Tangent-point self-avoidance energies for curves

We study a two-point self-avoidance energy $E_q$ which is defined for all rectifiable curves in $R^n$ as the double integral along the curve of $1/r^q$. Here $r$ stands for the radius of the (smallest) circle that is tangent to the curve at one point and passes through another point on the curve, with obvious natural modifications of this definition in the exceptional, non-generic cases. It turns out that finiteness of $E_q(\gamma)$ for $q\ge 2$ guarantees that $\gamma$ has no self-intersections or triple junctions and therefore must be homeomorphic to the unit circle or to a closed interval. For $q>2$ the energy $E_q$ evaluated on curves in $R^3$ turns out to be a knot energy separating different knot types by infinite energy barriers and bounding the number of knot types below a given energy value. We also establish an explicit upper bound on the Hausdorff-distance of two curves in $R^3$ with finite $E_q$-energy that guarantees that these curves are ambient isotopic. This bound depends only on $q$ and the energy values of the curves. Moreover, for all $q$ that are larger than the critical exponent $2$, the arclength parametrization of $\gamma$ is of class $C^{1,1-2/q}$, with H\"{o}lder norm of the unit tangent depending only on $q$, the length of $\gamma$, and the local energy. The exponent $1-2/q$ is optimal.Comment: 23 pages, 1 figur

Evaluation or perfusion and thermal parameters of skiin tissue using cold provocation and thermographic measurements

Measurement of the perfusion coefficient and thermal parameters of skin tissue using dynamic thermography is presented in this paper. A novel approach based on cold provocation and thermal modelling of skin tissue is presented. The measurement was performed on a person’s forearm using a special cooling device equipped with the Peltier module. The proposed method first cools the skin, and then measures the changes of its temperature matching the measurement results with a heat transfer model to estimate the skin perfusion and other thermal parameters. In order to assess correctness of the proposed approach, the uncertainty analysis was performed

Trash on Arctic beach: Coastal pollution along Calypsostranda, Bellsund, Svalbard

Beach pollution is one of the most common hazards in present-day anthropogenic environments. Even in the remote Svalbard Archipelago, pollution impacts the beach system and can pose environmental threats. The significant increase in human activity observed in Svalbard over the last 20–30 years has resulted in a visible change in the amount of coastal pollution. A 5 km long transect of modern beach developed along Calypsostranda (Recherchefjorden, Bellsund) was surveyed in the summer of 2015 in order to characterize the beach pollution. During the survey 296 pieces of trash were found on beach surface. 82% of found trash was plastic, followed by glass (8%), and metal (5%). The comparison with previous pollution survey showed the significant increase of plastic waste in local beach environment. Similar problem has been recently recorded in other parts of Svalbard suggesting an urgent need for coastal pollution monitoring

Cross-correlation based movement correction method for biomedical dynamic infrared imaging

Abstract During dynamic infrared imaging there is a need of temperature measurement along time at a point or area. The paper shows the recent studies using dynamic infrared imaging in medicine and problems of proper data extraction which is the result of an object movement. The method of movement correction based on cross correlation calculated for dynamic thermal imaging is presented. The influence of movement correction on extracted data and point tracking precision is shown. The proposed method has been successfully applied for cold stress diagnosis during breast cancer screening

System Response Kernel Calculation for List-mode Reconstruction in Strip PET Detector

Reconstruction of the image in Positron Emission Tomographs (PET) requires the knowledge of the system response kernel which describes the contribution of each pixel (voxel) to each tube of response (TOR). This is especially important in list-mode reconstruction systems, where an efficient analytical approximation of such function is required. In this contribution, we present a derivation of the system response kernel for a novel 2D strip PET.Comment: 10 pages, 2 figures; Presented at Symposium on applied nuclear physics and innovative technologies, Cracow, 03-06 June 201

Arctic rock coast responses under a changing climate

It has been widely reported that Arctic sea ice has decreased in both extent and thickness, coupled with steadily rising mean annual temperatures. These trends have been particularly severe along the rock coast of southern Svalbard. Concerns have been raised over the potential for higher energy storms and longer ice-free open water seasons to increase the exposure of Arctic coasts, and consequently the concentration of infrastructure critical to Arctic community survival, to enhanced rates of erosion. Here we present and apply innovative remote sensing, monitoring and process analyses to assess the impact of recent coastal climatic changes. High resolution analyses demonstrate that the small scale (<0.001 m3) changes that are rarely considered quantitatively exhibit geomorphic responses distinct from those of larger, more readily detected cliff failures. We monitor temperature depth profiles in both the shore platform and the cliff face to show rock sensitivity over time to both global and local influences. The results demonstrate the efficacy of thermal processes on Arctic rock cliffs relative to platforms, and may hold implications for understanding strandflat development rates. New three-dimensional thermography (thermal mapping) and process zone characterisation has been used to spatially assess the sensitivity of Arctic rock coast responses to contemporary processes on deglaciating coasts. Through the spatial and temporal analyses of key geomorphic behaviour zones and comparison over a range of sites, the complex and changing interplay between subaerial weathering and cryogenic and intertidal processes has been highlighted. These data challenge long standing assumptions over the future of Arctic rock coasts and identify new, focused lines of enquiry on the decline in cryogenic processes and understanding the sensitivity of Arctic rock coasts to climatic changes

A novel method for calibration and monitoring of time synchronization of TOF-PET scanners by means of cosmic rays

All of the present methods for calibration and monitoring of TOF-PET scanner detectors utilize radioactive isotopes such as e.g. $^{22}$Na or $^{68}$Ge, which are placed or rotate inside the scanner. In this article we describe a novel method based on the cosmic rays application to the PET calibration and monitoring methods. The concept allows to overcome many of the drawbacks of the present methods and it is well suited for newly developed TOF-PET scanners with a large longitudinal field of view. The method enables also monitoring of the quality of the scintillator materials and in general allows for the continuous quality assurance of the PET detector performance.Comment: 10 pages, 7 figure

Application of Compressive Sensing Theory for the Reconstruction of Signals in Plastic Scintillators

Compressive Sensing theory says that it is possible to reconstruct a measured signal if an enough sparse representation of this signal exists in comparison to the number of random measurements. This theory was applied to reconstruct signals from measurements of plastic scintillators. Sparse representation of obtained signals was found using SVD transform.Comment: 7 pages, 3 figures; Presented at Symposium on applied nuclear physics and innovative technologies, Cracow, 03-06 June 201