Geographic context is often consider relevant to motor insurance risk, yet public actuarial datasets provide limited location identifiers, constraining how this information can be incorporated and evaluated in claim-frequency models. This study examines how geographic information from alternative data sources can be incorporated into actuarial models for Motor Third Party Liability (MTPL) claim prediction under such constraints. Using the BeMTPL97 dataset, we adopt a zone-level modeling framework and evaluate predictive performance on unseen postcodes. Geographic information is introduced through two channels: environmental indicators from OpenStreetMap and CORINE Land Cover, and orthoimagery released by the Belgian National Geographic Institute for academic use. We evaluate the predictive contribution of coordinates, environmental features, and image embeddings across three baseline models: generalized linear models (GLMs), regularized GLMs, and gradient-boosted trees, while raw imagery is modeled using convolutional neural networks. Our results show that augmenting actuarial variables with constructed geographic information improves accuracy. Across experiments, both linear and tree-based models benefit most from combining coordinates with environmental features extracted at 5 km scale, while smaller neighborhoods also improve baseline specifications. Generally, image embeddings do not improve performance when environmental features are available; however, when such features are absent, pretrained vision-transformer embeddings enhance accuracy and stability for regularized GLMs. Our results show that the predictive value of geographic information in zone-level MTPL frequency models depends less on model complexity than on how geography is represented, and illustrate that geographic context can be incorporated despite limited individual-level spatial information.

Protecting individual privacy is essential across research domains, from socio-economic surveys to big-tech user data. This need is particularly acute in healthcare, where analyses often involve sensitive patient information. A typical example is comparing treatment efficacy across hospitals or ensuring consistency in diagnostic laboratory calibrations, both requiring privacy-preserving statistical procedures. However, standard equivalence testing procedures for differences in proportions or means, commonly used to assess average equivalence, can inadvertently disclose sensitive information. To address this problem, we develop differentially private equivalence testing procedures that rely on simulation-based calibration, as the finite-sample distribution is analytically intractable. Our approach introduces a unified framework, termed DP-TOST, for conducting differentially private equivalence testing of both means and proportions. Through numerical simulations and real-world applications, we demonstrate that the proposed method maintains type-I error control at the nominal level and achieves power comparable to its non-private counterpart as the privacy budget and/or sample size increases, while ensuring strong privacy guarantees. These findings establish a reliable and practical framework for privacy-preserving equivalence testing in high-stakes fields such as healthcare, among others.

We introduce a novel score-based diffusion framework named Twigs that incorporates multiple co-evolving flows for enriching conditional generation tasks. Specifically, a central or trunk diffusion process is associated with a primary variable (e.g., graph structure), and additional offshoot or stem processes are dedicated

How the US left Ukraine exposed to Russia's winter war Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? Russia-Ukraine talks resume in Geneva as US claims'meaningful' progress Day two of the third round of trilateral talks between Russia, Ukraine and the United States is under way in Geneva, Switzerland, as the four-year anniversary of Russia's full-scale invasion of its neighbour looms next week, with vague references to "progress" but nothing tangible yet shared. Little has been made public about the talks' contents since negotiations kicked off on Tuesday behind closed doors and continued on Wednesday morning. The thorniest of issues, territory and the yielding of it, remains the key sticking point.

How the US left Ukraine exposed to Russia's winter war Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? Three people were killed in a Russian drone attack on a civilian car in the city of Mykolaivka in the Kramatorsk district of Ukraine's Donetsk region, the state's emergency service said in a statement. The three people, as well as another person injured in the attack, were workers at the Sloviansk Thermal Power Station, the Kyiv Independent news outlet reported. A woman died after being injured in a Russian drone attack in Ukraine's Zaporizhia region, Governor Ivan Fedorov wrote on the Telegram messaging app.

How the US left Ukraine exposed to Russia's winter war Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? The United States is set to host talks between envoys from Russia and Ukraine in Geneva, Switzerland, on Tuesday and Wednesday, days before the fourth anniversary of the full-scale Russian invasion of its neighbour. Ukrainian President Volodymyr Zelenskyy says diplomacy will be more effective with "justice and strength", after Russia launched a large-scale missile and drone attack at targets across Ukraine. For its part, Russia also reported dozens of Ukrainian drones were fired overnight.

Could Ukraine hold a presidential election right now? Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? 'Ukraine is running out of men, money and time' Ukrainian officials have left for Geneva, Switzerland, where another round of negotiations aimed at ending the war with Russia is set to take place. The next round of negotiations is ahead.

Interacting systems are prevalent in nature.