A Simple, Approximate Method for Analysis of Kerr-Newman Black Hole Dynamics and Thermodynamics

In this work we present a simple, approximate method for analysis of the basic dynamical and thermodynamical characteristics of Kerr-Newman black hole. Instead of the complete dynamics of the black hole self-interaction we consider only such stable (stationary) dynamical situations determined by condition that black hole (outer) horizon circumference holds the integer number of the reduced Compton wave lengths corresponding to mass spectrum of a small quantum system (representing quant of the black hole self-interaction). Then, we show that Kerr-Newman black hole entropy represents simply the quotient of the sum of static part and rotation part of mass of black hole on the one hand and ground mass of small quantum system on the other hand. Also we show that Kerr-Newman black hole temperature represents the negative value of the classical potential energy of gravitational interaction between a part of black hole with reduced mass and small quantum system in the ground mass quantum state. Finally, we suggest a bosonic great canonical distribution of the statistical ensemble of given small quantum systems in the thermodynamical equilibrium with (macroscopic) black hole as thermal reservoir. We suggest that, practically, only ground mass quantum state is significantly degenerate while all other, excited mass quantum states are non-degenerate. Kerr-Newman black hole entropy is practically equivalent to the ground mass quantum state degeneration. Given statistical distribution admits a rough (qualitative) but simple modeling of Hawking radiation of the black hole too.Comment: 8 pages, no figure

Towards diagnosing hybrid systems

This paper reports on the findings of an on-going project to investigate techniques to diagnose complex dynamical systems that are modeled as hybrid systems. In particular, we examine continuous systems with embedded supervisory controllers which experience abrupt, partial or full failure of component devices. The problem we address is: given a hybrid model of system behavior, a history of executed controller actions, and a history of observations, including an observation of behavior that is aberrant relative to the model of expected behavior, determine what fault occurred to have caused the aberrant behavior. Determining a diagnosis can be cast as a search problem to find the most likely model for the data. Unfortunately, the search space is extremely large. To reduce search space size and to identify an initial set of candidate diagnoses, we propose to exploit techniques originally applied to qualitative diagnosis of continuous systems. We refine these diagnoses using parameter estimation and model fitting techniques. As a motivating case study, we have examined the problem of diagnosing NASA’s Sprint AERCam, a small spherical robotic camera unit with 12 thrusters that enable both linear and rotational motion.

Decision-Theoretic Golog with Qualitative Preferences

Personalization is becoming increasingly important in agent programming, particularly as it relates to the Web. We propose to develop underspecified, task-specific agent programs, and to automatically personalize them to the preferences of individual users. To this end, we propose a framework for agent programming that integrates rich, non-Markovian, qualitative user preferences expressed in a linear temporal logic with quantitative Markovian reward functions. We begin with DTGOLOG, a first-order, decisiontheoretic agent programming language in the situation calculus. We present an algorithm that compiles qualitative preferences into GOLOG programs and prove it sound and complete with respect to the space of solutions. To integrate these preferences into DTGOLOG we introduce the notion of multiprogram synchronization and restate the semantics of the language as a transition semantics. We demonstrate the utility of this framework with an application to personalized travel planning over the Web. To the best of our knowledge this is the first work to combine qualitative and quantitative preferences for agent programming. Further, while the focus of this paper is on the integration of qualitative and quantitative preferences, a side effect of this work is realization of the simpler task of integrating qualitative preferences alone into agent programming as well as the generation of GOLOG programs from LTL formulae.

SAT-Based Approach for Learning Optimal Decision Trees with Non-Binary Features

Decision trees are a popular classification model in machine learning due to their interpretability and performance. Traditionally, decision-tree classifiers are constructed using greedy heuristic algorithms, however these algorithms do not provide guarantees on the quality of the resultant trees. Instead, a recent line of work has studied the use of exact optimization approaches for constructing optimal decision trees. Most of the recent approaches that employ exact optimization are designed for datasets with binary features. While numeric and categorical features can be transformed to binary features, this transformation can introduce a large number of binary features and may not be efficient in practice. In this work, we present a novel SAT-based encoding for decision trees that supports non-binary features and demonstrate how it can be used to solve two well-studied variants of the optimal decision tree problem. We perform an extensive empirical analysis that shows our approach obtains superior performance and is often an order of magnitude faster than the current state-of-the-art exact techniques on non-binary datasets