The Brownian Web: Characterization and Convergence

The Brownian Web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in ${\mathbb R}\times{\mathbb R}$. We extend the earlier work of Arratia and of T\'oth and Werner by providing characterization and convergence results for the BW distribution, including convergence of the system of all coalescing random walkssktop/brownian web/finale/arXiv submits/bweb.tex to the BW under diffusive space-time scaling. We also provide characterization and convergence results for the Double Brownian Web, which combines the BW with its dual process of coalescing Brownian motions moving backwards in time, with forward and backward paths ``reflecting'' off each other. For the BW, deterministic space-time points are almost surely of ``type'' $(0,1)$ -- {\em zero} paths into the point from the past and exactly {\em one} path out of the point to the future; we determine the Hausdorff dimension for all types that actually occur: dimension 2 for type $(0,1)$, 3/2 for $(1,1)$ and $(0,2)$, 1 for $(1,2)$, and 0 for $(2,1)$ and $(0,3)$.Comment: 52 pages with 4 figure

Metasone furoate induced acneiform eruption

Acne is the chronic inflammatory disease of the pilosebaceous unit, characterized by the formation of comedones, erythematous papules and pustules. Steroid induced acne is an acneiform eruption characterized by sudden onset of follicular papules and pustules shortly after starting topical or oral corticosteroid. Here, we report a case of a 25-year-old female patient who presented herself to the Dermatology out-patient department with the complaints of acne all over the face after the application of mometasone furoate ointment

Randomness amplification against no-signaling adversaries using two devices

Recently, a physically realistic protocol amplifying the randomness of Santha-Vazirani sources producing cryptographically secure random bits was proposed; however for reasons of practical relevance, the crucial question remained open whether this can be accomplished under the minimal conditions necessary for the task. Namely, is it possible to achieve randomness amplification using only two no-signaling components and in a situation where the violation of a Bell inequality only guarantees that some outcomes of the device for specific inputs exhibit randomness? Here, we solve this question and present a device-independent protocol for randomness amplification of Santha-Vazirani sources using a device consisting of two non-signaling components. We show that the protocol can amplify any such source that is not fully deterministic into a fully random source while tolerating a constant noise rate and prove the composable security of the protocol against general no-signaling adversaries. Our main innovation is the proof that even the partial randomness certified by the two-party Bell test (a single input-output pair ($\textbf{u}^*, \textbf{x}^*$) for which the conditional probability $P(\textbf{x}^* | \textbf{u}^*)$ is bounded away from $1$ for all no-signaling strategies that optimally violate the Bell inequality) can be used for amplification. We introduce the methodology of a partial tomographic procedure on the empirical statistics obtained in the Bell test that ensures that the outputs constitute a linear min-entropy source of randomness. As a technical novelty that may be of independent interest, we prove that the Santha-Vazirani source satisfies an exponential concentration property given by a recently discovered generalized Chernoff bound.Comment: 15 pages, 3 figure

Ciprofloxacin induced fixed drug eruption

Fixed drug eruption (FDE) is a clinical entity occurring in the same site or sites each time the drug is administered. Acute lesions appear as sharply marginated erythematous plaques, which are usually found on lips, genitalia, abdomen, and legs. The eruptions usually occur within hours of administration of the offending agent and resolves spontaneously without scarring after few weeks of onset. Most common drugs causing FDE are sulfonamides, tetracyclines, salicylates, barbiturates, doxycycline, fluconazole, clarithromycin, etc. Ciprofloxacin, a widely used fluoroquinolone antimicrobial, induces cutaneous adverse drug reactions (ADRs) in about 1-2% of treated patients. Urticaria, angioedema, maculopapular exanthems, and photosensitivity are the most frequently documented cutaneous adverse reactions. In this case report, the patient soon after taking ciprofloxacin tablets, developed itching in the lips, palms and in scrotal region. On continuing the treatment, the next day he developed fluid filled lesions over palm, knuckle, and hyperpigmentation. He gives a history of severe itching and rashes in scrotal region. He gives a history of similar complaints in the previous month after taking ciprofloxacin medication. There was no history of intake of any other medication. On examination, bullous lesions and pustules in finger webs, hyperpigmentation on knuckles, and scrotal erosions were seen. In the present case report, the patient presented with FDE immediately after oral administration of ciprofloxacin and got completely cured after stopping the drug and taking adequate treatment. According to the Naranjo’s ADR probability scale (score=8), this ADR is categorized as a “probable” reaction to the drug