Bit String Research Articles

Generalized predecessor existence problems for Boolean finite dynamical systems on directed graphs

A Boolean Finite Synchronous Dynamical System (BFDS, for short) consists of a finite number of objects that each maintains a boolean state, where after individually receiving state assignments, the objects update their state with respect to object-specific time-independent boolean functions synchronously in discrete time steps. The present paper studies the computational complexity of determining, given a boolean finite synchronous dynamical system, a configuration, which is a boolean vector representing the states of the objects, and a positive integer t, whether there exists another configuration from which the given configuration can be reached in t steps. It was previously shown that this problem, which we call the t-Predecessor Problem, is NP-complete even for t=1 if the update function of an object is either the conjunction of arbitrary fan-in or the disjunction of arbitrary fan-in.This paper studies the computational complexity of the t-Predecessor Problem for a variety of sets of permissible update functions as well as for polynomially bounded t. It also studies the t-Garden-Of-Eden Problem, a variant of the t-Predecessor Problem that asks whether a configuration has a t-predecessor, which itself has no predecessor. The paper obtains complexity theoretical characterizations of all but one of these problems.

Extreme Witnesses and Their Applications

We study the problem of computing the so called minimum and maximum witnesses for Boolean vector convolution. We also consider a generalization of the problem which is to determine for each positive value at a coordinate of the convolution vector, q smallest (largest) witnesses, where q is the minimum of a parameter k and the number of witnesses for this coordinate. We term this problem the smallest k-witness problem or the largest k-witness problem, respectively. We also study the corresponding smallest and largest k-witness problems for Boolean matrix product. First, we present an tilde{O}(n^{1.5}k^{0.5})-time algorithm for the smallest or largest k-witness problem for the Boolean convolution of two n-dimensional vectors, where the notation tilde{O}( ) suppresses polylogarithmic in n factors. In consequence, we obtain new upper time bounds on reporting positions of mismatches in potential string alignments and on computing restricted cases of the (min , +) vector convolution. Next, we present a fast (substantially subcubic in n and linear in k) algorithm for the smallest or largest k-witness problem for the Boolean matrix product of two ntimes n Boolean matrices. It yields fast algorithms for reporting k lightest (heaviest) triangles in a vertex-weighted graph.

Analogical proportions: From equality to inequality

Analogical proportions are statements of the form a is to b as c is to d. Such expressions compare the pair (a,b) with the pair (c,d). Previous papers have developed logical modelings of such proportions both in Boolean and in multiple-valued settings. They emphasize a reading of the proportion as “the way a and b differ is the same as c and d differ”. The ambition of this paper is twofold. The paper first provides a deeper understanding and further justifications of the Boolean modeling, before introducing analogical inequalities, where “as” is replaced by “as much as” in the comparison of two pairs. From an abstract viewpoint, analogical proportions are supposed to obey at least three postulates expressing reflexivity, symmetry, and stability under central permutation. Nevertheless these postulates are not enough to determine a single model and a minimality condition has to be added as shown in this paper. These models are organized in a complete lattice based on set inclusion. This leads us to discuss lower and upper approximations of the minimal model. Apart from being minimal, this model can also be evaluated in terms of Kolmogorov complexity via an expression reflecting the intended meaning of analogy. We show that the six Boolean patterns of the minimal model that make Boolean analogy true minimize this expression. Besides, analogical proportions extend to 4-tuples of Boolean vectors. This enables us to explain why analogical proportions also reads in terms of similarity (rather than difference, i.e., dissimilarity): a and d share the same presence or absence of features as b and c. Moreover, we establish a link between analogical proportion and Hamming distances between components of the proportion. We also emphasize that analogical proportions are pervasive in any comparison of two vectors a and d that implicitly induce the existence of “intermediary” vectors b and c forming together such a proportion. The similarity reading and the dissimilarity reading of a Boolean analogical proportion are no longer equivalent in the multiple-valued setting, where they give birth to two distinct options that are recalled. These options are also discussed with respect to their capability to handle so-called “continuous” logical proportions of the form a is to b as b is to c involving some idea of “betweenness”. In all the previously investigated issues, the pairs involved in the 4-tuples were compared via equalities of similarities or equalities of dissimilarities. This observation suggests to also consider statements of the form “a is to b at least as much as c is to d”, leading to the concept of “analogical inequalities”. Thus, instead of expressing equality between differences or similarities, as it is the case for analogical proportions, it is also interesting to express inequalities between such differences or similarities. Starting from the modeling of analogical proportions, we investigate the logical modeling of analogical inequalities, both in the Boolean and in the multiple-valued cases, and discuss their potential use in relation with some recent related work in computer vision.

Approaching Miscorrection-Free Performance of Product Codes With Anchor Decoding

Product codes (PCs) protect a 2-D array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the component codes. For this coding scheme, undetected errors in the component decoding-also known as miscorrections-significantly degrade the performance. In this paper, we propose a novel iterative decoding algorithm for PCs which can detect and avoid most miscorrections. The algorithm can also be used to decode many recently proposed classes of generalized PCs, such as staircase, braided, and half-product codes. Depending on the component code parameters, our algorithm significantly outperforms the conventional iterative decoding method. As an example, for double-error-correcting Bose-Chaudhuri-Hocquenghem component codes, the net coding gain can be increased by up to 0.4 dB. Moreover, the error floor can be lowered by orders of magnitude, up to the point where the decoder performs virtually identical to a genie-aided decoder that avoids all miscorrections. We also discuss post-processing techniques that can be used to reduce the error floor even further.

IMCS2: Novel Device-to-Architecture Co-Design for Low-Power In-Memory Computing Platform Using Coterminous Spin Switch

Spin switch (SS) is a promising spintronic device which exhibits compactness, low power, non-volatility, input–output isolation leveraging giant spin Hall effect, spin transfer torque, and dipolar coupling. In this paper, we propose a novel device-to-architecture co-design for an in-memory computing platform using coterminous SS (IMCS2), which could simultaneously work as non-volatile memory and reconfigurable in-memory logic (AND/NAND, OR/NOR, and XOR/XNOR) without add-on logic circuits to memory chip. The computed logic output could be simply read out like a normal magnetic random access memory bit cell using the shared memory peripheral circuits. Such intrinsic in-memory logic could be used to process data within memory to greatly reduce power-hungry and long distance data communication in the conventional von Neumann computing system. The IMCS2-based in-memory bulk bitwise Boolean vector operation shows ${\sim }9\times $ energy saving and ${\sim }3\times $ speedup compared with that of DRAM-based in-memory computing platform. We further employ in-memory multiplication to evaluate the performance of the proposed in-memory computing platform for vector–vector multiplication with different vector sizes.

Attribute reduction based on the Boolean matrix

Attribute reduction is an important preprocessing step in machine learning and pattern recognition. This paper introduces condition-attribute Boolean matrix and decision-attribute Boolean matrix and proposes a new attribute reduction model based on Boolean operations according to the concept of neighborhood rough set. Some operation rules of Boolean vectors are defined and an uncertainty measure, named attribute support function, is proposed to evaluate the importance degree of candidate attributes with respect to decision attributes. An attribute reduction algorithm based on the proposed measure is designed. Ten data sets selected from public data sources are used to compare the proposed algorithm with some existing algorithms. The experimental results show that the proposed reduction algorithm is feasible and effective.

Effects of fiber nonlinearity on error vector magnitude and bit error ratio for advanced modulation formats

Fiber nonlinear (NLI) noise, as well as amplified spontaneous emission (ASE) noise, degrades the performance of coherent optical fiber communications. We find that the temporal distribution of NLI noise, which is unlike that of ASE noise and depends on the waveform of signal pulse, has an impact on the estimation of error vector magnitude (EVM) and bit error ratio (BER). The influences of NLI noise, as well as ASE noise, on EVM and BER are analyzed for quadrature phase-shift keying and M-ary quadrature amplitude modulation systems. Modified theoretical formulas are proposed to estimate EVM and BER for the system under the effect of NLI noise, ASE noise, or mixing of these two noises. For system with mixing of ASE and NLI noises, according to our model, the optimal channel power for the best EVM is not corresponding to the best optical-signal-to-noise ratio. Our model is validated by numerical simulations.

Modeling DNA & RNA mutation using mset and topology

Mathematical equations are now found not only in the books, but also they help in finding solutions for the biological problems by explaining the technicality of the current biological models and providing predictions that can be validated and complemented to experimental and clinical studies. In this research paper, we use the mset theory to study DNA & RNA mutations to discover the mutation occurrence. Also, we use the link between the concept of the mset and topology to determine the compatibility or similarity between “types”, which may be the strings of bits, vectors, DNA or RNA sequences, etc.

DISTRIBUTED VIDEO IDENTIFICATION WITH PERCEPTUAL TAGS IN PEER-TO-PEER NETWORKS

Existing methods in Peer-to-Peer (P2P) networks mainly use file tags or cryptographic hashes of the entire file for video searching and identification. These methods however become insufficient to correctly identify a video when the name and format of the files are changed. In this paper, a distributed solution is proposed for video identification and copy detection in P2P networks, which represents a video file in the network with a set of (64-256) bits, named as perceptual tags. As such information is derived from the perceptual content of the video rather than its bitstream representation as in the case of cryptographic hashes, it provides a robust identification after the alterations in the file names and formats provided that the visual quality of the video is at acceptable levels. The paper first briefly discusses the requirements for a distributed perceptual tagging system considering the low computational power and low bandwidth of internet users. Then, it presents the proposed perceptual tag extraction method using the temporal differences between the video frame averages and the proposed distributed searching scheme for a P2P implementation. The proposed extraction and searching methods provide robustness to the alterations in video formats and small additions and cuttings in the video content as the typical processing in P2P environment and also achieve uniform distribution and storage load between the peers.

Analysis and Implementation of High Performance Reconfigurable Finite Impulse Response Filter Using Distributed Arithmetic

The finite impulse response (FIR) digital filters are commonly used in many digital signal processing systems. For higher order filters the implementation of reconfigurable random access memory based FIR filter becomes costly and the speed is reduced. This research paper presents an efficient distributed arithmetic (DA) based approach for reduced area and low power implementation of the FIR filters whose filter coefficients are dynamic in nature. Due to the complexity in implementation of higher order filters, a portion of bit serial based computation in the look up table (LUT) is used. However the shared LUTs are used instead of RAM based LUTs, Shared LUTs involves the concept of LUT partitioning where the coefficients are split into vectors of smaller bit lengths which reduce the depth of the LUT. The possible partial DA results for these vectors are stored in register banks that are shared between multiple DA units. Since the register banks are shared, the area is effectively reduced. Hence an application specific integrated circuits implementation is used. When compared to the existing 256 tap FIR filter, the area has been reduced by 62.16% for vector bit length (M), M = 2 and by 75.84% for M = 4 and the power consumption has been reduced by 42.67% for M = 2 and by 64.02% for M = 4.

Discovering grammar of an unknown text as an optimisation problem

This paper concerns the problem of discovering an unknown grammar from a text sample. The discovering methods are formulated as optimisation problems based on a binary representation of context-sensitive grammars. The representation starts with a longest possible vector of bits to, finally, make it more compact so as to be usable in practical applications. For the sake of simplicity, considered are only noncontracting (length preserving) grammars of order 2, excluding productions of the form P:A→B and those deriving the empty string, i.e P:A→ε.

Multiset topology via DNA and RNA mutation

Topology is the most important branch of modern mathematics, which plays an important role in applications. In this paper, we use the concept of the topology, based on the concept of multiset to solve an important problems in life (DNA and RNA mutation) to detect diseases and help biologists in the treatment of diseases. Also, we introduce a new theory that explains if there is an existence of a mutation or not, and we have a set of metric functions through which we examine the congruence and similarity and dissimilarity between “types,” which may be a strings of bits, vectors, DNA or RNA sequences, …, etc. Finally, we will introduce a theory that which can be used to know the existence and place of mutation.

Extraction of the Characteristic Attributes of Student Athletes using a Questionnaire using the Support Vector Machine

Providing special support for student athletes and creating future educational strategies are major issues for many universities. In this study, we created a questionnaire that comprised 77 multiple choice questions. After collecting the responses from 100 student athletes and 141 other students, we analyzed the characteristic attributes of student athletes. We considered the 278 combinations of question items and the response choices as the attributes to represent the students. A student is represented as a 278 dimensional boolean vector. Then, we applied the support vector machine (SVM) machine learning method with feature selection. The result confirmed that it is possible to distinguish between student athletes and other students with a 90% accuracy based on 16 characteristic attributes of the students, such as the following: they spend a lot of time in athletics clubs and not on their studies; they want to work for an economically rich life; they think that it is advantageous to search for jobs or complete their graduation if they have good grades; they have less interests in the international activities in campus life. Students aiming for professional and semiprofessional athletic careers are motivated for studying because of the competitiveness cultivated in their athletic careers.

Detection of Double-Compressed H.264/AVC Video Incorporating the Features of the String of Data Bits and Skip Macroblocks

Today’s H.264/AVC coded videos have a high quality, high data-compression ratio. They also have a strong fault tolerance, better network adaptability, and have been widely applied on the Internet. With the popularity of powerful and easy-to-use video editing software, digital videos can be tampered with in various ways. Therefore, the double compression in the H.264/AVC video can be used as a first step in the study of video-tampering forensics. This paper proposes a simple, but effective, double-compression detection method that analyzes the periodic features of the string of data bits (SODBs) and the skip macroblocks (S-MBs) for all I-frames and P-frames in a double-compressed H.264/AVC video. For a given suspicious video, the SODBs and S-MBs are extracted for each frame. Both features are then incorporated to generate one enhanced feature to represent the periodic artifact of the double-compressed video. Finally, a time-domain analysis is conducted to detect the periodicity of the features. The primary Group of Pictures (GOP) size is estimated based on an exhaustive strategy. The experimental results demonstrate the efficacy of the proposed method.

BoolFilter: an R package for estimation and identification of partially-observed Boolean dynamical systems

BackgroundGene regulatory networks govern the function of key cellular processes, such as control of the cell cycle, response to stress, DNA repair mechanisms, and more. Boolean networks have been used successfully in modeling gene regulatory networks. In the Boolean network model, the transcriptional state of each gene is represented by 0 (inactive) or 1 (active), and the relationship among genes is represented by logical gates updated at discrete time points. However, the Boolean gene states are never observed directly, but only indirectly and incompletely through noisy measurements based on expression technologies such as cDNA microarrays, RNA-Seq, and cell imaging-based assays. The Partially-Observed Boolean Dynamical System (POBDS) signal model is distinct from other deterministic and stochastic Boolean network models in removing the requirement of a directly observable Boolean state vector and allowing uncertainty in the measurement process, addressing the scenario encountered in practice in transcriptomic analysis.ResultsBoolFilter is an R package that implements the POBDS model and associated algorithms for state and parameter estimation. It allows the user to estimate the Boolean states, network topology, and measurement parameters from time series of transcriptomic data using exact and approximated (particle) filters, as well as simulate the transcriptomic data for a given Boolean network model. Some of its infrastructure, such as the network interface, is the same as in the previously published R package for Boolean Networks BoolNet, which enhances compatibility and user accessibility to the new package.ConclusionsWe introduce the R package BoolFilter for Partially-Observed Boolean Dynamical Systems (POBDS). The BoolFilter package provides a useful toolbox for the bioinformatics community, with state-of-the-art algorithms for simulation of time series transcriptomic data as well as the inverse process of system identification from data obtained with various expression technologies such as cDNA microarrays, RNA-Seq, and cell imaging-based assays.

Logical characterization of groups of data: a comparative study

This paper presents an approach for characterizing groups of data represented by Boolean vectors. The purpose is to find minimal set of attributes that allow to distinguish data from different groups. In this work, we precisely defined the multiple characterization problem and the algorithms that can be used to solve its different variants. Our data characterization approach can be related to Logical Analysis of Data and we propose thus a comparison between these two methodologies. The purpose of this paper is also to precisely study the properties of the solutions that are computed with regards to the topological properties of the instances. Experiments are thus conducted on real biological data.

Amplifying the Randomness of Weak Sources Correlated With Devices

The problem of device-independent randomness amplification against no-signaling adversaries has so far been studied under the assumption that the weak source of randomness is uncorrelated with the (quantum) devices used in the amplification procedure. In this work, we relax this assumption, and reconsider the original protocol of Colbeck and Renner using a Santha-Vazirani (SV) source. To do so, we introduce an SV-like condition for devices, namely that any string of SV source bits remains weakly random conditioned upon any other bit string from the same SV source and the outputs obtained when this further string is input into the devices. Assuming this condition, we show that a quantum device using a~singlet state to violate the chained Bell inequalities leads to full randomness in the asymptotic scenario of a large number of settings, for a restricted set of SV sources (with $0 \leq \varepsilon < (2^{(1/12)} - 1)/(2(2^{(1/12)} + 1)) \approx 0.0144$). We also study a device-independent protocol that allows for correlations between the sequence of boxes used in the protocol and the SV source bits used to choose the particular box from whose output the randomness is obtained. Assuming the SV-like condition for devices, we show that the honest parties can achieve amplification of the weak source, for the parameter range $0 \leq \varepsilon<0.0132$, against a class of attacks given as a mixture of product box sequences, made of extremal no-signaling boxes, with additional symmetry conditions. Composable security proof against this class of attacks is provided.

Efficient Length Doubling from Tweakable Block Ciphers

We present a length doubler, LDT, that turns an n-bit tweakable block cipher into an efficient and secure cipher that can encrypt any bit string of length [n..2n − 1]. The LDT mode is simple, uses only two cryptographic primitive calls (while prior work needs at least four), and is a strong length-preserving pseudorandom permutation if the underlying tweakable block ciphers are strong tweakable pseudorandom permutations. We demonstrate that LDT can be used to neatly turn an authenticated encryption scheme for integral data into a mode for arbitrary-length data.

Thermocompression bonding technology for multilayer superconducting quantum circuits

Extensible quantum computing architectures require a large array of quantum bits operating with low error rates. A quantum processor based on superconducting devices can be scaled up by stacking microchips that perform wiring, shielding, and computational functionalities. In this article, we demonstrate a vacuum thermocompression bonding technology that utilizes thin indium films as a welding agent to attach pairs of lithographically patterned chips. At 10 mK, we find a specific dc bond resistance of 49.2 μΩ cm2. We show good transmission up to 6.8 GHz in a tunnel-capped, bonded device as compared to a similar uncapped device. Finally, we fabricate and measure a set of tunnel-capped superconducting resonators, demonstrating that our bonding technology can be used in quantum computing applications.

Global-Local Temporal Saliency Action Prediction.

Action prediction on a partially observed action sequence is a very challenging task. To address this challenge, we first design a global-local distance model, where a global-temporal distance compares subsequences as a whole and local-temporal distance focuses on individual segment. Our distance model introduces temporal saliency for each segment to adapt its contribution. Finally, a global-local temporal action prediction model is formulated in order to jointly learn and fuse these two types of distances. Such a prediction model is capable of recognizing action of: 1) an on-going sequence and 2) a sequence with arbitrarily frames missing between the beginning and end (known as gap-filling). Our proposed model is tested and compared with related action prediction models on BIT, UCF11, and HMDB data sets. The results demonstrated the effectiveness of our proposal. In particular, we showed the benefit of our proposed model on predicting unseen action types and the advantage on addressing the gapfilling problem as compared with recently developed action prediction models.