We prove that the persistence diagram of the sublevel set filtration of the quadratic form f(x) = x^T M x restricted to the unit sphere S^{n-1} is analytically determined by the eigenvalues of the symmetric matrix M. By Morse theory, the diagram has exactly n-1 finite bars, with the k-th bar living in homological dimension k-1 and having length equal to the k-th eigenvalue spacing s_k = λ_{k+1} - λ_k. This identification transfers random matrix theory (RMT) universality to persistence diagram universality: for matrices drawn from the Gaussian Orthogonal Ensemble (GOE), we derive the closed-form persistence entropy PE = log(8n/π) - 1, and verify numerically that the coefficient of variation of persistence statistics decays as n^{-0.6}. Different random matrix ensembles (GOE, GUE, Wishart) produce distinct universal persistence diagrams, providing topological fingerprints of RMT universality classes. As a practical consequence, we show that persistence entropy outperforms the standard level spacing ratio \langle r \rangle for discriminating GOE from GUE matrices (AUC 0.978 vs. 0.952 at n = 100, non-overlapping bootstrap 95% CIs), and detects global spectral perturbations in the Rosenzweig-Porter model to which \langle r \rangle is blind. These results establish persistence entropy as a new spectral diagnostic that captures complementary information to existing RMT tools.

MP wants Elon Musk's chatbot shut down over claim he enabled grooming gangs An MP has called for Elon Musk's artificial intelligence (AI) chatbot to be shut down after it called him a rape enabler. The Grok chatbot made the post on X about SNP MP Pete Wishart, after a user asked it to comment on the member's opinion on whether there should be an inquiry into grooming gangs in Scotland. Mr Wishart said he was seeking legal advice over the deeply distressing accusation and called for Musk to recalibrate the bot to shut it down. The BBC has approached XAI, the parent company of X, for comment. I was genuinely shocked to be described in such an appalling and defamatory way, Mr Wishart said in a statement.

This paper tackles the problem of jointly estimating the noise covariance matrix alongside primary parameters (such as poses and points) from measurements corrupted by Gaussian noise. In such settings, the noise covariance matrix determines the weights assigned to individual measurements in the least squares problem. We show that the joint problem exhibits a convex structure and provide a full characterization of the optimal noise covariance estimate (with analytical solutions) within joint maximum a posteriori and likelihood frameworks and several variants. Leveraging this theoretical result, we propose two novel algorithms that jointly estimate the primary parameters and the noise covariance matrix. To validate our approach, we conduct extensive experiments across diverse scenarios and offer practical insights into their application in robotics and computer vision estimation problems with a particular focus on SLAM.

With the development of generative models like GPT-3, it is increasingly more challenging to differentiate generated texts from human-written ones. There is a large number of studies that have demonstrated good results in bot identification. However, the majority of such works depend on supervised learning methods that require labelled data and/or prior knowledge about the bot-model architecture. In this work, we propose a bot identification algorithm that is based on unsupervised learning techniques and does not depend on a large amount of labelled data. By combining findings in semantic analysis by clustering (crisp and fuzzy) and information techniques, we construct a robust model that detects a generated text for different types of bot. We find that the generated texts tend to be more chaotic while literary works are more complex. We also demonstrate that the clustering of human texts results in fuzzier clusters in comparison to the more compact and well-separated clusters of bot-generated texts.

IN RECENT YEARS, underground chemists have increasingly made small chemical tweaks on known recreational drugs to skirt laws, creating novel designer versions. Instead of cannabis, for instance, these chemists could offer up XLR-11, or instead of PCP they might have 3-MeO-PCE. Novel designer drugs, also called research chemicals or legal highs, still produce physiological and psychological effects, though experts say that they can come with a slew of risks. Synthetic opioids such as fentanyl, for instance, are increasingly cited among the number of opioid-related deaths in the United States, which reached more than 75,000 this year. According to the Centers for Disease Control and Prevention, synthetic cannabinoids can cause heart attacks, kidney failure, and, in some cases, death.

In recent years, underground chemists have increasingly made small chemical tweaks on known recreational drugs to skirt laws, creating novel designer versions. Instead of cannabis, for instance, these chemists could offer up XLR-11, or instead of PCP they might have 3-MeO-PCE. Novel designer drugs, also called research chemicals or legal highs, still produce physiological and psychological effects, though experts say that they can come with a slew of risks. Synthetic opioids such as fentanyl, for instance, are increasingly cited among the number of opioid-related deaths in the United States, which reached more than 75,000 this year. According to the Centers for Disease Control and Prevention, synthetic cannabinoids can cause heart attacks, kidney failure, and, in some cases, death.

New drugs are created all the time. And many are extremely dangerous. This is why researchers trained computers to predict what designer drugs will emerge onto the scene before they hit the market, according to a recent study published in the journal Nature Machine Intelligence. With highly-addictive drugs flooding regions throughout the U.S., this program could save countless lives. But it could also unlock an entire "dark matter" world of unknown psychoactive possibilities.

We investigate the computational complexity of several basic linear algebra primitives, including largest eigenvector computation and linear regression, in the computational model that allows access to the data via a matrix-vector product oracle. We show that for polynomial accuracy, $\Theta(d)$ calls to the oracle are necessary and sufficient even for a randomized algorithm. Our lower bound is based on a reduction to estimating the least eigenvalue of a random Wishart matrix. This simple distribution enables a concise proof, leveraging a few key properties of the random Wishart ensemble.

In this document we are going to derive the equations needed to implement a Variational Bayes estimation of the parameters of the simplified probabilistic linear discriminant analysis (SPLDA) model. This can be used to adapt SPLDA from one database to another with few development data or to implement the fully Bayesian recipe. Our approach is similar to Bishop's VB PPCA.