Efficient Optimization of Loops and Limits with Randomized Telescoping Sums

We consider optimization problems in which the objective requires an inner loop with many steps or is the limit of a sequence of increasingly costly approximations. Meta-learning, training recurrent neural networks, and optimization of the solutions to differential equations are all examples of optimization problems with this character. In such problems, it can be expensive to compute the objective function value and its gradient, but truncating the loop or using less accurate approximations can induce biases that damage the overall solution. We propose randomized telescope (RT) gradient estimators, which represent the objective as the sum of a telescoping series and sample linear combinations of terms to provide cheap unbiased gradient estimates. We identify conditions under which RT estimators achieve optimization convergence rates independent of the length of the loop or the required accuracy of the approximation. We also derive a method for tuning RT estimators online to maximize a lower bound on the expected decrease in loss per unit of computation. We evaluate our adaptive RT estimators on a range of applications including meta-optimization of learning rates, variational inference of ODE parameters, and training an LSTM to model long sequences

Fermionic Symmetry Protected Topological Phases and Cobordisms

It has been proposed recently that interacting Symmetry Protected Topological (SPT) phases can be classified using cobordism theory. We test this proposal in the case of fermionic SPT phases with Z/2 symmetry, where Z/2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known fermionic SPT phases in space dimension less than or equal to 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases.Comment: 26 pages, new references added and a new section on decorated domain walls in v

The Falling Factorial Basis and Its Statistical Applications

We study a novel spline-like basis, which we name the "falling factorial basis", bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations in basis matrix multiplication and basis matrix inversion. The falling factorial functions are not actually splines, but are close enough to splines that they provably retain some of the favorable properties of the latter functions. We examine their application in two problems: trend filtering over arbitrary input points, and a higher-order variant of the two-sample Kolmogorov-Smirnov test.Comment: Full version for the ICML paper with the same titl

Kerouac\u27s Dharma Bums (1958) & DeLillo\u27s Americana (1971): An Investigation of the Influences of Media, Spatiality, & Buddhism on Selfhood in Mid-twentieth-century American Culture & Consciousness

In Dharma Bums (1958), by Jack Kerouac, and Americana (1971), by Don DeLillo, the authors explore the complexity of selfhood as pertaining to individual identity and subjectivity in mid-twentieth century American culture and consciousness, paying specific attention to the relation that these concepts have with media, spatiality, and Buddhism. Although numerous critics provide extensive analyses of these texts, authors, and themes, no critic has paired these texts and authors, and investigated these particular themes in relation to selfhood. I argue that in Dharma Bums and Americana, Kerouac and DeLillo each investigate the influence of media, spatiality, and Buddhism on selfhood, as well as provide competing models of selfhood that offer either self-transformation or self-limitation

Academic Executives’ Perceptions of Team Relations and How These Relationships Impact Leadership and Institutions

Research suggests there are many factors that contribute to the success or failure of university leaders. This study explores one of these factors—the relationships between the university president and their executive team and the group’s collective sociability—and uses social capital theory to suggest executive teams utilize relationships to influence leadership and the institution. The researcher employs a qualitative phenomenological approach using purposeful sampling to reveal how presidents and their executive teams perceive how their relational experiences impact the team and university. The research found that three themes emerged that broadly cover how organizational structure promotes or hinders relationship building, how relations are maintained and how the environment provides obstacles and opportunities for these academic executives to navigate. This study contributes to the body of literature related to educational leadership by offering current university executives and individuals aspiring to be a university or college executive insight into how the relationships among the executive team can be helpful or a hindrance

Academic Executives’ Perceptions of Team Relations and How These Relationships Impact Leadership and Institutions

Research suggests there are many factors that contribute to the success or failure of university leaders. This study explores one of these factors—the relationships between the university president and their executive team and the group’s collective sociability—and uses social capital theory to suggest executive teams utilize relationships to influence leadership and the institution. The researcher employs a qualitative phenomenological approach using purposeful sampling to reveal how presidents and their executive teams perceive how their relational experiences impact the team and university. The research found that three themes emerged that broadly cover how organizational structure promotes or hinders relationship building, how relations are maintained and how the environment provides obstacles and opportunities for these academic executives to navigate. This study contributes to the body of literature related to educational leadership by offering current university executives and individuals aspiring to be a university or college executive insight into how the relationships among the executive team can be helpful or a hindrance

Identification of Critical Points for Bacterial Contamination in the Microbrewery Environment

There are 8,884 craft breweries producing over 23 million barrels of beer in the United States as of 2020. These 23 million barrels of craft beer account for 12.3% of the United States beer consumption in 2020. The American craft beer industry is substantial and needs to protect its product from bacterial contamination. Overall, beer is a microbially stable product. Beers pH, ethanol levels, CO2 concentrations, the presence of hop-derived antimicrobial compounds, and low levels of O2 make beer a highly unfavorable environment for most bacterial species. Furthermore, the brewing process, which involves heat treatments and chemical sanitizers further protect beer from bacterial contamination. However, beer sometimes does become contaminated by unwanted bacteria. Primarily these bacteria are members of the Genera Lactobacillus, Pediococcus, Pectinatus, and Megasphaera. These bacteria contaminate beer due to a variety of factors that allow them to evade beer’s antibacterial properties or the process hurdles of the brewing process. Protecting beer from these spoilage organisms is crucial to maintain quality and shelf stability. Microbreweries and brewpub are especially vulnerable to bacterial contamination due to the unique challenges they face. These challenges include the use of modular chlorobutyl hose systems and mobile pumps, the overall “open” nature of smaller brewhouses and cellars exposed to the outside environment (such as opening tanks to pitch yeast, dry hop, or introduction of additions), and the proximity of the production and packaging areas to the public. Research was conducted to determine steps in the brewing process that bacterial species were most likely to contaminate the microbrewery/brewpub environment. Samples were collected from three breweries of similar size and scale in Upstate South Carolina, from eleven common locations throughout the brewing process and analyzed via HybriScan D Beer rapid molecular testing kits for the cell counts at each location. The racking arm valve had the highest levels of bacterial contamination

Systemic design: Two Canadian case studies

The currently fragmented state of ‘systems + design’ praxis is curious in light of the affinities between the two interdisciplines. To explain why designers and systems thinkers have not been talking to each other, we may look to their differences. Whereas the designer learns by doing in concrete situations, the systems thinker’s knowledge accrues by abstracting away from the particular details of any specific instance of practice. But if this is sufficient to account for the lack of dialogue between and synthesis of systems + design, then the two interdisciplines are on a collision course. Since the mid-20th Century, design has followed a trajectory of increasing abstractness, migrating from the design of objects, to the design of services, identities, interfaces, networks, projects, and discourses. At the same time, systems thinking has all but abandoned its ambitions to provide a unity for science. Instead, a diversity of systems approaches have flourished as forms of reflective practice, grounded in the methods of action research.The authors of this chapter are approaching the scene of the accident from opposite, but not opposing, directions. One of us is a systems thinker who got involved in the messy business of institutionalizing design within the U.S. military. The other is a business designer who increasingly needs systems thinking to fold design into the core of business strategy development. Although our systemic design methodologies were developed independently, we have found they provide enough similarity to be commensurable, and enough difference to stimulate critical reflection.In this paper, we present two new case studies where systemic design was applied with impact to address strategy and organizational challenges. Before introducing the case studies, we briefly define what we mean by systemic design and provide a common framework for our analysis. In the following section, our first case study concerns a public procurement project within the University of Toronto, where design and a systems mindset helped the Central Procurement Department re-envision how public policy is implemented and how value is created in the broader university purchasing ecosystem. Our second case study involves improving the effectiveness of the Clean Energy and Natural Resources Group (CENRG) within the Government of Alberta. Design was used here to reframe the way that the five departments within CENRG work together and to create a learning system for continuous improvement. We conclude the chapter by interpreting these case studies as a contribution to knowledge on how systems + design might be synthesized to create a practical approach to systemic design