4d4d steady gradient Ricci solitons with nonnegative curvature away from a compact set

In the paper, we analysis the asymptotic behavior of noncompact $\kappa$-noncollapsed steady gradient Ricci soliton $(M, g)$ with nonnegative curvature operator away from a compact set $K$ of $M$. In particular, we prove: any $4d$ noncompact $\kappa$-noncollapsed steady gradient Ricci soliton $(M^4, g)$ with nonnegative sectional curvature must be a Bryant Ricci soliton up to scaling if it admits a sequence of rescaled flows of $(M^4, g)$, which converges subsequently to a family of shrinking quotient cylinders.Comment: Proof of Proposition 4.1 has been modified. Also some typos are correcte

The Impact of Open Market Share Repurchases on Bondholders and Shareholders

Past studies examined the impact of open market repurchase announcements on bond and stock prices and identified its main causes, such as signaling, free cash flow, and wealth redistribution. Building on the work by Maxwell and Stephens (2003), we introduce daily bond return data to analyze abnormal bond and stock returns around share repurchase announcements and examine these hypotheses. We find a strong wealth transfer effect, as well as some evidence of undervaluation signaling. The wealth gain or loss of bondholders is a function of the size of the repurchase program, the leverage ratio, and the book-to-market ratio

High Performance Silicon Photonic Interconnected Systems

Advances in data-driven applications, particularly artificial intelligence and deep learning, are driving the explosive growth of computation and communication in today’s data centers and high-performance computing (HPC) systems. Increasingly, system performance is not constrained by the compute speed at individual nodes, but by the data movement between them. This calls for innovative architectures, smart connectivity, and extreme bandwidth densities in interconnect designs. Silicon photonics technology leverages mature complementary metal-oxide-semiconductor (CMOS) manufacturing infrastructure and is promising for low cost, high-bandwidth, and reconfigurable interconnects. Flexible and high-performance photonic switched architectures are capable of improving the system performance. The work in this dissertation explores various photonic interconnected systems and the associated optical switching functionalities, hardware platforms, and novel architectures. It demonstrates the capabilities of silicon photonics to enable efficient deep learning training. We first present field programmable gate array (FPGA) based open-loop and closed-loop control for optical spectral-and-spatial switching of silicon photonic cascaded micro-ring resonator (MRR) switches. Our control achieves wavelength locking at the user-defined resonance of the MRR for optical unicast, multicast, and multiwavelength-select functionalities. Digital-to-analog converters (DACs) and analog-to-digital converters (ADCs) are necessary for the control of the switch. We experimentally demonstrate the optical switching functionalities using an FPGA-based switch controller through both traditional multi-bit DAC/ADC and novel single-wired DAC/ADC circuits. For system-level integration, interfaces to the switch controller in a network control plane are developed. The successful control and the switching functionalitiesachieved are essential for system-level architectural innovations as presented in the following sections. Next, this thesis presents two novel photonic switched architectures using the MRR-based switches. First, a photonic switched memory system architecture was designed to address memory challenges in deep learning. The reconfigurable photonic interconnects provide scalable solutions and enable efficient use of disaggregated memory resources for deep learning training. An experimental testbed was built with a processing system and two remote memory nodes using silicon photonic switch fabrics and system performance improvements were demonstrated. The collective results and existing high-bandwidth optical I/Os show the potential of integrating the photonic switched memory to state-of-the-art processing systems. Second, the scaling trends of deep learning models and distributed training workloads are challenging network capacities in today’s data centers and HPCs. A system architecture that leverages SiP switch-enabled server regrouping is proposed to tackle the challenges and accelerate distributed deep learning training. An experimental testbed with a SiP switch-enabled reconfigurable fat tree topology was built to evaluate the network performance of distributed ring all-reduce and parameter server workloads. We also present system-scale simulations. Server regrouping and bandwidth steering were performed on a large-scale tapered fat tree with 1024 compute nodes to show the benefits of using photonic switched architectures in systems at scale. Finally, this dissertation explores high-bandwidth photonic interconnect designs for disaggregated systems. We first introduce and discuss two disaggregated architectures leveraging extreme high bandwidth interconnects with optically interconnected computing resources. We present the concept of rack-scale graphics processing unit (GPU) disaggregation with optical circuit switches and electrical aggregator switches. The architecture can leverage the flexibility of high bandwidth optical switches to increase hardware utilization and reduce application runtimes. A testbed was built to demonstrate resource disaggregation and defragmentation. In addition, we also present an extreme high-bandwidth optical interconnect accelerated low-latency communication architecture for deep learning training. The disaggregated architecture utilizes comb laser sources and MRR-based cross-bar switching fabrics to enable an all-to-all high bandwidth communication with a constant latency cost for distributed deep learning training. We discuss emerging technologies in the silicon photonics platform, including light source, transceivers, and switch architectures, to accommodate extreme high bandwidth requirements in HPC and data center environments. A prototype hardware innovation - Optical Network Interface Cards (comprised of FPGA, photonic integrated circuits (PIC), electronic integrated circuits (EIC), interposer, and high-speed printed circuit board (PCB)) is presented to show the path toward fast lanes for expedited execution at 10 terabits. Taken together, the work in this dissertation demonstrates the capabilities of high-bandwidth silicon photonic interconnects and innovative architectural designs to accelerate deep learning training in optically connected data center and HPC systems

Measuring 3D Optic Nerve Head Deformations using Digital Volume Correlation of in vivo Optical Coherence Tomography Data

The optic nerve head (ONH), located in the back of the eye, is a critical site in understanding the pathophysiology of glaucoma. However, longitudinal changes of the ONH as disease develops have not been well characterized. Our goal was to develop an improved tool to quantify these changes in an in vivo monkey model of glaucoma. Longitudinal spectral-domain optical coherence tomography (OCT) imaging of the ONH was performed every other week under manometric intraocular pressure (IOP) control (10 mmHg) in a monkey during baseline and after induction of unilateral experimental glaucoma. We developed a computational pipeline that applied digital volume correlation (DVC) to measure the 3D ONH deformations. The chronic changes, akin to stretch, compression and shear strain were computed from OCT scans acquired in vivo at multiple stages of experimental glaucoma. Custom programs were developed to verify the robustness of the DVC algorithm and calculate a confidence map. Two regions of the ONH were segmented to focus the DVC analysis: the lamina cribrosa (LC), which plays an important role in glaucoma, and a region of the peripapillary retina, which is expected to thin through glaucoma progression. We successfully developed a set of programs to calculate chronic tissue changes from OCT scans. We use classic DVC terminology and refer to them as displacements and strains. However, this is not exactly the case because these are long-term changes that could include deformation, and other changes such as shrinkage, growth and remodeling. The verification results of the displacement map demonstrated high robustness of the DVC algorithm. The computed strain map suggested that chronic elevated IOP and glaucoma progression caused deformations of the ONH. The maximum chronic stretch, compression, and shear strains did not always colocalize. The LC tended to be more sensitive to chronic IOP elevation compared to the peripheral retinal nerve fiber layer. The ONH deformations did not necessarily follow the trend of chronic IOP elevation in glaucoma. To the best of our knowledge, this is the first study to analyze the longitudinal and in vivo ONH deformations in glaucoma. Results from this study can help clarify the pathophysiology of glaucoma

Efforts to untie the multicollinearity knot and identify factors controlling macropore structures in shale oil reservoirs

Traditional correlation analyses based on whole-rock data have limitations in discerning pore development determinants in shale oil reservoir, given the complex lithology of shale formations and intricate interdependencies (multicollinearity) among geological variables. In this study, mercury injection capillary pressure and digital analysis of scanning electron microscopy were employed to examine the macropore structures of both whole rocks and their constituent lithologies for the Upper Triassic Chang-7 shale of the Ordos Basin. Variations were observed among clay shale (shale primarily consisting of clay-sized mineral grains), massive siltstone and silty laminae within the Chang-7 shale. Through the combination of correlation analysis and scanning electron microscope digital technique, it was demonstrated that total organic carbon content primarily controls the level of macropore development, while lithology primarily governs macropore types and structures. Although quartz and pyrite exhibit correlations with macropore volume, they do not emerge as primary factors; instead, they appear interconnected to total organic carbon. Due to detrital mineral framework preservation during compaction, larger macropores are more developed in massive siltstones and silty laminae than in clay shale. Additionally, silty laminae, situated closer to the source rock and influenced by organic acids, exhibit a higher abundance of larger dissolution pores, potentially favoring shale oil development. This study overcomes traditional method constraints, disentangling multi-correlations, and providing new insights into shale macropore development mechanisms, potentially advancing shale oil exploration and production.Document Type: Original articleCited as: Wang, Z., Dong, L., Jin, Z., Zou, S., Fu, J., Zhu, R. Efforts to untie the multicollinearity knot and identify factors controlling macropore structures in shale oil reservoirs. Advances in Geo-Energy Research, 2024, 11(3): 194-207. https://doi.org/10.46690/ager.2024.03.0

CoDi-2: In-Context, Interleaved, and Interactive Any-to-Any Generation

We present CoDi-2, a versatile and interactive Multimodal Large Language Model (MLLM) that can follow complex multimodal interleaved instructions, conduct in-context learning (ICL), reason, chat, edit, etc., in an any-to-any input-output modality paradigm. By aligning modalities with language for both encoding and generation, CoDi-2 empowers Large Language Models (LLMs) to not only understand complex modality-interleaved instructions and in-context examples, but also autoregressively generate grounded and coherent multimodal outputs in the continuous feature space. To train CoDi-2, we build a large-scale generation dataset encompassing in-context multimodal instructions across text, vision, and audio. CoDi-2 demonstrates a wide range of zero-shot capabilities for multimodal generation, such as in-context learning, reasoning, and compositionality of any-to-any modality generation through multi-round interactive conversation. CoDi-2 surpasses previous domain-specific models on tasks such as subject-driven image generation, vision transformation, and audio editing. CoDi-2 signifies a substantial breakthrough in developing a comprehensive multimodal foundation model adept at interpreting in-context language-vision-audio interleaved instructions and producing multimodal outputs.Comment: Project Page: https://codi-2.github.io

Online Metro Origin-Destination Prediction via Heterogeneous Information Aggregation

Metro origin-destination prediction is a crucial yet challenging time-series analysis task in intelligent transportation systems, which aims to accurately forecast two specific types of cross-station ridership, i.e., Origin-Destination (OD) one and Destination-Origin (DO) one. However, complete OD matrices of previous time intervals can not be obtained immediately in online metro systems, and conventional methods only used limited information to forecast the future OD and DO ridership separately. In this work, we proposed a novel neural network module termed Heterogeneous Information Aggregation Machine (HIAM), which fully exploits heterogeneous information of historical data (e.g., incomplete OD matrices, unfinished order vectors, and DO matrices) to jointly learn the evolutionary patterns of OD and DO ridership. Specifically, an OD modeling branch estimates the potential destinations of unfinished orders explicitly to complement the information of incomplete OD matrices, while a DO modeling branch takes DO matrices as input to capture the spatial-temporal distribution of DO ridership. Moreover, a Dual Information Transformer is introduced to propagate the mutual information among OD features and DO features for modeling the OD-DO causality and correlation. Based on the proposed HIAM, we develop a unified Seq2Seq network to forecast the future OD and DO ridership simultaneously. Extensive experiments conducted on two large-scale benchmarks demonstrate the effectiveness of our method for online metro origin-destination prediction