Resilience refers to the ability of systems to withstand, adapt to, and recover from disruptive events. While studies on resilience have attracted significant attention across various research domains, the precise definition of this concept within the field of cooperative artificial intelligence remains unclear. This paper addresses this gap by proposing a clear definition of `cooperative resilience' and outlining a methodology for its quantitative measurement. The methodology is validated in an environment with RL-based and LLM-augmented autonomous agents, subjected to environmental changes and the introduction of agents with unsustainable behaviors. These events are parameterized to create various scenarios for measuring cooperative resilience. The results highlight the crucial role of resilience metrics in analyzing how the collective system prepares for, resists, recovers from, sustains well-being, and transforms in the face of disruptions. These findings provide foundational insights into the definition, measurement, and preliminary analysis of cooperative resilience, offering significant implications for the broader field of AI. Moreover, the methodology and metrics developed here can be adapted to a wide range of AI applications, enhancing the reliability and effectiveness of AI in dynamic and unpredictable environments.

Trajectory planning is a fundamental task on various autonomous driving platforms, such as social robotics and self-driving cars. Many trajectory planning algorithms use a reference curve based Frenet frame with time to reduce the planning dimension. However, there is a common implicit assumption in classic trajectory planning approaches, which is that the generated trajectory should follow the reference curve continuously. This assumption is not always true in real applications and it might cause some undesired issues in planning. One issue is that the projection of the planned trajectory onto the reference curve maybe discontinuous. Then, some segments on the reference curve are not the image of any part of the planned path. Another issue is that the planned path might self-intersect when following a simple reference curve continuously. The generated trajectories are unnatural and suboptimal ones when these issues happen. In this paper, we firstly demonstrate these issues and then introduce an efficient trajectory generation method which uses a new transformation from the Cartesian frame to Frenet frames. Experimental results on a simulated street scenario demonstrated the effectiveness of the proposed method.

In this paper, we perform registration of noisy curves. We provide an appropriate model in estimating the rotation and scaling parameters to adjust a set of curves through a M-estimation procedure. We prove the consistency and the asymptotic normality of our estimators. Numerical simulation and a real life aeronautic example are given to illustrate our methodology.

In this work, we consider the class of multi-state autoregressive processes that can be used to model non-stationary time-series of interest. In order to capture different autoregressive (AR) states underlying an observed time series, it is crucial to select the appropriate number of states. We propose a new model selection technique based on the Gap statistics, which uses a null reference distribution on the stable AR filters to check whether adding a new AR state significantly improves the performance of the model. To that end, we define a new distance measure between AR filters based on mean squared prediction error (MSPE), and propose an efficient method to generate random stable filters that are uniformly distributed in the coefficient space. Numerical results are provided to evaluate the performance of the proposed approach.

Using a proper model to characterize a time series is crucial in making accurate predictions. In this work we use time-varying autoregressive process (TVAR) to describe non-stationary time series and model it as a mixture of multiple stable autoregressive (AR) processes. We introduce a new model selection technique based on Gap statistics to learn the appropriate number of AR filters needed to model a time series. We define a new distance measure between stable AR filters and draw a reference curve that is used to measure how much adding a new AR filter improves the performance of the model, and then choose the number of AR filters that has the maximum gap with the reference curve. To that end, we propose a new method in order to generate uniform random stable AR filters in root domain. Numerical results are provided demonstrating the performance of the proposed approach.

--A novel methodology is introduced here that exploits 2D images of arbitrary elastic body deformation instances, so as to quantify mechano-elastic characteristics that are deformation invariant. Determination of such characteristics allows for developing methods offering an image of the undeformed body . General assumptions about the mechano-elastic properties of the bodies are stated, which lead to two different approaches for obtaining bodies' deformation invariants. One was developed to spot deformed body's neutral line and its cross sections, while the other solves deformation PDEs by performing a set of equivalent image operations on the deformed body images. Both these processes may furnish a body undeformed version from its deformed image. This was confirmed by obtaining the undeformed shape of deformed parasites, cells (protozoa), fibers and human lips. In addition, the method has been applied to the important problem of parasite automatic classification from their microscopic images. T o achieve this, we first apply the previous method to straighten the highly deformed parasites and then we apply a dedicated curve classification method to the straightened parasite contours. It is demonstrated that essentially different deformations of the same parasite give rise to practically the same undeformed shape, thus confirming the consistency of the introduced methodology . Finally, the developed pattern recognition method classifies the unwrapped parasites into 6 families, with an accuracy rate of 97.6 %. Index Terms --deformation invariant elastic properties, automatic curve classification, parasite automatic identification, straightening deformed objects, image analysis, elastic deformation, pattern classification techniques. In these cases, one frequently encounters two important problems: a) to make consistent and reliable estimation of the body undeformed shape from images of random instances of body deformation and b) to identify the deformed body from these images. W e would like to emphasize that, as a rule, identification of bodies on the basis of images of their deformation, is practically prohibited by the randomness of the deformation.