With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently emerged and succeeded in various forward and inverse PDE problems thanks to their excellent properties, such as flexibility, mesh-free solutions, and unsupervised training. However, their slower convergence speed and relatively inaccurate solutions often limit their broader applicability in many science and engineering domains. This paper proposes a new kind of data-driven PDEs solver, physics-informed cell representations (PIXEL), elegantly combining classical numerical methods and learning-based approaches. We adopt a grid structure from the numerical methods to improve accuracy and convergence speed and overcome the spectral bias presented in PINNs. Moreover, the proposed method enjoys the same benefits in PINNs, e.g., using the same optimization frameworks to solve both forward and inverse PDE problems and readily enforcing PDE constraints with modern automatic differentiation techniques. We provide experimental results on various challenging PDEs that the original PINNs have struggled with and show that PIXEL achieves fast convergence speed and high accuracy. Project page: https://namgyukang.github.io/PIXEL/

Product-related reviews are based on users' experiences that are mostly shared on videos in YouTube. It is the second most popular website globally in 2021. People prefer to watch videos on recently released products prior to purchasing, in order to gather overall feedback and make worthy decisions. These videos are created by vloggers who are enthusiastic about technical materials and feedback is usually placed by experienced users of the product or its brand. Analyzing the sentiment of the user reviews gives useful insights into the product in general. This study is focused on three smartphone reviews, namely, Apple iPhone 13, Google Pixel 6, and Samsung Galaxy S21 which were released in 2021. VADER, which is a lexicon and rule-based sentiment analysis tool was used to classify each comment to its appropriate positive or negative orientation. All three smartphones show a positive sentiment from the users' perspective and iPhone 13 has the highest number of positive reviews. The resulting models have been tested using N\"aive Bayes, Decision Tree, and Support Vector Machine. Among these three classifiers, Support Vector Machine shows higher accuracies and F1-scores.

Image search engines enable the retrieval of images relevant to a query image. In this work, we consider the setting where a query for similar images is derived from a collection of images. For visual search, the similarity measurements may be made along multiple axes, or views, such as style and color. We assume access to a set of feature extractors, each of which computes representations for a specific view. Our objective is to design a retrieval algorithm that effectively combines similarities computed over representations from multiple views. To this end, we propose a self-supervised learning method for extracting disentangled view-specific representations for images such that the inter-view overlap is minimized. We show how this allows us to compute the intent of a collection as a distribution over views. We show how effective retrieval can be performed by prioritizing candidate expansion images that match the intent of a query collection. Finally, we present a new querying mechanism for image search enabled by composing multiple collections and perform retrieval under this setting using the techniques presented in this paper.

The problem of tensor completion has applications in healthcare, computer vision, and other domains. However, past approaches to tensor completion have faced a tension in that they either have polynomial-time computation but require exponentially more samples than the information-theoretic rate, or they use fewer samples but require solving NP-hard problems for which there are no known practical algorithms. A recent approach, based on integer programming, resolves this tension for nonnegative tensor completion. It achieves the information-theoretic sample complexity rate and deploys the Blended Conditional Gradients algorithm, which requires a linear (in numerical tolerance) number of oracle steps to converge to the global optimum. The tradeoff in this approach is that, in the worst case, the oracle step requires solving an integer linear program. Despite this theoretical limitation, numerical experiments show that this algorithm can, on certain instances, scale up to 100 million entries while running on a personal computer. The goal of this paper is to further enhance this algorithm, with the intention to expand both the breadth and scale of instances that can be solved. We explore several variants that can maintain the same theoretical guarantees as the algorithm, but offer potentially faster computation. We consider different data structures, acceleration of gradient descent steps, and the use of the Blended Pairwise Conditional Gradients algorithm. We describe the original approach and these variants, and conduct numerical experiments in order to explore various tradeoffs in these algorithmic design choices.

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Former federal prosecutor Trey Gowdy gives his take on the Alex Murdaugh trial and Hunter Biden's attorney calling for criminal probe of the laptop on'The Story.' High-profile lawyer Abbe Lowell again entered the national spotlight this week representing Hunter Biden in the legal battle involving his infamous laptop, and Lowell's hiring signals how seriously Biden is taking his situation, an attorney tells Fox News Digital. "Abbe is not cheap, and you don't bring in Abbe unless you want to go to war or prevent one," said the source who's worked with Lowell. He hasn't been charged with anything, but they're trying to prevent that because that would be bad for [President] Biden and Hunter." Lowell made a splash this week with letters urging prosecutors to launch state and federal investigations into John Paul Mac Isaac, who he accused of "unlawfully" accessing the younger Biden's personal data on his laptop after it was left at his repair shop in 2019. Former President Donald Trump's lawyer Rudy Giuliani, Steve Bannon and other notable Biden critics were also listed in the lawsuit for their role in disseminating the information to the public. Mac Isaac chose to work with President Donald Trump's personal lawyer to weaponize Mr. Biden's personal computer data against his father, Joseph R. Biden, by unlawfully causing the provision of Mr. Biden's personal data to the New York Post," Lowell wrote Wednesday.

In the classroom of the future--if there still are any--it's easy to imagine the endpoint of an arms race: an artificial intelligence that generates the day's lessons and prompts, a student-deployed A.I. that will surreptitiously do the assignment, and finally, a third-party A.I. that will determine if any of the pupils actually did the work with their own fingers and brain. Loop complete; no humans needed. If you were to take all the hype about ChatGPT at face value, this might feel inevitable. But a response to the hit software demo, released by OpenAI in November to instant fanfare, is coming. You only have to look at how schools dealt with the potential externalities of newly essential tech during the pandemic to see how a similarly paranoid reaction to chatbots like ChatGPT could go--and how it shouldn't. When schools had to shift on the fly to remote learning three years ago, there was a massive turn to what at that point was mainly enterprise software: Zoom.

By incorporating the residual of the differential equation into the loss function of a neural network-based surrogate model, PINNs can seamlessly combine measured data with physical constraints given by differential equations. PINNs can also be viewed as a surrogate model for solving differential equations by incorporating additional data or as a data-driven correction (or even discovery) of the underlying physical system. By the end of the year 2022, we had experienced several waves of the COVID-19 pandemic with different variants of the virus prevailing at different time intervals. Various levels of interventions and protective measures were implemented to counteract the uncontrolled spreading of the disease. We focus exemplarily on the time until the fourth wave (i.e., the omicron wave) of the COVID-19 pandemic in Germany that had its peak in February and March 2022. The B.1.617.2 (delta) variant of SARS-CoV-2, which is characterized by a higher contagiosity than the previous B.1.1.7 (alpha), B.1.351

3D face reconstruction algorithms from images and videos are applied to many fields, from plastic surgery to the entertainment sector, thanks to their advantageous features. However, when looking at forensic applications, 3D face reconstruction must observe strict requirements that still make unclear its possible role in bringing evidence to a lawsuit. Shedding some light on this matter is the goal of the present survey, where we start by clarifying the relation between forensic applications and biometrics. To our knowledge, no previous work adopted this relation to make the point on the state of the art. Therefore, we analyzed the achievements of 3D face reconstruction algorithms from surveillance videos and mugshot images and discussed the current obstacles that separate 3D face reconstruction from an active role in forensic applications.

According to the authors, such integration is like riding a bicycle made for two, also known as a tandem. This kind of vehicle requires a strong collaboration between the two riders to pedal synchronically and the one in front must be able and willing to drive the tandem towards a common destination, on which both riders agree. The structure of the bicycle should suit a diversity of users: tall and short; married couples and perfect strangers; sportspeople and lazy ones. The way it can be used must adapt to any kind of road, dirt trails and urban well-paved streets alike. Cycling metaphors aside, the convergence and integration of two different disciplines puts requirements to the method and the attitude of both and of all participants.