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We establish a list of characterizations of bounded twin-width for hereditary classes of totally ordered graphs: as classes of at most exponential growth studied in enumerative combinatorics, as monadically NIP classes studied in model theory, as classes that do not transduce the class of all graphs studied in finite model theory, and as classes for which model checking first-order logic is fixed-parameter tractable studied in algorithmic graph theory. This has several consequences. First, it allows us to show that every hereditary class of ordered graphs either has at most exponential growth, or has at least factorial growth. This settles a question first asked by Balogh et al. [5] on the growth of hereditary classes of ordered graphs, generalizing the Stanley-Wilf conjecture/Marcus-Tardos theorem. Second, it gives a fixed-parameter approximation algorithm for twin-width on ordered graphs. Third, it yields a full classification of fixed-parameter tractable first-order model checking on hereditary classes of ordered binary structures. Fourth, it provides a model-theoretic characterization of classes with bounded twin-width. Finally, it settles the small conjecture [8] in the case of ordered graphs. [ABSTRACT FROM AUTHOR]

Game comonads, introduced by Abramsky, Dawar and Wang and developed by Abramsky and Shah, give an interesting categorical semantics to some Spoiler-Duplicator games that are common in finite model theory. In particular they expose connections between one-sided and two-sided games, and parameters such as treewidth and treedepth and corresponding notions of decomposition. In the present paper, we expand the realm of game comonads to logics with generalised quantifiers. In particular, we introduce a comonad graded by two parameters n ≤ k such that isomorphisms in the resulting Kleisli category are exactly Duplicator winning strategies in Hella's n-bijection game with k pebbles. We define a one-sided version of this game which allows us to provide a categorical semantics for a number of logics with generalised quantifiers. We also give a novel notion of tree decomposition that emerges from the construction. [ABSTRACT FROM AUTHOR]

Let $\mathscr {C}$ be a class of finite and infinite graphs that is closed under induced subgraphs. The well-known Łoś–Tarski Theorem from classical model theory implies that $\mathscr {C}$ is definable in first-order logic by a sentence $\varphi $ if and only if $\mathscr {C}$ has a finite set of forbidden induced finite subgraphs. This result provides a powerful tool to show nontrivial characterizations of graphs of small vertex cover, of bounded tree-depth, of bounded shrub-depth, etc. in terms of forbidden induced finite subgraphs. Furthermore, by the Completeness Theorem, we can compute from $\varphi $ the corresponding forbidden induced subgraphs. This machinery fails on finite graphs as shown by our results: – There is a class $\mathscr {C}$ of finite graphs that is definable in first-order logic and closed under induced subgraphs but has no finite set of forbidden induced subgraphs. – Even if we only consider classes $\mathscr {C}$ of finite graphs that can be characterized by a finite set of forbidden induced subgraphs, such a characterization cannot be computed from a first-order sentence $\varphi $ that defines $\mathscr {C}$ and the size of the characterization cannot be bounded by $f(|\varphi |)$ for any computable function f. Besides their importance in graph theory, the above results also significantly strengthen similar known theorems for arbitrary structures. [ABSTRACT FROM AUTHOR]

Finite model theory is currently not one of the hot topics in the philosophy and history of mathematics, not even in the philosophy and history of mathematical logic. The philosophy of mathematics and mathematical logic has concentrated on infinite structures, closely related to foundational issues. In that context, finite models deserved only marginal attention because it was taken for granted that the study of finite structures is trivial compared to the study of infinite structures. In retrospect, research on finite structures turned out to be neither trivial nor irrelevant but had an important impact on theoretical computer science. A closer look at the early history of the spectrum problem shows that the birth of finite model theory has roots in formal logic, at a time when computer science did not yet exist. [ABSTRACT FROM AUTHOR]

The pebbling comonad, introduced by Abramsky, Dawar and Wang, provides a categorical interpretation for the k-pebble games from finite model theory. The coKleisli category of the pebbling comonad specifies equivalences under different fragments and extensions of infinitary k-variable logic. Moreover, the coalgebras over this pebbling comonad characterise treewidth and correspond to tree decompositions. In this paper we introduce the pebble-relation comonad, which characterises pathwidth and whose coalgebras correspond to path decompositions. We further show that the existence of a coKleisli morphism in this comonad is equivalent to truth preservation in the restricted conjunction fragment of k-variable infinitary logic. We do this using Dalmau’s pebble-relation game and an equivalent all-in-one pebble game. We then provide a similar treatment to the corresponding coKleisli isomorphisms via a bijective version of the all-in-one pebble game. Finally, we show as a consequence a new Lovász-type theorem relating pathwidth to the restricted conjunction fragment of k-variable infinitary logic with counting quantifiers. [ABSTRACT FROM AUTHOR]

There is no analytical solution to the deflection influence line of catenary hingeless arches nor an explicit solution to the deflection influence line difference curvature of variable section hingeless arches. Based on the force method equation, a deflection influence line analytical solution at any location before and after structural damage is obtained, and then an explicit solution of the deflection influence line difference curvature of the structural damage is obtained. The indexes suitable for arch structure damage identification are presented. Based on analytical theory and a finite element model, the feasibility of identifying damage at a single location and multiple locations of an arch bridge is verified. This research shows that when a moving load acts on a damaged area of an arch structure, the curvature of the deflection influence line difference will mutate, which proves theoretically that the deflection influence line difference curvature can be used for the damage identification of hingeless arch structures. This research has provided theoretical support for hingeless arch bridge design and evaluation. Combined with existing bridge monitoring methods, the new bridge damage identification method proposed in this paper has the potential to realize normal health status assessments of existing arch bridges in the future. [ABSTRACT FROM AUTHOR]

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative Hasse–Schmidt derivations [13] and about Galois actions [14]. As an application of our methods, we obtain a new model complete theory of actions of a finite group on fields of finite imperfection degree. [ABSTRACT FROM AUTHOR]

The morphological surface of the human brain is still puzzling to scientists. During the last few decades, studies have addressed different aspects of this phenomenon. The underlying cellular processes occurring at the microscopic scale are certainly important for the folding process. However, there is also an essential contribution from mechanical forces generated at the macroscopic scale during these processes. Many previous studies confirmed this fact, but still, most of them have not considered the link between cellular processes and mechanical forces. Recently, we have explained how the proliferation in different zones of the brain, cell migration, and neuronal connectivity affect the folding through a multifield computational model coupling an advection‐diffusion model with the theory of finite growth. We mathematically describe the cellular behavior of cells to control mechanical growth in both radial and circumferential directions. To deal with issues regarding numerical stability of the advection‐diffusion equation, which lead to temporal and spatial numerical oscillations, reduced efficiency of the numerical solver, and inaccurate results, we introduce an artificial diffusivity, which we apply only when the actual cell density does not satisfy the balance equation. The proposed method stabilizes the numerical solution and significantly improves the simulation results without additional numerical cost. It allows us to study brain development in 2D and 3D. [ABSTRACT FROM AUTHOR]

External bonding with fiber-reinforced polymer (FRP) offers a potential solution to mitigate the detrimental effects caused by load impact and corrosion, which can weaken the bond strength of reinforced concrete structures. However, existing models need to be improved in addressing the FRP confinement mechanism and failure modes. As a solution, the proposed model employs stress intensity factor (SIF)-based criteria to determine the internal pressure exerted on the steel-concrete interface during various stages of comprehensive concrete cracking. Critical parameters are evaluated using weight function theory and a finite element model. A bond-slip model is introduced for the FRP-concrete interface and reasonable assumptions on failure plane characteristics. The internal pressure model employed demonstrates that FRP confinement has the ability to generate dual peaks in stress distribution and modify their magnitude as the confinement level increases. The proposed predictive model demonstrates superior performance in failure modes, test methods, and wrap methods for assessing bond strength with FRP confinement. The accuracy of this model is indicated by an integral absolute error (IAE) of 9.6% based on 125 experimental data, surpassing the performance of the other three existing models. Moreover, a new confinement parameter is introduced and validated, showing an upper bound of 0.44 for enhancing FRP bond strength. Additionally, a general expression validating the bond strength model with FRP confinement is established, allowing for the prediction of bond length. [ABSTRACT FROM AUTHOR]

Composite beam theory was previously developed to establish an analytical solution for determining the transfer length of prestressed fiber-reinforced polymers (FRP) tendons in pretensioned concrete members. In the present study, a novel finite element (FE) modeling approach is proposed to provide further verification of the developed analytical method. The present FE model takes into account the friction coefficients obtained from pull-out tests on the FRP tendons and prestressed concrete members. Convergence analysis of two numerical simulations with different mesh densities is carried out as well. The results demonstrated that the transfer length predicted by the fine FE model with a friction coefficient of α   =   0.3 for high pretension is in good agreement with the measured values and the analytical solutions. The consistency between the analytical solution and FE simulation not only further proves the reliability of composite beam theory but also demonstrates the importance of the bond–slip relationship in predicting the transfer length of pretensioned concrete members prestressed with FRP tendons. [ABSTRACT FROM AUTHOR]

It is commonly known that the conjunctive query entailment problem for certain extensions of (the well-known ontology language) ALC is computationally harder than their knowledge base satisfiability problem while for others the complexities coincide, both under the standard and the finite-model semantics. We expose a uniform principle behind this divide by identifying a wide class of (finitely) locally-forward description logics, for which we prove that (finite) query entailment problem can be solved by a reduction to exponentially many calls of the (finite) knowledge base satisfiability problem. Consequently, our algorithm yields tight ExpTime upper bounds for locally-forward logics with ExpTime-complete knowledge base satisfiability problem, including logics between ALC and μALCHbregQ (and more), as well as ALCSCC with global cardinality constraints, for which the complexity of querying remained open. Moreover, to make our technique applicable in future research, we provide easy-to-check sufficient conditions for a logic to be locally-forward based on several novel versions of the model-theoretic notion of unravellings. Together with existing results, this provides a nearly complete classification of the "benign" vs. "malign" primitive modelling features extending ALC, missing out only the Self operator. We then show a rather surprising result, namely that the conjunctive entailment problem for ALCSelf is exponentially harder than for ALC. This places the seemingly innocuous Self operator among the "malign" modelling features, like inverses, transitivity or nominals. [ABSTRACT FROM AUTHOR]

Liquid crystal elastomers (LCEs) hold a major promise as a versatile material platform for smart soft coatings since their orientational order can be predesigned to program a desired dynamic profile. In this work, we introduce temperature-responsive dynamic coatings based on LCEs with arrays of singular defects-disclinations that run parallel to the surface. The disclinations form in response to antagonistic patterns of the molecular orientation at the top and bottom surfaces, imposed by the plasmonic mask photoalignment. Upon heating, an initially flat LCE coating develops linear microchannels located above each disclination. The stimulus that causes a non-flat profile of LCE coatings upon heating is the activation force induced by the gradients of molecular orientation around disclinations. To describe the formation of microchannels and their thermal response, we adopt a Frank–Oseen model of disclinations in a patterned director field and propose a linear elasticity theory to connect the complex spatially varying molecular orientation to the displacements of the LCE. The thermo-responsive surface profiles predicted by the theory and by the finite element modeling are in good agreement with the experimental data; in particular, higher gradients of molecular orientation produce a stronger modulation of the coating profile. The elastic theory and the finite element simulations allow us to estimate the material parameter that characterizes the elastomer coating's response to the thermal activation. The disclination-containing LCEs show potential as soft dynamic coatings with a predesigned responsive surface profile. [ABSTRACT FROM AUTHOR]

Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structures. In this paper, we develop a framework whereby the essential properties of these categories of coalgebras are captured in a purely axiomatic fashion. To this end, we introduce arboreal categories, which have an intrinsic process structure, allowing dynamic notions such as bisimulation and back-and-forth games, and resource notions such as number of rounds of a game, to be defined. These are related to extensional or "static" structures via arboreal covers, which are resource-indexed comonadic adjunctions. These ideas are developed in a general, axiomatic setting, and applied to relational structures, where the comonadic constructions for pebbling, Ehrenfeucht-Fraïssé and modal bisimulation games recently introduced by Abramsky, Dawar et al. are recovered, showing that many of the fundamental notions of finite model theory and descriptive complexity arise from instances of arboreal covers. [ABSTRACT FROM AUTHOR]

This note draws conclusions that arise by combining two recent papers, by Anuj Dawar, Erich Grädel and Wied Pakusa, published at ICALP 2019, and by Moritz Lichter, published at LICS 2021. In both papers, the main technical results rely on the combinatorial and algebraic analysis of the invertible-map equivalences |${\equiv ^{\text {IM}}_{k, Q}}$| on certain variants of Cai–Fürer–Immerman structures (CFI-structures for short). These |${\equiv ^{\text {IM}}_{k, Q}}$| -equivalences, for a natural number |$k$| and a set of primes |$Q$|⁠ , refine the well-known Weisfeiler–Leman equivalences used in algorithms for graph isomorphism. The intuition is that two graphs |$G{\equiv ^{\text {IM}}_{k, Q}}H$| cannot be distinguished by iterative refinements of equivalences on |$k$| -tuples defined via linear operators on vector spaces over fields of characteristic |$p \in Q$|⁠. In the first paper it has been shown, using considerable algebraic machinery, that for a prime |$q \notin Q$|⁠ , the |${\equiv ^{\text {IM}}_{k, Q}}$| equivalences are not strong enough to distinguish between non-isomorphic CFI-structures over the field |$\mathbb {F}_q$|⁠. In the second paper, a similar but not identical construction for CFI-structures over the rings |$\mathbb {Z}_{2^i}$| has, again by rather involved combinatorial and algebraic arguments, been shown to be indistinguishable with respect to |${\equiv ^{\text {IM}}_{k, \{2\}}}$|⁠. Together with an earlier work on rank logic, this second result suffices to separate rank logic from polynomial time. We show here that the two approaches can be unified to prove that CFI-structures over the rings |$\mathbb {Z}_{2^i}$| are in fact indistinguishable with respect to |${\equiv ^{\text {IM}}_{k, {\mathbb {P}}}}$|⁠ , for the set |${\mathbb {P}}$| of all primes. In particular, this implies the following two results. First, there is no fixed |$k$| such that the invertible-map equivalence |${\equiv ^{\text {IM}}_{k, {\mathbb {P}}}}$| coincides with isomorphism on all finite graphs. Second, no extension of fixed-point logic by linear-algebraic operators over fields can capture polynomial time. [ABSTRACT FROM AUTHOR]

Let G be a graph on n vertices with adjacency matrix A , and let 1 be the all-ones vector. We call G controllable if the set of vectors 1, A 1,..., An-1 1 spans the whole space Rn. We characterize the isomorphism problem of controllable graphs in terms of other combinatorial, geometric and logical problems. We also describe a polynomial time algorithm for graph isomorphism that works for almost all graphs. [ABSTRACT FROM AUTHOR]

The human brain has a highly complex structure both on the microscopic and on the macroscopic scales. Increasing evidence has suggested the role of mechanical forces for cortical folding -- a classical hallmark of the human brain. However, the link between cellular processes at the microscale and mechanical forces at the macroscale remains insufficiently understood. Recent findings suggest that an additional proliferating zone, the outer subventricular zone (OSVZ), is decisive for the particular size and complexity of the human cortex. To better understand how the OSVZ affects cortical folding, we establish a multifield computational model that couples cell proliferation in different zones and migration at the cell scale with growth and cortical folding at the organ scale by combining an advection- diffusion model with the theory of finite growth. We validate our model based on data from histologically stained sections of the human fetal brain and predict 3D pattern formation. Finally, we address open questions regarding the role of the OSVZ for the formation of cortical folds. The presented framework not only improves our understanding of human brain development, but could eventually help diagnose and treat neuronal disorders arising from disruptions in cellular development and associated malformations of cortical development. [ABSTRACT FROM AUTHOR]

The effect of normal stress variations on fault frictional strength has been extensively characterized in laboratory experiments and modelling studies based on a rate-and-state-dependent fault friction formalism. However, the role of pore pressure changes during injection-induced fault reactivation and associated frictional phenomena is still not well understood. We apply rate-and-state friction (RSF) theory in finite element models to investigate the effect of fluid pressurization rate on fault (re)activation and on the resulting frictional slip characteristics at the laboratory scale. We consider a stepwise injection scenario where each fluid injection cycle consists of a fluid pressurization phase followed by a constant fluid pressure phase. We first calibrate our model formulation to recently published laboratory results of injection-driven shear slip experiments. In a second stage, we perform a parametric study by varying fluid pressurization rates to cover a higher dimensional parameter space. We demonstrate that, for high permeability laboratory samples, the energy release rate associated with fault reactivation can be effectively controlled by a stepwise fluid injection scheme, i.e. by the applied fluid pressurization rate and the duration of the constant pressure phase between each successive fluid pressurization phase. We observe a gradual transition from fault creep to slow stick–slip as the fluid pressurization rate increases. Furthermore, computed peak velocities for an extended range of fluid pressurization rate scenarios (0.5 MPa/min to 10 MPa/min) indicate a non-linear (power-law) relationship between the imposed fluid pressurization rate and the peak slip velocities, and consequently with the energy release rate, for scenarios with a fluid pressurization rate higher than a critical value of 4 MPa/min. We also observe that higher pressurization rates cause a delay in the stress release by the fault. We therefore argue that by adopting a stepwise fluid injection scheme with lower fluid pressurization rates may provide the operator with a better control over potential induced seismicity. The implications for field-scale applications that we can derive from our study are limited by the high matrix and fault permeability of the selected sample and the direct hydraulic connection between the injection well and the fault, which may not necessarily represent the conditions typical for fracture dominated deep geothermal reservoirs. Nevertheless, our results can serve as a basis for further laboratory experiments and field-scale modelling studies focused on better understanding the impact of stepwise injection protocols on fluid injection-induced seismicity. [ABSTRACT FROM AUTHOR]

We consider two-variable first-order logic FO2 and its quantifier alternation hierarchies over both finite and infinite words. Our main results are forbidden patterns for deterministic automata (finite words) and for Carton-Michel automata (infinite words). In order to give concise patterns, we allow the use of subwords on paths in finite graphs. This concept is formalized as subword-patterns. For certain types of subword-patterns there exists a non-deterministic logspace algorithm to decide their presence or absence in a given automaton. In particular, this leads to NL algorithms for deciding the levels of the FO2 quantifier alternation hierarchies. This applies to both full and half levels, each over finite and infinite words. Moreover, we show that these problems are NL-hard and, hence, NL-complete. [ABSTRACT FROM AUTHOR]

Finite F-representation type is an important notion in characteristic p commutative algebra, but explicit examples of varieties with or without this property are few. We prove that a large class of homogeneous coordinate rings in positive characteristic will fail to have finite F-representation type. To do so, we prove a connection between differential operators on the homogeneous coordinate ring of X and the existence of global sections of a twist of (SymmΩX)V. By results of Takagi and Takahashi, this allows us to rule out finite F-representation type for coordinate rings of varieties with (SymmΩX)V not "positive." By using positivity and semistability conditions for the (co)tangent sheaves, we show that several classes of varieties fail to have finite F-representation type, including many Calabi-Yau varieties and complete intersections of general type. Our work also provides examples of the structure of the ring of differential operators for non-F-pure varieties, which to this point have largely been unexplored. [ABSTRACT FROM AUTHOR]

In the present work, nonlinear free vibration analysis of composite laminated plates and shallow cylindrical/spherical/hyperboloid shell panels considering geometric nonlinearity is carried out using non-polynomial inverse trigonometric higher-order shear deformation theory with seven degrees of freedo (DOFs). The present theory assumes parabolic variation of out-of-plane stresses and satisfies traction-free boundary conditions on the top and bottom surfaces of the composite as a priori. A nonlinear finite element model is developed and applied to obtain discretized nonlinear equations. The geometric nonlinearity in sense of Green-Lagrange considering von-Kármán assumptions is incorporated in formulation. An eight noded efficient C0 continuous isoparametric rectangular finite element is implemented in the present nonlinear analysis. The efficacy and accuracy of the present theory and finite element model is validated with the available literature results. For the analysis, various types of plates and shell panels with different material properties, lamination schemes, thickness ratios, aspect ratios, modular ratios, curvature ratios, and boundary conditions are considered. The effects of these different geometric and material properties on nonlinear frequency ratios at various amplitude ratios are examined in detail. [ABSTRACT FROM AUTHOR]

FC\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\textsf{FC}}$$\end{document} is a finite model variant on the theory of concatenation, FC[REG]\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\textsf{FC}[\textsf{REG}]}$$\end{document} extends FC\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\textsf{FC}}$$\end{document} with regular constraints. This paper considers the languages generated by their conjunctive query fragments, FC-CQ and FC[REG]-CQ. We compare the expressive power of FC[REG]-CQ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\textsf {FC[REG]-CQ}}$$\end{document} to that of various related language generators, such as regular expressions, patterns, and typed patterns. We then consider decision problems for FC-CQ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\textsf {FC-CQ}}$$\end{document} and FC[REG]-CQ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\textsf {FC[REG]-CQ}}$$\end{document}, and show that certain static analysis problems (such as equivalence and regularity) are undecidable. While this paper defines FC-CQ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\textsf {FC-CQ}}$$\end{document} based on the logic FC\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\textsf{FC}}$$\end{document}, it can equally be understood as synchronized intersections of pattern languages, or as systems of restricted word equations. [ABSTRACT FROM AUTHOR]

This article continues the theoretical study of weighted structures in mathematical fuzzy logic focusing on the finite model theory of fuzzy logics valued on arbitrary finite $\mathrm{MTL}$ -chains. We show that for any first-order (or infinitary with finitely many variables) formula $\varphi$ , there is a truth-value that $\varphi$ takes almost surely in every finite many-valued model and such that every other truth-value is almost surely not taken. This generalizes a theorem in the fuzzy setting due to Robert Kosik and Christian G. Fermüller. [ABSTRACT FROM AUTHOR]

This paper proposes a novel fully nonlinear refined beam element for pre-twisted structures undergoing large deformation and finite untwisting. The present model is constructed in the twisted basis to account for the effects of geometrical nonlinearity and initial twist. Cross-sectional deformation is allowed by introducing Lagrange polynomials in the framework of a Carrera unified formulation. The principle of virtual work is applied to obtain the Green–Lagrange strain tensor and second Piola–Kirchhoff stress tensor. In the nonlinear governing formulation, expressions are given for secant and tangent matrices with linear, nonlinear, and geometrically stiffening contributions. The developed beam model could detect the coupled axial, torsional, and flexure deformations, as well as the local deformations around the point of application of the force. The maximum difference between the present deformation results and those of shell/solid finite element simulations is 6%. Compared to traditional beam theories and finite element models, the proposed method significantly reduces the computational complexity and cost by implementing constant beam elements in the twisted basis. [ABSTRACT FROM AUTHOR]

We investigate the accuracies of different coupled cluster levels in a finite model solid, the 14 electron spin-non-polarised uniform electron gas. For densities between rs = 0.5 a0 and rs = 5 a0, we calculate ground state correlation energies with stochastic coupled cluster ranging from coupled cluster singles and doubles (CCSD) to coupled cluster including all excitations up to quintuples (CCSDTQ5). We find the need to add triple excitations for an accuracy of 0.01 eV/electron beyond rs = 0.5 a0. Quadruple excitations start being significant past rs = 3 a0. At rs = 5 a0, CCSD gives a correlation energy with a 16% error and coupled cluster singles doubles and triples is in error by 2% compared to the CCSDTQ5 result. CCSDTQ5 gives an energy in agreement with full configuration interaction quantum Monte Carlo results. [ABSTRACT FROM AUTHOR]

• Brain contusions caused by both free-fall and drop-hammer conditions are coup injuries. • Brain contusion occurs surrounding the impact location under free-fall condition. • Contusion occurs just right beneath the impact location under drop-hammer condition. • The impact force curves under two conditions go the same but different for ICPs. • The peak forces increase with impact energy in a power function, the same as ICPs. Brain contusion is a prevalent traumatic brain injury (TBI) in low-age children, bearing the potential for coma and fatality. Hence, it is imperative to undertake comprehensive research in this field. This study employed 4-week-old piglets as surrogates for children and introduced self-designed devices for both free-fall drop impact tests and drop-hammer impact tests. The study explored the characteristics of brain contusion and dynamic responses of brain under these distinct testing conditions. Brain contusions induced by free-fall and drop-hammer conditions both were categorized as the coup injury, except that slight difference in the contusion location was observed, with contusion occurring mainly in the surrounding regions beneath the impact location under free-fall condition and the region just right beneath the impact location under drop-hammer condition. Analysis of impact force and intracranial pressure (ICP) curves indicated similar trends in impact forces under both conditions, yet different trends in ICPs. Further examination of the peak impact forces and ICPs elucidated that, with increasing impact energy, the former followed a combined power and first-order polynomial function, while the latter adhered to a power function. The brain contusion was induced at the height (energy) of 2 m (17.2 J), but not at the heights of 0.4, 0.7, 1, 1.35 and 1.7 m, when the vertex of the piglet head collided with a rigid plate. In the case of a cylindrical rigid hammer (cross-sectional area constituting 40 % of the parietal bone) striking the head, the brain contusion was observed under the energy of 21.9 J, but not under energies of 8.1 J, 12.7 J and 20.3 J. Notably, the incidence of brain contusion was more pronounced under the free-fall condition. These findings not only facilitate a comprehensive understanding of brain contusion dynamics in pediatric TBIs, but also contribute to the validation of theories and finite element models for piglet heads, which are commonly employed as surrogates for children. [ABSTRACT FROM AUTHOR]

With the development of volleyball, the development of traditional school volleyball has been paid increasing attention. This has also aroused the concern of schools, coaches, and athletes and has become the focus of volleyball development and reserve talent training. The purpose of this paper is to use the knowledge of biomechanics to study serving technology and attacking technology in volleyball. In the aspect of biomechanics, this paper proposes the finite element modeling theory of the human body. The upper limbs of volleyball players are modeled and analyzed, and four powerful teams are selected for video analysis of volleyball offensive skills. The overall difference between athletes in different groups is very obvious. The phase with the longest time and the greatest difference was the P3 phase, which took 0.802 ± 0.085 seconds. [ABSTRACT FROM AUTHOR]

The celebrated Erdős–Stone–Simonovits theorem characterizes the asymptotic maximum edge density in F -free graphs as 1 − 1 / (χ (F) − 1) + o (1) , where χ (F) is the minimum chromatic number of a graph in F. In [6, Examples 25 and 31] , it was shown that this result can be extended to the general setting of graphs with extra structure: the asymptotic maximum edge density of a graph with extra structure without some induced subgraphs is 1 − 1 / (χ (I) − 1) + o (1) for an appropriately defined abstract chromatic number χ (I). As the name suggests, the original formula for the abstract chromatic number is so abstract that its (algorithmic) computability was left open. In this paper, we both extend this result to characterize maximum asymptotic density of t -cliques in graphs with extra structure without some induced subgraphs in terms of χ (I) and we present a more concrete formula for χ (I) that allows us to show its computability when both the extra structure and the forbidden subgraphs can be described by a finitely axiomatizable universal first-order theory. Our alternative formula for χ (I) makes use of a partite version of Ramsey's Theorem for structures on first-order relational languages. [ABSTRACT FROM AUTHOR]

Fatigue evolution under continued stresses is a process of degradation of material performance with many uncertainties. In order to quantify the uncertainties of materials and working conditions, a probabilistic method is utilized to estimate the reliability of structures by considering scatter of the fatigue life prediction model, in which improvements are provided to model the accumulation of the damage. Firstly, the fatigue parameters are modeled by the Bayesian theory and the finite element analysis. Secondly, the distributions of parameters are transformed by the probabilistic method into the distribution of fatigue life by using the fatigue life prediction model, and a damage accumulation model is chosen to characterize regulation evolution of properties. Finally, the probability distribution function transformation approach is employed to expound distribution of fatigue damage by the known distribution of fatigue life, and a general probabilistic method is then used to estimate the reliability. By combining the above methods, the framework for reliability analysis is established and then is used to calculate the reliability for high-pressure turbine blades in a low cycle fatigue region under variable amplitude loadings. [ABSTRACT FROM AUTHOR]

We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory. Employing synthetic accounts of enumerability and decidability, we give a full classification of FSAT depending on the first-order signature of non-logical symbols. On the one hand, our development focuses on Trakhtenbrot's theorem, stating that FSAT is undecidable as soon as the signature contains an at least binary relation symbol. Our proof proceeds by a many-one reduction chain starting from the Post correspondence problem. On the other hand, we establish the decidability of FSAT for monadic first-order logic, i.e. where the signature only contains at most unary function and relation symbols, as well as the enumerability of FSAT for arbitrary enumerable signatures. To showcase an application of Trakhtenbrot's theorem, we continue our reduction chain with a many-one reduction from FSAT to separation logic. All our results are mechanised in the framework of a growing Coq library of synthetic undecidability proofs. [ABSTRACT FROM AUTHOR]

In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer Science, but there may also be something of interest for model theorists and other logicians. The basic setting involves studying the category of relational structures via a resource-indexed family of adjunctions with some process category - which unfolds relational structures into tree-like forms, allowing natural resource parameters to be assigned to these unfoldings. One basic instance of this scheme allows us to recover, in a purely structural, syntax-free way: the Ehrenfeucht-Fraïssé game; the quantifier rank fragments of first-order logic; the equivalences on structures induced by (i) the quantifier rank fragments, (ii) the restriction of this fragment to the existential positive part, and (iii) the extension with counting quantifiers; and the combinatorial parameter of tree-depth (Nesetril and Ossona de Mendez). Another instance recovers the k-pebble game, the finite-variable fragments, the corresponding equivalences, and the combinatorial parameter of treewidth. Other instances cover modal, guarded and hybrid fragments, generalized quantifiers, and a wide range of combinatorial parameters. This whole scheme has been axiomatized in a very general setting, of arboreal categories and arboreal covers. Beyond this basic level, a landscape is beginning to emerge, in which structural features of the resource categories, adjunctions and comonads are reflected in degrees of logical and computational tractability of the corresponding languages. Examples include semantic characterisation and preservation theorems, and Lovász-type results on counting homomorphisms. [ABSTRACT FROM AUTHOR]

We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among finite graphs. (This fact is a consequence of a general theorem proved by L. Ham and M. Jackson, and the counterpart of this fact for all bipartite graphs in the class of all graphs is a well-known consequence of the compactness theorem.) Also, to exemplify that our method is applicable in various fields of mathematics, we prove that neither finite simple groups, nor the ordered sets of join-irreducible congruences of slim semimodular lattices can be described by finitely many axioms in the class of finite structures. Since a 2007 result of G. Grätzer and E. Knapp, slim semimodular lattices have constituted the most intensively studied part of lattice theory and they have already led to results even in group theory and geometry. In addition to the non-axiomatizability results mentioned above, we present a new property, called Decomposable Cyclic Elements Property, of the congruence lattices of slim semimodular lattices. [ABSTRACT FROM AUTHOR]

In this paper, we define soaker ideals in an MV -algebra, and study the relationships between soaker ideals and the other ideals in an involutive MV -algebras. Then we introduce a topology on the set of all the soaker ideals, which we call reflectional topology, and give a basis for it. By defining the notion of join-soaker ideals, we show that the reflectional topology is compact. We also give a characterization of connectedness of the reflectional topology. Finally, we investigate the properties of T0 and T1-space in this topology. [ABSTRACT FROM AUTHOR]

Probabilistic logic programming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of uncertainty. However, the behaviour of statistical relational representations across variable domain sizes is complex, and scaling inference and learning to large domains remains a significant challenge. In recent years, connections have emerged between domain size dependence, lifted inference and learning from sampled subpopulations. The asymptotic behaviour of statistical relational representations has come under scrutiny, and projectivity was investigated as the strongest form of domain size dependence, in which query marginals are completely independent of the domain size. In this contribution we show that every probabilistic logic program under the distribution semantics is asymptotically equivalent to an acyclic probabilistic logic program consisting only of determinate clauses over probabilistic facts. We conclude that every probabilistic logic program inducing a projective family of distributions is in fact everywhere equivalent to a program from this fragment, and we investigate the consequences for the projective families of distributions expressible by probabilistic logic programs. [ABSTRACT FROM AUTHOR]

Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures. In particular, Ehrenfeucht–Fraïssé games, pebble games and bisimulation games play a central role. We show how each of these types of games can be described in terms of an indexed family of comonads on the category of relational structures and homomorphisms. The index |$k$| is a resource parameter that bounds the degree of access to the underlying structure. The coKleisli categories for these comonads can be used to give syntax-free characterizations of a wide range of important logical equivalences. Moreover, the coalgebras for these indexed comonads can be used to characterize key combinatorial parameters: tree depth for the Ehrenfeucht–Fraïssé comonad, tree width for the pebbling comonad and synchronization tree depth for the modal unfolding comonad. These results pave the way for systematic connections between two major branches of the field of logic in computer science, which hitherto have been almost disjoint: categorical semantics and finite and algorithmic model theory. [ABSTRACT FROM AUTHOR]

We consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP, extend the guarded fragment of first-order logic and the guarded least fixpoint logic, respectively. They also extend the recently introduced unary negation fragments of first-order logic and of least fixpoint logic. We show that the satisfiability problem for GNFO and for GNFP is 2ExpTime-complete, both on arbitrary structures and on finite structures. We also study the complexity of the associated model checking problems. Finally, we show that GNFO and GNFP are not only computationally well behaved, but also model theoretically: we show that GNFO and GNFP have the tree-like model property and that GNFO has the finite model property, and we characterize the expressive power of GNFO in terms of invariance for an appropriate notion of bisimulation. Our complexity upper bounds for GNFO and GNFP hold true even for their "clique-guarded" extensions CGNFO and CGNFP, in which clique guards are allowed in the place of guards. [ABSTRACT FROM AUTHOR]

The logic MMSNP is a restricted fragment of existential second-order logic which can express many interesting queries in graph theory and finite model theory. The logic was introduced by Feder and Vardi, who showed that every MMSNP sentence is computationally equivalent to a finite-domain constraint satisfaction problem (CSP); the involved probabilistic reductions were derandomized by Kun using explicit constructions of expander structures. We present a new proof of the reduction to finite-domain CSPs that does not rely on the results of Kun. The new universalalgebraic proof allows us to obtain a stronger statement and to verify the more general Bodirsky--Pinsker dichotomy conjecture for CSPs in MMSNP. Our approach uses the fact that every MMSNP sentence describes a finite union of CSPs for countably infinite ѡ-categorical structures; moreover, by a recent result of Hubička and Nešetřil, these structures can be expanded to homogeneous structures with finite relational signature and the Ramsey property. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach that focuses on application of cooperative game theory model for automated finite element model updating. The approach involves transforming the conventional single-objective optimization finite element model updating problem into a game theory problem. Among the different alternatives, a cooperative game model is considered to solve the transformed updating problem. This new approach overcomes the limitations of the conventional single-objective optimization formulation, which include challenges related to selecting appropriate weighting factor of residuals and analysing their influence on optimization results. To demonstrate the effectiveness of the proposed approach, an ultralight fibre reinforced polymer footbridge is considered. The numerical model of the footbridge is updated using the experimentally determined inherent properties (natural frequencies and mode shapes) using the proposed approach. A comparison with the conventional sensitivity-based weighted single objective method reveals that the inclusion of the weighting factor in the optimization process under the cooperative game model method allows for more efficient solution of the single-objective updating optimization problem, while maintaining accuracy and quality in the updated model. [ABSTRACT FROM AUTHOR]

We introduce a new framework for a descriptive complexity approach to arithmetic computations. We define a hierarchy of classes based on the idea of counting assignments to free function variables in first-order formulae. We completely determine the inclusion structure and show that #P and # AC 0 appear as classes of this hierarchy. In this way, we unconditionally place # AC 0 properly in a strict hierarchy of arithmetic classes within #P. Furthermore, we show that some of our classes admit efficient approximation in the sense of FPRAS. We compare our classes with a hierarchy within #P defined in a model-theoretic way by Saluja et al. and argue that our approach is better suited to study arithmetic circuit classes such as # AC 0 which can be descriptively characterized as a class in our framework. [ABSTRACT FROM AUTHOR]