Vector Addition Research Articles

Digital Models and 3D Biomechanics Analysis in Orthodontics. Part 1: Vector Calculations

Biomechanics is essential for optimizing orthodontic appliances and controlling dental movement. Charles J. Burstone pioneered a three-dimensional (3D) approach in orthodontics, advocating for a shift beyond appliance-focused methods. Initially, biomechanics studies were constrained to two-dimensional (2D) analysis due to the complexities of 3D evaluation. Despite progress in computational tools and digital modeling, orthodontic biomechanics has largely maintained a 2D orientation. This paper advances orthodontic biomechanics into 3D, re-evaluating concepts previously limited to 2D frameworks. A dedicated software, DDP-Ortho (Ortolab, Poland), is introduced to enable orthodontists to analyze and resolve biomechanical challenges in 3D, facilitating appliance designs with precise 3D force systems. The representation and calculation of force vectors and moments in 3D are detailed, emphasizing the inherent complexity absent computational support. Key processes such as vector subtraction and addition, fundamental for assessing and refining orthodontic force systems, are explained. Additionally, the vector split (couple replacement) method, previously described in 2D, is extended to 3D, addressing the unique constraints and challenges of this approach. These tools promise to refine the accuracy and effectiveness of orthodontic treatments, setting the stage to examine the interactions between 3D force systems and dental movement, which will be addressed in a subsequent paper, to broaden the potential of contemporary orthodontic therapy.

Adaptive decomposition-based evolutionary algorithm for many-objective optimization with two-stage dual-density judgment

In order to better balance the convergence and diversity of MOEA/D for many objective optimization problems (MaOPs) with various Pareto fronts (PFs), an adaptive decomposition-based evolutionary algorithm for MaOPs with two-stage dual-density judgment is proposed. To solve the problem that weighted Tchebycheff decomposition may produce weakly Pareto optimal solutions when the solution is not unique or the uniqueness is difficult to guarantee, an augmented weighted Tchebycheff decomposition is adopted. To balance the convergence and diversity of non-dominated solutions in the external archive, different sparsity-level evaluations using vector angles or Euclidean distances are used to measure the distribution of solutions at different stages. To improve the diversity of solution sets obtained by MOEA/D for various PFs, an adaptive weight vector adjustment method based on two-stage dual-density judgment is presented. For weight vector addition, the potential search area is found according to the two-stage density judgment, and then a two-stage sparsity level judgment on the solutions of this area is performed for a second density judgment. For weight vector deletion, the degree of crowding is used to delete the weight vectors with a high crowding degree. Compared with nine advanced multi-objective optimization algorithms on DTLZ and WFG problems, the results demonstrate that the performance of the proposed algorithm is significantly better than other algorithms.

Some Generator Subgraphs of the Square of a Cycle

Graphs considered in this paper are finite simple graphs, which has no loops and multiple edges. Let $G= (V(G),E(G))$ be a graph with $E(G) = \{e_{1}, e_{2},\ldots, e_{m}\},$ for some positive integer $m.$ The \textit{edge space} of $G,$ denoted by $\mathscr{E}(G),$ is a vector space over the field $\zn_{2}.$ The elements of $\mathscr{E}(G)$ are all the subsets of $E(G)$. Vector addition is defined as $X+Y = X ~\Delta~ Y,$ the symmetric difference of sets $X$ and $Y,$ for $X,Y \in \mathscr{E}(G).$ Scalar multiplication is defined as $1\cdot X =X$ and $0 \cdot X = \emptyset$ for $X \in \mathscr{E}(G).$ Let $H$ be a subgraph of $G.$ The \textit{uniform set of $H$} with respect to $G,$ denoted by $E_{H}(G),$ is the set of all elements of $\mathscr E(G)$ that induces a subgraph isomorphic to $H.$ The subspace of $\mathscr E(G)$ generated by $E_{H}(G)$ shall be denoted by $\mathscr E_{H}(G).$ If $E_H(G)$ is a generating set, that is $\mathscr E_{H}(G)= \mathscr E(G),$ then $H$ is called a \textit{generator subgraph} of $G.$ This paper determines some generator subgraphs of the square of a cycle. Moreover, this paper established sufficient conditions for the generator subgraphs of the square of a cycle.

Quantum positive matrix-positive matrix multiplication algorithm

Abstract In quantum computing,
matrix multiplication occurs as a subroutine in more complex algorithms. 
We improve the quantum linear system algorithm 
[Harrow et al. 2009 Phys. Rev. Lett. 103 150502] 
to perform sparse matrix-matrix multiplication and propose a subroutine for parallel vector addition. 
Based on them, a quantum algorithm is exhibited for N×N positive matrix-positive matrix multiplication.
For some small ratio of the maximum element to the minimum element of the positive matrices (i.e.,O(poly logN)), 
this algorithm achieves exponential acceleration.

Monotone Procedure Summarization via Vector Addition Systems and Inductive Potentials

This paper presents a technique for summarizing recursive procedures operating on integer variables. The motivation of our work is to create more predictable program analyzers, and in particular to formally guarantee compositionality and monotonicity of procedure summarization. To summarize a procedure, we compute its best abstraction as a vector addition system with resets (VASR) and exactly summarize the executions of this VASR over the context-free language of syntactic paths through the procedure. We improve upon this technique by refining the language of syntactic paths using (automatically synthesized) linear potential functions that bound the number of recursive calls within valid executions of the input program. We implemented our summarization technique in an automated program verification tool; our experimental evaluation demonstrates that our technique computes more precise summaries than existing abstract interpreters and that our tool’s verification capabilities are comparable with state-of-the-art software model checkers.

A Recombinant Lentiviral Vegfr2-Silencing Vector Attenuates Roxarsone-Promoted Growth of Rat Vascular Endothelial Cells and Angiogenesis in Matrigel Plug and B16F10 Xenograft Models.

Roxarsone (ROX) is widely used as a feed addictive for livestock and poultry. ROX promotes angiogenesis, which can lead to health problems, and it is necessary to identify methods to counter this angiogenic effect of ROX. The VEGF/VEGFR2 signaling pathway is involved in the growth and reconstruction of new blood vessels during angiogenesis. In this study, a recombinant lentiviral vector encoding Vegfr2 shRNA was transfected into rat vascular endothelial cells and used in mouse matrigel plug and melanoma xenograft models to investigate its potential to regulate ROX-induced angiogenesis and tumor growth. Treating endothelial cells with ROX increased cell proliferation, migration, and a tube-like structure of growth relative to the control group. The addition of the lentiviral Vegfr2-silencing vector significantly attenuated the effects of ROX on endothelial cells. The hemoglobin content of mouse matrigel plugs treated with ROX was increased significantly. This effect was dramatically attenuated by the co-administration of shRNA targeting Vegfr2. The volume, weight and CD34 staining of the melanoma xenograft tumors increased by ROX were also attenuated by Vegfr2 silence. These results indicate that the down-regulation of VEGFR2 protein plays an inhibitory role in the ROX-promoted angiogenesis in vivo and in vitro. These data support the targeting of Vegfr2 gene as an effective means to treat ROX-induced angiogenesis and tumor growth.

Pyridine-Anchored Small Molecule Interlayer Enables Defect Passivation and Enhanced Carrier Transport for Perovskite Solar Cells.

Engineering of the interface between the perovskite and hole transport layer (HTL) has been crucial to achieving high performance. In this study, two interfacial materials, MN-CZ and CN-CZ, are designed by systematically regulating the group substitution site to study the relationship between spatial conformation and the passivation effect. The passivation groups of CN-CZ molecules exhibit a stronger "vector addition" effect, resulting in larger molecular dipoles and enhanced defect passivation and energy level regulation effects. Consequently, the CN-CZ-based perovskite solar cell (PSC) shows a high efficiency of 23.8%, which is much higher than that of the reference device. Meanwhile, the humidity and thermal stability of the unencapsulated device have been significantly improved.

Modeling Dipolar Molecules with PCP-SAFT: A Vector Group-Contribution Method.

Predicting thermodynamic equilibrium properties is essential to develop chemical and energy conversion processes in the absence of experimental data. For the modeling of thermodynamic properties, statistical associating fluid theory (SAFT)-based equations of state, such as perturbed-chain polar (PCP)-SAFT, have been proven powerful and found broad application. The PCP-SAFT parameters can be predicted by group-contribution (GC) methods. However, their application to the dipole term is substantially limited: current GC methods neglect the dipole term or only allow for a single dipolar group per substance to avoid handling the molecular dipole moment's symmetry effects. Still, substances with multiple dipolar groups are highly relevant, and their description substantially improves by including the dipole term in SAFT models. To overcome these limitations, this work proposes a vector-addition-based (Vector-)GC method for the dipole term of PCP-SAFT that accounts for molecular symmetry. The Vector-GC employs information on the substance's molecular 3D structure to predict the molecular dipole moment through a vector addition of bond contributions. Combining the proposed sum rule for dipole moments with established sum rules for the remaining parameters yields a consistent GC method for PCP-SAFT for dipolar substances. The prediction capabilities of the Vector-GC method are analyzed against experimental data for two substance classes: nonassociating oxygenated and halogenated substances. We demonstrate that the Vector-GC method improves vapor pressure and liquid density predictions compared to neglecting the dipole term. Moreover, we show that the Vector-GC method enables differentiation between cis- and trans-isomers. The Vector-GC method, hence, substantially increases the predictive capabilities and applicability domain of GC methods. All parameters are provided as JSON and CSV files, and the Vector-GC method is available through an open-source python package. Additionally, the developed regression framework for GC methods for PCP-SAFT is openly available. The regression framework can be employed to regress the Vector-GC method to other substance classes and is easily adaptable to other sum rules for PCP-SAFT.

Interval-Valued Multiobjective Programming Problems Based on Convex Cones

The new solution concepts of interval-valued multiobjective optimization problems using ordering cone are proposed in this paper. An equivalence relation is introduced to divide the collection of all bounded closed intervals into the equivalence classes. The family of all equivalence classes is also called a quotient set. In this case, this quotient set can turn into a vector space under some suitable settings for vector addition and scalar multiplication. The notions of ordering cone and partial ordering on a vector space are essentially equivalent. It means that an ordering in the quotient set can be defined to study the Pareto optimal solution in multiobjective optimization problems. In this paper, we consider the multiobjective optimization problem such that its coefficients are taken to be the bounded closed intervals. With the help of the convex cone, we can study the Pareto optimal solutions of the multiobjective optimization problem with interval-valued coefficients.

From Tiles to Worksheet: Exploring Concreteness Fading in Learning Vector Addition

From Tiles to Worksheet: Exploring Concreteness Fading in Learning Vector Addition

Students’ understanding of vector operations: With and without physics education technology simulation

This study aims to investigate the influence of technology integration (physics education technology simulation) in physics learning. A quantitative method with a quasi-experimental post-test-only design was applied to reveal the differences in students’ abilities to operate vectors between the group that learned and tested using simulation and the group that learned using graphics only. The test consisted of 16 questions on the addition and subtraction of two vectors divided into one and two dimensions. Student response data were analyzed using descriptive statistics and Kruskal-Wallis test. The analysis results show that the vector operation score for experimental group 1, which learned vector operations through graphic learning using simulation and tested with the same simulation (86.15), is higher than experimental group 2, which learned vector operations through graphic learning using simulation (76.59), and the control group, which learned vector operations through graphic learning without simulation assistance (71.81). All three groups have higher average scores for one-dimensional than two-dimensional vector operations. They also have higher average scores for vector addition compared to vector subtraction operations. Kruskal-Wallis test results indicate a significant difference in the average vector operation scores for the three groups (ρ=0.021). This suggests that integrating technology in the learning and testing processes leads to a significant difference. Moreover, the difference is significant for one-dimensional vector operations (ρ=0.004) and not significant for two-dimensional vector operations (ρ=0.107). These findings could support the implementation of similar approaches at the university and high school levels, especially for vector-related topics, in both learning and testing processes.

Prediction of Visual Acuity in Pseudophakic Cataract Population Based on Residual Refraction

Purpose The purpose of the study was to design a simple, handy prediction for the effect of spherical and cylindrical refractive error on the visual acuity degradation at different distances and validate this model on a clinical dataset. Methods This study examined 70 eyes from 35 patients’ post-cataract surgery with aberration-free intraocular lenses. Biometric and corneal data were analysed, and subjective refraction and visual acuity were evaluated by two experienced optometrists. The study computed the spherical equivalent (SEQ), and defocus equivalent via vector addition (DEQ vec), as the sum of absolute values (DEQ abs). Predictive models were developed using univariate regression, with confidence intervals (BCa 95%) calculated through non-parametric bootstrapping (10,000 cycles). Results Various calculated equivalents included −0.44 D for spherical equivalent (SEQ), 0.70 D for defocus equivalent based on vector calculation (DEQ vec), and 0.89 D for defocus equivalent based on absolute values (DEQ abs). Uncorrected and corrected visual acuity averaged 0.07 logMAR and −0.04 logMAR, respectively. The absolute defocus equivalent (DEQ abs) exhibited the smallest confidence interval (BCa 95%) at 0.07. Conclusion The defocus equivalent based on the addition of absolute values (DEQ abs) emerged as the most practical predictor for the described applications. Notably, it offers the advantage of easy calculability through a simple equation: VA loss = DEQ abs ⋅ 0.23. In 95% of cases, this predicted loss would have an accuracy of ±0.03 lines.

Form of salt rises as an indicator of interaction of geodynamic systems

The forms of salt uplifts are formed under the influence of stresses developing in the earth’s crust and, therefore, can be considered as sensitive indicators of the interaction of geodynamic systems. In the North German basin, in the Cis-Ural trough on the border with the Caspian depression and in the Pripyat trough, under the influ- ence of various sources of stress and deformation, forms of salt uplifts arose, reflecting the superposition of these systems. The mechanisms of such a superposition were both the formation of forms associated with the resulting addition of deformation vectors and the interference of forms associated with each geodynamic system separately.

Abstract B023: Modeling of new drugs clinical trials outcome with patients’ digital twins cohorts

Abstract There is a problem of clinical trial failure, as each new drug should surpass the effectiveness of existing treatment regimens, which becomes increasingly challenging over time. Another significant issue is treating patients who have developed resistance to the current therapies. Essentially, the use of drug combinations or off-label drug use, where the indication does not match the diagnosis, is akin to an experiment, as there is insufficient data on which drug or combination to use. This work proposes an approach utilizing computer modeling of patients using gene expression and clinical data. Deep learning and generative adversarial networks are employed as modeling tools. The training data for the algorithms were sourced from publicly available databases such as TCGA, Drugbank, CCLE, and GDSC. The modeling is based on the hypothesis of similarity between patients, similarity between drugs, as well as the similarity between individual organs and patient tissues with cell lines, with similarity being computed mathematically. As a result, a patient model is created, where the input consists of drugs and their combinations, and the output provides survival probability values. These model data can be generated in any required quantity with generative adversarial networks (GAN) technology to create observation and control groups. Consequently, it becomes possible to simulate clinical trials, forecasting their outcomes, and, most importantly, optimizing the trial parameters to maximize the likelihood of success. We obtained patient data and drug information from the TCGA (The Cancer Genome Atlas) database. Biologicals were excluded, and only small molecules, including targeted therapies and chemotherapeutic agents, were retained. The dataset consisted of information on 3225 patients and the effects of 161 drugs. According to our hypothesis, the patient's profile includes three groups of factors, and each of these groups contributes approximately equally to the duration of overall survival (OS) and disease-free survival (DFS) intervals. The first group comprises clinical data such as age, diagnosis, and disease stage. The second group consists of genetic data, specifically gene expression profiles, which capture the functional characteristics of genes. The third group represents the drug or combination of drugs used for patient treatment. Therefore, it is necessary to ensure that all three groups of factors have comparable dimensions of influence. For drug data, we obtained information from the DrugBank database. We represented the drug molecules using SMILES (Simplified Molecular Input Line Entry System) notation, which were then converted into 100-dimensional vectors using embedding techniques derived from natural language processing technologies. To represent combinations of drugs, we employed vector addition of the individual drug vectors. As the outcome measure for prediction, we considered numerical values representing the durations of OS and DFS intervals for each respective task. Citation Format: Dmitrii K. Chebanov, Vsevolod A. Misyurin. Modeling of new drugs clinical trials outcome with patients’ digital twins cohorts [abstract]. In: Proceedings of the AACR Special Conference on Ovarian Cancer; 2023 Oct 5-7; Boston, Massachusetts. Philadelphia (PA): AACR; Cancer Res 2024;84(5 Suppl_2):Abstract nr B023.

Quasitopological vector spaces

In this paper, motivated by a diffeological vector space with the D-topology, we introduce the concept of quasitopological vector space, which is a vector space with a topology satisfying the conditions that the vector addition is separately continuous in each variable, and the scalar multiplication is jointly continuous. The following results are proved: (1) Every quasitopological finite-dimensional vector space is a topological vector space. (2) For each infinite-dimensional vector space, we define a T1 non-Hausdorff topology on it such that it is a quasitopological vector space but is not a topological vector space.

Distributed computing with the cloud

We investigate the effect of omnipresent cloud storage on distributed computing. To this end, we specify a network model with links of prescribed bandwidth that connect standard processing nodes, and, in addition, passive storage nodes. Each passive node represents a cloud storage system, such as Dropbox, Google Drive etc. We study a few tasks in this model, assuming a single cloud node connected to all other nodes, which are connected to each other arbitrarily. We give implementations for basic tasks of collaboratively writing to and reading from the cloud, and for more advanced applications such as matrix multiplication and federated learning. Our results show that utilizing node-cloud links as well as node-node links can considerably speed up computations, compared to the case where processors communicate either only through the cloud or only through the network links. We first show how to optimally read and write large files to and from the cloud in general graphs using flow techniques. We use these primitives to derive algorithms for combining, where every processor node has an input value and the task is to compute a combined value under some given associative operator. In the special but common case of “fat links,” where we assume that links between processors are bidirectional and have high bandwidth, we provide near-optimal algorithms for any commutative combining operator (such as vector addition). For the task of matrix multiplication (or other non-commutative combining operators), where the inputs are ordered, we present tight results in the simple “wheel” network, where procesing nodes are arranged in a ring, and are all connected to a single cloud node.

Reachability in Continuous Pushdown VASS

Pushdown Vector Addition Systems with States (PVASS) consist of finitely many control states, a pushdown stack, and a set of counters that can be incremented and decremented, but not tested for zero. Whether the reachability problem is decidable for PVASS is a long-standing open problem. We consider continuous PVASS , which are PVASS with a continuous semantics. This means, the counter values are rational numbers and whenever a vector is added to the current counter values, this vector is first scaled with an arbitrarily chosen rational factor between zero and one. We show that reachability in continuous PVASS is NEXPTIME-complete. Our result is unusually robust: Reachability can be decided in NEXPTIME even if all numbers are specified in binary. On the other hand, NEXPTIME-hardness already holds for coverability, in fixed dimension, for bounded stack, and even if all numbers are specified in unary.

Risk of a vector-borne endemic zoonosis for wildlife: Hosts, large-scale geography, and diversity of vector-host interactions for Trypanosoma cruzi

Drivers for wildlife infection are multiple and complex, particularly for vector-borne diseases. Here, we studied the role of host competence, geographic area provenance, and diversity of vector-host interactions as drivers of wild mammal infection risk to Trypanosoma cruzi, the aetiological agent of Chagas disease. We performed a systematic sampling of wild mammals in 11 states of Mexico, from 2017 to 2018. We tested the positivity of T. cruzi with the Tc24 marker in tissues samples for 61 wild mammal species (524 specimens sampled). 26 mammal species were positive for T. cruzi, of which 11 are new hosts recorded in Mexico 75 specimens were positive and 449 were negative for T. cruzi infection, yielding an overall prevalence of 14.3%. The standardized infection risk of T. cruzi of our examined specimens was similar, no matter the host species or their geographic origins. Additionally, we used published data of mammal positives for T. cruzi to complement records of T. cruzi infection in wild mammals and inferred a trophic network of Triatoma spp. (vectors) and wild mammal species in Mexico, using spatial data-mining modelling. Infection with T. cruzi was not homogeneously distributed in the inferred trophic network. This information allowed us to develop a predictive model for T. cruzi infection risk for wild mammals in Mexico, considering risk as a function of the diversity of vector-host spatial associations in a large-scale geographic context, finding that the addition of competent vectors to a multi-host parasite system amplifies host infection risk. The diversity of vector-host interactions per se constitutes a relevant driver of infection risk because hosts and vectors are not isolated from each other.

MaOEA/D with adaptive external population guided weight vector adjustment

In order to make multiobjective evolutionary algorithm based on decomposition (MOEA/D) have better performance in dealing with many-objective optimization problems (MaOPs) with different Pareto fronts (PFs), this paper proposes a MOEA/D with adaptive external population guided weight vector adjustment (MaOEA/D-AEW). The algorithm modifies the MOEA/D method of constructing mating pools by calculating the utility function value of individuals in the population to produce high-quality offspring. For the maintenance of non-dominated solutions in the external population (EP), solutions exceeding the capacity of the EP are removed by the method of minimum Euclidean distance combined with the aggregation function value to ensure the convergence and diversity of non-dominated solutions in the EP. For the addition of weight vectors, a new sparsity evaluating method (SL+) is proposed to determine the sparsity of weight vectors by multiplying parallel distances between individuals. For the deletion of the weight vector, the minimum Euclidean distance combined with the aggregation function value is used to delete the weight vector corresponding to invalid or crowded individuals in the population. Comparing MaOEA/D-AEW with six state-of-the-art algorithms on regular PF and irregular PF test problems respectively, simulation results show that the proposed algorithm can adapt well to MaOPs with different PFs and significantly outperforms other comparative algorithms in terms of convergence and diversity of solution sets.

Information Modeling of Energy Saving Processes in the Field of Design, Construction and Operation

Statement of the problem. Improving energy efficiency at various stages of the life cycle of objects in the construction industry, which is an absolute imperative of the current stage of development of society, can be achieved by integrating information modeling of the life cycle of a capital construction object with energy saving technologies. However, in domestic and foreign practice, the potential of such an integration is realized only to a small extent. In this regard, this work is devoted to the formulation of methods for overcoming this situation. Results. It is shown that the addition of the base vectors of hierarchical information models with data on the thermophysical properties of isotropic materials and orthotropic elements allows solving the research problem. Also, the formats of basic structures and clusters of higher ranks have been developed, which completely determine the information model of the energy efficiency of the life cycle of an object. Methods for optimizing the technology of information transfer between heterogeneous participants in the implementation of the life cycle are formulated. For standard construction objects, methods for simplifying the energy saving information model are formulated, which allow expanding the area of practical application of the developed models. Conclusions. The integration of technologies for information modeling of the life cycle of an object and energy saving makes it possible to optimize managerial and technical decisions to increase the energy efficiency / cost ratio both at the design stage and at the stages of construction and operation. The vector hierarchical model of energy efficiency of the project life cycle allows optimizing the updating and verification of the information model, and the mechanisms for transferring information between project participants.