Variational autoencoders (VAE) encode data into lower-dimensional latent vectors before decoding those vectors back to data. Once trained, decoding a random latent vector from the prior usually does not produce meaningful data, at least when the latent space has more than a dozen dimensions. In this paper, we investigate this issue by drawing insight from high dimensional statistics: in these regimes, the latent vectors of a standard VAE are by construction distributed uniformly on a hypersphere. We propose to formulate the latent variables of a VAE using hyperspherical coordinates, which allows compressing the latent vectors towards an island on the hypersphere, thereby reducing the latent sparsity and we show that this improves the generation ability of the VAE. We propose a new parameterization of the latent space with limited computational overhead.

In the digital era, the rapid propagation of fake news and rumors via social networks brings notable societal challenges and impacts public opinion regulation. Traditional fake news modeling typically forecasts the general popularity trends of different groups or numerically represents opinions shift. However, these methods often oversimplify real-world complexities and overlook the rich semantic information of news text. The advent of large language models (LLMs) provides the possibility of modeling subtle dynamics of opinion. Consequently, in this work, we introduce a Fake news Propagation Simulation framework (FPS) based on LLM, which studies the trends and control of fake news propagation in detail. Specifically, each agent in the simulation represents an individual with a distinct personality. They are equipped with both short-term and long-term memory, as well as a reflective mechanism to mimic human-like thinking. Every day, they engage in random opinion exchanges, reflect on their thinking, and update their opinions. Our simulation results uncover patterns in fake news propagation related to topic relevance, and individual traits, aligning with real-world observations. Additionally, we evaluate various intervention strategies and demonstrate that early and appropriately frequent interventions strike a balance between governance cost and effectiveness, offering valuable insights for practical applications. Our study underscores the significant utility and potential of LLMs in combating fake news.

Feature engineering describes the process of formulating relevant features that describe the underlying data science problem as accurately as possible and make it possible for algorithms to understand and learn patterns. Each feature describes a kind of information "piece". The sum of these pieces allows the algorithm to draw conclusions about the target variables -- at least if you have a data set that actually contains information about your target variable. According to the Forbes magazine, Data Scientists spend about 80% of their time collecting and preparing relevant data, with the data cleaning and data organizing alone taking up about 60% of the time. But this time is well spent.

The data consists of 100,000 observations of space taken by the SDSS (Sloan Digital Sky Survey). Every data point is described by 17 feature columns and 1 class column which identifies it to be either a star, galaxy, or quasar [1]. Note: The SDSS data is under the public domain. Please refer to the citation at the end. Celestial sphere: The celestial sphere is an imaginary sphere that has a large radius and is concentric on Earth.

"What do you think the rate of Covid-19 is for us?" This is the question that many Black people living in Berlin asked me at the beginning of March 2020. The answer: We don't know. Unlike other countries, notably the United States and the United Kingdom, the German government does not record racial identity information in official documents and statistics. Due to the country's history with the Holocaust, calling Rasse (race) by its name has long been contested.

Using artificial intelligence, scientists have confirmed that birds are more colourful near the equator. According to the study's author Christopher Cooney, ''We found that colourfulness was highest in birds from dense, closed forest habitats.'' "In vibrant rainforests, having colours that stand out from the crowd may help tropical species to distinguish themselves from others", he added. The researchers have proved a theory proposed by biologists Charles Darwin, Alexander von Humboldt, and Alfred Russel Wallace in 1850. After comparing the flora and fauna of northern Europe with the tropical region, they were all stunned.

Two centuries after Charles Darwin put the theory forward, a new study finally shows that birds living near the equator are more colourful. Scientists have used artificial intelligence (AI) to identify the amount of colour in photos of over 24,000 preserved birds from the Natural History Museum's collection. Tropical birds living near the equator are roughly 30 per cent more colourful than non-tropical birds living nearer the poles, the scientists found, but they don't know exactly why. The long-held theory, first suspected by Charles Darwin and other naturalists in the 18th and 19th centuries, hasn't been proven until now, the experts say. Research from the University of Sheffield found tropical birds living near the equator are roughly 30 per cent more colourful than non-tropical birds living nearer the poles.

Autoencoders have been proposed as a powerful tool for model-independent anomaly detection in high-energy physics. The operating principle is that events which do not belong to the space of training data will be reconstructed poorly, thus flagging them as anomalies. We point out that in a variety of examples of interest, the connection between large reconstruction error and anomalies is not so clear. In particular, for data sets with nontrivial topology, there will always be points that erroneously seem anomalous due to global issues. Conversely, neural networks typically have an inductive bias or prior to locally interpolate such that undersampled or rare events may be reconstructed with small error, despite actually being the desired anomalies. Taken together, these facts are in tension with the simple picture of the autoencoder as an anomaly detector. Using a series of illustrative low-dimensional examples, we show explicitly how the intrinsic and extrinsic topology of the dataset affects the behavior of an autoencoder and how this topology is manifested in the latent space representation during training. We ground this analysis in the discussion of a mock "bump hunt" in which the autoencoder fails to identify an anomalous "signal" for reasons tied to the intrinsic topology of $n$-particle phase space.

We've launched 9,600 satellites since 1957. For the first few decades, no one thought about what would happen once they reached the end of their lives. By the time space agencies decided to do something, it had become a problem. "A vast majority of objects in orbit are effectively stranded there," says Stijn Lemmens, a space debris analyst at the European Space Agency. "And they have a lifetime of hundreds, thousands of years."

Scientists have extracted a 400-year record of El Niño events using coral reef cores drilled from the Pacific Ocean, revealing crucial new insight on how these weather patterns have changed. And, the data so far suggest something'unusual' has been happening in recent decades. According to the new research, El Niño events appear to be cropping up more frequently in the central Pacific than they have in past centuries, and while eastern El Niños may be getting stronger. El Niño is caused by a shift in the distribution of warm water in the Pacific Ocean around the equator. Usually the wind blows strongly from east to west, due to the rotation of the Earth, causing water to pile up in the western part of the Pacific.