rarely observed unidirectional back-folded bands in KV$_3$Sb$_5$ may provide important insights into its peculiar charge order and superconductivity.

For decades, people are developing efficient numerical methods for solving the challenging quantum many-body problem, whose Hilbert space grows exponentially with the size of the problem. However, this journey is far from over, as previous methods all have serious limitations. The recently developed deep learning methods provide a very promising new route to solve the long-standing quantum many-body problems. We report that a deep learning based simulation protocol can achieve the solution with state-of-the-art precision in the Hilbert space as large as $2^{1296}$ for spin system and $3^{144}$ for fermion system , using a HPC-AI hybrid framework on the new Sunway supercomputer. With highly scalability up to 40 million heterogeneous cores, our applications have measured 94% weak scaling efficiency and 72% strong scaling efficiency. The accomplishment of this work opens the door to simulate spin models and Fermion models on unprecedented lattice size with extreme high precision., Comment: Massive ground state optimizations of CNN-based wave-functions for $J1$-$J2$ model and $t$-$J$ model carried out on a heterogeneous cores supercomputer

We report magnetometry data obtained on twin-free single crystals of Na3Co2SbO6, which is considered a candidate material for realizing the Kitaev honeycomb model for quantum spin liquids. Contrary to a common belief that such materials can be modeled with the symmetries of an ideal honeycomb lattice, our data reveal a pronounced two-fold symmetry and in-plane anisotropy of over 200%, despite the honeycomb layer's tiny orthorhombic distortion of less than 0.2%. We further use magnetic neutron diffraction to elucidate a rich variety of field-induced phases observed in the magnetometry. These phases manifest themselves in the paramagnetic state as diffuse scattering signals associated with competing ferro- and antiferromagnetic instabilities, consistent with a theory that also predicts a quantum spin liquid phase nearby. Our results call for theoretical understanding of the observed in-plane anisotropy, and render Na3Co2SbO6 a promising ground for finding exotic quantum phases by targeted external tuning., Comment: 19 pages, 15 figures, 1 animation; to appear in Phys. Rev. X

Computer experiments with both quantitative and qualitative (QQ) inputs are commonly used in science and engineering applications. Constructing desirable emulators for such computer experiments remains a challenging problem. In this article, we propose an easy-to-interpret Gaussian process (EzGP) model for computer experiments to reflect the change of the computer model under the different level combinations of qualitative factors. The proposed modeling strategy, based on an additive Gaussian process, is flexible to address the heterogeneity of computer models involving multiple qualitative factors. We also develop two useful variants of the EzGP model to achieve computational efficiency for data with high dimensionality and large sizes. The merits of these models are illustrated by several numerical examples and a real data application.

The recently discovered Kagome family ${\mathrm{AV}}_3{\mathrm{Sb}}_5$ (A = K, Rb, Cs) exhibits rich physical phenomena, including non-trivial topological electronic structure, giant anomalous Hall effect, charge density waves (CDW) and superconductivity. Notably, CDW in ${\mathrm{AV}}_3{\mathrm{Sb}}_5$ is evidenced to intertwine with its superconductivity and topology, but its nature remains elusive. Here, we combine x-ray scattering experiments and density-functional theory calculations to investigate the CDWs in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ and demonstrate the coexistence of 2 $\times$ 2 $\times$ 2 and 2 $\times$ 2 $\times$ 4 CDW stacking phases. Competition between these CDW phases is revealed by tracking the temperature evolution of CDW intensities, which also manifests in different transition temperatures during warming- and cooling measurements. We also identify a meta-stable quenched state of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ after fast-cooling process. Our study demonstrates the coexistence of competing CDW stacking in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$, offering new insights in understanding the novel properties of this system., Comment: 6 pages, 5 figures

A graphical regular representation (GRR) of a group $G$ is a Cayley graph of $G$ whose full automorphism group is equal to the right regular permutation representation of $G$. Towards a proof of the conjecture that only finitely many finite simple groups have no cubic GRR, this paper shows that $\mathrm{PSU}_3(q)$ has a cubic GRR if and only if $q\geq4$. Moreover, a cubic GRR of $\mathrm{PSU}_3(q)$ is constructed for each of these $q$.

We study the effects of higher-order deformations $\beta_\lambda$ ($\lambda=4,6,8,$ and $10$) on the ground state properties of superheavy nuclei (SHN) near the doubly magic deformed nucleus $^{270}$Hs by using the multidimensionally-constrained (MDC) relativistic mean-field (RMF) model with five effective interactions PC-PK1, PK1, NL3$^{*}$, DD-ME2, and PKDD. The doubly magic properties of $^{270}$Hs are featured by the large energy gaps at $N=162$ and $Z=108$ in the single-particle spectra. By investigating the binding energies and single-particle levels of $^{270}$Hs in multidimensional deformation space, we find that the deformation $\beta_6$ has the greatest impact on the binding energy among these higher-order deformations and influences the shell gaps considerably. Similar conclusions hold for other SHN near $^{270}$Hs. Our calculations demonstrate that the deformation $\beta_6$ must be considered when studying SHN by using MDC-RMF., Comment: accepted for publication in Chin. Phys. C

In the conventional ghost imaging (GI), the image is retrieved by correlating the reference intensity fluctuation at a charge-coupled device (CCD) with the signal intensity fluctuation at a bucket detector. In this letter, we present the protocol of GI, it is called Second-order Cumulants ghost imaging (SCGI). The image is retrieved by the fluctuation information of correlating intensity fluctuation at two detectors, and the resolution limit can be enhanced than conventional GI. The experimental results of SCGI agreement with theoretical results.

The superconducting critical temperature $T_{\mathrm{c}}$ of intercalated iron-selenide superconductor (Li,Fe)OHFeSe (FeSe11111) can be increased to 42 K from 8 K of bulk FeSe. It shows remarkably similar electronic properties as the high-$T_{\mathrm{c}}$ monolayer FeSe and provides a bulk counterpart to investigate the origin of enhanced superconductivity. Unraveling the nature of excitations is crucial for understanding the pairing mechanism in high-$T_{\mathrm{c}}$ iron selenides. Here we use resonant inelastic x-ray scattering (RIXS) to investigate the excitations in FeSe11111. Our high-quality data exhibit several Raman-like excitations, which are dispersionless and isotropic in momentum transfer and robust against varying $T_{\mathrm{c}}$. Using atomic multiplet calculations, we assign the low-energy $\sim 0.3$ and 0.7 eV Raman peaks as local $e_g-e_g$ and $e_g-t_{2g}$ orbital excitations. The intensity of these two features decreases with increasing temperature, suggesting a primary contribution of the orbital fluctuations. Our results highlight the importance of orbital degree of freedom for high-$T_{\mathrm{c}}$ iron selenides., Comment: 11 pages, 4 figures

Efficient numerical methods are promising tools for delivering unique insights into the fascinating properties of physics, such as the highly frustrated quantum many-body systems. However, the computational complexity of obtaining the wave functions for accurately describing the quantum states increases exponentially with respect to particle number. Here we present a novel convolutional neural network (CNN) for simulating the two-dimensional highly frustrated spin-$1/2$ $J_1-J_2$ Heisenberg model, meanwhile the simulation is performed at an extreme scale system with low cost and high scalability. By ingenious employment of transfer learning and CNN's translational invariance, we successfully investigate the quantum system with the lattice size up to $24\times24$, within 30 million cores of the new generation of sunway supercomputer. The final achievement demonstrates the effectiveness of CNN-based representation of quantum-state and brings the state-of-the-art record up to a brand-new level from both aspects of remarkable accuracy and unprecedented scales., Comment: This paper reviews the technical details of calculating spin-1/2 J1-J2 model using convolutional neural network ansatz on Sunway Supercomputer

Besides magnetic and charge order, regular arrangements of orbital occupation constitute a fundamental order parameter of condensed matter physics. Even though orbital order is difficult to identify directly in experiments, its presence was firmly established in a number of strongly correlated, three-dimensional Mott insulators. Here, reporting resonant X-ray scattering experiments on the layered Van der Waals compound $1T$-TiSe$_2$, we establish the emergence of orbital order in a weakly correlated, quasi-two-dimensional material. Our experimental scattering results are consistent with first-principles calculations that bring to the fore a generic mechanism of close interplay between charge redistribution, lattice displacements, and orbital order. It demonstrates the essential role that orbital degrees of freedom play in TiSe$_2$, and their importance throughout the family of correlated Van der Waals materials.

We introduce statistical techniques required to handle complex computer models with potential applications to astronomy. Computer experiments play a critical role in almost all fields of scientific research and engineering. These computer experiments, or simulators, are often computationally expensive, leading to the use of emulators for rapidly approximating the outcome of the experiment. Gaussian process models, also known as Kriging, are the most common choice of emulator. While emulators offer significant improvements in computation over computer simulators, they require a selection of inputs along with the corresponding outputs of the computer experiment to function well. Thus, it is important to select inputs judiciously for the full computer simulation to construct an accurate emulator. Space-filling designs are efficient when the general response surface of the outcome is unknown, and thus they are a popular choice when selecting simulator inputs for building an emulator. In this tutorial we discuss how to construct these space filling designs, perform the subsequent fitting of the Gaussian process surrogates, and briefly indicate their potential applications to astronomy research.

In this paper we introduce the definition of topological $r$-pressure of free semigroup actions on compact metric space and provide some properties of it. Through skew-product transformation into a medium, we can obtain the following two main results. 1. We extend the result that the topological pressure is the limit of topological $r$-pressure in\cite{C} to free semigroup actions ($r\to 0$). 2. Let $f_i,$ $i=0, 1, \cdots, m-1$, be homeomorphisms on a compact metric space. For any continuous function, we verify that the topological pressure of $f_0, \cdots, f_{m-1}$ equals the topological pressure of $f_0^{-1}, \cdots, f_{m-1}^{-1}.$

Inspired to the work of Ma and Wu\cite{Ma} and Climenhaga\cite{Climenhaga}, we introduce the new nation of topological pressure of a semigroup of maps by using the Carath\'{e}odory-Pesin structure (C-P structure) with respect to arbitrary subset in this paper. Moreover, by Bowen's equation, we characterize the Hausdorff dimension of an arbitrary subset, where the points of the subset have the positive lower Lyapunov exponents and satisfy a so called tempered contraction condition.

Efficient Latin hypercube designs (LHDs), including maximin distance LHDs, maximum projection LHDs and orthogonal LHDs, are widely used in computer experiments. It is challenging to construct such designs with flexible sizes, especially for large ones. In the current literature, various algebraic methods and search algorithms have been proposed for identifying efficient LHDs, each having its own pros and cons. In this paper, we review, summarize and compare some currently popular methods aiming to provide guidance for experimenters on what method should be used in practice. Using the R package we developed which integrates and improves various algebraic and searching methods, many of the designs found in this paper are better than the existing ones. They are easy to use for practitioners and can serve as benchmarks for the future developments on LHDs.

Climenhaga showed the applicability of Bowen equation to arbitrary subset of a compact metric space. The main purpose of this paper is to generalize the main result of Climenhaga to free semigroup actions for non-compact sets. We introduce the notions of the topological pressure and lower and upper capacity topological pressure of a free semigroup action for non-compact sets by using the Caratheodory- Pesin structure. Some properties of these notions are given, followed by three main results. One is to characterize the Hausdorff dimension of arbitrary subset in term of the topological pressure by Bowen equation, whose points have the positive lower Lyapunov exponents and satisfy a tempered contraction condition, the other is the estimation of topological pressure of a free semigroup action on arbitrary subset of X and the third is the relationship between the upper capacity topological pressure of a skew-product transformation and the upper capacity topological pressure of a free semigroup action with respect to arbitrary subset., Comment: 34 pages

We present the design methodology of a light reconfigurable geometric phase optical element with multi-stable diffraction efficiency states, enabled by a photoresponsive self-organized chiral liquid crystal. Experimental demonstration shows the device exhibits a broad diffraction efficiency tunable range that can be smoothly modulated under alternate stimulation of ultraviolet and green lights. Distinctive to previous designs, the regulation of diffraction efficiency fundamentally stems from the modulation of geometric phase together with dynamical phase retardation, and any intermediate diffractive state is memorized. Such multi-stability facilitates applications including energy-saving all-optical signal processing in classical and quantum level, and phase hologram for anti-counterfeit., Comment: 6 pages, 2 figures

In this paper, the imbalance edge cloud based computing offloading for multiple mobile users (MUs) with multiple tasks per MU is studied. In which, several edge cloud servers (ECSs) are shared and accessed by multiple wireless access points (APs) with the backhaul links, and each MU has multiple computing intensive and latency critical tasks should be offloaded to execute, which involves both the AP association and ECS selection, with the objective of minimizing the offloading cost. Distinguished with existing research, besides the transmission delay and energy consumption from MU to AP, the ECS access-cost which characterizes the ECS access delay and (or) resource using cost is introduced, thus finally formulates the delay-energy-cost tradeoff based offloading cost criteria, for the MUs' offloading decision and resource allocation problems. In specific, in our system, the ECS access-cost depends on both the AP and ECS, which reflects the effects of different backhaul techniques used by these APs, and their negotiated payments of ECS resource using under different service level agreements. Both problems of minimizing the sum offloading costs for all MUs (efficiency-based) and minimizing the maximal offloading cost per MU (fairness-based) are discussed. Since these problems are all NP-hard. Therefore, some centralized and distributed heuristic algorithms are proposed to find the suboptimal solutions. Further analysis and numerical results are presented at last to demonstrate the performance of these algorithms from several aspects, such as efficiency, complexity and fairness., Comment: 36 pages, 10 figures, submitted to IEEE journal for possible publication

It is of keen interest to researchers understanding different approaches to confine massless Dirac fermions in graphene, which is also a central problem in making electronic devices based on graphene. Here, we studied spatial confinement, magnetic localization and their interactions on massless Dirac fermions in an angled graphene wedge formed by two linear graphene p-n boundaries with an angle 34. Using scanning tunneling microscopy, we visualized quasibound states temporarily confined in the studied graphene wedge. Large perpendicular magnetic fields condensed the massless Dirac fermions in the graphene wedge into Landau levels (LLs). The spatial confinement of the wedge affects the Landau quantization, which enables us to experimentally measure the spatial extent of the wave functions of the LLs. The magnetic fields induce a sudden and large increase in energy of the quasibound states because of a pi Berry phase jump of the massless Dirac fermions in graphene. Such a behavior is the hallmark of the Klein tunneling in graphene. Our experiment demonstrated that the angled wedge is a unique system with the critical magnetic fields for the pi Berry phase jump depending on distance from summit of the wedge., Comment: 4 Figures in main text

Ordered atomic-scale superlattices on surface hold great interest both for basic science and for potential applications in advanced technology. However, controlled fabrication of superlattices down to atomic scale has proven exceptionally challenging. Here we demonstrate the segregation-growth and self-organization of ordered S atomic superlattices confined at the interface between graphene and S-rich Cu substrates. Scanning tunneling microscope (STM) studies show that, by finely controlling the growth temperature, we obtain well-ordered S (sub)nanometer-cluster superlattice and monoatomic superlattices with various periods at the interface. These atomic superlattices are stable in atmospheric environment and robust even after high-temperature annealing (~ 350 oC). Our experiments demonstrate that the S monoatomic superlattice can drive graphene into the electronic Kekul\'e distortion phase when the period of the ordered S adatoms is commensurate with graphene lattice. Our results not only open a road to realize atomic-scale superlattices at interfaces, but also provide a new route to realize exotic electronic states in graphene., Comment: 4 figures

Combinatorial drugs have been widely applied in disease treatment, especially chemotherapy for cancer, due to its improved efficacy and reduced toxicity compared with individual drugs. The study of combinatorial drugs requires efficient experimental designs and proper follow-up statistical modelling techniques. Linear and non-linear models are often used in the response surface modelling for such experiments. We propose the use of Kriging models to better depict the response surfaces of combinatorial drugs and take into account the measurement error. We further study how proper experimental designs can reduce the required number of runs. We illustrate our method via a combinatorial drug experiment on lung cancer. We demonstrate that only 27 runs are needed to predict all 512 runs in the original experiment and achieve better precision than existing analysis., Comment: Submitted to "Statistics in Medicine"

PT-symmetric quantum mechanics, the extension of conventional quantum mechanics to the non-Hermitian Hamiltonian invariant under the combined parity (P) and time reversal (T) symmetry, has been successfully applied to a variety of fields such as solid state physics, mathematical physics, optics, quantum field theory. Recently, the extension of PT-symmetrical theory to entangled quantum systems was challenged in that PT formulation within the conventional Hilbert space violates the no-signaling principle. Here, we revisit the derivation of non-signaling principle in the framework of PT inner product prescription. Our results preserve the no-signaling principle for a two-qubit system, reaffirm the invariance of the entanglement, and reproduce the Clauser-Horne-Shimony-Holt (CHSH) inequality. We conclude that PT-symmetric quantum mechanics satisfies the requirements for a fundamental theory and provides a consistent description of quantum systems., Comment: 13 pages, will appear in Journal of Physics A: Mathematical and Theoretical

Following the work in graphene, we report a first-principles study of electron-phonon coupling (EPC) in low-buckled (LB) monolayer silicene and germanene. Despite of the similar honeycomb atomic arrangement and linear band dispersion, the EPC matrix-element squares of the $\Gamma$-$E_g$ and K-$A_1$ modes in silicene are only about 50% of those in graphene. However, the smaller Fermi velocity in silicene compensates this reduction by providing a larger joint electronic density of states near the Dirac point. We predict that Kohn anomalies associated with these two optical modes are significant in silicene. In addition, the EPC-induced frequency shift and linewidth of the Raman-active $\Gamma$-$E_g$ mode in silicene are calculated as a function of doping. The results are comparable to those in graphene, indicating a similar non-adiabatic dynamical origin. In contrast, the EPC in germanene is found to be much reduced., Comment: 5 pages, 4 figures

We have performed dispersion-corrected density-functional transition state calculations on atomic Au- and Pd- catalysis of water conversion to peroxide. The Au- ion is found to be an excellent catalyst; however, atomic Pd- has a higher catalytic effect on the formation of peroxide. The Au^{-}(H2O)2 and Pd^{-}(H2O)2 anion molecular complexes formation in the transition state is identified as the fundamental mechanism for breaking the hydrogen bonding strength during the water catalysis. Our theoretical results provide crucial insight into the mechanism of the atomic Au- and Pd- catalysis in good agreement with recent experimental observations., Comment: 8 Pages,3 Figures

Manipulation is an important issue for both developed and emerging stock markets. For the study of manipulation, it is critical to analyze investor behavior in the stock market. In this paper, an analysis of the full transaction records of over a hundred stocks in a one-year period is conducted. For each stock, a trading network is constructed to characterize the relations among its investors. In trading networks, nodes represent investors and a directed link connects a stock seller to a buyer with the total trade size as the weight of the link, and the node strength is the sum of all edge weights of a node. For all these trading networks, we find that the node degree and node strength both have tails following a power-law distribution. Compared with non-manipulated stocks, manipulated stocks have a high lower bound of the power-law tail, a high average degree of the trading network and a low correlation between the price return and the seller-buyer ratio. These findings may help us to detect manipulated stocks., Comment: 18 pages, 7 figures

There are experimental evidences for the existence of narrow states $\Theta^+$ and $\Theta_c$ with the same quantum numbers of $uudd\bar s$ and $uudd\bar c$ pentaquarks and also $NK^{(*)}$ and $ND^{(*)}$ molecular states. Their masses deviate from many theoretical estimates of the pure pentaquark and molecular states. In this work we study the possibility that the observed $\Theta^+$ and $\Theta_c$ are mixtures of pure pentaquark and molecular states. The mixing parameters are in general related to non-perturbative QCD which are not calculable at present. We determine them by fitting data from known states and then generalize the mechanism to $\Theta_b$ to predict its mass and width. The mixing mechanism can also naturally explain the narrow width for $\Theta^+$ and $\Theta_c$ through destructive interferences, even if the pure pentaquark and molecular states have much larger decay widths. We also briefly discuss the properties of the partner eigenstates of $\Theta^+$ and $\Theta_c$ and the possibility of experimentally observe them. Moreover, probable consequences of multi-state mixing are also addressed., Comment: 23 pages, 4 figures. Published version in EPJC

The mapping between the metal-insulator transition of the quantum Hall system and a superfluid-to-insulator transition is revisited based on a disordered anyon model. The one-parameter scaling of the superfluid-to-insulator transition is employed for the analysis of the scaling behavior of the integer quantum Hall transitions. The analysis reveals the direct transition from a quantum Hall plateau to the insulator in weak disorder limit, and a float-down transition for strong disorders. In either cases, the transition corresponds to a non-chirality superfluid-to-insulator transition, with the longitudinal and transverse quantum Hall conductivities following a semi-circle relation.

We show that a recently developed method for generating bounds for the discrete energy states of the non-hermitian $-ix^3$ potential (Handy 2001) is applicable to complex rotated versions of the Hamiltonian. This has important implications for extension of the method in the analysis of resonant states, Regge poles, and general bound states in the complex plane (Bender and Boettcher (1998))., Comment: Submitted to J. Phys. A

The recent work of Delabaere and Trinh (2000 J. Phys. A 33 8771) discovered the existence of ${\cal P}{\cal T}$-symmetry breaking, complex energy, $L^2$ solutions for the one dimensional Hamiltonian, $P^2+iX^3+i\alpha X$, in the asymptotic limit, $\alpha \to -\infty$. Their asymptotic analysis produced questionable results for moderate values of $\alpha$. We can easily confirm the existence of ${\cal P}{\cal T}$-symmetry breaking solutions, by explicitly computing the low lying states, for $|\alpha| < O (10)$. Our analysis makes use of the Multiscale Reference Function (MRF) approach, developed by Tymczak et al (1998 Phys. Rev. Lett. 80 3678; 1998 Phys. Rev. A 58, 2708). The MRF results can be validated by comparing them with the converging eigenenergy bounds generated through the Eigenvalue Moment Method, as recently argued by Handy (2001a,b). Given the reliability of the MRF analysis, its fast numerical implementation, high accuracy, and theoretical simplicity, the present formalism defines an effective and efficient procedure for analyzing many related problems that have appeared in the recent literature., Comment: Submitted to J. Phys. A

We devise a new and highly accurate quantization procedure for the inner product representation, both in configuration and momentum space. Utilizing the representation $\Psi(\xi) = \sum_{i}a_i[E]\xi^i R_{\beta}(\xi)$, for an appropriate reference function, $R_{\beta}(\xi)$, we demonstrate that the (convergent) zeroes of the coefficient functions, $a_i[E] = 0$, approximate the exact bound/resonance state energies with increasing accuracy as $i \to \infty$. The validity of the approach is shown to be based on an extension of the Hill determinant quantization procedure. Our method has been applied, with remarkable success, to various quantum mechanical problems., Comment: Four Pages REVTEX, Three Postscript figures

The critical phenomenon of the zero temperature superfluid--Bose-glass phase transition for hard-core bosons on a three-dimensional disordered lattice is studied using a quantum real-space renormalization-group method. The correlation-length exponent $\nu$ and the dynamic exponent z are computed. The critical exponent z is found to be 2.5 for compressible states and 1.3 for incompressible states. The exponent $\nu$ is shown to be insensitive to z as that in the two-dimensional case, and has value roughly equal to 1., Comment: 11 pages, REVTEX