We study the estimation of the offspring mean of a supercritical branching process in a random environment when multiple conditionally independent populations evolve in a common environment. Extending the single-population self-normalized Cramér moderate deviation theory to this multi-population setting, we introduce a pooled Lotka–Nagaev estimator and construct its associated martingale difference sequence. The core of the analysis is an exact decomposition of the pooled conditional variance, which, owing to the shared environment and conditional independence of the populations, separates the environmental and demographic sources of variability. This decomposition reveals a structural dichotomy: the environmental variance is undiluted by pooling, while the demographic variance is attenuated at a rate proportional to the inverse square of the number of populations. Verifying the two conditions of the martingale moderate-deviation theorem yields self-normalized Cramér moderate deviations for the pooled Student t-statistic, together with a Berry–Esseen bound, a moderate deviation principle, and confidence intervals for the offspring mean. The resulting pooling efficiency gain, in which the demographic variance decays inversely with the number of populations while the environmental variance forms an irreducible floor, has no analogue in any single-population framework and is confirmed by Monte Carlo simulation.
The ability to define a temperature scale that is independent of any particular material is important for testing quantum thermodynamic concepts at the nanoscale. Here, we present a method for constructing a thermodynamic temperature scale from the reversible operation of quantum dot heat engines. In the limit of vanishing dissipation and lifetime broadening, temperature ratios can be determined directly from measurable open-circuit voltages and combined into a self-consistent temperature scale.
Secure transmission and storage of color images remain challenging tasks due to strong inter-pixel correlations and high data volume. This work proposes a one-dimensional sine-tent-logistic-exponential map (STLEM) equipped with numerical boundary correction rules to mitigate finite-precision numerical degradation so as to enhance the unpredictability of chaos-driven cryptosystems. We benchmark STLEM against classic logistic, tent, and sine maps via Lyapunov exponents, autocorrelation, approximate entropy, permutation entropy, Lempel-Ziv complexity, and Kolmogorov–Sinai entropy. Bifurcation diagrams, the 0–1 test, and NIST statistical tests are further adopted to characterize its chaotic dynamics and randomness. Comparative results verify that STLEM achieves improved dynamical complexity and randomness performance. Built upon the proposed STLEM, this paper constructs a color-image encryption scheme that employs a 256-bit master key and two groups of chaotic parameters to produce key-related chaotic sequences. The cryptosystem integrates dynamic edge expansion, chaotic permutation, position-dependent adaptive DNA encoding, DNA-domain chained diffusion, and two successive row-column permutation phases. HMAC-SHA-256 is utilized to generate plaintext-aware initial conditions and perform ciphertext authentication prior to decryption. Experimental validations demonstrate complete plaintext recovery under valid secret inputs, while authentication rejects invalid keys and tampered ciphertexts. Ciphered images exhibit high information entropy, negligible adjacent-pixel correlations, and satisfactory number of pixel change rate (NPCR) and unified average changing intensity (UACI) metrics. Benefiting from a sufficiently large key space and O(MNlog(MN)) computational complexity, the proposed scheme is resilient against brute-force attacks and well suited for secure color-image communication scenarios, rather than acting as a general-purpose replacement for standard block ciphers.
Multimodal sentiment analysis is challenging because textual, visual, and acoustic evidence is heterogeneous and oft en weakly aligned. Here, we present QRSAN, a quantum-inspired residual self-attention network that integrates an LSTM text encoder, modality-specific multilayer perceptrons for visual and acoustic inputs, normalized complex-valued encoding, a TFN-derived interaction expansion, real-valued residual self-attention, and classical projection-score mapping. QRSAN runs entirely on classical hardware and does not perform physical quantum computation. Across CMU-MOSI, CMU-MOSEI, and IEMOCAP, QRSAN was evaluated using a common protocol. It achieved the highest numerical mean ACC and Binary_F1 among the evaluated models on CMU-MOSI, whereas its IEMOCAP label-wise accuracy was below that of EF-LSTM. These findings support the utility of combining constrained complex-valued representations with residual self-attention using the evaluated settings, without claiming universal state-of-the-art performance.
Artificially replicating the extraordinary adaptive potential of organisms remains difficult. Machine learning approaches based on big data pursue behavioral adaptation through generalization from training data, but often learn slowly and struggle with out-of-distribution situations. We propose that organisms may not adapt primarily through generalization alone but by rapidly eliminating infeasible solutions through online trial-and-error, effectively performing a search over the behavior space. If this search is complete, it is guaranteed to find an existing physically robust solution within a finite but unbounded time. For continuous behavioral domains that contain uncountably infinite behaviors, we introduce a mathematical framework for constructing a countably infinite dense subset of all behaviors using a mutable graph to segment behavior space, allowing any behavior to be progressively approximated arbitrarily well. Graph evolution is regulated by a heuristic feedback loop between outward growth and internal refinement; refinement is partially determined by a Bernoulli variance term related to binary entropy. Using this construction, we implement a proof-of-concept behavioral search algorithm and evaluate it on maze navigation and simple continuous control tasks. These preliminary results establish the practical feasibility of this approach in low-dimensional simulated environments while exposing unresolved limitations in terms of dimensional scaling and the incorporation of prior information.
