Strength estimation and adjustment are crucial in designing human-AI interactions, particularly in games where AI surpasses human players. This paper introduces a novel strength system, including a strength estimator (SE) and an SE-based Monte Carlo tree search, denoted as SE-MCTS, which predicts strengths from games and offers different playing strengths with human styles. The strength estimator calculates strength scores and predicts ranks from games without direct human interaction. SE-MCTS utilizes the strength scores in a Monte Carlo tree search to adjust playing strength and style. We first conduct experiments in Go, a challenging board game with a wide range of ranks. Our strength estimator significantly achieves over 80% accuracy in predicting ranks by observing 15 games only, whereas the previous method reached 49% accuracy for 100 games. For strength adjustment, SE-MCTS successfully adjusts to designated ranks while achieving a 51.33% accuracy in aligning to human actions, outperforming a previous state-of-the-art, with only 42.56% accuracy. To demonstrate the generality of our strength system, we further apply SE and SE-MCTS to chess and obtain consistent results. These
A novel analytical framework for power system strength was recently introduced in the IEEE Transactions on Power Systems, providing a unified formulation for assessing voltage and frequency strength. Building upon this formulation, this paper addresses a series of practical challenges for translating the theoretical framework into a real-world application. In particular, simplified analytical solutions for network-wide bus-level strength metrics are provided, together with compact expressions to capture the impact of relevant devices on strength. In addition, novel normalized strength metrics at a device level are defined, enabling the comparison of strength across different systems. A strength source model is introduced to study the behavior of devices under varying strength conditions. Finally, the framework is implemented in a real-world study case, demonstrating its applicability and potential as a practical tool for a comprehensive strength assessment.
Material strength is a classical concept with renewed importance in fracture mechanics, particularly in crack nucleation in brittle solids. We formulate material strength in finite elasticity and examine its geometric, constitutive, and symmetry-theoretic foundations. Spatial covariance requires a strength function to depend on both stress and the corresponding strain measure, so that strength is governed by the pair (stress,strain), not stress alone, and only then can representations based on different stress measures be consistently related, with classical stress-based criteria recovered as a special case. We analyze covariance under spatial diffeomorphisms and relate formulations based on the first Piola--Kirchhoff, second Piola--Kirchhoff, and Cauchy stresses. For stress-based criteria, we define the strength hypersurface as a subset of the constitutively admissible stress manifold and study the associated safe domain. Under standard regularity assumptions and the requirement that sufficiently large stresses are inadmissible, the strength surface is a smooth compact hypersurface of this manifold. For isotropic solids, we show that the safe domain is star-shaped under a proporti
In order to make argumentation-based inference contestable, it is crucial to explain what changes can achieve a desired (instead of the contested) inference result. To this end, we introduce strength change explanations for quantitative (bipolar) argumentation graphs. Strength change explanations describe changes to the initial strengths of a subset of the arguments in a given graph that can achieve a desired ordering based on the final strengths of some (potentially different) subset of arguments. We show that the existing notions of inverse and counterfactual problems can be reduced to strength change explanations. We also prove basic soundness and completeness properties of our strength change explanations, and demonstrate their existence and non-existence in some special cases. By applying a heuristic search, we demonstrate that we can often successfully find strength change explanations for layered graphs that are common in typical application scenarios; still, limitations remain for settings where we do not provide guarantees for the presence (or absence) of explanations.
As a generalization of super magic strength, the strength of a graph was introduced in [R. Ichishima, F.A. Muntaner-Batle, A. Oshima, Bounds for the strength of graphs, Austral. J. of Combin. 72(3) (2018) 492-508]. For a vertex ordering $f$ of graph $G$, the strength of $f$ is the maximum sum of the labels on any pair of adjacent vertices. The strength of $G$ is defined as the minimum strength of $f$, taken over all vertex orderings of $G$. The strength of the hypercube is unknown, but bounded. In this note, we provide an improved upper bound for the strength of a hypercube.
In this paper, we study the existence problem for spherical \(T\)-designs on the \(d\)-dimensional sphere, where \(T\) is an infinite subset of \(\mathbb N\). We show that, if \(d\ge 2\), then a finite subset of \(S^d\) has infinite harmonic strength if and only if it is antipodal. For \(d=1\), we show that infinite strength spherical designs are exactly cyclotomic designs, and we characterize their existence in terms of certain \(0\)-\(1\) polynomials. We also prove that the harmonic strength of every infinite strength spherical design has the weak GCD property. Finally, for a given infinite subset \(T\subset \mathbb N\) with the weak GCD property, we give a finite procedure to decide whether there exists \(X\subset S^1\) such that \(\operatorname{Hst}(X)=T\), and apply this criterion to concrete existence and non-existence examples.
This paper explores the relationship between accent strength and articulatory features inferred from acoustic speech. To quantify accent strength, we compare phonetic transcriptions with transcriptions based on dictionary-based references, computing phoneme-level difference as a measure of accent strength. The proposed framework leverages recent self-supervised learning articulatory inversion techniques to estimate articulatory features. Analyzing a corpus of read speech from American and British English speakers, this study examines correlations between derived articulatory parameters and accent strength proxies, associating systematic articulatory differences with indexed accent strength. Results indicate that tongue positioning patterns distinguish the two dialects, with notable differences inter-dialects in rhotic and low back vowels. These findings contribute to automated accent analysis and articulatory modeling for speech processing applications.
We establish new lower bounds for the strength and partition rank of the determinant. For every prime $p$, we prove the exact identity \[ \operatorname{str}(\mathrm{det}_p)=p. \] A weak monotonicity argument, combined with a bound for gaps between consecutive primes, then gives $\operatorname{str}(\mathrm{det}_n)\ge (1-o(1))n^{0.475}$ for sufficiently large $n$. Since the Birch rank of $\mathrm{det}_n$ is always $4$, this gives the first explicit family showing that the dependence on the degree in bounds for strength in terms of Birch rank is unavoidable. Viewing $\mathrm{det}_n$ as an $n$-linear form in its columns, we also prove that its partition rank is at least the largest prime not exceeding $n$. Consequently, \[ n-n^{0.525}\le \operatorname{prk}(\mathrm{det}_n)\le n \] for all sufficiently large $n$, and hence the partition rank of the determinant is $n-o(n)$. The proof introduces an intersection-theoretic method for lower-bounding strength: a short strength decomposition produces a nowhere-vanishing section of a split vector bundle on the complement of the determinantal hypersurface, while a nonzero top Chern class in the Chow ring of $\mathrm{PGL}_n$ obstructs such a secti
In a generic hybrid network, classical, quantum, and no-signaling sources emit local hidden variables, stabilizer states, and no-signaling systems, respectively. We investigate the maximal correlation strength as the non-classical feature in this network. Given the associated fully-quantum network of a hybrid network, we exploit the stabilizing operators of the distributed quantum state to construct segmented Bell operators and the Bell inequalities tailored to the state. We derive the upper bounds of the maximal correlation strengths in the associated full-classical, full-quantum, and fully-no-signaling networks as the benchmarks. Our study shows that the achievable correlation strength depends on the number of type-A measurements and that of nonlocal sources. We also introduce the t-nonlocality criteria, indicating that the achievable maximal correlation strength cannot modeled by the network with at least t observers with local hidden variables performing type-A measurements.
This paper proposes a methodology for architecting microstructures with extremal stiffness, yield, and buckling strength using topology optimization. The optimized microstructures reveal an interesting transition from simple lattice like structures for yield-dominated situations to hierarchical lattice structures for buckling-dominated situations. The transition from simple to hierarchical is governed by the relative yield strength of the constituent base material as well as the volume fraction. The overall performances of the optimized microstructures indicate that maximum strength is determined by the buckling strength at low volume fractions and yield strength at higher volume fractions, regardless of the base material's relative yield strength. The non-normalized properties of the optimized microstructures show that higher base material Young's modulus leads to both higher Young's modulus and strength of the architected microstructures. Furthermore, the polynomial order of the maximum strength lines with respect to mass density obtained from the optimized microstructures reduces as base material relative yield strength decreases, reducing from 2.3 for buckling dominated Thermop
The basic input for many real objects is a finite cloud of unordered points. The strongest equivalence between objects in practice is rigid motion in a Euclidean space. A recent polynomial-time classification of point clouds required a Lipschitz continuous function that vanishes on degenerate simplices, while the usual volume is not Lipschitz. We define the strength of any geometric simplex and prove its continuity under perturbations with explicit bounds for Lipschitz constants.
Despite advancements in silicon-based anodes for high-capacity lithium-ion batteries, their widespread commercial adoption is still hindered by significant volume expansion during cycling, especially at high active mass loadings crucial for practical use. The root of these challenges lies in the mechanical instability of the material, which subsequently leads to the structural failure of the electrode. Here, we present a novel synthesis of a composite combining expanded graphite and silicon nanoparticles. This composite features a unique interlayer-bonded graphite structure, achieved through the application of a modified spark plasma sintering method. Notably, this innovative structure not only facilitates efficient ion and electron transport but also provides exceptional mechanical strength (Vickers hardness: up to 658 MPa, Young's modulus: 11.6 GPa). This strength effectively accommodates silicon expansion, resulting in an impressive areal capacity of 2.9 mA h cm-2 (736 mA h g-1) and a steady cycle life (93% after 100 cycles). Such outstanding performance is paired with features appropriate for large-scale industrial production of silicon batteries, such as active mass loading of
The metallurgy and materials communities have long known and exploited fundamental links between chemical and structural ordering in metallic solids and their mechanical properties. The highest reported strength achievable through the combination of multiple metals (alloying) has rapidly climbed and given rise to new classifications of materials with extraordinary properties. Metallic glasses and high-entropy alloys are two limiting examples of how tailored order can be used to manipulate mechanical behavior. Here, we show that the complex electronic-structure mechanisms governing the peak strength of alloys and pure metals can be reduced to a few physically-meaningful parameters based on their atomic arrangements and used (with no fitting parameters) to predict the maximum strength of any metallic solid, regardless of degree of structural or chemical ordering. Predictions of maximum strength based on the activation energy for a stress-driven phase transition to an amorphous state is shown to accurately describe the breakdown in Hall-Petch behavior at the smallest crystallite sizes for pure metals, intermetallic compounds, metallic glasses, and high-entropy alloys. This activation
A numbering $f$ of a graph $G$ of order $n$ is a labeling that assigns distinct elements of the set $\{1,2, \ldots, n \}$ to the vertices of $G$. The strength $\mathrm{str}\left(G\right) $ of $G$ is defined by $\mathrm{str}\left( G\right) =\min \left\{ \mathrm{str}_{f}\left( G\right)\left\vert f\text{ is a numbering of }G\right. \right\}$, where $\mathrm{str}_{f}\left( G\right) =\max \left\{ f\left( u\right) +f\left( v\right) \left\vert uv\in E\left( G\right) \right. \right\} $. A few lower and upper bounds for the strength are known and, although it is in general hard to compute the exact value for the strength, a reasonable approach to this problem is to study for which graphs a lower bound and an upper bound for the strength coincide. In this paper, we study general conditions for graphs that allow us to determine which graphs have the property that lower and upper bounds for the strength coincide and other graphs for which this approach is useless.
We use the quasiparticle random phase approximation with a few Skyrme density functionals to calculate strength functions in the Jpi = 0+, 1-, and 2+ channels for even Ca, Ni, and Sn isotopes, from the proton drip line to the neutron drip line. We show where and how low-lying strength begins to appear as N increases. We also exhibit partial energy-weighted sums of the transition strength as functions of N for all nuclei calculated, and transition densities for many of the interesting peaks. We find that low-energy strength increases with N in all multipoles, but with distinctive features in each. The low-lying 0+ strength near the neutron at large N barely involves protons at all, with the strength coming primarily from a single two-quasineutron configuration with very large spatial extent. The low-lying 1- strength is different, with protons contributing to the transition density in the nuclear interior together with neutrons at large radii. The low-lying 2+ transition strength goes largely to more localized states. The three Skyrme interactions we test produce similar results, differing most significantly in their predictions for the location of the neutron drip line, the boundar
The alignment strength of a graph matching is a quantity that gives the practitioner a measure of the correlation of the two graphs, and it can also give the practitioner a sense for whether the graph matching algorithm found the true matching. Unfortunately, when a graph matching algorithm fails to find the truth because of weak signal, there may be "phantom alignment strength" from meaningless matchings that, by random noise, have fewer disagreements than average (sometimes substantially fewer); this alignment strength may give the misleading appearance of significance. A practitioner needs to know what level of alignment strength may be phantom alignment strength and what level indicates that the graph matching algorithm obtained the true matching and is a meaningful measure of the graph correlation. The {\it Phantom Alignment Strength Conjecture} introduced here provides a principled and practical means to approach this issue. We provide empirical evidence for the conjecture, and explore its consequences.
For any graph $G$ of order $p$, a bijection $f: V(G)\to [1,p]$ is called a numbering of the graph $G$ of order $p$. The strength $str_f(G)$ of a numbering $f: V(G)\to [1,p]$ of $G$ is defined by $str_f(G) = \max\{f(u)+f(v)\; |\; uv\in E(G)\},$ and the strength $str(G)$ of a graph $G$ itself is $str(G) = \min\{str_f(G)\;|\; f \mbox{ is a numbering of } G\}.$ A numbering $f$ is called a strength labeling of $G$ if $str_f(G)=str(G)$. In this paper, we obtained a sufficient condition for a graph to have $str(G)=|V(G)|+\d(G)$. Consequently, many questions raised in [Bounds for the strength of graphs, {\it Aust. J. Combin.} {\bf72(3)}, (2018) 492--508] and [On the strength of some trees, {\it AKCE Int. J. Graphs Comb.} (Online 2019) doi.org/10.1016/j.akcej.2019.06.002] are solved. Moreover, we showed that every graph $G$ either has $str(G)=|V(G)|+\d(G)$ or is a proper subgraph of a graph $H$ that has $str(H) = |V(H)| + \d(H)$ with $\d(H)=\d(G)$. Further, new good lower bounds of $str(G)$ are also obtained. Using these, we determined the strength of 2-regular graphs and obtained new lower bounds of $str(Q_n)$ for various $n$, where $Q_n$ is the $n$-regular hypercube.
Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In this paper I present counterexamples, natural instances of nonlinearity and illfoundedness in the hierarchy of large cardinal consistency strength, as natural or as nearly natural as I can make them. I present diverse cautious enumerations of ZFC and large cardinal set theories, which exhibit incomparability and illfoundedness in consistency strength, and yet, I argue, are natural. I consider the philosophical role played by "natural" in the linearity phenomenon, arguing ultimately that we should abandon empty naturality talk and aim instead to make precise the mathematical and logical features we had found desirable.
The level densities and $γ$-ray strength functions of $^{105,106,111,112}$Cd have been extracted from particle-$γ$ coincidence data using the Oslo method. The level densities are in very good agreement with known levels at low excitation energy. The $γ$-ray strength functions display no strong enhancement for low $γ$ energies. However, more low-energy strength is apparent for $^{105,106}$Cd than for $^{111,112}$Cd. For $γ$ energies above $\approx$ 4 MeV, there is evidence for some extra strength, similar to what has been previously observed for the Sn isotopes. The origin of this extra strength is unclear; it might be due to $E1$ and $M1$ transitions originating from neutron skin oscillations or the spin-flip resonance, respectively.
Interaction strength is introduced in a model of evolution in d-dimension space. It is realized by imposing a constraint concerning 2d differences of fitnesses between that of any extremal site and those of its 2d nearest neighbours at each time step in the evolution of the model. For any given interaction strength between 0 and 1 the model can self-organize to a critical state. Two exact equations found in Bak-Sneppen model still hold in our model for different interaction strength. Simulations of one- and two-dimensional models for ten different values of interaction are given. It is found that self-organized threshold decreases with interaction strength increasing. It is also shown that the critical exponent, and two basic exponents, avalanche distribution, and avalanche dimension, are interaction strength dependent.