Universal deformation rings of modules over Frobenius algebras

Let $k$ be a field, and let $\Lambda$ be a finite dimensional $k$-algebra. We prove that if $\Lambda$ is a self-injective algebra, then every finitely generated $\Lambda$-module $V$ whose stable endomorphism ring is isomorphic to $k$ has a universal deformation ring $R(\Lambda,V)$ which is a complete local commutative Noetherian $k$-algebra with residue field $k$. If $\Lambda$ is also a Frobenius algebra, we show that $R(\Lambda,V)$ is stable under taking syzygies. We investigate a particular Frobenius algebra $\Lambda_0$ of dihedral type, as introduced by Erdmann, and we determine $R(\Lambda_0,V)$ for every finitely generated $\Lambda_0$-module $V$ whose stable endomorphism ring is isomorphic to $k$.Comment: 25 pages, 2 figures. Some typos have been fixed, the outline of the paper has been changed to improve readabilit

Equianalytic and equisingular families of curves on surfaces

We consider flat families of reduced curves on a smooth surface S such that each member C has the same number of singularities of fixed singularity types and the corresponding (locally closed) subscheme H of the Hilbert scheme of S. We are mainly concerned with analytic resp. topological singularity types and give a sufficient condition for the smoothness of H (at C). Our results for S=P^2 seem to be quite sharp for families of cuves of small degree d.Comment: LaTeX v 2.0

Homological Type of Geometric Transitions

The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \emph{homological type} of a geometric transition. The obtained results agree with, and go further than, most results and estimates, given to date by several authors, both in mathematical and physical literature.Comment: 36 pages. Minor changes: A reference and a related comment in Remark 3.2 were added. This is the final version accepted for publication in the journal Geometriae Dedicat

Population history from the Neolithic to present on the Mediterranean island of Sardinia: an ancient DNA perspective

Recent ancient DNA studies of western Eurasia have revealed a dynamic history of admixture, with evidence for major migrations during the Neolithic and Bronze Age. The population of the Mediterranean island of Sardinia has been notable in these studies –} Neolithic individuals from mainland Europe cluster more closely with Sardinian individuals than with all other present-day Europeans. The current model to explain this result is that Sardinia received an initial influx of Neolithic ancestry and then remained relatively isolated from expansions in the later Neolithic and Bronze Age that took place in continental Europe. To test this model, we generated genome-wide capture data (approximately 1.2 million variants) for 43 ancient Sardinian individuals spanning the Neolithic through the Bronze Age, including individuals from Sardinia{’}s Nuragic culture, which is known for the construction of numerous large stone towers throughout the island. We analyze these new samples in the context of previously generated genome-wide ancient DNA data from 972 ancient individuals across western Eurasia and whole-genome sequence data from approximately 1,500 modern individuals from Sardinia. The ancient Sardinian individuals show a strong affinity to western Mediterranean Neolithic populations and we infer a high degree of genetic continuity on the island from the Neolithic (around fifth millennium BCE) through the Nuragic period (second millennium BCE). In particular, during the Bronze Age in Sardinia, we do not find significant levels of the {“}Steppe{” ancestry that was spreading in many other parts of Europe at that time. We also characterize subsequent genetic influx between the Nuragic period and the present. We detect novel, modest signals of admixture between 1,000 BCE and present-day, from ancestry sources in the eastern and northern Mediterranean. Within Sardinia, we confirm that populations from the more geographically isolated mountainous provinces have experienced elevated levels of genetic drift and that northern and southwestern regions of the island received more gene flow from outside Sardinia. Overall, our genetic analysis sheds new light on the origin of Neolithic settlement on Sardinia, reinforces models of genetic continuity on the island, and provides enhanced power to detect post-Bronze-Age gene flow. Together, these findings offer a refined demographic model for future medical genetic studies in Sardinia

Integrated computational and Drosophila cancer model platform captures previously unappreciated chemicals perturbing a kinase network

Drosophila provides an inexpensive and quantitative platform for measuring whole animal drug response. A complementary approach is virtual screening, where chemical libraries can be efficiently screened against protein target(s). Here, we present a unique discovery platform integrating structure-based modeling with Drosophila biology and organic synthesis. We demonstrate this platform by developing chemicals targeting a Drosophila model of Medullary Thyroid Cancer (MTC) characterized by a transformation network activated by oncogenic dRetM955T. Structural models for kinases relevant to MTC were generated for virtual screening to identify unique preliminary hits that suppressed dRetM955T-induced transformation. We then combined features from our hits with those of known inhibitors to create a ‘hybrid’ molecule with improved suppression of dRetM955T transformation. Our platform provides a framework to efficiently explore novel kinase inhibitors outside of explored inhibitor chemical space that are effective in inhibiting cancer networks while minimizing whole body toxicity

On operad structures of moduli spaces and string theory

Recent algebraic structures of string theory, including homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from the topology of the moduli spaces of punctured Riemann spheres. The principal reason for these structures to appear is as simple as the following. A conformal field theory is an algebra over the operad of punctured Riemann surfaces, this operad gives rise to certain standard operads governing the three kinds of algebras, and that yields the structures of such algebras on the (physical) state space naturally.Comment: 33 pages (An elaboration of minimal area metrics and new references are added

Elucidating glycosaminoglycan–protein–protein interactions using carbohydrate microarray and computational approaches

Glycosaminoglycan polysaccharides play critical roles in many cellular processes, ranging from viral invasion and angiogenesis to spinal cord injury. Their diverse biological activities are derived from an ability to regulate a remarkable number of proteins. However, few methods exist for the rapid identification of glycosaminoglycan–protein interactions and for studying the potential of glycosaminoglycans to assemble multimeric protein complexes. Here, we report a multidisciplinary approach that combines new carbohydrate microarray and computational modeling methodologies to elucidate glycosaminoglycan–protein interactions. The approach was validated through the study of known protein partners for heparan and chondroitin sulfate, including fibroblast growth factor 2 (FGF2) and its receptor FGFR1, the malarial protein VAR2CSA, and tumor necrosis factor-α (TNF-α). We also applied the approach to identify previously undescribed interactions between a specific sulfated epitope on chondroitin sulfate, CS-E, and the neurotrophins, a critical family of growth factors involved in the development, maintenance, and survival of the vertebrate nervous system. Our studies show for the first time that CS is capable of assembling multimeric signaling complexes and modulating neurotrophin signaling pathways. In addition, we identify a contiguous CS-E-binding site by computational modeling that suggests a potential mechanism to explain how CS may promote neurotrophin-tyrosine receptor kinase (Trk) complex formation and neurotrophin signaling. Together, our combined microarray and computational modeling methodologies provide a general, facile means to identify new glycosaminoglycan–protein–protein interactions, as well as a molecular-level understanding of those complexes

Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets

We show that the quantum field theoretical formulation of the $\tau$-function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that i) the partial charge transformations preserving the neutral sector are Laplace transformations, ii) the basic vertex operators are Levy and adjoint Levy transformations and iii) the diagonal soliton vertex operators generate fundamental transformations. We also show that the bilinear identity for the multicomponent Kadomtsev-Petviashvili hierarchy becomes, through a generalized Miwa map, a bilinear identity for the multidimensional quadrilateral lattice equations.Comment: 28 pages, 3 Postscript figure