ABSTRACT
Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space and the number of data points. To tackle the big data challenge, a quantum SVM algorithm was proposed, which is claimed to achieve exponential speedup for least squares SVM (LS-SVM). Here, inspired by the quantum SVM algorithm, we present a quantum-inspired classical algorithm for LS-SVM. In our approach, an improved fast sampling technique, namely indirect sampling, is proposed for sampling the kernel matrix and classifying. We first consider the LS-SVM with a linear kernel, and then discuss the generalization of our method to nonlinear kernels. Theoretical analysis shows our algorithm can make classification with arbitrary success probability in logarithmic runtime of both the dimension of data space and the number of data points for low rank, low condition number, and high dimensional data matrix, matching the runtime of the quantum SVM.
ABSTRACT
Two extremely rare ß-cyclodextrin (ß-CD) supported metal-organic frameworks (MOFs), CD-MOF-1 and CD-MOF-2, were induced to crystallize for the first time through a template-induced approach. The targeted CD-MOFs were employed to perform controlled drug delivery and cytotoxicity assays that confirmed their favourable biological potential of being used as drug carriers.
Subject(s)
Biological Products/chemistry , Drug Delivery Systems , Metal-Organic Frameworks/chemistry , Biocompatible Materials/chemistry , Cell Survival/drug effects , Dose-Response Relationship, Drug , Drug Carriers/chemistry , Hep G2 Cells , Humans , Models, Molecular , Particle Size , Porosity , Structure-Activity Relationship , Surface Properties , beta-Cyclodextrins/chemistryABSTRACT
Synchronization is of great scientific interest due to the abundant applications in a wide range of systems. We propose an all-optical scheme to achieve the controllable long-distance synchronization of two dissimilar optomechanical systems, which are unidirectionally coupled through a fiber with light. Synchronization, unsynchronization, and the dependence of the synchronization on driving laser strength and intrinsic frequency mismatch are studied based on the numerical simulation. Taking the fiber attenuation into account, we show that two optomechanical resonators can be unidirectionally synchronized over a distance of tens of kilometers. We also analyze the unidirectional synchronization of three optomechanical systems, demonstrating the scalability of our scheme.
