Understanding Higher-Order Interactions in Information Space.

Methods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. One such setting is a finite collection of discrete probability distributions embedded in the probability simplex measured with the relative entropy (Kullback-Leibler divergence). More generally, one can work with a Bregman divergence parameterized by a different notion of entropy. While theoretical algorithms exist for this setup, there is a paucity of implementations for exploring and comparing geometric-topological properties of various information spaces. The interest of this work is therefore twofold. First, we propose the first robust algorithms and software for geometric and topological data analysis in information space. Perhaps surprisingly, despite working with Bregman divergences, our design reuses robust libraries for the Euclidean case. Second, using the new software, we take the first steps towards understanding the geometric-topological structure of these spaces. In particular, we compare them with the more familiar spaces equipped with the Euclidean and Fisher metrics.

[A 27-year-old patient with recurrent Fever]. / 27-jähriger Patient mit rezidivierendem Fieber.

BACKGROUND: In spite of a decreasing incidence of tuberculosis in highly industrialized countries, an obvious increase of the disease is observed worldwide. In times of progressing international migration, the early detection of tuberculosis is also becoming important in Germany. The diagnosis, however, is often impaired by unspecific symptomatology and ambiguous imaging results. CASE REPORT: A 27-year-old patient from Iraq presented with unclear recurring and antibiotic-resistant fever and inconspicuous thoracic X-ray. Only by thoracic computed tomography, markedly necrotizing mediastinal lymph nodes could be detected. Following lymph node biopsy and histologic investigation, the diagnosis of mediastinal lymph node tuberculosis could be ascertained. Test-adjusted antituberculotic combination treatment resulted in a normalization of body temperature and cessation of complaints. Starting from the case report presented, the importance of various investigative methods for the quick and secure diagnosis of tuberculosis and subsequent therapy are discussed. CONCLUSION: Unclear febrile disease even in young patients with an inconspicuous conventional thoracic X-ray may be caused by tuberculosis. In this situation, early extension of imaging diagnostics appears to be advantageous.

Cervical metastases of microcystic adnexal carcinoma in an otherwise healthy woman.

Microcystic adnexal carcinoma is a rare cutaneous neoplasm characterized by slow but locally aggressive growth, which normally does not lead to systemic metastasis. Frequent local recurrences are reported, which are most likely due to insufficient operative technique. We present the fourth case of cervical ipsilateral metastatic microcystic adnexal carcinoma in an otherwise healthy woman. The patient presented with a previously diagnosed but not completely resected microcystic adnexal carcinoma in the area of the right posterior scalp and two palpable ipsilateral lymph nodes. The tumor was resected using intraoperative snap frozen histological evaluation of the resection borders. In the same procedure two lymph nodes were resected from the right neck. The lymph nodes were histologically assessed and showed infiltration by small strains of tumor cells. After exclusion of a second primary tumor, e.g., mammary carcinoma, as the cause for cervical lymph node metastases, we performed a modified radical neck dissection with resection of the sternocleidomastoid muscle and the accessory nerve, which was histologically proven to be perineurally infiltrated by tumor cells. In this second procedure the histological evaluation of the specimen showed no sign of remaining tumor infiltration. After exclusion of distant metastasis the patient was irradiated with 60 Gy. The patient is well 1 year after the initial treatment without signs of recurrence.