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.

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.

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.

Enzymatic formation of modular cell-instructive fibrin analogs for tissue engineering

The molecular engineering of cell-instructive artificial extracellular matrices is a powerful means to control cell behavior and enable complex processes of tissue formation and regeneration. This work reports on a novel method to produce such smart biomaterials by recapitulating the crosslinking chemistry and the biomolecular characteristics of the biopolymer fibrin in a synthetic analog. We use activated coagulation transglutaminase factor XIIIa for site-specific coupling of cell adhesion ligands and engineered growth factor proteins to multiarm poly(ethylene glycol) macromers that simultaneously form proteolytically sensitive hydrogel networks in the same enzyme-catalyzed reaction. Growth factor proteins are quantitatively incorporated and released upon cell-derived proteolytic degradation of the gels. Primary stromal cells can invade and proteolytically remodel these networks both in an in vitro and in vivo setting. The synthetic ease and potential to engineer their physicochemical and bioactive characteristics makes these hybrid networks true alternatives for fibrin as provisional drug delivery platforms in tissue engineering.

Language Boxes: Bending the Host Language with Modular Language Changes

As domain-specific modeling begins to attract widespread acceptance, pressure is increasing for the development of new domain-specific languages. Unfortunately these DSLs typically conflict with the grammar of the host language, making it difficult to compose hybrid code except at the level of strings; few mechanisms (if any) exist to control the scope of usage of multiple DSLs; and, most seriously, existing host language tools are typically unaware of the DSL extensions, thus hampering the development process. Language boxes address these issues by offering a simple, modular mechanism to encapsulate (i) compositional changes to the host language, (ii) transformations to address various concerns such as compilation and highlighting, and (iii) scoping rules to control visibility of language extensions. We describe the design and implementation of language boxes, and show with the help of several examples how modular extensions can be introduced to a host language and environment.

A Gag peptide encompassing B- and T-cell epitopes of the caprine arthritis encephalitis virus functions as modular carrier peptide

Short synthetic peptides are important tools in biomedical research permitting to generate hapten specific polyclonal sera for analytical purposes or functional studies. In this paper we provide proof of principle that a peptide located in a highly conserved portion of the Gag protein of the caprine arthritis encephalitis virus and carrying an immunodominant T helper cell epitope functions as an efficient carrier peptide, mediating a strong antibody response to a peptidic hapten encompassing a well-characterized B cell epitope of Env. The carrier and hapten peptides were collinearly synthesized permutating their molecular arrangement. While the antibody response to the hapten was similar for both constructs, the antibody response to a B cell epitope overlapping the T helper cell epitope of the Gag carrier peptide was considerably different. This permits a modular use of the carrier peptide to generate antibody directed exclusively to the hapten peptide or a strong humoral response to both carrier- and hapten-peptide. Finally, we have mapped the epitopes involved in this polarized antibody response and discussed the potential immunological implications.

A modular LHC built on the DNA three-way junction

A light-harvesting complex composed of a p-stacked multichromophoric array in a DNA three-way junction is described. The modular design allows for a ready exchange of non-covalently attached energy acceptors

Modular organization of the cortical connections linking visual areas V1, V2 and V4 in Macaque monkeys

The macaque cortical visual system is hierarchically organized into two streams, the ventral stream for recognizing objects and the dorsal stream for analyzing spatial relationships. The ventral stream extends from striate cortex or area V1 to inferior temporal cortex (IT) through extra-striate areas V2 and V4. Between V1 and V2, the ventral stream consists of two roughly parallel sub-streams, one extending from the cytochrome oxidase (CO) rich blobs in V1 to the CO rich thin stripes in V2, the other extending from the interblobs in V1 to interstripes, in V2. The blob-dominated sub-stream is thought to analyze the surface features such as color, whereas the interblob-dominated one is thought to analyze the contour features such as shape. ^ In the current study, the organization of cortical pathways linking V2 thin stripe and interstripe compartments with area V4 was investigated using a combination of physiological and anatomical techniques. Different compartments of V2 were first characterized, in vivo, using optical recording of intrinsic cortical signals. These functionally derived maps of V2 stripe compartments were then used to guide iontophoretic injections of multiple, distinguishable, anterograde tracers into specific V2 compartments. The distribution of labeled axons was analyzed either in horizontal sections through the prelunate gyrus, or in tangentially sectioned portions of physically unfolded cortex containing the lunate sulcus, prelunate gyrus and superior temporal sulcus. When a V2 thin stripe and adjacent interstripe were injected with distinguishable tracers, a large primary and several secondary foci were observed in V4. The primary focus from the thin stripe injection was spatially segregated from the primary focus from the V2 interstripe injection, suggesting a retention of the pattern of compartmentation. ^ We examined the distribution of retrogradely labeled cells in V1 following the injections of tracers into V2 different compartments, in order to quantitate just how parallel the two sub-streams are from V1 to V2. Our results suggest that both blobs and interblobs project to thin stripes in V2, whereas only interblobs project to interstripes. This asymmetrical segregation argues against the original proposal of strict parallelism. (Abstract shortened by UMI.) ^