In the late 19th century, Georg Cantor believed his new theory could help the Church understand the infinite nature of the divine. It might have escaped lay people at the time, but for some observers the ascension of Leo XIV as head of the Catholic Church this year was a reminder that the last time a Pope Leo sat in St. Peter's Chair in the Vatican, from 1878 to 1903, the modern view of infinity was born. Georg Cantor's completely original "naïve" set theory caused both revolution and revolt in mathematical circles, with some embracing his ideas and others rejecting them. Cantor was deeply disappointed with the negative reactions, of course, but never with his own ideas. Because he held firm to the belief that he had a main line to the absolute--that his ideas came direct from (the divine intellect).

In 1991, Moore [20] raised a question about whether hydrodynamics is capable of performing computations. Similarly, in 2016, Tao [25] asked whether a mechanical system, including a fluid flow, can simulate a universal Turing machine. In this expository article, we review the construction in [8] of a "Fluid computer" in dimension 3 that combines techniques in symbolic dynamics with the connection between steady Euler flows and contact geometry unveiled by Etnyre and Ghrist. In addition, we argue that the metric that renders the vector field Beltrami cannot be critical in the Chern-Hamilton sense [9]. We also sketch the completely different construction for the Euclidean metric in $\mathbb R^3$ as given in [7]. These results reveal the existence of undecidable fluid particle paths. We conclude the article with a list of open problems.

With the advent of large language models(LLMs) enhanced by the chain-of-thought(CoT) methodology, visual reasoning problem is usually decomposed into manageable sub-tasks and tackled sequentially with various external tools. However, such a paradigm faces the challenge of the potential "determining hallucinations" in decision-making due to insufficient visual information and the limitation of low-level perception tools that fail to provide abstract summaries necessary for comprehensive reasoning. We argue that converging visual context acquisition and logical reasoning is pivotal for tackling visual reasoning tasks. This paper delves into the realm of multimodal CoT to solve intricate visual reasoning tasks with multimodal large language models(MLLMs) and their cognitive capability. To this end, we propose an innovative multimodal CoT framework, termed Cantor, characterized by a perception-decision architecture. Cantor first acts as a decision generator and integrates visual inputs to analyze the image and problem, ensuring a closer alignment with the actual context. Furthermore, Cantor leverages the advanced cognitive functions of MLLMs to perform as multifaceted experts for deriving higher-level information, enhancing the CoT generation process. Our extensive experiments demonstrate the efficacy of the proposed framework, showing significant improvements in multimodal CoT performance across two complex visual reasoning datasets, without necessitating fine-tuning or ground-truth rationales. Project Page: https://ggg0919.github.io/cantor/ .

Given that rich information is hidden behind ubiquitous numbers in text, numerical reasoning over text should be an essential skill of AI systems. To derive precise equations to solve numerical reasoning problems, previous work focused on modeling the structures of equations, and has proposed various structured decoders. Though structure modeling proves to be effective, these structured decoders construct a single equation in a pre-defined autoregressive order, potentially placing an unnecessary restriction on how a model should grasp the reasoning process. Intuitively, humans may have numerous pieces of thoughts popping up in no pre-defined order; thoughts are not limited to the problem at hand, and can even be concerned with other related problems. By comparing diverse thoughts and chaining relevant pieces, humans are less prone to errors. In this paper, we take this inspiration and propose CANTOR, a numerical reasoner that models reasoning steps using a directed acyclic graph where we produce diverse reasoning steps simultaneously without pre-defined decoding dependencies, and compare and chain relevant ones to reach a solution. Extensive experiments demonstrated the effectiveness of CANTOR under both fully-supervised and weakly-supervised settings.

Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously complicated, however, even if the chain is finite state: no finite expression for their Shannon entropy rate exists, as the set of their predictive features is generically infinite. As such, to date one cannot make general statements about how random they are nor how structured. Here, we address the first part of this challenge by showing how to efficiently and accurately calculate their entropy rates. We also show how this method gives the minimal set of infinite predictive features. A sequel addresses the challenge's second part on structure.

Artificial intelligence (AI) is trending globally in commerce, science, health care, geopolitics, and more areas. Deep learning, a subset of machine learning, is the lever that launched the worldwide rush--an area of strategic interest for researchers, scientists, visionary CEOs, academics, geopolitical think tanks, pioneering entrepreneurs, astute venture capitalists, strategy consultants, and management executives from companies of all sizes. Yet in the midst of this AI renaissance, is a relatively fundamental unsolvable problem with machine learning that is not commonly known, nor frequently discussed outside of the small cadre of philosophers, and artificial intelligence experts. A global research team of researchers have recently demonstrated that machine learning has an unsolvable problem, and published their findings in Nature Machine Intelligence in January 2019. Researchers from Princeton University, the University of Waterloo, Technion-IIT, Tel Aviv University, and the Institute of Mathematics of the Academy of Sciences of the Czech Republic, proved that AI learnability cannot be proved nor refuted when using the standard axioms of mathematics.

With the passage of the Chronic Care Act, Medicare Advantage plans have been scrambling to figure out how to offer supplemental benefits to their members. Passed as part of a Bipartisan Budget Act last year, the Chronic Care Act promotes the use of benefits that maintain health or keep a beneficiary's health from deteriorating, and the benefits don't have to be health-related. Instead, they can include help for social determinants of health that include housing, nutrition and transportation. Michael Cantor, MD, chief medical officer at CareCentrix, a company that works with payers and providers to create programs that improve quality of care while lowering costs, says social determinants are "significant barriers" to achieving good health for some beneficiaries and the Chronic Care Act is opening doors to improve outcomes. Under the act, the supplements can also be tailored to the individual, when it comes to qualifications.

Franz Schubert composed his Symphony No.8 in 1822, but never completed it, making only two movements along with an outline of a third. Nearly 200 years later, Huawei, Emmy-awarding composer Lucas Cantor, and artificial intelligence (A.I.) inside the Mate 20 Pro smartphone have done what the renowned composer didn't. They've finished the unfinished symphony. The project is a continued illustration of not only the power of Huawei's Kirin 980 processor and Dual-Neural Processing Unit (NPU) artificial intelligence accelerator, but also the potential for using A.I. in varied creative projects. We're familiar with A.I. modes on smartphone cameras, and Huawei has previously demonstrated the power and speed of its A.I. in a self-driving car, where a phone was used to identify and help avoid obstacles.

This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point. Pointwise dimension is invariant under a broad class of transformations. As a result, dimensional clustering can be usefully applied to a wide range of datasets. Concretely, we present a statistical model which estimates the pointwise dimension of a dataset around the points in that dataset using the distance of each point from its $n^{\text{th}}$ nearest neighbor. We demonstrate the applicability of our technique to the analysis of dynamical systems, images, and complex human movements.

With the mandate of fostering an ecosystem of applied machine learning startups, Google on Wednesday revealed the first four companies to join its Launchpad Studio and said this initial track is aimed squarely at healthcare and biotech. It--s no secret that Google and rivals Amazon, Apple, IBM and Microsoft are eyeing the $2.7 trillion healthcare market as fertile ground for technological disruption--though it appears Google is the first of the titans to formally establish a program for working with startups specific to the industry. The first four startups, Augmedix, BrainQ, Byteflies and Cytovale, get what Google deftly described as --equity-free support,-- and access to Google mentors, community engagement as well as datasets and testing environments for prototyping, as examples. Augmedix is working to minimize the time doctors spend on a computer during patient visits by leveraging Google Glass to automate scribing and collect audio, video and written notes then use natural language processing to help clinicians make sense of that information. Cantor described BrainQ as a research project concentrating on taking advances in neural networks and applying machine learning to signal processing to develop customized treatment protocols for people who cannot walk anymore, whether because of a stroke, spinal or brain injuries.