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The trends and reactions of the general public towards global events can be analyzed using data from social platforms, including Twitter. The number of tweets has been reported to help detect variations in communication traffic within subsets like countries, age groups and industries. Similarly, publicly accessible data and (in particular) data from social media about agricultural issues provide a great opportunity for obtaining instantaneous snapshots of farmer opinions and a method to track changes in opinion through temporal analysis. In this paper we hypothesize that the presence of keywords like precision agriculture, digital agriculture, Internet of Things (IoT), BigData, remote sensing, GPS, etc., in tweets could serve as an indicator of discussions centered around interest in modern farming practices. We extracted relevant tweets using keywords such as IoT, BigData and Geographical Information System (GIS), and then analyzed their geographical origin and frequency of their mention. We analyzed the Twitter data for the period of 1st -11th January 2018 to understand these trends and the factors affecting them. These factors, such as special events, projects, biogeography, etc., were further analyzed using tweet sources and trending hashtags from the database. The regions with the highest interest in the keywords were United States, Egypt, Brazil, Japan and China. A comparison of frequency of keywords revealed IoT as the most tweeted word (77.6%) in the downloaded data. The most used language was English followed by Spanish, Japanese and French. Periodical tweets on IoT from an account handled by IoT project on Twitter and Seminars on IoT in January in Santa Catarina (Brazil) were found to be the underlying factors for the observed trends., Comment: 7 pages, conference accepted

We present a unified framework of combinatorial descriptions, and the analogous asymptotic growth of the coefficients of two general families of functions related to integer partitions. In particular, we resolve several conjectures and verify several claims that are posted on the On-Line Encyclopedia of Integer Sequences. We perform the asymptotic analysis by systematically applying the Mellin transform, residue analysis, and the saddle point method. The combinatorial descriptions of these families of generalized partition functions involve colorings of Young tableaux, along with their ``divisor diagrams'', denoted with sets of colors whose sizes are controlled by divisor functions., Comment: 31 pages, 8 figures, 6 tables

The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the asymptotic ($n\rightarrow\infty$) mean of this number in the cases of different and identical pairs. In this paper we are interested in all asymptotic moments in the identical case, in the asymptotic variance in the different case and in the asymptotic distribution in both cases. We use two approaches: the first one, the probabilistic approach, leads to variances in both cases and to some conjectures on all moments in the identical case and on the distribution in both cases. The second approach, the combinatorial one, relies on multivariate pattern matching techniques, yielding exact formulas for first and second moments. We use such tools as Mellin transforms, Analytic Combinatorics, Markov Chains., Comment: 47 pages, 4 figures

Measurements of proton-nucleus scattering and high resolution neutrino-nucleus interaction imaging are key to reduce neutrino oscillation systematic uncertainties in future experiments. A High Pressure Time Projection Chamber (HPTPC) prototype has been constructed and operated at Royal Holloway University of London and CERN as a first step in the development of a HPTPC capable of performing these measurements as part of a future long-baseline neutrino oscillation experiment such as the Deep Underground Neutrino Experiment. In this paper we describe the design and operation of the prototype HPTPC with an argon based gas mixture. We report on the successful hybrid charge and optical readout, using four CCD cameras, of signals from Am-241 sources., Comment: 40 pages, 24 figures

In order to contain the COVID-19 pandemic, countries around the world have introduced social distancing guidelines as public health interventions to reduce the spread of the disease. However, monitoring the efficacy of these guidelines at a large scale (nationwide or worldwide) is difficult. To make matters worse, traditional observational methods such as in-person reporting is dangerous because observers may risk infection. A better solution is to observe activities through network cameras; this approach is scalable and observers can stay in safe locations. This research team has created methods that can discover thousands of network cameras worldwide, retrieve data from the cameras, analyze the data, and report the sizes of crowds as different countries issued and lifted restrictions (also called ''lockdown''). We discover 11,140 network cameras that provide real-time data and we present the results across 15 countries. We collect data from these cameras beginning April 2020 at approximately 0.5TB per week. After analyzing 10,424,459 images from still image cameras and frames extracted periodically from video, the data reveals that the residents in some countries exhibited more activity (judged by numbers of people and vehicles) after the restrictions were lifted. In other countries, the amounts of activities showed no obvious changes during the restrictions and after the restrictions were lifted. The data further reveals whether people stay ''social distancing'', at least 6 feet apart. This study discerns whether social distancing is being followed in several types of locations and geographical locations worldwide and serve as an early indicator whether another wave of infections is likely to occur soon., Comment: 10 pages, 15 figures

COVID-19 has resulted in a worldwide pandemic, leading to "lockdown" policies and social distancing. The pandemic has profoundly changed the world. Traditional methods for observing these historical events are difficult because sending reporters to areas with many infected people can put the reporters' lives in danger. New technologies are needed for safely observing responses to these policies. This paper reports using thousands of network cameras deployed worldwide for the purpose of witnessing activities in response to the policies. The network cameras can continuously provide real-time visual data (image and video) without human efforts. Thus, network cameras can be utilized to observe activities without risking the lives of reporters. This paper describes a project that uses network cameras to observe responses to governments' policies during the COVID-19 pandemic (March to April in 2020). The project discovers over 30,000 network cameras deployed in 110 countries. A set of computer tools are created to collect visual data from network cameras continuously during the pandemic. This paper describes the methods to discover network cameras on the Internet, the methods to collect and manage data, and preliminary results of data analysis. This project can be the foundation for observing the possible "second wave" in fall 2020. The data may be used for post-pandemic analysis by sociologists, public health experts, and meteorologists., Comment: 7 pages, 20 figures

A sequence of geometric random variables of length $n$ is a sequence of $n$ independent and identically distributed geometric random variables ($\Gamma_1, \Gamma_2, \dots, \Gamma_n$) where $\mathbb{P}(\Gamma_j=i)=pq^{i-1}$ for $1~\leq~j~\leq~n$ with $p+q=1.$ We study the number of distinct adjacent two letter patterns in such sequences. Initially we directly count the number of distinct pairs in words of short length. Because of the rapid growth of the number of word patterns we change our approach to this problem by obtaining an expression for the expected number of distinct pairs in words of length $n$. We also obtain the asymptotics for the expected number as $n \to \infty$., Comment: 18 pages, 1 table, 1 figure. This is the final version for publication

The P\'olya urn scheme is a discrete-time process concerning the addition and removal of colored balls. There is a known embedding of it in continuous-time, called the P\'olya process. We deal with a generalization of this stochastic model, where the initial values and the entries of the transition matrix (corresponding to additions or removals) are not necessarily fixed integer values as in the standard P\'olya process. In one of the scenarios, we even allow the entries of the matrix to be random variables. As a result, we no longer have a combinatorial model of "balls in an urn," but a broader interpretation as a random walk in a possibly high number of dimensions. In this paper, we study several parametric classes of these generalized continuum P\'olya-like random walks.

We study the joint distribution of the number of occurrences of members of a collection of nonoverlapping motifs in digital data. We deal with finite and countably infinite collections. For infinite collections, the setting requires that we be very explicit about the specification of the underlying measure-theoretic formulation. We show that (under appropriate normalization) for such a collection, any linear combination of the number of occurrences of each of the motifs in the data has a limiting normal distribution. In many instances, this can be interpreted in terms of the number of occurrences of individual motifs: They have a multivariate normal distribution. The methods of proof include combinatorics on words, integral transforms, and poissonization.

We make a conjecture that characterizes the periods of the nim values in subtraction games with subtraction set of size 3.

The precise analysis of the variance of the profile of a suffix tree has been a longstanding open problem. We analyze three regimes of the asymptotic growth of the variance of the profile of a suffix tree built from a randomly generated binary string, in the nonuniform case. We utilize combinatorics on words, singularity analysis, and the Mellin transform., Comment: 19 pages, 0 figures