On the high density behavior of Hamming codes with fixed minimum distance

We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n -> oo, d -> oo, d/n=delta. The problem is relevant for coding theory. We find a solution to the equations describing the liquid up to very large values of the density, but we show that this solution gives a negative entropy for the liquid phase when the density is large enough. We then conjecture that a phase transition towards a different phase might take place, and we discuss possible scenarios for this transition. Finally we discuss the relation between our results and known rigorous bounds on the maximal density of the system.Comment: 15 pages, 6 figure

Slow Dynamics in Glasses

We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a pure dynamical transition in some of these systems. We show how the results obtained for a random Hamiltonian may be also applied to a given Hamiltonian. These two results open the way to a better understanding of the glassy transition in real systems

Loop expansion around the Bethe-Peierls approximation for lattice models

We develop an effective field theory for lattice models, in which the only non-vanishing diagrams exactly reproduce the topology of the lattice. The Bethe-Peierls approximation appears naturally as the saddle point approximation. The corrections to the saddle-point result can be obtained systematically. We calculate the lowest loop corrections for magnetisation and correlation function.Comment: 8 page

A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model

In this paper we study the fluctuations of the probability distributions of the overlap in mean field spin glasses in the presence of a magnetic field on the De Almeida-Thouless line. We find that there is a large tail in the left part of the distribution that is dominated by the contributions of rare samples. Different techniques are used to examine the data and to stress on different aspects of the contribution of rare samples.Comment: 13 pages, 11 figure

Optimising the use of Materials for Construction MSMEs: Building a Comprehensive Framework for Decision-Making and Resource Allocation through an Analytic Hierarchy Process

The efficiency, governance, and compliance with environmental ideals in construction is made possible thanks to a decision support system that ensures Materials, Models, and Methods (3Ms) are adaptable and integrated. Recent advances in Information Technology (IT), for instance, facilitate the visualisation of sequences and production stages in construction. Yet, this falls short in giving compatibility among the 3Ms, their suitability and workability, and their financial and legislative viability. To this end, this manuscript rethinks the concept of productivity, and lays the foundation for a new decision support system that is simple, affordable, and portable enough to attract large enterprises and MSMEs. Ideally, an efficient construction project has good flow of workstreams, is least complex, cost minimised but with added value, timely and in symbiosis with natural health provisions of the ecosystem. A mixed methodology based on gathering data from document reviews, semi-structured interviews, and observations of selected construction MSMEs, will allow to carry out longitudinal research and then code, group, link and analyse the collected raw data through the Analytic Hierarchy Process (AHP) Multi Criteria Decision Making technique. This technique is chosen to develop overall priorities for ranking the alternatives, measure, and monetise the impacting factors to draw out the main impediments to achieve good levels of efficiency. The outputs of the AHP analysis feeds into the novel decision support system, the concepts of which are introduced in this contribution

Understanding the complexity of materials procurement in construction projects to build a conceptual framework influencing supply chain management of MSMEs

Purchasing is a fundamental step of materials procurement in the construction sector, and since materials can represent up to 70% of the project's construction costs, reducing wastage and improving productivity can have big benefits, both for the environment and the economy, especially for Micro, Small, and Medium-sized Enterprises (MSMEs). This manuscript will focus on the process of purchasing materials from these companies’ perspective, seeking to investigate the impact of effective materials management on site. In light of the acknowledged absence of system thinking for MSMEs, this research aims to build a new conceptual framework that illustrates the complexity of the materials purchasing process in construction and embodies the risks linked to materials, relationships, information, and cash flows. The conceptual framework aims to influence supply management in construction and is based on the recognition of five main levels, going from the specification of materials to data management and feedback. It is designed to illustrate the sequence, logical structure, and complexities of the purchasing process. Data from the literature, followed by on-site observations, feeds into the framework

Connecting scaling with short-range correlations

We reexamine several issues related to the physics of scaling in electron scattering from nuclei. A basic model is presented in which an assumed form for the momentum distribution having both long- and short-range contributions is incorporated in the single-particle Green function. From this one can obtain saturation of nuclear matter for an NN interaction with medium-range attraction and short-range repulsion, and can obtain the density-density polarization propagator and hence the electromagnetic response and scaling function. For the latter, the shape of the scaling function and how it approaches scaling as a function of momentum transfer are both explored.Comment: 24 pages, 15 figures. A reference has been corrected and update

Modified Thouless-Anderson-Palmer equations for the Sherrington-Kirkpatrick spin glass: Numerical solutions

For large but finite systems the static properties of the infinite ranged Sherrington-Kirkpatrick model are numerically investigated in the entire the glass regime. The approach is based on the modified Thouless-Anderson-Palmer equations in combination with a phenomenological relaxational dynamics used as a numerical tool. For all temperatures and all bond configurations stable and meta stable states are found. Following a discussion of the finite size effects, the static properties of the state of lowest free energy are presented in the presence of a homogeneous magnetic field for all temperatures below the spin glass temperature. Moreover some characteristic features of the meta stable states are presented. These states exist in finite temperature intervals and disappear via local saddle node bifurcations. Numerical evidence is found that the excess free energy of the meta stable states remains finite in the thermodynamic limit. This implies a the `multi-valley' structure of the free energy on a sub-extensive scale.Comment: Revtex 10 pages 13 figures included, submitted to Phys.Rev.B. Shortend and improved version with additional numerical dat

QCD Saturation Equations including Dipole-Dipole Correlation

We derive two coupled non-linear evolution equations corresponding to the truncation of the Balitsky infinite hierarchy of saturation equations after inclusion of dipole-dipole correlations, i.e. one step beyond the Balitsky-Kovchegov (BK) equation. We exhibit an exact solution for maximal correlation which still satisfies the same asymptotic geometric scaling as BK but with the S-matrix going to 1/2 (instead of 0) in the full saturation region.Comment: 4 pages, no figure. Comment, references and acknowledgment adde