Partial Map Research Articles

Besov regularity for solutions of elliptic equations with variable exponents

AbstractWe establish the higher fractional differentiability of the solutions of a problem in divergence form of the type The main features consist in assuming that the partial map has ‐growth, the datum F is Besov regular and both the partial map and the function are Orlicz–Besov regular.

Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n

Let I_n, S_n and A_n be the symmetric inverse semigroup, the symmetric group and the alternating group on X_n={1,…,n}, for n≥2, respectively. Also let I_(n,r) be the subsemigroup consists of all partial injective maps with height less than or equal to r for 1≤r≤n-1, and let SI_(n,r)=I_(n,r)∪S_n and AI_(n,r)=I_(n,r)∪A_n. A non-idempotent element whose square is an idempotent is called a quasi-idempotent. In this paper we obtain the rank and the quasi-idempotent rank of SI_(n,r) (of AI_(n,r)). Also we obtain the relative rank and the relative quasi-idempotent rank of SI_(n,r) modulo S_n (of AI_(n,r) modulo A_n).

Effects of different concept map activities on chemistry learning

There is widespread evidence showing that concept maps are effective for learning. However, little is known about the effects of various concept map activities. We conducted an experiment to examine the comparative effectiveness of three concept map activities: (i) translating a complete map to a paragraph format, (ii) filling in concepts in a partial map, and (iii) filling in labels in a partial map. Undergraduate students enrolled in an introductory general chemistry course were randomly assigned to the three groups. Each concept map depicted the relationships between concepts on the topic of reaction enthalpy. Results showed that the map-translation group significantly outperformed the fill-in-concepts and fill-in-labels groups in conceptual understanding indicated by open-ended questions while there were no significant differences among the three groups in conceptual understanding indicated by multiple-choice questions.

Oil Pipeline Weld Defect Identification System Based on Convolutional Neural Network

The automatic identification and classification of image-based weld defects is a difficult task due to the complex texture of the X-ray images of the weld defect. Several depth learning methods for automatically identifying welds were proposed and tested. In this work, four different depth convolutional neural networks were evaluated and compared on the 1631 image set. The concavity, undercut, bar defects, circular defects, unfused defects and incomplete penetration in the weld image 6 different types of defects are classified. Another contribution of this paper is to train a CNN model RayNet for the dataset from scratch. In the experiment part, the parameters of convolution operation are compared and analyzed, in which the experimental part performs a comparative analysis of various parameters in the convolution operation, compares the size of the input image, gives the classification results for each defect, and finally shows the partial feature map during feature extraction with the classification accuracy reaching 96.5%, which is 6.6% higher than the classification accuracy of other existing fine-tuned models, and even improves the classification accuracy compared with the traditional image processing methods, and also proves that the model trained from scratch also has a good performance on small-scale data sets. Our proposed method can assist the evaluators in classifying pipeline welding defects.

A Meta-Methodology for Improving Land Cover and Land Use Classification with SAR Imagery

Per-point classification is a traditional method for remote sensing data classification, and for radar data in particular. Compared with optical data, the discriminative power of radar data is quite limited, for most applications. A way of trying to overcome these difficulties is to use Region-Based Classification (RBC), also referred to as Geographical Object-Based Image Analysis (GEOBIA). RBC methods first aggregate pixels into homogeneous objects, or regions, using a segmentation procedure. Moreover, segmentation is known to be an ill-conditioned problem because it admits multiple solutions, and a small change in the input image, or segmentation parameters, may lead to significant changes in the image partitioning. In this context, this paper proposes and evaluates novel approaches for SAR data classification, which rely on specialized segmentations, and on the combination of partial maps produced by classification ensembles. Such approaches comprise a meta-methodology, in the sense that they are independent from segmentation and classification algorithms, and optimization procedures. Results are shown that improve the classification accuracy from Kappa = 0.4 (baseline method) to a Kappa = 0.77 with the presented method. Another test site presented an improvement from Kappa = 0.36 to a maximum of 0.66 also with radar data.

Direct Versus Indirect: Control, Moral Responsibility, and Free Action

AbstractThis article has two primary aims. The first is to identify relationships among direct control, direct moral responsibility for an action, and directly free action. The second is to provide a partial map depicting the bearing of some familiar competing views about moral responsibility and free action – traditional compatibilism, semicompatibilism, and event‐causal libertarianism – on differences in conceptions of direct and indirect species of moral responsibility and free action.

Computational exploration of molecular receptive fields in the olfactory bulb reveals a glomerulus-centric chemical map

Progress in olfactory research is currently hampered by incomplete knowledge about chemical receptive ranges of primary receptors. Moreover, the chemical logic underlying the arrangement of computational units in the olfactory bulb has still not been resolved. We undertook a large-scale approach at characterising molecular receptive ranges (MRRs) of glomeruli in the dorsal olfactory bulb (dOB) innervated by the MOR18-2 olfactory receptor, also known as Olfr78, with human ortholog OR51E2. Guided by an iterative approach that combined biological screening and machine learning, we selected 214 odorants to characterise the response of MOR18-2 and its neighbouring glomeruli. We found that a combination of conventional physico-chemical and vibrational molecular descriptors performed best in predicting glomerular responses using nonlinear Support-Vector Regression. We also discovered several previously unknown odorants activating MOR18-2 glomeruli, and obtained detailed MRRs of MOR18-2 glomeruli and their neighbours. Our results confirm earlier findings that demonstrated tunotopy, that is, glomeruli with similar tuning curves tend to be located in spatial proximity in the dOB. In addition, our results indicate chemotopy, that is, a preference for glomeruli with similar physico-chemical MRR descriptions being located in spatial proximity. Together, these findings suggest the existence of a partial chemical map underlying glomerular arrangement in the dOB. Our methodology that combines machine learning and physiological measurements lights the way towards future high-throughput studies to deorphanise and characterise structure-activity relationships in olfaction.

Subspace Codes Based on Partial Injective Maps of Vector Spaces Over Finite Fields

Subspace codes are widely used in error corrections of random network coding. In this article, subspace codes based on partial injective maps of vector spaces over finite fields are considered. Several bounds of the subspace codes (n, M, 2b, e)q based on e-partial injective maps of F <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(n)</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> are presented. The anticode bound and Ahlswede-Aydinian bound of the subspace codes (n, M, 2b, e) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> are obtained by using the EKR theorem for e-partial injective maps of F <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(n)</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> . Finally, we show that the (n, M, 2b, e) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> subspace codes based on e-partial injective maps of F <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(n)</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> reach the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures in I <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.</sub>

Fault Diagnosis of Power Transmission Lines Using a UAV-Mounted Smart Inspection System

Fault diagnosis of power transmission systems (PTSs) is crucial for ensuring the reliability of power grids because most grids are exposed to harsh environments. For integrity diagnosis of PTSs, this article proposes a nondestructive patrol inspection method that employs a smart inspection system (SIS) mounted on an unmanned aerial vehicle (UAV). This system overcomes the geographical limitations faced in accessing PTSs. The SIS includes an ultraviolet camera system that can detect partial discharges on the damaged surfaces of PTSs. The SIS is characterized by three main features. First, it employs an automatic line-tracking method based on image-processing methods. Second, defect locations are automatically estimated on the basis of the consistency of partial discharges, where consistency indicates the steadiness of corona discharges in one-dimensional global coordinates. Third, an alarm is triggered on the basis of the combination of the result from a statistical outlier detection method and the estimated partial discharge locations on a two-dimensional partial discharge map. Finally, a UAV equipped with the proposed system is field-tested for PTS inspection in the autopilot mode. Field tests conducted on ultrahigh-voltage PTSs confirmed the damage detection capabilities of the proposed method and demonstrated its effectiveness and convenience.

Ambient Noise Tomography With Common Receiver Clusters in Distributed Sensor Networks

Near-surface imaging with distributed sensor networks (DSN) is promising for planet exploration, which affordably generates a near-surface velocity model. Recently, an Eikonal tomography-based ambient noise seismic imaging (ANSI) algorithm was implemented in a DSN to realize real-time and in-situ near-surface imaging. However, only using data from neighbors to generate a velocity map cannot have enough stacking samples to generate high-quality results. Also, the neighbor range increase will result in the exponential rise of communication costs. To overcome this problem, we propose a new decentralized Eikonal tomography algorithm in the DSN. The main idea is to change the source-based algorithm to a receiver-based one, which we call common receiver decentralized Eikonal tomography (CR-TomoEK). With CR-TomoEK, nodes fully utilize signals from neighbors to generate partial velocity maps, when combined, lead to the final output. When compared with the original Eikonal algorithm, the stacking number is significantly increased, output quality is higher than before, and there is a significant reduction in communication cost. We performed experiments on both synthetic data and real data from the USArray Transportable Array. Both imaging quality and communication cost are considered in the algorithm validation. The result shows that our algorithm significantly increases the output quality while keeping the communication cost safe to generate a real-time result.

Parallelizable Global Conformal Parameterization of Simply-Connected Surfaces via Partial Welding

Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data, dense 3D surface meshes are common nowadays. While meshes with higher resolution better resemble smooth surfaces, they pose computational difficulties for the existing parameterization algorithms. In this work, we propose a novel parallelizable algorithm for computing the global conformal parameterization of simply-connected surfaces via partial welding maps. A given simply-connected surface is first partitioned into smaller subdomains. The local conformal parameterizations of all subdomains are then computed in parallel. The boundaries of the parameterized subdomains are subsequently integrated consistently using a novel technique called partial welding, which is developed based on conformal welding theory. Finally, by solving the Laplace equation for each subdomain using the updated boundary conditions, we obtain a global conformal parameterization of the given surface, with bijectivity guaranteed by quasi-conformal theory. By including additional shape constraints, our method can be easily extended to achieve disk conformal parameterization for simply-connected open surfaces and spherical conformal parameterization for genus-0 closed surfaces. Experimental results are presented to demonstrate the effectiveness of our proposed algorithm. When compared to the state-of-the-art conformal parameterization methods, our method achieves a significant improvement in both computational time and accuracy.

On inverse submonoids of the monoid of almost monotone injective co-finite partial selfmaps of positive integers

In this paper we study submonoids of the monoid $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ of almost monotone injective co-finite partial selfmaps of positive integers $\mathbb{N}$. Let $\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N})$ be a submonoid of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ which consists of cofinite monotone partial bijections of $\mathbb{N}$ and $\mathscr{C}_{\mathbb{N}}$ be a subsemigroup of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ which is generated by the partial shift $n\mapsto n+1$ and its inverse partial map. We show that every automorphism of a full inverse subsemigroup of $\mathscr{I}_{\infty}^{\!\nearrow}(\mathbb{N})$ which contains the semigroup $\mathscr{C}_{\mathbb{N}}$ is the identity map. We construct a submonoid $\mathbf{I}\mathbb{N}_{\infty}^{[\underline{1}]}$ of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ with the following property: if $S$ is an inverse submonoid of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ such that $S$ contains $\mathbf{I}\mathbb{N}_{\infty}^{[\underline{1}]}$ as a submonoid, then every non-identity congruence $\mathfrak{C}$ on $S$ is a group congruence. We show that if $S$ is an inverse submonoid of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ such that $S$ contains $\mathscr{C}_{\mathbb{N}}$ as a submonoid then $S$ is simple and the quotient semigroup $S/\mathfrak{C}_{\mathbf{mg}}$, where $\mathfrak{C}_{\mathbf{mg}}$ is the minimum group congruence on $S$, is isomorphic to the additive group of integers. Also, we study topologizations of inverse submonoids of $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ which contain $\mathscr{C}_{\mathbb{N}}$ and embeddings of such semigroups into compact-like topological semigroups.

Partial Finite-Time Stabilization of Perturbed Nonlinear Systems Based on the Novel Concept of Nonsingular Terminal Sliding Mode Method

Abstract In this article, a new technique to design a robust controller to achieve finite-time partial stabilization for a class of nonlinear perturbed systems is proposed. Indeed the system is partially stabilized in a finite time, based on the novel concept of the nonsingular terminal sliding mode (TSM) control method. In the first step, the nonlinear dynamical system is divided into two subsystems based on their required stability properties of the system's states (where finite-time stability is only desired for the first subsystem). Then, using a partial diffeomorphism map to transform the first subsystem into the normal form, the control law is designed. Indeed, by introducing this new concept of the TSM method, robust finite-time stability of only a part of the system's state is guaranteed. Subsequently, simulation results demonstrate the effectiveness of the proposed method, and the results are compared with the existing methods.

Continuous Partial Maps on Block Designs

This paper studies the properties of balanced incomplete block designs – the systems of k-element subsets (blocks) of some finite set of elements, such that every element is included in r blocks, and every pair of elements is included in λ blocks. The block designs were introduced for the planning of statistical experiments, and since then they have found lots of other uses. One can define a continuous partial map on a block design as a partial map for which the preimage of every block is either a block or an empty set. The paper lists the main known properties of continuous partial maps on block designs are listed. One of the important properties which, in particular, provides a necessary condition for existence of continuous partial maps on a given block design, is the homogeneous lemma: for a nonempty continuous map on a block design the number of the elements in a (nonempty) preimage of every element is fixed and equals to a number d, a divisor of the block size k. The dual homogeneous hypothesis conjectures that every block which is a preimage of some other block has to be a preimage of a fixed number of blocks. If this hypothesis holds, one would get a property for the block designs and the continuous maps on them, which is as important as the homogeneous lemma, and it would be able to build new block designs by taking continuous map images of other block designs. The main new result of this work is a counterexample to the dual homogeneous hypothesis built as a composite block design – block design whose set of blocks can be partitioned into groups, each one making a block design on the same element set. In the last section two necessary conditions for a block design to be composite are provided. Also a way of reduction of the search for a block designs with given parameters to the Boolean satisfiability problem and to the pseudo-Boolean satisfiability problem is given. The paper provides an explicit algorithm that builds a system of Boolean or pseudo-Boolean expressions equivalent to the problem of search for a block designs is provided. Finally, it demonstrates the results of application of existing solvers to the obtained problems.

Three-year changes of cortical 18F-FDG in amnestic vs. non-amnestic sporadic early-onset Alzheimer's disease.

To examine and compare longitudinal changes of cortical glucose metabolism in amnestic and non-amnestic sporadic forms of early-onset Alzheimer's disease and assess potential associations with neuropsychological performance over a 3-year period time. Eighty-two participants meeting criteria for early-onset (< 65years) sporadic form of probable Alzheimer's disease and presenting with a variety of clinical phenotypes (47 amnestic and 35 non-amnestic forms) were included at baseline and followed up for 1.44 ± 1.23years. All of the participants underwent a work-up at baseline and every year during the follow-up period, which includes clinical examination, neuropsychological testing, genotyping, cerebrospinal fluid biomarker assays, and structural MRI and 18F-FDG PET. Vertex-wise partial volume-corrected glucose metabolic maps across the entire cortical surface were generated and longitudinally assessed together with the neuropsychological scores using linear mixed-effects modeling as a function of amnestic and non-amnestic sporadic forms of early-onset Alzheimer's disease. Similar evolution patterns of glucose metabolic decline between amnestic and non-amnestic forms were observed in widespread neocortical cortices. However, only non-amnestic forms appeared to have a greater reduction of glucose metabolism in lateral orbitofrontal and bilateral medial temporal cortices associated with more severe declines of neuropsychological performance compared with amnestic forms. Furthermore, results suggest that glucose metabolic decline in amnestic forms would progress along an anterior-to-posterior axis, whereas glucose metabolic decline in non-amnestic forms would progress along a posterior-to-anterior axis. We found differences in spatial distribution and temporal trajectory of glucose metabolic decline between amnestic and non-amnestic early-onset Alzheimer's disease groups, suggesting that one might want to consider treating the two forms of the disease as two separate entities.

A priori estimates for solutions to a class of obstacle problems under p, q-growth conditions

In this paper we would like to complement the results contained in Gavioli (Forum Math, to appear) by dealing with the higher differentiability of integer order of solutions to a class of obstacle problems under non-standard growth conditions, fulfilling variational inequalities of the kind $$\begin{aligned} \int _{\varOmega } \langle {\mathcal {A}}(x, Du), D(\varphi - u) \rangle \, dx \ge 0 \qquad \forall \, \varphi \in {\mathcal {K}}_{\psi }(\varOmega ). \end{aligned}$$Here the operator $${\mathcal {A}}$$ satisfies p, q-growth conditions with p and q related by 1$$\begin{aligned} \frac{q}{p} n$$. More precisely the function $$\psi \in W^{1,p}(\varOmega )$$, called obstacle, is such that $$D\psi \in W^{1,r}_{\mathrm{loc}}(\varOmega )$$ and $${\mathcal {K}}_{\psi }=\{w \in W^{1,p}(\varOmega ): w \ge \psi \,\, \text {a.e. in }\varOmega \}$$ is the class of admissible functions. The main difference with the previous work (Gavioli in Forum Math, to appear) is that here we assume the same regularity both for the gradient of the obstacle $$D\psi$$ and for the partial map $$x\mapsto {\mathcal {A}}(x,\xi )$$, that is, a higher differentiability of Sobolev order in the space $$W^{1,r}$$ with the same $$r>n$$ appearing in (1). For the sake of clarity, we focus on the derivation of the a priori estimates since the approximation procedure is standard and can be found in Cupini et al. (Nonlinear Anal 154:7–24, 2017), Cupini et al. (Differ Equ 265(9):4375–4416, 2018), Cupini et al. (Nonlinear Anal 54(4):591–616, 2003), Eleuteri et al. Ann Mat Pura Appl (195(5):1575–1603, 2016) and Gavioli (Forum Math, to appear).

Phytoplasmas associated with declining of hazelnut (Corylus avellana) in Slovenia

Hazelnut (Corylus avellana) is cultivated on 118 ha and ranks eighth in Slovenian fruit growing production, representing 2.8% of the total area of fruit plantations in the country. However, decline of some of the trees appeared in 2012 in two plantations located in eastern Slovenia. Together these orchards cover 5 ha, with around 1600 trees planted 12 to 15 years ago. By October 2018, ~12% of these trees had died, and an additional 12% showed decay symptoms. The dead and dying trees were scattered throughout both orchards, with no apparent pattern. The most affected cultivar was ‘Istrska dolgoplodna leska’. Using molecular diagnostic methods, we showed infection of symptomatic trees with three unrelated phytoplasmas: ‘Candidatus Phytoplasma fragariae’, of the 16SrXII-E phytoplasma subgroup, and phytoplasma of the 16SrV and 16SrIX groups. In 2018, the presence of ‘Ca. P. fragariae’ and/or phytoplasma of 16SrV group were confirmed in decayed hazelnut trees in eastern, north-eastern, central, south-eastern and western Slovenia. ‘Ca. P. fragariae’ has also been detected in a forest in south-western Slovenia, for Acer campestre, Carpinus betulus, Crataegus laevigata, Fraxinus ornus and Quercus petraea. All infected forest trees showed unusual dense proliferation of sprouts from roots and/or trunks. Molecular characterisations of partial 16S rRNA, secY, map and ribosomal protein genetic locus of hazelnut 16SrV phytoplasma isolates show that they are identical to isolates that can cause grapevine flavescence dorée disease. Here, the results of our recent study and the open questions on this burning issue for hazelnut production are presented.

Deep Reinforcement Learning-Based Automatic Exploration for Navigation in Unknown Environment.

This paper investigates the automatic exploration problem under the unknown environment, which is the key point of applying the robotic system to some social tasks. The solution to this problem via stacking decision rules is impossible to cover various environments and sensor properties. Learning-based control methods are adaptive for these scenarios. However, these methods are damaged by low learning efficiency and awkward transferability from simulation to reality. In this paper, we construct a general exploration framework via decomposing the exploration process into the decision, planning, and mapping modules, which increases the modularity of the robotic system. Based on this framework, we propose a deep reinforcement learning-based decision algorithm that uses a deep neural network to learning exploration strategy from the partial map. The results show that this proposed algorithm has better learning efficiency and adaptability for unknown environments. In addition, we conduct the experiments on the physical robot, and the results suggest that the learned policy can be well transferred from simulation to the real robot.

Smooth extension theorems for one variable maps

We characterize the real valued functions f defined on perfect subsets P of R which admit n-times differentiable extensions F:R→R. In this characterization no continuity of F(n) is imposed. In particular, it generalizes Jarník's Extension Theorem, according to which f admits differentiable extension F:R→R if, and only if, f is differentiable. The new characterization is also closely related to the Whitney's Extension Theorem, which characterizes partial maps f admitting n-times differentiable extensions F:R→R with continuous nth derivative F(n). We also provide an elegant description of a linear extension operator Tn:C(P)→C(R) such that Tn(f)∈Dn(R) for every Dn(R)-extendable f∈C(P) and Tn(f)∈Cn(R) whenever f∈C(P) is Cn(R)-extendable.

Algebraic graph rewriting with controlled embedding

Graph transformation is a specification technique suitable for a wide range of applications, specially the ones that require a sophisticated notion of state. In graph transformation, states are represented by graphs and actions are specified by rules. Most algebraic approaches to graph transformation proposed in the literature ensure that if an item is preserved by a rule, so are its connections with the graph where it is embedded. But there are applications in which it is desirable to specify different embeddings. For example when cloning an item, there may be a need to handle the original and the copy in different ways. We propose a new algebraic approach to graph transformation, AGREE: Algebraic Graph Rewriting with controllEd Embedding, where rules allow one to specify how the embedding should be carried out. We define this approach in the framework of classified categories which are categories endowed with partial map classifiers. This new approach leads to graph transformations in which effects may be non-local, e.g. a rewrite step may alter a node of the host graph which is outside the image of the left-hand side of the considered rule. We propose a syntactic condition on AGREE rules which guarantees the locality of transformations. We also compare AGREE with other algebraic approaches to graph transformation.