On Probability Estimation by Exponential Smoothing

Probability estimation is essential for every statistical data compression algorithm. In practice probability estimation should be adaptive, recent observations should receive a higher weight than older observations. We present a probability estimation method based on exponential smoothing that satisfies this requirement and runs in constant time per letter. Our main contribution is a theoretical analysis in case of a binary alphabet for various smoothing rate sequences: We show that the redundancy w.r.t. a piecewise stationary model with $s$ segments is $O\left(s\sqrt n\right)$ for any bit sequence of length $n$, an improvement over redundancy $O\left(s\sqrt{n\log n}\right)$ of previous approaches with similar time complexity

Mixing Strategies in Data Compression

We propose geometric weighting as a novel method to combine multiple models in data compression. Our results reveal the rationale behind PAQ-weighting and generalize it to a non-binary alphabet. Based on a similar technique we present a new, generic linear mixture technique. All novel mixture techniques rely on given weight vectors. We consider the problem of finding optimal weights and show that the weight optimization leads to a strictly convex (and thus, good-natured) optimization problem. Finally, an experimental evaluation compares the two presented mixture techniques for a binary alphabet. The results indicate that geometric weighting is superior to linear weighting.Comment: Data Compression Conference (DCC) 201

Linear and Geometric Mixtures - Analysis

Linear and geometric mixtures are two methods to combine arbitrary models in data compression. Geometric mixtures generalize the empirically well-performing PAQ7 mixture. Both mixture schemes rely on weight vectors, which heavily determine their performance. Typically weight vectors are identified via Online Gradient Descent. In this work we show that one can obtain strong code length bounds for such a weight estimation scheme. These bounds hold for arbitrary input sequences. For this purpose we introduce the class of nice mixtures and analyze how Online Gradient Descent with a fixed step size combined with a nice mixture performs. These results translate to linear and geometric mixtures, which are nice, as we show. The results hold for PAQ7 mixtures as well, thus we provide the first theoretical analysis of PAQ7.Comment: Data Compression Conference (DCC) 201

On Probability Estimation via Relative Frequencies and Discount

Probability estimation is an elementary building block of every statistical data compression algorithm. In practice probability estimation is often based on relative letter frequencies which get scaled down, when their sum is too large. Such algorithms are attractive in terms of memory requirements, running time and practical performance. However, there still is a lack of theoretical understanding. In this work we formulate a typical probability estimation algorithm based on relative frequencies and frequency discount, Algorithm RFD. Our main contribution is its theoretical analysis. We show that the code length it requires above an arbitrary piecewise stationary model with bounded and unbounded letter probabilities is small. This theoretically confirms the recency effect of periodic frequency discount, which has often been observed empirically

A linear control design structure to maintain loop properties during limit operation in a multi-nozzle turbofan engine

The implementation of multi-variable control systems on turbofan engines requires the use of limit protection to maintain safe engine operation. Since a turbofan engine typically encounters limits during transient operation, the use of a limit protection scheme that modifies the feedback loop may void the desired 'guarantees' associated with linear multi-variable control design methods, necessitating considerable simulation to validate the control with limited protection. An alternative control design structure is proposed that maintains the desired linear feedback properties when certain safety limits are encountered by moving the limit protection scheme outside the feedback loop. This proposed structure is compared to a structure with a limit protection scheme that modifies the feedback loop properties. The two design structures are compared using both linear and nonlinear simulations. The evaluation emphasizes responses where the fan surge margin limit is encountered

Propulsion system performance resulting from an integrated flight/propulsion control design

Propulsion-system-specific results are presented from the application of the integrated methodology for propulsion and airframe control (IMPAC) design approach to integrated flight/propulsion control design for a 'short takeoff and vertical landing' (STOVL) aircraft in transition flight. The IMPAC method is briefly discussed and the propulsion system specifications for the integrated control design are examined. The structure of a linear engine controller that results from partitioning a linear centralized controller is discussed. The details of a nonlinear propulsion control system are presented, including a scheme to protect the engine operational limits: the fan surge margin and the acceleration/deceleration schedule that limits the fuel flow. Also, a simple but effective multivariable integrator windup protection scheme is examined. Nonlinear closed-loop simulation results are presented for two typical pilot commands for transition flight: acceleration while maintaining flightpath angle and a change in flightpath angle while maintaining airspeed. The simulation nonlinearities include the airframe/engine coupling, the actuator and sensor dynamics and limits, the protection scheme for the engine operational limits, and the integrator windup protection. Satisfactory performance of the total airframe plus engine system for transition flight, as defined by the specifications, was maintained during the limit operation of the closed-loop engine subsystem

Structure and Fragmentation of a high line-mass filament: Nessie

An increasing number of hundred-parsec scale, high line-mass filaments have been detected in the Galaxy. Their evolutionary path, including fragmentation towards star formation, is virtually unknown. We characterize the fragmentation within the Nessie filament, covering size-scales between $\sim$ 0.1-100 pc. We also connect the small-scale fragments to the star-forming potential of the cloud. We combine near-infrared data from the VVV survey with mid-infrared GLIMPSE data to derive a high-resolution dust extinction map and apply a wavelet decomposition technique on it to analyze the fragmentation characteristics of the cloud, which are compared with predictions from fragmentation models. We compare the detected objects to those identified in $\sim$ 10 times coarser resolution from ATLASGAL data. We present a high-resolution extinction map of Nessie. We estimate the mean line-mass of Nessie to be $\sim$ 627 M$_\odot$/pc and the distance to be $\sim$ 3.5 kpc. We find that Nessie shows fragmentation at multiple size scales. The nearest-neighbour separations of the fragments at all scales are within a factor of 2 of the Jeans' length at that scale. However, the relationship between the mean densities of the fragments and their separations is significantly shallower than expected for Jeans' fragmentation. The relationship is similar to the one predicted for a filament that exhibits a Larson-like scaling between size-scale and velocity dispersion; such a scaling may result from turbulent support. Based on the number of YSOs in Nessie, we estimate that the star formation rate is $\sim$ 371 M$_\odot$/Myr; similar values result if using the number of dense cores, or the amount of dense gas, as the proxy of star formation. The star formation efficiency is 0.017. These numbers indicate that Nessie's star-forming content is comparable to the Solar neighborhood giant molecular clouds like Orion A