Rayleigh-Ritz majorization error bounds of the mixed type

The absolute change in the Rayleigh quotient (RQ) for a Hermitian matrix with respect to vectors is bounded in terms of the norms of the residual vectors and the angle between vectors in [\doi{10.1137/120884468}]. We substitute multidimensional subspaces for the vectors and derive new bounds of absolute changes of eigenvalues of the matrix RQ in terms of singular values of residual matrices and principal angles between subspaces, using majorization. We show how our results relate to bounds for eigenvalues after discarding off-diagonal blocks or additive perturbations.Comment: 20 pages, 1 figure. Accepted to SIAM Journal on Matrix Analysis and Application

Explicit model predictive control accuracy analysis

Model Predictive Control (MPC) can efficiently control constrained systems in real-time applications. MPC feedback law for a linear system with linear inequality constraints can be explicitly computed off-line, which results in an off-line partition of the state space into non-overlapped convex regions, with affine control laws associated to each region of the partition. An actual implementation of this explicit MPC in low cost micro-controllers requires the data to be "quantized", i.e. represented with a small number of memory bits. An aggressive quantization decreases the number of bits and the controller manufacturing costs, and may increase the speed of the controller, but reduces accuracy of the control input computation. We derive upper bounds for the absolute error in the control depending on the number of quantization bits and system parameters. The bounds can be used to determine how many quantization bits are needed in order to guarantee a specific level of accuracy in the control input.Comment: 6 pages, 7 figures. Accepted to IEEE CDC 201

EFFECTS OF TEMPERATURE, ORIENTATION, LOAD LEVEL AND INDENTER SHAPE ON THE INDENTATION RESPONSE OF NITI-BASED SHAPE MEMORY ALLOYS

Owing the capability of recovering large deformations through reversible phase transformation, shape memory alloys (SMAs) are well-known for their unique behaviors such as shape memory effect (SME) and superelasticity (SE), which can also be characterized by instrumented indentation techniques. Nickel titanium (NiTi) SMAs have been extensively used for nano/micro-indentation studies and widely applied to biomedical and other elaborate medical devices. In this study, indentation responses of NiTi, NiTiHf, NiTiHfPd and NiTiHfCu alloys were investigated using spherical and Berkovich indenters at room temperature. Spherical and Berkovich indentation hardness, modulus, and work/depth recoverable ratio of these NiTi-based alloys were revealed as a function of maximum loading level at nano and macro scales. It has been revealed that indentation responses are highly composition, aging and load level dependent. Perfect work/depth recovery was observed in superelastic NiTiHfPd alloys using the spherical indenter. Temperature-dependent shape memory properties of equiatomic NiTi, Nickel rich NiTi, and as-received and aged NiTiHf alloys were investigated using a spherical indenter between 30-340 ºC under selected load levels. Ti-6Al-4V was also tested for comparison. Spherical indentation response of aged high temperature NiTiHf alloys showed a clear relationship between the work recoverable ratio and transformation temperatures, superelastic and plastic behavior. It was concluded that indentation response can be used to measure local superelasticity response, determine phase transformation temperatures and reveal the temperature intervals of the deformation mechanisms of shape memory alloys. Spherical indentation hardness and modulus as a function of temperature can be used to exam the phase transformation, but cannot provide sufficient information regarding the superelastic and plastic behavior. Orientation dependence of the shape memory properties in aged Nickel rich Ni50.3Ti29.7Hf20 single crystals were investigated along the [100], [110] and [111] orientations under room and high temperatures through indentation techniques. Indentation hardness, modulus and work /depth recoverable ratio were investigated as a function of temperature and indentation depth/load. It was found that indentation response of work recovery ratio is orientation independent, however, shape memory properties (e.g. transformation temperatures) determined from the indentation responses are almost orientation independent

Angles between subspaces and their tangents

Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced via their cosines. The cosines and sines of PABS are commonly defined using the singular value decomposition. We utilize the same idea for the tangents, i.e., explicitly construct matrices, such that their singular values are equal to the tangents of PABS, using several approaches: orthonormal and non-orthonormal bases for subspaces, as well as projectors. Such a construction has applications, e.g., in analysis of convergence of subspace iterations for eigenvalue problems.Comment: 15 pages, 1 figure, 2 tables. Accepted to Journal of Numerical Mathematic

EFFECT OF BILE ACID FEEDING AND SEQUESTRATION ON LIVER BILE ACID COMPOSITION AND GENE REGULATION IN MICE

The dissertation investigates the non-hepatotoxic doses of five bile acids (BAs) in the feed of mice, as well as adaptations in the expression of genes involved in BA homeostasis and the possible roles of FXR-mediated signaling in regulating these genes. Mice were fed four main BAs, cholic acid (CA), chenodeoxycholic acid (CDCA), deoxycholic acid (DCA), and lithocholic acid (LCA), and the therapeutic BA ursodeoxycholic acid (UDCA), at various concentrations in their diets (0.01, 0.03, 0.1, 0.3, 1.0, or 3.0%), as well as the BA sequestrant cholestyramine (resin) at 2% in their diets, for one week. Subsequently, serum alanine aminotransferase (ALT), serum and hepatic BA concentrations, as well as mRNAs of genes involved in BA homeostasis were quantified. The data showed: 1) LCA produced hepatotoxicity at 0.03%, indicated by increases in serum ALT and serum BA concentration, as did DCA at 0.1%, and CDCA and CA at 0.3% in the diet. UDCA at 0.3% in the diet might be hepatotoxic because the serum BA concentration was increased but the serum ALT did not increase. 2) Feeding BAs at hepatotoxic doses altered liver BA composition. 3) The mRNA of SHP and Cyp7a1 in the liver was increased by all doses of BAs. In contrast, BA regulation of the mRNA of the hepatic Cyp8b1 and the ileal Fgf15 are BA species dependent: CA and DCA at all doses increased Fgf15 and decreased Cyp8b1, whereas, CDCA and LCA at high doses increased Fgf15 and decreased Cyp8b1 mRNA. 4) Feeding resin increased the mRNA Cyp7a1 and Cyp8b1 in the liver and Fgf15 in the ileum. In conclusion, my dissertation demonstrates the non-hepatotoxic doses of individual BAs are as follows: 0.1% or lower in the diets for CA, CDCA, and UDCA, 0.03% for DCA, and 0.01% or lower for LCA. In addition, the altered liver BA composition after non-hepatotoxic doses of BA-feeding are able to trigger the hepatic FXR-SHP and the ileal FXR-Fgf15 signaling pathways, which coordinately regulate Cyp7a1 and Cyp8b1. Moreover, the the decreased expression of the ileal Fgf15 after feeding resin caused increases in mRNA expression of CYp7a1 and Cyp8b1

Service Abstractions for Scalable Deep Learning Inference at the Edge

Deep learning driven intelligent edge has already become a reality, where millions of mobile, wearable, and IoT devices analyze real-time data and transform those into actionable insights on-device. Typical approaches for optimizing deep learning inference mostly focus on accelerating the execution of individual inference tasks, without considering the contextual correlation unique to edge environments and the statistical nature of learning-based computation. Specifically, they treat inference workloads as individual black boxes and apply canonical system optimization techniques, developed over the last few decades, to handle them as yet another type of computation-intensive applications. As a result, deep learning inference on edge devices still face the ever increasing challenges of customization to edge device heterogeneity, fuzzy computation redundancy between inference tasks, and end-to-end deployment at scale. In this thesis, we propose the first framework that automates and scales the end-to-end process of deploying efficient deep learning inference from the cloud to heterogeneous edge devices. The framework consists of a series of service abstractions that handle DNN model tailoring, model indexing and query, and computation reuse for runtime inference respectively. Together, these services bridge the gap between deep learning training and inference, eliminate computation redundancy during inference execution, and further lower the barrier for deep learning algorithm and system co-optimization. To build efficient and scalable services, we take a unique algorithmic approach of harnessing the semantic correlation between the learning-based computation. Rather than viewing individual tasks as isolated black boxes, we optimize them collectively in a white box approach, proposing primitives to formulate the semantics of the deep learning workloads, algorithms to assess their hidden correlation (in terms of the input data, the neural network models, and the deployment trials) and merge common processing steps to minimize redundancy

Latent Embeddings for Collective Activity Recognition

Rather than simply recognizing the action of a person individually, collective activity recognition aims to find out what a group of people is acting in a collective scene. Previ- ous state-of-the-art methods using hand-crafted potentials in conventional graphical model which can only define a limited range of relations. Thus, the complex structural de- pendencies among individuals involved in a collective sce- nario cannot be fully modeled. In this paper, we overcome these limitations by embedding latent variables into feature space and learning the feature mapping functions in a deep learning framework. The embeddings of latent variables build a global relation containing person-group interac- tions and richer contextual information by jointly modeling broader range of individuals. Besides, we assemble atten- tion mechanism during embedding for achieving more com- pact representations. We evaluate our method on three col- lective activity datasets, where we contribute a much larger dataset in this work. The proposed model has achieved clearly better performance as compared to the state-of-the- art methods in our experiments.Comment: 6pages, accepted by IEEE-AVSS201

Geometry-aware Line Graph Transformer Pre-training for Molecular Property Prediction

Molecular property prediction with deep learning has gained much attention over the past years. Owing to the scarcity of labeled molecules, there has been growing interest in self-supervised learning methods that learn generalizable molecular representations from unlabeled data. Molecules are typically treated as 2D topological graphs in modeling, but it has been discovered that their 3D geometry is of great importance in determining molecular functionalities. In this paper, we propose the Geometry-aware line graph transformer (Galformer) pre-training, a novel self-supervised learning framework that aims to enhance molecular representation learning with 2D and 3D modalities. Specifically, we first design a dual-modality line graph transformer backbone to encode the topological and geometric information of a molecule. The designed backbone incorporates effective structural encodings to capture graph structures from both modalities. Then we devise two complementary pre-training tasks at the inter and intra-modality levels. These tasks provide properly supervised information and extract discriminative 2D and 3D knowledge from unlabeled molecules. Finally, we evaluate Galformer against six state-of-the-art baselines on twelve property prediction benchmarks via downstream fine-tuning. Experimental results show that Galformer consistently outperforms all baselines on both classification and regression tasks, demonstrating its effectiveness.Comment: 9 pages, 5 figure

Ubiquitin carboxyl-terminal hydrolases are required for period maintenance of the circadian clock at high temperature in Arabidopsis

Protein ubiquitylation participates in a number of essential cellular processes including signal transduction and transcription, often by initiating the degradation of specific substrates through the 26S proteasome. Within the ubiquitin-proteasome system, deubiquitylating enzymes (DUBs) not only help generate and maintain the supply of free ubiquitin monomers, they also directly control functions and activities of specific target proteins by modulating the pool of ubiquitylated species. Ubiquitin carboxyl-terminal hydrolases (UCHs) belong to an enzymatic subclass of DUBs, and are represented by three members in Arabidopsis, UCH1, UCH2 and UCH3. UCH1 and UCH2 influence auxin-dependent developmental pathways in Arabidopsis through their deubiquitylation activities, whereas biological and enzymatic functions of UCH3 remain unclear. Here, we demonstrate that Arabidopsis UCH3 acts to maintain the period of the circadian clock at high temperatures redundantly with UCH1 and UCH2. Whereas single uch1, uch2 and uch3 mutants have weak circadian phenotypes, the triple uch mutant displays a drastic lengthening of period at high temperatures that is more extreme than the uch1 uch2 double mutant. UCH3 also possesses a broad deubiquitylation activity against a range of substrates that link ubiquitin via peptide and isopeptide linkages. While the protein target(s) of UCH1-3 are not yet known, we propose that these DUBs act on one or more factors that control period length of the circadian clock through removal of their bound ubiquitin moieties, thus ensuring that the clock oscillates with a proper period even at elevated temperature

Interpretable bilinear attention network with domain adaptation improves drug-target prediction

Predicting drug-target interaction is key for drug discovery. Recent deep learning-based methods show promising performance but two challenges remain: (i) how to explicitly model and learn local interactions between drugs and targets for better prediction and interpretation; (ii) how to generalize prediction performance on novel drug-target pairs from different distribution. In this work, we propose DrugBAN, a deep bilinear attention network (BAN) framework with domain adaptation to explicitly learn pair-wise local interactions between drugs and targets, and adapt on out-of-distribution data. DrugBAN works on drug molecular graphs and target protein sequences to perform prediction, with conditional domain adversarial learning to align learned interaction representations across different distributions for better generalization on novel drug-target pairs. Experiments on three benchmark datasets under both in-domain and cross-domain settings show that DrugBAN achieves the best overall performance against five state-of-the-art baselines. Moreover, visualizing the learned bilinear attention map provides interpretable insights from prediction results.Comment: 16 pages, 6 figure