Healthcare sector indices consolidate the economic health of pharmaceutical, biotechnology, and healthcare service firms. The short-term movements in these indices are closely intertwined with capital allocation decisions affecting research and development investment, drug availability, and long-term health outcomes. This research investigates whether historical open-high-low-close (OHLC) index data contain sufficient information for predicting the directional movement of the opening index on the subsequent trading day. The problem is formulated as a supervised classification task involving a one-step-ahead rolling window. A diverse feature set is constructed, comprising original prices, volatility-based technical indicators, and a novel class of nowcasting features derived from mutual OHLC ratios. The framework is evaluated on data from healthcare indices in the U.S. and Indian markets over a five-year period spanning multiple economic phases, including the COVID-19 pandemic. The results demonstrate robust predictive performance, with accuracy exceeding 0.8 and Matthews correlation coefficients above 0.6. Notably, the proposed nowcasting features have emerged as a key determinant of the market movement. We have employed the Shapley-based explainability paradigm to further elucidate the contribution of the features: outcomes reveal the dominant role of the nowcasting features, followed by a more moderate contribution of original prices. This research offers a societal utility: the proposed features and model for short-term forecasting of healthcare indices can reduce information asymmetry and support a more stable and equitable health economy.

Singular learning theory (SLT) \citep{watanabe2009algebraic,watanabe2018mathematical} provides a rigorous asymptotic framework for Bayesian models with non-identifiable parameterizations, yet the statistical meaning of its second-order invariant, the \emph{singular fluctuation}, has remained unclear. In this work, we show that singular fluctuation admits a precise and natural interpretation as a \emph{specific heat}: the second derivative of the Bayesian free energy with respect to temperature. Equivalently, it measures the posterior variance of the log-likelihood observable under the tempered Gibbs posterior. We further introduce a collection of related thermodynamic quantities, including entropy flow, prior susceptibility, and cross-susceptibility, that together provide a detailed geometric diagnosis of singular posterior structure. Through extensive numerical experiments spanning discrete symmetries, boundary singularities, continuous gauge freedoms, and piecewise (ReLU) models, we demonstrate that these thermodynamic signatures cleanly distinguish singularity types, exhibit stable finite-sample behavior, and reveal phase-transition--like phenomena as temperature varies. We also show empirically that the widely used WAIC estimator \citep{watanabe2010asymptotic, watanabe2013widely} is exactly twice the thermodynamic specific heat at unit temperature, clarifying its robustness in singular models.Our results establish a concrete bridge between singular learning theory and statistical mechanics, providing both theoretical insight and practical diagnostics for modern Bayesian models.

Both resources in the natural environment and concepts in a semantic space are distributed patchily, with large gaps in between the patches. To describe people's internal and external foraging behavior, various random walk models have been proposed. In particular, internal foraging has been modeled as sampling: in order to gather relevant information for making a decision, people draw samples from a mental representation using random-walk algorithms such as Markov chain Monte Carlo (MCMC). However, two common empirical observations argue against people using simple sampling algorithms such as MCMC for internal foraging. First, the distance between samples is often best described by a Levy flight distribution: the probability of the distance between two successive locations follows a power-law on the distances.

The performance of neural networks on high-dimensional data distributions suggests that it may be possible to parameterize a representation of a given high-dimensional function with controllably small errors, potentially outperforming standard interpolation methods. We demonstrate, both theoretically and numerically, that this is indeed the case. We map the parameters of a neural network to a system of particles relaxing with an interaction potential determined by the loss function. We show that in the limit that the number of parameters $n$ is large, the landscape of the mean-squared error becomes convex and the representation error in the function scales as $O(n^{-1})$. In this limit, we prove a dynamical variant of the universal approximation theorem showing that the optimal representation can be attained by stochastic gradient descent, the algorithm ubiquitously used for parameter optimization in machine learning. In the asymptotic regime, we study the fluctuations around the optimal representation and show that they arise at a scale $O(n^{-1})$. These fluctuations in the landscape identify the natural scale for the noise in stochastic gradient descent. Our results apply to both single and multi-layer neural networks, as well as standard kernel methods like radial basis functions.

We analyze the dynamics of finite width effects in wide but finite feature learning neural networks. Starting from a dynamical mean field theory description of infinite width deep neural network kernel and prediction dynamics, we provide a characterization of the $\mathcal{O}(1/\sqrt{\text{width}})$ fluctuations of the DMFT order parameters over random initializations of the network weights. Our results, while perturbative in width, unlike prior analyses, are non-perturbative in the strength of feature learning. In the lazy limit of network training, all kernels are random but static in time and the prediction variance has a universal form. However, in the rich, feature learning regime, the fluctuations of the kernels and predictions are dynamically coupled with a variance that can be computed self-consistently.

The logit outputs of a feedforward neural network at initialization are conditionally Gaussian, given a random covariance matrix defined by the penultimate layer. In this work, we study the distribution of this random matrix. Recent work has shown that shaping the activation function as network depth grows large is necessary for this covariance matrix to be non-degenerate. However, the current infinite-width-style understanding of this shaping method is unsatisfactory for large depth: infinite-width analyses ignore the microscopic fluctuations from layer to layer, but these fluctuations accumulate over many layers. To overcome this shortcoming, we study the random covariance matrix in the shaped infinite-depth-and-width limit. We identify the precise scaling of the activation function necessary to arrive at a non-trivial limit, and show that the random covariance matrix is governed by a stochastic differential equation (SDE) that we call the Neural Covariance SDE. Using simulations, we show that the SDE closely matches the distribution of the random covariance matrix of finite networks. Additionally, we recover an if-and-only-if condition for exploding and vanishing norms of large shaped networks based on the activation function.

If a major disaster like Fukushima or Chernobyl ever happens again, the world would know almost straight away, thanks to an array of government and DIY radiation-monitoring programs running globally.

Accurate electricity forecasting is crucial for grid stability and energy planning, especially in Benghazi, Libya, where frequent load shedding, generation deficits, and infrastructure limitations persist. This study proposes a data-driven approach to forecast electricity load, generation, and deficits for 2025 using historical data from 2019 (a year marked by instability) and 2023 (a more stable year). Multiple time series models were applied, including ARIMA, seasonal ARIMA, dynamic regression ARIMA, exponential smoothing, extreme gradient boosting, and Long Short-Term Memory (LSTM) neural networks. The dataset was enhanced through missing value imputation, outlier smoothing, and log transformation. Performance was assessed using mean squared error, root mean squared error, mean absolute error, and mean absolute percentage error. LSTM outperformed all other models, showing strong capabilities in modeling non-stationary and seasonal patterns. A key contribution of this work is an optimized LSTM framework that integrates exogenous factors such as temperature and humidity, offering robust performance in forecasting multiple electricity indicators. These results provide practical insights for policymakers and grid operators to enable proactive load management and resource planning in data-scarce, volatile regions.

Deep neural networks (DNNs) exhibit crackling-like avalanches whose origin lacks a mechanistic explanation. Here, I derive a stochastic theory of deep information propagation (DIP) by incorporating Central Limit Theorem (CLT)-level fluctuations. Four effective couplings $(r, h, D_1, D_2)$ characterize the dynamics, yielding a Landau description of the static exponents and a Directed Percolation (DP) structure of activity cascades. Tuning the couplings selects between avalanche dynamics generated by a Brownian Motion (BM) in a logarithmic trap and an absorbed free BM, each corresponding to a distinct universality classes. Numerical simulations confirm the theory and demonstrate that activation function design controls the collective dynamics in random DNNs.

A clearer understanding of when coordination emerges, fluctuates, or collapses in decentralized multi-agent reinforcement learning (MARL) is increasingly sought in order to characterize the dynamics of multi-agent learning systems. We revisit fully independent Q-learning (IQL) as a minimal decentralized testbed and run large-scale experiments across environment size L and agent density rho. We construct a phase map using two axes - the cooperative success rate (CSR) and a stability index derived from TD-error variance - revealing three distinct regimes: a coordinated and stable phase, a fragile transition region, and a jammed or disordered phase. A sharp double Instability Ridge separates these regimes and corresponds to persistent kernel drift, the time-varying shift of each agent's effective transition kernel induced by others' policy updates. Synchronization analysis further shows that temporal alignment is required for sustained cooperation, and that competition between drift and synchronization generates the fragile regime. Removing agent identifiers eliminates drift entirely and collapses the three-phase structure, demonstrating that small inter-agent asymmetries are a necessary driver of drift. Overall, the results show that decentralized MARL exhibits a coherent phase structure governed by the interaction between scale, density, and kernel drift, suggesting that emergent coordination behaves as a distribution-interaction-driven phase phenomenon.