Decomposed Form Research Articles

The eigenfunctions method in relation to diffuse reflection problems of the radiative energy transfer theory

Using the new method proposed earlier by the author, a solution of diffuse reflection problem is given in this report. A case of diffuse reflection of radiation from a semi-infinite absorbing and isotropically reflecting medium is presented, when in the elementary act of scattering there is a general law of redistribution of radiation by frequencies. In the approach presented here, conventionally called the method of ”decomposition of the resulting field” - DRF, in contrast to the previously widely used traditional method of ”decomposition of a single act” of scattering - DSA, the problem of diffuse reflection is solved without the use of any decomposition or special representation of the characteristic of the elementary act of scattering, i.e., the redistribution function of radiation by frequencies. The resulting radiation field, formed in the medium by means of multiple scatterings, is sought and constructed directly in the form of a bilinear series through a specially derived system of its own eigenfunctions. The physical basis of this approach lies in the fact that after each successive act of scattering, the field formed in the medium becomes more and more smoothed, so its direct representation in a decomposed form is more expedient than the traditionally used decomposition of a pre-known ”unsmoothed” characteristic of the elementary act of scattering.

The Effect of Aqueous Extract of Fenugreek Plant on the Pancreas in Rabbits Induced with Diabetes and the Histological Changes Occurring in Them

The study aimed to induce alloxan-induced diabetes in local white rabbits, study its effect on the pancreas, treat them with aqueous extract of fenugreek at a concentration of 200 mg/kg orally, and observe the histological changes. To complete the study 20 white rabbits were taken and divided into three groups; 1st group is the control group and this group was dosed with distilled water. 2nd group was treated with Alloxan and was injected intraperitoneally at a dose of 175 mg/kg. 3rd group is the group that was treated with the aqueous extract of fenugreek at a concentration of 200 mg/kg for 30 days. After the end of the injection and dosing period after 30 days, the animals were killed and the pancreas was removed to perform histological techniques on them. its the group treated with alloxan was observed that the pancreas was composed of exocrine glandular lobules with enlarged secretory cells within the pancreatic acinus, with the presence of pale nuclei lacking pigment. Also, blood congestion of the blood vessels was found between the lobules of the gland and the pancreatic gland showed hyperplasia of its glandular epithelial cells with nuclei devoid of pigment due to the loss of the basal pigment in them. Blood congestion of the blood vessels appeared in the gland between the lobules, and dense colloidal fibers appeared in them and contained fibroblasts and phagocytic cells and the group treated with the aqueous extract of the fenugreek plant :The pancreatic parenchyma contained normal exocrine glandular secretion units, where the cytoplasm and nuclei of these cells were located in the form of regular axes, septations between the lobules of the pancreas surrounded by thick-walled arteries containing blood. and the islets of Lankerhans appeared between the yeast-secreting lobules of the pancreas. They contained endocrine cells of alpha and beta cells surrounded by blood sinusoids. The interstitial tissue between the lobules is composed of loose connective tissue containing colloidal fibers the pancreatic tissue contained the serous secretory vasculature of yeasts, which were uniform in shape, and between them were found blood vessels excessive with blood, where blood was found in a decomposed form in them, with the presence of small channels inside the lobules that transport yeasts.

Design and Fabrication of Organic Waste Shredding System

Organic composting forms the backbone & basic necessity of a poor farmer. The traditional methods are not sufficient & satisfactory for chopping the crop residues. Whereas buying the chemical fertilizer is not possible for every farmer due to its high cost and also food waste contains high calorific and nutritive values. In all the cities and places, organic waste is dumped or disposed in landfill or discarded, which causes the public health hazards and diseases like malaria, cholera, typhoid. Inadequate management of wastes like uncontrolled dumping bears several adverse consequences. Shredding machine is used for shredding and converting macro organic waste products into small or micro easily decomposable form, which can be used as organic manure. Organic waste shredder designed should perfect to shred all kinds of waste products. The organic waste shredded will be in small pieces to enable the farmer to make use of it as feed for manure or organic manure and biogas feed. This shredder can be operated with a motor.

A Compiler for Weak Decomposable Negation Normal Form

This paper integrates weak decomposable negation normal form (wDNNF) circuits, introduced by Akshay et al. in 2018, into the knowledge compilation map. This circuit type generalises decomposable negation normal form (DNNF) circuits in such a way that they allow a restricted form of sharing variables among the inputs of a conjunction node. We show that wDNNF circuits have the same properties as DNNF circuits regarding the queries and transformations presented in the knowledge compilation map, whilst being strictly more succinct than DNNF circuits (that is, they can represent Boolean functions compactly). We also present and evaluate a knowledge compiler, called Bella, for converting CNF formulae into wDNNF circuits. Our experiments demonstrate that wDNNF circuits are suitable for configuration instances.

Efficient Learning of PDEs via Taylor Expansion and Sparse Decomposition into Value and Fourier Domains

Accelerating the learning of Partial Differential Equations (PDEs) from experimental data will speed up the pace of scientific discovery. Previous randomized algorithms exploit sparsity in PDE updates for acceleration. However such methods are applicable to a limited class of decomposable PDEs, which have sparse features in the value domain. We propose Reel, which accelerates the learning of PDEs via random projection and has much broader applicability. Reel exploits the sparsity by decomposing dense updates into sparse ones in both the value and frequency domains. This decomposition enables efficient learning when the source of the updates consists of gradually changing terms across large areas (sparse in the frequency domain) in addition to a few rapid updates concentrated in a small set of “interfacial” regions (sparse in the value domain). Random projection is then applied to compress the sparse signals for learning. To expand the model applicability, Taylor series expansion is used in Reel to approximate the nonlinear PDE updates with polynomials in the decomposable form. Theoretically, we derive a constant factor approximation between the projected loss function and the original one with poly-logarithmic number of projected dimensions. Experimentally, we provide empirical evidence that our proposed Reel can lead to faster learning of PDE models (70-98% reduction in training time when the data is compressed to 1% of its original size) with comparable quality as the non-compressed models.

Copulas, possession, and the temporary-permanent distinction in Mashi: Evidence for decompositional HAVE

It is cross-linguistically common to find a distinction between “temporary” vs. “permanent” states in copular verbs, e.g., Spanish estar and ser (see Deo et al. 2017). In Mashi [shr] (Bantu, JD53; Maho 2009), a similar temporary-permanent distinction holds not only of the two copular be-verbs in the language, -li (temporary state) and -ba (permanent state), but also of the two possessive have-verbs, -dwiire and -jira; -dwiire indicates temporary possession, while -jira instead indicates permanent possession. This parallelism provides a novel argument in favor of a decompositional approach to possessive verbs (Freeze 1992, Kayne 1993, Harley 1998). The analysis is further supported through patterns of allomorphy where HAVE is realized in its decomposed form, BE + comitative, in Mashi. I analyze the patterns using a Spanning Insertion analysis (Williams 2003, Svenonius 2012, 2016, Merchant 2015).

The Image Biomarker Standardization Initiative: Standardized Convolutional Filters for Reproducible Radiomics and Enhanced Clinical Insights.

Filters are commonly used to enhance specific structures and patterns in images, such as vessels or peritumoral regions, to enable clinical insights beyond the visible image using radiomics. However, their lack of standardization restricts reproducibility and clinical translation of radiomics decision support tools. In this special report, teams of researchers who developed radiomics software participated in a three-phase study (September 2020 to December 2022) to establish a standardized set of filters. The first two phases focused on finding reference filtered images and reference feature values for commonly used convolutional filters: mean, Laplacian of Gaussian, Laws and Gabor kernels, separable and nonseparable wavelets (including decomposed forms), and Riesz transformations. In the first phase, 15 teams used digital phantoms to establish 33 reference filtered images of 36 filter configurations. In phase 2, 11 teams used a chest CT image to derive reference values for 323 of 396 features computed from filtered images using 22 filter and image processing configurations. Reference filtered images and feature values for Riesz transformations were not established. Reproducibility of standardized convolutional filters was validated on a public data set of multimodal imaging (CT, fluorodeoxyglucose PET, and T1-weighted MRI) in 51 patients with soft-tissue sarcoma. At validation, reproducibility of 486 features computed from filtered images using nine configurations × three imaging modalities was assessed using the lower bounds of 95% CIs of intraclass correlation coefficients. Out of 486 features, 458 were found to be reproducible across nine teams with lower bounds of 95% CIs of intraclass correlation coefficients greater than 0.75. In conclusion, eight filter types were standardized with reference filtered images and reference feature values for verifying and calibrating radiomics software packages. A web-based tool is available for compliance checking.

On completely decomposable defining equations of finite sets in P n

Let I ( Γ ) be the homogeneous ideal of a finite set Γ in P n of d points in linearly general position. In 1972, Saint-Donat proved that if d ≤ 2 n then I ( Γ ) is generated by completely decomposable quadratic polynomials. Later, R. Treger generalized this result by showing that I ( Γ ) is generated by forms of degree ≤ m if d ≤ mn for some m ≥ 2 . This paper aims to generalize Saint-Donat’s work in a different direction by proving that the degree m piece of I ( Γ ) can be generated by completely decomposable forms of degree m if and only if d ≤ mn . Communicated by Daniel Erman

On the role of logical separability in knowledge compilation

Knowledge compilation is an alternative solution to address demanding reasoning tasks with high complexity via converting knowledge bases into a suitable target language. The notion of logical separability, proposed by Levesque, offers a general explanation for the tractability of clausal entailment for two remarkable languages: decomposable negation normal form and prime implicates. It is interesting to explore what role logical separability plays in problem tractability. In this paper, we apply the notion of logical separability to a number of reasoning problems within the context of propositional logic: satisfiability checking (CO), clausal entailment checking (CE), model counting (CT), model enumeration (ME) and forgetting (FO), as well as their dual tasks, contributing to several recursive procedures. We provide the corresponding logical separability based properties: CO-logical separability, CE-logical separability, CT-logical separability, ME-logical separability and their duals. Based on these properties, we then identify four novel normal forms: CO-LSNNF, CE-LSNNF, CT-LSNNF and ME-LSNNF, as well as their dual languages. We show that each of them is the necessary and sufficient condition under which the corresponding procedure is correct. We finally integrate the above normal forms into the knowledge compilation map.

Can we recover an integral quadratic form by representing all its subforms?

Let o be the ring of integers of a number field. If f is a quadratic form over o and g is another quadratic form over o which represents all proper subforms of f, does g represent f? We show that if g is indefinite, then g indeed represents f. However, when f is positive definite and indecomposable, then there exists a g which represents all proper subforms of f but not f itself. Along the way we give a new characterization of positive definite decomposable quadratic forms over o and a number-field generalization of the finiteness theorem of representations of quadratic forms by quadratic forms over Z[13, Theorem 3.3] which asserts that given any infinite set S of classes of positive definite integral quadratic forms over o of a fixed rank, there exists a finite subset S0 of S with the property that a positive definite quadratic form over o represents all classes in S if and only if it represents all classes in S0.

Wage Differentials in the Post Liberalized Labor Market in Paksitan

ABSTRACT: In this paper, we investigate the wage differentials that exist in the post-liberalized labor market in Pakistan. The increasing wage differential contradicts standard labor theories and models. The literature also confirms the existence of wage differentials across different labor markets both in industrialized and non-industrialized countries. The firms compensate the workers both on their observable and unobservable characteristics. The mincer equation used in its semi-logarithmic decomposed form to derive wage differentials. The weighted adjusted standard deviation technique is used for further decomposition of the level and regional variations in sectoral wage gaps, as suggested by Horrace and Oaxaca. The sectoral heterogeneity, skill characteristics and regional dispersions derived by using the micro labor force data sets spread over thirty years. The results confirm the existence of inter-industry wage differentials. However, the size varies across the regions, levels of education, and types of occupations. A substantial difference in the wage gap observed in firms both in the formal and informal sectors. The financial services firms pay higher than the average national wage followed by firms in utility services, the services sector, and the mining sector. The firms in the agricultural sector pay lower than the average national wage. The dispersion in wages has risen to the magnitude of almost 25 percent over the last three decades. Firms pay higher wages to high-skill workers, while industries requiring jobs with low skills pay lower wages. The wage differentials in various regions are attributable to the persistent and relative backwardness of provinces. The high-skilled occupations in general are likely to have more benefits than those involving low-skilled workers. Individual and household characteristics account for almost 50 percent of variation regardless of the sectoral affiliation. The increase in the minimum wage, with targeted social policies in educational attainment, increased participation of women, and provision of social services in the informal sector may reduce the gap in wage difference.

Characterizing Tseitin-Formulas with Short Regular Resolution Refutations

Tseitin-formulas are systems of parity constraints whose structure is described by a graph. These formulas have been studied extensively in proof complexity as hard instances in many proof systems. In this paper, we prove that a class of unsatisfiable Tseitin-formulas of bounded degree has regular resolution refutations of polynomial length if and only if the treewidth of all underlying graphs G for that class is in O(log |V (G)|). It follows that unsatisfiable Tseitin-formulas with polynomial length of regular resolution refutations are completely determined by the treewidth of the underlying graphs when these graphs have bounded degree. To prove this, we show that any regular resolution refutation of an unsatisfiable Tseitin-formula with graph G of bounded degree has length 2Ω(tw(G))/|V (G)|, thus essentially matching the known 2O(tw(G))poly(|V (G)|) upper bound. Our proof first connects the length of regular resolution refutations of unsatisfiable Tseitin-formulas to the size of representations of satisfiable Tseitin-formulas in decomposable negation normal form (DNNF). Then we prove that for every graph G of bounded degree, every DNNF-representation of every satisfiable Tseitin-formula with graph G must have size 2Ω(tw(G)) which yields our lower bound for regular resolution.

Magnetohydrodynamics Micropolar Boundary Layer Flow Past a Stretching Sheet with Microstructural Slip Heat Generation with Convective Boundary Condition

The formulation depicting the magnetohydrodynamics MHD boundary layer of a micropolar fluid on a moving sheet with heat generation and convective boundary conditions in its rectangular form is presented. The PDEs formulated are transformed into nonlinear ODEs via the stream functions and appropriate similarity variables. The solution to the nonlinear coupled equations were presented in decomposed form. The comparison of skin friction values with literatures for validation were carried out and an agreement depicted. The implications of dimensionless physical parameters that appear in this work are graphically studied in the presence of microstructural slip. Physical parameters such as Biot number and heat generation parameters are found to enhance the fluid temperature profile.

Direct Canonical-Polyadic-Decomposition of the Potential Energy Surface from Discrete Data by Decoupled Gaussian Process Regression.

A Gaussian process regression (GPR) approach for directly constructing the canonical polyadic decomposition (CPD) of a multidimensional potential energy surface (PES) by discrete training energies is proposed and denoted by CPD-GPR. The present CPD-GPR method requires the kernel function in a product of a series of one-dimensional functions. To test CPD-GPR, the reactive probabilities of H + H2 as a function of kinetics energy are performed. Comparing the dynamics results computed by the CPD-GPR PES with those by the original PES, a good agreement between these results can be clearly found. Discussions on the previous algorithms for building the decomposed form are also given. We further show that the CPD-GPR method might be the general algorithm for building the decomposed form. However, further development is needed to reduce the CPD rank. Therefore, the present CPD-GPR method might be helpful to inspire ideas for developing new tools in building decomposed potential functions.

Post‑crisis Economic Environment of Two Central and Eastern European Regional Centres: A Comparative Approach

Our research studies the economic background of recovery and catching‑up after the global financial and economic crisis, comparing the case study areas of Cluj‑Napoca in Romania and Pécs in Hungary. We use explorative statistical data analysis to describe the post‑crisis regional economic environment in the context of the differential outcomes of the high‑pressure economy in these two countries. Then, we analyse the evolution of the per capita gross domestic product in a decomposed form which provides insights into the main challenges of regional development in the two regional centres. The results show that long‑run economic challenges must be handled with an efficiency‑oriented regional policy that relies upon capital and knowl­edge‑intensive growth.

Valorisation by composting of sawdust for agronomic use in the commune of (Marcory), Abidjan, Ivory Coast

The environmental challenges in the context of climate change require the design of a sustainable organic agriculture. To achieve such a challenge, the use of organic fertilizers is highly recommended. Among these organic fertilizers, compost is of paramount importance as it is widely recommended and used in the agricultural world. However, the quality of compost depends on the organic matter used. The search for several sources of compost is necessary in order to offer several choices to producers, depending on the source of organic matter available. With this in mind, a study on the use of sawdust from carpentry by composting was conducted in the south of Côte d'Ivoire, in the commune of Marcory, with a view to its use for agronomic purposes. In a 2 x 1.5 x 1 m pit, 50 kg of fresh sawdust and 20 kg of chicken litter were composted over a period of 5 months. The mature compost obtained is in decomposed form (detritus), black in color, oily, free of pathogenic micro-organisms and with appreciable contents expressed in g/kg of assimilable mineral elements such as: N(28.8) K(19.2) Ca(04.5) P(03.1) and Mg(01.5). Its use as a substrate in soilless tomato cultivation has resulted in a yield of 0.75 kg per plant, compared to 0.20 kg per plant in full soil cultivation. This represents a yield of 45 t per hectare, compared to 11 t.

On the representation of integers by decomposable forms in several variables

On the representation of integers by decomposable forms in several variables

Complexity investigations on decomposable form equations

Complexity investigations on decomposable form equations

Multistage Energy Management of Coordinated Smart Buildings: A Multiagent Markov Decision Process Approach

Smart buildings provide an important opportunity for large-scale development of demand response, due to their existing flexibility that can be harvested through Internet-of-Things technologies with minimal cost of new equipment. However, after taking an energy management action, the resulting energy consumption of a building depends on several uncertain factors. Thus, the consumption of the smart building is not directly controllable and, contrary to the typical approach taken in the literature, it cannot be modeled as a decision variable in practice. In this paper, we consider the problem of coordinating the stochastic load control actions of multiple smart buildings under such endogenous uncertainties. We model the problem as a Multi-agent Markov Decision Process and, after reformulations, we bring it to a solvable decomposed form. Our simulations compare the proposed approach with a myopic approach that does not consider future uncertainties, and also quantify the trade-off between cost-effectiveness and computational time in terms of the look-ahead horizon length.

Knowledge Compilation Meets Logical Separability

Knowledge compilation is an alternative solution to address demanding reasoning tasks with high complexity via converting knowledge bases into a suitable target language. Interestingly, the notion of logical separability, proposed by Levesque, offers a general explanation for the tractability of clausal entailment for two remarkable languages: decomposable negation normal form and prime implicates. It is interesting to explore what role logical separability on earth plays in problem tractability. In this paper, we apply the notion of logical separability in three reasoning problems within the context of propositional logic: satisfiability check (CO), clausal entailment check (CE) and model counting (CT), contributing to three corresponding polytime procedures. We provide three logical separability based properties: CO- logical separability, CE-logical separability and CT-logical separability. We then identify three novel normal forms: CO-LSNNF, CE-LSNNF and CT-LSNNF based on the above properties. Besides, we show that every normal form is the necessary and sufficient condition under which the corresponding procedure is correct. We finally integrate the above four normal forms into the knowledge compilation map.