Lasko Basnarkov

Here, we investigate whether stochastic resetting, a technique that periodically reverts training to beneficial checkpoints, recently explored in the context of deep learning with noisy labels, can improve the decoding of anomalous diffusion trajectories, a task made challenging by noise and limited trajectory lengths, which often render subtle differences between diffusion processes indistinguishable. First, we find that incorporating stochastic resets of neural network parameters improves the validation loss across different hyperparameters and noise levels, confirming its applicability in trajectory decoding tasks. Second, we find that the relative benefit of resetting increases with trajectory length, and we offer a mechanistic explanation supported by minibatch-gradient ensemble diagnostics that links this observation to the underlying optimization dynamics. Furthermore, we observe that there exists an optimal resetting probability that yields the best performance, highlighting the importance of tuning this hyperparameter. Building on this insight, we introduce time-varying resetting mechanisms that dynamically adjust the resetting probability during training. Our results show that these mechanisms often match or surpass the performance of the best fixed-resetting probabilities and offer a solid basis for designing effective dynamic resetting strategies for regularization.

Background: The rapid expansion of digital data poses a unique challenge for retrieving relevant and insightful information efficiently. In particular, the increasing volume of scientific publications has made literature reviews time-consuming. The emergence of large language models (LLMs) offers new opportunities to streamline this process. Methods: This paper explores the use of generative artificial intelligence (GenAI) for query reformulation and evaluates the performance of nine massive text embedding models, varying in size and fine-tuning strategies, in the context of document retrieval. We apply multiple prompt engineering techniques to evaluate the ability of LLMs to generate effective queries, comparing them with human-crafted queries. These are used to retrieve documents utilizing nine embedding models. The evaluation is across five datasets using metrics such as recall, average precision, and rank-based measures. Results: Results show that embedding models fine-tuned for semantic similarity consistently outperform general-purpose models, with UAE Large proving most robust across diverse domains. Furthermore, queries generated using zero-shot and few-shot prompting techniques often surpass the performance of human-formulated queries. Conclusion: These findings highlight the value of integrating LLMs and massive text embeddings to reduce manual effort in literature reviews. GenAI provides a reliable starting point for query formulation, with human input reserved for refinement when needed.

The basic reproduction number [ ] is a key epidemiological quantity, representing the expected number of new cases obtained from receiving a pathogen from one infected individual in totally susceptible population. Here is studied the effective reproduction number [ ] as its generalized version, by considering that in the population might be present other infected persons, besides the one introduced, which are absent in the definition of [ ]. To calculate the theoretical value of the effective reproduction number, we use an integral formula based on the age of infection. The approach is applied to the classical SIR model and the two-strain SIIS model. It is obtained that such theoretical values deviate from the classical values which assume constant susceptible population, if the susceptible compartment size changes substantially during the typical period of infectiousness. Numerical simulations of the stochastic version of the models give values that match very well to those from the integral formula. The findings suggest that in scenarios where the population has nonnegligible number of infected individuals and the change of the compartment sizes is considerable, one has to be cautious in using the classical results. The numerical simulations also show that the shape of the generation interval distribution depends on whether the susceptible population is changing. Thus, the estimates of the generation interval distribution should be considered carefully as well.

We study a generalized Langevin equation framework that incorporates stochastic resetting of a truncation power-law memory kernel. The inclusion of stochastic resetting enables the emergence of resonance phenomena even in parameter regimes where conventional settings (without resetting) do not exhibit such behavior. Specifically, we explore the response of the system to an external field under three scenarios: (i) a free particle, (ii) a particle in a harmonic potential, and (iii) the effect of truncation in the memory kernel. In each case, the primary focus is on understanding how the resetting mechanism interacts with standard parameters to induce stochastic resonance. In addition, we explore the effect of resetting on the dielectric loss.

The basic reproduction number R0 is a concept which originated in population dynamics, mathematical epidemiology, and ecology and is closely related to the mean number of children in branching processes.We offer below three new contributions to the literature: 1) We order a universal algorithmic definition of a (F, V) gradient decomposition (and hence of the resulting R0), which requires a minimal input from the user, namely the specification of an admissible set of disease/infection variables. We also present examples where other choices may be more reasonable, with more terms in F, or more terms in V . 2) We glean out from the works of Bacaer a fixed point equation (8) for the extinction probabilities of a stochastic model associated to a deterministic ODE model, which may be expressed in terms of the (F, V ) decomposition. The fact that both R0 and the extinction probabilities are functions of (F, V ) underlines the centrality of this pair, which may be viewed as more fundamental than the famous next generation matrix FV^{-1}. 3) We suggest introducing a new concept of sufficient/minimal disease/infection set (sufficient for determining R0). More precisely, our universal recipe of choosing "new infections" once the "infections" are specified suggests focusing on the choice of the latter, which is also not unique. The maximal choice of choosing all compartments which become 0 at the given boundary point seems to always work, but is the least useful for analytic computations, therefore we propose to investigate the minimal one. As a bonus, this idea seems useful for understanding the Jacobian factorization approach for computing R0 . Last but not least, we offer Mathematica scripts and implement them for a large variety of examples, which illustrate that our recipe others always reasonable results, but that sometimes other reasonable (F, V ) decompositions are available as well.