Entanglement and its Role in Shor's Algorithm

Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their classical counterparts. The nature of this resource is still not fully understood: here we use numerical simulation to investigate how entanglement between register qubits varies as Shor's algorithm is run on a quantum computer. The shifting patterns in the entanglement are found to relate to the choice of basis for the quantum Fourier transform.Comment: 15 pages, 4 eps figures, v1-3 were for conference proceedings (not included in the end); v4 is improved following referee comments, expanded explanations and added reference

The Iron Catalyzed Reaction between Nitrosyl Disulfonate and Hydroxylamine Monosulfonate Ions

Potassium nitrosyl disulfonate, K2NO(SO3)2, is noteworthy because the solid salt is orange in color and diamagnetic while its neutral aqueous solutions are purple in color and paramagnetic. These neutral solutions hydrolyze slowly to form N2O and hydroxylamine sulfonates; on the addition of acid the rate of hydrolysis is markedly increased. The mechanism of the hydrolytic reaction is unexpectedly complex as was found by Murib and Ritter [1] and, independently, by us. In order to obtain a more comprehensive picture of the mechanism of the hydrolytic reaction we have explored additional reactions which may play a part in the hydrolysis

The possible shapes of numerical ranges

Which convex subsets of the complex plane are the numerical range W(A of some matrix A? This paper gives a precise characterization of these sets. In addition to this we show that for any A there exists a symmetric matrix B of the same size such that W(A)=W(B).Comment: 4 page

Can a five minute, three question survey foretell first-year engineering student performance and retention?

This research paper examines first-year student performance and retention within engineering. A considerable body of literature has reported factors influencing performance and retention, including high school GPA and SAT scores,1,2,3 gender,4 self-efficacy,1,5 social status,2,6,7 hobbies,4 and social integration.6,7 Although these factors can help explain and even partially predict student outcomes, they can be difficult to measure; typical survey instruments are lengthy and can be invasive of student privacy. To address this limitation, the present paper examines whether a much simpler survey can be used to understand student motivations and anticipate student outcomes. The survey was administered to 347 students in an introductory Engineering Graphics and Design course. At the beginning of the first day of class, students were given a three-question, open-ended questionnaire that asked: “In your own words, what do engineers do?”, “Why did you choose engineering?”, and “Was there any particular person or experience that influenced your decision?” Two investigators independently coded the responses, identifying dozens of codes for both motivations for pursuing engineering and understanding of what it is. Five hypotheses derived from Dweck’s mindset theory7 and others8,9 were tested to determine if particular codes were predictive of first-semester GPA or first-year retention in engineering. Codes that were positively and significantly associated with first-semester GPA included: explaining why engineers do engineering or how they do it, stating that engineers create ideas, visions, and theories, stating that engineers use math, science, physics or analysis, and expressing enjoyment of math and science, whereas expressing interest in specific technical applications or suggesting that engineers simplify and make life easier were negatively and significantly related to first-semester GPA. Codes positively and significantly associated with first-year retention in engineering included: stating that engineers use math or that engineers design or test things, expressing enjoyment of math, science, or problem solving, and indicating any influential person who is an engineer. Codes negatively and significantly associated with retention included: citing an extrinsic motivation for pursuing engineering, stating that they were motivated by hearing stories about engineering, and stating that parents or family pushed the student to become an engineer. Although many prior studies have suggested that student self-efficacy is related to retention,1,5 this study found that student interests were more strongly associated with retention. This finding is supported by Dweck’s mindset theory: students with a “growth” mindset (e.g., “I enjoy math”) would be expected to perform better and thus be retained at a higher rate than those with a “fixed” mindset (e.g., “I am good at math”).7 We were surprised that few students mentioned activities expressly designed to stimulate interest in engineering, such as robotics competitions and high school engineering classes. Rather, they cited general interests in math, problem solving, and creativity, as well as family influences, all factors that are challenging for the engineering education community to address. These findings demonstrate that relative to its ease of administration, a five minute survey can indeed help to anticipate student performance and retention. Its minimalism enables easy implementation in an introductory engineering course, where it serves not only as a research tool, but also as a pedagogical aid to help students and teacher discover student perceptions about engineering and customize the curriculum appropriately

A Copernican View of Health Care Antitrust

Sage and Hammer use the analogy of Copernican astronomy to suggest that understanding the dramatic change wrought by managed care requires a conceptual reorientation regarding the meaning of competition in health care and its appropriate legal and regulatory oversight. Both share the belief that misperceiving the world limits potential for technical and social progress