Randomness Conservation over Algorithms

Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation inequalities. We address this issue by proving tight bounds of randomness and information conservation with respect to recursively enumerable transformations, i.e. processing by algorithms. We also show conservation of randomness of finite strings with respect to enumerable distributions, i.e. semicomputable semi-measures.Comment: 6 page

An online distributed algorithm for inferring policy routing configurations

We present an online distributed algorithm, the Causation Logging Algorithm (CLA), in which Autonomous Systems (ASes) in the Internet individually report route oscillations/flaps they experience to a central Internet Routing Registry (IRR). The IRR aggregates these reports and may observe what we call causation chains where each node on the chain caused a route flap at the next node along the chain. A chain may also have a causation cycle. The type of an observed causation chain/cycle allows the IRR to infer the underlying policy routing configuration (i.e. the system of economic relationships and constraints on route/path preferences). Our algorithm is based on a formal policy routing model that captures the propagation dynamics of route flaps under arbitrary changes in topology or path preferences. We derive invariant properties of causation chains/cycles for ASes which conform to economic relationships based on the popular Gao-Rexford model. The Gao-Rexford model is known to be safe in the sense that the system always converges to a stable set of paths under static conditions. Our CLA algorithm recovers the type/property of an observed causation chain of an underlying system and determines whether it conforms to the safe economic Gao-Rexford model. Causes for nonconformity can be diagnosed by comparing the properties of the causation chains with those predicted from different variants of the Gao-Rexford model

Foundational Theory for Understanding Policy Routing Dynamics

In this paper we introduce a theory of policy routing dynamics based on fundamental axioms of routing update mechanisms. We develop a dynamic policy routing model (DPR) that extends the static formalism of the stable paths problem (introduced by Griffin et al.) with discrete synchronous time. DPR captures the propagation of path changes in any dynamic network irrespective of its time-varying topology. We introduce several novel structures such as causation chains, dispute fences and policy digraphs that model different aspects of routing dynamics and provide insight into how these dynamics manifest in a network. We exercise the practicality of the theoretical foundation provided by DPR with two fundamental problems: routing dynamics minimization and policy conflict detection. The dynamics minimization problem utilizes policy digraphs, that capture the dependencies in routing policies irrespective of underlying topology dynamics, to solve a graph optimization problem. This optimization problem explicitly minimizes the number of routing update messages in a dynamic network by optimally changing the path preferences of a minimal subset of nodes. The conflict detection problem, on the other hand, utilizes a theoretical result of DPR where the root cause of a causation cycle (i.e., cycle of routing update messages) can be precisely inferred as either a transient route flap or a dispute wheel (i.e., policy conflict). Using this result we develop SafetyPulse, a token-based distributed algorithm to detect policy conflicts in a dynamic network. SafetyPulse is privacy preserving, computationally efficient, and provably correct.National Science Foundation (CISE/CCF 0820138, CISE/CSR 0720604, CISE/CNS 0524477, CNS/ITR 0205294, CISE/EIA RI #0202067

Measurement of water in rhyolitic glasses; calibration of an infrared spectroscopic technique

A series of natural rhyolitic obsidians were analyzed for their total water contents by a vacuum extraction technique. The grain size of the crushed samples can significantly affect these analyses. Coarse powders must be used in order to avoid surface-correlated water. These analyses were used to calibrate infrared spectroscopic measurements of water in glass using several infrared and near-infrared absorption bands. We demonstrate that infrared spectroscopy can yield precise determinations of not only total dissolved water contents, but also the concentrations of individual H-bearing species in natural and synthetic rhyolitic glasses on spots as small as a few tens of micrometers in diameter

Uniform Tests and Algorithmic Thermodynamic Entropy

We prove that given a computable metric space and two computable measures, the set of points that have high universal uniform test scores with respect to the first measure will have a lower bound with respect to the second measure. This result is transferred to thermodynamics, showing that algorithmic thermodynamic entropy must oscillate in the presence of dynamics. Another application is that outliers will become emergent in computable dynamics of computable metric spaces

On the Algorithmic Probability of Sets

The combined universal probability m(D) of strings x in sets D is close to max \m(x) over x in D: their logs differ by at most D's information I(D:H) about the halting sequence H. As a result of this, given a binary predicate P, the length of the smallest program that computes a complete extension of P is less than the size of the domain of P plus the amount of information that P has with the halting sequence.Comment: 22 Page