Entropy

Large language models increasingly operate over long multi-turn interactions, where behavioral stability matters as much as single-answer correctness. We study the detection of behavioral anomalies—abrupt shifts in persona, topic, style, or use of context, independent of factual accuracy—from response embeddings and, for the predictive detector, embeddings of incoming user messages, without anomaly labels, external knowledge, or reference outputs; detectors are trained only on normal dialogues and calibrated on clean data. We release a reproducible primary benchmark of 700 multi-turn dialogues generated with Mistral-7B-Instruct—100 per anomaly type—together with cross-generator replications generated with Qwen2.5-7B-Instruct (139 dialogues) and Qwen3-8B (310 dialogues), plus matched six- and twenty-exchange corpora that vary conversation length. The benchmark spans four controlled anomaly types, clean controls, a natural topic adaptation control, per-turn intervention labels, and blind audits by LLMs and humans. Under a deliberately leakage-free protocol, we compare twelve detectors in terms of ROC- and PR-AUC, per-type performance, latency, and recall at a fixed false-positive budget, with cluster-bootstrap confidence intervals, multiple training seeds, and two encoders. The prediction-error + anchor fusion leads overall on the primary corpus (ROC-AUC of 0.762; PR-AUC of 0.771) and significantly exceeds the static anchor in the paired bootstrap, while no single detector leads for every anomaly type. The fusion also provides zero median latency and a 0.002 false-alarm rate under natural adaptation, where the anchor reaches 0.110. Proper change-point detectors do not beat the fusion or anchor, and lexical features remain useful for style shifts but false-alarm under natural adaptation. The context_ignore construction uses user questions that require prior context, manifests visibly in 13/16 audited cases, and is detectable (best per-type ROC-AUC of 0.865). Detector rankings remain stable across two encoders (ρ = 0.95) and dialogue lengths from six to twenty exchanges (ρ = 0.75–0.91). Cross-generator performance remains generator-dependent: fusion reaches 0.617 on Qwen2.5-139 and 0.688 (95% CI: [0.645, 0.732]) on Qwen3-310, versus 0.762 on size-matched Mistral-310; on Qwen3, its point advantage over the anchor (0.667) is inconclusive. These results show that detector choice depends on anomaly type, temporal shape, dialogue length, and generator.

DICOM files store diagnostic pixels together with structured patient attributes that stay linked to the examination in routine hospital use. Most image ciphers leave these tags in plaintext, and encrypting the whole bitstream can break the syntax required by PACS and DICOM viewers. The proposed dual-domain encryption algorithm targets both the sensitive tags (metadata domain) and the pixel data (image domain) of DICOM images, providing holistic protection for medical records by a two-dimensional quadratic memristive sine map (2D-QMSM). Under the selected parameters, both Lyapunov exponents stay positive over a wide interval, and the map supplies the pseudo-random source. Sensitive tag values are serialized, encrypted by AES-GCM with a key and nonce derived from the map, stored in private tags, and cleared from their original fields. Pixel data then pass through multiple rounds of encryption. A coordinate offset and joint plaintext–ciphertext feedback let the same keystream be reused, while a local change still spreads across the image. On several randomly selected 8-bit images from the RSNA Pneumonia Detection Challenge, the cipher-image entropy is 7.9998, adjacent-pixel correlations fall close to zero, and NPCR and UACI stay near 99.609% and 33.464%. Compared with recent medical-image ciphers, the scheme offers similar resistance to statistical and differential attacks and is the only one that also protects sensitive DICOM tags.

Purpose: To explore the estimated algorithmic complexity of encoded optical-filter transmittance spectra and visual-response data using the Block Decomposition Method (BDM), alongside conventional optical descriptors and symbol-frequency Shannon entropy. Methods: Four filters with different pigmentation times were each measured in a single spectral acquisition. Visual thresholds for detection, separation, alignment, and recognition were measured under baseline and four filter conditions in 235 eyes from 118 participants. Each spectrum and task–condition response column was independently min–max normalized and discretized. Wavelength-ordered one-dimensional BDM was the primary spectral analysis; two-dimensional arrangements were supplementary. Sensitivity to encoding, block size, observation order, remainder handling, and matrix representation was assessed. Visual changes were summarized descriptively within eyes; unavailable participant linkage prevented adjustment for fellow-eye dependence. Results: Under the original binary encoding, spectral Shannon entropy increased with pigmentation time, whereas one-dimensional normalized BDM (nBDM) ranged from 0.010058 to 0.010326 and followed a different filter ordering. Several spectral and visual-response rankings changed across computational settings. Within-eye mean threshold changes were negative across filters for detection and recognition, while separation and alignment showed different patterns. Visual-response nBDM described the encoded sequences and did not directly quantify these threshold changes. Conclusions: BDM provided an exploratory characterization conditional on the selected representation and analysis settings. Sensitivity analyses did not establish sampling uncertainty or statistical robustness. The findings do not validate filter classes or demonstrate clinical benefit, causality, or prediction of visual outcomes from spectral complexity. Repeated measurements, broader filter sampling, participant-linked data, and independent validation are required to assess practical utility.