The Structure of Qubit Unextendible Product Bases

Unextendible product bases have been shown to have many important uses in quantum information theory, particularly in the qubit case. However, very little is known about their mathematical structure beyond three qubits. We present several new results about qubit unextendible product bases, including a complete characterization of all four-qubit unextendible product bases, which we show there are exactly 1446 of. We also show that there exist p-qubit UPBs of almost all sizes less than $2^p$.Comment: 20 pages, 3 tables, 7 figure

La veritat de la Viquipèdia

What does it mean to assert that Wikipedia has a relation to truth? That there is, despite regular claims to the contrary, an entire apparatus of truth in Wikipedia? In this article, I show that Wikipedia has in fact two distinct relations to truth: one which is well known and forms the basis of existing popular and scholarly commentaries, and another which refers to equally well-known aspects of Wikipedia, but has not been understood in terms of truth. I demonstrate Wikipedia’s dual relation to truth through a close analysis of the Neutral Point of View core content policy (and one of the project’s “Five Pillars”). I conclude by indicating what is at stake in the assertion that Wikipedia has a regime of truth and what bearing this has on existing commentaries

Devil in a New Dress: Reframing as an Alternative Method of Motivated Reasoning

Much research has been conducted in the field of motivated reasoning, with most of this work focused on the tendency of motivated reasoners to reject counterarguments out of hand, the so-called disconfirmation bias. The objective of this work is markedly different. Borrowing from the prodigious body of work on framing, this investigation suggests an alternative route of motivated reasoning: when presented with a counterargument, subjects engage in motivated reasoning not by wholly rejecting the counter, but by reframing their attitudes so as to reduce the importance of the challenged belief. To this end, we conducted a series of experiments centered around challenging popular political beliefs and measuring the impact of the challenge on the receiver. This was accomplished first by conducting surveys to uncover prevailing political beliefs around several topics ranging from gun control to the legalization of prostitution. With the most common beliefs clearly established, we then conducted an experiment in which these beliefs were challenged through the creation of specifically tailored and previously evaluated counterarguments. Experimental subjects were asked to provide their (positive or negative) attitude toward a given political topic, and then asked to rank and rate the four most common beliefs surrounding that topic – with the first ranked belief representing the one the subject felt was most important. This belief was then challenged, and after a period – a week in the first trial, and ten minutes in the second trial – the subjects were asked to repeat their rankings and ratings of the offered beliefs. The results showed virtually no attitude change resulting from these challenges, but a significant number of subjects lowered their first-ranked belief after having been challenged. We interpret this behavior as engaging in motivated reasoning via reframing. Further research to determine when individuals engage in motivated reasoning via disconfirmation vs. reframing is needed, but these early results suggest that reframing is a legitimate alternative route through which individuals maintain their attitudes in the face of challenges.No embargoAcademic Major: Political Scienc

Universal Communication, Universal Graphs, and Graph Labeling

We introduce a communication model called universal SMP, in which Alice and Bob receive a function f belonging to a family ?, and inputs x and y. Alice and Bob use shared randomness to send a message to a third party who cannot see f, x, y, or the shared randomness, and must decide f(x,y). Our main application of universal SMP is to relate communication complexity to graph labeling, where the goal is to give a short label to each vertex in a graph, so that adjacency or other functions of two vertices x and y can be determined from the labels ?(x), ?(y). We give a universal SMP protocol using O(k^2) bits of communication for deciding whether two vertices have distance at most k in distributive lattices (generalizing the k-Hamming Distance problem in communication complexity), and explain how this implies a O(k^2 log n) labeling scheme for deciding dist(x,y) ? k on distributive lattices with size n; in contrast, we show that a universal SMP protocol for determining dist(x,y) ? 2 in modular lattices (a superset of distributive lattices) has super-constant ?(n^{1/4}) communication cost. On the other hand, we demonstrate that many graph families known to have efficient adjacency labeling schemes, such as trees, low-arboricity graphs, and planar graphs, admit constant-cost communication protocols for adjacency. Trees also have an O(k) protocol for deciding dist(x,y) ? k and planar graphs have an O(1) protocol for dist(x,y) ? 2, which implies a new O(log n) labeling scheme for the same problem on planar graphs

Labeling Theory and the Effects of Sanctioning on Delinquent Peer Association: A New Approach to Sentencing Juveniles

This is a review of contemporary theory and studies published in various scholarly journals regarding the labeling effect of criminal justice system involvement at a young age on offenders. Drawing on studies that have taken place over the past several decades in order to increase the generalizability of the conclusions, this paper discusses the relationship between formal sanctioning and delinquent peer association among offenders. Results from the studies lend support to the tenets of labeling theory. They also suggest that the relative rate of increased recidivism among offenders is positively correlated with an operationalized measure of their “stakes in conformity” (e.g. marriage, employment, civic involvement, etc.). This literature review highlights the need for a reassessment of current sentencing policy for juveniles, as their life-course orientation is particularly vulnerable to negative influences. More generally, this review brings together theory and data to call for a rejection of sentencing policies which claim to “get tough on crime.