Recent results on self-dual configurations on the torus

We review the recent progress on our understanding of self-dual SU(N) Yang-Mills configurations on the torus.Comment: Latex 3 pages, 1 figure. Contribution to the Lat99 Proceeding

Monopole Constituents inside SU(n) Calorons

We present a simple result for the action density of the SU(n) charge one periodic instantons - or calorons - with arbitrary non-trivial Polyakov loop P_oo at spatial infinity. It is shown explicitly that there are n lumps inside the caloron, each of which represents a BPS monopole, their masses being related to the eigenvalues of P_oo. A suitable combination of the ADHM construction and the Nahm transformation is used to obtain this result.Comment: 8 pages, 1 figure (in three parts), late

Pixel classification for automated diabetic foot diagnosis

Worldwide, more than 180 million people suffer from diabetes mellitus. Approximately 50% of these patients will develop complications to their feet. Neuropathy, combined with poor blood supply and biomechanical changes results in a high risk for foot ulcers, which is a key problem in the diabetic foot; when these wounds become infected, this can ultimately result in lower extremity amputation, which has a serious effect on the quality of life of the patient, and causes a large economic burden on society.\ud \ud This was the motivation for a collaborate project (Vincent50) in which a photographic foot imaging device was developed. The system allows scanning of the foot soles on a daily basis which may lead to early recognition of foot problems. The goal of the present study is to determine whether pixel classification is a useful intermediate step towards automatically assessing the images of the foot soles for signs of diabetic foot disease. If successful, this approach will further relief health care professionals in assessing the foot and enable the placement of more devices in the future. \ud \ud The best agreement between automated recognition and expert diagnosis was achieved with a combination of RGB and derived features, proves that the RGB data is informative with respect to detection of ulcers. However, the automatic detection of pre-signs of ulcers and other anomalies needs more sophistication than pixel classification alone. Firstly, other physical features, such as hyperspectral data, infrared and/or textural features are expected to be more informative. Secondly, we expect to be able to boost the performance by using the context between neighboring pixels. Thirdly, an individualized and normalized classification process might help with the large variability in foot soles between individuals. \u

Small volume expansion of almost supersymmetric large N theories

We consider the small-volume dynamics of nonsupersymmetric orbifold and orientifold field theories defined on a three-torus, in a test of the claimed planar equivalence between these models and appropriate supersymmetric ``parent models". We study one-loop effective potentials over the moduli space of flat connections and find that planar equivalence is preserved for suitable averages over the moduli space. On the other hand, strong nonlinear effects produce local violations of planar equivalence at special points of moduli space. In the case of orbifold models, these effects show that the "twisted" sector dominates the low-energy dynamics.Comment: 20 pages, 3 figures; added references, minor change

New Instanton Solutions at Finite Temperature

We discuss the newly found exact instanton solutions at finite temperature with a non-trivial Polyakov loop at infinity. They can be described in terms of monopole constituents and we discuss in this context an old result due to Taubes how to make out of monopoles non-trivial topological charge configurations, with possible applications to abelian projection.Comment: 6 pages, 2 figures (in 5 parts), latex using espcrc1.sty, presented at "QCD at Finite Baryon Density", April 27-30, 1998, Bielefeld, German

Center-stabilized Yang-Mills theory: confinement and large NN volume independence

We examine a double trace deformation of SU(N) Yang-Mills theory which, for large $N$ and large volume, is equivalent to unmodified Yang-Mills theory up to $O(1/N^2)$ corrections. In contrast to the unmodified theory, large $N$ volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which would otherwise disrupt large $N$ volume independence in small volumes. For small values of $N$, if the theory is formulated on $\R^3 \times S^1$ with a sufficiently small compactification size $L$, then an analytic treatment of the non-perturbative dynamics of the deformed theory is possible. In this regime, we show that the deformed Yang-Mills theory has a mass gap and exhibits linear confinement. Increasing the circumference $L$ or number of colors $N$ decreases the separation of scales on which the analytic treatment relies. However, there are no order parameters which distinguish the small and large radius regimes. Consequently, for small $N$ the deformed theory provides a novel example of a locally four-dimensional pure gauge theory in which one has analytic control over confinement, while for large $N$ it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories.Comment: 29 pages, expanded discussion of multiple compactified dimension