Papers

Nanopore-based single-molecule protein sequencing promises direct readout of amino acid sequences without amplification. This review examines three core nanopore strategies: (1) direct sequencing using aerolysin and Cu(II)-functionalized MspA nanopores that electrically discriminate all twenty proteinogenic amino acids with up to 99.1% classification accuracy; (2) label-assisted sensing that converts protein identity into DNA barcode or chemical tag signals for multiplexed detection; and (3) native protein sensing via electroosmotic flow through engineered CytK pores, enabling translocation of full-length proteins under opposing electrophoretic force. Deep learning-assisted post-translational modification detection at single-residue resolution is also discussed. Key challenges in translocation control, signal resolution, and bioinformatic infrastructure are evaluated.

Abstract The Erd˝os–Gy´arf´as conjecture asks whether every finite simple graph of minimum degree at least three contains a cycle whose length is a power of two. Suppose that a counterexample G exists and choose one first with minimum order and, subject to that, minimum size. Write a =|V3(G)|, b =|V≥4(G)|. Building on the minimal-counterexample structure developed by Markstr¨om and Carr, we obtain two computer-assisted additive constraints on the degree distribution. First, a ≥2b+8 for every such minimal counterexample. Equivalently, |V3(G)| ≥ 2|V(G)|+8 3 Second, in the range b ≥ 14 we prove the stronger bound a ≥2b+10. . The proof suppresses certain cubic vertices to a simple 2-degenerate graph Q on the high-degree vertices and uses the exact identity a =2b+d+E+z, d=2b−e(Q), d≡z (mod2). For large b, fixed-defect extremal bounds on Q suffice. The remaining small orders are reduced to finite families. Their lift obstructions are verified using independent forbidden-cycle imple mentations, exact component enumerations, and small integer charging certificates. For the +10 theorem, the final path-only obstruction consists of 1943 static endpoint-budget certificates λ : E(Q) → {0,1,2}. Full source code, finite case data, certificates, hashes, and reproduction scripts are separated from the manuscript in the accompanying reproducibility package.

Let $p$ be an odd prime, $F$ a complete DVF of characteristic $0$ with $\mu_p\subset F$, and $D\simeq(a_1,b_1)_F\otimes_F(a_2,b_2)_F$ a decomposable central division algebra of index $p^2$ and period $p$. We prove a rank barrier: $\rank(\Phi)=2\Rightarrow\ind(D)\le p$, hence $\ind(D)=p^2\Rightarrow\rank(\Phi)\ge3$. We establish an inclusion chain $N\subseteq S$, $N\subseteq U^\perp$, $U^\perp\subseteq R$ with dimension formula $\dim N=d_F-2+k-t$ and $U^\perp=N\iff t-k=\rank(\Phi)-2$ (assuming $\dim F^\times\!/F^{\times p}<\infty$). Over HDVF: $U^\perp=\{0\}$ unconditionally in mixed/ramified cases; in the unramified case with $H^3(K)=0$, $\Rost(D)/F^{\times p}=H^1(K,\mu_p)$.

线粒体是真核细胞中负责能量代谢的关键细胞器，其自身携带的线粒体DNA（mtDNA）突变可导致多种严重的遗传性疾病。近年来，线粒体基因编辑技术的快速发展为治疗这类疾病提供了新的可能。本文综述了线粒体基因编辑技术的发展历程，从早期的锌指核酸酶（ZFN）和转录激活因子样效应物核酸酶（TALEN）到新一代的碱基编辑技术（DdCBE、TALED等），介绍了各类编辑工具的核心原理及其在线粒体中的适配策略。同时，本文总结了该技术在线粒体遗传病治疗、农业育种以及疾病模型构建等方面的应用进展，并对当前面临的脱靶效应、递送效率、伦理争议等挑战进行了分析，最后展望了未来的发展方向。

Recently developed fused-ring organic electron-acceptors such as Y6 have strong oscillator strength, good charge-carrier transport and low bandgaps. They therefore have enormous current technical application to optoelectronic devices, such as solar cells. Due to the large number of atoms involved in representative aggregates of these materials, we need an efficient electronic structure method to model them. Standard density functional theory poorly describe charge-transfer states, and were developed for vacuum calculations of individual molecules. In this work we tune a range-separated hybrid functional for Y6. We characterise representative dimers of the solid-state and show that Y6 dimers show the extensive solvatochromic effects are due, in part, to oscillator strength borrowing. We provide an explanation for the short optimally tuned range-separation parameter, based in the Penn model for the frequency dependent dielectric of a semiconductor. We caution that standard range-separated hybrids are less accurate than global hybrids for these, and similar, materials. We show how reducing the range-separation length improves the accuracy of standard functionals, without an involved tuning process.

We demonstrate that the three-movement structure of Beethoven’s Piano Sonata No. 14 in C♯ minor (“Moonlight Sonata,” Op. 27 No. 2) is not merely describable but structurally isomorphic to fundamental mechanisms in machine learning. Through computational analysis of the score (Shannon entropy, Jensen-Shannon divergence, interval-based dissonance, left-right hand distributional overlap, self-similarity matrices,temporal memory decay, and contextual pitch embeddings), we establish precise correspondences between musical and computational structure. Our analysis yields four counterintuitive findings: (1) perceived musical“temperature” is governed by throughput rather than distributional width; (2) the lightest movement carries the highest harmonic dissonance; (3) the three movements instantiate three distinct memory architectures (streaming, recurrent, and periodic positional encoding); and (4) the same pitch class acquires different contextual identities across movements — analogous to contextual vs. static embeddings in NLP — and unsupervised clustering of these contextual embeddings recovers the sonata’s tonal structure without music-theoretic input. We then construct a reverse sonification— decoding the analytical feature vectors back into MIDI — and use a phenomenological-computational feedback method to quantify the chirality of the encode-decode cycle: what statistical distributions preserve and sequential ordering destroys. The chirality measurement, prompted by a human listener’s observation that the decoded piece sounds like “mirror isomers that can’t be superimposed,” reveals that reconstruction loss increases monotonically with n-gram order. Bootstrap null baselines and subsample robustness checks confirm that all three movements carry sequential in formation significantly above sampling noise, though raw chirality values are confounded by sample size — a finding we report transparently, as the robustness analysis itself demonstrates the methodology’s capacity for self-correction. Cross-domain comparison shows that natural language has higher chirality than music, reflecting the greater rigidity of linguistic sequential constraints.