Evaluation of Incidence and Clinical Features of Antibody-Associated Autoimmune Encephalitis Mimicking Dementia

Background. Anti-neuronal autoimmunity may cause cognitive impairment that meets the criteria for dementia. Objective. Our aim was to detect the incidence and clinical features of autoimmune encephalitis imitating clinical findings of primary dementia disorders and to delineate the validity of anti-neuronal antibody screening in dementia patients. Methods. Fifty consecutive patients fulfilling the clinical criteria for primary dementia, 130 control patients, and 50 healthy controls were included. Their sera were investigated for several ion channel and glutamic acid decarboxylase (GAD) antibodies by a cell-based assay, radioimmunoassay, and ELISA, as required. Results. Sixteen patients satisfying dementia criteria had atypical findings or findings suggestive of autoimmune encephalitis. N-methyl-D-aspartate receptor (NMDAR) antibody was detected in a patient with dementia, Parkinsonism, and REM sleep behavior disorder (RBD) fulfilling the criteria for dementia with Lewy bodies (DLB). One control patient with bipolar disease displayed low anti-GAD antibody levels. Conclusions. Our study showed for the first time the presence of parkinsonism and RBD in an anti-NMDAR encephalitis patient mimicking DLB. Although autoimmune encephalitis patients may occasionally present with cognitive decline, most dementia patients do not exhibit anti-neuronal antibodies, suggesting that routine analysis of these antibodies in dementia is not mandatory, even though they display atypical features

The fluctuationlessness approach to the numerical integration of functions with a single variable by integrating Taylor expansion with explicit remainder term

In this paper we give the definition of the Fluctuationlessness concept and using this concept we make approximations to univariate functions by using Taylor expansion with the explicit remainder term. Then integrating this approximate expression we obtain a new quadrature-like numerical integration method. The results of numerical experiments are compared with the results obtained from the corresponding Taylor series expansion without the remainder term and errors are analyzed

Multi Nodalset Fluctuation Free Approximation in Taylor Remainder's Evaluation

The matrix representation of a univariate function is equal to the image of the independent variable matrix representation under that function at the no fluctuation limit. In recent studies this fact is extended in such a way that the matrix representation of a univariate function can be expressed as a linear combination of the same function with two different matrix arguments. This idea makes us think for more than two matrices whose images under the target function are combined to get better approximation. This paper focuses on the application of this approximation method on the integral representation of the remainder term of the Taylor series expansion. In this work the basic conceptual background is given. Some illustrative implementations will be given at the relevant conference presentation

Analitik olmayan ve/veya yüksek salınımlı fonksiyonların ağırlık fonksiyonu altındaki Taylor açılımlarının integral formundaki kalan terimine sendelenimsizlik teoremi uygulanmak suretiyle yaklaştırımlarının yapılması ve buna bağlı olarak nümerik integrasyon yöntemlerinin geliştirilmesi

ÖZETGerek yapısal olarak gerekse doğa bilimlerine temel teşkil etmesi bakımından yaklaşık değer hesaplamaları, fonksiyon yaklaştırımları ve kuadratürler matematikle uğraşanların kaçınılmaz ilgi alanlarından olagelmistir. Bu tezde bir yaklaştırım yöntemi olarak önemli bir yer tutan ve bir çok yeni yöntemin oluşturulmasına esas olan Taylor açılımı esas alınmış ve Taylor açılımının integral formunda yazılmış kalan terimi üzerinde çalışılarak yeni ve daha verimli yaklaştırımlar geliştirilmeye çalışılmıştır. Tezin birinci bölümünde konuya kısa bir giriş yapılmış, yaklaştırımların sınıflandırılmasına değinilmiş, bunlardan gerek interpolasyon gerekse eğri uydurma yoluyla yapılan yaklaştırımların temel felsefesine değinilmiştir. Tezin ikinci bölümünde yapılan çalısmalara esas teşkil eden Sendelenimsizlik Yaklaştırımı, Sendelenimsizlik Teoreminin Taylor açılımına uygulanması, Taylor açılımının sendelenimsizlik uygulamasına imkan verecek biçimde düzenlenmesi ve son olarak da Çok Değişkenliliği Yükseltilmis Çarpımsal Gösterilim (ÇYÇG) konuları ile ilgili yapılmış çalışmalara değinilerek bu çerçevede gerekli bilgiler verilmistir. Tezin üçüncü bölümünde yeni çalışmalar ve bulgular ele alınarak varılan sonuçlar üzerinde tartısılmıstır. Öncelikle operatör çarpımları ve ayrıştırımlarının sonlu ve sonsuz aralıktaki matris gösterilimlerinde sendelenim incelemeleri ve etkileri araştırılmıştır. Sonrasında oldukça önemli bir sadeleştirme sağlayan üç terimli özyineleme yoluyla matris gösterilimi üzerinde durulmuştur. Sonrasında trigonometrik taban fonksiyonları kullanılarak Taylor açılımının kalan terimine sendelenimsizlikuygulanmak suretiyle çok salınımlı fonksiyonlara yaklaştırım ele alınmıstır. Bunu takiben ÇYÇG’nin Cauchy integral formunda ifade edilmiş Taylor açılımına uygulanması üzerinde çalışılmıs ve yine sendelenimsizlik yaklaştırımının dairesel konturlar yoluyla kontur integrasyonu tarafından desteklenmesi üzerinde çalışılmıstır. Daha sonrasında ise önce kontur integrasyonu ve ÇYÜDÇG yoluyla ve devamında aynı işin Taylor serisi kalan terimi üzerinde nasıl sonuç vereceği sorgulanmıstır. Son olarak ise Başlangıç Değer problemlerinde temel yöntemlerden biri olan Euler metodu ve yüksek mertebeli Taylor metodları ele alınarak sendelenimsizlik yoluyla bunlarda iyileştirme sağlanmıştır. Tezin dördüncü ve son bölümünde ise varılan sonuçlar kısaca ele alınarak özetlenmistir.--------------------ABSTRACTApproximate value calculations, function approximations and quadratures, either because of structural reasons or because they constitute a basis for natural sciences, have always been a center of attention for mathematicians. In this thesis Taylorexpansion which has an important place in the approximation theory and which makes an important starting point for the construction of many new methods, is taken into consideration and some more productive methods are searched by workingon the remainder term expressed in integral form. In the first part of the thesis a short introduction is given, approximations areclassified and the basic philosophies of interpolation and curve fitting are mentioned. In the second part of the thesis Fluctuation Theorem, its application to Taylor expansion, the reorganisation of Taylor expansion to make room for this applicationand finally theorems and applications concerning EMPR are given in detail. In the third part new research and findings are given and discussed in details. It starts with fluctuation studies on the matrix representation of operator multiplicationand decomposition. Then the approximation to highly oscillatory functions by applying trigonometric basis functions to the remainder term of Taylor expansion. This is followed by the application of EMPR to the remainder term of Taylor expansionexpressed as a contour integration and the application of Fluctuationlessness Theorem on contour integration with circular contours. Then using TKEMPR on the remainder term of Taylor expansion expressed in contour integral form is takeninto consideration. Finally Euler and higher order Taylor methods for initial value problems are worked on and beter results are reached through fluctuationlessness approximation applied on them. In the fourth section some corollaries are liste

Numerical Integration Based on Nested Taylor Decomposition of Univariate Functions under Fluctuationlessness Approximation

The application of the Fluctuationlessness theorem to the remainder term of Taylor decomposition on which both sides are integrated has been already worked on. In this work the novelty brought to the previous work is to apply the Fluctuationlessness theorem to the remainder part which, itself also is decomposed in Taylor sense

Rotational angiography - technique and optimization of parameters for 3D-reconstruction of rotational cerebral angiograms

Evaluierung von Parametern für eine optimierte Visualisierung von 3D-Rotationsangiographien mit standardisierten Einstellungen. Bei einem Phantommodell mit einem künstlichen Gefäßbaum wurden mit unterschiedlichen Parametern (Rotationszeit, Dosis, BV-Größe, Volumen, Matrix) 24 Rotationen durchgeführt (Neurostar Plus, Siemens). Anschließend wurden diese an einer Workstation (3D-Virtuoso, Siemens) rekonstruiert und ausgewertet (36 Rekonstruktionen). Die erhaltenen Rekonstruktionen wurden hinsichtlich Detailerkennbarkeit, Oberflächenbeschaffenheit, Artefakte, Kontrast und Zeitaufwand ausgewertet. Der Vergleich zeigt eine höhere Qualität der Rekonstruktionen mit langen Rotationszeiten, höherer Dosis und großer Matrix. Der Zeitaufwand für die Volumenrekonstruktionen ist bei kurzen Rotationszeiten mit großem Volumen und kleiner Matrix am kürzesten. Der Zeitaufwand für die Nachbearbeitung ist bei langen Rotationszeiten bei kleinem Volumen und großer Matrix am geringsten. Schlußfolgernd sind für diagnostische prätherapeutische Untersuchungen eine Rotationszeit von 5s mit hoher Dosis und 70kV praktikabel. Für Darstellungen von größeren Gefäßausschnitten ist eine Matrix von 256x256, für die Darstellung selektierter Abschnitte (z.B. Aneurysmen) eine Matrix von 128x128 ausreichend. Für die Darstellung von vaskulären Strukturen in Nachbarschaft zu Knochen und zur Therapieplanung sollten lange Rotationszeiten (8s, 14s) wegen der höheren räumlichen Aussagekraft und der besseren Diskriminierung zum Knochen eingesetzt werden. Die Rotationsangiographie stellt einen wichtigen Fortschritt in der Diagnostik und endovaskulären Therapieplanung zerebraler Aneurysmen dar. Die diagnostische Aussagekraft ist höher als bei der konventionellen 2D-Angiographie unter Einsparung von Strahlendosis und Kontrastmittel bei entsprechend bewusstem Einsatz der Akquisitions- und Nachverarbeitungsparameter. Inwieweit eine Ausweitung der Anwendungsgebiete auf periphere, kardiale, pelvine und renale vaskuläre Indikationen, 3D-Cholangiographien und 3D-Dakryozystographien sowie eine Ergänzung oder sogar Ersatz zur 2-Ebenen-Radiographie erfolgen wird, bleibt abzuwarten. Mit raschem Fortschreiten der Hardware- und Softwareentwicklung ist die konsekutive Fortsetzung der 3D-Rotationsangiographie die 4D-Angiographie mit dynamischer Flussanalyse durch eine additive zeitliche Auflösung zur bestehenden räumlichen Auflösung der 3D-Rotationsangiographie.PURPOSE: To evaluate parameters that optimize the reconstruction of rotational angiograms for clinical applications. METHOD/MATERIALS: A phantom model with an artificial vessel system filled with pure contrast agent was used to create rotational angiograms with different parameter settings: rotation times of 5s, 8s or 14s; image intensifier of 33cm or 22cm, high or low radiation dose. The obtained angiograms were then reconstructed on a workstation (3D-Virtuoso Siemens) using another set of different parameters: matrix size 128x128, 256x256, 512x512; voxel size 0,05-1,0mm. Finally, the images were evaluated using the same threshold level with regard to resolution, artifacts, surface quality, contrast and reconstruction time. RESULTS: The visualized volumes of rotational angiograms with long rotational times (14s), higher dose and a matrix size of 512 x 512 were superior. The highest resolution and the smoothest surface was obtained using a high matrix (512x512), a small voxel size (0,05mm) and the 22cm image intensifier. A short rotational time, voxels larger than 0.5 mm and a small matrix (256 x 256) resulted in short reconstruction times. Long rotational times with small voxel sizes and a matrix of 512 x 512 shortened the postreconstruction rendering time. CONCLUSION: For pre-therapeutic, diagnostic purposes a rotation time of 5 sec. and a high dose is most useful. In order to demonstrate larger (longer) vessel segments a matrix of 256x256 should be deployed, for smaller sections (e.g. intracranial aneurysm) a matrix of 128x128 is sufficient. In order to demonstrate vessel segments in close vicinity to bony structures an for preoperative planning, long rotation times (8sec, 14sec.) should be used for better spatial understanding and facilitated distinction between bone and vessel. The rotational angiography is an important advancement for the diagnosis and planning of endovascular treatment of cerebral aneurysms. Its meaningfulness diagnostic value is higher than that of conventional 2D angiography with minimal use of radiation dose and contrast agent if acquisition and reconstruction parameters are set effectively. It remains to be seen, to what extent its application can be expanded to the demonstration of vessels that are in the peripheral, cardiac, pelvine and renal region, and also if it is suitable for 3D cholangiographies, 3D dacryocystographies and as a substitute for 2D radiography. With the continuous advancement of hardware and software development, the next step following 3D-rotational angiography will be 4D-angiography that has dynamic flow analysis using an additional temporal resolution in combination with the spatial resolution of the 3D-rotational angiography

Multivariate Numerical Integration via Fluctuationlessness Theorem: Case Study

In this work we come up with the statement of the Fluctuationlessness theorem recently conjectured and proven by M. Demiralp and its application to numerical integration of univariate functions by restructuring the Taylor expansion with explicit remainder term. The Fluctuationlessness theorem is stated. Following this step an orthonormal basis set is formed and the necessary formulae for calculating the coefficients of the three term recursion formula are constructed. Then for multivariate numerical integration, instead of dealing with a single formula for multiple remainder terms, a new approach that is already mentioned for bivariate functions is taken into consideration. At every step of a multivariate integration one variable is considered and the others are held constant. In such a way, this gives us the possibility to get rid of the complexity of calculations. The trivariate case is taken into account and its generalization is step by step explained. At the final stage implementations are done for some trivariate functions and the results are tabulated together with the implementation times

Fluctuation Studies on the Finite Interval Matrix Representations of Operator Products and Their Decompositions

In this work an experimental study on finite dimensional matrix approximations to products of various operators under a basis set orthonormalized on a finite interval is conducted. The elements of the matrices corresponding to the matrix representation of various operators, are calculated based on various term recursive relations. It is shown that higher the values of n, lower the relative marginal change will be obtained from the norm of the difference of the matrix representation of a product of two operators and the product of the matrix representations of the same operators

Separate Node Ascending Derivatives Expansion (SNADE) for Univariate Functions: Node Optimization via Partial Fluctuation Suppression

This work's content finds its root in the material given in the first three companion papers on the very newly proposed method called Separate Node Ascending Derivatives Expansion (SNADE) for Univariate Functions. Those three and the present companion papers are to appear in this proceedings. This work focuses on the determination of the nodal values which make the Euclidean distance between the target function and the SNADE truncation polynomial under consideration. The minimization procedure uses certain elements of the mathematical fluctuation theory. We obtain nonlinear equations after the minimization of the Euclidean distance mentioned above. The solutions of these equations can be numerically obtained unless the target function has a very specific structure. This is a so-called baby age theory and needs very specific care for robustness and sophistication. Here, the purpose is just formalism and conceptuality. Practicality has been left to future works

UNIVARIATE APPROXIMATE INTEGRATION VIA NESTED TAYLOR MULTIVARIATE FUNCTION DECOMPOSITION

This work is based on the idea of nesting one or more Taylor decompositions in the remainder term of a Taylor decomposition of a function. This provides us with a better approximation quality to the original function. In addition to this basic idea each side of the Taylor decomposition is integrated and the limits of integrations are arranged in such a way to obtain a universal [0, 1] interval without losing from the generality. Thus a univariate approximate integration technique is formed at the cost of getting multivariance in the remainder term. Moreover the remainder term expressed as an integral permits us to apply Fluctuationlessness theorem to it and obtain better results