Adaptive Regularization for Nonconvex Optimization Using Inexact Function Values and Randomly Perturbed Derivatives

A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function with Lipschitz continuous $p$-th derivative and given an arbitrary optimality order $q \leq p$, it is shown that this algorithm will, in expectation, compute such a point in at most $O\left(\left(\min_{j\in\{1,\ldots,q\}}\epsilon_j\right)^{-\frac{p+1}{p-q+1}}\right)$ inexact evaluations of $f$ and its derivatives whenever $q\in\{1,2\}$, where $\epsilon_j$ is the tolerance for $j$th order accuracy. This bound becomes at most $O\left(\left(\min_{j\in\{1,\ldots,q\}}\epsilon_j\right)^{-\frac{q(p+1)}{p}}\right)$ inexact evaluations if $q>2$ and all derivatives are Lipschitz continuous. Moreover these bounds are sharp in the order of the accuracy tolerances. An extension to convexly constrained problems is also outlined.Comment: 22 page

Adaptive Regularization Algorithms with Inexact Evaluations for Nonconvex Optimization

A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that is constraints whose evaluation and enforcement has negligible cost) under the assumption that the derivative of highest degree is $\beta$-H\"{o}lder continuous. It features a very flexible adaptive mechanism for determining the inexactness which is allowed, at each iteration, when computing objective function values and derivatives. The complexity analysis covers arbitrary optimality order and arbitrary degree of available approximate derivatives. It extends results of Cartis, Gould and Toint (2018) on the evaluation complexity to the inexact case: if a $q$th order minimizer is sought using approximations to the first $p$ derivatives, it is proved that a suitable approximate minimizer within $\epsilon$ is computed by the proposed algorithm in at most $O(\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ iterations and at most $O(|\log(\epsilon)|\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ approximate evaluations. An algorithmic variant, although more rigid in practice, can be proved to find such an approximate minimizer in $O(|\log(\epsilon)|+\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ evaluations.While the proposed framework remains so far conceptual for high degrees and orders, it is shown to yield simple and computationally realistic inexact methods when specialized to the unconstrained and bound-constrained first- and second-order cases. The deterministic complexity results are finally extended to the stochastic context, yielding adaptive sample-size rules for subsampling methods typical of machine learning.Comment: 32 page

Tailoring correlations of the local density of states in disordered photonic materials

We present experimental evidence for the different mechanisms driving the fluctuations of the local density of states (LDOS) in disordered photonic systems. We establish a clear link between the microscopic structure of the material and the frequency correlation function of LDOS accessed by a near-field hyperspectral imaging technique. We show, in particular, that short- and long-range frequency correlations of LDOS are controlled by different physical processes (multiple or single scattering processes, respectively) that can be---to some extent---manipulated independently. We also demonstrate that the single scattering contribution to LDOS fluctuations is sensitive to subwavelength features of the material and, in particular, to the correlation length of its dielectric function. Our work paves a way towards a complete control of statistical properties of disordered photonic systems, allowing for designing materials with predefined correlations of LDOS.Comment: 5+9 pages, 5+6 figures. Fixed confusion of references between the main text and the supplemental material in version

Dielectric Effects in FeO x-Coated Au Nanoparticles Boost the Magnetoplasmonic Response: Implications for Active Plasmonic Devices

Plasmon resonance modulation with an external magnetic field (magnetoplasmonics) represents a promising route for the improvement of the sensitivity of plasmon-based refractometric sensing. To this purpose, an accurate material choice is needed to realize hybrid nanostructures with an improved magnetoplasmonic response. In this work, we prepared core@shell nanostructures made of an 8 nm Au core surrounded by an ultrathin iron oxide shell (≤1 nm). The presence of the iron oxide shell was found to significantly enhance the magneto-optical response of the noble metal in the localized surface plasmon region, compared with uncoated Au nanoparticles. With the support of an analytical model, we ascribed the origin of the enhancement to the shell-induced increase in the dielectric permittivity around the Au core. The experiment points out the importance of the spectral position of the plasmonic resonance in determining the magnitude of the magnetoplasmonic response. Moreover, the analytical model proposed here represents a powerful predictive tool for the quantification of the magnetoplasmonic effect based on resonance position engineering, which has significant implications for the design of active magnetoplasmonic devices

Picosecond Nonlinear Relaxation of Photoinjected Carriers in a Single GaAs/AlGaAs Quantum Dot

Photoemission from a single self-organized GaAs/AlGaAs quantum dot (QD) is temporally resolved with picosecond time resolution. The emission spectra consisting of the multiexciton structures are observed to depend on the delay time and the excitation intensity. Quantitative agreement is found between the experimental data and the calculation based on a model which characterizes the successive relaxation of multiexcitons. Through the analysis we can determine the carrier relaxation time as a function of population of photoinjected carriers. Enhancement of the intra-dot carrier relaxation is demonstrated to be due to the carrier-carrier scattering inside a single QD.Comment: 4 pages, 4 figures, to be published in Phys. Rev. B, Rapid

Endometrioid Cancer Associated With Endometriosis: From the Seed and Soil Theory to Clinical Practice

Endometriosis is a benign condition characterized by the presence of ectopic endometrial tissue. It is still debated whether endometriosis is a disease that can predispose to the pathogenesis of endometrial cancer outside the uterus. Deficiencies in mismatch repair (MMR) genes are a known risk factor for developing endometrioid cancer. Starting from two cases of patients with abnormal MMR endometrioid carcinoma of the uterus and synchronous endometrioid carcinoma in non-ovarian and ovarian endometriosis, we performed a somatic mutation profile and phylogenetic analysis of the lesions in order to identify if they were metastasis or primary de novo tumors. In the first case, we identified de novo activating mutations in PIK3CA and KRAS in endometrioid cancer lesions but not in endometriosis. Although the acquisition of a de novo mutation in ESR1 and a decrease in mutant allele fraction (MAF) from the endometrial tumor to the localizations in the endometriosis lesions, the clonal relationship was confirmed by the limited number of heteroplasmic mutations in D-loop mitochondrial DNA region. In the other case, the clonal behavior was demonstrated by the overlap of MAF at each site. Our data support the hypothesis of a retrograde dissemination of tumor cells, moving from the primary carcinoma in the endometrium to ectopic sites of endometriosis where localizations of tumor arise

Circulating tumor cell gene expression and plasma AR gene copy number as biomarkers for castration-resistant prostate cancer patients treated with cabazitaxel

Background: Cabazitaxel improves overall survival (OS) in metastatic castration-resistant prostate cancer (mCRPC) patients progressing after docetaxel. In this prospective study, we evaluated the prognostic role of CTC gene expression on cabazitaxel-treated patients and its association with plasma androgen receptor (AR) copy number (CN). Methods: Patients receiving cabazitaxel 20 or 25 mg/sqm for mCRPC were enrolled. Digital PCR was performed to assess plasma AR CN status. CTC enrichment was assessed using the AdnaTest EMT-2/StemCell kit. CTC expression analyses were performed for 17 genes. Data are expressed as hazard ratio (HR) or odds ratio (OR) and 95% CI. Results: Seventy-four patients were fully evaluable. CTC expression of AR-V7 (HR=2.52, 1.24–5.12, p=0.011), AKR1C3 (HR=2.01, 1.06–3.81, p=0.031), AR (HR=2.70, 1.46–5.01, p=0.002), EPCAM (HR=3.75, 2.10–6.71, p< 0.0001), PSMA (HR=2.09, 1.19–3.66, p=0.01), MDK (HR=3.35, 1.83–6.13, p< 0.0001), and HPRT1 (HR=2.46, 1.44–4.18, p=0.0009) was significantly associated with OS. ALDH1 (OR=5.50, 0.97–31.22, p=0.05), AR (OR=8.71, 2.32–32.25, p=0.001), EPCAM (OR=7.26, 1.47–35.73, p=0.015), PSMA (OR=3.86, 1.10–13.50, p=0.035), MDK (OR=6.84, 1.87–24.98, p=0.004), and HPRT1 (OR=7.41, 1.82–30.19, p=0.005) expression was associated with early PD. AR CN status was significantly correlated with AR-V7 (p=0.05), EPCAM (p=0.02), and MDK (p=0.002) expression. In multivariable model, EPCAM and HPRT1 CTC expression, plasma AR CN gain, ECOG PS=2, and liver metastases and PSA were independently associated with poorer OS. In patients treated with cabazitaxel 20 mg/sqm, median OS was shorter in AR-V7 positive than negative patients (6.6 versus 14 months, HR=3.46, 1.47–8.17], p=0.004). Conclusions: Baseline CTC biomarkers may be prognosticators for cabazitaxel-treated mCRPC patients. Cabazitaxel at lower (20 mg/sqm) dose was associated with poorer outcomes in AR-V7 positive patients compared to AR-V7 negative patients in a post hoc subgroup analysis. Trial registration: Clinicaltrials.govNCT03381326. Retrospectively registered on 18 December 2017

A history of deformation within Pietre Cotte rhyolite flow (Vulcano)

International audienc

On the exciton binding energy in a quantum well

We consider a model describing the one-dimensional confinement of an exciton in a symmetrical, rectangular quantum-well structure and derive upper and lower bounds for the binding energy $E_b$ of the exciton. Based on these bounds, we study the dependence of $E_b$ on the width of the confining potential with a higher accuracy than previous reports. For an infinitely deep potential the binding energy varies as expected from $1 Ry$ at large widths to $4 Ry$ at small widths. For a finite potential, but without consideration of a mass mismatch or a dielectric mismatch, we substantiate earlier results that the binding energy approaches the value $1 Ry$ for both small and large widths, having a characteristic peak for some intermediate size of the slab. Taking the mismatch into account, this result will in general no longer be true. For the specific case of a $Ga_{1-x}Al_{x}As/GaAs/Ga_{1-x}Al_{x}As$ quantum-well structure, however, and in contrast to previous findings, the peak structure is shown to survive.Comment: 32 pages, ReVTeX, including 9 figure