We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale $ell$ in an infinite heterogeneous medium, in a situation where the medium is only known in a box of diameter $Lggell$
around the support of the charge. We propose a boundary condition that with overwhelming probability is (near) optimal with respect to scaling in terms of $ell$ and $L$, in the setting where the medium is a sample from a stationary ensemble with a finite range of dependence (set to be unity and with the assumption that $ell gg 1$). The boundary condition is motivated by quantitative stochastic homogenization that allows for a multipole expansion [BGO20]. This work extends [LO21] from two to three dimensions, and thus we need to take quadrupoles, next to dipoles, into account. This in turn relies on stochastic estimates of second-order, next to first-order, correctors. These estimates are provided for finite range ensembles under consideration, based on an extension of the semi-group approach of [GO15].
Mitotic count is the most important morphological feature of breast cancer grading. Many deep learning-based methods have been proposed but suffer from domain shift. In this work, we construct a Fourier-based segmentation model for mitosis detection
to address the problem. Swapping the low-frequency spectrum of source and target images is shown effective to alleviate the discrepancy between different scanners. Our Fourier-based segmentation method can achieve F1 with 0.7456 on the preliminary test set.
Binary stars plays important role in the evolution of stellar populations . The intrinsic binary fraction ($f_{bin}$) of O and B-type (OB) stars in LAMOST DR5 was investigated in this work. We employed a cross-correlation approach to estimate relativ
e radial velocities for each of the stellar spectra. The algorithm described by cite{2013A&A...550A.107S} was implemented and several simulations were made to assess the performance of the approach. Binary fraction of the OB stars are estimated through comparing the uni-distribution between observations and simulations with the Kolmogorov-Smirnov tests. Simulations show that it is reliable for stars most of whom have $6,7$ and $8$ repeated observations. The uncertainty of orbital parameters of binarity become larger when observational frequencies decrease. By adopting the fixed power exponents of $pi=-0.45$ and $kappa=-1$ for period and mass ratio distributions, respectively, we obtain that $f_{bin}=0.4_{-0.06}^{+0.05}$ for the samples with more than 3 observations. When we consider the full samples with at least 2 observations, the binary fraction turns out to be $0.37_{-0.03}^{+0.03}$. These two results are consistent with each other in $1sigma$.
Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensor
s form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. We discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states (TTNS), and the multiscale entanglement renormalization ansatz (MERA) are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states (PEPS) are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grain
Remote photoplethysmography (rPPG) monitors heart rate without requiring physical contact, which allows for a wide variety of applications. Deep learning-based rPPG have demonstrated superior performance over the traditional approaches in controlled
context. However, the lighting situation in indoor space is typically complex, with uneven light distribution and frequent variations in illumination. It lacks a fair comparison of different methods under different illuminations using the same dataset. In this paper, we present a public dataset, namely the BH-rPPG dataset, which contains data from twelve subjects under three illuminations: low, medium, and high illumination. We also provide the ground truth heart rate measured by an oximeter. We evaluate the performance of three deep learning-based methods to that of four traditional methods using two public datasets: the UBFC-rPPG dataset and the BH-rPPG dataset. The experimental results demonstrate that traditional methods are generally more resistant to fluctuating illuminations. We found that the rPPGNet achieves lowest MAE among deep learning-based method under medium illumination, whereas the CHROM achieves 1.5 beats per minute (BPM), outperforming the rPPGNet by 60%. These findings suggest that while developing deep learning-based heart rate estimation algorithms, illumination variation should be taken into account. This work serves as a benchmark for rPPG performance evaluation and it opens a pathway for future investigation into deep learning-based rPPG under illumination variations.
Systems with different interactions could develop the same critical behaviour due to the underlying symmetry and universality. Using this principle of universality, we can embed critical correlations modeled on the 3D Ising model into the simulated d
ata of heavy-ion collisions, hiding weak signals of a few inter-particle correlations within a large particle cloud. Employing a point cloud network with dynamical edge convolution, we are able to identify events with critical fluctuations through supervised learning, and pick out a large fraction of signal particles used for decision-making in each single event.
We study a model in which before a conflict between two parties escalates into a war (in the form of an all-pay auction), a party can offer a take-it-or-leave-it bribe to the other one for a peaceful settlement. We distinguish between various degrees
of peace prospects--implementability, weak security and strong security. We first characterize the necessary and sufficient conditions for peace implementability and weak security. We then show that weak security implies strong security. We also consider a requesting-a-bribe game and characterize the necessary and sufficient conditions for existence of a robust peaceful equilibrium. We find that all such robust peaceful equilibria share the same request.
For gapped periodic systems (insulators), it has been established that the insulator is topologically trivial (i.e., its Chern number is equal to $0$) if and only if its Fermi projector admits an orthogonal basis with finite second moment (i.e., all
basis elements satisfy $int |boldsymbol{x}|^2 |w(boldsymbol{x})|^2 ,textrm{d}{boldsymbol{x}} < infty$). In this paper, we extend one direction of this result to non-periodic gapped systems. In particular, we show that the existence of an orthogonal basis with slightly more decay ($int |boldsymbol{x}|^{2+epsilon} |w(boldsymbol{x})|^2 ,textrm{d}{boldsymbol{x}} < infty$ for any $epsilon > 0$) is a sufficient condition to conclude that the Chern marker, the natural generalization of the Chern number, vanishes.
Boundary-based instance segmentation has drawn much attention since of its attractive efficiency. However, existing methods suffer from the difficulty in long-distance regression. In this paper, we propose a coarse-to-fine module to address the probl
em. Approximate boundary points are generated at the coarse stage and then features of these points are sampled and fed to a refined regressor for fine prediction. It is end-to-end trainable since differential sampling operation is well supported in the module. Furthermore, we design a holistic boundary-aware branch and introduce instance-agnostic supervision to assist regression. Equipped with ResNet-101, our approach achieves 31.7% mask AP on COCO dataset with single-scale training and testing, outperforming the baseline 1.3% mask AP with less than 1% additional parameters and GFLOPs. Experiments also show that our proposed method achieves competitive performance compared to existing boundary-based methods with a lightweight design and a simple pipeline.
Numerical solutions to high-dimensional partial differential equations (PDEs) based on neural networks have seen exciting developments. This paper derives complexity estimates of the solutions of $d$-dimensional second-order elliptic PDEs in the Barr
on space, that is a set of functions admitting the integral of certain parametric ridge function against a probability measure on the parameters. We prove under some appropriate assumptions that if the coefficients and the source term of the elliptic PDE lie in Barron spaces, then the solution of the PDE is $epsilon$-close with respect to the $H^1$ norm to a Barron function. Moreover, we prove dimension-explicit bounds for the Barron norm of this approximate solution, depending at most polynomially on the dimension $d$ of the PDE. As a direct consequence of the complexity estimates, the solution of the PDE can be approximated on any bounded domain by a two-layer neural network with respect to the $H^1$ norm with a dimension-explicit convergence rate.
