Continuous-time systems are often represented by differential equations, including Ordinary Differential Equations (ODEs) like the motion of a pendulum and Partial Differential Equations (PDEs) such as the heat equation, which describe system behavior in response to time and other variables. For systems that evolve at discrete intervals, difference equations--using linear or nonlinear recursive functions--capture state changes over time, as seen in models of population growth. Dynamical systems can also be described geometrically via phase or state space, where each point represents a system state, and trajectories represent system evolution. Alternatively, vector fields describe time evolution as a flow, mapping system states across time steps, thereby outlining the system's path on its phase space manifold. In physics, it's more common to describe the dynamical systems using Hamiltonian or Lagrangian formalisms, which provide a more structured way of capturing the energy dynamics of a system. In systems where randomness or noise plays a role, stochastic differential equations (SDEs) are used.

In recent years, there has been a growing demand for reliable identification of children across various applications, including missing children, border security, humanitarian, and health care. This highlights the need to explore the potential of face recognition technology for children. However, The need for reliable identification of children in various traditional face recognition systems have primarily focused emerging applications has sparked interest in leveraging on adults, which poses limitations when applied to child face recognition technology. This study introduces a children due to the unique characteristics of juvenile facial longitudinal approach to enrollment and verification accuracy features and how they change over time [16].

Generating realistic images to accurately predict changes in the structure of brain MRI is a crucial tool for clinicians. Such applications help assess patients' outcomes and analyze how diseases progress at the individual level. However, existing methods for this task present some limitations. Some approaches attempt to model the distribution of MRI scans directly by conditioning the model on patients' ages, but they fail to explicitly capture the relationship between structural changes in the brain and time intervals, especially on age-unbalanced datasets. Other approaches simply rely on interpolation between scans, which limits their clinical application as they do not predict future MRIs. To address these challenges, we propose a Temporally-Aware Diffusion Model (TADM), which introduces a novel approach to accurately infer progression in brain MRIs. TADM learns the distribution of structural changes in terms of intensity differences between scans and combines the prediction of these changes with the initial baseline scans to generate future MRIs. Furthermore, during training, we propose to leverage a pre-trained Brain-Age Estimator (BAE) to refine the model's training process, enhancing its ability to produce accurate MRIs that match the expected age gap between baseline and generated scans. Our assessment, conducted on the OASIS-3 dataset, uses similarity metrics and region sizes computed by comparing predicted and real follow-up scans on 3 relevant brain regions. TADM achieves large improvements over existing approaches, with an average decrease of 24% in region size error and an improvement of 4% in similarity metrics. These evaluations demonstrate the improvement of our model in mimicking temporal brain neurodegenerative progression compared to existing methods. Our approach will benefit applications, such as predicting patient outcomes or improving treatments for patients.

Delaying "brain age" may sound like the latest quick-fix gimmick on a late-night infomercial, but the science underlying the concept is very real. Rather than reflecting the average functional state of your chronological age, brain age looks at how well your brain is aging relative to how many birthdays you've celebrated. We all know people that seem sharper and act much younger than their age--that incredulous moment when you realize the 40-year-old you've been chatting with on the plane is actually a grandma in her 70s. Brain age, as a concept, hopes to capture the biological intricacies behind that cognitive dissociation. Longevity researchers have increasingly realized that how long you've lived isn't the best predictor of overall health.

A new video shows a 10-year-old boy unlocking his mother's iPhone X using the Face ID, proving the facial recognition technology on the device can be fooled regardless of the age gap. The mother, Sana Sherwani, and the son, Ammar, realized the Face ID could be fooled shortly after purchasing the device, Attaullah Malik, the father of Ammar, said in a LinkedIn post. "We were sitting down in our bedroom and were just done setting up the Face IDs, our 10-year-old son walked in anxious to get his hands on the new iPhone X," Malik wrote. "Right away my wife declared that he was not going to access her phone. Acting exactly as a kid would do when asked to not do something, he picked up her phone and with just a glance got right in." "It was funny at first," Malik told WIRED.