Decomposed Form Research Articles

Tractable Explanations for d-DNNF Classifiers

Compilation into propositional languages finds a growing number of practical uses, including in constraint programming, diagnosis and machine learning (ML), among others. One concrete example is the use of propositional languages as classifiers, and one natural question is how to explain the predictions made. This paper shows that for classifiers represented with some of the best-known propositional languages, different kinds of explanations can be computed in polynomial time. These languages include deterministic decomposable negation normal form (d-DNNF), and so any propositional language that is strictly less succinct than d-DNNF. Furthermore, the paper describes optimizations, specific to Sentential Decision Diagrams (SDDs), which are shown to yield more efficient algorithms in practice.

Lower Bounds on Intermediate Results in Bottom-Up Knowledge Compilation

Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a class of circuits - because optimal compiled representations are provably large, the problem is not the compilation algorithm as much as the choice of a language too restrictive for the input. In contrast, in this paper, we look at CNF formulas for which very small circuits exists and look at the efficiency of their bottom-up compilation in one of the most general languages, namely that of structured decomposable negation normal forms (str-DNNF). We prove that, while the inputs have constant size representations as str-DNNF, any bottom-up compilation in the general setting where conjunction and structure modification are allowed takes exponential time and space, since large intermediate results have to be produced. This unconditionally proves that the inefficiency of bottom-up compilation resides in the bottom-up paradigm itself.

Propagation complete encodings of smooth DNNF theories

We investigate conjunctive normal form (CNF) encodings of a function represented with a decomposable negation normal form (DNNF). Several encodings of DNNFs and decision diagrams were considered by (Abío et al., 2016). The authors differentiate between encodings which implement consistency or domain consistency by unit propagation from encodings which are unit refutation complete or propagation complete. The difference is that in the former case we do not care about propagation strength of the encoding with respect to the auxiliary variables while in the latter case we treat all variables (the main and the auxiliary ones) in the same way. The currently known encodings of DNNF theories implement domain consistency. Building on these encodings we generalize the result of (Abío et al., 2016) on a propagation complete encoding of decision diagrams and present a propagation complete encoding of a DNNF and its generalization for variables with finite domains.

SF6 and SOF2 interaction studies on novel Tricycle Red Phosphorene sheets based on first-principles studies

Nowadays, the two-dimensional semiconductor-based sensor has been widely used to sense different toxic gas and vapour molecules due to their high sensitivity, selectivity, and stability. In the present work, we explored the structural firmness including electronic properties and adsorption behaviour of insulating gas, sulfur hexafluoride (SF6), and its decomposed form thionyl fluoride (SOF2) on Tricycle Red Phosphorene (TRP) using density functional theory method. Noticeably, the TRP nanosheet shows semiconducting nature with an indirect band gap of 1.139 eV. Chiefly, three dissimilar prominent interaction sites comprising bridge, top, and valley-sites of SF6 and SOF2 gases on TRP nanosheet were explored. In addition, the computed adsorption energy of these interaction sites is observed between −0.089 eV to −0.407 eV supporting van der Waals's interaction with regard to insulating gas and TRP substrate. The overall outcomes support that the TRP nanosheet can be cogently used as a sensor to monitor the leakage of insulating gases present in gas-insulated switch gears.

Orbital decompositions and integrable pseudosymmetries of control systems

Local decompositions of nonlinear dynamical control systems are investigated. We use orbital equivalences to transform systems into decomposed forms. In the language of infinite jets, every control system is interpreted as an infinite dimensional manifold. Each orbital decomposition of the system defines an invariant distribution on this manifold. A local basis of this distribution is an integrable pseudosymmetry of the system. An algorithm for constructing orbital decompositions is given and demonstrated by the example of the Kapitsa pendulum system. It is also shown how to use orbital decompositions to plan trajectories.

Going beyond the traditional EKC hypothesis: a panel quantile approach

ABSTRACT The traditional environmental Kuznets curve (EKC) hypothesis focuses on the relationship between economic growth and a few types of pollutants. Moreover, most previous studies examined EKC based on ‘Black-box structure’ rather than decomposed form. Therefore, this study investigates the effect of decomposed growth on environmental quality for 108 countries from 2000–2018 using the panel mean and quantile regressions. The panel data result confirms that most countries’ environment is worse because of the scale and technique effects, which supports the rising part of EKC. But, the quantile result reveals that the relationship between decomposed growth and environmental quality is insignificant in most quantiles in most countries. Therefore, countries need to achieve more environment-friendly economic activities and technologies, develop a self-correcting mechanism, and apply the Porter hypothesis.

Covariant 3+1 correspondence of the spatially covariant gravity and the degeneracy conditions

A necessary condition for a generally covariant scalar-tensor theory to be ghostfree is that it contains no extra degrees of freedom in the unitary gauge, in which the Lagrangian corresponds to the spatially covariant gravity. Compared with analyzing the scalar-tensor theory directly, it is simpler to map the spatially covariant gravity to the generally covariant scalar-tensor theory using the gauge recovering procedures. In order to ensure the resulting scalar-tensor theory to be ghostfree absolutely, i.e., no matter if the unitary gauge is accessible, a further covariant degeneracy/constraint analysis is required. We develop a method of covariant $3+1$ correspondence, which maps the spatially covariant gravity to the scalar-tensor theory in $3+1$ decomposed form without fixing any coordinates. Then the degeneracy conditions to remove the extra degrees of freedom can be found easily. As an illustration of this approach, we show how the Horndeski theory is recovered from the spatially covariant gravity. This approach can be used to find more general ghostfree scalar-tensor theory.

Quintic-scaling rank-reduced coupled cluster theory with single and double excitations.

We consider the rank-reduced coupled-cluster theory with single and double (RR-CCSD) excitations introduced recently [Parrish et al., J. Chem. Phys. 150, 164118 (2019)]. The main feature of this method is the decomposed form of doubly excited amplitudes, which are expanded in the basis of largest magnitude eigenvectors of MP2 or MP3 amplitudes. This approach enables a substantial compression of amplitudes with only minor loss of accuracy. However, the formal scaling of the computational costs with the system size (N) is unaffected in comparison with the conventional CCSD theory (∝N6) due to the presence of some terms quadratic in amplitudes, which do not naturally factorize to a simpler form even within the rank-reduced framework. We show how to solve this problem, exploiting the fact that their effective rank increases only linearly with the system size. We provide a systematic way to approximate the problematic terms using the singular value decomposition and reduce the scaling of the RR-CCSD iterations down to the level of N5. This is combined with an iterative method of finding dominant eigenpairs of MP2 or MP3 amplitudes, which eliminates the necessity to perform the complete diagonalization, making the cost of this step proportional to the fifth power of the system size, as well. Next, we consider the evaluation of perturbative corrections to CCSD energies resulting from triply excited configurations. The triply excited amplitudes present in the CCSD(T) method are decomposed to the Tucker-3 format using the higher-order orthogonal iteration procedure. This enables us to compute the energy correction due to triple excitations non-iteratively with N6 cost. The accuracy of the resulting rank-reduced CCSD(T) method is studied for both total and relative correlation energies of a diverse set of molecules. Accuracy levels better than 99.9% can be achieved with a substantial reduction of the computational costs. Concerning the computational timings, the break-even point between the rank-reduced and conventional CCSD implementations occurs for systems with about 30-40 active electrons.

On Some Modules Supported in the Chow Variety

The study of Chow varieties of decomposable forms lies at the confluence of algebraic geometry, commutative algebra, representation theory and combinatorics. There are many open questions about homological properties of Chow varieties and interesting classes of modules supported on them. The goal of this note is to survey some fundamental constructions and properties of these objects, and to propose some new directions of research. Our main focus will be on the study of certain maximal Cohen-Macaulay modules of covariants supported on Chow varieties, and on defining equations and syzygies. We also explain how to assemble Tor groups over Veronese subalgebras into modules over a Chow variety, leading to a result on the polynomial growth of these groups.

Coarticulation across morpheme boundaries: An ultrasound study of past-tense inflection in Scottish English

It has been hypothesized that morphologically-complex words are mentally stored in a decomposed form, often requiring online composition during processing. Morphologically-simple words can only be stored as a whole. The way a word is stored and retrieved is thought to influence its realization during speech production, so that when retrieval requires less time, the articulatory plan is executed faster. Faster articulatory execution could result in more coarticulation. Accordingly, we hypothesized that morphologically-simple words might be produced with more coarticulation than apparently homophonous morphologically-complex words, because the retrieval of monomorphemic forms is direct, in contrast to morphologically-complex ones, which might need to be composed online into full word forms. Using Ultrasound Tongue Imaging, we tested this hypothesis with nine speakers of Scottish English. Over two days of training, participants learned phonemically identical monomorphemic and morphologically-complex nonce words, while on the third consecutive testing day, they produced them in two prosodic contexts. Two types of articulatory analyses revealed no systematic differences in coarticulation between monomorphemic and morphologically-complex items, yet a few speakers did idiosyncratically produce some morphological effects on articulation. Our work contributes to our understanding of how morphologically complex words are stored and processed during speech production.

Breast cancer detection using an ensemble deep learning method

In this work, the effectiveness of the deep learning model is applied for one-dimensional data when converted to images. This work is based on the effective conversion of one-dimensional data to images and designing a stacked ensemble deep learning model that can increase the performance of classification accuracy in comparison to single models. Breast cancer detection from gene expression dataset and breast histopathology images is considered using the proposed ensemble model. The gene expression data is one-dimensional. Using the t-Distributed Stochastic Neighbor embedding technique and Convex Hull algorithm the one-dimensional data is converted to an image. Existing methods are using the datasets directly for training and classification, whereas the proposed method uses the dataset as well as the decomposed forms of the same for improving the performance. It involves two-stage classification. The first stage consists of three Convolutional Neural Networks as the base classifiers. Empirical Wavelet Transform and Variational Mode Decomposition are the two methods used to decompose the dataset so that the models can be trained at the molecular level, making our model robust in comparison to state-of-the-art methods. The first stage classification outcomes are used to train the second stage classifier “Multilayer Perceptron”. The gene expression dataset collected from Mendeley and is used for the generation of two-dimensional synthetic datasets. The synthetic datasets and breast histopathology image datasets are used for the training and validation of the proposedmodel. The improved results obtained in this work show the effectiveness of our method

Decentralized Failure-Tolerant Optimization of Electric Vehicle Charging

We present a decentralized failure-tolerant algorithm for optimizing electric vehicle (EV) charging, using charging stations as computing agents. The algorithm is based on the alternating direction method of multipliers (ADMM) and it has the following features: (i) It handles coupling constraints for capacity, peak demand, and ancillary services. (ii) It does not require a central agent collecting information and performing coordination (e.g., an aggregator), instead all agents exchange information and computations are carried out in a fully decentralized fashion. (iii) It can withstand the failure of any number of computing agents, as long as the remaining computing agents are in a connected communications network. We construct this algorithm by reformulating the optimal EV charging problem in a decomposable form, amenable to ADMM, and then developing efficient decentralized solution methods for the subproblems dealing with coupling constraints. We conduct numerical experiments on industry-scale synthetic EV charging datasets, with up to 1 152 charging stations, using a high-performance computing cluster. The experiments demonstrate that the proposed algorithm can solve the optimal EV charging problem fast enough to permit the integration of EV charging with real-time electricity markets, even in the presence of failures.

Stability Analysis of Multiscale Bubble Entropy and Power Metric based Seizure Detection Technique with MLA

In this paper, we explore the use of multiscale bubble entropy and power metric for feature extraction procedure and extend it with MLA and stability analysis to design a reliable multichannel seizure detection technique. First, we represent the multichannel EEG signal in 2D matrix form and then apply AM FM model to exploit the decomposed form of EEG. Thereafter, we construct the complexity coefficient using multiscale bubble entropy analysis from decomposed EEG wave. Then, second feature set is formed by using simple and efficient power procedure to obtain absolute power index and relative power index. Using two machine learning approaches, classification performance of proposed approach is explored to correctly identify the epileptic seizures. To show the robustness of multiscale bubble entropy, the stability analysis is performed with normal EEG dataset. Experimental results demonstrate that our proposed technique can effectively detect the epileptic seizures and achieve a superior classification performance with the ANN classifier compared to KNN classifier. This method provides higher discriminating capability with greater stability, so that they could detect wider range of seizure and thus help advance the current diagnosis system.

Bell-Type Correlation at Quantum Phase Transitions in Spin-1 Chain.

For the identification of non-trivial quantum phase, we exploit a Bell-type correlation that is applied to the one-dimensional spin-1 XXZ chain. It is found that our generalization of bipartite Bell correlation can take a decomposed form of transverse spin correlation together with high-order terms. The formulation of the density-matrix renormalisation group is utilized to obtain the ground state of a given Hamiltonian with non-trivial phase. Subsequently Bell-type correlation is evaluated through the analysis of the matrix product state. Diverse classes of quantum phase transitions in the spin-1 model are identified precisely through the evaluation of the first and the second moments of the generalized Bell correlations. The role of high-order terms in the criticality has been identified and their physical implications for the quantum phase have been revealed.

Multi-target tracking algorithm based on PHD filter against multi-range-false-target jamming

Multi-range-false-target (MRFT) jamming is particularly challenging for tracking radar due to the dense clutter and the repeated multiple false targets. The conventional association-based multi-target tracking (MTT) methods suffer from high computational complexity and limited usage in the presence of MRFT jamming. In order to solve the above problems, an efficient and adaptable probability hypothesis density (PHD) filter is proposed. Based on the gating strategy, the obtained measurements are firstly classified into the generalized newborn target and the existing target measurements. The two categories of measurements are independently used in the decomposed form of the PHD filter. Meanwhile, an amplitude feature is used to suppress the dense clutter. In addition, an MRFT jamming suppression algorithm is introduced to the filter. Target amplitude information and phase quantization information are jointly used to deal with MRFT jamming and the clutter by modifying the particle weights of the generalized newborn targets. Simulations demonstrate the proposed algorithm can obtain superior correct discrimination rate of MRFT, and high-accuracy tracking performance with high computational efficiency in the presence of MRFT jamming in the dense clutter.

Corrigendum to ``Bounds for the solutions of $S$-unit equations and decomposable form equations II", Publ. Math. Debrecen 94 (2019), 507--526

Corrigendum to ``Bounds for the solutions of $S$-unit equations and decomposable form equations II", Publ. Math. Debrecen 94 (2019), 507--526

Vortex force maps for three-dimensional unsteady flows with application to a delta wing

Abstract

An Extension of Gröbner Basis Theory to Indexed Polynomials Without Eliminations

In computer algebra, it remains to be challenging to establish general computational theories for determining the equivalence of indexed polynomials. In previous work, the author solved the equivalence determination problem for Riemann tensor polynomials by extending Grobner basis theory. This paper extends the previous work to more general indexed polynomials that involve no eliminations of indices and functions, by the method of ST-restricted rings. A decomposed form of the Grobner basis of the defining syzygy set in each ST-restricted ring is provided, and then the canonical form of an indexed polynomial proves to be the normal form with respect to the Grobner basis in the ST-fundamental restricted ring.

Visible-light-induced addition of carboxymethanide to styrene from monochloroacetic acid.

Where monochloroacetic acid is widely used as a starting material for the synthesis of relevant groups of compounds, many of these synthetic procedures are based on nucleophilic substitution of the carbon chlorine bond. Oxidative or reductive activation of monochloroacetic acid results in radical intermediates, leading to reactivity different from the traditional reactivity of this compound. Here, we investigated the possibility of applying monochloroacetic acid as a substrate for photoredox catalysis with styrene to directly produce γ-phenyl-γ-butyrolactone. Instead of using nucleophilic substitution, we cleaved the carbon chlorine bond by single-electron reduction, creating a radical species. We observed that the reaction works best in nonpolar solvents. The reaction does not go to full conversion, but selectively forms γ-phenyl-γ-butyrolactone and 4-chloro-4-phenylbutanoic acid. Over time the catalyst precipitates from solution (perhaps in a decomposed form in case of fac-[Ir(ppy)3]), which was proven by mass spectrometry and EPR spectroscopy for one of the catalysts (N,N-5,10-di(2-naphthalene)-5,10-dihydrophenazine) used in this work. The generation of HCl resulting from lactone formation could be an additional problem for organometallic photoredox catalysts used in this reaction. In an attempt to trap one of the radical intermediates with TEMPO, we observed a compound indicating the generation of a chloromethyl radical.

An Offloading Mechanism Towards SE–EE Experiences Tradeoff in Heterogeneous Cellular Networks

To achieve a tradeoff between spectral efficiency (SE) and energy efficiency (EE) experiences, we design an offloading mechanism to maximize the sum of weighted logarithmic utilities with respect to SE and EE for heterogeneous cellular networks, where the weighting parameters are used for adjusting the SE–EE experiences. Unlike the most existing offloading mechanisms that often try to find a tradeoff between SE and EC (energy consumption), we concentrate on a tradeoff between SE–EE experiences in our mechanism. That is to say, our mechanism directly optimizes EE and is weighted in favour of SE–EE fairness. To solve the finally formulated problem in a mixed-integer and nonlinear form, we firstly make some relaxation for the optimization objective to obtain its an upper bound. Then, we perform a decoupling operation to achieve a decomposable form of dual problem. Finally, we develop a feasible algorithm that can be well implemented in a distributed manner. Numerical results show that the designed mechanism can definitely reach a tradeoff between SE–EE experiences.