Combinatorial Model Research Articles

Blueprint for a Universal Theory of Learning to Read: The Combinatorial Model

AbstractIn this essay, I outline some of the essential ingredients of a universal theory of reading acquisition, one that seeks to highlight commonalities while embracing the global diversity of languages, writing systems, and cultures. I begin by stressing the need to consider insights from multiple disciplines including neurobiology, cognitive science, linguistics, socio‐cultural, and historical inquiry, although my major emphasis is on a writing systems approach. A theme common to several of these perspectives is the need to attain a level of word reading speed and effortlessness necessary to overcome the severe limitations of human (sequential) information processing thereby allowing the reader to devote maximum cognitive resources to comprehension. I then present the Combinatorial Model—a universal theory of learning to read based on the fundamental principle of spoken and written language combinatoriality. This principle (“infinite ends from finite means”) makes it possible for children to learn how to decipher (i.e., decode), combine and chunk/unitize a limited and learnable set of rudimentary (typically meaningless) elements such as letters, aksharas, syllabograms, and character components into a nested hierarchy of meaningful higher‐order units such as morphemes and words that can be recognized instantly and effortlessly via rapid parallel processing of their constituent elements. Combinatoriality enables an orthography to provide learnability and decipherability for the novice reader (via phonological transparency) as well as unitizability and automatizability for the expert (via morphemic transparency). I then elaborate on the (i) dual nature of this model and the unfamiliar‐to‐familiar/novice‐to‐expert framework, (ii) the unit/s of unitization, and (iii) the dual nature of writing. I liken the development of reading to a tree that grows both upwards and outwards. Vertical growth can be thought of as a universal 3‐phase progression from sub‐morphemic, through morpho‐lexical, to supra‐lexical phases in which later‐developing phases do not replace earlier phases but are added in a nested combinatorial hierarchy. Outward growth is conceptualized as a process of knowledge arborization—ongoing refinement, elaboration, and diversification. I conclude by noting that, despite important recent advances, our knowledge of learning to read in non‐European and non‐alphabetic systems is still in its infancy. Current research is over‐reliant on English—an outlier orthography—together with a handful of Roman‐script Western European languages. This has led reading science to neglect many issues of global significance such as homography, tone, diacritics, visual complexity, non‐linearity, linguistic distance, multilingualism, multiscriptism, and more. An appreciation of the specifics of the particular language (or languages) and orthography (or orthographies) a child is learning to read within the broader context of global linguistic, orthographic, and cultural diversity is crucial not only for a deeper understanding of learning to read a specific language but for a truly global non‐ethnocentric science of reading.

Identification of Potential Candida albicans Inhibitors Through Pharmacophore Modeling and Virtual Screening Techniques

Fungal infections have increased significantly in recent years and represent a major threat to human health. A large number of these infections are caused by the opportunistic pathogen Candida albicans. Lanosterol 14-alpha demethylase (CYP51), a critical enzyme in the cytochrome P450 family, is a well-established target for antifungal drugs. However, the development of resistance to current antifungal treatments has created an urgent need to develop new inhibitors that are more effective and less likely to promote the emergence of resistance in candida albicans. Azoles are a large and relatively new group of synthetic compounds, of which imidazoles and triazoles are two clinically useful families used in the treatment of systemic fungal infections. In this study, we focused on Candida albicans and used the target protein (PDB code: 1EA1) to perform an In silico analysis of a series of benzimidazole derivatives. The aim was to identify novel chemotherapeutic agents with potential antifungal activity. To discover new Candida albicans inhibitors, pharmacophore models based on the molecular structure of benzimidazole derivatives were generated and validated using various methods. A virtual screening of the Enamine database containing 535,326 molecules was performed based on the combinatorial pharmacophore model. Compounds selected after virtual screening were subjected to molecular docking protocols (HTVS, SP, XP and IFD). 26 new compounds were identified and their absorption, distribution, metabolism and excretion (ADME) properties were calculated. These results suggest that the identified compounds could serve as promising chemical starting points for further structural optimisation in the development of Candida albicans inhibitors.

B7-H3 CAR-T cell therapy combined with irradiation is effective in targeting bulk and radiation-resistant chordoma cancer cells

BackgroundChordoma is a slow-growing, primary malignant bone tumor that arises from notochordal tissue in the midline of the axial skeleton. Surgical excision with negative margins is the mainstay of treatment,...

Farmers’ livelihood resilience and its optimisation path in world heritage sites: a Chinese case study

ABSTRACT In the context of global environmental change and tourism market volatility, the livelihood resilience in World Heritage Site (WHS) faces serious challenges. We designed a combinatorial assessment model aimed at analyzing and enhancing the household livelihood resilience in WHS. By combining barrier degree model and fuzzy set qualitative comparative analysis, we provide an identification of the key factors determining the livelihood resilience in WHS and selects Yulong River National Area in Guangxi, China, as a case site. Results suggested that (i) The livelihood resilience in WHS is generally low, with relatively high self-organization capacity, medium levels of psychological perception and buffer capacity, and the weakest learning capacity; (ii) The Livelihood Resilience Index varies according to the type of main livelihood activity of the household, which is ranked in ascending order as tourism livelihood, worker livelihood, farming livelihood, and multi-income source livelihood; (iii) On different livelihood dimensions, buffer capacity has the most significant impact among tourism livelihood and farming livelihood, while self-organization capacity plays a key role among farming livelihood and multi-income source livelihood. In addition, the size of tourism operated house, voice in rural tourism development, social connectivity and household educational inputs were the major barriers to livelihood resilience among all types of households; (iv) Through configurational analysis, we further reveal three main pathways for achieving high livelihood resilience.

Improved combinatorial optimization model for vessel scheduling in constrained channel ports

Improved combinatorial optimization model for vessel scheduling in constrained channel ports

Mixed Dimer Configuration Model in Type D Cluster Algebras II: Beyond the Acyclic Case

This is a sequel to the second and third author's Mixed Dimer Configuration Model in Type D Cluster Algebras where we extend our model to work for quivers that contain oriented cycles. Namely, we extend a combinatorial model for F-polynomials for type D using dimer and double dimer configurations. In particular, we give a graph theoretic recipe that describes which monomials appear in such F-polynomials, as well as a graph theoretic way to determine the coefficients of each of these monomials. To prove this formula, we provide an explicit bijection between mixed dimer configurations and dimension vectors of submodules of an indecomposable Jacobian algebra module.

Exact and approximation algorithms for the contiguous translocation distance problem

Biological computation is the field that studies the computations performed by the biological systems and includes the development of algorithms or other computational techniques inspired by nature. The genome rearrangements that occur during genome evolution are an important example of a natural computation process which inspired multiple problems that can be solved using combinatorial models. A popular problem inspired by genome evolution is computing the genetic distance between two organisms by identifying the minimum number of genome rearrangements needed to obtain one genome from the other. Given two chromosomes, represented as strings over the DNA alphabet {A, C, G, T}, the translocation operation is defined as a prefix interchange between these chromosomes. Thus, two new chromosomes are obtained after a translocation. When the chromosomes are interchanging equal length prefixes, the translocation operation is called uniform. A translocation sequence is a series of translocation operations applied to an initial genome, represented as a set of strings (initial set), resulting in a new genome, also represented as a set of strings (target set). Given a translocation sequence, if the strings exchanging prefixes are part of the initial set or have additional copies created by preceding translocations than those utilised, then the translocation sequence is referred to as contiguous. The translocation distance between two given genomes is defined as the minimum number of translocation operations necessary to obtain one genome from the other. We introduce a new polynomial time exact algorithm to compute the uniform contiguous translocation distance for a target genome of size two. Then, we present a polynomial time 2-approximation algorithm for the non-uniform contiguous translocation distance considering a target genome of size one.

Bounding the beta invariant of 3-connected graphs

The beta invariant is closely related to the Chromatic and Tutte Polynomials and has been extensively studied, see Brylawski [A combinatorial model for series-parallel networks, Trans. Amer. Math. Soc. 154 (1971) 1–22], Crapo [A higher invariant for matroids, J. Combin. Theory 2 (1967) 406–417], Lee and Wu [Bounding the beta invariant of 3-connected matroids, Discrete Math. 354 (2022) 1–11], Oxley [On Crapo’s beta invariant for matroids, Stud. Appl. Math. 66(3) (1982) 267–277], and others. Lee and Wu [Bounding the beta invariant of 3-connected matroids, Discrete Math. 354 (2022) 1–11] established that a [Formula: see text]-connected graph with [Formula: see text] vertices possesses a beta invariant of at least [Formula: see text], reaching equality only when the graph is a wheel or the Prism. Additionally, Oxley [On Crapo’s beta invariant for matroids, Stud. Appl. Math. 66(3) (1982) 267–277] provided characterizations for matroids with beta invariant values of two, three, and four. This paper extends the findings of Lee and Wu by offering a comprehensive characterization of all [Formula: see text]-connected graphs with [Formula: see text] vertices that have a beta invariant of either [Formula: see text] or [Formula: see text]. As a consequence, we prove that any [Formula: see text]-connected graph with at least [Formula: see text] vertices other than a Wheel has a beta invariant of at least [Formula: see text].

On J-folded Alcove Paths and Combinatorial Representations of Affine Hecke Algebras

We introduce the combinatorial model of J-folded alcove paths in an affine Weyl group and construct representations of affine Hecke algebras using this model. We study boundedness of these representations, and we state conjectures linking our combinatorial formulae to Kazhdan-Lusztig theory and Opdam’s Plancherel Theorem.

Short-term photovoltaic power prediction model based on VMD-DBO-KELM

Abstract Aiming at the problem that the current photovoltaic power prediction model has poor generalization performance and cannot achieve accurate prediction under different environmental conditions, in this paper, a combinatorial prediction model of a kernel extreme learning machine is optimized by a dung beetle optimization algorithm after variational mode decomposition. A number of different time scales of photovoltaic power data are selected for the experiment. From the experimental results, compared with the traditional model, the proposed model has strong generalization performance and outstanding prediction results in all data sets, and has broad application prospects.

Precision and uncertainty in natural gas calorific value estimation: advanced combinatorial predictive models for complex pipeline systems

Abstract In recent years, natural gas pipelines have been characterized by multiple intake points, the mixing of different gas sources, and significant variations in gas quality. The existing volumetric measurement system is no longer suitable for the development and operation of natural gas pipelines in China. To ensure accurate and equitable implementation of natural gas measurement, there is a gradual shift towards energy measurement. However, due to numerous measurement interfaces, installing chromatographs at all measurement stations would lead to substantial investment costs. Therefore, predicting the calorific value of natural gas is a key technology for energy measurement. In view of the issues existing in the current methods of obtaining natural gas calorific value, different prediction models of natural gas calorific value are constructed. According to the influencing factors of natural gas calorific value, the uncertainty evaluation is carried out, and the accuracy of different calorific value prediction models is analyzed by case data. The maximum error of regression equation, response surface analysis, BP neural network and genetic algorithm prediction model is 2.29%, 0.43%, 0.59% and 0.45% respectively. However, the combined calorific value (CCV) prediction model is 0.41%. The results indicate that the predicted value calculated by the CCV prediction model is closer to the actual value and has higher prediction performance, which provides a new method for the calorific value prediction and measurement management of natural gas.

Influence of block arrangement on mechanical performance in topological interlocking assemblies: A study of the versatile block

Topological interlocking assemblies (TIA) are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are prevented by the neighbouring blocks and the frame. In the literature, several blocks are introduced that can be arranged into interlocking assemblies, however only few of them can be arranged in non-unique ways. This study investigates a particularly versatile interlocking block called the Versatile Block: this block can be arranged in three different doubly periodic ways given by wallpaper symmetries. We investigate the hypothesis that the arrangement of copies of the same block influences the mechanical response of a TIA. We examine the interlocking mechanism and the correlation between arrangement and overall structural performance in planar TIA consisting of the Versatile Block. Furthermore, we analyse load transfer mechanisms within the assemblies and from the assemblies onto the frame. For fast apriori evaluation of the load transfer onto the frame we introduce a combinatorial model called Interlocking Flows. To investigate our assemblies from a mechanical point of view we conduct several finite element studies. These reveal a strong influence of arrangement on the structural behaviour, for instance, an impact on both the point and amount of maximum deflection under a given load, thereby confirming our hypothesis. We also evaluate the accuracy of the proposed Interlocking Flow model by a comparison with the finite element simulations.

Combinatorics of Double Grothendieck Polynomials

We give a thorough combinatorial treatment of double Grothendieck polynomials that is accessible to anyone with a basic knowledge of algebra and combinatorics. The text includes many new combinatorial models for these and related polynomials and provides detailed combinatorial proofs. We generalize the Giambelli formula for double Schubert polynomials to a $k$-theoretic version and our proof specializes to a new combinatorial proof of the former.

Accurate Oil Temperature Prediction Model and Oil Refilling Parameters Optimization for Hydraulic Closed-Circuit System

Oil temperature plays a crucial role in hydraulic closed-circuit systems (HCS), and conventional thermal equilibrium models and coupled simulation models face challenges in terms of accuracy, efficiency, and cost when calculating oil temperature. This study introduces an innovative HCS oil temperature precise prediction model and oil refilling parameter optimization method. The initial sample space was determined through a Sobol sensitivity analysis and improved Latin hypercube sampling, leading to the development of a combinatorial agent model (CAM) suitable for oil temperature prediction with superior accuracy and stability compared to other methods. Based on CAM, the optimal oil refilling flow rates under various operational conditions are computed. To validate the efficacy of the theoretical analysis, an HCS experiment platform was established. The data indicates that the temperature prediction error range of the CAM model falls between 0.30 °C and 1.05 °C, and optimizing the oil refilling flow rate can effectively enhance system efficiency while ensuring that the oil temperature remains within permissible limits. The research methodology and findings are applicable in engineering practice and can be extended to optimize the design of other hydraulic systems.

Oriented posets, rank matrices and q-deformed Markov numbers

We define oriented posets with corresponding rank matrices, where linking two posets by an edge corresponds to matrix multiplication. In particular, linking chains via this method gives us fence posets, and taking traces gives us circular fence posets. As an application, we give a combinatorial model for q-deformed Markov numbers. We also resolve a conjecture of Leclere and Morier-Genoud and give several identities between circular rank polynomials.

A combinatorial model reduction method for the finite element analysis of wind instruments

AbstractA high‐fidelity finite element model is proposed for the complete simulation of the time‐harmonic acoustic propagation in wind instruments. The challenge is to meet the extremely high accuracy required by professional musicians, in a complex domain, for all fingerings and over a wide frequency range, within an affordable computational time. Several modelling assumptions are made to limit the numerical complexity of the problem while preserving all relevant physics. A dedicated high‐performance solution strategy is also proposed, based on partitioning, condensation and model order reduction, exploiting the combinatorial nature of wind instrument fingerings. Finally, the proposed approach is applied to the simulation of an alto saxophone. An order of magnitude reduction in memory and computational cost is achieved.

Cellular automata-lattice Boltzmann model for polycrystalline solidification with motion of numerous dendrites

A GPU-accelerated cellular automata-lattice Boltzmann combinatorial model is developed for calculating the preferred growth, movement, and collision behavior of equiaxed crystals in supercooled melts of binary alloys. For moving dendrites, the growth is computed in a dynamic grid that grows with the body, and continuous movement is achieved by moving the dynamic grid. The impulse-based method is used for the collision of dendrites to calculate the post-collision velocity. Each module of the model was rigorously benchmarked, proving that the model has good computational accuracy and efficiency. The model was used for modeling the solidification of an Al-3 wt% Cu alloy, simulating the growth of abundant kinematic equiaxed crystals in a rotating flow and the falling and stacking of dendrites in droves and subsequent grain growth during the columnar to equiaxed transition, respectively.

Acyclic Reorientation Lattices and Their Lattice Quotients

We prove that the acyclic reorientation poset of a directed acyclic graph D is a lattice if and only if the transitive reduction of any induced subgraph of D is a forest. We then show that the acyclic reorientation lattice is always congruence normal, semidistributive (thus congruence uniform) if and only if D is filled, and distributive if and only if D is a forest. When the acyclic reorientation lattice is semidistributive, we introduce the ropes of D that encode the join irreducible acyclic reorientations and exploit this combinatorial model in three directions. First, we describe the canonical join and meet representations of acyclic reorientations in terms of non-crossing rope diagrams. Second, we describe the congruences of the acyclic reorientation lattice in terms of lower ideals of a natural subrope order. Third, we use Minkowski sums of shard polytopes of ropes to construct a quotientope for any congruence of the acyclic reorientation lattice.

A classifier based on mixed radial basis function network and combinatorial optimization model for medical diseases diagnosis

A classifier based on mixed radial basis function network and combinatorial optimization model for medical diseases diagnosis

A combinatorial model for q-characters of fundamental modules of type Dn

In this paper, we introduce a combinatorial path model of representation of the quantum affine algebra of type D n , inspired by Mukhin and Young’s combinatorial path models of representations of the quantum affine algebras of types A n and B n . In particular, we give a combinatorial formula for q-characters of fundamental modules of type D n by assigning each path to a monomial or binomial. By counting our paths, a new expression on dimensions of fundamental modules of type D n is obtained.