The prospects of assessing neural complexity (NC) by $q$-statistics of the systemic organization of different types and levels of brain activity were studied. In 70 adult subjects, NC was assessed via the parameter $q$ of $q$-statistics, applied to the ongoing and EEG and its spectral power of 20 scalp points (channels). The NC were estimated both globally for all channels (AllCh) and locally (for each single channel) in different Functional States (FSs). The values of $q$ was compared among FSs and single channels, as well they were correlated with the power of $θ$ (4-8Hz), $β_1$ (15-25Hz) and others EEG bands, in each FS. The value of $q$ across all FSs was higher for AllCh than for the single channels FSs. Consistently with previous studies, we found a negative correlation between NC and age. The FSs did not influence the $q$ of the EEG in AllCh, although locally the FS modulated $q$ in a consistent manner (e.g., reducing $q$ in posterior sites with eyes closed). The $q$ was correlated positively with the power of the $θ$ and negatively with that of the $β_1$ band in general. These findings support the idea that, as a first approach, $q$-statistics can describe the human NC. The relationship between $q$ and $θ$ power aligns with greater NC during FSs such as listening music and resting with eyes open, which is consistent with high-order representations rather than low-informative attentional tasks (OddBall).

The inverse problem of statistical mechanics involves finding the minimal Hamiltonian that is consistent with some observed set of correlation functions. This problem has received renewed interest in the analysis of biological networks; in particular, several such networks have been described successfully by maximum entropy models consistent with pairwise correlations. These correlations are usually weak in an absolute sense (e.g., correlation coefficients ~ 0.1 or less), and this is sometimes taken as evidence against the existence of interesting collective behavior in the network. If correlations are weak, it should be possible to capture their effects in perturbation theory, so we develop an expansion for the entropy of Ising systems in powers of the correlations, carrying this out to fourth order. We then consider recent work on networks of neurons [Schneidman et al., Nature 440, 1007 (2006); Tkacik et al., arXiv:0912.5409 [q-bio.NC] (2009)], and show that even though all pairwise correlations are weak, the fact that these correlations are widespread means that their impact on the network as a whole is not captured in the leading orders of perturbation theory. More positively, this means that recent successes of maximum entropy approaches are not simply the result of correlations being weak.

Many of the most consequential dynamics in human cognition occur \emph{before} events become explicit: before decisions are finalized, emotions are labeled, or meanings stabilize into narrative form. These pre-event states are characterized by ambiguity, contextual tension, and competing latent interpretations. Rogue Variable Theory (RVT) formalizes such states as \emph{Rogue Variables}: structured, pre-event cognitive configurations that influence outcomes while remaining unresolved or incompatible with a system's current representational manifold. We present a quantum-consistent information-theoretic implementation of RVT based on a time-indexed \emph{Mirrored Personal Graph} (MPG) embedded into a fixed graph Hilbert space, a normalized \emph{Quantum MPG State} (QMS) constructed from node and edge metrics under context, Hamiltonian dynamics derived from graph couplings, and an error-weighted `rogue operator'' whose principal eigenvectors identify rogue factor directions and candidate Rogue Variable segments. We further introduce a \emph{Rosetta Stone Layer} (RSL) that maps user-specific latent factor coordinates into a shared reference Hilbert space to enable cross-user comparison and aggregation without explicit node alignment. The framework is fully implementable on classical systems and does not assume physical quantum processes; \emph{collapse} is interpreted as informational decoherence under interaction, often human clarification.

Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the correlated spiking activity of populations of 40 neurons in the salamander retina responding to natural movies. We show that pairwise interactions between neurons account for observed higher-order correlations, and that for groups of 10 or more neurons pairwise interactions can no longer be regarded as small perturbations in an independent system. We then construct network ensembles that generalize the network instances observed in the experiment, and study their thermodynamic behavior and coding capacity. Based on this construction, we can also create synthetic networks of 120 neurons, and find that with increasing size the networks operate closer to a critical point and start exhibiting collective behaviors reminiscent of spin glasses. We examine closely two such behaviors that could be relevant for neural code: tuning of the network to the critical point to maximize the ability to encode diverse stimuli, and using the metastable states of the Ising Hamiltonian as neural code words.

Recordings of electrical brain activity carry information about a person's cognitive health. For recording EEG signals, a very common setting is for a subject to be at rest with its eyes closed. Analysis of these recordings often involve a dimensionality reduction step in which electrodes are grouped into 10 or more regions (depending on the number of electrodes available). Then an average over each group is taken which serves as a feature in subsequent evaluation. Currently, the most prominent features used in clinical practice are based on spectral power densities. In our work we consider a simplified grouping of electrodes into two regions only. In addition to spectral features we introduce a secondary, non-redundant view on brain activity through the lens of Tsallis Entropy $S_{q=2}$. We further take EEG measurements not only in an eyes closed (ec) but also in an eyes open (eo) state. For our cohort of healthy controls (HC) and individuals suffering from Parkinson's disease (PD), the question we are asking is the following: How well can one discriminate between HC and PD within this simplified, binary grouping? This question is motivated by the commercial availability of inexpensive and easy to use portable EEG devices. If enough information is retained in this binary grouping, then such simple devices could potentially be used as personal monitoring tools, as standard screening tools by general practitioners or as digital biomarkers for easy long term monitoring during neurological studies.

Daily probability changes in Kalshi macro prediction markets forecast cryptocurrency realized volatility through two distinct channels. The monetary policy channel, measured by Fed rate repricing on KXFED contracts, predicts Bitcoin volatility in sample with t = 3.63 and p < 0.001 but exhibits regime dependence tied to the 2024-2025 rate-cutting cycle. The recession risk signal from KXRECSSNBER proves more stable out of sample, delivering an MSFE ratio of 0.979 with Clark-West p = 0.020. The inflation channel, measured by CPI repricing on KXCPI contracts, predicts altcoin volatility for Ethereum, Solana, Cardano, and Chainlink with t-statistics ranging from -2.1 to -3.4 and out-of-sample gains for Ethereum at MSFE = 0.959 with p = 0.010 and Solana at p = 0.048. Both the Bitcoin--Fed-dovish and Chainlink--CPI specifications survive Benjamini-Hochberg correction at q = 0.05. Orthogonalization and baseline comparisons against Fed Funds futures, Treasury yields, and the Deribit implied volatility index confirm that these signals carry information not embedded in conventional financial instruments. The sample covers ten Kalshi event series and six cryptocurrency assets over January 2023 to March 2026.

The dynamical evolution of multiscaling in financial time series is investigated using time-dependent Generalized Hurst Exponents (GHE), $H_q$, for various values of the parameter $q$. Using $H_q$, we introduce a new visual methodology to algorithmically detect critical changes in the scaling of the underlying complex time-series. The methodology involves the degree of multiscaling at a particular time instance, the multiscaling trend which is calculated by the Change-Point Analysis method, and a rigorous evaluation of the statistical significance of the results. Using this algorithm, we have identified particular patterns in the temporal co-evolution of the different $H_q$ time-series. These GHE patterns, distinguish in a statistically robust way, not only between time periods of uniscaling and multiscaling, but also among different types of multiscaling: symmetric multiscaling (M) and asymmetric multiscaling (A). We apply the visual methodology to time-series comprising of daily close prices of four stock market indices: two major ones (S\&P~500 and NIKKEI) and two peripheral ones (Athens Stock Exchange general Index and Bombay-SENSEX). Results show that multiscaling varies greatly with time: time periods of strong multiscaling behavior and time periods of uniscaling behavior are interchanged while transitions from uniscaling to multiscaling behavior occur before critical market events, such as stock market bubbles. Moreover, particular asymmetric multiscaling patterns appear during critical stock market eras and provide useful information about market conditions. In particular, they can be used as 'fingerprints' of a turbulent market period as well as provide warning signals for an upcoming stock market 'bubble'. The applied visual methodology also appears to distinguish between exogenous and endogenous stock market crises, based on the observed patterns before the actual events.

Universal power laws have been scrutinised in physics and beyond, and a long-standing debate exists in econophysics regarding the strict universality of the nonlinear price impact, commonly referred to as the square-root law (SRL). The SRL posits that the average price impact $I$ follows a power law with respect to transaction volume $Q$, such that $I(Q) \propto Q^δ$ with $δ\approx 1/2$. Some researchers argue that the exponent $δ$ should be system-specific, without universality. Conversely, others contend that $δ$ should be exactly $1/2$ for all stocks across all countries, implying universality. However, resolving this debate requires high-precision measurements of $δ$ with errors of around $0.1$ across hundreds of stocks, which has been extremely challenging due to the scarcity of large microscopic datasets -- those that enable tracking the trading behaviour of all individual accounts. Here we conclusively support the universality hypothesis of the SRL by a complete survey of all trading accounts for all liquid stocks on the Tokyo Stock Exchange (TSE) over eight years. Using this comprehensive microscopic dataset, we show that the exponent $δ$ is equal to $1/2$ within statistical errors at both the individual stock level and the individual trader level. Additionally, we rejected two prominent models supporting the nonuniversality hypothesis: the Gabaix-Gopikrishnan-Plerou-Stanley and the Farmer-Gerig-Lillo-Waelbroeck models (Nature 2003, QJE 2006, and Quant. Finance 2013). Our work provides exceptionally high-precision evidence for the universality hypothesis in social science and could prove useful in evaluating the price impact by large investors -- an important topic even among practitioners.

We introduce Tail-Safe, a deployability-oriented framework for derivatives hedging that unifies distributional, risk-sensitive reinforcement learning with a white-box control-barrier-function (CBF) quadratic-program (QP) safety layer tailored to financial constraints. The learning component combines an IQN-based distributional critic with a CVaR objective (IQN--CVaR--PPO) and a Tail-Coverage Controller that regulates quantile sampling through temperature tilting and tail boosting to stabilize small-$α$ estimation. The safety component enforces discrete-time CBF inequalities together with domain-specific constraints -- ellipsoidal no-trade bands, box and rate limits, and a sign-consistency gate -- solved as a convex QP whose telemetry (active sets, tightness, rate utilization, gate scores, slack, and solver status) forms an auditable trail for governance. We provide guarantees of robust forward invariance of the safe set under bounded model mismatch, a minimal-deviation projection interpretation of the QP, a KL-to-DRO upper bound linking per-state KL regularization to worst-case CVaR, concentration and sample-complexity results for the temperature-tilted CVaR estimator, and a CVaR trust-region improvement inequality under KL limits, together with feasibility persistence under expiry-aware tightening. Empirically, in arbitrage-free, microstructure-aware synthetic markets (SSVI $\to$ Dupire $\to$ VIX with ABIDES/MockLOB execution), Tail-Safe improves left-tail risk without degrading central performance and yields zero hard-constraint violations whenever the QP is feasible with zero slack. Telemetry is mapped to governance dashboards and incident workflows to support explainability and auditability. Limitations include reliance on synthetic data and simplified execution to isolate methodological contributions.

We employ deep reinforcement learning (RL) to train an agent to successfully translate a high-frequency trading signal into a trading strategy that places individual limit orders. Based on the ABIDES limit order book simulator, we build a reinforcement learning OpenAI gym environment and utilise it to simulate a realistic trading environment for NASDAQ equities based on historic order book messages. To train a trading agent that learns to maximise its trading return in this environment, we use Deep Duelling Double Q-learning with the APEX (asynchronous prioritised experience replay) architecture. The agent observes the current limit order book state, its recent history, and a short-term directional forecast. To investigate the performance of RL for adaptive trading independently from a concrete forecasting algorithm, we study the performance of our approach utilising synthetic alpha signals obtained by perturbing forward-looking returns with varying levels of noise. Here, we find that the RL agent learns an effective trading strategy for inventory management and order placing that outperforms a heuristic benchmark trading strategy having access to the same signal.