A Walsh-Fourier approach to the circulant Hadamard conjecture

We describe an approach to the circulant Hadamard conjecture based on Walsh-Fourier analysis. We show that the existence of a circulant Hadamard matrix of order $n$ is equivalent to the existence of a non-trivial solution of a certain homogenous linear system of equations. Based on this system, a possible way of proving the conjecture is proposed.Comment: 8 page

Attacks by “Anonymous” WikiLeaks Proponents not Anonymous

On November 28, 2010, the world started watching the whistle blower website WikiLeaks to begin publishing part of the 250,000 US Embassy Diplomatic cables. These confidential cables provide an insight on U.S. international affairs from 274 different embassies, covering topics such as analysis of host countries and leaders and even requests for spying out United Nations leaders.\ud The release of these cables has caused reactions not only in the real world, but also on the Internet. In fact, a cyberwar started just before the initial release. Wikileaks has reported that their servers were experiencing distributed denial-of-service attacks (DDoS). A DDoS attack consists of many computers trying to overload a server by firing a high number of requests, leading ultimately to service disruption. In this case, the goal was to avoid the release of the embassy cables.\ud After the initial cable release, several companies started severed ties with WikiLeaks. One of the first was Amazon.com, that removed the WikiLeaks web- site from their servers. Next, EveryDNS, a company in which the domain wikileaks.org was registered, dropped the domain entries from its servers. On December 4th, PayPal cancelled the account that WikiLeaks was using to receive on-line donations. On the 6th, Swiss bank PostFinance froze the WikiLeaks assets and Mastercard stopped receiving payments to the WikiLeaks account. Visa followed Mastercard on December 7th.\ud These reactions caused a group of Internet activists (or “hacktivists”) named Anonymous to start a retaliation against PostFinance, PayPay, MasterCard, Visa, Moneybrookers.com and Amazon.com, named “Operation Payback”. The retaliation was performed as DDoS attacks to the websites of those companies, disrupting their activities (except for the case of Amazon.com) for different periods of time.\ud The Anonymous group consists of volunteers that use a stress testing tool to perform the attacks. This tool, named LOIC (Low Orbit Ion Cannon), can be found both as a desktop application and as a Web page.\ud Even though the group behind the attacks claims to be anonymous, the tools they provide do not offer any security services, such as anonymization. As a consequence, a hacktivist that volunteers to take part in such attacks, can be traced back easily. This is the case for both current versions of the LOIC tool. Therefore, the goal of this report is to present an analysis of privacy issues in the context of these attacks, and raise awareness on the risks of taking part in them

Photon Splitting in a Strong Magnetic Field: Recalculation and Comparison With Previous Calculations

We recalculate the amplitude for photon splitting in a strong magnetic field below the pair production threshold, using the worldline path integral variant of the Bern--Kosower formalism. Numerical comparison (using programs that we have made available for public access on the Internet) shows that the results of the recalculation are identical to the earlier calculations of Adler and later of Stoneham, and to the recent recalculation by Baier, Milstein, and Shaisultanov.Comment: Revtex, 9 pages, no figure

Coloring translates and homothets of a convex body

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in \RR^n.Comment: 11 pages, 2 figure

An easy way to solve two-loop vertex integrals

Negative dimensional integration is a step further dimensional regularization ideas. In this approach, based on the principle of analytic continuation, Feynman integrals are polynomial ones and for this reason very simple to handle, contrary to the usual parametric ones. The result of the integral worked out in $D<0$ must be analytically continued again --- of course --- to real physical world, $D>0$, and this step presents no difficulties. We consider four two-loop three-point vertex diagrams with arbitrary exponents of propagators and dimension. These original results give the correct well-known particular cases where the exponents of propagators are equal to unity.Comment: 13 pages, LaTeX, 4 figures, misprints correcte

Neutron Scattering Study of Crystal Field Energy Levels and Field Dependence of the Magnetic Order in Superconducting HoNi2B2C

Elastic and inelastic neutron scattering measurements have been carried out to investigate the magnetic properties of superconducting (Tc~8K) HoNi2B2C. The inelastic measurements reveal that the lowest two crystal field transitions out of the ground state occurat 11.28(3) and 16.00(2) meV, while the transition of 4.70(9) meV between these two levels is observed at elevated temperatures. The temperature dependence of the intensities of these transitions is consistent with both the ground state and these higher levels being magnetic doublets. The system becomes magnetically long range ordered below 8K, and since this ordering energy kTN ~ 0.69meV << 11.28meV the magnetic properties in the ordered phase are dominated by the ground-state spin dynamics only. The low temperature structure, which coexists with superconductivity, consists of ferromagnetic sheets of Ho{3+ moments in the a-b plane, with the sheets coupled antiferromagnetically along the c-axis. The magnetic state that initially forms on cooling, however, is dominated by an incommensurate spiral antiferromagnetic state along the c-axis, with wave vector qc ~0.054 A-1, in which these ferromagnetic sheets are canted from their low temperature antiparallel configuration by ~17 deg. The intensity for this spiral state reaches a maximum near the reentrant superconducting transition at ~5K; the spiral state then collapses at lower temperature in favor of the commensurate antiferromagnetic state. We have investigated the field dependence of the magnetic order at and above this reentrant superconducting transition. Initially the field rotates the powder particles to align the a-b plane along the field direction, demonstrating that the moments strongly prefer to lie within this plane due to the crystal field anisotropy. Upon subsequently increasing the field atComment: RevTex, 7 pages, 11 figures (available upon request); Physica

The cultivation of adaptability in Japan

This paper explores the adaptability of buildings in Japan from the perspective of three distinct practice typologies: large general contractors, large architectural design firms, and small design ateliers. The paper illustrates the cultivation of adaptability in Japan revealing a maturing of concepts into current innovations, trends, priorities, and obstacles in relation to adaptability in design. The paper contextualizes the situation by reviewing the evolution of residential development in support of building adaptability, and the ways in which these policies and concepts have shaped practice and transcended residential design. This evolution is then explored through non-residential case studies undertaken by the three practice types, and supported through a review of critical themes emerging from the interviews. The importance of particular physical characteristics are examined including storey height, location of services, planning modules and structural spacing/spans. The interviews expose the critical relationship between adaptability and different social variables - the state of the market, the role of planning regulations and other legal frameworks; as well as, the misconceptions and variations in the perceptions on the role and meaning adaptability has in practice. The paper is concluded by revealing the lessons learnt, including the unfolding of dependencies outside the ‘black box’ of adaptability (e.g. practice culture, material and, stakeholder mindsets) and the requirement of effective communication of concepts to allow an informed conversation between professionals and with clients and users. Like many other philosophical design concepts in complex processes, adaptability benefits from a mutual understanding, good relationships, communication, integration, and shared goals amongst team members

Defect-induced condensation and central peak at elastic phase transitions

Static and dynamical properties of elastic phase transitions under the influence of short--range defects, which locally increase the transition temperature, are investigated. Our approach is based on a Ginzburg--Landau theory for three--dimensional crystals with one--, two-- or three--dimensional soft sectors, respectively. Systems with a finite concentration $n_{\rm D}$ of quenched, randomly placed defects display a phase transition at a temperature $T_c(n_{\rm D})$, which can be considerably above the transition temperature $T_c^0$ of the pure system. The phonon correlation function is calculated in single--site approximation. For $T>T_c(n_{\rm D})$ a dynamical central peak appears; upon approaching $T_c(n_{\rm D})$, its height diverges and its width vanishes. Using an appropriate self--consistent method, we calculate the spatially inhomogeneous order parameter, the free energy and the specific heat, as well as the dynamical correlation function in the ordered phase. The dynamical central peak disappears again as the temperatur is lowered below $T_c(n_{\rm D})$. The inhomogeneous order parameter causes a static central peak in the scattering cross section, with a finite $k$ width depending on the orientation of the external wave vector ${\bf k}$ relative to the soft sector. The jump in the specific heat at the transition temperatur of the pure system is smeared out by the influence of the defects, leading to a distinct maximum instead. In addition, there emerges a tiny discontinuity of the specific heat at $T_c(n_{\rm D})$. We also discuss the range of validity of the mean--field approach, and provide a more realistic estimate for the transition temperature.Comment: 11 pages, 11 ps-figures, to appear in PR