Parity Calibration

In a sequential regression setting, a decision-maker may be primarily concerned with whether the future observation will increase or decrease compared to the current one, rather than the actual value of the future observation. In this context, we introduce the notion of parity calibration, which captures the goal of calibrated forecasting for the increase-decrease (or "parity") event in a timeseries. Parity probabilities can be extracted from a forecasted distribution for the output, but we show that such a strategy leads to theoretical unpredictability and poor practical performance. We then observe that although the original task was regression, parity calibration can be expressed as binary calibration. Drawing on this connection, we use an online binary calibration method to achieve parity calibration. We demonstrate the effectiveness of our approach on real-world case studies in epidemiology, weather forecasting, and model-based control in nuclear fusion.Comment: To appear at UAI 2023; 19 pages and 10 figure

The Power of Fair Pricing Mechanisms

We explore the revenue capabilities of truthful, monotone (“fair”) allocation and pricing functions for resource constrained auction mechanisms within a general framework that encompasses unlimited supply auctions, knapsack auctions, and auctions with general non-decreasing convex production cost functions. We study and compare the revenue obtainable in each fair pricing scheme to the profit obtained by the ideal omniscient multi-price auction. We show that for capacitated knapsack auctions, no constant pricing scheme can achieve any approximation to the optimal profit, but proportional pricing is as powerful as general monotone pricing. In addition, for auction settings with arbitrary bounded non-decreasing convex production cost functions, we present a proportional pricing mechanism which achieves a poly-logarithmic approximation. Unlike existing approaches, all of our mechanisms have fair (monotone) prices, and all of our competitive analysis is with respect to the optimal profit extraction

An electrostatic levitator for high-temperature containerless materials processing in 1-g

This article discusses recent developments in high-temperature electrostatic levitation technology for containerless processing of metals and alloys. Presented is the first demonstration of an electrostatic levitation technology which can levitate metals and alloys (2–4 mm diam spheres) in vacuum and of superheating-undercooling-recalescence cycles which can be repeated while maintaining good positioning stability. The electrostatic levitator (ESL) has several important advantages over the electromagnetic levitator. Most important is the wide range of sample temperature which can be achieved without affecting levitation. This article also describes the general architecture of the levitator, electrode design, position control hardware and software, sample heating, charging, and preparation methods, and operational procedures. Particular emphasis is given to sample charging by photoelectric and thermionic emission. While this ESL is more oriented toward ground-based operation, an extension to microgravity applications is also addressed briefly. The system performance was demonstrated by showing multiple superheating-undercooling-recalescence cycles in a zirconium sample (Tm=2128 K). This levitator, when fully matured, will be a valuable tool both in Earth-based and space-based laboratories for the study of thermophysical properties of undercooled liquids, nucleation kinetics, the creation of metastable phases, and access to a wide range of materials with novel properties

Structure theorems and extremal problems in incidence geometry

In this thesis, we prove variants and generalisations of the Sylvester-Gallai theorem, which states that a finite non-collinear point set in the plane spans an ordinary line. Green and Tao proved a structure theorem for sufficiently large sets spanning few ordinary lines, and used it to find exact extremal numbers for ordinary and 3-rich lines, solving the Dirac-Motzkin conjecture and the classical orchard problem respectively. We prove structure theorems for sufficiently large sets spanning few ordinary planes, hyperplanes, circles, and hyperspheres, showing that such sets lie mostly on algebraic curves (or on a hyperplane or hypersphere). We then use these structure theorems to solve the corresponding analogues of the Dirac-Motzkin conjecture and the orchard problem. For planes in 3-space and circles in the plane, we are able to find exact extremal numbers for ordinary and 4-rich planes and circles. We also show that there are irreducible rational space quartics such that any n-point subset spans only O(n8=3) coplanar quadruples, answering a question of Raz, Sharir, and De Zeeuw [51]. For hyperplanes in d-space, we are able to find tight asymptotic bounds on the extremal numbers for ordinary and (d + 1)-rich hyperplanes. This also gives a recursive method to compute exact extremal numbers for a fixed dimension d. For hyperspheres in d-space, we are able to find a tight asymptotic bound on the minimum number of ordinary hyperspheres, and an asymptotic bound on the maximum number of (d + 2)-rich hyperspheres that is tight in even dimensions. The recursive method in the hyperplanes case also applies here. Our methods rely on Green and Tao's results on ordinary lines, as well as results from classical algebraic geometry, in particular on projections, inversions, and algebraic curves

Are Consensus Ratings of Functional Job Analysis Scales More Reliable than Ratings Made by Independent Raters?

This study addresses an open research question in regard to a well-established and widely-used job analysis system, Functional Job Analysis (FJA): Are consensus ratings of the FJA scales more reliable than the independent scale ratings that are the norm in job analysis application and the related research literature? In our experimental study, we found that this is not the case: no significant difference is found between consensus and independent ratings of the FJA scales. The reasons for this finding are explored as well as its relevance to the validity of the FJA system. Implications for other work and job analysis systems are discussed

UAVino

UAVino is a drone solution that uses aerial imagery to determine the overall plant health and water content of vineyards. In general, the system focuses on automating crop inspection by taking aerial imagery of a vineyard, conducting post-processing, and outputting an easily interpreted map of the vineyard\u27s overall health. The project\u27s key innovation is an auto-docking system that allows the drone to automatically return to its launch point and recharge in order to extend mission duration. Long term, UAVino is envisioned as a multi-year, interdisciplinary project involving both the Santa Clara University Robotics Systems Laboratory and local wineries in order to develop a fully functional drone agricultural inspection service

Decentralized formation pose estimation for spacecraft swarms

For spacecraft swarms, the multi-agent localization algorithm must scale well with the number of spacecraft and adapt to time-varying communication and relative sensing networks. In this paper, we present a decentralized, scalable algorithm for swarm localization, called the Decentralized Pose Estimation (DPE) algorithm. The DPE considers both communication and relative sensing graphs and defines an observable local formation. Each spacecraft jointly localizes its local subset of spacecraft using direct and communicated measurements. Since the algorithm is local, the algorithm complexity does not grow with the number of spacecraft in the swarm. As part of the DPE, we present the Swarm Reference Frame Estimation (SRFE) algorithm, a distributed consensus algorithm to co-estimate a common Local-Vertical, Local-Horizontal (LVLH) frame. The DPE combined with the SRFE provides a scalable, fully-decentralized navigation solution that can be used for swarm control and motion planning. Numerical simulations and experiments using Caltech’s robotic spacecraft simulators are presented to validate the effectiveness and scalability of the DPE algorithm