Trivial Operation Research Articles

The existence of nontrivial monadic operators on linearly ordered monadic nilpotent minimum algebras

In this paper, we explore the existence of nontrivial monadic operators on linearly ordered monadic nilpotent minimum algebras (NM-algebras, for short) and achieve the necessary and sufficient conditions for a linearly ordered monadic NM-algebra having monadic operators. We verify that each finite linearly ordered monadic NM-algebra with more than 4 elements has nontrivial monadic operators. We study the simple and subdirectly irreducible monadic NM-algebras and derive the necessary and sufficient conditions for a monadic NM-algebra to be simple and subdirectly irreducible, respectively. In addition, we discuss finite monadic involutive monoidal t-norm based algebras (IMTL-algebras, for short) and give some examples to show that there exist finite linearly ordered monadic IMTL-algebras having only trivial monadic operators. We establish the conditions for finite linearly ordered perfect monadic IMTL-algebras having nontrivial monadic operators.

Real-World Implementation and Integration of an Automatic Scoring System for Workplace Safety Courses in Italian

Artificial Intelligence and Natural Language Processing techniques can have a very significant impact on the e-learning sector, with the introduction of chatbots, automatic correctors, or scoring systems. However, integrating such technologies into the business environment in an effective way is not a trivial operation, and it not only requires realising a model with good predictive performance, but also it requires the following: (i) a proper study of the task, (ii) a data collection process, (iii) a real-world evaluation of its utility. Moreover, it is also very important to build an entire IT infrastructure that connects the AI system with the company database, with the human employees, the users, etc. In this work, we present a real-world system, based on the state-of-the-art BERT model, which implements an automatic scoring system for open-ended questions written in Italian. More specifically, these questions pertain to the workplace safety courses which every worker must attend by law, often via e-learning platforms such as the one offered by Mega Italia Media. This article describes how our system has been designed, evaluated, and finally deployed for commercial use with complete integration with the other services provided by the company.

Vanishing of Avramov obstructions for products of sequentially transverse ideals

Two ideals I and J are called transverse if I ∩ J = I J . We show that the obstructions defined by Avramov for products of (sequentially) transverse ideals in regular local rings are always 0. In particular, we compute an explicit free resolution and Koszul homology for all such ideals. Moreover, we construct an explicit trivial Massey operation on the associated Koszul complex and hence (by Golod's construction) a minimal free resolution of the residue field over the quotient defined by the product of transverse ideals. We conclude with questions about the existence of associative multiplicative structures on the minimal free resolution of the quotient defined by products of transverse ideals.

Reducing circuit complexity in optical quantum computation using 3D architectures.

Integrated photonic architectures based on optical waveguides are one of the leading candidates for the future realisation of large-scale quantum computation. One of the central challenges in realising this goal is simultaneously minimising loss whilst maximising interferometric visibility within waveguide circuits. One approach is to reduce circuit complexity and depth. A major constraint in most planar waveguide systems is that beamsplitter transformations between distant optical modes require numerous intermediate SWAP operations to couple them into nearest neighbour proximity, each of which introduces loss and scattering. Here, we propose a 3D architecture which can significantly mitigate this problem by geometrically bypassing trivial intermediate operations. We demonstrate the viability of this concept by considering a worst-case 2D scenario, where we interfere the two most distant optical modes in a planar structure. Using femtosecond laser direct-writing technology we experimentally construct a 2D architecture to implement Hong-Ou-Mandel interference between its most distant modes, and a 3D one with corresponding physical dimensions, demonstrating significant improvement in both fidelity and efficiency in the latter case. In addition to improving fidelity and efficiency of individual non-adjacent beamsplitter operations, this approach provides an avenue for reducing the optical depth of circuits comprising complex arrays of beamsplitter operations.

Axioms for a Logic of Consequential Counterfactuals

Abstract The basis of the paper is a logic of analytical consequential implication, CI.0, which is known to be equivalent to the well-known modal system KT thanks to the definition A → B = df A ⥽ B ∧ Ξ (Α, Β), Ξ (Α, Β) being a symbol for what is called here Equimodality Property: (□A ≡ □B) ∧ (◊A ≡ ◊B). Extending CI.0 (=KT) with axioms and rules for the so-called circumstantial operator symbolized by *, one obtains a system CI.0*Eq in whose language one can define an operator ↠ suitable to formalize context-dependent conditionals (so to counterfactual conditionals) via the definition (Def ↠) A ↠ B = df *A ⥽ B ∧ Ξ (Α, Β).. The central problem of the paper is to identify inside CI.0*Eq + Def ↠ a set of axioms yielding the fragment consisting of all and only theorems in which only truth-functional operators and the two operators → and ↠ occur. This system, here called CI.0, is introduced in §3. In view of the intended purpose, it is introduced a complete and tableau-decidable system KTw, which is an extension of KT with axioms for the so-called quasi-variables w(A), w(B)… Three translation functions among the three languages used in the paper are then introduced. The first, Tr, maps every wff of form *A into wffs of form w(A) ∧ A and translates theorems of CI.0*Eq into theorems of KTw. The second, t°, translates theorems of CI.0 into theorems of CI.0*Eq by applying Def↠. A third one, t, translates theorems of CI.0 into theorems of KTw. As a consequence, it follows that t°A = TrtA. In §4 it is proved that CI.0 is complete w.r.t. the class of CI.0-models of form <W, f, R,V > where f is a selection function and R an access relation. It is then proved (i) that CI.0 models may be converted into KTw-models; (ii) that the truth-value of a proposition in a world of a CI.0-model is preserved in the same world of the derived KTw-model; (iii) that A is a CI.0-thesis iff its translation tA is KTw-thesis. It follows that, if A is not a CI.0-thesis, tA is not a KTw-thesis, so also that TrtA is not a CI.0*Eq-thesis. Since t°A = TrtA and t°A is a function built on Def↠, this proves that every t°-translation of a CI.0-wff that is a CI.0*Eq-theorem is a CI.0-theorem. Since the converse proposition is proved in §2, their conjunction establishes the desired result. In the final section, it is proved that CI.0 is tableau-decidable, that ↠ is not a trivial operator and that ↠ enjoys the positive and negative properties required in §1 for context-dependent conditionals. Some final remarks suggest that studying the relations between CI.0 and systems of classical conditional logic may be a promising line of investigation.

An artificial intelligence method for improving upscaling in complex reservoirs

The upscaling of geological properties is a fundamental requirement to construct a suitable simulation model since the geological model typically contains millions of cells, which makes it computationally difficult to simulate it on such a scale. The process consists of a scale transfer that adapts the petrophysical properties of a high-resolution grid to a coarser grid. Nevertheless, this is not a trivial operation, especially for absolute permeability, which is a non-additive property. One of the most reliable methods is to perform a flow simulation on fine-scale cells that correspond to the coarse block and derive the single permeability value that reflects the same flow value. Still, this is a very time-consuming method and depends on the imposed boundary conditions. This work aims to take advantage of recent advances in artificial intelligence to produce results with similar or better quality of flow-based methods, and more adaptive. It handles models with multiple geological realizations by employing machine learning to capture patterns from a subset of scenarios and use it to generalize for all others. The methodology is divided into two stages — local and global. In the first one, a deep neural network is trained with a fraction of geological realizations using the flow-based results as a reference. In the second stage, clustering analysis is employed along with a neural network optimization to learn an adjustment procedure for the coarse simulation model concerning the cumulative field production predicted by the fine model simulation. Afterward, the trained network performs the upscaling of remaining realizations, but more efficiently in terms of computational time and providing better output in terms of production and injection. The method was applied to a benchmark model and the experimental results demonstrate that the local technique was capable of reproducing very similar values to the flow-based upscaling using only one scenario in training and at the global stage the coarse model was improved even further matching the field oil production forecast of the fine model. Different scenarios were used for training and testing and the results were consistent showing no bias towards a specific configuration and capability of generalization to different scenarios. Ultimately, the proposed artificial intelligence approach performed an accurate upscaling, surpassing the reference approach with forecast production similar to the fine model, and also fast to compute when considering multiple geological realizations, since it reduces the required numerical simulations to a fraction of the total.

The elasticity of the outer boundary and the solution of two-region composite reservoir seepage model

Considering the characteristic of the outer boundary of the two-region composite reservoir has elasticity, firstly, a new two-region composite reservoir seepage model which considers the wellbore storage and effective well radius is established to describe the seepage laws of the two-region composite reservoir more accurately. Then, by combining the Laplace transform and the similar construction method, the solution of dimensionless bottom hole pressure is obtained in the Laplace space. Meanwhile, the solution is also inverted into real space by means of the Stehfest numerical inversion method. Finally, the characteristic curves of dimensionless bottom hole pressure and its derivative are drawn, and the influence of elastic coefficient and reservoir parameters on the characteristic curves is also analyzed. The results reveal that the characteristic curves have affine similarities, and the characteristic curves under the elastic outer boundary condition are always between the closed outer boundary condition and constant pressure outer boundary condition. It can be seen that the conventional three idealized outer boundary conditions (closed, constant pressure and infinite) of two-region composite reservoirs are actually three special cases of elastic outer boundary condition. The introduction of elastic outer boundary condition not only expands the range of data interpretation reasonably, but also shows the actual state of the outer boundary of the two-region composite reservoir better. The similar construction method can avoid complicated and trivial operation processes, and greatly accelerate the model solving speed. The findings of this study can help for better understanding of the real situation of the outer boundary of the two-region composite reservoir, which improves the matching degree between the theoretical model and the actual reservoir, and provides convenience for the development of related well test analysis software.

A Mixed-Initiative Approach to Reusing Infographic Charts.

Infographic bar charts have been widely adopted for communicating numerical information because of their attractiveness and memorability. However, these infographics are often created manually with general tools, such as PowerPoint and Adobe Illustrator, and merely composed of primitive visual elements, such as text blocks and shapes. With the absence of chart models, updating or reusing these infographics requires tedious and error-prone manual edits. In this paper, we propose a mixed-initiative approach to mitigate this pain point. On one hand, machines are adopted to perform precise and trivial operations, such as mapping numerical values to shape attributes and aligning shapes. On the other hand, we rely on humans to perform subjective and creative tasks, such as changing embellishments or approving the edits made by machines. We encapsulate our technique in a PowerPoint add-in prototype and demonstrate the effectiveness by applying our technique on a diverse set of infographic bar chart examples.

The Constructive Solution of the Fractal Composite Reservoir with Stress-Sensitivity Formation

The concentric two-zone composite reservoir model is a boundary value problems (BVPs) of modified Bessel equations. In this paper, we propose a constructive method to solve the BVPs for the system of modified Bessel equations with Robin mixed outer boundary condition and apply it to solve a two-zone fractal composite reservoir seepage model with stress-sensitivity formation. By using Pedrosa variable substitution, regular perturbation technique, Laplace transform, and Stehfest numerical inversion technique, the unified expression for the solutions of the reservoir model with three outer boundary (infinite, impermeable, and constant pressure) conditions is constructed. Type curves of bottom-hole pressure and pressure derivative are drawn, and sensitivity analysis of reservoir parameters are carried out. In comparison with the traditional approach, the solutions of this model are simple and regular, with continued fraction form, the constructive method is efficient and easy to operate. The application of this method avoids the complicated and trivial derivative operation and the use of Cramer’s rule to solve the system of linear equations. It can help to better understand the relationship between the solutions of the reservoir model and the inner and outer boundary conditions. The constructive method can be applied not only to solve the fractal composite reservoir model but also to solve more general reservoir model, BVPs of fluid diffusion, heat conduction, and so on.

Toeplitz Operators whose Symbols Are Borel Measures

In this paper, we are concerned with Toeplitz operators whose symbols are complex Borel measures. When a complex Borel measure μ on the unit circle is given, we give a formal definition of a Toeplitz operator T μ with symbol μ , as an unbounded linear operator on the Hardy space. We then study various properties of T μ . Among them, there is a theorem that the domain of T μ is represented by a trichotomy. Also, it was shown that if the domain of T μ contains at least one polynomial, then T μ is densely defined. In addition, we give evidence for the conjecture that T μ with a singular measure μ reduces to a trivial linear operator.

Distilling Structure from Imagery:Graph-based Models for the Interpretation of Document Images

From its early stages, the community of Pattern Recognition and Computer Vision has considered the importance of leveraging the structural information when understanding images. Usually, graphs have been proposed as a suitable model to represent this kind of information due to their flexibility and representational power able to codify both, the components, objects, or entities and their pairwise relationship. Even though graphs have been successfully applied to a huge variety of tasks, as a result of their symbolic and relational nature, graphs have always suffered from some limitations compared to statistical approaches. Indeed, some trivial mathematical operations do not have an equivalence in the graph domain. For instance, in the core of many pattern recognition applications, there is a need to compare two objects. This operation, which is trivial when considering feature vectors defined in ℝn, is not properly defined for graphs. In this thesis, we have investigated the importance of the structural information from two perspectives, the traditional graph-based methods and the new advances on Geometric Deep Learning. On the one hand, we explore the problem of defining a graph representation and how to deal with it on a large scale and noisy scenario. On the other hand, Graph Neural Networks are proposed to first redefine a Graph Edit Distance methodologies as a metric learning problem, and second, to apply them in a real use case scenario for the detection of repetitive patterns which define tables in invoice documents. As experimental framework, we have validated the different methodological contributions in the domain of Document Image Analysis and Recognition.

A novel UAV path planning algorithm to search for floating objects on the ocean surface based on object’s trajectory prediction by regression

Search and find mission in ocean environment is a none trivial operation given the amount of random parameters associated with it. The uncertain and dynamic aspects related to ocean current movement make the trajectory prediction of drifting lost object onto sea water a very complicated task. In this work we present a novel lost target searching algorithm based on Recursive Area Clustering and target trajectory predication in ocean environment. Based on the widely known GlobCurrent v2 dataset which model the drifting of ocean surface current using satellite sensory data combined with mathematical and simulation modeling, we propose a regression algorithm based on our Recursive Area Clustering algorithm that we have developed previously to determine the strategic zones (weight centers) characterizing the high density areas extracted from drifting target history. Given those weight centers, we predict the object trajectory through refined regression. The predicted lost object trajectory is used to plan the path of UAV search mission. The model developed has a significant impact as we have tested our strategy in a scenario for searching an area covering 68517 km2, we have shown that 78% of the time, the lost object can be found within 32 km distance of the predicted trajectories limiting the significant search area to be about 5% of the whole searched area.

The implicit fully coupled numerical method for flows in thermochemical nonequilibrium

A new effective implicit fully coupled numerical method to compute a high-speed flowfield that is in thermochemical nonequilibrium has been developed. Such a flowfield is described by coupled partial differential equations for the conservation of mass, momentum, total energy, vibrational energies, rotational energy, mass conservation for each species, etc. The total number of equations can be very large, which greatly complicates the solution of general finite volume vector equation when using the standard fully implicit approach. The proposed method allows us to reduce operations with block tridiagonal matrices to inversion of 4x4 matrices and trivial matrix multiplication operations. Moreover, the approximation factorization error is minimized. The numerical procedures were applied to solve chemical and thermal nonequilibrium flow past a sphere body at Mach 27 and chemically nonequilibrium heterogeneous flow in the channel of a combined ramjet with a solid fuel gas generator. The results indicate that new method is 4-5 times more efficient than the standard fully implicit method.

Compactness and hypercyclicity of co-analytic Toeplitz operators on de Branges-Rovnyak spaces

Abstract We study the compactness and the hypercyclicity of Toeplitz operators T ϕ ¯ , b {T_{\bar \varphi ,b}} with co-analytic and bounded symbols on de Branges-Rovnyak spaces ℋ(b). For the compactness of T ϕ ¯ , b {T_{\bar \varphi ,b}} , we will see that the result depends on the boundary spectrum of b. We will prove that there are non trivial compact operators of the form T ϕ ¯ , b {T_{\bar \varphi ,b}} , with ϕ ∈ H ∞ ∩ C(𝕋), if and only if m(σ(b) ∩ 𝕋) = 0. We will also show that, when b is non-extreme, then T ϕ ¯ , b {T_{\bar \varphi ,b}} is hypercyclic if and only if ϕ is non-constant and ϕ(𝔻) ∩ 𝕋 ≠ ∅.

On the structure of ⋆-power conductor domains

Let D be an integral domain and a star operation defined on D. We say that D is a -power conductor domain (-PCD) if for each pair and for each positive integer n we have We study -PCDs and characterize them as root closed domains satisfying for all nonzero a, b and all natural numbers . From this it follows easily that Prüfer domains are d-PCDs (where d denotes the trivial star operation), and v-domains (e.g. Krull domains) are v-PCDs. We also consider when a -PCD is completely integrally closed, and this leads to new characterizations of Krull domains. In particular, we show that a Noetherian domain is a Krull domain if and only if it is a w-PCD.

Angular momentum switching and orthogonal field construction of C-points.

In this Letter, we take on the non-trivial problem of transforming a C-point singularity into its orthogonal state by switching its angular momentum components. For homogeneous distribution, orthogonal transformation is a trivial operation using a single half-wave plate. For C-point singularity, this entails a change in the handedness without disturbing the index, followed by rotation of the state of polarizations in the distribution. Swapping the spin angular momentum (SAM) components of C-point singularities leads to index and handedness inversion, whereas, switching of orbital angular momentum (OAM) components results only in handedness inversion. By changing the SAM and OAM components in sequence, a C-point can be transformed into its orthogonal state. While experimentally demonstrating this, a spiral phase plate, which is a phase element, is shown to perform polarization transformation operation.

Ridge–based curvilinear structure detection for identifying road in remote sensing image and backbone in neuron dendrite image

The curvilinear structure detection is widely applied in many real tasks, such as the fiber classification, river finding, blood vessel detection, and so on. In this paper, we proposed to use the ridge-based curvilinear structure detection (RCSD) for the road extraction from the remote sensing images. First, we employed the morphology trivial opening operation to filter out almost all the small clusters of noise and the small paths. Then RCSD was used to find the road from the remote sensing images. The experiments showed that our proposed method is efficient and give better results than the current existing road-detection methods. Considering the similar structure between backbone in the neuron dendrite images and the road in remote sensing images, we extended the application of RCSD to the backbone detection in neuron dendrite images. The results on backbone detection also proved the efficiency of RCSD.

Finite Element Modeling of Superplastic Forming of Friction Stir Processed AZ31B Mg Alloy

Superplastic forming (SPF) is considered to be a near net shape manufacturing technique, mainly adopted to realize aircraft and automotive parts, which requires relatively high tooling and assembly costs. Furthermore the tuning of the process is a non trivial operation since very limited reliable models have been developed to predict the complex geometries obtained through SPF. In such context several researches, based on finite element method (FEM,) have been conducted on the numerical optimization of conventional SPF processes. Friction Stir Processing (FSP) can be used combined with conventional SPF to enhance the superplastic material behavior by means of grain refinement treatment locally performed. From this point of view very few models have been developed to simulate the different superplastic behavior distinguishing the materials after the application of FSP. In this work free bulge forming tests of AZ31B Mg alloy was experimentally performed by means of blow forming laboratory-scale equipment as well as FEM analysis were conducted to simulate the SPF in two different cases: unprocessed and friction stir processed (FSProcessed) condition. The most relevant parameters of the constitutive numerical model were optimized by numerical-experimental comparison. More specifically material strength factor (K) and strain rate sensitivity index (m) were considered during the parametric optimization. Strain and thickness distributions were compared to the experimental measurements in order to individuate the optimized constitutive equations governing the superplastic behavior in both case studies.

Classical many-particle systems with unique disordered ground states.

Classical ground states (global energy-minimizing configurations) of many-particle systems are typically unique crystalline structures, implying zero enumeration entropy of distinct patterns (aside from trivial symmetry operations). By contrast, the few previously known disordered classical ground states of many-particle systems are all high-entropy (highly degenerate) states. Here we show computationally that our recently proposed "perfect-glass" many-particle model [Sci. Rep. 6, 36963 (2016)10.1038/srep36963] possesses disordered classical ground states with a zero entropy: a highly counterintuitive situation . For all of the system sizes, parameters, and space dimensions that we have numerically investigated, the disordered ground states are unique such that they can always be superposed onto each other or their mirror image. At low energies, the density of states obtained from simulations matches those calculated from the harmonic approximation near a single ground state, further confirming ground-state uniqueness. Our discovery provides singular examples in which entropy and disorder are at odds with one another. The zero-entropy ground states provide a unique perspective on the celebrated Kauzmann-entropy crisis in which the extrapolated entropy of a supercooled liquid drops below that of the crystal. We expect that our disordered unique patterns to be of value in fields beyond glass physics, including applications in cryptography as pseudorandom functions with tunable computational complexity.

Bounded Local Resolvents for Operators with Single-Valued Extension Property

Let T be a bounded operator with (SVEP) on its localizable spectrum \(\sigma _\mathrm{loc}(T)\). We show that for every open subset U of \(\sigma _\mathrm{loc}(T)\), there exists a unit vector x whose local spectrum coincides with the closure of U, and such that its local resolvent function is bounded. This result answers positively to an open question stated by several authors, and extends the both cases of operators with trivial divisible subspace and operators whose point spectrum has empty interior.