Adaptive Stochastic Variance Reduction for Subsampled Newton Method with Cubic Regularization

The cubic regularized Newton method of Nesterov and Polyak has become increasingly popular for nonconvex optimization because of its capability of finding an approximate local solution with a second order guarantee and its low iteration complexity. Several recent works extend this method to the setting of minimizing the average of N smooth functions by replacing the exact gradients and Hessians with subsampled approximations. It is shown that the total Hessian sample complexity can be reduced to be sublinear in N per iteration by leveraging stochastic variance reduction techniques. We present an adaptive variance reduction scheme for a subsampled Newton method with cubic regularization and show that the expected Hessian sample complexity is [Formula: see text] for finding an [Formula: see text]-approximate local solution (in terms of first and second order guarantees, respectively). Moreover, we show that the same Hessian sample complexity is retained with fixed sample sizes if exact gradients are used. The techniques of our analysis are different from previous works in that we do not rely on high probability bounds based on matrix concentration inequalities. Instead, we derive and utilize new bounds on the third and fourth order moments of the average of random matrices, which are of independent interest on their own.

Anomalous tracer diffusion in hard-sphere suspensions

Coupled equations describing diffusion and cross-diffusion of tracer particles in hard-sphere suspensions are derived and solved numerically. In concentrated systems with strong excluded volume and viscous interactions the tracer motion is subdiffusive. Cross diffusion generates transient perturbations to the host-particle matrix, which affect the motion of the tracer particles leading to nonlinear mean squared displacements. Above a critical host-matrix concentration the tracers experience clustering and uphill diffusion, moving in opposition to their own concentration gradient. A linear stability analysis indicates that cross diffusion can lead to unstable concentration fluctuations in the suspension. The instability is a potential mechanism for the appearance of dynamic and structural heterogeneity in suspensions near the glass transition.

Antifungal Effect of Liposomal α-Bisabolol and When Associated with Fluconazole

Fungal pathologies caused by the genus Candida have increased in recent years due to the involvement of immunosuppressed people and the advance of resistance mechanisms acquired by these microorganisms. Liposomes are nanovesicles with lipid bilayers in which they store compounds. α-Bisabolol is a sesquiterpene with proven biological activities, and in this work it was tested alone in liposomes and in association with Fluconazole in vitro to evaluate the antifungal potential, Fluconazole optimization, and virulence inhibitory effect in vitro. Antifungal assays were performed against standard strains of Candida albicans, Candida tropicalis, and Candida krusei by microdilution to identify the IC50 values and to obtain the cell viability. The Minimum Fungicidal Concentration (MFC) was performed by subculturing on the solid medium, and at their subinhibitory concentration (Matrix Concentration (MC): 16,384 µg/mL) (MC/16), the compounds, both isolated and liposomal, were associated with fluconazole in order to verify the inhibitory effect of this junction. Tests to ascertain changes in morphology were performed in microculture chambers according to MC concentrations. Liposomes were characterized from the vesicle size, polydispersity index, average Zeta potential, and scanning electron microscopy. The IC50 value of the liposomal bisabolol associated with fluconazole (FCZ) was 2.5 µg/mL against all strains tested, revealing a potentiating effect. Liposomal bisabolol was able to potentiate the effect of fluconazole against the CA and CT strains by reducing its concentration and completely inhibiting fungal growth. α-Bisabolol in liposomal form inhibited the morphological transition in all strains tested at a concentration of MC/8. The liposomes were homogeneous, with vesicles with diameters of 203.8 nm for the liposomal bisabolol and a surface charge potential of −34.2 mV, conferring stability to the nanosystem. Through scanning microscopy, the spherical shapes of the vesicles were observed.

Current challenges in thermodynamic aspects of rubber foam

Natural rubber (NR) foam can be prepared by the Dunlop method using concentrated natural latex with chemical agents. Most previous studies have focused on the thermodynamic parameters of solid rubber in extension. The main objective of this study is to investigate the effect of the NR matrix concentration on the static and dynamic properties of NR foams, especially the new approach of considering the thermodynamic aspects of NR foam in compression. We found that the density and compression strength of NR foams increased with increasing NR matrix concentration. The mechanical properties of NR foam were in agreement with computational modelling. Moreover, thermodynamic aspects showed that the ratio of internal energy force to the compression force, Fu/F, and the entropy, S, increased with increasing matrix concentration. The activation enthalpy, ∆Ha, also increased with increasing matrix concentration in the NR foam, indicating the greater relaxation time of the backbone of the rubber molecules. New scientific concepts of thermodynamic parameters of the crosslinked NR foam in compression mode are proposed and discussed. Our results will improve both the knowledge and the development of rubber foams based on the structure–properties relationship, especially the new scientific concept of the thermodynamical parameters under compression.

Decreased cell stiffness facilitates cell detachment and cell migration from breast cancer spheroids in 3D collagen matrices of different rigidity

PurposeTumour-cell detachment is a critical early event in the metastatic cascade. Although several mechanisms have been reported, the role of cell mechanical properties in facilitating cell detachment and migration is not well understood. We, therefore, investigated how cells alter intracellular stiffness during these processes.MethodsMDA-MB-231 cells were embedded as 10,000-cell spheroids in 2 and 4 mg/ml collagen matrices. Using mitochondrial-based particle tracking microrheology (PTM), the intracellular stiffness of cells that have migrated different distances from the spheroid were assessed. Here, 0dC, 4dC and 6dC represented no, medium and high migration, respectively.ResultsFor 2 and 4 mg/ml collagen matrices, the MSD and cell stiffness of 0dC cells were larger than for migrated 4dC and 6dC cells. The MSD of 4dC and 6dC cells were similar; however, the cell stiffness of 4dC cells was smaller than that of 6dC cells. The stiffness of 0dC cells was lower for higher matrix concentration and rigidity compared to lower matrix rigidity, whereas matrix rigidity did not affect the stiffness of 4dC and 6dC cells.ConclusionsPTM was capable of quantifying intracellular mechanics during tumour detachment and migration in 3D environments. Based on our findings, it is proposed that decreased cell stiffness drives cellular detachment and migration. Increased matrix rigidity physically hinders migration and cells need to either soften or remodel the environment to migrate. The finding that matrix rigidity did not affect the stiffness of migrated cells suggests that cells facilitate migration by remodelling their environment through cleavage of matrix proteins.