We establish closed-form enumeration formulas for chromatic feature vectors of 2-trees under the bichromatic triangle constraint. These efficiently computable structural features derive from constrained graph colorings where each triangle uses exactly two colors, forbidding monochromatic and rainbow triangles, a constraint arising in distributed systems where components avoid complete concentration or isolation. For theta graphs Theta_n, we prove r_k(Theta_n) = S(n-2, k-1) for k >= 3 (Stirling numbers of the second kind) and r_2(Theta_n) = 2^(n-2) + 1, computable in O(n) time. For fan graphs Phi_n, we establish r_2(Phi_n) = F_{n+1} (Fibonacci numbers) and derive explicit formulas r_k(Phi_n) = sum_{t=k-1}^{n-1} a_{n-1,t} * S(t, k-1) with efficiently computable binomial coefficients, achieving O(n^2) computation per component. Unlike classical chromatic polynomials, which assign identical features to all n-vertex 2-trees, bichromatic constraints provide informative structural features. While not complete graph invariants, these features capture meaningful structural properties through connections to Fibonacci polynomials, Bell numbers, and independent set enumeration. Applications include Byzantine fault tolerance in hierarchical networks, VM allocation in cloud computing, and secret-sharing protocols in distributed cryptography.

This study evaluates a 40-item mathematics placement examination administered to 198 students using a multi-method framework combining Classical Test Theory, machine learning, and unsupervised clustering. Classical Test Theory analysis reveals that 55\% of items achieve excellent discrimination ($D \geq 0.40$) while 30\% demonstrate poor discrimination ($D < 0.20$) requiring replacement. Question 6 (Graph Interpretation) emerges as the examination's most powerful discriminator, achieving perfect discrimination ($D = 1.000$), highest ANOVA F-statistic ($F = 4609.1$), and maximum Random Forest feature importance (0.206), accounting for 20.6\% of predictive power. Machine learning algorithms demonstrate exceptional performance, with Random Forest and Gradient Boosting achieving 97.5\% and 96.0\% cross-validation accuracy. K-means clustering identifies a natural binary competency structure with a boundary at 42.5\%, diverging from the institutional threshold of 55\% and suggesting potential overclassification into remedial categories. The two-cluster solution exhibits exceptional stability (bootstrap ARI = 0.855) with perfect lower-cluster purity. Convergent evidence across methods supports specific refinements: replace poorly discriminating items, implement a two-stage assessment, and integrate Random Forest predictions with transparency mechanisms. These findings demonstrate that multi-method integration provides a robust empirical foundation for evidence-based mathematics placement optimization.

The application of AI in oncology has been limited by its reliance on large, annotated datasets and the need for retraining models for domain-specific diagnostic tasks. Taking heed of these limitations, we investigated in-context learning as a pragmatic alternative to model retraining by allowing models to adapt to new diagnostic tasks using only a few labeled examples at inference, without the need for retraining. Using four vision-language models (VLMs)-Paligemma, CLIP, ALIGN and GPT-4o, we evaluated the performance across three oncology datasets: MHIST, PatchCamelyon and HAM10000. To the best of our knowledge, this is the first study to compare the performance of multiple VLMs on different oncology classification tasks. Without any parameter updates, all models showed significant gains with few-shot prompting, with GPT-4o reaching an F1 score of 0.81 in binary classification and 0.60 in multi-class classification settings. While these results remain below the ceiling of fully fine-tuned systems, they highlight the potential of ICL to approximate task-specific behavior using only a handful of examples, reflecting how clinicians often reason from prior cases. Notably, open-source models like Paligemma and CLIP demonstrated competitive gains despite their smaller size, suggesting feasibility for deployment in computing constrained clinical environments. Overall, these findings highlight the potential of ICL as a practical solution in oncology, particularly for rare cancers and resource-limited contexts where fine-tuning is infeasible and annotated data is difficult to obtain.

Edward Snowden has finally laid it all out - documenting his memoires in a new 432-page book, Permanent Record, which will be published worldwide on Tuesday, September 17. Meeting with both The Guardian and Spiegel Online in Moscow as part of its promotion, the infamous whistleblower spent nearly five hours with the two media outlets - offering a taste of what's in the book, details on his background, and his thoughts on artificial intelligence, facial recognition, and other intelligence gathering tools coming to a dystopia near you. While The Guardian interview is'okay,' scroll down for the far more interesting Spiegel interview, where Snowden goes way deeper into his cloak-and-dagger life, including thoughts on getting suicided. Snowden describes in detail for the first time his background, and what led him to leak details of the secret programmes being run by the US National Security Agency (NSA) and the UK's secret communication headquarters, GCHQ. He describes the 18 years since the September 11 attacks as "a litany of American destruction by way of American self-destruction, with the promulgation of secret policies, secret laws, secret courts and secret wars".

Fri 13 Sep 2019 17.00 BST Last modified on Fri 13 Sep 2019 17.00 BST The world's most famous whistleblower, Edward Snowden, says he has detected a softening in public hostility towards him in the US over his disclosure of top-secret documents that revealed the extent of the global surveillance programmes run by American and British spy agencies. In an exclusive two-hour interview in Moscow to mark the publication of his memoirs, Permanent Record, Snowden said dire warnings that his disclosures would cause harm had not come to pass, and even former critics now conceded "we live in a better, freer and safer world" because of his revelations. In the book, Snowden describes in detail for the first time his background, and what led him to leak details of the secret programmes being run by the US National Security Agency (NSA) and the UK's secret communication headquarters, GCHQ. He describes the 18 years since the September 11 attacks as "a litany of American destruction by way of American self-destruction, with the promulgation of secret policies, secret laws, secret courts and secret wars". Snowden also said: "The greatest danger still lies ahead, with the refinement of artificial intelligence capabilities, such as facial and pattern recognition. "An AI-equipped surveillance camera would be not a mere recording device, but could be made into something closer to an automated police officer." He is concerned the US and other governments, aided by the big internet companies, are moving towards creating a permanent record of everyone on earth, recording the whole of their daily lives. While Snowden feels justified in what he did six years ago, he told the Guardian he was reconciled to being in Russia for years to come and was planning for his future on that basis. He reveals he secretly married his partner, Lindsay Mills, two years ago in a Russian courthouse. While he would rather be in the US or somewhere like Germany, he is relaxed in Russia, now able to lead a more or less normal daily life. He is less fearful than when he first arrived in 2013, when he felt lonely, isolated and paranoid that he could be targeted in the streets by US agents seeking retribution. "I was very much a person the most powerful government in the world wanted to go away.