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Glass transition is a reversible transition that occurs in most amorphous materials. However, the nature of glass transition remains far from being clarified. A key to understand the glass transition is to clarify what determines the glass transition temperature (Tg) and liquid fragility (m). Here the glass transition thermodynamics for 150 different glass-forming systems are studied statistically. It is found that the activation characters in the energy landscape are crucial to precisely portray the glass transition and, in particular, both the activation free energy (G*) and the activation entropy (S*) play critical roles. G* determines Tg, Tg=G*/290+25.5, while S* determines m, m=S*/Rln10+15 with R is gas constant. Based on the Boltzmann definition of entropy, the fragility is an indication of the number of the degeneracy of the evolution paths. This explains why the nano-confined, low-dimension or high-pressured glasses exhibit stronger characteristics, which has been a puzzling phenomenon for a long time.

In this study, we re-evaluated the superconducting properties of LK-99. The LK-99 samples were synthesized using the process proposed by the original Korean team. Additionally, we examined whether the results of the Korean team are related to Cu$_2$S by using ammonia solution (NH$_3$-H$_2$O) to remove Cu$_2$S . Through x-ray diffraction (XRD) analysis, a distinct Cu$_2$S phase was identified in the LK-99 samples. A subsequent treatment using an ammonia solution effectively eliminated this phase. The appearance of blue Cu$^{+2}$ ions in the solution and the elimination of the Cu$_2$S peak in XRD support the conclusion. The magnetic and electrical properties of LK-99 with and without Cu$_2$S postulate that the superconducting-like behavior in LK-99 predominantly arises from a transition in resistivity due to the influence of Cu$_2$S . As such, LK-99 is better classified as a diamagnetic semiconductor than a room-temperature superconductor. The room-temperature superconductors still require further research.

Complex systems, such as life and languages, are governed by principles of evolution. The analogy and comparison between biology and linguistics\cite{alphafold2, RoseTTAFold, lang_virus, cell language, faculty1, language of gene, Protein linguistics, dictionary, Grammar of pro_dom, complexity, genomics_nlp, InterPro, language modeling, Protein language modeling} provide a computational foundation for characterizing and analyzing protein sequences, human corpora, and their evolution. However, no general mathematical formula has been proposed so far to illuminate the origin of quantitative hallmarks shared by life and language. Here we show several new statistical relationships shared by proteins and words, which inspire us to establish a general mechanism of evolution with explicit formulations that can incorporate both old and new characteristics. We found natural selection can be quantified via the entropic formulation by the principle of least effort to determine the sequence variation that survives in evolution. Besides, the origin of power law behavior and how changes in the environment stimulate the emergence of new proteins and words can also be explained via the introduction of function connection network. Our results demonstrate not only the correspondence between genetics and linguistics over their different hierarchies but also new fundamental physical properties for the evolution of complex adaptive systems. We anticipate our statistical tests can function as quantitative criteria to examine whether an evolution theory of sequence is consistent with the regularity of real data. In the meantime, their correspondence broadens the bridge to exchange existing knowledge, spurs new interpretations, and opens Pandora's box to release several potentially revolutionary challenges. For example, does linguistic arbitrariness conflict with the dogma that structure determines function?

A congruence on an inverse semigroup $S$ is determined uniquely by its kernel and trace. Denoting by $\rho_k$ and $\rho_t$ the least congruence on $S$ having the same kernel and the same trace as $\rho$, respectively, and denoting by $\omega$ the universal congruence on $S$, we consider the sequence $\omega$, $\omega_k$, $\omega_t$, $(\omega_k)_t$, $(\omega_t)_k$, $((\omega_k)_t)_k$, $((\omega_t)_k)_t$, $\cdots$. The quotients $\{S/\omega_k\}$, $\{S/\omega_t\}$, $\{S/(\omega_k)_t\}$, $\{S/(\omega_t)_k\}$, $\{S/((\omega_k)_t)_k\}$, $\{S/((\omega_t)_k)_t\}$, $\cdots$, as $S$ runs over all inverse semigroups, form quasivarieties. This article explores the relationships among these quasivarieties.

One of the ultimate goals for linguists is to find universal properties in human languages. Although words are generally considered as representing arbitrary mapping between linguistic forms and meanings, we propose a new universal law that highlights the equally important role of syllables, which is complementary to Zipf's. By plotting rank-rank frequency distribution of word and syllable for English and Chinese corpora, visible lines appear and can be fit to a master curve. We discover the multi-layer network for words and syllables based on this analysis exhibits the feature of self-organization which relies heavily on the inclusion of syllables and their connections. Analytic form for the scaling structure is derived and used to quantify how Internet slang becomes fashionable, which demonstrates its usefulness as a new tool to evolutionary linguistics., Comment: 8 pages, 5 figures

Origami and crumpling are two extreme tools to shrink a 3-D shell. In the shrink/expand process, the former is reversible due to its topological mechanism, while the latter is irreversible because of its random-generated creases. We observe a morphological transition between origami and crumple states in a twisted cylindrical shell. By studying the regularity of crease pattern, acoustic emission and energetics from experiments and simulations, we develop a model to explain this transition from frustration of geometry that causes breaking of rotational symmetry. In contrast to solving von Karman-Donnell equations numerically, our model allows derivations of analytic formula that successfully describe the origami state. When generalized to truncated cones and polygonal cylinders, we explain why multiple and/or reversed crumple-origami transitions can occur., Comment: 6 pages, 5 figures

This paper enriches the list of known properties of congruence sequences starting from the universal relation and successively performing the operators lower $k$ and lower $t$. Two series of inverse semigroups, namely $\ker{\alpha_n}$-is-Clifford semigroups and $\beta_n$-is-over-$E$-unitary semigroups, are investigated. Two congruences, namely $\alpha_{n+2}$ and $\beta_{n+2}$, are found to be the least $\ker{\alpha_n}$-is-Clifford and least $\beta_n$-is-over-$E$-unitary congruences on $S$, respectively. A new system of implications is established for the quasivarieties of inverse semigroups induced by the min network.

This paper enriches the list of properties of the congruence sequences starting from the universal relation and successively performing the operations of lower $t$ and lower $k$. Three classes of completely regular semigroups, namely semigroups for which $\ker{\sigma}$ is a cryptogroup, semigroups for which $\ker{\nu}$ is a cryptogroup and semigroups for which $\kappa$ is over rectangular bands, are studied. $((\omega_t)_k)_t$, $((\mathcal{D}_t)_k)_t$ and $((\omega_k)_t)_k$ are found to be the least congruences on $S$ such that the quotient semigroups are semigroups for which $\ker{\sigma}$ is a cryptogroup, $\ker{\nu}$ is a cryptogroup and $\kappa$ is over rectangular bands, respectively. The results obtained present a response to three problems in Petrich and Reilly's textbook \textquoteleft\textquoteleft Completely Regular Semigroups\textquoteright\textquoteright.