Diophantine approximation by special primes

We show that whenever $\delta>0$, $\eta$ is real and constants $\lambda_i$ satisfy some necessary conditions, there are infinitely many prime triples $p_1,\, p_2,\, p_3$ satisfying the inequality $|\lambda_1p_1 + \lambda_2p_2 + \lambda_3p_3+\eta|<(\max p_j)^{-1/12+\delta}$ and such that, for each $i\in\{1,2,3\}$, $p_i+2$ has at most $28$ prime factors

Left-handed nuclei

The orientation of the angular momentum vector with respect to the triaxial density distribution selects a left-handed or right-handed system principal axes. This breaking of chiral symmetry manifests itself as pairs of nearly identical $\Delta I=1$-bands. The chiral structures combine high-j particles and high-j holes with a triaxial rotor. Tilted axis cranking calculations predict the existence of such configurations in different mass regions. There is experimental evidence in odd-odd nuclei around mass 134. The quantized motion of the angular momentum vector between the left- and right-handed configurations, which causes the splitting between the chiral sister bands, can be classified as tunneling (chiral rotors) or oscillation (chiral vibrators).Comment: Invited lecture at the Conference on Frontiers of Nuclear Structure, Berkeley, 200

Therapeutic antibodies: current state and future trends--is a paradigm change coming soon?

Antibody-based therapeutics currently enjoy unprecedented success, growth in research and revenues, and recognition of their potential. It appears that the promise of the "magic bullet" has largely been realized. There are currently 22 monoclonal antibodies (mAbs) approved by the United States Food and Drug Administration (FDA) for clinical use and hundreds are in clinical trials for treatment of various diseases including cancers, immune disorders, and infections. The revenues from the top five therapeutic antibodies (Rituxan, Remicade, Herceptin, Humira, and Avastin) nearly doubled from $6.4 billion in 2004 to$11.7 billion in 2006. During the last several years major pharmaceutical companies raced to acquire antibody companies, with a recent example of MedImmune being purchased for $15.6 billion by AstraZeneca. These therapeutic and business successes reflect the major advances in antibody engineering which have resulted in the generation of safe, specific, high-affinity, and non-immunogenic antibodies during the last three decades. Currently, second and third generations of antibodies are under development, mostly to improve already existing antibody specificities. However, although the refinement of already known methodologies is certainly of great importance for potential clinical use, there are no conceptually new developments in the last decade comparable, for example, to the development of antibody libraries, phage display, domain antibodies (dAbs), and antibody humanization to name a few. A fundamental question is then whether there will be another change in the paradigm of research as happened 1-2 decades ago or the current trend of gradual improvement of already developed methodologies and therapeutic antibodies will continue. Although any prediction could prove incorrect, it appears that conceptually new methodologies are needed to overcome the fundamental problems of drug (antibody) resistance due to genetic or/and epigenetic alterations in cancer and chronic infections, as well as problems related to access to targets and complexity of biological systems. If new methodologies are not developed, it is likely that gradual saturation will occur in the pipeline of conceptually new antibody therapeutics. In this scenario we will witness an increase in combination of targets and antibodies, and further attempts to personalize targeted treatments by using appropriate biomarkers as well as to develop novel scaffolds with properties that are superior to those of the antibodies now in clinical use