An upper bound on the sum of squares of degrees in a hypergraph

AbstractWe give an upper bound on the sum of squares of ℓ-degrees in a k-uniform hypergraph in terms of ℓ,k and the number of vertices and edges of the hypergraph, where a ℓ-degree is the number of edges of the hypergraph containing a fixed ℓ-element subset of the vertices. For ordinary graphs this bound coincides with one given by de Caen. We show that our bound implies the quadratic LYM-inequality for 2-level antichains of subsets of a finite set

AZ-identities and Strict 2-part Sperner Properties of Product Posets

One of the central issues in extremal set theory is Sperner's theorem and its generalizations. Among such generalizations is the best-known BLYM inequality and the Ahlswede--Zhang (AZ) identity which surprisingly generalizes the BLYM inequality into an identity. Sperner's theorem and the BLYM inequality has been also generalized to a wide class of posets. Another direction in this research was the study of more part Sperner systems. In this paper we derive AZ type identities for regular posets. We also characterize all maximum 2-part Sperner systems for a wide class of product posets

Strong Qualitative Independence

AbstractThe subsets A,B of the n-element X are said to be s-strongly separating if the two sets divide X into four sets of size at least s. The maximum number h(n,s) of pairwise s-strongly separating subsets was asymptotically determined by Frankl (Ars Combin. 1 (1976) 53) for fixed s and large n. A new proof is given. Also, estimates for h(n,cn) are found where c is a small constant

Quadratic LYM-type inequalities for intersecting Sperner families

Let $\mathcal{F}\subseteq 2^{[n]}$ be a intersecting Sperner family (i.e. $A \not\subset B, A \cap B \neq \emptyset$ for all $A,B \in \mathcal{F}$) with profile vector $(f_i)_{i=0 \ldots n}$ (i.e. $f_i=|\mathcal{F} \cap \binom{[n]}{i}|$). We present quadratic inequalities in the $f_i$'s which sharpen the previously known linear $\mathrm{LYM}$-type inequalities

Invariant measure and universality of the 2D Yang-Mills Langevin dynamic

We prove that the Yang-Mills (YM) measure for the trivial principal bundle over the two-dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge-fixing, and Bourgain's method for invariant measures. Several corollaries are presented including a gauge-fixed decomposition of the YM measure into a Gaussian free field and an almost Lipschitz remainder, and a proof of universality for the YM measure that we derive from a universality for the Langevin dynamic for a wide class of discrete approximations. The latter includes standard lattice gauge theories associated to Wilson, Villain, and Manton actions. An important step in the argument, which is of independent interest, is a proof of uniqueness for the mass renormalisation of the gauge-covariant continuum Langevin dynamic, which allows us to identify the limit of discrete approximations. This latter result relies on Euler estimates for singular SPDEs and for Young ODEs arising from Wilson loops.Comment: 157 pages. Shortened the earlier version. Strengthened uniqueness result in Sec 8 which allows simplifications in Sec 3 and 5.1. Simplified Sec 5.5. Minor corrections elsewhere in the pape

Combinatorics

[no abstract available

An Economic Analysis of Hazard Analysis Critical Control Point-Based Risk Management Programme in the New Zealand Meat Industry

The replacement of the Meat Act 1981 by the Animal Products Act 1999 opened a new era for food safety management in New Zealand. Administering food legislation is now the sole responsibility of the New Zealand Food Safety Authority instead of being shared between the Ministry of Agriculture and Forestry and the Ministry of Health as previously. At the core of the legislative change is the requirement for Risk Management Programmes (RMP). Every single animal primary processing business is required to have an RMP for each type of product. An RMP is required to embrace the principles of Hazard Analysis and Critical Control Point (HACCP). While there have been some studies considering the implementation of HACCP in food businesses worldwide, there has not been any study focusing on HACCP adoption in New Zealand. The mandating of RMP has also made the implementation process more complex. On the other hand, it also brings new experience in terms of food safety management. This thesis examines the implementation process of HACCP/RMP in New Zealand. It also explores the interaction between food safety management and international competitiveness through an economic analysis of the impacts of the program on a New Zealand food processing industry. The meat industry was chosen as a case study as it is one of the first industries that had to comply with the first deadline of the implementation (July 2003). Also, being a significant export-oriented industry of New Zealand, the meat industry provides an ideal case for the purpose of this study. The thesis consists of four parts. Part I presents an introduction to the study including a review of international and national food safety issues, the relationship between food safety and trade and international competitiveness, and the HACCP economic literature. This background helps to shape the research objectives and methodology as described in Chapter 3. Chapter 4 discusses the design of the survey to collect plant experience regarding the implementation of HACCP/RMP in New Zealand. Part II analyses the experiences within the New Zealand meat industry regarding the implementation of HACCP/RMP. It discusses plant motivations to adopt the program and the implementation issues they are facing. Plant observations on the costs and benefits of the implementation are reported. Further, data gathered from the survey are used in a non-parametric analysis of the influences of the plant characteristics on the HACCP/RMP implementation process. The analysis provides implications for HACCP/RMP policy design. Part III presents the modelling techniques to quantify the costs and benefits of HACCP/RMP implementation. In Chapter 8, a quality-adjusted cost function is used to estimate the change in variable cost of production due to HACCP/RMP. It shows that this type of cost can make up a significant proportion of the total implementation cost. In Chapter 9, an export model is employed to analyse the impact of HACCP/RMP on meat industry export performance. The results show that the programme can bring a positive impact on exports. However, the magnitude of the impact depends on the status of existing food safety management before HACCP/RMP implementation. In Chapter 10, the Global Trade Analysis Project (GTAP) model is used to simulate the scenarios where market accesses to significant export destinations are lost when HACCP/RMP is not adopted. The estimated costs of these losses signal the potential benefits of HACCP/RMP. The research results show that HACCP/RMP can deliver a net benefit to the New Zealand meat industry. The thesis concludes with implications for policy design and future research directions. It signifies that the research findings, in addition to reporting an investigation into HACCP/RMP implementation process in New Zealand, provide an important foundation for future research on food safety and international competitiveness

Notes on the 1974 summer study program in geophysical fluid dynamics at the Woods Hole Oceanographic Institution

This year the central topic was the general circulation of the oceans. Some of the basic ideas used in wind-driven and thermohaline studies were presented in the introductory course of lectures and simple models that have guided our thinking in the development of the topic were discussed. As part of the introductory lectures Peter Niiler developed a model of the mixed layer, exploring the reasoning and the parameterization behind the theories of this important boundary region at the surface of the ocean. Dennis Moore gave a careful account of transient flows in equatorial regions and showed how dynamical conditions on the eastern and western boundaries are satisfied by a superposition of planetary, Kelvin and Yanai waves. Peter Rhines concluded the series with a discussion of topographically induced low frequency motions. At the request of the students Joseph B. Keller gave a lecture on "Solution of Partial Differential Equations by Ray Theory".National Science Foundatio

Three Sides to Every Story: Engaging an Autoethnographic Everyday Lived Experience of Race and Crime to Explore Legislative Policy-Practice Tackling the U.K. Gang

This thesis draws on entries from a personal journal to revisit selected publications from a body of work as part of an autoethnographic methodology to explored issues of race and crime and critically examine the implications of gang legislative policy-practice for urban black male youth. Through a reflexive process, findings and recommendations from selected policy research published between 2002 and 2011 is revisited and critically assessed against an everyday lived experience of race and crime. Findings from this research resists how criminological ideas are used to support an official view and approach to ‘problem youth’ and gangs in the U.K that developed after 2003. It analyses how young people and communities speak about local problems as a means of reconceptualising how youth behaviour is understood and develop alternative ways of tackling it