Option Valuation As an Expectation in The Complex Domain: The Black-Scholes Case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call.european call, fourier transform, generalized function, laplace transform, error function.

Geometrical Calibration of X-Ray Imaging With RGB Cameras for 3D Reconstruction

(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.We present a methodology to recover the geometrical calibration of conventional X-ray settings with the help of an ordinary video camera and visible fiducials that are present in the scene. After calibration, equivalent points of interest can be easily identifiable with the help of the epipolar geometry. The same procedure also allows the measurement of real anatomic lengths and angles and obtains accurate 3D locations from image points. Our approach completely eliminates the need for X-ray-opaque reference marks (and necessary supporting frames) which can sometimes be invasive for the patient, occlude the radiographic picture, and end up projected outside the imaging sensor area in oblique protocols. Two possible frameworks are envisioned: a spatially shifting X-ray anode around the patient/object and a moving patient that moves/rotates while the imaging system remains fixed. As a proof of concept, experiences with a device under test (DUT), an anthropomorphic phantom and a real brachytherapy session have been carried out. The results show that it is possible to identify common points with a proper level of accuracy and retrieve three-dimensional locations, lengths and shapes with a millimetric level of precision. The presented approach is simple and compatible with both current and legacy widespread diagnostic X-ray imaging deployments and it can represent a good and inexpensive alternative to other radiological modalities like CT.This work was carried out with the support of Information Storage S.L., University of Valencia (grant #CPI-15-170), CSD2007-00042 Consolider Ingenio CPAN (grant #CPAN13-TR01) as well as with the support of the Spanish Ministry of Industry, Energy and Tourism (Grant TSI-100101-2013-019).Albiol Colomer, F.; Corbi, A.; Albiol Colomer, A. (2016). Geometrical Calibration of X-Ray Imaging With RGB Cameras for 3D Reconstruction. IEEE Transactions on Medical Imaging. 35(8):1952-1961. https://doi.org/10.1109/TMI.2016.2540929S1952196135

Live Heap Space Analysis for Languages with Garbage Collection

The peak heap consumption of a program is the maximum size of the live data on the heap during the execution of the program, i.e., the minimum amount of heap space needed to run the program without exhausting the memory. It is well-known that garbage collection (GC) makes the problem of predicting the memory required to run a program difficult. This paper presents, the best of our knowledge, the first live heap space analysis for garbage-collected languages which infers accurate upper bounds on the peak heap usage of a program’s execution that are not restricted to any complexity class, i.e., we can infer exponential, logarithmic, polynomial, etc., bounds. Our analysis is developed for an (sequential) object-oriented bytecode language with a scoped-memory manager that reclaims unreachable memory when methods return. We also show how our analysis can accommodate other GC schemes which are closer to the ideal GC which collects objects as soon as they become unreachable. The practicality of our approach is experimentally evaluated on a prototype implementation.We demonstrate that it is fully automatic, reasonably accurate and efficient by inferring live heap space bounds for a standardized set of benchmarks, the JOlden suite

Evaluation of modern camera calibration techniques for conventional diagnostic X-ray imaging settings

[EN] We explore three different alternatives for obtaining intrinsic and extrinsic parameters in conventional diagnostic X-ray frameworks: the direct linear transform (DLT), the Zhang method, and the Tsai approach. We analyze and describe the computational, operational, and mathematical background differences for these algorithms when they are applied to ordinary radiograph acquisition. For our study, we developed an initial 3D calibration frame with tin cross-shaped fiducials at specific locations. The three studied methods enable the derivation of projection matrices from 3D to 2D point correlations. We propose a set of metrics to compare the efficiency of each technique. One of these metrics consists of the calculation of the detector pixel density, which can be also included as part of the quality control sequence in general X-ray settings. The results show a clear superiority of the DLT approach, both in accuracy and operational suitability. We paid special attention to the Zhang calibration method. Although this technique has been extensively implemented in the field of computer vision, it has rarely been tested in depth in common radiograph production scenarios. Zhang¿s approach can operate on much simpler and more affordable 2D calibration frames, which were also tested in our research. We experimentally confirm that even three or four plane-image correspondences achieve accurate focal lengths.This work was carried out with the support of Information Storage S. L., University of Valencia (Grant #CPI-15170), CSD2007-00042 Consolider Ingenio CPAN (Grant #CPAN13TR01), Spanish Ministry of Industry, Energy and Tourism (Grant #TSI-100101-2013-019), IFIC (Severo Ochoa Centre of Excellence #SEV-2014-0398), and Dr. Bellot's medical clinic.Albiol Colomer, F.; Corbi, A.; Albiol Colomer, A. (2017). Evaluation of modern camera calibration techniques for conventional diagnostic X-ray imaging settings. Radiological Physics and Technology. 10(1):68-81. https://doi.org/10.1007/s12194-016-0369-yS6881101Selby BP, Sakas G, Groch W-D, Stilla U. Patient positioning with X-ray detector self-calibration for image guided therapy. Aust Phys Eng Sci Med. 2011;34:391–400.Markelj P, Likar B. Registration of 3D and 2D medical images. PhD Thesis, University of Ljubljana; 2010.Miller T, Quintana E. Stereo X-ray system calibration for three-dimensional measurements. Springer, 2014. pp. 201–207.Rougé A, Picard C, Ponchut C, Trousset Y. Geometrical calibration of X-ray imaging chains for three-dimensional reconstruction. Comput Med Imaging Graph. 1993; 295–300.Trucco E, Verri A. Introductory techniques for 3-D computer vision. Prentice Hall Englewood Cliffs, 1998.Moura DC, Barbosa JG, Reis AM, Tavares JMRS. A flexible approach for the calibration of biplanar radiography of the spine on conventional radiological systems. Comput Model Eng Sci. 2010; 115–137.Schumann S, Thelen B, Ballestra S, Nolte L-P, Buchler P, Zheng G. X-ray image calibration and its application to clinical orthopedics. Med Eng Phys. 2014;36:968–74.Selby B, Sakas G, Walter S, Stilla U. Geometry calibration for X-ray equipment in radiation treatment devices. 2007. pp. 968–974.de Moura DC, Barbosa JMG, da Silva Tavares JMR, Reis A. Calibration of bi-planar radiography with minimal phantoms. In: Symposium on Informatics Engineering. 2008. pp. 1–10.Medioni G, Kang SB. Emerging topics in computer vision. Prentice Hall. 2004.Bushong S. Radiologic science for technologists: physics, biology, and protection. Elsevier. 2012.Rowlands JA. The physics of computed radiography. Phys Med Biol. 2002;47:123–66.Dobbins JT, Ergun DL, Rutz L, Hinshaw DA, Blume H, Clark DC. DQE(f) of four generations of computed radiography acquisition devices. Med Phys. 1995;22:1581–93.Hartley R. Self-calibration from multiple views with a rotating camera. In: European Conference on Computer Vision. 1994. pp. 471–478.Tsai R. A versatile camera calibration technique for high accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses. IEEE J Robot Autom. 1985;3(4):323–44.Hartley R, Zisserman A. Multiple view geometry in computer vision. Cambridge University Press. 2004.Zhang Z. A flexible new technique for camera calibration. IEEE Trans Pattern Anal Mach Intell. 2000;22:1330–4.Remondino F, Fraser C. Digital camera calibration methods: considerations and comparisons. Symposium Image Eng Vis Metrol. 2006;36:266–72.Zollner H, Sablatnig R. Comparison of methods for geometric camera calibration using planar calibration targets. In: Digital Imaging in Media and Education. 2004. pp. 237–244

A simple and efficient face detection algorithm for video database applications

The objective of this work is to provide a simple and yet efficient tool to detect human faces in video sequences. This information can be very useful for many applications such as video indexing and video browsing. In particular the paper focuses on the significant improvements made to our face detection algorithm presented by Albiol, Bouman and Delp (see IEEE Int. Conference on Image Processing, Kobe, Japan, 1999). Specifically, a novel approach to retrieve skin-like homogeneous regions is presented, which is later used to retrieve face images. Good results have been obtained for a large variety of video sequences.Peer ReviewedPostprint (published version

3D measurements in conventional X-ray imaging with RGB-D sensors

[EN] A method for deriving 3D internal information in conventional X-ray settings is presented. It is based on the combination of a pair of radiographs from a patient and it avoids the use of X-ray-opaque fiducials and external reference structures. To achieve this goal, we augment an ordinary X-ray device with a consumer RGB-D camera. The patient' s rotation around the craniocaudal axis is tracked relative to this camera thanks to the depth information provided and the application of a modern surface-mapping algorithm. The measured spatial information is then translated to the reference frame of the X-ray imaging system. By using the intrinsic parameters of the diagnostic equipment, epipolar geometry, and X-ray images of the patient at different angles, 3D internal positions can be obtained. Both the RGB-D and Xray instruments are first geometrically calibrated to find their joint spatial transformation. The proposed method is applied to three rotating phantoms. The first two consist of an anthropomorphic head and a torso, which are filled with spherical lead bearings at precise locations. The third one is made of simple foam and has metal needles of several known lengths embedded in it. The results show that it is possible to resolve anatomical positions and lengths with a millimetric level of precision. With the proposed approach, internal 3D reconstructed coordinates and distances can be provided to the physician. It also contributes to reducing the invasiveness of ordinary X-ray environments and can replace other types of clinical explorations that are mainly aimed at measuring or geometrically relating elements that are present inside the patient's body.(C) 2017 IPEM. Published by Elsevier Ltd. All rights reserved.The authors would like to thank the Radiation Oncology Department of the Physics Section at La Fe Hospital for the anthropomorphic phantom used in this work and Jose Manuel Monserrate (Instituto de Física Corpuscular) for his contribution in the development of the calibration frame shown in Fig. 3. This research has the support of Information Storage S.L., University of Valencia (grant CPI-15-170), CSD-2007-00042 Con solider Ingenio CPAN (grant CPAN-13TR01), IFIC (Severo Ochoa Centre of Excellence SEV20140398) as well as the support of the Spanish Ministry of Industry, Energy, and Tourism (grant TSI1001012013019).Albiol Colomer, F.; Corbi, A.; Albiol Colomer, A. (2017). 3D measurements in conventional X-ray imaging with RGB-D sensors. Medical Engineering & Physics. 42:73-79. https://doi.org/10.1016/j.medengphy.2017.01.024S73794

A portable geometry-independent tomographic system for gamma-ray, a next generation of nuclear waste characterization

One of the main activities of the nuclear industry is the characterisation of radioactive waste based on the detection of gamma radiation. Large volumes of radioactive waste are classified according to their average activity, but often the radioactivity exceeds the maximum allowed by regulators in specific parts of the bulk. In addition, the detection of the radiation is currently based on static detection systems where the geometry of the bulk is fixed and well known. Furthermore, these systems are not portable and depend on the transport of waste to the places where the detection systems are located. However, there are situations where the geometry varies and where moving waste is complex. This is especially true in compromised situations.We present a new model for nuclear waste management based on a portable and geometry-independent tomographic system for three-dimensional image reconstruction for gamma radiation detection. The system relies on a combination of a gamma radiation camera and a visible camera that allows to visualise radioactivity using augmented reality and artificial computer vision techniques. This novel tomographic system has the potential to be a disruptive innovation in the nuclear industry for nuclear waste management

Les competències emocionals i les dificultats quotidianes a l’adolescència. Existeix alguna correlació?

Postgrau en Educació Emocional i Benestar, Facultat de Pedagogia, Departament de Mètodes d’Investigació i Diagnòstic en Educació, Universitat de Barcelona, curs: 2014-2015, Tutor/Tutora: Núria Pérez EscodaEl present treball és una recerca sobre com les dificultats quotidianes en els adolescents i les competències emocionals es poden veure relacionades. L'autora defensa que trobar la possible relació entre ambdues variables pot obrir camí cap a una nova justificació i pot posar l'atenció en la importància que l'educació emocional té pels adolescents i la necessitat de potenciar-la als instituts i a altres institucions educatives. En el projecte es fa una anàlisis sobre el grau de competències emocionals i de les dificultats quotidianes per separat d'una mostra d'adolescents, per poder finalment establir les correlacions entre ambdues variables