Sign-rank Can Increase under Intersection

The communication class UPP cc is a communication analog of the Turing Machine complexity class PP . It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension complexity), and is essentially the most powerful communication class against which we know how to prove lower bounds. For a communication problem f , let f ∧ f denote the function that evaluates f on two disjoint inputs and outputs the AND of the results. We exhibit a communication problem f with UPP cc ( f ) = O (log n ), and UPP cc ( f ∧ f ) = Θ (log 2 n ). This is the first result showing that UPP communication complexity can increase by more than a constant factor under intersection. We view this as a first step toward showing that UPP cc , the class of problems with polylogarithmic-cost UPP communication protocols, is not closed under intersection. Our result shows that the function class consisting of intersections of two majorities on n bits has dimension complexity n Omega Ω(log n ) . This matches an upper bound of (Klivans, O’Donnell, and Servedio, FOCS 2002), who used it to give a quasipolynomial time algorithm for PAC learning intersections of polylogarithmically many majorities. Hence, fundamentally new techniques will be needed to learn this class of functions in polynomial time.

Effective Communication Approaches for Decision Analytics

Analysts ignore the context that shapes and constrains communication at their peril. The rhetorical context in which analytics is enacted influences the communicative approach. In this chapter, two dominate elements are considered: 1) analytic complexity and 2) rhetorical context. Along this analytic-rhetorical spectrum, a four-square matrix is developed using these elements to describe distinct environments in which analytics is enacted. While each of the four positions are addressed for inclusion in this chapter, the focus is narrowed to an exposition of strategies for effectively communicating insights within the realm of decision analytics. Marked by a more basic analytic framework, decision analytics aims to support successful consumption and utilization at senior levels of organizations. Decision analytics differ from other types of analytics since they support the process of making decisions versus providing information. This chapter focuses on how analysts can use decision analytics to effectively communicate analytic results and insights to senior leaders of organizations.

Upper Bounds for the Analytic Complexity of Puiseux Polynomial Solutions to Bivariate Hypergeometric Systems

The paper deals with the analytic complexity of solutions to bivariate holonomic hypergeometric systems of the Horn type. We obtain estimates on the analytic complexity of Puiseux polynomial solutions to the hypergeometric systems defined by zonotopes. We also propose algorithms of the analytic complexity estimation for polynomials

Challenges in Strategy-Making

This chapter describes how state leaders encounter five difficulties while crafting strategies for governing. The first is conflict between the goals identified in Chapter 5. A familiar conflict of goals is that between internal order and human rights. Another conflict among goals arises between external security and internal order. Moreover, the desire to promote economic growth may collide with several other goals, such as national security, internal order, and human rights. A second challenge in crafting governance strategies is uncertainty about the techniques to use to achieve goals. Even when leaders are clear about their priorities, they may be unsure about the most effective ways to pursue them. A third challenge in crafting governance strategies is managing cultural and institutional inheritances, while the fourth challenge derives from turbulence in the governing environment. Some aspects of the environment may remain relatively constant, but other aspects change quickly. This can throw a leader's calculations into disarray. The final challenge is analytic complexity—that is, the difficulty of absorbing knowledge and making judgments about large and complicated questions.

The Possibilities of Uncertainty

This article describes the rationale, development, and implementation of a digital archival curriculum within the first-year composition program at Oklahoma State University. Such a curriculum helps students engage genuine inquiry to discover arguments rather than defend their existing beliefs. Analytic complexity and hidden information are offered as potential sources of uncertainty.