Spectral Simplicity of Apparent Complexity, Part I: The Nondiagonalizable Metadynamics of Prediction

Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type of question---correlation, predictability, predictive cost, observer synchronization, and the like---induces a distinct generator class. Answers are then functions of the class-appropriate transition dynamic. Unfortunately, these dynamics are generically nonnormal, nondiagonalizable, singular, and so on. Tractably analyzing these dynamics relies on adapting the recently introduced meromorphic functional calculus, which specifies the spectral decomposition of functions of nondiagonalizable linear operators, even when the function poles and zeros coincide with the operator's spectrum. Along the way, we establish special properties of the projection operators that demonstrate how they capture the organization of subprocesses within a complex system. Circumventing the spurious infinities of alternative calculi, this leads in the sequel, Part II, to the first closed-form expressions for complexity measures, couched either in terms of the Drazin inverse (negative-one power of a singular operator) or the eigenvalues and projection operators of the appropriate transition dynamic.Comment: 24 pages, 3 figures, 4 tables; current version always at http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt1.ht

On the linear complexity and linear complexity profile of sequences in finite fields

Pseudo random sequences, that are used for stream ciphers, are required to havetheproperties of unpredictability and randomness. An important tool for measuringthese features is the linear complexity profile of the sequence in use.In this thesis we present a survey of some recent results obtained on linearcomplexity and linear complexity profile of pseudo random sequences. The relationbetween the polynomial degree and the linear complexity of a function over a finite field is given, bounds for linear complexity of the "power generator" and "the selfshrinking generator" are presented and a new method of construction of sequences of high linear complexity profile is illustrated

Complexity analysis of binary nonlinear feedforward sequences through minimum polynomials of compound matrices

AbstractThe problem of finding the complexity of the Nonlinear feedforward sequences has been analysed and a unified method has been developed for finding the complexity of such sequences for the cases when feedback is 1.(i) an irreducible polynomial;2.(ii) product of two irreducible polynomials;3.(iii) power of an irreducible polynomial. The method is based on the minimum polynomial of the compound matrix formed from the companion matrix of the feedback polynomial. Apart from being a unified method, this approach has the advantage that it can be applied to any level of logic and one can get the minimal generator of all possible non-linear feedforward sequences

Recent advances in the theory of nonlinear pseudorandom number generators

The classical linear congruential method for generating uniform pseudorandom numbers has some deficiencies that can render them useless for some simulation problems. This fact motivated the design and the analysis of nonlinear congruential methods for the generation of pseudorandom numbers. In this thesis, we aim to review the recent developments in the study of nonlinear congruential pseudorandom generators. Our exposition concentrates on inversive generators. We also describe the so-called power generator and the quadratic exponential generator which are particularly interesting for cryptographic applications. We give results on the period length and theoretical analysis of these generators. The emphasis is on the lattice structure, discrepancy and linear complexity of the generated sequences

Linear extractors for extracting randomness from noisy sources

Linear transformations have many applications in information theory, like data compression and error-correcting codes design. In this paper, we study the power of linear transformations in randomness extraction, namely linear extractors, as another important application. Comparing to most existing methods for randomness extraction, linear extractors (especially those constructed with sparse matrices) are computationally fast and can be simply implemented with hardware like FPGAs, which makes them very attractive in practical use. We mainly focus on simple, efficient and sparse constructions of linear extractors. Specifically, we demonstrate that random matrices can generate random bits very efficiently from a variety of noisy sources, including noisy coin sources, bit-fixing sources, noisy (hidden) Markov sources, as well as their mixtures. It shows that low-density random matrices have almost the same efficiency as high-density random matrices when the input sequence is long, which provides a way to simplify hardware/software implementation. Note that although we constructed matrices with randomness, they are deterministic (seedless) extractors - once we constructed them, the same construction can be used for any number of times without using any seeds. Another way to construct linear extractors is based on generator matrices of primitive BCH codes. This method is more explicit, but less practical due to its computational complexity and dimensional constraints

Quadrupole Electromagnetic Linear Positioning System (QELPS):: Optimal Design, Modelling and Analysis for Linear Motion Application

In linear motion systems, including linear motors and actuators, precise and controlled linear motion is provided for various applications. However, they have several drawbacks: high costs, complexity, limited stroke length, high energy consumption, speed limitations, heat generation, noise and vibration, limited load capacity, environmental considerations, and integration challenges. High costs are especially significant for applications requiring high precision. The components' complexity and additional control electronics can increase maintenance and trouble-shooting requirements. Ensuring accurate and efficient operation necessitates regular maintenance. The limitation in stroke length, determined by the drive's size and guide length, can pose challenges for applications requiring long strokes. High energy consumption can be a concern, and speed limitations may be challenging. Managing heat generation is crucial to prevent component damage. Noise and vibration can be problematic, particularly in quiet applications. Integration challenges can arise when dealing with complex systems or automation processes. To overcome some of these drawbacks, an innovative coil configuration design for linear positioning system applications is proposed. The proposed design focuses on the Quadrupole Electromagnetic linear Positioning System (QELPS), comprising four coils generating a uniform electromagnetic field to produce a Lorentz force on the slider. The QELPS design is meticulously crafted using 3D modeling in ANSYS software, and the magnetic characteristics indicate the potential for scaling this model to different levels. The power circuit of the QELPS is simulated using ANSYS Simplorer and incorporates silicon-controlled rectifiers (SCR) and a pulse width modulation (PWM) pulse generator. The design achieves a force of 27.6 newtons with the paper presenting current and force plots in comprehensive detail. Furthermore, an interactive design algorithm is introduced, facilitating the customization of this model for various linear track dimensions. This research aims to advance linear drive technology and enhance linear motion applications by developing this new coil configuration design and harnessing the Quadrupole Electromagnetic System

Diseño eléctrico de una boya para energía olamotriz

Renewable energies have been taking an important role in the disperse generation in the last years. A new renewable energy is the wave power, that transports energy by ocean surface waves, and capture that energy to do useful work. In this project is studied, discussed and designed the electrical parts needed to transform the wave power into electrical power as the control of the buoy (reactive and latching control), system (electrical or hydraulic), generators (linear or rotating),converter systems (depending on generator, speed control and grid), grid connections and transmissions systems, cables and transformers. The material produced in this report is definitely the beginning of new knowledge which can be deeply developed. From these studies some conclusions can be done as electrical systems offer excellent prospects for superior performance and other benefits compared with hydraulic systems, and the development of electrical system prototypes is justified. Phase control avoids the drawback of high power peaks keeping the advantage of increased power extraction. The rotating generation is preferred against a linear electric power generation in terms of efficiency and cost. In a plant, the wave energy converters (base units) can be connected in larger arrays ranging from tenths up to thousands of individual converters. The connections of these converters to the grid can be implemented in various ways (converters and transformer offshore or onshore and connections cables schemes) depending on the size of the farm and the proximity to the grid among other criteria as availability or cost. Taking into account cable losses and complexity the better option is place these devices onshore for small farms close to the grid and offshore for medium to large farms. Comparing connection schemes in terms of cable cost, both material and installation, and availability, systems with clusters and subclusters (small amount of base units) and one cable to the shore are the better options.Ingeniería Industria

Remarks on a cyclotomic sequence

We analyse a binary cyclotomic sequence constructed via generalized cyclotomic classes by Bai et al. (IEEE Trans Inforem Theory 51: 1849-1853, 2005). First we determine the linear complexity of a natural generalization of this binary sequence to arbitrary prime fields. Secondly we consider k-error linear complexity and autocorrelation of these sequences and point out certain drawbacks of this construction. The results show that the parameters for the sequence construction must be carefully chosen in view of the respective application