Ever since artist James Sanborn unveiled Kryptos, an outdoor sculpture that sits at CIA headquarters, amateur and professional cryptanalysts have been feverishly attempting to crack the code hidden in its nearly 1800-character message. While they have decoded 3 of the 4 panels of ciphertext in the S-shaped copper artwork, the final panel, known as K4, still defies solution. Only one human being on Earth knows the message of K4: Sanborn. But soon someone else will join the club. Sanborn is putting the answer up for sale.

Causality and game theory are two influential fields that contribute significantly to decision-making in various domains. Causality defines and models causal relationships in complex policy problems, while game theory provides insights into strategic interactions among stakeholders with competing interests. Integrating these frameworks has led to significant theoretical advancements with the potential to improve decision-making processes. However, practical applications of these developments remain underexplored. To support efforts toward implementation, this paper clarifies key concepts in game theory and causality that are essential to their intersection, particularly within the context of probabilistic graphical models. By rigorously examining these concepts and illustrating them with intuitive, consistent examples, we clarify the required inputs for implementing these models, provide practitioners with insights into their application and selection across different scenarios, and reference existing research that supports their implementation. We hope this work encourages broader adoption of these models in real-world scenarios.

Automatic detection of visual anomalies and changes in the environment has been a topic of recurrent attention in the fields of machine learning and computer vision over the past decades. A visual anomaly or change detection algorithm identifies regions of an image that differ from a reference image or dataset. The majority of existing approaches focus on anomaly or fault detection in a specific class of images or environments, while general purpose visual anomaly detection algorithms are more scarce in the literature. In this paper, we propose a comprehensive deep learning framework for detecting anomalies and changes in a priori unknown environments after a reference dataset is gathered, and without need for retraining the model. We use the SuperPoint and SuperGlue feature extraction and matching methods to detect anomalies based on reference images taken from a similar location and with partial overlapping of the field of view. We also introduce a self-calibrating method for the proposed model in order to address the problem of sensitivity to feature matching thresholds and environmental conditions. To evaluate the proposed framework, we have used a ground robot system for the purpose of reference and query data collection. We show that high accuracy can be obtained using the proposed method. We also show that the calibration process enhances changes and foreign object detection performance

In this paper, we present a new framework to obtain tail inequalities for sums of random matrices. Compared with existing works, our tail inequalities have the following characteristics: 1) high feasibility--they can be used to study the tail behavior of various matrix functions, e.g., arbitrary matrix norms, the absolute value of the sum of the sum of the $j$ largest singular values (resp. eigenvalues) of complex matrices (resp. Hermitian matrices); and 2) independence of matrix dimension --- they do not have the matrix-dimension term as a product factor, and thus are suitable to the scenario of high-dimensional or infinite-dimensional random matrices. The price we pay to obtain these advantages is that the convergence rate of the resulting inequalities will become slow when the number of summand random matrices is large. We also develop the tail inequalities for matrix random series and matrix martingale difference sequence. We also demonstrate usefulness of our tail bounds in several fields. In compressed sensing, we employ the resulted tail inequalities to achieve a proof of the restricted isometry property when the measurement matrix is the sum of random matrices without any assumption on the distributions of matrix entries. In probability theory, we derive a new upper bound to the supreme of stochastic processes. In machine learning, we prove new expectation bounds of sums of random matrices matrix and obtain matrix approximation schemes via random sampling. In quantum information, we show a new analysis relating to the fractional cover number of quantum hypergraphs. In theoretical computer science, we obtain randomness-efficient samplers using matrix expander graphs that can be efficiently implemented in time without dependence on matrix dimensions.