The Fourier-domain Douglas-Rachford (FDR) algorithm is analyzed for phase retrieval with a single random mask. Since the uniqueness of phase retrieval solution requires more than a single oversampled coded diffraction pattern, the extra information is imposed in either of the following forms: 1) the sector condition on the object; 2) another oversampled diffraction pattern, coded or uncoded. For both settings, the uniqueness of projected fixed point is proved and for setting 2) the local, geometric convergence is derived with a rate given by a spectral gap condition. Numerical experiments demonstrate global, power-law convergence of FDR from arbitrary initialization for both settings as well as for 3 or more coded diffraction patterns oversampling. In practice, the geometric convergence can be recovered from the power-law regime by a simple projection trick, resulting in highly accurate reconstruction from generic initialization.

Alternating projection (AP) of various forms, including the Parallel AP (PAP), Real-constrained AP (RAP) and the Serial AP (SAP), are proposed to solve phase retrieval with at most two coded diffraction patterns. The proofs of geometric convergence are given with sharp bounds on the rates of convergence in terms of a spectral gap condition.To compensate for the local nature of convergence, the null initialization is proposed for initial guess and proved to produce asymptotically accurate initialization for the case of Gaussian random measurement. Numerical experiments show that the null initialization produces more accurate initial guess than the spectral initialization and that AP converges faster to the true object than other iterative schemes for non-convex optimization such as the Wirtinger Flow. In numerical experiments AP with the null initialization converges globally to the true object.1.1. Set-up. Let us recall the measurement schemes of [28]. Let x 0 (n) be a discrete object function with n = (n 1 , n 2 , · · · , n d ) ∈ Z d . Consider the object space consisting of all functions supported in M = {0 ≤ m 1 ≤ M 1 , 0 ≤ m 2 ≤ M 2 , · · · , 0 ≤ m d ≤ M d }.We assume d ≥ 2.

Nano-immunotherapy improves breast cancer outcomes but not all patients respond and none are cured. To improve efficacy, research focuses on drugs that reprogram cancer-associated fibroblasts (CAFs) to improve therapeutic delivery and immunostimulation. These drugs, however, have a narrow therapeutic window and cause adverse effects. Developing strategies that increase CAF-reprogramming while limiting adverse effects is urgent. Here, taking advantage of the CAF-reprogramming capabilities of tranilast, we developed tranilast-loaded micelles. Strikingly, a 100-fold reduced dose of tranilast-micelles induces superior reprogramming compared to free drug owing to enhanced intratumoral accumulation and cancer-associated fibroblast uptake. Combination of tranilast-micelles and epirubicin-micelles or Doxil with immunotherapy increases T-cell infiltration, resulting in cures and immunological memory in mice bearing immunotherapy-resistant breast cancer. Furthermore, shear wave elastography (SWE) is able to monitor reduced tumor stiffness caused by tranilast-micelles and predict response to nano-immunotherapy. Micellar encapsulation is a promising strategy for TME-reprogramming and SWE is a potential biomarker of response.

Abstract. Uniqueness of solution is proved for any ptychographic scheme with a random masks under a minimum overlap condition and local geometric convergence analysis is given for the alternating projection (AP) and Douglas-Rachford (DR) algorithms. DR is shown to possess a unique fixed point in the object domain and for AP a simple criterion for distinguishing the true solution among possibly many fixed points is given.A minimalist scheme is proposed where the adjacent masks overlap 50% of area and each pixel of the object is illuminated by exactly four times during the whole measurement process. Such a scheme is conveniently parametrized by the number q of shifted masks in each direction. The lower bound 1 − C/q 2 is proved for the geometric convergence rate of the minimalist scheme, predicting a poor performance with large q which is confirmed by numerical experiments.Extensive numerical experiments are performed to explore what the general features of a wellperforming mask are like, what the best-performing values of q for a given mask are, how robust the minimalist scheme is with respect to measurement noise and what the significant factors affecting the noise stability are.

Abstract-We propose eP lace-M S, an electrostatics based placement algorithm for large-scale mixed-size circuits. ePlace-MS is generalized, flat, analytic and nonlinear. The density modeling method eDensity is extended to handle the mixedsize placement. We conduct detailed analysis on the correctness of the gradient formulation and the numerical solution, as well as the rationale of direct-current removal and the advantages over prior density functions. Nesterov's method is used as the nonlinear solver, which shows high yet stable performance over mixed-size circuits. The steplength as the inverse of Lipschitz constant of the gradient function, while we develop a backtracking method to prevent overestimation. An approximated nonlinear preconditioner is developed to minimize the topological and physical differences between large macros and standard cells. Besides, we devise a simulated annealer to legalize the layout of macros and use a second-phase global placement to reoptimize the standard cell layout. All the above innovations are integrated into our mixed-size placement prototype ePlace-MS, which outperforms all the related works in literature with better quality and efficiency. Compared to the leading-edge mixed-size placer NTUplace3 [13], ePlace-MS produces up to 22.98% and on average 8.22% shorter wirelength over all the sixteen modern mixed-size (MMS) benchmark circuits with the same runtime.