J. Liu

L. Wang, J. Liu, A. S. Morse et al.

A discrete-time modulus consensus model is considered in which the interaction among a family of networked agents is described by a time-dependent gain graph whose vertices correspond to agents and whose arcs are assigned complex numbers from a cyclic group. Limiting behavior of the model is studied using a graphical approach. It is shown that, under appropriate connectedness, a certain type of clustering will be reached exponentially fast for almost all initial conditions if and only if the sequence of gain graphs is "repeatedly jointly structurally balanced" corresponding to that type of clustering, where the number of clusters is at most the order of a cyclic group. It is also shown that the model will reach a consensus asymptotically at zero if the sequence of gain graphs is repeatedly jointly strongly connected and structurally unbalanced. In the special case when the cyclic group is of order two, the model simplifies to the so-called Altafini model whose gain graph is simply a signed graph.

J. Nehls, C. Dineen, J. Liu et al.

We have developed a new fully anisotropic 3D FDTD Maxwell solver for arbitrary electrically and magnetically anisotropic media for piecewise constant electric and magnetic materials that are co-located over the primary computational cells. Two numerical methods were developed that are called non-averaged and averaged methods, respectively. The non-averaged method is first order accurate, while the averaged method is second order accurate for smoothly-varying materials and reduces to first order for discontinuous material distributions. For the standard FDTD field locations with the co-location of the electric and magnetic materials at the primary computational cells, the averaged method require development of the different inversion algorithms of the constitutive relations for the electric and magnetic fields. We provide a mathematically rigorous stability proof followed by extensive numerical testing that includes long-time integration, eigenvalue analysis, tests with extreme, randomly placed material parameters, and various boundary conditions. For accuracy evaluation we have constructed a test case with an explicit analytic solution. Using transformation optics, we have constructed complex, spatially inhomogeneous geometrical object with fully anisotropic materials and a large dynamic range of $\underlineε$ and $\underlineμ$, such that a plane wave incident on the object is perfectly reconstructed downstream. In our implementation, the considerable increase in accuracy of the averaged method only increases the computational run time by 20%.

R. Li, J. Liu, X. L. Deng et al.

The diagnosis and monitoring of Castrate Resistant Prostate Cancer (CRPC) are crucial for cancer patients, but the current models (such as P-NET) have limitations in terms of parameter count, generalization, and cost. To address the issue, we develop a more accurate and efficient Prostate Cancer patient condition prediction model, named PR-NET. By compressing and optimizing the network structure of P-NET, the model complexity is reduced while maintaining high accuracy and interpretability. The PR-NET demonstrated superior performance in predicting prostate cancer patient outcomes, outshining P-NET and six other traditional models with a significant margin. In our rigorous evaluation, PR-NET not only achieved impressive average AUC and Recall scores of 0.94 and 0.83, respectively, on known data but also maintained robust generalizability on five unknown datasets with a higher average AUC of 0.73 and Recall of 0.72, compared to P-NET's 0.68 and 0.5. PR-NET's efficiency was evidenced by its shorter average training and inference times, and its gene-level analysis revealed 46 key genes, demonstrating its enhanced predictive power and efficiency in identifying critical biomarkers for prostate cancer. Future research can further expand its application domains and optimize the model's performance and reliability.

Z. Ma, L. Song, X. Feng et al.

Intracranial aneurysm (IA) is a life-threatening blood spot in human's brain if it ruptures and causes cerebral hemorrhage. It is challenging to detect whether an IA has ruptured from medical images. In this paper, we propose a novel graph based neural network named GraphNet to detect IA rupture from 3D surface data. GraphNet is based on graph convolution network (GCN) and is designed for graph-level classification and node-level segmentation. The network uses GCN blocks to extract surface local features and pools to global features. 1250 patient data including 385 ruptured and 865 unruptured IAs were collected from clinic for experiments. The performance on randomly selected 234 test patient data was reported. The experiment with the proposed GraphNet achieved accuracy of 0.82, area-under-curve (AUC) of receiver operating characteristic (ROC) curve 0.82 in the classification task, significantly outperforming the baseline approach without using graph based networks. The segmentation output of the model achieved mean graph-node-based dice coefficient (DSC) score 0.88.

L. Wang, A. S. Morse, D. Fullmer et al.

A hybrid observer is described for estimating the state of an $m>0$ channel, $n$-dimensional, continuous-time, distributed linear system of the form $\dot{x} = Ax,\;y_i = C_ix,\;i\in\{1,2,\ldots, m\}$. The system's state $x$ is simultaneously estimated by $m$ agents assuming each agent $i$ senses $y_i$ and receives appropriately defined data from each of its current neighbors. Neighbor relations are characterized by a time-varying directed graph $\mathbb{N}(t)$ whose vertices correspond to agents and whose arcs depict neighbor relations. Agent $i$ updates its estimate $x_i$ of $x$ at "event times" $t_1,t_2,\ldots $ using a local observer and a local parameter estimator. The local observer is a continuous time linear system whose input is $y_i$ and whose output $w_i$ is an asymptotically correct estimate of $L_ix$ where $L_i$ a matrix with kernel equaling the unobservable space of $(C_i,A)$. The local parameter estimator is a recursive algorithm designed to estimate, prior to each event time $t_j$, a constant parameter $p_j$ which satisfies the linear equations $w_k(t_j-τ) = L_kp_j+μ_k(t_j-τ),\;k\in\{1,2,\ldots,m\}$, where $τ$ is a small positive constant and $μ_k$ is the state estimation error of local observer $k$. Agent $i$ accomplishes this by iterating its parameter estimator state $z_i$, $q$ times within the interval $[t_j-τ, t_j)$, and by making use of the state of each of its neighbors' parameter estimators at each iteration. The updated value of $x_i$ at event time $t_j$ is then $x_i(t_j) = e^{Aτ}z_i(q)$. Subject to the assumptions that (i) the neighbor graph $\mathbb{N}(t)$ is strongly connected for all time, (ii) the system whose state is to be estimated is jointly observable, (iii) $q$ is sufficiently large, it is shown that each estimate $x_i$ converges to $x$ exponentially fast as $t\rightarrow \infty$ at a rate which can be controlled.

A. Sanchez-Gonzalez, P. Micaelli, C. Olivier et al.

X-ray free-electron lasers (XFELs) are the only sources currently able to produce bright few-fs pulses with tunable photon energies from 100 eV to more than 10 keV. Due to the stochastic SASE operating principles and other technical issues the output pulses are subject to large fluctuations, making it necessary to characterize the x-ray pulses on every shot for data sorting purposes. We present a technique that applies machine learning tools to predict x-ray pulse properties using simple electron beam and x-ray parameters as input. Using this technique at the Linac Coherent Light Source (LCLS), we report mean errors below 0.3 eV for the prediction of the photon energy at 530 eV and below 1.6 fs for the prediction of the delay between two x-ray pulses. We also demonstrate spectral shape prediction with a mean agreement of 97%. This approach could potentially be used at the next generation of high-repetition-rate XFELs to provide accurate knowledge of complex x-ray pulses at the full repetition rate.