Smooth and Strong PCPs

Probabilistically checkable proofs (PCPs) can be verified based only on a constant amount of random queries, such that any correct claim has a proof that is always accepted, and incorrect claims are rejected with high probability (regardless of the given alleged proof). We consider two possible features of PCPs: - A PCP is strong if it rejects an alleged proof of a correct claim with probability proportional to its distance from some correct proof of that claim. - A PCP is smooth if each location in a proof is queried with equal probability. We prove that all sets in NP have PCPs that are both smooth and strong, are of polynomial length, and can be verified based on a constant number of queries. This is achieved by following the proof of the PCP theorem of Arora, Lund, Motwani, Sudan and Szegedy (JACM, 1998), providing a stronger analysis of the Hadamard and Reed - Muller based PCPs and a refined PCP composition theorem. In fact, we show that any set in NP has a smooth strong canonical PCP of Proximity (PCPP), meaning that there is an efficiently computable bijection of NP witnesses to correct proofs. This improves on the recent construction of Dinur, Gur and Goldreich (ITCS, 2019) of PCPPs that are strong canonical but inherently non-smooth. Our result implies the hardness of approximating the satisfiability of "stable" 3CNF formulae with bounded variable occurrence, where stable means that the number of clauses violated by an assignment is proportional to its distance from a satisfying assignment (in the relative Hamming metric). This proves a hypothesis used in the work of Friggstad, Khodamoradi and Salavatipour (SODA, 2019), suggesting a connection between the hardness of these instances and other stable optimization problems

‘Being an artist you kind of, I mean, you get used to excellence’: Identity, Values and Fine Art Assessment Practices

In this article I report on a study into fine art lecturers’ assessment practices in higher education. This study explores the ways that lecturers bring themselves into the act of assessment (Hand & Clewes 2000). I interviewed twelve fine art lecturers who worked across six English universities. Lecturers were asked to relate to me how they learnt to assess student artwork and what informed their judgement making. My research explores the interfaces between fine art lecturers’ assessment practices, their values and identity/ies. My analysis offers a rendering of the ways that values underpin lecturers’ assessment practices. The article explores the ways that lecturers’ assessment decisions relate to their experiences as ex art students, their identity as artists, their own artistic practices, their conceptualisation of the arts arenas and the HE sector. My key overarching argument is that identity/ies and values underpin and enrich fine art lecturers’ assessment practices

Height bounds and the Siegel property

Let $G$ be a reductive group defined over $\mathbb{Q}$ and let $\mathfrak{S}$ be a Siegel set in $G(\mathbb{R})$. The Siegel property tells us that there are only finitely many $\gamma \in G(\mathbb{Q})$ of bounded determinant and denominator for which the translate $\gamma.\mathfrak{S}$ intersects $\mathfrak{S}$. We prove a bound for the height of these $\gamma$ which is polynomial with respect to the determinant and denominator. The bound generalises a result of Habegger and Pila dealing with the case of $GL_2$, and has applications to the Zilber-Pink conjecture on unlikely intersections in Shimura varieties. In addition we prove that if $H$ is a subset of $G$, then every Siegel set for $H$ is contained in a finite union of $G(\mathbb{Q})$-translates of a Siegel set for $G$.Comment: 24 pages, minor revision

Siena Italian Studies

STEP Category: Education AbroadSynopsis of an 8 week study abroad program in Siena, Italy.The Ohio State University Second-year Transformational Experience Program (STEP)Academic Major: Pharmaceutical Science

Entering China : an operations management case study

Market forces and international competition are driving companies to reduce costs. The operations management issues experienced by 50 Australian companies when investing in China were examined. Many experiences were found to be common to most of the participant\u27s industries. Relationships with government, associations, local partners and members of supply chains were considered highly important. Levels of technology in China were not considered to be a significant issue. Access to staff with sufficient technology training (particularly for product development) and technology implementation was an important issue. The paper presents a model relating the various operations management issues identified to one another.<br /

Poems for My Woofie The Story of Lt. Wilfred V. Michaud, 1st Parachute Battalion, 1st Marine Division

My senior capstone project is the creation of a book of investigative poetry. The subject of the work is my grandfather, Wilfred V. Michaud. He was a lieutenant in the United States Marine Corps during World War II. The poetry addresses the history of Michaud’s battalion and the battles it fought, as well as personal stories of Michaud’s life and experience in the service. Several secondary sources were used to gain historical context for the poetry. Additionally, primary sources were used to provide information about Michaud’s personal experiences. The combination of primary and secondary sources established the necessary background and inspiration for the project

Composite bulkhead fabrication development

Composite bulkhead is produced by a fabrication concept utilizing vacuum and/or autoclave pressure to hold preformed welded sandwich elements in place during bonding and aging