The past decade has seen a proliferation of topological materials for both insulators and semimetals in electronic systems and classical waves. Topological semimetals exhibit topologically protected band degeneracies, such as nodal points and nodal l
ines. Dirac nodal line semimetals (DNLS), which own four-fold line degeneracy, have drawn particular attention. DNLSs have been studied in electronic systems but there is no photonic DNLS. Here in this work, we provide a new mechanism which is unique for photonic systems to investigate a stringent photonic DNLS. When truncated, the photonic DNLS exhibits double-bowl states (DBS), which comprises two sets of perpendicularly polarized surface states. In sharp contrast to nondegenerate surface states in other photonic systems, here the two sets of surface states are almost degenerate over the whole spectrum range. The DBS and the bulk Dirac nodal ring (DNR) dispersion along the relevant directions, are experimentally resolved.
Link and sign prediction in complex networks bring great help to decision-making and recommender systems, such as in predicting potential relationships or relative status levels. Many previous studies focused on designing the special algorithms to pe
rform either link prediction or sign prediction. In this work, we propose an effective model integration algorithm consisting of network embedding, network feature engineering, and an integrated classifier, which can perform the link and sign prediction in the same framework. Network embedding can accurately represent the characteristics of topological structures and cooperate with the powerful network feature engineering and integrated classifier can achieve better prediction. Experiments on several datasets show that the proposed model can achieve state-of-the-art or competitive performance for both link and sign prediction in spite of its generality. Interestingly, we find that using only very low network embedding dimension can generate high prediction performance, which can significantly reduce the computational overhead during training and prediction. This study offers a powerful methodology for multi-task prediction in complex networks.
This paper is devoted to the existence, uniqueness and comparison theorem on unbounded solutions of a scalar backward stochastic differential equation (BSDE) whose generator grows (with respect to both unknown variables $y$ and $z$) in a super-linear
way like $|y||ln |y||^{(lambda+1/2)wedge 1}+|z||ln |z||^{lambda}$ for some $lambdageq 0$. For the following four different ranges of the growth power parameter $lambda$: $lambda=0$, $lambdain (0,1/2)$, $lambda=1/2$ and $lambda>1/2$, we give reasonably weakest possible different integrability conditions of the terminal value for the existence of an unbounded solution to the BSDE. In the first two cases, they are stronger than the $Lln L$-integrability and weaker than any $L^p$-integrability with $p>1$; in the third case, the integrability condition is just some $L^p$-integrability for $p>1$; and in the last case, the integrability condition is stronger than any $L^p$-integrability with $p>1$ and weaker than any $exp(L^epsilon)$-integrability with $epsilonin (0,1)$. We also establish the comparison theorem, which yields naturally the uniqueness, when either generator of both BSDEs is convex (concave) in both unknown variables $(y,z)$, or satisfies a one-sided Osgood condition in the first unknown variable $y$ and a uniform continuity condition in the second unknown variable $z$.
In this paper, we study the problem of consensus-based distributed optimization where a network of agents, abstracted as a directed graph, aims to minimize the sum of all agents cost functions collaboratively. In existing distributed optimization app
roaches (Push-Pull/AB) for directed graphs, all agents exchange their states with neighbors to achieve the optimal solution with a constant stepsize, which may lead to the disclosure of sensitive and private information. For privacy preservation, we propose a novel state-decomposition based gradient tracking approach (SD-Push-Pull) for distributed optimzation over directed networks that preserves differential privacy, which is a strong notion that protects agents privacy against an adversary with arbitrary auxiliary information. The main idea of the proposed approach is to decompose the gradient state of each agent into two sub-states. Only one substate is exchanged by the agent with its neighbours over time, and the other one is kept private. That is to say, only one substate is visible to an adversary, protecting the privacy from being leaked. It is proved that under certain decomposition principles, a bound for the sub-optimality of the proposed algorithm can be derived and the differential privacy is achieved simultaneously. Moreover, the trade-off between differential privacy and the optimization accuracy is also characterized. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed approach.
In this study, we propose and experimentally demonstrate a novel kind of Tamm plasmon topological superlattice (TTS) by engineering Tamm photonic crystals (TPCs) belonging to a different class of topology. Utilizing specifically designed double-layer
metasurfaces etching on planar multilayered photonic structures, the TPC that supports the Tamm plasmon photonic bandgap is realized in the visible regime. Through the coupling of topological interface states existing between different TPCs, hybrid topological interface states of Tamm plasmon, called supermodes, are obtained that can be fully described by a tight-binding model. Meanwhile, we can achieve a tunable bandwidth of supermodes via varying the etching depth difference between double-layer metasurfaces. We show that the bandwidth decreases with the increase of etching depth difference, resulting in a nearly flat dispersion of supermodes with strong localization regardless of excitation angles. All the results are experimentally verified by measuring angular-resolved reflectance spectra. The TTS and supermodes proposed here open a new pathway for the manipulation of Tamm plasmons, based on which various promising applications such as integrated photonic devices, optical sensing, and enhancing light-matter interactions can be realized.
Measures of face identification proficiency are essential to ensure accurate and consistent performance by professional forensic face examiners and others who perform face identification tasks in applied scenarios. Current proficiency tests rely on s
tatic sets of stimulus items, and so, cannot be administered validly to the same individual multiple times. To create a proficiency test, a large number of items of known difficulty must be assembled. Multiple tests of equal difficulty can be constructed then using subsets of items. Here, we introduce a proficiency test, the Triad Identity Matching (TIM) test, based on stimulus difficulty measures based on Item Response Theory (IRT). Participants view face-image triads (N=225) (two images of one identity and one image of a different identity) and select the different identity. In Experiment 1, university students (N=197) showed wide-ranging accuracy on the TIM test. Furthermore, IRT modeling demonstrated that the TIM test produces items of various difficulty levels. In Experiment 2, IRT-based item difficulty measures were used to partition the TIM test into three equally easy and three equally difficult subsets. Simulation results indicated that the full set, as well as curated subsets, of the TIM items yielded reliable estimates of subject ability. In summary, the TIM test can provide a starting point for developing a framework that is flexible, calibrated, and adaptive to measure proficiency across various ability levels (e.g., professionals or populations with face processing deficits)
We consider growing random networks ${mathcal{G}_n}_{n ge 1}$ where, at each time, a new vertex attaches itself to a collection of existing vertices via a fixed number $m ge 1$ of edges, with probability proportional to a function $f$ of their degree
s. It was shown in cite{BBpersistence} that such network models exhibit two distinct regimes: (i) the persistent regime, corresponding to $sum_{i=1}^{infty}f(i)^{-2} < infty$, where the top $K$ maximal degree vertices fixate over time for any given $K$, and (ii) the non-persistent regime with $sum_{i=1}^{infty}f(i)^{-2} = infty$ where the identities of these vertices keep changing infinitely often over time. In this article, we develop root finding algorithms based on the empirical degree structure of a snapshot of such a network at some large time. In the persistent regime, the algorithm is purely based on degree centrality. In this case, the size of the confidence set of the root is shown to be stable in network size, and is explicitly characterized in terms of the attachment function $f$. In the non-persistent regime, analogous algorithms are developed based on centrality measures where one assigns to each vertex $v$ the maximal degree among vertices in a neighborhood of $v$ of radius $r_n$, where $r_n$ is much smaller than the diameter of the network. A bound on the size of the associated confidence set is also obtained, and it is shown that, when $f(k) = k^{alpha}, k ge 1,$ for any $alpha in (0,1/2]$, this size grows at a smaller rate than any positive power of the network size.
We prove that Khovanov homology with coefficients in $mathbb{Z}/2mathbb{Z}$ detects the $(2,5)$ torus knot. Our proof makes use of a wide range of deep tools in Floer homology, Khovanov homology, and Khovanov homotopy. We combine these tools with cla
ssical results on the dynamics of surface homeomorphisms to reduce the detection question to a problem about mutually braided unknots, which we then solve with computer assistance.
We conduct a combined experimental and theoretical study of the quantum-confined Stark effect in GaAs/AlGaAs quantum dots obtained with the local droplet etching method. In the experiment, we probe the permanent electric dipole and polarizability of
neutral and positively charged excitons weakly confined in GaAs quantum dots by measuring their light emission under the influence of a variable electric field applied along the growth direction. Calculations based on the configuration-interaction method show excellent quantitative agreement with the experiment and allow us to elucidate the role of Coulomb interactions among the confined particles and -- even more importantly -- of electronic correlation effects on the Stark shifts. Moreover, we show how the electric field alters properties such as built-in dipole, binding energy, and heavy-light hole mixing of multiparticle complexes in weakly confining systems, underlining the deficiencies of commonly used models for the quantum-confined Stark effect.
In high speed CNC (Compute Numerical Control) machining, the feed rate scheduling has played an important role to ensure machining quality and machining efficiency. In this paper, a novel feed rate scheduling method is proposed for generating smooth
feed rate profile conveniently with the consideration of both geometric error and kinematic error. First, a relationship between feed rate value and chord error is applied to determine the feed rate curve. Then, breaking points, which can split whole curve into several blocks, can be found out using proposed two step screening method. For every block, a feed rate profile based on the Sigmoid function is generated. With the consideration of kinematic limitation and machining efficiency, a time-optimal feed rate adjustment algorithm is proposed to further adjust feed rate value at breaking points. After planning feed rate profile for each block, all blocks feed rate profile will be connected smoothly. The resulting feed rate profile is more concise compared with the polynomial profile and more efficient compared with the trigonometric profile. Finally, simulations with two free-form NURBS curves are conducted and comparison with the sine-curve method are carried out to verify the feasibility and applicability of the proposed method.
