Stability radius and internal versus external stability in Banach spaces: an evolution semigroup approach

In this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems. These include time-varying systems modeled with unbounded state-space operators acting on Banach spaces. This approach allows one to apply the classical theory of strongly continuous semigroups to time-varying systems. In particular, the complex stability radius may be expressed explicitly in terms of the generator of a (evolution) semigroup. Examples are given to show that classical formulas for the stability radius of an autonomous Hilbert-space system fail in more general settings. Upper and lower bounds on the stability radius are provided for these general systems. In addition, it is shown that the theory of evolution semigroups allows for a straightforward operator-theoretic analysis of internal stability as determined by classical frequency-domain and input-output operators, even for nonautonomous Banach-space systemsComment: Also at http://www.math.missouri.edu/~stephen/preprint

Subset Sum in Time 2^{n/2} / poly(n)

A major goal in the area of exact exponential algorithms is to give an algorithm for the (worst-case) n-input Subset Sum problem that runs in time 2^{(1/2 - c)n} for some constant c > 0. In this paper we give a Subset Sum algorithm with worst-case running time O(2^{n/2} ? n^{-?}) for a constant ? > 0.5023 in standard word RAM or circuit RAM models. To the best of our knowledge, this is the first improvement on the classical "meet-in-the-middle" algorithm for worst-case Subset Sum, due to Horowitz and Sahni, which can be implemented in time O(2^{n/2}) in these memory models [Horowitz and Sahni, 1974]. Our algorithm combines a number of different techniques, including the "representation method" introduced by Howgrave-Graham and Joux [Howgrave-Graham and Joux, 2010] and subsequent adaptations of the method in Austrin, Kaski, Koivisto, and Nederlof [Austrin et al., 2016], and Nederlof and W?grzycki [Jesper Nederlof and Karol Wegrzycki, 2021], and "bit-packing" techniques used in the work of Baran, Demaine, and P?tra?cu [Baran et al., 2005] on subquadratic algorithms for 3SUM

Testing Sumsets is Hard

A subset $S$ of the Boolean hypercube $\mathbb{F}_2^n$ is a sumset if $S = \{a + b : a, b\in A\}$ for some $A \subseteq \mathbb{F}_2^n$. Sumsets are central objects of study in additive combinatorics, featuring in several influential results. We prove a lower bound of $\Omega(2^{n/2})$ for the number of queries needed to test whether a Boolean function $f:\mathbb{F}_2^n \to \{0,1\}$ is the indicator function of a sumset. Our lower bound for testing sumsets follows from sharp bounds on the related problem of shift testing, which may be of independent interest. We also give a near-optimal $2^{n/2} \cdot \mathrm{poly}(n)$-query algorithm for a smoothed analysis formulation of the sumset refutation problem.Comment: 18 page

Individual and Community Quality of Life in Nonmetropolitan Nebraska: Nebraska Rural Poll Research Report 18-3

Table of Contents: Executive Summary / Introduction / Trends in Community Ratings (1996 - 2018) / Figure 1 Community Change, 1996 - 2018 / Figure 2 Expected Community Change Ten Years from Now: 2011 – 2018 / Figure 3 Expected Destination of Those Planning to Move: 1998 - 2018 / Table 1 Proportions of Respondents Very or Somewhat Satisfied with Each Service, 1997 - 2018 / The Community and Its Attributes in 2018 / Figure 4 Perceptions of Community Change by Region / Figure 5 Expected Community Change in Ten Years by Community Size / Figure 6 Feelings of Community Powerlessness by Region / Figure 7 Satisfaction with Retail Shopping by Region / Figure 8 Satisfaction with Cost of Housing by Community Size / Figure 9 Satisfaction with Cellular Phone Service by Community Size / Table 2 Opinions About Community / Figure 10 Change in Community Political Discussions During the Past Five Years by Community Siz

Community Involvement and Leadership in Nonmetropolitan Nebraska: Rural Poll Research Report 19-1

Community leadership and involvement are important parts of community development. Rural communities rely on volunteers for many community development activities as well as local leadership positions. In smaller communities in particular, community members often take on multiple roles. Given these challenges, how involved are rural Nebraskans in community and political activities? How do they feel about the leadership in their community? How often do they have social interactions with others during a typical month? This paper provides a detailed analysis of these questions. This report details 1,776 responses to the 2019 Nebraska Rural Poll, the 24th annual effort to understand rural Nebraskans’ perceptions. Respondents were asked a series of questions about their community involvement and community leadership. Trends for some of the questions are examined by comparing data from the 2015 Rural Poll. In addition, comparisons are made among different respondent subgroups, that is, comparisons by age, occupation, region, etc. Based on these analyses, some key findings emerged

Perceptions of Immigration Among Nonmetropolitan Nebraskans: Nebraska Rural Poll Research Report 19-2

The percent of Nebraska’s population that is foreign born has steadily increased during the past decade. In fact, its growth in foreign born population since 2010 ranks in the top 10 among all states. Given these changes, are rural Nebraskans aware of recent immigrants in their community? How do they perceive immigrants and their impacts on rural Nebraska? How do they view various immigration policies? This paper provides a detailed analysis of these questions. This report details 1,776 responses to the 2019 Nebraska Rural Poll, the 24th annual effort to understand rural Nebraskans’ perceptions. Respondents were asked a series of questions about immigration. Trends for some of the questions are examined by comparing data from the 2006 Rural Poll. In addition, comparisons are made among different respondent subgroups, that is, comparisons by age, occupation, region, etc. Based on these analyses, some key findings emerged

Trends in Well-Being in Nonmetropolitan Nebraska: Nebraska Rural Poll Research Report 19-3

Nebraska’s economy remained strong in the beginning of 2019. However, the continued weakness of the agriculture sector had the possibility of hampering the state’s economic growth. In addition, the March flooding had the potential for negative economic effects. Given these challenges, how do rural Nebraskans feel about their community? Are they satisfied with the services provided by their community? How do rural Nebraskans believe they are doing and how do they view their future? How satisfied are they with various items that influence their well-being? Have these views changed over the past 24 years? This paper provides a detailed analysis of these questions. This report details 1,776 responses to the 2019 Nebraska Rural Poll, the 24th annual effort to understand rural Nebraskans’ perceptions. Respondents were asked a series of questions about their community and well-being. Trends for some of the questions are examined by comparing data from the 23 previous polls to this year’s results. In addition, comparisons are made among different respondent subgroups, that is, comparisons by age, occupation, region, etc. Based on these analyses, some key findings emerged

Validating a Plasma Momentum Flux Sensor to an Inverted Pendulum Thrust Stand

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76451/1/AIAA-35706-298.pd