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Mathematics, Volume 11, Issue 24 (December-2 2023) – 136 articles

Cover Story (view full-size image): This paper is about binary linear self-complementary codes. A natural goal in coding theory is to find a linear code with a given length n and dimension k such that the minimum distance d is maximal. Codes with these properties are called optimal. Another important issue is classifying the optimal codes, i.e., finding exactly one representative of each equivalence class. In some sense, the classification problem is more general than the minimum distance bounds problem. In this work, we summarize the classification results for self-complementary codes with the maximum possible minimum distance and a length of up to 20. For the classification, we developed a new algorithm that is much more efficient compared to existing ones in some cases. View this paper
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20 pages, 4804 KiB  
Article
Optimal Investment and Reinsurance Policies in a Continuous-Time Model
Mathematics 2023, 11(24), 5005; https://doi.org/10.3390/math11245005 - 18 Dec 2023
Viewed by 542
Abstract
In the field of finance and insurance, addressing the optimal investment and reinsurance issue is a focal point for researchers. This paper contemplates the optimal strategy for insurance companies within a model where wealth dynamics adhere to a jump–diffusion process. The fractional structure [...] Read more.
In the field of finance and insurance, addressing the optimal investment and reinsurance issue is a focal point for researchers. This paper contemplates the optimal strategy for insurance companies within a model where wealth dynamics adhere to a jump–diffusion process. The fractional structure of the diffusion term is extremely interpretative. This model encompasses elements of risky assets, risk-free assets, and proportional reinsurance. Based on this model and grounded in the principles of stochastic control, the corresponding HJB equation is derived and solved. Consequently, explicit expressions for the optimal investment and reinsurance ratios are obtained, and the solution’s verification theorem is proven. Finally, through a numerical analysis with varying parameters, results consistent with real-world scenarios are achieved. Full article
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20 pages, 323 KiB  
Article
Leveraging Zero and Few-Shot Learning for Enhanced Model Generality in Hate Speech Detection in Spanish and English
Mathematics 2023, 11(24), 5004; https://doi.org/10.3390/math11245004 - 18 Dec 2023
Viewed by 611
Abstract
Supervised training has traditionally been the cornerstone of hate speech detection models, but it often falls short when faced with unseen scenarios. Zero and few-shot learning offers an interesting alternative to traditional supervised approaches. In this paper, we explore the advantages of zero [...] Read more.
Supervised training has traditionally been the cornerstone of hate speech detection models, but it often falls short when faced with unseen scenarios. Zero and few-shot learning offers an interesting alternative to traditional supervised approaches. In this paper, we explore the advantages of zero and few-shot learning over supervised training, with a particular focus on hate speech detection datasets covering different domains and levels of complexity. We evaluate the generalization capabilities of generative models such as T5, BLOOM, and Llama-2. These models have shown promise in text generation and have demonstrated the ability to learn from limited labeled data. Moreover, by evaluating their performance on both Spanish and English datasets, we gain insight into their cross-lingual applicability and versatility, thus contributing to a broader understanding of generative models in natural language processing. Our results highlight the potential of generative models to bridge the gap between data scarcity and model performance across languages and domains. Full article
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23 pages, 398 KiB  
Article
Transition to Multicellularity and Peto Paradox
Mathematics 2023, 11(24), 5003; https://doi.org/10.3390/math11245003 - 18 Dec 2023
Viewed by 481
Abstract
This paper aims to explain the transition to multicellularity as a consequence of the evolutionary response to stress. The proposed model is composed of three parts. The first part details stochastic biochemical kinetics within a reactor (potentially compartmentalized), where kinetic rates are influenced [...] Read more.
This paper aims to explain the transition to multicellularity as a consequence of the evolutionary response to stress. The proposed model is composed of three parts. The first part details stochastic biochemical kinetics within a reactor (potentially compartmentalized), where kinetic rates are influenced by random stress parameters, such as temperature, toxins, oxidants, etc. The second part of the model is a feedback mechanism governed by a genetic regulation network (GRN). The third component involves stochastic dynamics that describe the evolution of this network. We assume that the organism remains viable as long as the concentrations of certain key reagents are maintained within a defined range (the homeostasis domain). For this model, we calculate the probability estimate that the system will stay within the homeostasis domain under stress impacts. Under certain assumptions, we show that a GRN expansion increases the viability probability in a very sharp manner. It is shown that multicellular organisms increase their viability due to compartment organization and stem cell activity. By the viability probability estimates, an explanation of the Peto paradox is proposed: why large organisms are stable with respect to cancer attacks. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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23 pages, 1546 KiB  
Article
Parallel Prediction Method of Knowledge Proficiency Based on Bloom’s Cognitive Theory
Mathematics 2023, 11(24), 5002; https://doi.org/10.3390/math11245002 - 18 Dec 2023
Viewed by 469
Abstract
Knowledge proficiency refers to the extent to which students master knowledge and reflects their cognitive status. To accurately assess knowledge proficiency, various pedagogical theories have emerged. Bloom’s cognitive theory, proposed in 1956 as one of the classic theories, follows the cognitive progression from [...] Read more.
Knowledge proficiency refers to the extent to which students master knowledge and reflects their cognitive status. To accurately assess knowledge proficiency, various pedagogical theories have emerged. Bloom’s cognitive theory, proposed in 1956 as one of the classic theories, follows the cognitive progression from foundational to advanced levels, categorizing cognition into multiple tiers including “knowing”, “understanding”, and “application”, thereby constructing a hierarchical cognitive structure. This theory is predominantly employed to frame the design of teaching objectives and guide the implementation of teaching activities. Additionally, due to the large number of students in real-world online education systems, the time required to calculate knowledge proficiency is significantly high and unacceptable. To ensure the applicability of this method in large-scale systems, there is a substantial demand for the design of a parallel prediction model to assess knowledge proficiency. The research in this paper is grounded in Bloom’s Cognitive theory, and a Bloom Cognitive Diagnosis Parallel Model (BloomCDM) for calculating knowledge proficiency is designed based on this theory. The model is founded on the concept of matrix decomposition. In the theoretical modeling phase, hierarchical and inter-hierarchical assumptions are initially established, leading to the abstraction of the mathematical model. Subsequently, subject features are mapped onto the three-tier cognitive space of “knowing”, “understanding”, and “applying” to derive the posterior distribution of the target parameters. Upon determining the objective function of the model, both student and topic characteristic parameters are computed to ascertain students’ knowledge proficiency. During the modeling process, in order to formalize the mathematical expressions of “understanding” and “application”, the notions of “knowledge group” and “higher-order knowledge group” are introduced, along with a parallel method for identifying the structure of higher-order knowledge groups. Finally, the experiments in this paper validate that the model can accurately diagnose students’ knowledge proficiency, affirming the scientific and meaningful integration of Bloom’s cognitive hierarchy in knowledge proficiency assessment. Full article
(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)
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16 pages, 2530 KiB  
Article
Semi-Markov Models for Process Mining in Smart Homes
Mathematics 2023, 11(24), 5001; https://doi.org/10.3390/math11245001 - 18 Dec 2023
Viewed by 462
Abstract
Generally, these days people live longer but often with increased impairment and disabilities; therefore, they can benefit from assistive technologies. In this paper, we focus on the completion of activities of daily living (ADLs) by such patients, using so-called Smart Homes and Sensor [...] Read more.
Generally, these days people live longer but often with increased impairment and disabilities; therefore, they can benefit from assistive technologies. In this paper, we focus on the completion of activities of daily living (ADLs) by such patients, using so-called Smart Homes and Sensor Technology to collect data, and provide a suitable analysis to support the management of these conditions. The activities here are cast as states of a Markov-type process, while changes of state are indicated by sensor activations. This facilitates the extraction of key performance indicators (KPIs) in Smart Homes, e.g., the duration of an important activity, as well as the identification of anomalies in such transitions and durations. The use of semi-Markov models for such a scenario is described, where the state durations are represented by mixed gamma models. This approach is illustrated and evaluated using a publicly available Smart Home dataset comprising an event log of sensor activations, together with an annotated record of the actual activities. Results indicate that the methodology is well-suited to such scenarios. Full article
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23 pages, 2010 KiB  
Article
The Inverse Weber Problem on the Plane and the Sphere
Mathematics 2023, 11(24), 5000; https://doi.org/10.3390/math11245000 - 18 Dec 2023
Viewed by 1143
Abstract
Weber’s inverse problem in the plane is to modify the positive weights associated with n fixed points in the plane at minimum cost, ensuring that a given point a priori becomes the Euclidean weighted geometric median. In this paper, we investigate Weber’s inverse [...] Read more.
Weber’s inverse problem in the plane is to modify the positive weights associated with n fixed points in the plane at minimum cost, ensuring that a given point a priori becomes the Euclidean weighted geometric median. In this paper, we investigate Weber’s inverse problem in the plane and generalize it to the surface of the sphere. Our study uses a subspace orthogonal to a subspace generated by two vectors X and Y associated with the given points and weights. The main achievement of our work lies in determining a vector perpendicular to the vectors X and Y, in Rn; which is used to determinate a solution of Weber’s inverse problem. In addition, lower bounds are obtained for the minimum of the Weber function, and an upper bound for the difference of the minimal of Weber’s direct and inverse problems. Examples of application at the plane and unit sphere are given. Full article
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15 pages, 2813 KiB  
Article
Non-Stationary Helical Flows for Incompressible Couple Stress Fluid
Mathematics 2023, 11(24), 4999; https://doi.org/10.3390/math11244999 - 18 Dec 2023
Viewed by 520
Abstract
We explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space (the Cauchy problem). In our presentation, the case of non-stationary helical flows with constant coefficient of proportionality [...] Read more.
We explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space (the Cauchy problem). In our presentation, the case of non-stationary helical flows with constant coefficient of proportionality α between velocity and the curl field of flow is investigated. In the given analysis for this given type of couple stress fluid flows, an absolutely novel class of exact solutions in theoretical hydrodynamics is illuminated. Conditions for the existence of the exact solution for the aforementioned type of flows were obtained, for which non-stationary helical flow with invariant Bernoulli-function satisfying to the Laplace equation was considered. The spatial and time-dependent parts of the pressure field of the fluid flow should be determined via Bernoulli-function if components of the velocity of the flow are already obtained. Analytical and numerical findings are outlined, including outstanding graphical presentations of various types of constructed solutions, in order to elucidate dynamic snapshots that show the timely development of the topological behavior of said solutions. Full article
(This article belongs to the Section Engineering Mathematics)
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17 pages, 2459 KiB  
Article
Characterization of the Mean First-Passage Time Function Subject to Advection in Annular-like Domains
Mathematics 2023, 11(24), 4998; https://doi.org/10.3390/math11244998 - 18 Dec 2023
Viewed by 423
Abstract
Cell migration in a biological medium towards a blood vessel is modeled, as a random process, sucessively inside an annulus (two-dimensional domain) and an annular cylinder (three-dimensional domain). The conditional probability function u for the cell moving inside such domains (tissue) fulfills by [...] Read more.
Cell migration in a biological medium towards a blood vessel is modeled, as a random process, sucessively inside an annulus (two-dimensional domain) and an annular cylinder (three-dimensional domain). The conditional probability function u for the cell moving inside such domains (tissue) fulfills by assumption a diffusion–advection equation that is subject to a Dirichlet boundary condition on the outer boundary and a Robin boundary condition on the inner boundary. The mean first-passage time (MFPT) function determined by u estimates the average time for the travelling cell to reach various interesting targets. The MFPT function fulfills a Poisson equation inside a domain with suitable boundary conditions, which give rise to various mathematical problems. The main novelty of this study is the characterization of such an MFPT function inside an annulus and an annular cylinder, which is subject to a Robin boundary condition on the inner boundary and a Dirichlet boundary condition on the outer one, and these are integral functions whose densities are the solution of an inhomogeneous system of linear integral equations. Full article
(This article belongs to the Section Mathematical Biology)
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15 pages, 364 KiB  
Article
Approximation Properties of Parametric Kantorovich-Type Operators on Half-Bounded Intervals
Mathematics 2023, 11(24), 4997; https://doi.org/10.3390/math11244997 - 18 Dec 2023
Viewed by 421
Abstract
The main purpose of this paper is to introduce a new family of parametric Kantorovichtype operators on the half-bounded interval. The convergence properties of these new operators are investigated. The Voronovskaja-type weak inverse theorem and the rate of uniform convergence are obtained. Furthermore, [...] Read more.
The main purpose of this paper is to introduce a new family of parametric Kantorovichtype operators on the half-bounded interval. The convergence properties of these new operators are investigated. The Voronovskaja-type weak inverse theorem and the rate of uniform convergence are obtained. Furthermore, we obtain some shape preserving properties of these operators, including monotonicity, convexity, starshapeness, and semi-additivity preserving properties. Finally, some numerical illustrative examples show that these new operators have a better approximation performance than the classical ones. Full article
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15 pages, 279 KiB  
Article
Plane Partitions and a Problem of Josephus
Mathematics 2023, 11(24), 4996; https://doi.org/10.3390/math11244996 - 18 Dec 2023
Viewed by 538
Abstract
The Josephus Problem is a mathematical counting-out problem with a grim description: given a group of n persons arranged in a circle under the edict that every kth person will be executed going around the circle until only one remains, find the [...] Read more.
The Josephus Problem is a mathematical counting-out problem with a grim description: given a group of n persons arranged in a circle under the edict that every kth person will be executed going around the circle until only one remains, find the position L(n,k) in which you should stand in order to be the last survivor. Let Jn be the order in which the first person is executed on counting when k=2. In this paper, we consider the sequence (Jn)n1 in order to introduce new expressions for the generating functions of the number of strict plane partitions and the number of symmetric plane partitions. This approach allows us to express the number of strict plane partitions of n and the number of symmetric plane partitions of n as sums over partitions of n in terms of binomial coefficients involving Jn. Also, we introduce interpretations for the strict plane partitions and the symmetric plane partitions in terms of colored partitions. Connections between the sum of the divisors’ functions and Jn are provided in this context. Full article
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12 pages, 4684 KiB  
Article
Optimal Joint Path Planning of a New Virtual-Linkage-Based Redundant Finishing Stage for Additive-Finishing Integrated Manufacturing
Mathematics 2023, 11(24), 4995; https://doi.org/10.3390/math11244995 - 18 Dec 2023
Viewed by 569
Abstract
This paper describes the optimal path planning of a redundant finishing mechanism developed for joint space-based additive-finishing integrated manufacturing (AFM). The research motivation results from an inevitable one-sided layout of a finishing stage (FS) with regard to the additive stage (AS) in the [...] Read more.
This paper describes the optimal path planning of a redundant finishing mechanism developed for joint space-based additive-finishing integrated manufacturing (AFM). The research motivation results from an inevitable one-sided layout of a finishing stage (FS) with regard to the additive stage (AS) in the AFM. These two stages share a 2-dof bed stage (BS), and the FS can lightly shave off the rough-surfaced 3D print on the bed. Since the FS located at the side of the AS cannot reach all the target points of the 3D print, the bed should be able to rotate the 3D print about the z-axis and translate it in the z-axis. As a result, the AS has 4-dof joints for 2P and 1P1R during the additive process with AS-BS, and FS has 4-dof and 2-dof integrated joints for 2P2R and 1P1R during the finishing process with FS-BS, respectively. For the kinematic modeling of the FS part and the BS, the virtual linkage connecting the bed frame origin and the FS’s joint frame for approaching the BS is considered to realize seamless kinematic redundancy. The minimum Euclidian norm of the joint velocity space is the objective function to find the optimal joint space solution for a given tool path. To confirm the feasibility of the developed joint path planning algorithm in the proposed FS-BS mechanism, layer-by-layer slicing of a given 3D print’s CAD model and tool path generation were performed. Then, the numerical simulations of the optimal joint path planning for some primitive 3D print geometries were conducted. As a result, we confirmed that the maximum and mean pose error in point-by-point only, with the developed optimal joint path planning algorithm, were less than 202 nm and 153 nm, respectively. Since precision and general machining accuracies in tool path generation are in the range of ±10 μm and 20 μm, the pose error in this study fully satisfies the industry requirements. Full article
(This article belongs to the Special Issue Mathematical Methods in Artificial Intelligence and Robotics)
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18 pages, 3975 KiB  
Article
Demand Prediction of Shared Bicycles Based on Graph Convolutional Network-Gated Recurrent Unit-Attention Mechanism
Mathematics 2023, 11(24), 4994; https://doi.org/10.3390/math11244994 - 18 Dec 2023
Viewed by 446
Abstract
Shared bicycles provide a green, environmentally friendly, and healthy mode of transportation that effectively addresses the “final mile” problem in urban travel. However, the uneven distribution of bicycles and the imbalance of user demand can significantly impact user experience and bicycle usage efficiency, [...] Read more.
Shared bicycles provide a green, environmentally friendly, and healthy mode of transportation that effectively addresses the “final mile” problem in urban travel. However, the uneven distribution of bicycles and the imbalance of user demand can significantly impact user experience and bicycle usage efficiency, which makes it necessary to predict bicycle demand. In this paper, we propose a novel shared-bicycle demand prediction method based on station clustering. First, to address the challenge of capturing patterns in station-level bicycle demand, which exhibits significant fluctuations, we employ a clustering method that combines graph information from the bicycle transfer graph and potential energy. This method aggregates closely related stations into corresponding prediction regions. Second, we use the GCN-CRU-AM (Graph Convolutional Network-Gated Recurrent Unit-Attention Mechanism) model to predict bicycle demand in each region. This model extracts the spatial information and correlation between regions, integrates time feature data and local weather data, and assigns weights to the input features. Finally, experimental results based on the data from Citi Bike System in New York City demonstrate that the proposed model achieves a more accurate demand prediction. Full article
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13 pages, 305 KiB  
Article
Limit Distributions of Products of Independent and Identically Distributed Random 2 × 2 Stochastic Matrices: A Treatment with the Reciprocal of the Golden Ratio
Mathematics 2023, 11(24), 4993; https://doi.org/10.3390/math11244993 - 18 Dec 2023
Viewed by 489
Abstract
Consider a sequence (Xn)n1 of i.i.d. 2×2 stochastic matrices with each Xn distributed as μ. This μ is described as follows. Let (Cn,Dn)T denote the first [...] Read more.
Consider a sequence (Xn)n1 of i.i.d. 2×2 stochastic matrices with each Xn distributed as μ. This μ is described as follows. Let (Cn,Dn)T denote the first column of Xn and for a given real r with 0<r<1, let r1Cn and r1Dn each be Bernoulli distributions with parameters p1 and p2, respectively, and 0<p1,p2<1. Clearly, the weak limit of the sequence μn, namely λ, is known to exist, whose support is contained in the set of all 2×2 rank one stochastic matrices. In a previous paper, we considered 0<r12 and obtained λ explicitly. We showed that λ is supported countably on many points, each with positive λ-mass. Of course, the case 0<r12 is tractable, but the case r>12 is very challenging. Considering the extreme nontriviality of this case, we stick to a very special such r, namely, r=512 (the reciprocal of the golden ratio), briefly mention the challenges in this nontrivial case, and completely identify λ for a very special situation. Full article
18 pages, 4727 KiB  
Article
Protecting Infrastructure Networks: Solving the Stackelberg Game with Interval-Valued Intuitionistic Fuzzy Number Payoffs
Mathematics 2023, 11(24), 4992; https://doi.org/10.3390/math11244992 - 18 Dec 2023
Viewed by 420
Abstract
Critical infrastructure is essential for the stability and development of modern society, and a combination of complex network theory and game theory has become a new research direction in the field of infrastructure protection. However, existing studies do not consider the fuzziness and [...] Read more.
Critical infrastructure is essential for the stability and development of modern society, and a combination of complex network theory and game theory has become a new research direction in the field of infrastructure protection. However, existing studies do not consider the fuzziness and subjective factors of human judgment, leading to challenges when analyzing strategic interactions between decision makers. This paper employs interval-valued intuitionistic fuzzy numbers (IVIFN) to depict the uncertain payoffs in a Stackelberg game of infrastructure networks and then proposes an algorithm to solve it. First, we construct IVIFN payoffs by considering the different complex network metrics and subjective preferences of decision makers. Next, we propose a lexicographic algorithm to solve this game based on the concept of a strong Stackelberg equilibrium (SSE). Finally, we conduct experiments on target scale-free networks. Our results illustrate that in an SSE, for the defender in a weak position, it is better to defend nodes with high degrees. The experiments also indicate that taking fuzziness into account leads to higher SSE payoffs for the defender. Our work aims to solve a Stackelberg game with IVIFN payoffs and apply it to enhance the protection of infrastructure networks, thereby improving their overall security. Full article
(This article belongs to the Special Issue Advances in Fuzzy Decision Theory and Applications, 2nd Edition)
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25 pages, 429 KiB  
Article
Verification and Enforcement of (ϵ, ξ)-Differential Privacy over Finite Steps in Discrete Event Systems
Mathematics 2023, 11(24), 4991; https://doi.org/10.3390/math11244991 - 18 Dec 2023
Viewed by 549
Abstract
In the realm of data protection strategies, differential privacy ensures that unauthorized entities cannot reconstruct original data from system outputs. This study explores discrete event systems, specifically through probabilistic automata. Central is the protection of state data, particularly the initial state privacy of [...] Read more.
In the realm of data protection strategies, differential privacy ensures that unauthorized entities cannot reconstruct original data from system outputs. This study explores discrete event systems, specifically through probabilistic automata. Central is the protection of state data, particularly the initial state privacy of multiple starting states. We introduce an evaluation criterion to safeguard initial states. Using advanced algorithms, the proposed method counters the probabilistic identification of any state within this collection by adversaries from observed data points. The efficacy is confirmed when the probability distributions of data observations tied to these states converge. If a system’s architecture does not meet state differential privacy demands, we propose an enhanced supervisory control mechanism. This control upholds state differential privacy across all initial states, maintaining operational flexibility within the probabilistic automaton framework. Concluding, a numerical analysis validates the approach’s strength in probabilistic automata and discrete event systems. Full article
(This article belongs to the Section Mathematics and Computer Science)
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19 pages, 2324 KiB  
Article
Comparison of Different Optimization Techniques for Model-Based Design of a Buck Zero Voltage Switching Quasi-Resonant Direct Current to Direct Current Converter
Mathematics 2023, 11(24), 4990; https://doi.org/10.3390/math11244990 - 18 Dec 2023
Viewed by 388
Abstract
The present paper provides a comparison of different optimization techniques applied to the model-based design of a Buck Zero Voltage Switching (ZVS) Quasi-Resonant DC-DC Converter. The comparison was made both on the basis of the duration of the optimization procedures and in terms [...] Read more.
The present paper provides a comparison of different optimization techniques applied to the model-based design of a Buck Zero Voltage Switching (ZVS) Quasi-Resonant DC-DC Converter. The comparison was made both on the basis of the duration of the optimization procedures and in terms of guaranteeing the performance of the power electronic device. The main task of the paper is to present various techniques based on the use of mathematical software for the optimal design of Quasi-Resonant DC-DC converters. These topologies were chosen because in them, the design is carried out according to computational procedures, in which several iterations are often necessary for the successful completion of the process. An optimization procedure with a target function reference curve of the output voltage was used. In this way, the optimization is performed without the need for a complete design of the device but only by using base ratios, design constraints, and past experience to determine initial values and intervals of change in circuit parameters. This is also the main advantage of the used optimization of the reference curve type of the output, compared to applying other objective functions, such as achieving minimum losses or maximum efficiency of the device. Full article
(This article belongs to the Special Issue Control, Optimization and Intelligent Computing in Energy)
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12 pages, 302 KiB  
Article
AIOL: An Improved Orthogonal Lattice Algorithm for the General Approximate Common Divisor Problem
Mathematics 2023, 11(24), 4989; https://doi.org/10.3390/math11244989 - 18 Dec 2023
Viewed by 434
Abstract
The security of several fully homomorphic encryption (FHE) schemes depends on the intractability assumption of the approximate common divisor (ACD) problem over integers. Subsequent efforts to solve the ACD problem as well as its variants were also developed during the past decade. In [...] Read more.
The security of several fully homomorphic encryption (FHE) schemes depends on the intractability assumption of the approximate common divisor (ACD) problem over integers. Subsequent efforts to solve the ACD problem as well as its variants were also developed during the past decade. In this paper, an improved orthogonal lattice (OL)-based algorithm, AIOL, is proposed to solve the general approximate common divisor (GACD) problem. The conditions for ensuring the feasibility of AIOL are also presented. Compared to the Ding–Tao OL algorithm, the well-known LLL reduction method is used only once in AIOL, and when the error vector r is recovered in AIOL, the possible difference between the restored and the true value of p is given. Experimental comparisons between the Ding-Tao algorithm and ours are also provided to validate our improvements. Full article
(This article belongs to the Special Issue New Advances in Cryptographic Theory and Application)
10 pages, 1093 KiB  
Article
Diffusion Simulation on Mammograms: A Technique for Analyzing and Monitoring Breast Tumors
Mathematics 2023, 11(24), 4988; https://doi.org/10.3390/math11244988 - 18 Dec 2023
Viewed by 507
Abstract
We have developed an imaging biomarker for quantitatively monitoring the response to clinical treatment in cancer patients. Similar to other diffusion-weighted imaging DWI techniques, our method allows for the monitoring of breast cancer progression based on the diffusion coefficient values in the affected [...] Read more.
We have developed an imaging biomarker for quantitatively monitoring the response to clinical treatment in cancer patients. Similar to other diffusion-weighted imaging DWI techniques, our method allows for the monitoring of breast cancer progression based on the diffusion coefficient values in the affected area. Our technique has the advantage of using images from mammograms and mesoscopic multiparticle collision MPC simulation, making it more affordable and easier to implement compared to other DWI techniques, such as diffusion-weighted MRI. To create our simulation, we start with the region of interest from a mammogram where the lesion is located and build a flat simulation box with impenetrable cylindrical obstacles of varying diameters to represent the tissue’s heterogeneity. The volume of each obstacle is based on the intensity of the mammogram pixels, and the diffusion coefficient is calculated by simulating the behavior of a point particle fluid inside the box using MPC. We tested our technique on two mammograms of a male patient with a moderately differentiated breast ductal carcinoma lesion, taken before and after the first cycle of four chemotherapy sessions. As seen in other DWI studies, our technique demonstrated significant changes in the fluid concentration map of the tumor lesion, and the relative values of the diffusion coefficient showed a clear difference before and after chemotherapy. Full article
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9 pages, 298 KiB  
Article
On a Linear Differential Game in the Hilbert Space 2
Mathematics 2023, 11(24), 4987; https://doi.org/10.3390/math11244987 - 17 Dec 2023
Viewed by 582
Abstract
Two player pursuit evasion differential game and time optimal zero control problem in <i>ℓ</i><sup>2</sup> are considered. Optimal control for the corresponding zero control problem is found. A strategy for the pursuer that guarantees the solution for the pursuit problem is constructed. Full article
(This article belongs to the Special Issue Differential Games and Its Applications, 2nd Edition)
17 pages, 592 KiB  
Article
Revocable-Attribute-Based Encryption with En-DKER from Lattices
Mathematics 2023, 11(24), 4986; https://doi.org/10.3390/math11244986 - 17 Dec 2023
Viewed by 548
Abstract
Cloud computing offers abundant computing resources and scalable storage, but data leakage in the cloud storage environment is a common and critical concern due to inadequate protection measures. Revocable-attribute-based encryption (RABE) is introduced as an advanced form of identity-based encryption (IBE), which encrypts [...] Read more.
Cloud computing offers abundant computing resources and scalable storage, but data leakage in the cloud storage environment is a common and critical concern due to inadequate protection measures. Revocable-attribute-based encryption (RABE) is introduced as an advanced form of identity-based encryption (IBE), which encrypts sensitive data while providing fine-grained access control and an effective user revocation mechanism. However, most existing RABE schemes are not resistant to quantum attacks and are limited in their application scenarios due to the revocation model. In this paper, we propose a RABE scheme constructed from lattices. Our scheme has several advantages, including a near-zero periodic workload for the key generation center (KGC), ensuring scalability as the number of users increases. Additionally, the encryptor is relieved from managing a revocation list. Moreover, our scheme guarantees the confidentiality and privacy of other ciphertexts even if the decryption key for a specific period is compromised. We validated the correctness of our scheme and demonstrated its security under the assumption of learning with errors (LWE), which is widely believed to be resistant to quantum attacks. Finally, we provide an application example of our RABE scheme in the electronic healthcare scenario. Full article
(This article belongs to the Special Issue New Advances in Cryptographic Theory and Application)
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33 pages, 4834 KiB  
Article
Prediction of the Health Status of Older Adults Using Oversampling and Neural Network
Mathematics 2023, 11(24), 4985; https://doi.org/10.3390/math11244985 - 17 Dec 2023
Viewed by 582
Abstract
Self-rated health (SRH) serves as an important indicator for measuring the physical and mental well-being of older adults, holding significance for their health management and disease prevention. In this paper, we introduce a novel classification method based on oversampling and neural network with [...] Read more.
Self-rated health (SRH) serves as an important indicator for measuring the physical and mental well-being of older adults, holding significance for their health management and disease prevention. In this paper, we introduce a novel classification method based on oversampling and neural network with the objective of enhancing the accuracy of predict the SRH of older adults. Utilizing data from the 2020 China Family Panel Studies (CFPS), we included a total of 6596 participants aged 60 years and above in our analysis. To mitigate the impact of imbalanced data, an improved oversampling was proposed, known as weighted Tomek-links adaptive semi-unsupervised weighted oversampling (WTASUWO). It firstly removes the features that are not relevant to the classification by ReliefF. Consequently, it combines undersampling and oversampling. To improve the prediction accuracy of the classifier, an improved multi-layer perception (IMLP) for predicting the SRH was constructed based on bagging and adjusted learning rate. Referring to the experimental results, WTASUWO can effectively improve the prediction performance of a classifier when being applied on an imbalanced dataset, and the IMLP using WTASUWO achieves a higher accuracy. This method can more objectively and accurately assess the health status and identify factors affecting the SRH of older adults. By mining relevant information related the health status of older adults and constructing the prediction model, we can provide policymakers and healthcare professionals with targeted intervention techniques to focus on the health needs of older adults. Meanwhile, this method provides a practical research basis for improving the health level of older adults in China. Full article
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41 pages, 12257 KiB  
Article
Comparative Sensitivity Analysis of Some Fuzzy AHP Methods
Mathematics 2023, 11(24), 4984; https://doi.org/10.3390/math11244984 - 17 Dec 2023
Viewed by 555
Abstract
A precise evaluation of the actual situation is a significant aspect of making a correct and informed decision. Due to the bounded accuracy and elements of uncertainty in the data itself, a point estimate may be less adjusted and rough than an estimate [...] Read more.
A precise evaluation of the actual situation is a significant aspect of making a correct and informed decision. Due to the bounded accuracy and elements of uncertainty in the data itself, a point estimate may be less adjusted and rough than an estimate based on fuzzy set theory. The stability of the Fuzzy AHP Arithmetic mean, Geometric mean, Extent analysis, and Lambda Max methods, widely used in practice, is verified. Three stages of verification are considered, investigating the impact of the following: (a) the scale applied; (b) methods of aggregation of the AHP matrices into the FAHP matrix; and (c) methods of combining several FAHP judgments. Slight changes in experts’ estimates are programmatically simulated tens of thousands of times to track changes in ranking and deviations of results from the initial estimate. This continues the study of FAHP’s stability due to the ambiguous results of such verification by the method of extent analysis. As a result of a comparative analysis of the listed evaluation methods, their specific features and advantages are identified. Full article
(This article belongs to the Special Issue Fuzzy Decision Making and Applications)
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14 pages, 294 KiB  
Article
Killing and 2-Killing Vector Fields on Doubly Warped Products
Mathematics 2023, 11(24), 4983; https://doi.org/10.3390/math11244983 - 17 Dec 2023
Cited by 1 | Viewed by 491
Abstract
We provide a condition for a 2-Killing vector field on a compact Riemannian manifold to be Killing and apply the result to doubly warped product manifolds. We establish a connection between the property of a vector field on a doubly warped product manifold [...] Read more.
We provide a condition for a 2-Killing vector field on a compact Riemannian manifold to be Killing and apply the result to doubly warped product manifolds. We establish a connection between the property of a vector field on a doubly warped product manifold and its components on the factor manifolds to be Killing or 2-Killing. We also prove that a Killing vector field on the doubly warped product gives rise to a Ricci soliton factor manifold if and only if it is an Einstein manifold. If a component of a Killing vector field on the doubly warped product is of a gradient type, then, under certain conditions, the corresponding factor manifold is isometric to the Euclidean space. Moreover, we provide necessary and sufficient conditions for a doubly warped product to reduce to a direct product. As applications, we characterize the 2-Killing vector fields on the doubly warped spacetimes, particularly on the standard static spacetime and on the generalized Robertson–Walker spacetime. Full article
(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)
13 pages, 786 KiB  
Article
Application of Decimated Mathematical Equations and Polynomial Root-Finding Method in Protection of Text Messages
Mathematics 2023, 11(24), 4982; https://doi.org/10.3390/math11244982 - 17 Dec 2023
Viewed by 604
Abstract
Cryptography is the process of transforming data so that only the recipient of the message can read it. It uses an algorithm and a key to convert an input into an encrypted output. In this study, we introduce a novel method for protecting [...] Read more.
Cryptography is the process of transforming data so that only the recipient of the message can read it. It uses an algorithm and a key to convert an input into an encrypted output. In this study, we introduce a novel method for protecting readable messages through the utilization of a polynomial root-finding technique in conjunction with the decimated output of Zaslavsky equations. The innovative approach we have developed is a block encryption algorithm that offers both protection for sensitive information as well as adaptability to various block sizes, including dynamically changing block sizes. Precise security analysis is provided for the proposed algorithm using key space analysis and strong statistical tests. The presented results show that the novel block encryption protection provides a high level of security. Full article
(This article belongs to the Special Issue Codes, Designs, Cryptography and Optimization, 2nd Edition)
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13 pages, 372 KiB  
Article
Conditions for Implicit-Degree Sum for Spanning Trees with Few Leaves in K1,4-Free Graphs
Mathematics 2023, 11(24), 4981; https://doi.org/10.3390/math11244981 - 17 Dec 2023
Cited by 1 | Viewed by 401
Abstract
A graph with n vertices is called an n-graph. A spanning tree with at most k leaves is referred to as a spanning k-ended tree. Spanning k-ended trees are important in various fields such as network design, graph theory, and [...] Read more.
A graph with n vertices is called an n-graph. A spanning tree with at most k leaves is referred to as a spanning k-ended tree. Spanning k-ended trees are important in various fields such as network design, graph theory, and communication networks. They provide a structured way to connect all the nodes in a network while ensuring efficient communication and minimizing unnecessary connections. In addition, they serve as fundamental components for algorithms in routing, broadcasting, and spanning tree protocols. However, determining whether a connected graph has a spanning k-ended tree or not is NP-complete. Therefore, it is important to identify sufficient conditions for the existence of such trees. The implicit-degree proposed by Zhu, Li, and Deng is an important indicator for the Hamiltonian problem and the spanning k-ended tree problem. In this article, we provide two sufficient conditions for K1,4-free connected graphs to have spanning k-ended trees for k = 2, 3. We prove the following: Let G be a K1,4-free connected n-graph. For k = 2, 3, if the implicit-degree sum of any k + 1 independent vertices of G is at least nk + 2, then G has a spanning k-ended tree. Moreover, we give two examples to show that the lower bounds n and n − 1 are the best possible. Full article
(This article belongs to the Special Issue Advanced Graph Theory and Combinatorics)
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18 pages, 438 KiB  
Article
On Solvability Conditions for the Cauchy Problem for Non-Volterra Functional Differential Equations with Pointwise and Integral Restrictions on Functional Operators
Mathematics 2023, 11(24), 4980; https://doi.org/10.3390/math11244980 - 17 Dec 2023
Viewed by 400
Abstract
Cauchy problems are considered for families of, generally speaking, non-Volterra functional differential equations of the second order. For each family considered, in terms of the parameters of this family, necessary and sufficient conditions for the unique solvability of the Cauchy problem for all [...] Read more.
Cauchy problems are considered for families of, generally speaking, non-Volterra functional differential equations of the second order. For each family considered, in terms of the parameters of this family, necessary and sufficient conditions for the unique solvability of the Cauchy problem for all equations of the family are obtained. Such necessary and sufficient conditions are obtained for the following four kinds of families: integral restrictions are imposed on positive and negative functional operators, namely, operator norms are specified; pointwise restrictions are imposed on positive and negative functional operators in the form of values of operators’ actions on the unit function; an integral constraint is imposed on a positive functional operator, a pointwise constraint is imposed on a negative functional operator; a pointwise constraint is imposed on a positive functional operator, an integral constraint is imposed on a negative functional operator. In all cases, effective conditions for the solvability of the Cauchy problem for all equations of the family are obtained, expressed through some inequalities regarding the parameters of the families. The set of parameters of families of equations for which Cauchy problems are uniquely solvable can be easily calculated approximately with any accuracy. The resulting solvability conditions improve the solvability conditions following from the Banach contraction principle. An example of the Cauchy problem for an equation with a coefficient changing sign is given. Taking into account various restrictions for the positive and negative parts of functional operators allows us to significantly improve the known solvability conditions. Full article
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21 pages, 1457 KiB  
Article
Variable Selection for Sparse Logistic Regression with Grouped Variables
Mathematics 2023, 11(24), 4979; https://doi.org/10.3390/math11244979 - 17 Dec 2023
Viewed by 510
Abstract
We present a new penalized method for estimation in sparse logistic regression models with a group structure. Group sparsity implies that we should consider the Group Lasso penalty. In contrast to penalized log-likelihood estimation, our method can be viewed as a penalized weighted [...] Read more.
We present a new penalized method for estimation in sparse logistic regression models with a group structure. Group sparsity implies that we should consider the Group Lasso penalty. In contrast to penalized log-likelihood estimation, our method can be viewed as a penalized weighted score function method. Under some mild conditions, we provide non-asymptotic oracle inequalities promoting the group sparsity of predictors. A modified block coordinate descent algorithm based on a weighted score function is also employed. The net advantage of our algorithm over existing Group Lasso-type procedures is that the tuning parameter can be pre-specified. The simulations show that this algorithm is considerably faster and more stable than competing methods. Finally, we illustrate our methodology with two real data sets. Full article
(This article belongs to the Section Probability and Statistics)
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10 pages, 293 KiB  
Article
On Some Formulas for the Lauricella Function
Mathematics 2023, 11(24), 4978; https://doi.org/10.3390/math11244978 - 16 Dec 2023
Viewed by 763
Abstract
Lauricella, G. in 1893 defined four multidimensional hypergeometric functions FA, FB, FC and FD. These functions depended on three variables but were later generalized to many variables. Lauricella’s functions are infinite sums of products of variables [...] Read more.
Lauricella, G. in 1893 defined four multidimensional hypergeometric functions FA, FB, FC and FD. These functions depended on three variables but were later generalized to many variables. Lauricella’s functions are infinite sums of products of variables and corresponding parameters, each of them has its own parameters. In the present work for Lauricella’s function FA(n), the limit formulas are established, some expansion formulas are obtained that are used to write recurrence relations, and new integral representations and a number of differentiation formulas are obtained that are used to obtain the finite and infinite sums. In the presentation and proof of the obtained formulas, already known expansions and integral representations of the considered FA(n) function, definitions of gamma and beta functions, and the Gaussian hypergeometric function of one variable are used. Full article
(This article belongs to the Section Difference and Differential Equations)
18 pages, 98620 KiB  
Article
Enhancing Dropout Prediction in Distributed Educational Data Using Learning Pattern Awareness: A Federated Learning Approach
Mathematics 2023, 11(24), 4977; https://doi.org/10.3390/math11244977 - 16 Dec 2023
Viewed by 651
Abstract
Learning patterns are crucial for predicting student dropout in educational settings, providing insights into students’ behaviors and motivations. However, existing mainstream dropout prediction models have limitations in effectively mining these learning patterns and cannot mine these learning patterns in large-scale, distributed educational datasets. [...] Read more.
Learning patterns are crucial for predicting student dropout in educational settings, providing insights into students’ behaviors and motivations. However, existing mainstream dropout prediction models have limitations in effectively mining these learning patterns and cannot mine these learning patterns in large-scale, distributed educational datasets. In this study, we analyze the representations of mainstream models and identify their inability to capture students’ distinct learning patterns and personalized variations across courses. Addressing these challenges, our study adopts a federated learning approach, tailoring the analysis to leverage distributed data while maintaining privacy and decentralization. We introduce the Federated Learning Pattern Aware Dropout Prediction Model (FLPADPM), which utilizes a one-dimensional convolutional neural network (CNN) and a bidirectional long short-term memory (LSTM) layer within a federated learning framework. This model is designed to effectively capture nuanced learning patterns and adapt to variations across diverse educational settings. To evaluate the performance of LPADPM, we conduct an empirical evaluation using the KDD Cup 2015 and XuetangX datasets. Our results demonstrate that LPADPM outperforms state-of-the-art models in accurately predicting student dropout behavior. Furthermore, we visualize the representations generated by LPADPM, which confirm its ability to effectively mine learning patterns in different courses. Our results showcase the model’s ability to capture and analyze learning patterns across various courses and institutions within a federated learning context. Full article
(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)
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19 pages, 4125 KiB  
Article
Benchmarking Perception to Streaming Inputs in Vision-Centric Autonomous Driving
Mathematics 2023, 11(24), 4976; https://doi.org/10.3390/math11244976 - 16 Dec 2023
Viewed by 587
Abstract
In recent years, vision-centric perception has played a crucial role in autonomous driving tasks, encompassing functions such as 3D detection, map construction, and motion forecasting. However, the deployment of vision-centric approaches in practical scenarios is hindered by substantial latency, often deviating significantly from [...] Read more.
In recent years, vision-centric perception has played a crucial role in autonomous driving tasks, encompassing functions such as 3D detection, map construction, and motion forecasting. However, the deployment of vision-centric approaches in practical scenarios is hindered by substantial latency, often deviating significantly from the outcomes achieved through offline training. This disparity arises from the fact that conventional benchmarks for autonomous driving perception predominantly conduct offline evaluations, thereby largely overlooking the latency concerns prevalent in real-world deployment. Although a few benchmarks have been proposed to address this limitation by introducing effective evaluation methods for online perception, they do not adequately consider the intricacies introduced by the complexity of input information streams. To address this gap, we propose the Autonomous driving Streaming I/O (ASIO) benchmark, aiming to assess the streaming input characteristics and online performance of vision-centric perception in autonomous driving. To facilitate this evaluation across diverse streaming inputs, we initially establish a dataset based on the CARLA Leaderboard. In alignment with real-world deployment considerations, we further develop evaluation metrics based on information complexity specifically tailored for streaming inputs and streaming performance. Experimental results indicate significant variations in model performance and ranking under different major camera deployments, underscoring the necessity of thoroughly accounting for the influences of model latency and streaming input characteristics during real-world deployment. To enhance streaming performance consistently across distinct streaming input features, we introduce a backbone switcher based on the identified streaming input characteristics. Experimental validation demonstrates its efficacy in perpetually improving streaming performance across varying streaming input features. Full article
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