Compact Map Research Articles

Chlamydia infection with vaccination asymptotic for qualitative and chaotic analysis using the generalized fractal fractional operator

In this work, we solve a system of fractional differential equations utilizing a Mittag-Leffler type kernel through a fractal fractional operator with two fractal and fractional orders. A six-chamber model with a single source of chlamydia is studied using the concept of fractal fractional derivatives with nonsingular and nonlocal fading memory. The fractal fractional model of the Chlamydia system can be solved by using the characteristics of a non-decreasing and compact mapping. A suggested model with the Lipschitz criteria and linear growth is studied both qualitatively and quantitatively, taking into account boundedness, uniqueness, and positive solutions at equilibrium points with Leray-Schauder results under time scale concepts. We examined the framework of local and global stability and insight into Lyapunov function properties for the infectious disease model. Chaos Control will employ the regulate for linear responses approach to stabilize the system following its equilibrium points. This will take into consideration a fractional order framework with a managed design, where solutions are bounded in the feasible domain and have a greater impact at the lower minimum infectious rate. To illustrate the implications of fractional and fractal dimensions with varying interest rate values through simulations with Newton’s polynomial method under the Mittag-Lefller kernel. Additionally, a comparative analysis of results is also derived by employing power and exponential decay kernels at various fractional orders.

Real-Time LiDAR–Inertial Simultaneous Localization and Mesh Reconstruction

In this paper, a novel LiDAR–inertial-based Simultaneous Localization and Mesh Reconstruction (LI-SLAMesh) system is proposed, which can achieve fast and robust pose tracking and online mesh reconstruction in an outdoor environment. The LI-SLAMesh system consists of two components, including LiDAR–inertial odometry and a Truncated Signed Distance Field (TSDF) free online reconstruction module. Firstly, to reduce the odometry drift errors we use scan-to-map matching, and inter-frame inertial information is used to generate prior relative pose estimation for later LiDAR-dominated optimization. Then, based on the motivation that the unevenly distributed residual terms tend to degrade the nonlinear optimizer, a novel residual density-driven Gauss–Newton method is proposed to obtain the optimal pose estimation. Secondly, to achieve fast and accurate 3D reconstruction, compared with TSDF-based mapping mechanism, a more compact map representation is proposed, which only maintains the occupied voxels and computes the vertices’ SDF values of each occupied voxels using an iterative Implicit Moving Least Squares (IMLS) algorithm. Then, marching cube is performed on the voxels and a dense mesh map is generated online. Extensive experiments are conducted on public datasets. The experimental results demonstrate that our method can achieve significant localization and online reconstruction performance improvements. The source code will be made public for the benefit of the robotic community.

Antigenic cartography using variant-specific hamster sera reveals substantial antigenic variation among Omicron subvariants

Severe acute respiratory syndrome Coronavirus 2 (SARS-CoV-2) has developed substantial antigenic variability. As the majority of the population now has pre-existing immunity due to infection or vaccination, the use of experimentally generated animal immune sera can be valuable for measuring antigenic differences between virus variants. Here, we immunized Syrian hamsters by two successive infections with one of nine SARS-CoV-2 variants. Their sera were titrated against 16 SARS-CoV-2 variants, and the resulting titers were visualized using antigenic cartography. The antigenic map shows a condensed cluster containing all pre-Omicron variants (D614G, Alpha, Delta, Beta, Mu, and an engineered B.1+E484K variant) and considerably more diversity among a selected panel of Omicron subvariants (BA.1, BA.2, BA.4/BA.5, the BA.5 descendants BF.7 and BQ.1.18, the BA.2.75 descendant BN.1.3.1, the BA.2-derived recombinants XBB.2 and EG.5.1, and the BA.2.86 descendant JN.1). Some Omicron subvariants were as antigenically distinct from each other as the wildtype is from the Omicron BA.1 variant. Compared to titers measured in human sera, titers in hamster sera are of higher magnitude, show less fold change, and result in a more compact antigenic map topology. The results highlight the potential of sera from hamsters for the continued antigenic characterization of SARS-CoV-2.

On some results related to the Karlsson–Nussbaum conjecture in geodesic spaces

We show a Wolff–Denjoy type theorem in the case of a one-parameter continuous semigroup of nonexpansive mappings in which there is a compact mapping. Using the notion of attractor, we are also able to prove some specific properties directly related to the Karlsson–Nussbaum conjecture.

(p, q)-Compactness in spaces of holomorphic mappings

Abstract Based on the concept of ( p , q ) \left(p,q) -compact operator for p ∈ [ 1 , ∞ ] p\in \left[1,\infty ] and q ∈ [ 1 , p * ] q\in \left[1,{p}^{* }] , we introduce and study the notion of ( p , q ) \left(p,q) -compact holomorphic mapping between Banach spaces. We prove that the space formed by such mappings is a surjective p q ∕ ( p + q ) pq/\left(p+q) -Banach bounded-holomorphic ideal that can be generated by composition with the ideal of ( p , q ) \left(p,q) -compact operators. In addition, we study Mujica’s linearization of such mappings, its relation with the ( u * v * + t v * + t u * ) ∕ t u * v * \left({u}^{* }{v}^{* }+t{v}^{* }+t{u}^{* })/t{u}^{* }{v}^{* } -Banach bounded-holomorphic composition ideal of the ( t , u , v ) \left(t,u,v) -nuclear holomorphic mappings for t , u , v ∈ [ 1 , ∞ ] t,u,v\in \left[1,\infty ] , its holomorphic transposition via the injective hull of the ideal of ( p , q * , 1 ) \left(p,{q}^{* },1) -nuclear operators, the Möbius invariance of ( p , q ) \left(p,q) -compact holomorphic mappings on D {\mathbb{D}} , and its full compact factorization through a compact holomorphic mapping, a ( p , q ) \left(p,q) -compact operator, and a compact operator.

Fixed point theorems for continuous single-valued and upper semicontinuous set-valued mappings in $p$-vector and locally $p$-convex spaces

The goal of this paper is to establish a general fixed point theorem for compact single-valued continuous mappings in Hausdorff $p$-vector spaces, and a fixed point theorem for upper semicontinuous set-valued mappings in locally $p$-convex spaces for $p\in (0, 1]$. These results not only provide a solution to Schauder conjecture in the affirmative under the setting of $p$-vector spaces for compact single-valued continuous mappings, but also show the existence of fixed points for upper semicontinuous set-valued mappings defined on $s$-convex subsets in Hausdorff locally $p$-convex spaces, which would be fundamental for nonlinear functional analysis, where $s, p \in (0, 1]$.

Sphere-Graph: A Compact 3D Topological Map for Robotic Navigation and Segmentation of Complex Environments

Sphere-Graph: A Compact 3D Topological Map for Robotic Navigation and Segmentation of Complex Environments

Dynamics of a model of polluted lakes via fractal–fractional operators with two different numerical algorithms

We employ Mittag-Leffler type kernels to solve a system of fractional differential equations using fractal–fractional (FF) operators with two fractal and fractional orders. Using the notion of FF-derivatives with nonsingular and nonlocal fading memory, a model of three polluted lakes with one source of pollution is investigated. The properties of a non-decreasing and compact mapping are used in order to prove the existence of a solution for the FF-model of polluted lake system. For this purpose, the Leray–Schauder theorem is used. After exploring stability requirements in four versions, the proposed model of polluted lakes system is then simulated using two new numerical techniques based on Adams–Bashforth and Newton polynomials methods. The effect of fractal–fractional differentiation is illustrated numerically. Moreover, the effect of the FF-derivatives is shown under three specific input models of the pollutant: linear, exponentially decaying, and periodic.

A practical optimization framework for political redistricting: A case study in Arizona

Following the decennial census, each state in the U.S. redraws its congressional and state legislative district boundaries, which must satisfy various legal criteria. For example, Arizona’s Constitution describes six legal criteria, including contiguity, population balance, competitiveness, compactness, and the preservation of communities of interest, political subdivisions and majority–minority districts, each of which is to be enforced “to the extent practicable”. Optimization algorithms are well suited to draw district maps, although existing models and methods have limitations that inhibit their ability to draw legally-valid maps. Adapting existing optimization methods presents two major challenges: the complexity of modeling to achieve multiple and subjective criteria, and the computational intractability when dealing with large redistricting input graphs. In this paper, we present a multi-stage optimization framework tailored to redistricting in Arizona. This framework combines key features from existing methods, such as a multilevel algorithm that reduces graph input sizes and a larger local search neighborhood that encourages faster exploration of the solution space. This framework heuristically optimizes geographical compactness and political competitiveness while ensuring that other criteria in Arizona’s Constitution are satisfied relative to existing norms. Compared to Arizona’s enacted map (CD118) to be used until 2032, the most compact map produced by the algorithm is 41% more compact, and the most competitive map has five more competitive districts. To enable accessibility and to promote future research, we have created Optimap, a publicly accessible tool to interact with a part of this framework. Beyond the creation of these maps, this case study demonstrates the positive impact of adapting optimization-based methodologies for political redistricting in practice.

Asymmetries in Potential for Partisan Gerrymandering

This article investigates the effectiveness of potential partisan gerrymandering of the US House of Representatives across a range of states. We use a heuristic algorithm to generate district maps that optimize for multiple objectives, including compactness, partisan benefit, and competitiveness. While partisan gerrymandering is highly effective for both sides, we find that the majority of states are moderately biased toward Republicans when optimized for either compactness or partisan benefit, meaning that Republican gerrymanders have the potential to be more effective. However, we also find that more densely populated and more heavily Hispanic states show less Republican bias or even Democratic bias. Additionally, we find that in almost all cases we can generate reasonably compact maps with very little sacrifice to partisan objectives through a mixed‐objective function. This suggests that there is a strong potential for stealth partisan gerrymanders that are both compact and beneficial to one party. Nationwide, partisan gerrymandering is capable of swinging over 100 seats in the US House, even when compact districts are simultaneously sought.

Functor of Idempotent Probability Measures with Compact Support and Open Mappings

Functor of Idempotent Probability Measures with Compact Support and Open Mappings

A Review on the Structure of Fuzzy Regular Proper Mappings in Fuzzy Topological Spaces and Their Properties

The purpose of this paper is construct the concept of fuzzy regular proper mapping in fuzzy topological spaces. We give some characterization of fuzzy regular compact mapping and fuzzy regular coercive mapping. We study the relation among the concepts of fuzzy regular proper mapping, fuzzy regular compact mapping and fuzzy regular coercive mapping and we obtained several properties.

Penerapan Alat Bantu Pengaduk dan Manajemen Rantai Pasok untuk UMKM Pembuat Rendang

This community service program aims to solve the unstandardized production process and the high bargaining power from suppliers in rendang making for Small, Micro, and Medium Businesses (MSMEs). The appropriate technology and consultation training implementation are the applied method in achieving the goal. Therefore, the main problems to be solved are uniformity mixture between seasoning and meat during cooking process within 4-5 hours and low management skill to organize the supply chain components. The results are a uniform mixture of all ingredients and SMMB has basic supply chain management skills. The stirring process with constant speed and intermittent monitoring process during the entire cooking process produces the uniformity mixture. The SMMB is equipped with the skill to identify the supply chain components in the form of compact map. This community service program can blend technology and management implementation into interconnected activities to increase the MSMEs competitiveness, unlike similar community service program.

An implicit Z-bus based sequential power flow algorithm for VSC AC/DC systems

AC/DC power flow algorithms have been proposed and developed as essential analysis tools for the Voltage Source Converter (VSC) based AC/DC hybrid grid. However, prevailing AC/DC power flow algorithms, e.g., the Newton-Raphson based algorithm, suffer from limitations in terms of convergence, multiple solutions, and high computational complexity. To address these issues, this paper presents a novel sequential AC/DC power flow algorithm based on the implicit Z-bus (IZB) method. We firstly provide a general AC/DC power flow model in real vector space, which takes into account the interface data, internal connection and various control modes of VSC stations. Then, simple and compact IZB iterative mappings in real vector space are derived for the AC solver and DC solver. A sequential algorithmic architecture and data exchange mechanisms are designed considering losses calculation, capacity limits and control strategy switching. The impacts of tolerance settings, initial value selections and load levels on the convergence and accuracy of the algorithm are theoretically analysed. Notably, rigorous convergence analyses substantiate the superior attributes of the proposed algorithm over existing models, guaranteeing convergence to high-voltage solutions (feasible and stable solutions). Numerical tests are performed to compare the proposed algorithm with existing works in terms of accuracy, efficiency, scalability and reliability.

PERFORMANCE ASSESSMENT OF A MINI MOBILE MAPPING SYSTEM: IPHONE 14 PRO INSTALLED ON A E-SCOOTER

Abstract. In this study, we investigate the feasibility of using an iPhone 14 Pro's camera and LiDAR sensors to collect high-accuracy spatial data on a mobile e-scooter. Given the widespread availability of e-scooters in urban areas, they present an ideal platform for creating a compact mobile mapping system. The iPhone is securely mounted on the e-scooter and paired with a viDoc RTK Rover, which offers real-time kinematic (RTK) positioning accuracy in open sky areas. As the e-scooter traverses the area of interest, data is collected using the LiDAR sensor, while images are captured using the camera. The collected data is then processed using Pix4Dmatic software, enabling the generation of a fused point cloud and a detailed digital model of the surveyed area. In situations where the Global Navigation Satellite System (GNSS) signal is compromised or unavailable, such as indoor environments or urban canyons, alternative methods like Simultaneous Localization and Mapping (SLAM) can be employed. Additionally, Total Stations can be utilized to track the entire system's movement in GNSS-denied environments and provide accurate georeferencing for the acquired data. Control and check points throughout the area of interest are established using the Total Station as well. This approach offers a flexible and cost-effective means of collecting high-accuracy spatial data in small areas across a variety of environments, leveraging the readily available e-scooters for public use. The results of various experiments conducted using an iPhone 14 Pro and viDoc RTK on an e-scooter are thoroughly analyzed and reported in this paper.

On Successive Approximations for Compact-Valued Nonexpansive Mappings

We show that for a given initial point the typical, in the sense of Baire category, nonexpansive compact valued mapping F has the following properties: there is a unique sequence of successive approximations and this sequence converges to a fixed point of F. In the case of separable Banach spaces we show that for the typical mapping there is a residual set of initial points that have a unique trajectory.

Texts Classification with the usage of Neural Network based on the Word2vec’s Words Representation

Assigning the submitted text to one of the predetermined categories is required when dealing with application-oriented texts. There are many different approaches to solving this problem, including using neural network algorithms. This article explores using neural networks to sort news articles based on their category. Two word vectorization algorithms are being used — The Bag of Words (BOW) and the word2vec distributive semantic model. For this work the BOW model was applied to the FNN, whereas the word2vec model was applied to CNN. We have measured the accuracy of the classification when applying these methods for ad texts datasets. The experimental results have shown that both of the models show us quite the comparable accuracy. However, the word2vec encoding used for CNN showed more relevant results, regarding to the texts semantics. Moreover, the trained CNN, based on the word2vec architecture, has produced a compact feature map on its last convolutional layer, which can then be used in the future text representation. I.e. Using CNN as a text encoder and for learning transfer.

On the Extended Version of Krasnoselśkiĭ’s Theorem for Kannan-Type Equicontractive Mappings

The purpose of the paper is to establish a sufficient condition for the existence of a solution to the equation T(u,C(u))=u using Kannan-type equicontractive mappings, T:A×C(A)¯→Y, where C is a compact mapping, A is a bounded, closed and convex subset of a Banach space Y. To achieve this objective, the authors have presented Sadovskii’s theorem, which utilizes the measure of noncompactness. The relevance of the obtained results has been illustrated through the consideration of various initial value problems.

On a theorem by Browder and its application to nonlinear boundary value problems

AbstractIn a paper from 1960, Felix Browder established a theorem concerning the continuation of the fixed points of a family of continuous functions depending continuously on a parameter , where is a convex and compact subset of . Here, the result is presented for a compact mapping where is a convex, closed, and bounded subset of an arbitrary normed space and is an arcwise connected topological space. Applications to nonlinear boundary value problems are given; specifically, we shall present new viewpoints of known results, introduce some novel results, and exhibit some open problems.

A note on the category of c-spaces

We prove that the category of c-spaces with continuous maps is not cartesian closed. As a corollary the category of locally finitary compact spaces with continuous maps is also not cartesian closed.