Eichler–Shimura theory for mock modular forms

We use mock modular forms to compute generating functions for the critical values of modular $L$ -functions, and we answer a generalized form of a question of Kohnen and Zagier by deriving the “extra relation” that is satisfied by even periods of weakly holomorphic cusp forms. To obtain these results we derive an Eichler–Shimura theory for weakly holomorphic modular forms and mock modular forms. This includes two “Eichler–Shimura isomorphisms”, a “multiplicity two” Hecke theory, a correspondence between mock modular periods and classical periods, and a “Haberland-type” formula which expresses Petersson’s inner product and a related antisymmetric inner product on $M_{k}^{!}$ in terms of periods.     

Effects of structural modification on gene transfection and self-assembling properties of amphiphilic dendrimers

A library of novel amphiphilic, self-assembling dendrimers was designed and synthesised to evaluate the effects of structural changes on transfection efficiency.     

Estimates of Fourier Coefficients of Siegel Cusp Forms for Subgroups and in the Case of Small Weight

Here we develop estimates for Fourier coefficients of Siegelcusp forms. First we consider the case of Siegel modular formsfor the full modular group     

Dynamic programming based algorithms for the discounted {0-1} knapsack problem

The discounted {0-1} knapsack problem (DKP) is an extension of the classical {0-1} knapsack problem (KP) that consists of selecting a set of item groups where each group includes three items and at most one of the three items can be selected. The DKP is more challenging than the KP because four choices of items in an item group diversify the selection of the items. Consequently, it is not possible to solve the DKP based on a classical definition of a core consisting of a small number of relevant variables. This paper partitions the DKP into several easier sub-problems to achieve problem reductions by imitating the core concept of the KP to derive an alternative core for the DKP. Numerical experiments with DP-based algorithms are conducted to evaluate the effectiveness of the problem partition by solving the partitioned problem and the original problem based on different types of DKP instances.     

Genetic Encoding of bicyclononynes and trans-cyclooctenes for site-specific protein labeling in vitro and in live mammalian cells via rapid fluorogenic Diels-Alder reactions

Rapid, site-specific labeling of proteins with diverse probes remains an outstanding challenge for chemical biologists. Enzyme-mediated labeling approaches may be rapid but use protein or peptide fusions that introduce perturbations into the protein under study and may limit the sites that can be labeled, while many "bioorthogonal" reactions for which a component can be genetically encoded are too slow to effect quantitative site-specific labeling of proteins on a time scale that is useful for studying many biological processes. We report a fluorogenic reaction between bicyclo[6.1.0]non-4-yn-9-ylmethanol (BCN) and tetrazines that is 3-7 orders of magnitude faster than many bioorthogonal reactions. Unlike the reactions of strained alkenes, including trans-cyclooctenes and norbornenes, with tetrazines, the BCN-tetrazine reaction gives a single product of defined stereochemistry. We have discovered aminoacyl-tRNA synthetase/tRNA pairs for the efficient site-specific incorporation of a BCN-containing amino acid, 1, and a trans-cyclooctene-containing amino acid 2 (which also reacts extremely rapidly with tetrazines) into proteins expressed in Escherichia coli and mammalian cells. We demonstrate the rapid fluorogenic labeling of proteins containing 1 and 2 in vitro, in E. coli , and in live mammalian cells. These approaches may be extended to site-specific protein labeling in animals, and we anticipate that they will have a broad impact on labeling and imaging studies.     

Site-specific traceless coupling of potent cytotoxic drugs to recombinant antibodies for pharmacodelivery

Aldehyde drugs are gaining increasing research interest, considering that aldehyde dehydrogenases overexpression is characteristic of cancer stem cells. Here, we describe the traceless site-specific coupling of a novel potent drug, containing an aldehyde moiety, to recombinant antibodies, which were engineered to display a cysteine residue at their N-terminus, or a 1,2-aminothiol at their C-terminus. The resulting chemically defined antibody-drug conjugates represent the first example in which a thiazolidine linkage is used for the targeted delivery and release of cytotoxic agents.     

Localization and tensorization properties of the curvature-dimension condition for metric measure spaces

This paper is devoted to the analysis of metric measure spaces satisfying locally the curvature-dimension condition CD(K,N) introduced by the second author and also studied by Lott & Villani. We prove that the local version of CD(K,N) is equivalent to a global condition CD^∗(K,N), slightly weaker than the (usual, global) curvature-dimension condition. This so-called reduced curvature-dimension condition CD^∗(K,N) has the local-to-global property. We also prove the tensorization property for CD^∗(K,N). As an application we conclude that the fundamental group π₁(M,x₀) of a metric measure space (M,d,m) is finite whenever it satisfies locally the curvature-dimension condition CD(K,N) with positive K and finite N.     

Photoelectron emission spectroscopy of liquid water

The threshold energy E_t = 10.06 eV (0.002 eV standard deviation) is determined for photoelectron emission by liquid water and is correlated with E_t = 8.45 eV for OH^? (aq). Free energy changes and standard reduction potentials are calculated for both emission processes. Reorganization free energies are correlated to solvation free energies for H₂O⁺(aq) and OH^?(aq).     

Bioaerosol analysis based on a label-free microarray readout method using surface-enhanced Raman scattering

Bacterial contamination of indoor air is a serious threat to human health. Pathogenic germs can be transferred from the liquid to the aerosol phase, for instance, when water is sprayed in the air, such as in shower rooms, air conditioners, or fountains. Existing analytical methods for biological indoor air-quality assessment and contamination monitoring are mostly time consuming as they generally require a cultivation step. The need for a rapid, sensitive, and selective detection method for bioaerosols is evident. Our approach is based on the combination of a commercial wet particle sampler (Coriolis μ, Bertin Technologies, France) and a label-free microarray readout based on surface-enhanced Raman scattering (SERS) for detection, which was established in our laboratories. Heat-inactivated Escherichia coli bacteria were used as test microorganisms. An E. coli suspension was sprayed into the chamber by a jet air nebulizer. The resulting bioaerosol was dried, neutralized, and then collected by a Coriolis μ sampler. The bacteria collected were detected by a recently developed microarray readout system, based on label-free SERS detection. A special data evaluation procedure was applied in order to fully exploit the selectivity of the detection scheme, resulting in a detection limit of 144 particles per cubic centimeter.     

Pion interferometry in jet events at the CERN Intersecting Storage Rings

We have revised the additive quark model for inelastic hadronic cross sections with its implications to the average charged multiplicities. The correction to the additive quark model is on the level of 2 mb only if we take into account all possible quark-quark cross sections with respect to flavour. The quark-quark constitutent cross sections have been evaluated. We have attributed average charged multiplicities to the constituent quark cross sections and have found some regularities according to the flavour of the quarks.