Computations of Vector-Valued Siegel Modular Forms

We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.

Monogenic forms of hypertension

Arterial hypertension in childhood is less frequent as compared to adulthood but is more likely to be secondary to an underlying disorder. After ruling out more obvious causes, some patients still present with strongly suspected secondary hypertension of yet unknown etiology. A number of these children have hypertension due to single gene mutations inherited in an autosomal dominant or recessive fashion. The finding of abnormal potassium levels (low or high) in the presence of suppressed renin secretion, and metabolic alkalosis or acidosis should prompt consideration of these familial diseases. However, mild hypertension and the absence of electrolyte abnormalities do not exclude hereditary conditions. In monogenic hypertensive disorders, three distinct mechanisms leading to the common final pathway of increased sodium reabsorption, volume expansion, and low plasma renin activity are documented. The first mechanism relates to gain-of-function mutations with a subsequent hyperactivity of renal sodium and chloride reabsorption leading to plasma volume expansion (e.g., Liddle's syndrome, Gordon's syndrome). The second mechanism involves deficiencies of enzymes that regulate adrenal steroid hormone synthesis and deactivation (e.g., subtypes of congenital adrenal hyperplasia, apparent mineralocorticoid excess (AME)). The third mechanism is characterized by excessive aldosterone synthesis that escapes normal regulatory mechanisms and leading to volume-dependent hypertension in the presence of suppressed renin release (glucocorticoid remediable aldosteronism). Hormonal studies coupled with genetic testing can help in the early diagnosis of these disorders.

Preschool children's eye-movements during pictorial recall

We investigated eye-movements during preschool children’s pictorial recall of seen objects. Thirteen 3- to 4-year-old children completed a perceptual encoding and a pictorial recall task. First, they were exposed to 16 pictorial objects, which were positioned in one of four distinct areas on the computer screen. Subsequently, they had to recall these pictorial objects from memory in order to respond to specific questions about visual details. We found that children spent more time fixating the areas in which the pictorial objects were previously displayed.We conclude that as early as age 3–4 years old, children show specific eye-movements when they recall pictorial contents of previously seen objects.

The vascular-disrupting agent combretastatin impairs splitting and sprouting forms of physiological angiogenesis

Vascular-disrupting agents like combretastatin (CA-4-P), used to attenuate tumor blood flow in vivo, exert anti-mitotic and anti-migratory effects on endothelial cells in vitro. We tested whether anti-vascular or anti-angiogenic effects of CA-4-P are evident with physiological angiogenesis in skeletal muscle (EDL) due to sustained hyperemia (intraluminal splitting) and chronic muscle overload (abluminal sprouting).

Verifying Harder's Conjecture for Classical and Siegel Modular Forms

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form. Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.

Plato's Doctrine Of Forms: Modern Misunderstandings

Among the philosophical ideas of Plato, perhaps the most famous is his doctrine of forms. This doctrine has faced harsh criticism due, in large part, to the interpretations of this position by modern philosophers such as René Descartes, John Locke, and Immanuel Kant. For example, Plato has been interpreted as presenting a ¿two-worlds¿ approach to form and thing and as advancing a rationalist approach to epistemology. His forms have often been interpreted as ideas and as perfect copies of the things of the visible world. In this thesis, I argue that these, along with other interpretations of Plato presented by the moderns, are based on misunderstandings of Plato¿s overall philosophy. In so doing, I attempt to show that the doctrine of forms cannot be directly interpreted into the language of Cartesian, Lockean, and Kantian metaphysics and epistemology, and thus should not be prematurely dismissed because of these modern Platonic interpretations. By analyzing the Platonic dialogues beside the writings of the modern philosophers, I conclude that three of the most prominent modern philosophers, as representatives of their respective philosophical frameworks, have fundamentally misunderstood the nature of Plato¿s famous doctrine of forms. This could have significant implications for the future of metaphysics and epistemology by providing an interpretation of Plato which adds to, instead of contradicts, the developments of modern philosophy.

Zeros of Weakly Holomorphic Modular Forms of Levels 2 and 3

Let M-k(#)(N) be the space of weakly holomorphic modular forms for Gamma(0)(N) that are holomorphic at all cusps except possibly at infinity. We study a canonical basis for M-k(#)(2) and M-k(#)(3) and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.

The Institutional Framework around Successful Art Forms in Communist Czechoslovakia

Mr. Michl posed the question of how the institutional framework that the former communist regime set up around art production contributed to the success of Czech applied arts. In his theoretical review of the question he discussed the reasons for the lack of success of socialist industrial design as opposed to what he terms pre-industrial arts (such as art glass), and also for the current lack of interest into art institutions of the past regime. His findings in the second, historical section of his work were based largely on interviews with artists and other insiders, as an initial attempt to use questionnaires was unsuccessful. His original assumption that the institutional framework was imposed on artists against their will in fact proved mistaken, as it turned out to have been proposed by the artists themselves. The basic blueprint for communist art institutions was the Memorandum document published on behalf of Czechoslovak visual artists in March 1947, i.e. before the communist coup of February 1948. Thus, while the communist state provided a beneficial institutional framework for artists' work, it was the artists themselves who designed this framework. Mr. Michl concludes that the text of the memorandum appealed to the general left-wing and anti-market sentiments of the immediate post-war period and by this and by later working through the administrative channels of the new state, the artists succeeded in gaining all of their demands over the next 15 years. The one exception was artistic freedom, although this they came to enjoy, if only by default and for a short time, during the ideological thaw of the 1960s. Mr. Michl also examined the art-related legislative framework in detail and looked at the main features of key art institutions in the field, such as the Czech Fund for Visual Arts and the 1960s art export enterprise Art Centrum, which opened the doors into foreign markets for artists.

Ethnosciences - A step towards the integration of scientific and non-scientific forms of knowledge in the management of natural resources for the future

Integration of indigenous knowledge and ethnoscientific approaches into contemporary frameworks for conservation and sustainable management of natural resources will become increasingly important in policies on an international and national level. We set the scene on how this can be done by exploring the key conditions and dimensions of a dialogue between ‘ontologies’ and the roles, which ethnosciences could play in this process. First, the roles which ethnosciences in the context of sustainable development were analysed, placing emphasis on the implications arising when western sciences aspire to relate to indigenous forms of knowledge. Secondly, the contributions of ethnosciences to such an ‘inter-ontological dialogue’ were explored, based on an ethnoecological study of the encounter of sciences and indigenous knowledge in the Andes of Bolivia, and reviewed experiences from mangrove systems in Kenya, India and Sri Lanka, and from case-studies in other ecosystems world-wide.