A fully discrete framework for the adaptive solution of inverse problems

We investigate and contrast the differences between the discretize-then-differentiate and differentiate-then-discretize approaches to the numerical solution of parameter estimation problems. The former approach is attractive in practice due to the use of automatic differentiation for the generation of the dual and optimality equations in the first-order KKT system. The latter strategy is more versatile, in that it allows one to formulate efficient mesh-independent algorithms over suitably chosen function spaces. However, it is significantly more difficult to implement, since automatic code generation is no longer an option. The starting point is a classical elliptic inverse problem. An a priori error analysis for the discrete optimality equation shows consistency and stability are not inherited automatically from the primal discretization. Similar to the concept of dual consistency, We introduce the concept of optimality consistency. However, the convergence properties can be restored through suitable consistent modifications of the target functional. Numerical tests confirm the theoretical convergence order for the optimal solution. We then derive a posteriori error estimates for the infinite dimensional optimal solution error, through a suitably chosen error functional. This estimates are constructed using second order derivative information for the target functional. For computational efficiency, the Hessian is replaced by a low order BFGS approximation. The efficiency of the error estimator is confirmed by a numerical experiment with multigrid optimization

Space-time adaptive solution of inverse problems with the discrete adjoint method

Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in science and engineering require the solution of inverse problems where parameters for a given model are estimated based on available measurement information. In contrast to forward (regular) simulations, inverse problems have not extensively benefited from the adaptive solver technology. Previous research in inverse problems has focused mainly on the continuous approach to calculate sensitivities, and has typically employed fixed time and space meshes in the solution process. Inverse problem solvers that make exclusive use of uniform or static meshes avoid complications such as the differentiation of mesh motion equations, or inconsistencies in the sensitivity equations between subdomains with different refinement levels. However, this comes at the cost of low computational efficiency. More efficient computations are possible through judicious use of adaptive mesh refinement, adaptive time steps, and the discrete adjoint method. This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the intergrid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided for the discontinuous Galerkin (DG) method. The adjoint model development is considerably simplified by decoupling the adaptive mesh refinement mechanism from the forward model solver, and by selectively applying automatic differentiation on individual algorithms. In forward models discontinuous Galerkin discretizations can efficiently handle high orders of accuracy, $h/p$-refinement, and parallel computation. The analysis reveals that this approach, paired with Runge Kutta time stepping, is well suited for the adaptive solutions of inverse problems. The usefulness of discrete discontinuous Galerkin adjoints is illustrated on a two-dimensional adaptive data assimilation problem

Does economic convergence with the European Union mean more FDI flows to an economy? Analysis on 5 Central and Eastern Europe countries

In this paper we analyze the relationship between economic convergence with the European Union (EU) and foreign direct investment flows to 5 EU countries (Bulgaria, Czech Republic, Poland, Romania and Hungary) in the period 2001 – 2010, in order to determine if the process of economic convergence with the EU level influences FDI inflows in these economies. We use an economic convergence index, made up of real and structural convergence indexes, to assess the level of economic convergence. The study does not provide us with a clear response to our question. We report a tight relationship between convergence index and FDI inflows in Bulgaria, but quite divergent evolutions of the two variables in the case of Hungary.convergence index; foreign direct investments; European Union

SIE-SECURITY

The purpose of this paper is to present the application named SIE-Security providing web programmers with a tool that searches vulnerable links within their web site (i.e. a product page), attempting to perform an SQL Injection and finally, trying to find the admin login page and crack the MD5 hashed password (inappropriately called “crack” because we are actually using Rainbow tables). The application is structured on three tabs, each corresponding to the actions performed by the application and, if you take into consideration that this is a project in development, it could be considered an All-In-One database security testing utility.commerce, application, vulnerable, attack, decryption, security, testing

Laggards or performers? CEE vs. PIIGS countries’ catch-up with the Euro area in the last ten years

This research paper develops a comparative analysis between the new members states of the European Union (EU) – from Central and Eastern Europe (CEE) – and PIIGS countries (Portugal, Italy, Ireland, Greece and Spain) in terms of economic convergence with the Euro area, in the last decade. In addition, the paper emphasizes the changes in the economic convergence levels determined by the recent international crisis. In order to assess these evolutions, we compute an aggregated index of economic convergence, made up of real and structural convergence indexes. Then, by using cluster methodology, we highlight the similarities between the states in the two groups, CEE and PIIGS, from the economic convergence perspective. The comparative analysis reveals that in 2010 only Estonia, Hungary and Slovenia report resembling characteristics to PIIGS group. We also report an important progress of the countries analyzed, as regards real and structural convergence with the Euro area. However, after a decade of catching-up, Romania remains by far the most distanced country from the Euro area.real convergence, structural convergence, Central and Eastern Europe, PIIGS, clusterization

Second order adjoints for solving PDE-constrained optimization problems

Inverse problems are of utmost importance in many fields of science and engineering. In the variational approach inverse problems are formulated as PDE-constrained optimization problems, where the optimal estimate of the uncertain parameters is the minimizer of a certain cost functional subject to the constraints posed by the model equations. The numerical solution of such optimization problems requires the computation of derivatives of the model output with respect to model parameters. The first order derivatives of a cost functional (defined on the model output) with respect to a large number of model parameters can be calculated efficiently through first order adjoint sensitivity analysis. Second order adjoint models give second derivative information in the form of matrix-vector products between the Hessian of the cost functional and user defined vectors. Traditionally, the construction of second order derivatives for large scale models has been considered too costly. Consequently, data assimilation applications employ optimization algorithms that use only first order derivative information, like nonlinear conjugate gradients and quasi-Newton methods. In this paper we discuss the mathematical foundations of second order adjoint sensitivity analysis and show that it provides an efficient approach to obtain Hessian-vector products. We study the benefits of using of second order information in the numerical optimization process for data assimilation applications. The numerical studies are performed in a twin experiment setting with a two-dimensional shallow water model. Different scenarios are considered with different discretization approaches, observation sets, and noise levels. Optimization algorithms that employ second order derivatives are tested against widely used methods that require only first order derivatives. Conclusions are drawn regarding the potential benefits and the limitations of using high-order information in large scale data assimilation problems

Transbronchic lung biopsy

Este o metoda semiinvazivă de prelevare endobronșică, utilă pentru diagnosticul afectâțiunilor pulmonare, având sediul dincolo de zonele de vizualizare directă endoscopică (din periferia câmpurilor pulmonare). Constă în recoltarea de țesut pulmonar situat între două bronhii distale. Indicații dpdv radiologic - Opacități interstițiale – difuze sau localizate; Opacități periferice (dincolo de vizualizarea directă endoscopică). Indicații dpdv etiologic - Patologie tumorală malignă; Boli interstițiale pulmonare; Boli infecțioase pulmonare; Boli fungice. Contraindicații ale BPT sunt generale ale bronhoscopiei - cardiovasculare - cardiopatie ischemică, pulmonare; neurologice, sau contraindicații speciale - deficit de coagulare, plămân unic, HTA. Materiale necesare și dotări - nu este necesară o dotare specială față de dotarea standard a unei săli de bronhoscopie – fibrobronhoscop și pensa de biopsie. Este prudent să se efectueze în vecinatatea unei secții ATI sau chirurgie toracică (datorită posibilelor incidente). Tehnica - pensa de biopsie este impinsa închisă în periferie în bronhia corespunzătoare existând apoi două variante de continuare: 1. miscări “du-te vino” pe o distanță de cca. 1cm și se închide pensa; și 2. pacientul este pus să inspire adânc, pensa este deschisă și împinsă către distal cu apnee. Se recoltează 4 - 6 fragmente. Incidente – accidente: Durere; Sângerări 10 - 20% din cazuri; Pneumotorax - 5 -10 % din cazuri; Sincopa - f. rar. Pentru creșterea siguranței tehnice și a randamentului se utilizează urmărirea sub ecran fluoroscopic a BPT cu un echipament Rontgen complex, cu brat în C și monitor Tv. Crioterapia este folosită în bronhoscopie de mulți ani, iar utilizarea sa principală este tratamentul și excizia leziunilor endobronsice, în special în cazurile de obstrucție bronșică. Obținerea unui diagnostic histologic precis cu BPT convențională este limitată de dimensiunea redusă a fragmentului de biopsie. În cazul probelor de criobiopsie dimensiunile sunt duble, iar structurile sunt păstrate. BPT este soluția de elecție recomandată înainte de metodele chirurgicale de prelevare bioptică – toracoscopie sau toracotomie. BPT scade indicația manevrelor chirurgicale de prelevare cu 50 – 60%. Asocierea BPT – LBA duce la creșterea randamentului și rapiditatea diagnosticului NBP cu localizare periferică, chiar în faza precoce.It is a semi-invasive method of endobronchial sampling useful for the diagnosis of lung diseases based beyond the areas of direct endoscopic visualization (from the periphery of the lung fields). It consists in the collection of lung tissue located between two distal bronchi Radiological indications - Interstitial opacities - diffuse or localized; Peripheral opacities (beyond direct endoscopic visualization). Etiological indications - Malignant tumor pathology; Interstitial lung diseases; Infectious pulmonary diseases; Fungal diseases Contraindications of BPT are: general bronchoscopy - cardiovascular - ischemic cardiopathy, pulmonary; neurological. or special contraindications - coagulation deficiency, single lung, hypertension Necessary materials and equipment - no special equipment is required compared to the standard equipment of a bronchoscopy room - fibrobronchoscope and biopsy forceps. It is prudent to perform it in the vicinity of an ATI or thoracic surgery department (due to possible incidents). Technique - the biopsy forceps is pushed closed in the periphery into the corresponding bronchus, and there are then two options for continuation: 1. "go and come" movements over a distance of approx. 1cm and close the clamp; and 2. - the patient is made to inhale deeply, the clamp is opened and pushed distally with apnea. 4 - 6 fragments are collected. Incidents - accidents: Pain; Bleeding 10 - 20% of cases; Pneumothorax - 5-10% of cases; Syncope - rarely. In order to increase technical safety and efficiency, BPT monitoring under a fluoroscopic screen is used with a complex X-ray equipment, with C-arm and TV monitor Cryotherapy has been used in bronchoscopy for many years, and its main use is the treatment and excision of endobronchial lesions, especially in cases of bronchial obstruction. Obtaining a precise histological diagnosis with conventional BPT is limited by the small size of the biopsy fragment. In the case of cryobiopsy samples, the sizes are double, and the structures are preserved BPT is the solution of choice recommended before the surgical methods of biopsy sampling - thoracoscopy or thoracotomy. BPT reduces the indication of surgical sampling maneuvers by 50-60%. The association of BPT - LBA leads to an increase in the yield and speed of diagnosis of NBP with peripheral localization, even in the early phase