The human cerebellum has recently been discovered to contribute to cognition and emotion beyond the planning and execution of movement, suggesting its functional heterogeneity. We aimed to identify the functional parcellation of the cerebellum using information from resting-state functional magnetic resonance imaging (rs-fMRI). For this, we introduced a new data-driven decomposition-based functional parcellation algorithm, called Sparse Dictionary Learning Clustering (SDLC). SDLC integrates dictionary learning, sparse representation of rs-fMRI, and k-means clustering into one optimization problem. The dictionary is comprised of an over-complete set of time course signals, with which a sparse representation of rs-fMRI signals can be constructed. Cerebellar functional regions were then identified using k-means clustering based on the sparse representation of rs-fMRI signals. We solved SDLC using a multi-block hybrid proximal alternating method that guarantees strong convergence. We evaluated the reliability of SDLC and benchmarked its classification accuracy against other clustering techniques using simulated data. We then demonstrated that SDLC can identify biologically reasonable functional regions of the cerebellum as estimated by their cerebello-cortical functional connectivity. We further provided new insights into the cerebello-cortical functional organization in children.

We show that Multivariate Public Key Cryptosystems (MPKCs) over fields of small odd prime characteristic, say 31, can be highly efficient. Indeed, at the same design security of 2^{80} under the best known attacks, odd-char MPKC is generally faster than prior MPKCs over \GF{2^k}, which are in turn faster than "traditional'' alternatives. This seemingly counter-intuitive feat is accomplished by exploiting the comparative over-abundance of small integer arithmetic resources in commodity hardware, here embodied by SSE2 or more advanced special multimedia instructions on modern x86-compatible CPUs. We explain our implementation techniques and design choices in implementing our chosen MPKC instances modulo small a odd prime. The same techniques are also applicable in modern FPGAs which often contains a large number of multipliers.

We propose a graph cut based global minimization method for image segmentation by representing the segmentation label function with a series of nested binary super-level set functions. This representation enables us to use K-1 binary functions to partition any images into K phases. Both continuous and discretized formulations will be treated. For the discrete model, we propose a new graph cut algorithm which is faster than the existing graph cut methods to obtain the exact global solution. In the continuous case, we further improve the segmentation accuracy using a number of techniques that are unique to the continuous segmentation models. With the convex relaxation and the dual method, the related continuous dual model is convex and we can mathematically show that the global minimization can be achieved. The corresponding continuous max-flow algorithms are easy and stable. Experimental results

In this paper we show how to totally break the fully homomorphic encryption scheme of eprint 2017/458.

Almost all three dimensional manifolds admit canonical metrics with constant sectional curvature. In this paper we proposed a new algorithm pipeline to compute such canonical metrics for hyperbolic 3-manifolds with high genus boundary surfaces. The computation is based on the discrete curvature flow for 3-manifolds, where the metric is deformed in an angle-preserving fashion until the curvature becomes uniform inside the volume and vanishes on the boundary. We also proposed algorithms to visualize the canonical metric by realizing the volume in the hyperbolic space ³, both in single period and in multiple periods. The proposed methods could not only facilitate the theoretical study of 3-manifold topology and geometry using computers, but also have great potentials in volumetric parameterizations, 3D shape comparison, volumetric biomedical image analysis and etc.