Papers

This paper investigates a hierarchical approach to the optimal scheduling of flexibility offered as transactive energy by thermostatically controlled loads (TCLs). The two-stage scheduling framework includes the lower stage in which TCLs are aggregated as a virtual battery. The aggregated TCL power can offer the required flexibility for the upper stage with significant impacts on power system scheduling as transactive energy. Comparisons are also made between the virtual battery model of TCLs and a conventional battery model. At the lower stage, a transactive control strategy is also employed to regulate TCLs for preserving the end-user's information privacy. At the upper stage, a transactive energy market is developed in which peer-to-peer trading of the available TCL flexibility is considered among aggregators. Accordingly, TCL scheduling at power system and device levels are coordinated to regulate TCLs in a distributed fashion. The simulation results demonstrate that the scalability concerns of traditionally centralized operations are addressed by the proposed distributed alternative solution. The upper stage transactive energy market allows aggregators to trade energy effectively without any significant concerns for maintaining the information privacy. The results also point out that the lower stage virtual battery model can accurately characterize the TCL flexibility where TCLs can be effectively regulated in the proposed energy trading model.

大型语言模型(LLM)和自治Agent在动态环境中需要有效的知识更新以保持准确性，但现有的知识编辑方法存在灾难性的遗忘和主题主导性的干扰--修改一个事实--不经意地破坏了相关知识。同时，因果表示学习方法通常假设静态因果结构，而不能解决知识的时间演变。我们提出了因果蜘蛛网(CSW)，这是一种将知识表示为分层因果图的分层存储体系结构，它具有三个基本创新：(1)通过不覆盖现有节点的同级萌芽协议仅附加因果更新；(2)Bayesian张力模型，将节点可信度作为原则不确定性量化的Beta分布后验，以及(3)带有上下文覆盖的自动沉淀，该模型将稳定的知识提升到不可变的核心层，同时允许在不可辩驳的新证据到达时临时掩蔽过时的公理。证明了CSW是有界的、收敛的和因果一致的，大量的实验表明，CSW在保持近零的灾难性遗忘和完全有界的活动节点增长的同时，实现了最先进的多跳一致性，有效地消除了语义湮灭。

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.

Multi-unmanned aerial vehicle (Multi-UAV) path planning in complex three-dimensional (3D) environments is a challenging task due to high-dimensional search spaces, multiple constraints, and numerous local optima. To address these issues, this paper proposes a particle swarm optimization-based orthogonal perturbation operator algorithm (OPOPSO). The proposed algorithm, which introduces an orthogonal perturbation operator to break the rigid update pattern of traditional particle swarm optimization, can enhance global exploration and alleviate premature convergence. A dynamic topology reorganization mechanism is designed to establish randomized interaction topologies and select guiding exemplars for each particle, which enhances population diversity. Furthermore, an adaptive parameter control framework based on reinforcement learning is proposed. This framework integrates a Dueling Double Deep Q-Network with a dual reward mechanism to alleviate the sparse reward problem. Experiments are conducted on the CEC2017 benchmark suite, as well as on path planning simulations using real-world digital elevation model (DEM) maps derived from Australian LiDAR data. Experimental results illustrate that OPOPSO achieves competitive performance against 16 advanced optimization algorithms, including seven PSO variants, four differential evolution variants, and five other metaheuristics algorithms, on the benchmark suite, while also maintaining superior solution quality and scalability in complex 3D path planning tasks.

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 $H^3(K)=0$, $\Rost(D)/F^{\times p}=H^1(K,\mu_p)$.

We present a systematic and deliberately conservative synthesis of a 258-gate research archive on four-dimensional gravity, Batalin–Vilkovisky (BV) quantization, Bondi–Metzner–Sachs (BMS) boundary symmetry, infrared domains, and operator-theoretic completion. The archive contains exact finite checkers for each gate, but a finite checker is not identified with a proof of an infinite-dimensional theorem. We therefore separate four epistemic classes: (i) theorem-level statements whose hypotheses and analytic domains are fully stated; (ii) conditional theorems; (iii) finite algebraic or numerical skeletons; and (iv) open or retracted extrapolations. The strongest audited results are: the two-helicity quotient of linearized Einstein gravity; positive free graviton quantization away from zero momentum; the classical BV master equation and a local, formal causal-renormalization chain; a detailed classical BV–BFV/BMS boundary construction in specified jet and edge categories; a massless radiation Hilbert complex; a sharp collinear Sobolev trace theorem; and several no-go results showing that the standard angular L2 Fock representation does not support the actual order-zero collinear nonlinear block as a closable operator. For the diagonal trace Dt:Ht(S2)⊗2Ht(S2)⟶Ht(S2) we prove the sharp trichotomy t≤12:nonclosable,12<t≤1:closable but unbounded,t>1:bounded. Pure supertranslation phases intertwine exactly on the intrinsic collinear incidence measure, while a scalar complementary-series norm leaves only the candidate window 1/2<τ<1; that window is not an actual nonlinear Einstein–BV module. The audit also finds decisive failures in a later imported chain. In particular, a Lagrangian Weyl subalgebra was incorrectly treated as central; a nonconstant supertranslation multiplier was incorrectly assumed to commute with angular smoothing; an order-minus-two resolvent was incorrectly declared trace class on S2; and a sharp-cutoff compression proposal, tail-probability bounds, and uncertainty upper bounds were overinterpreted as self-adjoint truncation, dynamical barriers, and operational discreteness. Consequently the archive does not prove a one-loop boundary QME, an interacting BMS charge algebra, infrared-complete scattering, asymptotic completeness, black-hole information recovery, or complete quantum gravity. The paper includes the proof routes, dependency graph, failure modes, and a gate-by-gate evidence atlas needed for independent reconstruction.