A common generalization of two theorems on the face numbers of Cohen–Macaulay (CM, for short) simplicial complexes is established: the first is the theorem of Stanley (necessity) and Björner-Frankl-Stanley (sufficiency) that characterizes all possible face numbers of a-balanced CM complexes, while the second is the theorem of Novik (necessity) and Browder (sufficiency) that characterizes the fa...

Before discussing today’s topic matter, let’s take a step back and situate ourselves with respect to the big picture. As mentioned in Lecture 1, a primary focus of this course is optimal inference. As a first step toward reasoning about optimality, we began to examine which statistics of the data that we observe are actually relevant in a given inferential task. We learned about lossless data r...

Abstmet-Three parallel gaps in robust feedback control theory are examined: sufficiency versus necessity, deterministic versus stochastic uncertainty modeling, and stability versus performance. Deterministic and stochastic output-feedback control problems are considered with both static and dynamic controllers. The static and dynamic robust stabilization problems involve deterministically model...

Local electricity generation and sharing has been given considerable attention recently for its disaster resilience and other reasons. However, the process of designing local sharing communities (or local grids) is still unclear. Thus, this study empirically compares algorithms for electricity sharing community clustering in terms of self-sufficiency, sharing cost, and stability. The comparison...

The question “is this system secure?” is notoriously difficult to answer. The question implies that there is a system-wide property called “security,” which we can measure with some meaningful threshold of sufficiency. In this concept paper, we discuss the difficulty of measuring security sufficiency, either directly or through proxy such as the number of known vulnerabilities. We propose that ...

This article explores the way in which Mexico’s countryside was affected by the country’s economic integration to its northern neighbors since the start of the North American Free Trade Agreement (NAFTA). Mexico’s political technocracy placed its bet for economic growth on the comparative advantage of cheap labor, a losing bet: Mexico’s asymmetrical integration into the North American economy, ...

Estimating appropriate sample sizes to measure species abundance and richness is a fundamental problem for most biodiversity research. In this study, we explore a method to measure sampling sufficiency based on haplotype diversity in the ray-finned fishes (Animalia: Chordata: Actinopterygii). To do this, we use linear regression and hypothesis testing methods on haplotype accumulation curves fr...

The aim of this study is the development of approach to the assessment of information sufficiency for software quality determination (according to ISO 25010: 2011). The proposed approach to assessment of information sufficiency is based on the comparative analysis of fragments of ontology of the subject domain "Software Engineering" and ontologies, that are developed on the basis of software re...