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arXiv:2607.15280v1 Announce Type: new Abstract: Sequential diagnosis requires balancing diagnostic accuracy against resource costs through iterative information gathering. Existing Large Language Model (LLM) approaches exhibit a critical knowledge-reasoning gap: despite encoding extensive medical knowledge, they struggle to reason systematically under cost constraints, often resorting to excessive testing. We propose GraphDx, a knowledge-enhanced framework with two core innovations. First, we design an automated pipeline that leverages LLMs to construct Medical Diagnosis Knowledge Graphs (MDKGs) with quantized typicality, action-centric topology, and dual-objective attributes for both diagnostic relevance and cost-sensitivity. Second, we introduce three collaborative agents (Perception, Reasoning, and Decision) where the Perception and Decision Agents handle language understanding and generation, while the Reasoning Agent performs deterministic evidence scoring and cost-aware planning
arXiv:2607.15293v1 Announce Type: new Abstract: Dyadic and circular convolution can both be computed in $O(N\log N)$ time using the Hadamard transform and the FFT-computed discrete Fourier transform (DFT), respectively. The Hadamard transform is preferable for its real-valued sign flips, yet its substitution for the DFT introduces algebraic error. We present three complementary results that characterize this error. First, we identify exact error cancellation: two input and two output positions are universally error-free, and no reordering of the output can eliminate this error. Second, the error operator is nearly full rank, while its null space has only logarithmic dimension. Third, the expected error is governed by a single alignment scalar, with a closed-form expression obtained by averaging over random filters. In general, the substitution error asymptotically doubles the output energy, except for filters in the universal zero-error subspace, which incur no error. Collectively, the
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