Binary Words Research Articles

Improving the redundancy of Knuth’s balancing scheme for packet transmission systems

A simple scheme was proposed by Knuth to generate binary balanced code words from any information word. However, this method is limited in the sense that its redundancy is twice that of the full sets of balanced codes. The gap between Knuth?s algorithm?s redundancy and that of the full sets of balanced codes is significantly considerable. This paper attempts to reduce that gap. Furthermore, many constructions assume that a full balancing can be performed without showing the steps. A full balancing refers to the overall balancing of the encoded information together with the prefix. We propose an efficient way to perform a full balancing scheme that does not make use of lookup tables or enumerative coding.

Biological Neuron Coding Inspired Binary Word Embeddings

Word embeddings are the semantic representations of the words. They are derived from large corpus and work well on many natural language tasks, with one downside of costing large memory space. In this paper, we propose binary word embedding models based on inspirations from biological neuron coding mechanisms, converting the spike timing of neurons during specific time intervals into binary codes, reducing the space and speeding up computation. We build three types of models to post-process the original dense word embeddings, namely, the homogeneous Poission processing-based rate coding model, the leaky integrate-and-fire neuron-based model, and the Izhikevich’s neuron-based model. We test our binary embedding models on word similarity and text classification tasks of five public datasets. The experimental results show that the brain-inspired binary word embeddings (which reduce approximately 68.75% of the space) get similar results to original embeddings for word similarity task while better performance than traditional binary embeddings on text classification task.

Bundle-Updatable SRAM-Based TCAM Design for OpenFlow-Compliant Packet Processor

Static random-access memory (SRAM)-based ternary content-addressable memories (TCAMs) emulate TCAM functions with high throughput at low cost. However, the implementation of SRAM-based TCAM as a rule table in network switches tends to prolong updating latency, which can cause a false packet routing. This brief proposes a novel low-latency bundle-updatable TCAM (BU-TCAM) scheme that uses binary tree-based prefix encoding (BPE) to support single- and multiple-rule updating in a software-defined networking/OpenFlow network. The proposed encoding method transforms the original ternary rule data into a binary code word and determines the range of overlap in SRAM addresses to facilitate updating. This greatly decreases latency in cases where multiple rules are required to update on an SRAM-based TCAM. We implemented an emulated $64\times 32$ -bit TCAM of the proposed design on a Xilinx ZC-706 field-programmable gate array. The proposed scheme reduced updating latency by 79.6%, compared with a conventional updating structure, which had only 9.8% and 23% increases in LUTs and registers overhead, respectively.

Encoding discrete quantum algebras in a hierarchy of binary words

It is shown how to endow a hierarchy of sets of binary patterns with the structure of an abstract, normed C*-algebra. In the course we also recover an intermediate connection with the words of a Dyck language and Tempereley-Lieb algebras for which we also find that an effective arithmetic code is possible albeit of greater complexity. We also discuss possible applications associated with signal theory and waveform engineering on possible ways to embed discrete computational structures in an analog continuum substrate.

Generating all minimal petri net unsolvable binary words

Sets of finite words, as well as some infinite ones, can be described using finite systems, e.g. automata. On the other hand, some automata may be constructed with the use of even more compact systems, like Petri nets. We call such automata Petri net solvable. In this paper we consider the solvability of singleton languages over a binary alphabet (i.e. binary words). An unsolvable (i.e. not solvable) word w is called minimal if each proper factor of w is solvable. We present a complete language-theoretical characterisation of the set of all minimal unsolvable binary words. The characterisation utilises morphic-based transformations which expose the combinatorial structure of those words, and allows to introduce a pattern matching condition for unsolvability.

Hybrid self-organizing feature map (SOM) for anomaly detection in cloud infrastructures using granular clustering based upon value-difference metrics

We have witnessed an increase in the availability of data from diverse sources over the past few years. Cloud computing, big data and Internet-of-Things (IoT) are distinctive cases of such an increase which demand novel approaches for data analytics in order to process and analyze huge volumes of data for security and business use. Cloud computing has been becoming popular for critical structure IT mainly due to cost savings and dynamic scalability. Current offerings, however, are not mature enough with respect to stringent security and resilience requirements. Mechanisms such as anomaly detection hybrid systems are required in order to protect against various challenges that include network based attacks, performance issues and operational anomalies. Such hybrid AI systems include Neural Networks, blackboard systems, belief (Bayesian) networks, case-based reasoning and rule-based systems and can be implemented in a variety of ways. Traffic in the cloud comes from multiple heterogeneous domains and changes rapidly due to the variety of operational characteristics of the tenants using the cloud and the elasticity of the provided services. The underlying detection mechanisms rely upon measurements drawn from multiple sources. However, the characteristics of the distribution of measurements within specific subspaces might be unknown. We argue in this paper that there is a need to cluster the observed data during normal network operation into multiple subspaces each one of them featuring specific local attributes, i.e. granules of information. Clustering is implemented by the inference engine of a model hybrid NN system. Several variations of the so-called value-difference metric (VDM) are investigated like local histograms and the Canberra distance for scalar attributes, the Jaccard distance for binary word attributes, rough sets as well as local histograms over an aggregate ordering distance and the Canberra measure for vectorial attributes. Low-dimensional subspace representations of each group of points (measurements) in the context of anomaly detection in critical cloud implementations is based upon VD metrics and can be either parametric or non-parametric. A novel application of a Self-Organizing-Feature Map (SOFM) of reduced/aggregate ordered sets of objects featuring VD metrics (as obtained from distributed network measurements) is proposed. Each node of the SOFM stands for a structured local distribution of such objects within the input space. The so-called Neighborhood-based Outlier Factor (NOOF) is defined for such reduced/aggregate ordered sets of objects as a value-difference metric of histogrammes. Measurements that do not belong to local distributions are detected as anomalies, i.e. outliers of the trained SOFM. Several methods of subspace clustering using Expectation-Maximization Gaussian Mixture Models (a parametric approach) as well as local data densities (a non-parametric approach) are outlined and compared against the proposed method using data that are obtained from our cloud testbed in emulated anomalous traffic conditions. The results—which are obtained from a model NN system—indicate that the proposed method performs well in comparison with conventional techniques.

The asymptotic number of prefix normal words

We show that the number of prefix normal binary words of length n is 2n−Θ((log⁡n)2). We also show that the maximum number of binary words of length n with a given fixed prefix normal form is 2n−O(nlog⁡n).

Random Walk Enzymes: Information Theory, Quantum Isomorphism, and Entropy Dispersion.

Activation-induced deoxycytidine deaminase (AID) is a key enzyme in the human immune system. AID binds to and catalyzes random point mutations on the immunoglobulin (Ig) gene, leading to diversification of the Ig gene sequence by random walk motions, scanning for cytidines and turning them to uracils. The mutation patterns deposited by AID on its substrate DNA sequences can be interpreted as random binary words, and the information content of this stochastically generated library of mutated DNA sequences can be measured by its entropy. In this paper, we derive an analytical formula for this entropy and show that the stochastic scanning + catalytic dynamics of AID is controlled by a characteristic length that depends on the diffusion coefficient of AID and the catalytic rate. Experiments showed that the deamination rates have a sequence context dependence, where mutations are generated at higher intensities on DNA sequences with higher densities of mutable sites. We derive an isomorphism between this classical system and a quantum mechanical model and use this isomorphism to explain why AID appears to focus its scanning on regions with higher concentrations of deaminable sites. Using path integral Monte Carlo simulations of the quantum isomorphic system, we demonstrate how AID's scanning indeed depends on the context of the DNA sequence and how this affects the entropy of the library of generated mutant clones. Examining detailed features in the entropy of the experimentally generated clone library, we provide clear evidence that the random walk of AID on its substrate DNA is focused near hot spots. The model calculations applied to the experimental data show that the observed per-site mutation frequencies display similar contextual dependences as observed in the experiments, in which hot motifs are located adjacent to several different types of hot and cold motifs.

Some results on Parikh word representable graphs and partitions

Consequent to the introduction of the concept of Parikh matrix of a word which is based on the notion of subwords of a word, there has been an extensive research and study based on subwords. Parikh word representable graph is one such notion which has been introduced in the recent times. On the other hand connections of partitions of a number with counts of certain subword in a binary word are known. In this paper we introduce the notion of dual of a word and investigate its relationship with conjugate partition. As a result of this study, an expression for the number of nonisomorphic Parikh word representable graphs with a given number of edges, is obtained. Several other properties of Parikh word representable graphs are also derived.

Combinatorics on Binary Words and Codimensions of Identities in Left Nilpotent Algebras

Numerical characteristics of polynomial identities of left nilpotent algebras are examined. Previously, we came up with a construction which, given an infinite binary word, allowed us to build a two-step left nilpotent algebra with specified properties of the codimension sequence. However, the class of the infinite words used was confined to periodic words and Sturm words. Here the previously proposed approach is generalized to a considerably more general case. It is proved that for any algebra constructed given a binary word with subexponential function of combinatorial complexity, there exists a PI-exponent, and its precise value is computed.

Multiset-Partition Distribution Matching

Distribution matching is a fixed-length invertible mapping from a uniformly distributed bit sequence to shaped amplitudes and plays an important role in the probabilistic amplitude shaping framework. With conventional constant-composition distribution matching (CCDM), all output sequences have identical composition. In this paper, we propose multiset-partition distribution matching (MPDM), where the composition is constant over all output sequences. When considering the desired distribution as a multiset, MPDM corresponds to partitioning this multiset into equal-sized subsets. We show that MPDM allows addressing more output sequences and, thus, has a lower rate loss than CCDM in all nontrivial cases. By imposing some constraints on the partitioning, a constructive MPDM algorithm is proposed which comprises two parts. A variable-length prefix of the binary data word determines the composition to be used, and the remainder of the input word is mapped with a conventional CCDM algorithm, such as arithmetic coding, according to the chosen composition. Simulations of 64-ary quadrature amplitude modulation over the additive white Gaussian noise channel demonstrate that the block-length saving of MPDM over CCDM for a fixed gap to capacity is approximately a factor of 2.5–5 at medium to high signal-to-noise ratios.

Enumerating words with forbidden factors

This presentation is an exposition of an application of the theory of recurrence relations to enumerating strings over an alphabet with a forbidden factor (consecutive substring). As an illustration we examine the case of binary strings with a forbidden factor of k consecutive symbols 1 for given k, using generating function techniques that deserve to be better known.This allows us to derive a known upper bound for the number of prefix normal binary words: words with the property that no factor has more occurrences of the symbol 1 than the prefix of the same length. Such words arise in the context of indexed binary jumbled pattern matching.

A characterization of non-isometric binary words

In this paper, first, we introduce two classification criteria of non-isometric words, and characterize every type of non-isometric words. Then, according to those characterizations, a family of words that 2-isometric but not 3-isometric is found, and the words with maximum and minimum index are characterized. Next, an O(|f|2) algorithm is designed, which is presented to compute the index of a non-isometric word and determine what class that a word belongs to. Finally, several problems are listed for further investigation.

On Some Interesting Ternary Formulas

We obtain the following results about the avoidance of ternary formulas. Up to renaming of the letters, the only infinite ternary words avoiding the formula $ABCAB.ABCBA.ACB.BAC$ (resp. $ABCA.BCAB.BCB.CBA$) have the same set of recurrent factors as the fixed point of $0\mapsto 012$, $1\mapsto 02$, $2\mapsto 1$. The formula $ABAC.BACA.ABCA$ is avoided by polynomially many binary words and there exists arbitrarily many infinite binary words with different sets of recurrent factors that avoid it. If every variable of a ternary formula appears at least twice in the same fragment, then the formula is $3$-avoidable. The pattern $ABACADABCA$ is unavoidable for the class of $C_4$-minor-free graphs with maximum degree~$3$. This disproves a conjecture of Grytczuk. The formula $ABCA.ACBA$, or equivalently the palindromic pattern $ABCADACBA$, has avoidability index $4$.

Partial words with a unique position starting a square

We consider partial words with a unique position starting a power. We show that over a k letter alphabet, a partial word with a unique position starting a square can contain at most k squares. This is in contrast to full words which can contain at most one power if a unique position starts a power. For certain higher powers we exhibit binary partial words containing three powers all of which start at the same position.

Analysis and design of a terahertz microstrip antenna based on a synthesized photonic bandgap substrate using BPSO

A microstrip patch antenna based on a synthesized photonic bandgap (PBG) substrate is designed and analyzed by using a technique based on the combination of an evolutionary heuristic optimization algorithm with the CST Microwave Studio simulator, which is based on the finite integral technique. The initial antenna is designed by analyzing air cylinders embedded in a thick silicon substrate, which has high relative permittivity. Then, to synthesize the PBG substrate, a binary particle swarm optimization (BPSO) algorithm is implemented in MATLAB to design a two-dimensional (2D) photonic crystal on a square lattice that improves the initially designed microstrip antenna. The unit cell is divided equally into many square pixels, each of which is filled with one of two dielectric materials, silicon or air, corresponding to a binary word consisting of the binary digits 0 and 1. Finally, the performance of the initial antenna is compared with the BPSO-optimized antenna using different merit functions. The results show remarkable improvements in terms of the return loss and fractional bandwidth. Both microstrip patch antennas based on the synthesized photonic crystal substrate achieve noticeable sidelobe suppression. Furthermore, the first design, which is a dual-band antenna, shows a return loss improvement of 5.39 %, while the fractional bandwidth of the second design is increased by 128 % (bandwidth of 128 GHz), compared with the initial antenna based on the air-hole PBG substrate. Both antennas maintain a gain close to 9.17 dB. Also, the results show that the obtained antennas have resonant frequencies around 0.65 THz, as required for next-generation wireless communication technology and other interesting applications.

Recognizing binary shuffle squares is NP-hard

A shuffle of two words is formed by interleaving the characters into a new word, keeping the characters of each word in order. A word is a shuffle square if it is a shuffle of two identical words. Deciding whether a word is a shuffle square has been proved to be NP-complete independently by Buss and Soltys [5] and Rizzi and Vialette [20], the former proving the result for alphabets as small as 9 letters. We prove in this paper that deciding whether a binary word is a shuffle square is NP-complete.

The ideal entropy of BCI-algebras and its application in the binary linear codes

This paper defines the concept of ideal entropy for BCI-algebras in general, and it tries to describe some of its properties. Moreover, the present study will show that $$ F_{2}^{n} $$ (i.e., sets of every binary code word of length n) is a BCI-algebra, and that each ideal of $$ F_{2}^{n} $$ is a linear code. The present study defines the concept of cosets by using the quotient BCI-algebra $$ \frac{{F_{2}^{n} }}{I} $$ and obtains their properties. This study defines the complement of a linear code, which is itself a linear code, which is denoted by the symbol Cc. Further, the present study defines the standard complement of a linear code, which is unique. This study proves that each equivalence class in $$ F_{2}^{n} /C^{c} $$ contains one and only one code word of the linear code C. This property can be used for decoding. Finally, the present study shows that two linear codes are equivalent if and only if they have the same ideal entropy.

IBoW-LCD: An Appearance-Based Loop-Closure Detection Approach Using Incremental Bags of Binary Words

In this paper, we introduce iBoW-LCD, a novel appearance-based loop closure detection method. The presented approach makes use of an incremental Bag-of-Words (BoW) scheme based on binary descriptors to retrieve previously seen similar images, avoiding any vocabulary training stage usually required by classic BoW models. In addition, to detect loop closures, iBoW-LCD builds on the concept of dynamic islands, a simple but effective mechanism to group similar images close in time, which reduces the computational times typically associated to Bayesian frameworks. Our approach is validated using several indoor and outdoor public datasets, taken under different environmental conditions, achieving a high accuracy and outperforming other state-of-the-art solutions.

Subword complexity and power avoidance

We begin a systematic study of the relations between subword complexity of infinite words and their power avoidance. Among other things, we show that–the Thue–Morse word has the minimum possible subword complexity over all overlap-free binary words and all (73)-power-free binary words, but not over all (73)+-power-free binary words;–the twisted Thue–Morse word has the maximum possible subword complexity over all overlap-free binary words, but no word has the maximum subword complexity over all (73)-power-free binary words;–if some word attains the minimum possible subword complexity over all square-free ternary words, then one such word is the ternary Thue word;–the recently constructed 1-2-bonacci word has the minimum possible subword complexity over all symmetric square-free ternary words.