“Our framework allows any tomographic data - including archival datasets -- to be reinterpreted in terms of fundamental nonlocality tests.”

“The paper proves that determining the thinness of a tree is coNP-hard.”

“The paper initiates the study of EF orientations, mostly under the lens of parameterized complexity, presenting various tractable cases, hardness results, and parameterizations.”

“The discrete period matrix admits the same canonical decomposition $Π= rac{1}{2} H + i T$ as in the smooth setting, where $H$ encodes the topological type and $T$ is purely imaginary.”

“The paper proves that the local limit of the weighted spanning trees on any simple connected high degree almost regular sequence of electric networks is the Poisson(1) branching process conditioned to survive forever.”

“The paper clarifies the roles of wavefunctions and averaging over moduli, concluding that holographic computations may be performed with or without averaging.”

“The paper derives the graphicality of infinite sequences for double power-laws, uncovering a rich phase-diagram and pointing out the existence of five qualitatively distinct ways graphicality can be violated.”

“The paper proves that the chromatic number of $P_5$-free graphs is at most a polynomial function of the clique number.”

“The holographic duals are ''bubbling wormhole'' geometries: multi-covers of AdS$_5$ $ imes S^5$ whose conformal boundary consists of multiple four-spheres intersecting on a common circle.”

“The tracking of multiple, unknown targets is formulated as a harmonic extension problem on a cellular sheaf, accommodating nonlinear dynamics and external disturbances for all agents.”

“The paper develops a solid geometric framework for the theory by creating isochrons, which are the level sets of the asymptotic phase, using the Graph Transform theorem.”

“An acyclic mcp graph is amenable if and only if a.e. component has at most two nonvanishing ends, while it is nowhere amenable exactly when a.e. component has a nonempty perfect (closed) set of nonvanishing ends.”

“The paper finds novel non-supersymmetric domain walls interpolating between different pairs of AdS extrema.”

“The paper derives explicit conditions that determine when certain values of N are valid for the encryption scheme.”

“The algorithm achieves linear time complexity when the number of colors is greater than 3.637 times the maximum degree plus 1.”

“The paper proves that the 'chordality condition' is also sufficient.”

“HOLOGRAPH provides rigorous mathematical foundations while achieving competitive performance on causal discovery tasks.”

“The construction makes it possible to design infinite families of graphs on which exact and stable completion is possible for every fixed rank matrix through the sum-of-squares hierarchy.”

“The paper focuses on the real eigenvalues of the non-backtracking matrix and their relation to the non-backtracking Laplacian for node clustering.”

“The context is from ArXiv, indicating a research paper.”

“The coarsening is realized by collapsing short edges. In order to capture the topological information required to calibrate the reduction level, we adapt the construction of classical topological descriptors made for point clouds (the so-called persistent diagrams) to spatial graphs.”

“The combined effect of the magnetic field and the TsT deformation singles out the special value k = -1/H. At this point, the perpendicular modes are restored.”

“The factor graph provides a cleaner, compact and non-redundant alternative to the graph A_4(S) by Barrus and West, for the particular case of split graphs.”

“For all \( n \geq \exp\exp(30.5) \), \( \mathrm{PD}_n \) is graphic.”

“Reconstruction is governed by a unified thermodynamic mechanism where high-index facets correspond to specific local minima in the surface energy landscape.”

“The paper proposes list and unique decoding algorithms for TGRS codes and Roth-Lempel codes based on the Guruswami-Sudan algorithm, achieving near-linear running time.”

“Hojabr integrates relational algebra, tensor algebra, and constraint-based reasoning within a single higher-order algebraic framework.”

“The paper establishes asymptotically tight lower and upper bounds on the over-thresholds and shows that for infinitely many instances of m the two bounds coincide.”

“The paper introduces the term Hoffman-London to refer to graphs that are minimal in this sense (minimizing H-colorings with paths).”

“The paper offers 'deeper insight into the model's development and more detailed implementation guidance, including code examples and mathematical derivations.'”

“The paper presents polynomial-time algorithms for MSC in several nontrivial settings.”

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“The running time of our algorithm for the global minimum cut problem is asymptotically better than the fastest sequential deterministic global minimum cut algorithm.”

“The paper determines the exact value of $\mathrm{ex}_r(n, ext{Berge-} kP_{\ell})$ when $n$ is large enough for $k\geq 2$, $r\ge 3$, $\ell'\geq r$ and $2\ell'\geq r+7$, where $\ell'=\left\lfloorrac{\ell+1}{2} ight floor$.”

“The NPRG approach allows one, in principle, to take into account all nonlinearities present in the elastic theory, in contrast to the SCSA treatment which requires, already at the formal level, significant simplifications.”

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“The paper establishes a correspondence between kernels in graph theory and specialized equilibria.”

“Grapheurs are well-suited to modeling hubs and connections between them in large graphs; previous notions of graph limits based on subgraph densities fail to adequately model such global structures as subgraphs are inherently local.”

“Any tropical circuit calculating the optimal value of a Traveling Salesperson round tour uses at least $2^{Ω(k \log \log k)}$ gates.”

“The paper establishes improved upper and lower bounds on γ(C_ℓ^k) for general ℓ not divisible by k. It also determines the exact value of γ(C_ℓ^k) for integers ℓ not divisible by k in a set of (natural) density at least φ(k)/k.”

“The paper introduces 'graph-restricted tensors' and demonstrates their utility in constructing non-stabilizer tensors for holographic models.”

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“The paper shows that the equational theory of relational Kleene algebra with graph loop is PSpace-complete.”

“The system exhibits a sharp, switch-like transition between a token-saturated state and an empty state.”

“The paper determines the exact rainbow number rb(G, H) where G is a multi-hubbed wheel graph W_d(s) and H = θ_{t,ℓ} represents a cycle C_t of length t with 0 ≤ ℓ ≤ t-3 chords emanating from a common vertex.”