Binary Encoding Research Articles

Linear Tikhonov regularization against an edge field: an improved reconstruction algorithm in photothermal depth profilometry

This work introduces the concept of edge-field regularization into photothermal inverse depth profilometry problems. An edge field allows prior information concerning the depth location of material interfaces in a sample to be introduced into a Tikhonov regularization problem by a simple binary encoding. The edge-field regularization allows Nth-order Tikhonov stabilization constraints to be applied independently to multiple zones or segments of a depth profile between defined interface positions. This allows the reconstruction of continuous depth-profile information within known layers, without the globally imposed smoothing and edge oscillations of the classical regularization methods. This method successfully reconstructs both the amplitude of the interface discontinuities and the photothermal depth-contrast variations within the bounding edges, to a resolution limited by the resolving kernel for the underlying Nth-order Tikhonov constraint. The edge-field regularization dramatically reduces the errors associated with profiling photothermal contrast in bounded zones that are depth-displaced in the sample.

Second order phase transition in neural rate coding: binary encoding is optimal for rapid signal transmission.

Here, we derive optimal tuning functions for minimum mean square reconstruction from neural rate responses subjected to Poisson noise. The shape of these tuning functions strongly depends on the length T of the time window within which action potentials (spikes) are counted in order to estimate the underlying firing rate. A phase transition towards pure binary encoding occurs if the maximum mean spike count becomes smaller than approximately three. For a particular function class, we prove the existence of a second-order phase transition. The analytically derived critical decoding time window length is in precise agreement with numerical results. Our analysis reveals that binary rate encoding should dominate in the brain wherever time is the critical constraint.

SAT-Based Methods for Sequential Hardware Equivalence Verification without Synchronization

The BDD- and SAT-based model checking and verification methods normally require an initial state. Here we are concerned with sequential hardware verification, where an initial state must be one of the reset states. In practice, a reset state is not always given by the designer, and computing a reset state of a circuit is a hard problem. In this paper we propose a method allowing usage of SAT-based verification methods without a need for a user-given or a computed initial state. The idea is to employ a binary encoding of 3-valued modeling of circuits, and use the undefined state X as a reset state.

Combined fuzzy logic and genetic algorithm techniques—application to an electromagnetic field problem

The influence of a faulted electrical power transmission line on a buried pipeline is investigated. The induced electromagnetic field depends on several parameters, such as the position of the phase conductors, the currents flowing through conducting materials, and the earth resistivity. A fuzzy logic system was used to simulate the problem. It was trained using data derived from finite element method calculations for different configuration cases (training set) of the above electromagnetic field problem. After the training, the system was tested for several configuration cases, differing significantly from the training cases, with satisfactory results. It is shown that the proposed method is very time efficient and accurate in calculating electromagnetic fields compared to the time straining finite element method. In order to create the rule base for the fuzzy logic system a special incremental learning scheme is used during the training. The system is trained using genetic algorithms. Binary and real genetic encoding were implemented and compared.

Quantum key distribution with bright entangled beams.

We suggest a quantum cryptographic scheme using continuous EPR-like correlations of bright optical beams. For binary key encoding, the continuous information is discretized in a novel way by associating a respective measurement, amplitude, or phase, with a bit value "1" or "0." The secure key distribution is guaranteed by the quantum correlations. No predetermined information is sent through the quantum channel contributing to the security of the system.

A hybrid genetic algorithm with local search: I. Discrete variables: optimisation of complementary mobile phases

A hybrid genetic algorithm was developed for a combinatorial optimisation problem. The assayed hybridation modifies the reproduction pattern of the genetic algorithm through the application of a local search method, which enhances each individual in each generation. The method is applied to the optimisation of the mobile phase composition in liquid chromatography, using two or more mobile phases of complementary behaviour. Each of these phases concerns the optimal separation of certain compounds in the analysed mixture, while the others can remain overlapped. This optimisation approach may be useful in situations where full resolution with a single mobile phase is unfeasible. The optimisation is based on a local search method which alternates two combinatorial search spaces: one of them defined by combinations of solutes and the other by combinations of mobile phases. This gives rise to a protocol, able to interchange and improve data among both search spaces. An experimental design of algorithm settings was performed to find the optimal computation conditions. Lamarckian and Darwinian strategies, binary and real-value encoding and two ways of establishing the problem (a search space of solutes or mobile phases) were checked. Two problems involving the separation of 10 and 15 solutes with two and three mobile phase experimental factors were optimised up to reach base-line separation. The method was compared with a systematic examination of all candidate solutions and a classical genetic algorithm. The hybrid method, called LOGA (locally optimised genetic algorithm), exceeded the performance of both reference methods.

Floating-gate adaptation for focal-plane online nonuniformity correction

Stochastic adaptive algorithms are investigated for online correction of spatial nonuniformity in random-access addressable imaging systems. The adaptive architecture is implemented in analog VLSI, integrated with the photosensors on the focal plane. Random sequences of address locations selected with controlled statistics are used to adaptively equalize the intensity distribution at variable spatial scales. Through a logarithm transformation of system variables, adaptive gain correction is achieved through offset correction in the log-domain. This idea is particularly attractive for compact implementation using translinear floating-gate MOS circuits. Furthermore, the same architecture and random addressing provide for oversampled binary encoding of the image with equalized intensity histogram. The techniques apply to a variety of solid-state imagers, such as artificial retinas, active pixel sensors, and IR sensor arrays. Experimental results confirm gain correction and histogram equalization in a 64/spl times/64 pixel adaptive array integrated on a 2.2-mm/spl times/2.25-mm chip in 1.2-/spl mu/m CMOS technology.

An interval-based temporal algebra based on binary encoding of point relations

This paper presents a method for representing temporal interval relations using a bitencoded form of the relationships between interval end-points. The set of bit patterns for each interval relationship yields a unique, single-byte signature that forms the basis of a binary temporal algebra. Also presented is a matrix multiplication algorithm for computing transitive relations based on the definition of sum and product operations for the bit-encoded relation signatures. This bit-encoding encompasses the representation of unknown relations between endpoints of two intervals and captures ambiguities within a temporal system while providing an efficient binary algebra. Finally, an algorithm to compute the transitive closure over a set of intervals forming a temporal system is presented. The algorithm’s complexity is analyzed and is O(n), worst case, where n is the number of temporal intervals within the system. Empirical observations indicate that the closure algorithm completes in O(n) time, on average. The small memory footprint for the bit-code, the algorithmic transitive relation calculation, and the closure algorithm, together, form an efficient method for providing machine-based temporal reasoning capabilities. An Interval-based Temporal Algebra Based on Binary Encoding of Point Relations

COPAS: A New Algorithm for the Partial Input Encoding Problem

Frequently, the logic designer deals with functions with symbolic input variables. The binary encoding of such symbols should be chosen to optimize the final implementation. Conventionally, this input encoding (IE) problem has been solved in a two‐step process. First step generates constraints on the relationship between codes for different symbols, called group constraints. In a following step, symbols are encoded such that constraints are satisfied. This paper addresses the partial input encoding problem (PIE), a variation of the IE problem which generates codes of minimum length. The role of group constraints within the framework of the PIE problem has been questioned. This paper describes an algorithm that unlike conventional approaches, which try to maximize the number of satisfied constraints, targets the economical implementation of each input constraint. The proposed approach is based on a powerful heuristic that produces high quality results in shorter time compared to previous algorithm.

The stationary statistical properties of human coding sequences

We introduce a generally applicable method for the discovery and quantitation of all of the characteristic statistical properties of a class of biological sequences, given examples from the class. This method employs a reversible binary encoding of sequences into the binary digits −1 and +1. Then, provided that the sample is sufficient, the sample cumulants on the subsets of digit positions will manifest all of the statistical properties of the class. As an illustration, we present the main results of a complete characterization of the stationary statistical properties of human coding sequences, in terms of their sample cumulants. Many of the telling sample cumulants are described.

Local Search Heuristics for the Single Machine Total Weighted Tardiness Scheduling Problem

This paper presents several local search heuristics for the problem of scheduling a single machine to minimize total weighted tardiness. We introduce a new binary encoding scheme to represent solutions, together with a heuristic to decode the binary representations into actual sequences. This binary encoding scheme is compared to the usual “natural” permutation representation for descent, simulated annealing, threshold accepting, tabu search and genetic algorithms on a large set of test problems. Computational results indicate that all of the heuristics which employ our binary encoding are very robust in that they consistently produce good quality solutions, especially when multistart implementations are used instead of a single long run. The binary encoding is also used in a new genetic algorithm which performs very well and requires comparatively little computation time. A comparison of neighborhood search methods which use the permutation and binary representations shows that the permutation-based methods have a higher likelihood of generating an optimal solution, but are less robust in that some poor solutions are obtained. Of the neighborhood search methods, tabu search clearly dominates the others. Multistart descent performs remarkably well relative to simulated annealing and threshold accepting.

Design and Implementation of MP, a Protocol for Efficient Exchange of Mathematical Expressions

The Multi Project is an ongoing research effort at Kent State University aimed at providing an environment for distributed scientific computing. An integral part of this environment is the Multi Protocol (MP) which is designed to support efficient communication of mathematical data between scientifically-oriented software tools. MP exchanges data in the form of linearized annotated syntax trees. Syntax trees provide a simple, flexible and tool-independent way to represent and exchange data, and annotations provide a powerful and generic expressive facility for transmitting additional information. At a level above the data exchange protocol, dictionaries provide definitions for operators and constants, providing shared semantics across heterogeneous packages. A clear distinction between MP-defined and user-defined entities is enforced. Binary encodings are used for efficiency. Commonly used values and blocks of homogeneous data are further optimized. The protocol is independent of the underlying communication paradigm and can support parallel computation, distributed problem-solving environments, and the coupling of tools for specific applications.

A Fully Polynomial Approximation Scheme for Minimizing Makespan of Deteriorating Jobs

A fully polynomial approximation scheme for the problem of scheduling n deteriorating jobs on a single machine to minimize makespan is presented. Each algorithm of the scheme runs in O(n^5L^4/\epsilon^3) time, where L is the number of bits in the binary encoding of the largest numerical parameter in the input, and e is required relative error. The idea behind the scheme is rather general and it can be used to develop fully polynomial approximation schemes for other combinatorial optimization problems. Main feature of the scheme is that it does not require any prior knowledge of lower and/or upper bounds on the value of optimal solutions.

On the Parsimony of the Multi-Layer Perceptrons when Processing Encoded Symbolic Variables

This article addresses the issue of symbolic processing with Multi-Layer Perceptrons through encoding. Given an encoding, we propose a lower bound of the number of parameters for an MLP to perform a random mapping of its input symbolic space to its output symbolic space. In the case of what we call binary encoding, the needed number of parameters may be theoretically computed. Given these two results, we show that the most efficient encodings are the ones which use one input unit per value.

Efficient type inclusion tests

A type inclusion test determines whether one type is a subtype of another. Efficient type testing techniques exist for single subtyping, but not for languages with multiple subtyping. To date, the fast constant-time technique relies on a binary matrix encoding of the subtype relation with quadratic space requirements. In this paper, we present three new encodings of the subtype relation, the packed encoding , the bit-packed encoding and the compact encoding . These encodings have different characteristics. The bit-packed encoding delivers the best compression rates: on average 85% for real life programs. The packed encoding performs type inclusion tests in only 4 machine instructions. We present a fast algorithm for computing these encoding which runs in less than 13 milliseconds for PE and BPE, and 23 milliseconds for CE on an Alpha processor. Finally, we compare our results with other constant-time type inclusion tests on a suite of 11 large -benchmark hierarchies.

A genetic algorithm for continuous design space search

Genetic algorithms (GAs) have been extensively used as a means for performing global optimization in a simple yet reliable manner. However, in some realistic engineering design optimization domains the simple, classical implementation of a GA based on binary encoding and bit mutation and crossover is often inefficient and unable to reach the global optimum. In this paper we describe a GA for continuous design space optimization that uses new GA operators and strategies tailored to the structure and properties of engineering design domains. Empirical results in the domains of supersonic transport aircraft and supersonic missile inlets demonstrate that the newly formulated GA can be significantly better than the classical GA in both efficiency and reliability.

Sidelobe reduction in array-pattern synthesis using genetic algorithm

A simple and flexible genetic algorithm (GA) for pattern synthesis of antenna array with arbitrary geometric configuration is presented. Unlike conventional GA using binary coding and binary crossover, this approach directly represents the array excitation weighting vectors as complex number chromosomes and uses decimal linear crossover without a crossover site. Compared with conventional GAs, this approach has a few advantages: giving a clearer and simpler representation of the problem, simplifying chromosome construction, and totally avoiding binary encoding and decoding so as to simplify software programming and to reduce CPU time. This method also allows us to impose constraints on phases and magnitudes of complex excitation coefficients for preferable implementation in practice using digital phase shifters and digital attenuators. Successful applications show that the approach can be used as a general tool for pattern synthesis of arbitrary arrays.

Improvement of protein secondary structure prediction using binary word encoding.

We propose a binary word encoding to improve the protein secondary structure prediction. A binary word encoding encodes a local amino acid sequence to a binary word, which consists of 0 or 1. We use an encoding function to map an amino acid to 0 or 1. Using the binary word encoding, we can statistically extract the multiresidue information, which depends on more than one residue. We combine the binary word encoding with the GOR method, its modified version, which shows better accuracy, and the neural network method. The binary word encoding improves the accuracy of GOR by 2.8%. We obtain similar improvement when we combine this with the modified GOR method and the neural network method. When we use multiple sequence alignment data, the binary word encoding similarly improves the accuracy. The accuracy of our best combined method is 68.2%. In this paper, we only show improvement of the GOR and neural network method, we cannot say that the encoding improves the other methods. But the improvement by the encoding suggests that the multiresidue interaction affects the formation of secondary structure. In addition, we find that the optimal encoding function obtained by the simulated annealing method relates to nonpolarity. This means that nonpolarity is important to the multiresidue interaction.

A region-based theory for state assignment in speed-independent circuits

State assignment problems still need satisfactory solutions to make asynchronous circuit synthesis more practical. A well-known example of such a problem is that of complete state coding (CSC), which happens when a pair of different states in a specification has the same binary encoding. A standard way to approach state coding conflicts is to insert new state signals into the original specification in such a way that the original behavior remains intact. This paper proposes a method which improves over existing approaches by coupling generality, optimality, and efficiency. The method is based on the use of a class of "ground objects", called regions, that play the role of a bridge between state-based specifications (transition systems, TS's) and event-based specifications (signal transition graphs, STG's), We need to deal with both types of specification because designers usually prefer a timing diagram-like notation, such as STG, while optimization and cost analysis work better at the state level. A region in a transition system is a set of states that corresponds to a place in an STG (or the underlying Petri net). Regions are tightly connected with a set of properties that are to be preserved across the state encoding process, namely, 1) trace equivalence between the original and the encoded specification, and 2) implementability as a speed-independent circuit. We will build on a theoretical body of work that has shown the significance of regions for such property-preserving transformations, and describe a set of algorithms aimed at efficiently solving the encoding problem. The algorithms have been implemented in a software tool called petrify. Unlike many existing tools, petrify represents the encoded specification as an STG. This significantly improves the readability of the result (compared to a state-based description in which concurrency is represented implicitly by interleaving), and allows the designer to be more closely involved in the synthesis process. The efficiency of the method is demonstrated on a number of "difficult" examples.

An on-line variable-length binary encoding of text

We present a methodology for on-line variable-length binary encoding of a dynamically growing set of integers. Our encoding maintains the prefix property that enables unique decoding of a string of integers from the set. In order to develop the formalism of this on-line binary encoding, we define a unique binary tree data structure called the “phase in binary tree.” To show the utility of this on-line variable-length binary encoding, we apply this methodology to encode the pointers generated by the LZW algorithm. The experimental results obtained illustrate the superior performance of our algorithm compared to the most widely used algorithms. This on-line variable-length binary encoding can be applied in other dictionary-based text compression schemes as well to effectively encode the output pointers to enhance the compression ratio.