dx is a negative type metric Here, dx(i, j) is the distance of the shortest i-j path using x(e) as the length of edge e. Last time we proved that this is indeed a relaxation of the problem; in that proof, we could have replaced the inequality with ∑ i,j dx(i, j) = 1, and this time it will be useful to do so. Last time, we also showed a connection between this relaxation and λ2(LF ) where LF is ...

In general I am interested in real world problems that can be attacked with mathematical tools. For example, I ask the following question: Is the secure mode of Internet browsers really secure? The underlying cryptographic standard is DES. Therefore, the natural interpretation of the problem is to ask whether there exists a polynomial time algorithm for breaking DES-like constructions. However,...

Previous beat contraction history, in which the performance of the left ventricle on any one beat is influenced by the mechanical events of the previous beat, may be important in the beat-to-beat regulation of left ventricular performance in the intact cardiovascular system. Prior studies of this phenomenon have established that mechanical events of the previous beat influence the function of t...

Low back pain (LBP) affects approximately 60-85% of adults during some point in their lives. Fortunately, for the large majority of individuals, symptoms are mild and transient, with 90% subsiding within 6 weeks. Chronic low back pain, defined as pain symptoms persisting beyond 3 months, affects an estimated 15-45% of the population. For the minority with intractable symptoms, the impact on qua...

Fourteen patients with longstanding lipodermatosclerosis of their lower legs, secondary to venous disease in 11, were treated for three months with stanozolol, a drug that enhances fibrinolytic activity. No other treatment was given and no change made in existing treatment. All the patients improved. Two were cured in three months, three were able to stop treatment in the next three to 11 month...

Background: A sensory trick, or geste antagoniste, is defined as a physical gesture (such as a touch on a particular body part) that mitigates the production of an involuntary movement. This phenomenon is most commonly described as a feature of dystonia. Here we present a case of successful modulation of tics using sensory tricks. Case Report: A case report and video are presented. The case and...