Impatient PPSZ - A Faster Algorithm for CSP

PPSZ is the fastest known algorithm for (d,k)-CSP problems, for most values of d and k. It goes through the variables in random order and sets each variable randomly to one of the d colors, excluding those colors that can be ruled out by looking at few constraints at a time. We propose and analyze a modification of PPSZ: whenever all but 2 colors can be ruled out for some variable, immediately set that variable randomly to one of the remaining colors. We show that our new "impatient PPSZ" outperforms PPSZ exponentially for all k and all d ? 3 on formulas with a unique satisfying assignment

Dynamic Tensor Decomposition via Neural Diffusion-Reaction Processes

Tensor decomposition is an important tool for multiway data analysis. In practice, the data is often sparse yet associated with rich temporal information. Existing methods, however, often under-use the time information and ignore the structural knowledge within the sparsely observed tensor entries. To overcome these limitations and to better capture the underlying temporal structure, we propose Dynamic EMbedIngs fOr dynamic Tensor dEcomposition (DEMOTE). We develop a neural diffusion-reaction process to estimate dynamic embeddings for the entities in each tensor mode. Specifically, based on the observed tensor entries, we build a multi-partite graph to encode the correlation between the entities. We construct a graph diffusion process to co-evolve the embedding trajectories of the correlated entities and use a neural network to construct a reaction process for each individual entity. In this way, our model can capture both the commonalities and personalities during the evolution of the embeddings for different entities. We then use a neural network to model the entry value as a nonlinear function of the embedding trajectories. For model estimation, we combine ODE solvers to develop a stochastic mini-batch learning algorithm. We propose a stratified sampling method to balance the cost of processing each mini-batch so as to improve the overall efficiency. We show the advantage of our approach in both simulation study and real-world applications. The code is available at https://github.com/wzhut/Dynamic-Tensor-Decomposition-via-Neural-Diffusion-Reaction-Processes

Hypogonadotropic hypogonadism presenting with arhinia: a case report

INTRODUCTION: Arhinia, congenital absence of the nose, is a rare malformation. We present the third reported case of arhinia accompanied by hypogonadism and demonstrate that this is due to gonadotropin deficiency. CASE PRESENTATION: A 13-year-old Caucasian boy with congenital arhinia presented for evaluation of delayed puberty and micropenis. We examined genes known to be associated with hypogonadotropic hypogonadism for mutations and performed a chromosomal microarray to assess copy number variation. CONCLUSION: No mutations in KAL1, FGFR1, PROK2, PROKR2, FGF8, CHD7 and GnRHR were identified in our patient and there were no copy number variations observed that would explain the phenotype. Though studies are limited in such patients, we suggest that hypogonadotropic hypogonadism is associated with arhinia and that the two entities likely result from a common genetic cause that affects early nasal development and gonadotropin-releasing hormone neuron formation or migration

Self-synchronization theory of a dual mass vibrating system driven by two coupled exciters. Part 2: Numeric analysis

The coupling dynamic characteristics of the vibrating system with dual mass are analyzed quantitatively. Both the load torque and the coupling torque have three items. Two of them are concerned with the translation of the system, and the third item is related to the rotation of the system. Through numerical computation, the effects of translation and rotation in the system are considered in relation to the self-synchronization. The phase difference of two eccentric blocks is caused by the difference of the rated revolution of two motors. The stability of the synchronous operation is dependent on the structural parameters of the system, such as the mass ratio of two eccentric blocks and the distance between motor and centroid of the rigid frame. Simulation is carried out to verify that the system can be synchronized and the model can ensure the stability of synchronization if the parameters of the system meet the conditions of synchronous implementation and stability. Simulations are also performed for the case of self-synchronization of two motors with different rated revolutions

Self-synchronization theory of a dual mass vibrating system driven by two coupled exciters. Part 1: Theoretical analysis

A vibration model is proposed and analyzed dynamically to study the selfsynchronization theory of dual-mass vibration system. The differential equations of systematic motion are derived by applying Lagrange’s equations. As two uncertain parameters, the coefficients of instantaneous change of average angular velocity and the phase difference of two exciters are introduced to derive the coupling equations of angular velocity of the two exciters. The conditions of synchronous implementation and stability are derived by utilizing the modified small parameter average method treated as non-dimension to the parameters. The swing of the vibration model plays a major role in the self-synchronization of two motors. The mass ratio of two eccentric blocks has an effect on the stability of synchronous operation