Minimization of Binary Decision Diagrams for Systems of Completely Defined Boolean Functions using Algebraic Representations of Cofactors

In design systems for digital VLSI (very large integrated circuits), the BDD is used for VLSI verification, as well as for technologically independent optimization, performed as the first stage in the synthesis of logic circuits in various technological bases. BDD is an acyclic graph defining a Boolean function or a system of Boolean functions. Each vertex of this graph corresponds to the complete or reduced Shannon expansion formula. Having constructed BDD representation for systems of Boolean functions, it is possible to perform additional logical optimization based on the proposed method of searching for algebraic representations of cofactors (subfunctions) of the same BDD level in the form of a disjunction or conjunction of other cofactors of this BDD level. The method allows to reduce the number of literals by replacing the Shannon expansion formulas with simpler formulas that are disjunctions or conjunctions of cofactors, and to reduce the number of literals in specifying a system of Boolean functions. The number of literals in algebraic multilevel representations of systems of fully defined Boolean functions is the main optimization criterion in the synthesis of combinational circuits from library logic gates.

Logical minimization for combinatorial structure in FPGA

The paper describes the research results of application efficiency of minimization programs of functional descriptions of combinatorial logic blocks, which are included in digital devices projects that are implemented in FPGA. Programs are designed for shared and separated function minimization in a disjunctive normal form (DNF) class and minimization of multilevel representations of fully defined Boolean functions based on Shannon expansion with finding equal and inverse cofactors. The graphical form of such representations is widely known as binary decision diagrams (BDD). For technological mapping the program of "enlargement" of obtained Shannon expansion formulas was applied in a way that each of them depends on a limited number of k input variables and can be implemented on one LUT-k – a programmable unit of FPGA with k input variables. It is shown that a preliminary logic minimization, which is performed on the domestic programs, allows improving design results of foreign CAD systems such as Leonardo Spectrum (Mentor Graphics), ISE (Integrated System Environment) Design Suite and Vivado (Xilinx). The experiments were performed for FPGA families’ Virtex-II PRO, Virtex-5 and Artix-7 (Xilinx) on standard threads of industrial examples, which define both DNF systems of Boolean functions and systems represented as interconnected logical equations.

Feature Extraction Based on Non-Subsampled Shearlet Transform (NSST) with Application to SAR Image Data

Considering the defaults in synthetic aperture radar (SAR) image feature extraction, an SAR target recognition method based on non-subsampled Shearlet transform (NSST) was proposed with application to target recognition. NSST was used to decompose an SAR image into multilevel representations. These representations were translation-invariant, and they could well reflect the dominant and detailed properties of the target. During the machine learning classification stage, the joint sparse representation was employed to jointly represent the multilevel representations. The joint sparse representation could represent individual components independently while considering the inner correlations between different components. Therefore, the precision of joint representation could be enhanced. Finally, the target label of the test sample was determined according to the overall reconstruction error. Experiments were conducted on the MSTAR dataset to examine the proposed method, and the results confirmed its validity and robustness under the standard operating condition, configuration variance, depression angle variance, and noise corruption.

The search for subsystems of related functions from multilevel representation of systems of Boolean functions1

One of the directions of logical optimization of multilevel representations of systems of Boolean functions is the methods based on the search of subsystems of functions that have the same parts in the domains of functions of selected subsystems. Such subsystems are called related. The good relationship of functions leads to the appearance of a large number of identical structural parts (conjunctions, algebraic expressions, subfunctions, etc.) in optimized forms of representation of functions which are used in the construction of combinational logic circuits. The more the functions of the selected subsystem are related, the sooner it is expected that in the representations of the functions of this subsystem will be more identical subexpressions and synthesized logic circuits will have less complexity. We describe software-implemented algorithms for extracting subsystems of related functions from a BDD representation of a system of Boolean functions based on introduced numerical estimates of the relationship of BDD representations of functions. The relationship of Boolean functions is the presence of Boolean vectors, where the functions take the value as one, or of the same equations in BDD representations. BDD representations of Boolean functions are compact forms defining functions and are constructed as the result of Shannon decomposition of the functions of the original system (resulting from the decomposition of subfunctions) by all variables, which the functions of the original system depend on. The experiments show the effectiveness of proposed algorithms and programs in the synthesis of logic circuits from logic elements library.

Neural dynamics of semantic composition

Human speech comprehension is remarkable for its immediacy and rapidity. The listener interprets an incrementally delivered auditory input, millisecond by millisecond as it is heard, in terms of complex multilevel representations of relevant linguistic and nonlinguistic knowledge. Central to this process are the neural computations involved in semantic combination, whereby the meanings of words are combined into more complex representations, as in the combination of a verb and its following direct object (DO) noun (e.g., “eat the apple”). These combinatorial processes form the backbone for incremental interpretation, enabling listeners to integrate the meaning of each word as it is heard into their dynamic interpretation of the current utterance. Focusing on the verb-DO noun relationship in simple spoken sentences, we applied multivariate pattern analysis and computational semantic modeling to source-localized electro/magnetoencephalographic data to map out the specific representational constraints that are constructed as each word is heard, and to determine how these constraints guide the interpretation of subsequent words in the utterance. Comparing context-independent semantic models of the DO noun with contextually constrained noun models reflecting the semantic properties of the preceding verb, we found that only the contextually constrained model showed a significant fit to the brain data. Pattern-based measures of directed connectivity across the left hemisphere language network revealed a continuous information flow among temporal, inferior frontal, and inferior parietal regions, underpinning the verb’s modification of the DO noun’s activated semantics. These results provide a plausible neural substrate for seamless real-time incremental interpretation on the observed millisecond time scales.

Robust Anomaly Detection in Videos Using Multilevel Representations

Detecting anomalies in surveillance videos has long been an important but unsolved problem. In particular, many existing solutions are overly sensitive to (often ephemeral) visual artifacts in the raw video data, resulting in false positives and fragmented detection regions. To overcome such sensitivity and to capture true anomalies with semantic significance, one natural idea is to seek validation from abstract representations of the videos. This paper introduces a framework of robust anomaly detection using multilevel representations of both intensity and motion data. The framework consists of three main components: 1) representation learning using Denoising Autoencoders, 2) level-wise representation generation using Conditional Generative Adversarial Networks, and 3) consolidating anomalous regions detected at each representation level. Our proposed multilevel detector shows a significant improvement in pixel-level Equal Error Rate, namely 11.35%, 12.32% and 4.31% improvement in UCSD Ped 1, UCSD Ped 2 and Avenue datasets respectively. In addition, the model allowed us to detect mislabeled anomalies in the UCDS Ped 1.

MCLEAN: Multilevel Clustering Exploration As Network

Finding useful patterns in datasets has attracted considerable interest in the field of visual analytics. One of the most common tasks is the identification and representation of clusters. However, this is non-trivial in heterogeneous datasets since the data needs to be analyzed from different perspectives. Indeed, highly variable patterns may mask underlying trends in the dataset. Dendrograms are graphical representations resulting from agglomerative hierarchical clustering and provide a framework for viewing the clustering at different levels of detail. However, dendrograms become cluttered when the dataset gets large, and the single cut of the dendrogram to demarcate different clusters can be insufficient in heterogeneous datasets. In this work, we propose a visual analytics methodology called MCLEAN that offers a general approach for guiding the user through the exploration and detection of clusters. Powered by a graph-based transformation of the relational data, it supports a scalable environment for representation of heterogeneous datasets by changing the spatialization. We thereby combine multilevel representations of the clustered dataset with community finding algorithms. Our approach entails displaying the results of the heuristics to users, providing a setting from which to start the exploration and data analysis. To evaluate our proposed approach, we conduct a qualitative user study, where participants are asked to explore a heterogeneous dataset, comparing the results obtained by MCLEAN with the dendrogram. These qualitative results reveal that MCLEAN is an effective way of aiding users in the detection of clusters in heterogeneous datasets. The proposed methodology is implemented in an R package available athttps://bitbucket.org/vda-lab/mclean.

MCLEAN: Multilevel Clustering Exploration As Network

Finding useful patterns in datasets has attracted considerable interest in the field of visual analytics. One of the most common tasks is the identification and representation of clusters. However, this is non-trivial in heterogeneous datasets since the data needs to be analyzed from different perspectives. Indeed, highly variable patterns may mask underlying trends in the dataset. Dendrograms are graphical representations resulting from agglomerative hierarchical clustering and provide a framework for viewing the clustering at different levels of detail. However, dendrograms become cluttered when the dataset gets large, and the single cut of the dendrogram to demarcate different clusters can be insufficient in heterogeneous datasets. In this work, we propose a visual analytics methodology called MCLEAN that offers a general approach for guiding the user through the exploration and detection of clusters. Powered by a graph-based transformation of the relational data, it supports a scalable environment for representation of heterogeneous datasets by changing the spatialization. We thereby combine multilevel representations of the clustered dataset with community finding algorithms. Our approach entails displaying the results of the heuristics to users, providing a setting from which to start the exploration and data analysis. To evaluate our proposed approach, we conduct a qualitative user study, where participants are asked to explore a heterogeneous dataset, comparing the results obtained by MCLEAN with the dendrogram. These qualitative results reveal that MCLEAN is an effective way of aiding users in the detection of clusters in heterogeneous datasets. The proposed methodology is implemented in an R package available at https://bitbucket.org/vda-lab/mclean

MCLEAN: Multilevel Clustering Exploration As Network

Finding useful patterns in datasets has attracted considerable interest in the field of visual analytics. One of the most common tasks is the identification and representation of clusters. However, this is non-trivial in heterogeneous datasets since the data needs to be analyzed from different perspectives. Indeed, highly variable patterns may mask underlying trends in the dataset. Dendrograms are graphical representations resulting from agglomerative hierarchical clustering and provide a framework for viewing the clustering at different levels of detail. However, dendrograms become cluttered when the dataset gets large, and the single cut of the dendrogram to demarcate different clusters can be insufficient in heterogeneous datasets. In this work, we propose a visual analytics methodology called MCLEAN that offers a general approach for guiding the user through the exploration and detection of clusters. Powered by a graph-based transformation of the relational data, it supports a scalable environment for representation of heterogeneous datasets by changing the spatialization. We thereby combine multilevel representations of the clustered dataset with community finding algorithms. Our approach entails displaying the results of the heuristics to users, providing a setting from which to start the exploration and data analysis. To evaluate our proposed approach, we conduct a qualitative user study, where participants are asked to explore a heterogeneous dataset, comparing the results obtained by MCLEAN with the dendrogram. These qualitative results reveal that MCLEAN is an effective way of aiding users in the detection of clusters in heterogeneous datasets. The proposed methodology is implemented in an R package available at https://bitbucket.org/vda-lab/mclean