Incremental Model Building Homotopy Approach for Solving Exact AC-Constrained Optimal Power Flow

Alternating-Current Optimal Power Flow (AC-OPF) is framed as a NP-hard non-convex optimization problem that solves for the most economical dispatch of grid generation given the AC-network and device constraints. Although there are no standard methodologies for obtaining the global optimum for the problem, there is considerable interest from planning and operational engineers in finding a local optimum. Nonetheless, solving for the local optima of a large AC-OPF problem is challenging and time-intensive, as none of the leading non-linear optimization toolboxes can provide any timely guarantees of convergence. To provide robust local convergence for large complex systems, we introduce a homotopy-based approach that solves a sequence of primal-dual interior point problems. We utilize the physics of the grid to develop the proposed homotopy method and demonstrate the efficacy of this approach on U.S. Eastern Interconnection sized test networks

Knowledge-in-Context: Towards Knowledgeable Semi-Parametric Language Models

Fully-parametric language models generally require a huge number of model parameters to store the necessary knowledge for solving multiple natural language tasks in zero/few-shot settings. In addition, it is hard to adapt to the evolving world knowledge without the costly model re-training. In this paper, we develop a novel semi-parametric language model architecture, Knowledge-in-Context (KiC), which empowers a parametric text-to-text language model with a knowledge-rich external memory. Specifically, the external memory contains six different types of knowledge: entity, dictionary, commonsense, event, script, and causality knowledge. For each input instance, the KiC model adaptively selects a knowledge type and retrieves the most helpful pieces of knowledge. The input instance along with its knowledge augmentation is fed into a text-to-text model (e.g., T5) to generate the output answer, where both the input and the output are in natural language forms after prompting. Interestingly, we find that KiC can be identified as a special mixture-of-experts (MoE) model, where the knowledge selector plays the role of a router that is used to determine the sequence-to-expert assignment in MoE. This key observation inspires us to develop a novel algorithm for training KiC with an instance-adaptive knowledge selector. As a knowledge-rich semi-parametric language model, KiC only needs a much smaller parametric part to achieve superior zero-shot performance on unseen tasks. By evaluating on 40+ different tasks, we show that KiC_Large with 770M parameters easily outperforms large language models (LMs) that are 4-39x larger by a large margin. We also demonstrate that KiC exhibits emergent abilities at a much smaller model scale compared to the fully-parametric models

Exact and approximate maximum inner product search with LEMP

We study exact and approximate methods for maximum inner product search, a fundamental problem in a number of data mining and information retrieval tasks. We propose the LEMP framework, which supports both exact and approximate search with quality guarantees. At its heart, LEMP transforms a maximum inner product search problem over a large database of vectors into a number of smaller cosine similarity search problems. This transformation allows LEMP to prune large parts of the search space immediately and to select suitable search algorithms for each of the remaining problems individually. LEMP is able to leverage existing methods for cosine similarity search, but we also provide a number of novel search algorithms tailored to our setting. We conducted an extensive experimental study that provides insight into the performance of many state-of-the-art techniques—including LEMP—on multiple real-world datasets. We found that LEMP often was significantly faster or more accurate than alternative methods

The DiskMass Survey. I. Overview

We present a survey of the mass surface-density of spiral disks, motivated by outstanding uncertainties in rotation-curve decompositions. Our method exploits integral-field spectroscopy to measure stellar and gas kinematics in nearly face-on galaxies sampled at 515, 660, and 860 nm, using the custom-built SparsePak and PPak instruments. A two-tiered sample, selected from the UGC, includes 146 nearly face-on galaxies, with B<14.7 and disk scale-lengths between 10 and 20 arcsec, for which we have obtained H-alpha velocity-fields; and a representative 46-galaxy subset for which we have obtained stellar velocities and velocity dispersions. Based on re-calibration of extant photometric and spectroscopic data, we show these galaxies span factors of 100 in L(K) (0.03 < L/L(K)* < 3), 8 in L(B)/L(K), 10 in R-band disk central surface-brightness, with distances between 15 and 200 Mpc. The survey is augmented by 4-70 micron Spitzer IRAC and MIPS photometry, ground-based UBVRIJHK photometry, and HI aperture-synthesis imaging. We outline the spectroscopic analysis protocol for deriving precise and accurate line-of-sight stellar velocity dispersions. Our key measurement is the dynamical disk-mass surface-density. Star-formation rates and kinematic and photometric regularity of galaxy disks are also central products of the study. The survey is designed to yield random and systematic errors small enough (i) to confirm or disprove the maximum-disk hypothesis for intermediate-type disk galaxies, (ii) to provide an absolute calibration of the stellar mass-to-light ratio well below uncertainties in present-day stellar-population synthesis models, and (iii) to make significant progress in defining the shape of dark halos in the inner regions of disk galaxies.Comment: To appear in ApJ; 72 pages, 3 tables, 18 figures. High-resolution version available at http://www.astro.wisc.edu/~mab/publications/DMS_I_preprint.pd