Hyperbolic embedding of infinite-dimensional convex bodies

In this article, we use the second intrinsic volume to define a metric on the space of homothetic classes of Gaussian bounded convex bodies in a separable real Hilbert space. Using kernels of hyperbolic type, we can deduce that this space is isometrically embedded into an infinite-dimensional real hyperbolic space. Applying Malliavin calculus, it is possible to adapt integral geometry for convex bodies in infinite dimensions. Moreover, we give a new formula for computing second intrinsic volumes of convex bodies and offer a description of the completion for the hyperbolic embedding of Gaussian bounded convex bodies with dimension at least two and thus answer a question asked by Debin and Fillastre [DF22].Comment: 34 pages. Some typos are corrected and some comments on support functions are added. All comments are welcome

And Your Eyes Open

This piece explores the realties of dreams, and the blurring of dreams and reality

Big mapping class groups are not extremely amenable

This paper uses the renowned Kechris-Pestov-Todor\v{c}evi\'{c} machinery to show that (big) mapping class groups are not extremely amenable unless the underlying surface is a sphere or a once-punctured sphere, or equivalently when the mapping class group is trivial. The same techniques also show that the pure mapping class groups, as well as compactly supported mapping class groups, of a surface with genus at least one can never be extremely amenable.Comment: 9 pages, 2 figures. Comments are welcom

Automated Greenhouse Watering and Heating System for the Schenectady ARC

Everyone wants to feel useful and to be able to contribute to their community. The Schenectady ARC aims to provide people with developmental disabilities the resources, services, and support that enable them to advocate and participate within their communities. The program seeks to encourage these people to develop skills and hobbies that give them independence and purpose. One way is operating the ARC\u27s greenhouse. Individuals at the Maple Ridge Center are responsible for operating the water system to irrigate the plant growing tables, daily, and ensuring that the proper amount of water is distributed to the plants. This is a rewarding activity and offers them the opportunity to develop useful skills in greenhouse management and maintenance. However, despite offering manual and automatic options, the current equipment of the greenhouse is not user-friendly and vulnerable if water leaks. The objective of our project is to communicate with the Schenectady ARC to develop an automatic controller for heating and water delivery that will be easy to use, safe, robust, affordable and easy to maintain. This project was started by Guo Qianyue CPE class of 2016, kept on by Stengel Kyle CPE class of 2018, continued by Lisa Gu CPE class of 2019, and followed by Larissa Umulinga CPE class of 2020. The system we created is a wireless sensor system that reads and transmits the moisture and temperature data wirelessly to control the watering and heating system at the ARC greenhouse. This paper describes the problem, goals, design specifications, testing plan, standards and ethics for this project

Research on the Relationship Network in Customer Innovation Community based on Text Mining and Social Network Analysis

Relationship is the focus of the current study in the social phenomenon with social network theory, which is mainly about its meaning and strength. However, a different object, different relationship. Social network theory insists that the actor\u27s behavior is the result of the limitations and opportunities of many relationships that occur simultaneously and interaction. The behavior and characteristics of the whole group are also dependent on the integration of multi-dimensional relationships. There are multi-dimensional relationships among customers participated product innovation in the customer innovation community. Since the huge number of customers in customer innovation community and the complex relationships among the customers, the method is different in traditional ways. Therefore, this paper combines associated crawler algorithm, text mining, and social network analysis to study network relationship types, network structure and the relevance of the customer innovation community. Firstly, this paper analyzes the relationship type and the relationship network according to previous studies. Secondly, reptile technology is used to obtain structured data in the customer community. After cleaning and pre-processing, the data is transformed into relational data from the original structure, with format 1069 × 1069 size matrix. Analyzing the structure of relationship network using social network analysis methods and tools, the results show that interactive network, social network, and knowledge-sharing networks are all sparse network. Thirdly, the correlation among the relationship networks is studied. The results demonstrate that it is higher than the correlation between the interactive network and the knowledge-sharing network and lower than the social network correlated with the other two networks

Precision Digital Health

Accounting for individual and situational heterogeneity (i.e., precision) is now an important area of research and treatment in the field of medicine. This essay argues that precision should also be embraced within digital health artifacts, such as by designing digital health apps to tailor recommendations to individual user characteristics, needs, and situations, rather than only providing generic advice. The challenge, however, is that not much guidance is available for embracing precision when designing or researching digital health artifacts. The paper suggests that a shift toward precision in digital health will require embracing heterogeneous treatment effects (HTEs), which are variations in the effectiveness of treatment, such as variations in effects for individuals of different ages. Embracing precision via HTEs is not trivial, however, and will require new approaches to the research and design of digital health artifacts. Thus, this essay seeks to not only define precision digital health, but also to offer suggestions as to where and how machine learning, deep learning, and artificial intelligence can be used to enhance the precision of interventions provisioned via digital health artifacts (e.g., personalized advice from mental health wellbeing apps). The study emphasizes the value of applying emerging causal ML methods and generative AI features within digital health artifacts toward the goal of increasing the effectiveness of digitially provisioned interventions