Comparing persistence diagrams through complex vectors

The natural pseudo-distance of spaces endowed with filtering functions is precious for shape classification and retrieval; its optimal estimate coming from persistence diagrams is the bottleneck distance, which unfortunately suffers from combinatorial explosion. A possible algebraic representation of persistence diagrams is offered by complex polynomials; since far polynomials represent far persistence diagrams, a fast comparison of the coefficient vectors can reduce the size of the database to be classified by the bottleneck distance. This article explores experimentally three transformations from diagrams to polynomials and three distances between the complex vectors of coefficients.Comment: 11 pages, 4 figures, 2 table

Photonic Hall Effect in ferrofluids: Theory and Experiments

An experimental and theoretical study on the Photonic Hall Effect (PHE) in liquid and gelled samples of ferrofluids is presented. The ferrofluids are aqueous colloidal suspensions of Fe(_{2})CoO(_{4}) particles, which can be considered as anisotropic and absorbing Rayleigh scatterers. The PHE is found to be produced by the orientation of the magnetic moments of the particles, as is also the case for the Faraday effect. The dependence of the PHE with respect to the concentration of the scatterers, the magnetic field and the polarization of the incident light is measured in liquid and in gelled samples and is compared to a simple model based on the use of a scattering matrix and the single scattering approximation.Comment: 20 pages, 11 figures, submitte

Persistent topology for natural data analysis - A survey

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown

A high resolution wind&wave forecast model chain for the Mediterranean and Adriatic Sea

DHI (Danish Hydraulic Institute) and HyMOLab (Hydrodynamics and Met-Ocean Laboratory of the Dept. of Engineering and Architecture of the University of Trieste) have undertaken a joint applied research project with the aim to develop a state-of-art wind-wave forecast service at mid resolution for the Mediterranean Sea and at very high resolution for the Adriatic Sea. Weather routing, civil protection, coastal engineering, oil&gas and renewable energy fields, the planning of operations at sea, ... are just few among the multiple potential applications of this service. The meteorological model used in this study is WRF-ARW, one of the most widely used state-of-the-art open-source non-hydrostatic model. Global Forecast System (GFS) dataset provides the boundary and initial conditions. MIKE21-Spectral Waves is used as wave model with resolution ranging from 0.1 to 0.03 approximately. The use of a local area meteorological model guarantees higher levels of resolution and accuracy in an area such as the Mediterranean Sea where the complex orography and coastline induce short-time/small-space weather scales. The model chain runs daily (or twice a day on demand) on the High Performance Computing (HPC) infrastructure of HyMOLab. The validation of the entire model chain and specifically the forecast data obtained for the sea state is continuously updated according to new available data from satellites and buoys. Anyway, a major verification of the performance of the model chain against historic data (hindcast) is almost mandatory. For this aim, we performed a multi-decade test obtaining very good statistical parameters for the entire model chain performance. In this context the hindcast dataset developed by DHI and HyMOLab consists of 35 years of hourly data for the period 1979-2013, with the same model chain. The CFSR d093.0 hourly dataset with a spatial resolution of 0.5 provides the boundary and initial conditions. The atmospheric and wave models performance is checked against six satellite datasets, missions Envisat, ERS-2, Geosat FO, Jason-1, Jason-2, Topex-Poseidon, using a moving window technique procedure. Wave data close to coast are compared with available data from more than 20 buoys. The paper describes the validation procedure adopted for the hindcasted data. Furthermore the forecast service is described too, with specific emphasis to the very high resolution adopted in the Adriatic Sea

Persistence modules, shape description, and completeness

Persistence modules are algebraic constructs that can be used to describe the shape of an object starting from a geometric representation of it. As shape descriptors, persistence modules are not complete, that is they may not distinguish non-equivalent shapes. In this paper we show that one reason for this is that homomorphisms between persistence modules forget the geometric nature of the problem. Therefore we introduce geometric homomorphisms between persistence modules, and show that in some cases they perform better. A combinatorial structure, the $H_0$-tree, is shown to be an invariant for geometric isomorphism classes in the case of persistence modules obtained through the 0th persistent homology functor

Pheochromocytoma diagnosed during pregnancy: lessons learned from a series of ten patients

BACKGROUND: Pheochromocytoma (PHEO) in pregnancy is a life-threatening condition. Its management is challenging with regards to the timing and type of surgery. METHODS: A retrospective review of the management of ten patients diagnosed with pheochromocytoma during pregnancy was performed. Data were collected on the initial diagnostic workup, symptoms, treatment, and follow-up. RESULTS: PHEO was diagnosed in ten patients who were between the 10th and the 29th weeks of pregnancy. Six patients had none to mild symptoms, while four had complications of paroxysmal hypertension. Imaging investigations consisted of MRI, CT scan and ultrasounds. All had urinary metanephrines, measured as part of their workup. Three patients had MEN 2A, one VHL syndrome, one suspected SDH mutation. All patients were treated either with α/β blockers or calcium channel blockers to stabilize their clinical conditions. Seven patients underwent a laparoscopic adrenalectomy before delivery. Three out of these seven patients had a bilateral PHEO and underwent a unilateral adrenalectomy of the larger tumor during pregnancy, followed by a planned cesarean section and a subsequent contralateral adrenalectomy within a few months after delivery. Three patients had emergency surgery for maternal or fetal complications, with C-section followed by concomitant or delayed adrenalectomy. All newborns from the group of planned surgery were healthy, while two out three newborns within the emergency surgery group died shortly after delivery secondary to cardiac and pulmonary complications. CONCLUSIONS: PHEO in pregnancy is a rare condition. Maternal and fetal prognosis improved over the last decades, but still lethal consequences may be present if misdiagnosed or mistreated. A thorough multidisciplinary team approach should be tailored on an individual basis to better manage the pathology. Unilateral adrenalectomy in a pregnant patient with bilateral PHEO may be an option to avoid the risk of adrenal insufficiency after bilateral adrenalectomy