Conformalized matrix completion

Matrix completion aims to estimate missing entries in a data matrix, using the assumption of a low-complexity structure (e.g., low rank) so that imputation is possible. While many effective estimation algorithms exist in the literature, uncertainty quantification for this problem has proved to be challenging, and existing methods are extremely sensitive to model misspecification. In this work, we propose a distribution-free method for predictive inference in the matrix completion problem. Our method adapts the framework of conformal prediction, which provides confidence intervals with guaranteed distribution-free validity in the setting of regression, to the problem of matrix completion. Our resulting method, conformalized matrix completion (cmc), offers provable predictive coverage regardless of the accuracy of the low-rank model. Empirical results on simulated and real data demonstrate that cmc is robust to model misspecification while matching the performance of existing model-based methods when the model is correct.Comment: accepted to 37th Conference on Neural Information Processing Systems (NeurIPS 2023

Young's modulus, Poisson's ratio, and residual stress and strain in (111)-oriented scandium nitride thin films on silicon

Epitaxial scandium nitride films (225 nm thick) were grown on silicon by molecular beam epitaxy, using ammonia as a reactive nitrogen source. The main crystallographic orientation of ScN with respect to Si is (111)(ScN)parallel to(111)(Si) and [1-10](ScN)parallel to[0-11](Si); however, some twinning is also present in the films. The films displayed a columnar morphology with rough surfaces, due to low adatom mobility during growth. The strain-free lattice parameter of ScN films grown under optimized conditions was found to be 4.5047 +/- 0.0005 A, as determined using high-resolution x-ray diffraction (HRXRD). In-plane and out-of-plane strains were subsequently evaluated using HRXRD and were used to determine the Poisson ratio of ScN along the direction, which is found to be 0.188 +/- 0.005. Wafer curvature measurements were made and combined with the strain information to determine the average Young's modulus of the films, which is found to be 270 +/- 25 GPa. Residual film stresses ranged from -1 to 1 GPa (depending on film growth temperature and film thickness) due to competition between the tensile stress (induced by the differential thermal contraction between the ScN film and the Si substrate) and intrinsic compressive stresses generated during growth

Direct excitation of the forbidden clock transition in neutral 174Yb atoms confined to an optical lattice

We report direct single-laser excitation of the strictly forbidden (6s^2)^1S_0 -(6s6p)^3P_0 clock transition in the even 174Yb isotope confined to a 1D optical lattice. A small (~1.2 mT) static magnetic field was used to induce a nonzero electric dipole transition probability between the clock states at 578.42 nm. Narrow resonance linewidths of 20 Hz (FHWM) with high contrast were observed, demonstrating a record neutral-atom resonance quality factor of 2.6x10^13. The previously unknown ac Stark shift-canceling (magic) wavelength was determined to be 759.35+/-0.02 nm. This method for using the metrologically superior even isotope can be easily implemented in current Yb and Sr lattice clocks, and can create new clock possibilities in other alkaline earth-like atoms such as Mg and Ca.Comment: Submitted to Physics Review Letter

Complex refractive index of non-spherical particles in the vis-NIR region - application to Bacillus Subtilis spores

A method is presented for the estimation of optical constants in the ultraviolet-visible-near-infrared (UVVis-NIR) region of nonspherical particles in a suspension at concentrations where multiple scattering issignificant. The optical constants are obtained by an inversion technique using the adding-doubling method to solve the radiative transfer equation in combination with the single scattering theories for modelling scattering by nonspherical particles. Two methods for describing scattering by single scatteringare considered: the T-matrix method and the approximate but computationally simpler Rayleigh-Gans-Debye (RGD) approximation. The method is then applied to obtain the optical constants of Bacillussubtilis spores in the wavelength region 400-1200 nm. It is found that the optical constants obtained using the RGD approximation matches those obtained using the T-matrix method to within experimental error

Critical Exponent for the Density of Percolating Flux

This paper is a study of some of the critical properties of a simple model for flux. The model is motivated by gauge theory and is equivalent to the Ising model in three dimensions. The phase with condensed flux is studied. This is the ordered phase of the Ising model and the high temperature, deconfined phase of the gauge theory. The flux picture will be used in this phase. Near the transition, the density is low enough so that flux variables remain useful. There is a finite density of finite flux clusters on both sides of the phase transition. In the deconfined phase, there is also an infinite, percolating network of flux with a density that vanishes as $T \rightarrow T_{c}^{+}$. On both sides of the critical point, the nonanalyticity in the total flux density is characterized by the exponent $(1-\alpha)$. The main result of this paper is a calculation of the critical exponent for the percolating network. The exponent for the density of the percolating cluster is $\zeta = (1-\alpha) - (\varphi-1)$. The specific heat exponent $\alpha$ and the crossover exponent $\varphi$ can be computed in the $\epsilon$-expansion. Since $\zeta < (1-\alpha)$, the variation in the separate densities is much more rapid than that of the total. Flux is moving from the infinite cluster to the finite clusters much more rapidly than the total density is decreasing.Comment: 20 pages, no figures, Latex/Revtex 3, UCD-93-2

Frequency evaluation of the doubly forbidden 1S0→3P0^1S_0\to ^3P_0 transition in bosonic 174^{174}Yb

We report an uncertainty evaluation of an optical lattice clock based on the $^1S_0\leftrightarrow^3P_0$ transition in the bosonic isotope $^{174}$Yb by use of magnetically induced spectroscopy. The absolute frequency of the $^1S_0\leftrightarrow^3P_0$ transition has been determined through comparisons with optical and microwave standards at NIST. The weighted mean of the evaluations is $\nu$($^{174}$Yb)=518 294 025 309 217.8(0.9) Hz. The uncertainty due to systematic effects has been reduced to less than 0.8 Hz, which represents $1.5\times10^{-15}$ in fractional frequency.Comment: 4 pages, 3 figure -Submitted to PRA Rapid Communication

Anti-proliferative effect of main dietary phytosterols and \u3b2-cryptoxanthin alone or combined in human colon cancer Caco-2 cells through cytosolic Ca+2 \u2013 and oxidative stress induced apoptosis

\u3b2-cryptoxanthin (\u3b2-Cx) and phytosterols (Ps) have potential against different cancer types,including colon cancer. However, their combined action has not been reported so far. Human colon cancer Caco-2 cells were treated 24 h with \u3b2-Cx and/or main dietary Ps (\u3b2-sitosterol, campesterol and stigmasterol), alone or in combination, at concentrations compatible with physiological human serum levels. A decrease in cell viability due to apoptosis (rise in sub-G1 population and exposure of membrane phosphatidylserine) was accompanied with dephosphorylation of BAD, mitochondrial depolarization and caspase 3-dependent PARP cleavage, with intracellular Ca2+ influx and increase of RONS levels as initial triggers. Ps and \u3b2-Cx, alone or in combination showed anti-proliferative activity against human colon adenocarcinoma Caco-2 cells through the mitochondrial pathway of apoptosis. No additive or synergistic effects were observed.The importance of bioactivity-guided assays with mixtures of dietary bioactive compounds to determine their eventual interactions in the functional food context is demonstrated

Insulin-like growth factor binding proteins initiate cell death and extracellular matrix remodeling in the mammary gland

We have demonstrated that insulin-like growth factor binding protein-5 (IGFBP-5) production by mammary epithelial cells increases dramatically during forced involution of the mammary gland in rats, mice and pigs. We proposed that growth hormone (GH) increases the survival factor IGF-I, whilst prolactin (PRL) enhances the effects of GH by decreasing the concentration of IGFBP-5, which would otherwise inhibit the actions of IGFs. To demonstrate a causal relationship between IGFBP-5 and cell death, we created transgenic mice expressing IGFBP-5, specifically, in the mammary gland. DNA content in the mammary glands of transgenic mice was decreased as early as day 10 of pregnancy. Mammary cell number and milk synthesis were both decreased by approximately 50% during the first 10 days of lactation. The concentrations of the pro-apoptotic molecule caspase-3 was increased in transgenic animals whilst the concentrations of two pro-survival molecules Bcl-2 and Bcl-x were both decreased. In order to examine whether IGFBP-5 acts by inhibiting the survival effect of IGF-I, we examined IGF receptor- and Akt-phoshorylation and showed that both were inhibited. These studies also indicated that the effects of IGFBP-5 could be mediated in part by IGF-independent effects involving potential interactions with components of the extracellular matrix involved in tissue remodeling, such as components of the plasminogen system, and the matrix metallo-proteinases (MMPs). Mammary development was normalised in transgenic mice by R3-IGF-I, an analogue of IGF-I which binds weakly to IGFBPs, although milk production was only partially restored. In contrast, treatment with prolactin was able to inhibit early involutionary processes in normal mice but was unable to prevent this in mice over-expressing IGFBP-5, although it was able to inhibit activation of MMPs. Thus, IGFBP-5 can simultaneously inhibit IGF action and activate the plasminogen system thereby coordinating cell death and tissue remodeling processes. The ability to separate these properties, using mutant IGFBPs, is currently under investigatio