Koszul differential graded algebras and BGG correspondence

The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When the Koszul DG algebra $A$ is AS-regular, the Ext-algebra $E$ of $A$ is Frobenius. In this case, similar to the classical BGG correspondence, there is an equivalence between the stable category of finitely generated left $E$-modules, and the quotient triangulated category of the full triangulated subcategory of the derived category of right DG $A$-modules consisting of all compact DG modules modulo the full triangulated subcategory consisting of all the right DG modules with finite dimensional cohomology. The classical BGG correspondence can derived from the DG version.Comment: 29 page

Variable-frequency-controlled coupling in charge qubit circuits: Effects of microwave field on qubit-state readout

To implement quantum information processing, microwave fields are often used to manipulate superconuducting qubits. We study how the coupling between superconducting charge qubits can be controlled by variable-frequency magnetic fields. We also study the effects of the microwave fields on the readout of the charge-qubit states. The measurement of the charge-qubit states can be used to demonstrate the statistical properties of photons.Comment: 7 pages, 3 figure

Proteomics in biomarker discovery and drug development

Proteomics is a research field aiming to characterize molecular and cellular dynamics in protein expression and function on a global level. The introduction of proteomics has been greatly broadening our view and accelerating our path in various medical researches. The most significant advantage of proteomics is its ability to examine a whole proteome or sub-proteome in a single experiment so that the protein alterations corresponding to a pathological or biochemical condition at a given time can be considered in an integrated way. Proteomic technology has been extensively used to tackle a wide variety of medical subjects including biomarker discovery and drug development. By complement with other new technique advances in genomics and bioinformatics, proteomics has a great potential to make considerable contribution to biomarker identification and to revolutionize drug development process. This article provides a brief overview of the proteomic technologies and their application in biomarker discovery and drug development.postprin