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We first introduce a notation for multiple (n ≥ 3) q-hypergeometric functions, where negative values of summation indices are allowed. Then we extend the notation for q-Horn functions to include tilde values corresponding to powers of 2. Karlssons reduction formulas are correspondingly q-deformed by using these notations. A formula for sums of inverse q-shifted factorials is used to find further formulas. The second part of the paper is devoted to convergence aspects for q-Horn functions and ’abnormal’ q-Horn functions. It turns out that some simple estimates for convergence can be made in the q-case, these are then supplemented with tables of numerical values. It is shown that the convergence regions are significantly increased in the q-case, and we compare with convergence regions in the ordinary case.

\"Over an amazing 80-year career as a writer, Ernst Jünger (1895-1998) fought in WWI, became a leading writer of \"soldierly nationalism\" in the 1920s, and produced possibly the only anti-Nazi novel during the Third Reich, On the Marble Cliffs. Jünger's seeming moral ambiguities have made him the subject of much controversy in his home country. He has long been the subject of a series of highly charged debates about his work, and his presentation with the Goethe Prize (Germany's highest literary honor) in 1982 revived an old charge that Jünger had helped pave the way for fascism. The French, however, regard him as Germany's greatest twentieth-century author. Jünger's war diaries are important historical documents. He rejoined the army in 1941 and was sent to Paris, where he was in a unique position to observe the German occupation of France from the point of view of an occupier, but one who was not blinded by Nazi ideology. The First Paris Diary begins in 1941, when Jünger began his war duties as a mail censor of the occupying regime, and ends in October of 1942, as he leaves Paris to travel to the Eastern Front. Through his high-level contacts, Jünger was aware of the situation on the Eastern front and the atrocities being committed there. He was also a member of a secret circle of aristocratic officers, led by Rommel, who opposed Hitler's conduct of the war and were conspiring to arrest him in France in 1944 and turn him over to allies in exchange for lenient armistice conditions. In addition to descriptions of his official duties, the diaries describe Jünger's wanderings through Parisian bookshops and cafes, his conversations at salons with French intellectuals, and his reflections on books and nature (he was a trained biologist)\"-- Provided by publisher.

The purpose of this article is to study how q-real numbers can be used for computations of convergence regions, q-integral representations of certain multiple triple q-Lauricella functions. The corresponding q-difference equations are also given without proof. In the process, we slightly improve Exton’s original formulas. We also survey the current attempts to generalize the above functions to triple and quadruple hypergeometric functions. Finally, we compute some q-analogues of transformation formulas for Horn functions.

Throughout Ernst Ludwig Kirchner's career, one unifying theme emerges - the search for what he saw as unadulterated and primal. This volume explores the far-reaching influence of non-western art on Kirchner's oeuvre and the importance of his life in Davos, Switzerland, where he found a temporary peace despite the impending threat of censorship by the Nazis. Throughout the chapters of this book are reproductions of Kirchner's paintings as well as his sculptures, woodcuts, sketches, drawings, textiles, carvings, and furniture. Archival material in the form of letters and diary entries offer an unprecedented look into the artist's creative process. This study of one of the most talented and influential German Expressionist painters draws compelling conclusions about the influence of the imaginary on his work.

The purpose of this article is to introduce a new complete multiple q-hypergeometric symbolic calculus, which leads to q-Euler integrals and a very similar canonical system of q-difference equations for multiple q-hypergeometric functions. q-analogues of recurrence formulas in Horns paper and Borngässers thesis lead to a more exact way to find these Frobenius solutions. To find the right formulas, the parameters in q-shifted factorials can be changed to negative integers, which give no extra q-factors. In proving these q-formulas, in the limit q→1 we obtain versions of the paper by Debiard and Gaveau for the solution of differential or q-difference equations. The paper is also a correction of some of the statements in the paper by Debiard and Gaveau, e.g., the Euler integrals and other solutions to differential equations for Appell functions, also without references to page numbers in the standard work of Appell and Kampé de Fériet. Sometimes the q-binomial theorem is used to simplify q-integral formulas. By the Horn method, we find another solution to the Appell Φ1 function partial differential equation, which was not mentioned in the thesis by Le Vavasseur 1893.

Quantifying the volume of the cerebellum and its lobes is of profound interest in various neurodegenerative and acquired diseases. Especially for the most common spinocerebellar ataxias (SCA), for which the first antisense oligonculeotide-base gene silencing trial has recently started, there is an urgent need for quantitative, sensitive imaging markers at pre-symptomatic stages for stratification and treatment assessment. This work introduces CerebNet, a fully automated, extensively validated, deep learning method for the lobular segmentation of the cerebellum, including the separation of gray and white matter. For training, validation, and testing, T1-weighted images from 30 participants were manually annotated into cerebellar lobules and vermal sub-segments, as well as cerebellar white matter. CerebNet combines FastSurferCNN, a UNet-based 2.5D segmentation network, with extensive data augmentation, e.g. realistic non-linear deformations to increase the anatomical variety, eliminating additional preprocessing steps, such as spatial normalization or bias field correction. CerebNet demonstrates a high accuracy (on average 0.87 Dice and 1.742mm Robust Hausdorff Distance across all structures) outperforming state-of-the-art approaches. Furthermore, it shows high test-retest reliability (average ICC >0.97 on OASIS and Kirby) as well as high sensitivity to disease effects, including the pre-ataxic stage of spinocerebellar ataxia type 3 (SCA3). CerebNet is compatible with FreeSurfer and FastSurfer and can analyze a 3D volume within seconds on a consumer GPU in an end-to-end fashion, thus providing an efficient and validated solution for assessing cerebellum sub-structure volumes. We make CerebNet available as source-code (https://github.com/Deep-MI/FastSurfer).

Socioeconomic status is associated with cognitive development, but the extent to which this reflects neuroanatomical differences is unclear. In 1,099 children and adolescents, family income was nonlinearly associated with brain surface area, and this association was greatest among disadvantaged children. Further, surface area mediated links between income and executive functioning. Socioeconomic disparities are associated with differences in cognitive development. The extent to which this translates to disparities in brain structure is unclear. We investigated relationships between socioeconomic factors and brain morphometry, independently of genetic ancestry, among a cohort of 1,099 typically developing individuals between 3 and 20 years of age. Income was logarithmically associated with brain surface area. Among children from lower income families, small differences in income were associated with relatively large differences in surface area, whereas, among children from higher income families, similar income increments were associated with smaller differences in surface area. These relationships were most prominent in regions supporting language, reading, executive functions and spatial skills; surface area mediated socioeconomic differences in certain neurocognitive abilities. These data imply that income relates most strongly to brain structure among the most disadvantaged children.

The B-lymphoid transcription factors PAX5 and IKZF1 restrict the supply of glucose and energy to B cells to levels that are not enough to fuel a driver-oncogene, thereby acting as tumour suppressors and sensitizing acute lymphoblastic leukaemia B cells to glucocorticoid therapy. Metabolic gatekeeper restricts B-cell malignancies This report examines how in B-cell malignancies, lymphoid transcriptional programs in early differentiation act as metabolic gatekeepers by restricting glucose transport, an important tumour-suppressor function that is subverted during the transformation to cancer. The findings provide a potential explanation for the selective efficacy of glucocorticoid therapy in B-cell malignancies, and suggest potential therapeutic avenues aimed at exploiting their metabolic vulnerabilities. B-lymphoid transcription factors, such as PAX5 and IKZF1, are critical for early B-cell development 1 , 2 , yet lesions of the genes encoding these transcription factors occur in over 80% of cases of pre-B-cell acute lymphoblastic leukaemia (ALL) 3 , 4 . The importance of these lesions in ALL has, until now, remained unclear. Here, by combining studies using chromatin immunoprecipitation with sequencing and RNA sequencing, we identify a novel B-lymphoid program for transcriptional repression of glucose and energy supply. Our metabolic analyses revealed that PAX5 and IKZF1 enforce a state of chronic energy deprivation, resulting in constitutive activation of the energy-stress sensor AMPK 5 , 6 , 7 . Dominant-negative mutants of PAX5 and IKZF1 , however, relieved this glucose and energy restriction. In a transgenic pre-B ALL mouse model, the heterozygous deletion of Pax5 increased glucose uptake and ATP levels by more than 25-fold. Reconstitution of PAX5 and IKZF1 in samples from patients with pre-B ALL restored a non-permissive state and induced energy crisis and cell death. A CRISPR/Cas9-based screen of PAX5 and IKZF1 transcriptional targets identified the products of NR3C1 (encoding the glucocorticoid receptor) 8 , TXNIP (encoding a glucose-feedback sensor) 9 and CNR2 (encoding a cannabinoid receptor) 10 as central effectors of B-lymphoid restriction of glucose and energy supply. Notably, transport-independent lipophilic methyl-conjugates of pyruvate and tricarboxylic acid cycle metabolites bypassed the gatekeeper function of PAX5 and IKZF1 and readily enabled leukaemic transformation. Conversely, pharmacological TXNIP and CNR2 agonists and a small-molecule AMPK inhibitor strongly synergized with glucocorticoids, identifying TXNIP, CNR2 and AMPK as potential therapeutic targets. Furthermore, our results provide a mechanistic explanation for the empirical finding that glucocorticoids are effective in the treatment of B-lymphoid but not myeloid malignancies. Thus, B-lymphoid transcription factors function as metabolic gatekeepers by limiting the amount of cellular ATP to levels that are insufficient for malignant transformation.

The Horn–Karlsson approach to find convergence regions is applied to find convergence regions for triple q-hypergeometric functions. It turns out that the convergence regions are significantly increased in the q-case; just as for q-Appell and q-Lauricella functions, additions are replaced by Ward q-additions. Mostly referring to Krishna Srivastava 1956, we give q-integral representations for these functions.