Recently, we demonstrated the existence of nonextensivity in neuromuscular transmission [Phys. Rev. E 84, 041925 (2011)]. In the present letter, we propose a general criterion based on the q-calculus foundations and nonextensive statistics to estimate the values for both scale factor and q-index using the maximum likelihood q-estimation method (MLqE). We next applied our theoretical findings to electrophysiological recordings from neuromuscular junction (NMJ) where spontaneous miniature end plate potentials (MEPP) were analyzed. These calculations were performed in both normal and high extracellular potassium concentration, [K+]o. This protocol was assumed to test the validity of the q-index in electrophysiological conditions closely resembling physiological stimuli. Surprisingly, the analysis showed a significant difference between the q-index in high and normal [K+]o, where the magnitude of nonextensivity was increased. Our letter provides a general way to obtain the best q-index from the q-Gaussian distribution function. It also expands the validity of Tsallis statistics in a more realistic stimulus condition. Physical and physiological implications of these findings are discussed in detail.

Quantifying the neural signatures of consciousness remains a major challenge in neuroscience and AI. Although many theories link consciousness to rich, multiscale, and flexible neural organisation, robust quantitative measures are still lacking. This paper presents a theory-neutral framework that characterises consciousness-related dynamics through three properties: hierarchical integration (H), cross-frequency complexity (D), and metastability (M). Candidate subsystems are identified using predictive information, temporal complexity, and state-space exploration to distinguish structured from unstructured activity. We provide mathematical definitions for all components and implement the framework in a generative model of synthetic EEG, simulating nine brain states ranging from psychedelic and wakeful to dreaming, non-REM sleep, minimally conscious, anaesthetised, and seizure-like regimes. Across single trials and Monte Carlo ensembles, the composite index reliably separates high-consciousness from impaired or non-conscious states. We further validate the framework using real EEG from the Sleep-EDF dataset alongside matched synthetic EEG designed to reproduce state-dependent oscillatory structure. Across Wake, N2, and REM sleep, synthetic data recapitulate the empirical ordering and magnitude of the index, indicating that the index captures stable and biologically meaningful distinctions. This approach provides a principled and empirically grounded tool for quantifying consciousness-related neural organisation with potential applications to both biological and artificial systems.

Understanding the modularity of fMRI-derived brain networks or connectomes can inform the study of brain function organization. However, fMRI connectomes additionally involve negative edges, which are not rigorously accounted for by existing approaches to modularity that either ignores or arbitrarily weight these connections. Furthermore, most Q maximization-based modularity algorithms yield variable results with suboptimal reproducibility. Here we present an alternative, reproducible approach that exploits how frequent the BOLD-signal correlation between two nodes is negative. We validated this novel probability-based modularity approach on two independent publicly-available resting-state connectome dataset (the Human Connectome Project and the 1000 Functional Connectomes) and demonstrated that negative correlations alone are sufficient in understanding resting-state modularity. In fact, this approach a) permits a dual formulation, leading to equivalent solutions regardless of whether one considers positive or negative edges; b) is theoretically linked to the Ising model defined on the connectome, thus yielding modularity result that maximizes data likelihood. We additionally were able to detect sex differences in modularity that the most widely utilized methods did not. Results confirmed the superiority of our approach in that: a) correlations with the highest probability of being negative are consistently placed between modules, b) due to the equivalent dual forms, no arbitrary weighting factor is required to balance the influence between negative and positive correlations, unlike existing Q maximization-based modularity approaches. As datasets like HCP become widely available for analysis by the neuroscience community at large, appropriate computational tools to understand the neurobiological information of negative edges in fMRI connectomes are increasingly important.

We investigate the probability distributions of the recurrence intervals $τ$ between consecutive 1-min returns above a positive threshold $q>0$ or below a negative threshold $q<0$ of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresholds are symmetric, and display power-law tails tested by three goodness-of-fit measures including the Kolmogorov-Smirnov (KS) statistic, the weighted KS statistic and the Cramér-von Mises criterion. Both long-term and shot-term memory effects are observed in the recurrence intervals for positive and negative thresholds $q$. We further apply the recurrence interval analysis to the risk estimation for the Chinese stock markets based on the probability $W_q(Δ{t},t)$, Value-at-Risk (VaR) analysis and VaR analysis conditioned on preceding recurrence intervals.

Automated Market Makers (AMMs) have cemented themselves as an integral part of the decentralized finance (DeFi) space. AMMs are a type of exchange that allows users to trade assets without the need for a centralized exchange. They form the foundation for numerous decentralized exchanges (DEXs), which help facilitate the quick and efficient exchange of on-chain tokens. All present-day popular DEXs are static protocols, with fixed parameters controlling the fee and the curvature - they suffer from invariance and cannot adapt to quickly changing market conditions. This characteristic may cause traders to stay away during high slippage conditions brought about by intractable market movements. We propose an RL framework to optimize the fees collected on an AMM protocol. In particular, we develop a Q-Learning Agent for Market Making Protocols (QLAMMP) that learns the optimal fee rates and leverage coefficients for a given AMM protocol and maximizes the expected fee collected under a range of different market conditions. We show that QLAMMP is consistently able to outperform its static counterparts under all the simulated test conditions.

We study the statistical properties of the recurrence intervals $τ$ between successive trading volumes exceeding a certain threshold $q$. The recurrence interval analysis is carried out for the 20 liquid Chinese stocks covering a period from January 2000 to May 2009, and two Chinese indices from January 2003 to April 2009. Similar to the recurrence interval distribution of the price returns, the tail of the recurrence interval distribution of the trading volumes follows a power-law scaling, and the results are verified by the goodness-of-fit tests using the Kolmogorov-Smirnov (KS) statistic, the weighted KS statistic and the Cram{é}r-von Mises criterion. The measurements of the conditional probability distribution and the detrended fluctuation function show that both short-term and long-term memory effects exist in the recurrence intervals between trading volumes. We further study the relationship between trading volumes and price returns based on the recurrence interval analysis method. It is found that large trading volumes are more likely to occur following large price returns, and the comovement between trading volumes and price returns is more pronounced for large trading volumes.

I compare two quantum-theoretical approaches to the phenomenon of adaptive mutations, termed here Q-cell and Q-genome. I use 'fluctuation trapping' model as a general framework. I introduce notions of R-error and D-error and argue that the 'fluctuation trapping' model has to employ a correlation between the R- and D- errors. Further, I compare how the two approaches can justify the R-D-error correlation, focusing on the advantages of the Q-cell approach. The positive role of environmentally induced decoherence (EID) on both steps of the adaptation process is emphasized. A starving bacterial cell is proposed to be in an einselected state. The intracellular dynamics in this state has a unitary character and I propose to interpret it as 'exponential growth in imaginary time', analogously to the commonly considered 'diffusion' interpretation of the Schroedinger equation. Addition of a substrate leads to Wick rotation and a switch from 'imaginary time' reproduction to a 'real time' reproduction regime. Due to the variations at the genomic level (such as base tautomery), the starving cell has to be represented as a superposition of different components, all 'reproducing in imaginary time'. Adidtion of a selective substrate, allowing only one of these components to amplify, will cause Wick rotation and amplification of this component, thus justifying the occurence of the R-D-error correlation. Further ramifications of the proposed ideas for evolutionary theory are discussed.

Global Style Tokens (GSTs) are a recently-proposed method to learn latent disentangled representations of high-dimensional data. GSTs can be used within Tacotron, a state-of-the-art end-to-end text-to-speech synthesis system, to uncover expressive factors of variation in speaking style. In this work, we introduce the Text-Predicted Global Style Token (TP-GST) architecture, which treats GST combination weights or style embeddings as "virtual" speaking style labels within Tacotron. TP-GST learns to predict stylistic renderings from text alone, requiring neither explicit labels during training nor auxiliary inputs for inference. We show that, when trained on a dataset of expressive speech, our system generates audio with more pitch and energy variation than two state-of-the-art baseline models. We further demonstrate that TP-GSTs can synthesize speech with background noise removed, and corroborate these analyses with positive results on human-rated listener preference audiobook tasks. Finally, we demonstrate that multi-speaker TP-GST models successfully factorize speaker identity and speaking style. We provide a website with audio samples for each of our findings.

A recently implemented relativistic four-component configuration interaction approach to study ${\cal{P}}$- and ${\cal{T}}$-odd interaction constants in atoms and molecules is employed to determine the electron electric dipole moment effective electric field in the $Ω=1$ first excited state of the ThO molecule. We obtain a value of $E_{\text{eff}} = 75.6 \left[\frac{\rm GV}{\rm cm}\right]$ with an estimated error bar of $3\%$ and $10\%$ smaller than a previously reported result [arXiv:1308.0414 [physics.atom-ph]]. Using the same wavefunction model we obtain an excitation energy of $T_v^{Ω=1} = 5329$ [\cm], in accord with the experimental value within $2\%$. In addition, we report the implementation of the magnetic hyperfine interaction constant $A_{||}$ as an expectation value, resulting in $A_{||} = -1335$ [MHz] for the $Ω=1$ state in ThO. The smaller effective electric field increases the previously measured upper bound to the electron electric dipole moment interaction constant [arXiv:1310.7534v2 [physics.atom-ph]] and thus mildly mitigates constraints to possible extensions of the Standard Model of particle physics.

We propose an improved scheme of perturbation theory based on our exact solution [An Min Wang, quant-ph/0611216] in general quantum systems independent of time. Our elementary start-point is to introduce the perturbing parameter as late as possible. Our main skills are Hamiltonian redivision so as to overcome a flaw of the usual perturbation theory, and the perturbing Hamiltonian matrix product decomposition in order to separate the contraction and anti-contraction terms. Our calculational technology is the limit process for eliminating apparent divergences. Our central idea is ``dynamical rearrangement and summation" for the sake of the partial contributions from the high order even all order approximations absorbed in our perturbed solution. Consequently, we obtain the improved forms of the zeroth, first, second and third order perturbed solutions absorbing the partial contributions from the high order even all order approximations of perturbation. Then we deduce the improved transition probability. In special, we propose the revised Fermi's golden rule. Moreover, we apply our scheme to obtain the improved forms of perturbed energy and perturbed state. In addition, we study an easy understanding example of two-state system to illustrate our scheme and show its advantages. All of this implies the physical reasons and evidences why our improved scheme of perturbation theory are actually calculable, operationally efficient, conclusively more accurate. Our improved scheme is the further development and interesting application of our exact solution, and it has been successfully used to study on open system dynamics [An Min Wang, quant-ph/0601051].