We investigate a forecasting framework based on a simple discrete-time dynamic model with coefficients varying in time. The parameters of the model are recovered within a deep learning framework, which makes it possible to retain a transparent parametric structure while simultaneously accounting for complex and nonstationary patterns in the observed phenomenon. Our analysis covers two specifications of the noise process. Besides the standard Gaussian setting, we also consider Laplace-distributed noise, which can offer a more adequate description in the presence of heavier tails and sharper local fluctuations. For both cases, we formulate the predictive scheme of the model and analyze the associated uncertainty quantification, including the construction of prediction intervals. The results illustrate that a relatively simple model, when combined with time-dependent parameter estimation, can serve as a mathematically tractable and practically flexible tool for forecasting complex dynamics under different noise assumptions. The general model is stated for TVAR($p$), while the prediction-interval formulas and the numerical experiments are developed for the TVAR(1) case.

A PhD student spotted the wolves going after the so-called'king of the forest' on a trail camera. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy . While reviewing footage for her PhD research, Polish Academy of Sciences ecologist Robin Wijnands spotted something pretty wild .

Smoke rises from Crimea Bridge on Monday. The Ukrainian army is pounding supply routes and striking energy facilities across Crimea. Warsaw - For Yulia, a 23-year-old resident of Crimea, nights have become sleepless due to increased Ukrainian drone attacks on the peninsula annexed by Russia in 2014. Kyiv's army is pounding supply routes and striking energy facilities across the Black Sea territory -- a campaign it sees as fair retribution for Moscow's daily barrages of Ukrainian cities, and one that it hopes will turn the tide of the four-year war in its favor. On Thursday, the Moscow-installed governor of Crimea announced power cuts across the peninsula, which despite the war had been a popular holiday destination for Russians. In a time of both misinformation and too much information, quality journalism is more crucial than ever.

Ukraine's Volodymyr Zelensky has been stripped of Poland's highest state honour, the Order of the White Eagle, over Kyiv's decision to name a military unit after controversial World War Two fighters. Polish President Karol Nawrocki branded Ukraine's decision late last month to name the unit after the Ukrainian Insurgent Army (UPA) outrageous, incomprehensible and deeply disappointing. Nawrocki stressed the diplomatic row would not impact Poland's support for Ukraine against Russia. Ukraine's Foreign Minister Andrii Sybiha denounced Warsaw's move, calling it a strategic mistake and disrespectful. Many in Ukraine regard the UPA, which existed in the 1940s and 1950s, as heroes who fought for Ukrainian independence against the Soviet Red Army as well as Nazi Germany and Polish authorities.

Police in Poland are investigating the execution-style murder of a Russian artist and vocal critic of President Vladimir Putin. Polish prosecutors said Robert K, known as the artist Semyon Skrepetsky, was shot dead on Monday morning in the Polish city of Biała Podlaska, about 40km (25 miles) from the Belarusian border. The 44-year-old was shot five times in the head, chest and back in a car park in the city, located about 600m from the Belarusian consulate. He was known for his caricatures of politicians, including Putin, Belarusian leader Alexander Lukashenko and Chechen leader Ramzan Kadyrov. Marcin Kozak, spokesman for the District Prosecutor's Office in Lublin, said the artist was approached by an unidentified gunman who fired two shots at him.

PCWorld reports the Steam Deck has returned to market with nearly doubled pricing, featuring only OLED models at $789 for 512GB and $949 for 1TB versions. Valve discontinued cheaper LCD models and attributes price increases to rising memory and storage costs driven by AI industry demand affecting consumer hardware. This trend extends beyond Steam Deck to other gaming handhelds like Lenovo Legion Go, signaling broader affordability challenges in PC gaming hardware. The Steam Deck, harbinger of a portable PC gaming revolution, has been out of stock for three months. Now it's back at almost double the price of the original model. It'll cost you $789 USD to get the 512GB OLED version, $949 for the 1TB upgrade. The original LCD model, which debuted at $400, is resigned to the dustbin of history . Welcome to PC gaming in 2026, where the K-shaped economy has claimed the last remaining affordable option. The 512GB OLED model now costs $1,129 in Canada, 649 pounds in the UK, 779 euro in Europe, $1,199 in Australia, and 3,279 PLN in Poland.

Deep learning models for 12-lead electrocardiogram (ECG) analysis achieve high diagnostic performance but lack the intuitive interpretability required for clinical integration. Standard feature attribution methods are limited by the inherent difficulty in mapping abstract waveform fluctuations to physical anatomical pathologies. To resolve this, we propose a cross-modal method that projects feature attributions from high-performance 12-lead ECG models onto the CineECG 3D anatomical space. Our study reveals that while models trained directly on CineECG signals suffer from reduced accuracy and incoherent attributions, the proposed mapping mechanism effectively recovers clinically relevant feature rankings. Validated against a ground-truth dataset of 20 cases annotated by domain experts, the mapped explanations yield a Dice score of 0.56, significantly outperforming the 0.47 baseline of standard 12-lead attributions. These findings indicate that cross-modal averaging mapping effectively filters attribution instability and improves the localization of pathological features, combining the diagnostic expressiveness of standard ECG with the intuitive clarity of anatomical visualization.

What does the data tell us about immigration in Wales? Like many countries, Wales sees a steady flow of people arriving and leaving for other countries each year. The difference between those arriving and those leaving is known as net migration. Focusing on people moving from abroad, latest estimates say Wales' population - which was 3.2 million in June 2024 - had increased by about 23,000 over the previous year as a result of net international migration. A recent YouGov poll found a quarter of people surveyed in Wales believed that immigration, alongside the economy, should be among the issues prioritised by the Welsh government, even though immigration is controlled by the UK government.

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.