Product analysis of the reaction of OH with benzene,toluene, and 1,3,5-trimethylbenzene at 300 K

Products of the reaction of OH with benzene, toluene, and 1,3,5-trimethylbenzene have been identified in crossed molecular beam experiments conducted at 300 K. Ionization potentials of the most intense products were also measured.     

cyc-DEP: Cyclic immunofluorescence profiling of particles collected using dielectrophoresis

Cancer is a highly heterogenous disease that requires precise detection tools and active surveillance methods. Liquid biopsy assays provide an agnostic way to follow the complex trajectory of cancer, providing better patient stratification tools for optimized treatment. Here, we present the development of a low-volume liquid biopsy assay called cyc-DEP (cyclic immunofluorescent imaging on dielectrophoretic chip) to profile biomarkers collected on a dielectrophoretic microfluidic chip platform. To enable on-chip cyclic imaging, we optimized a fluorophore quenching method and sequential rounds of on-chip staining with fluorescently conjugated primary antibodies. cyc-DEP allows for the quantification of a multiplex array of proteins using 25 µl of a patient plasma sample. We utilized nanoparticles from a prostate adenocarcinoma (LNCaP) cell line and a panel of six target proteins to develop our proof-of-concept technique. We then used cyc-DEP to quantify blood plasma levels of target proteins from healthy individuals, low-grade and high-grade prostate cancer patients (n = 3 each) in order to demonstrate that our platform is suitable for liquid biopsy analysis in its present form. To ensure accurate quantification of signal intensities and comparisons between different samples, we incorporated a signal intensity normalization method (fluorescent beads) and a custom signal intensity quantification algorithm that account for the distribution of signal across hundreds of collection regions on each chip. Our technique enabled a threefold improvement in multiplicity for detecting proteins associated with fluid samples, opening doors for early detection, and active surveillance through quantification of a multiplex array of biomarkers from low-volume liquid biopsies.     

The nonexistence of a certain Steiner system S(3, 12, 112)

Although the automorphism group of a projective plane of order 10, if one exists, must be very small, such a plane could be the derived design of a Steiner system S(3, 12, 112) with a larger group. There are several reasons why the Frobenius group of order 56 is a promising candidate for the latter group. However, in this paper it is shown that there is no S(3, 12, 112) which is fixed by this Frobenius group.     

On asymmetric coverings and covering numbers

An asymmetric covering is a collection of special subsets S of an n‐set such that every subset T of the n‐set is contained in at least one special S with . In this paper we compute the smallest size of any for We also investigate “continuous” and “banded” versions of the problem. The latter involves the classical covering numbers , and we determine the following new values: , , , , and . We also find the number of non‐isomorphic minimal covering designs in several cases. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 218–228, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10022     

A Note on Projecting the Cubic Lattice

It is shown that, given any (n−1)-dimensional lattice Λ, there is a vector v∈ℤ ⁿ such that the orthogonal projection of ℤ ⁿ onto v ^⊥ is, up to a similarity, arbitrarily close to Λ. The problem arises in attempting to find the largest cylinder anchored at two points of ℤ ⁿ and containing no other points of ℤ ⁿ .     

Four icosahedra can meet at a point

What is the maximal number of nonoverlapping copies of a regular polyhedron ∏ that can share a common vertex? The answer is shown to be 4 if ∏ is an icosahedron or dodecahedron, and is conjectured to be 7 for an octahedron and 20 for a tetrahedron. (For a cube the answer is trivially 8.)     

Self-dual codes over GF(5)

It is shown that a self-orthogonal code over GF(5) which is generated by words of weight 4 has a decomposition into components belonging to three infinite families: d_n (n = 4, 5, 6, 7, 8, 10, 12,…), e_n (n = 6, 8, 10,…) and F_n (n = 6, 8, 10,…). All maximal self-orthogonal (and self-dual) codes of length ? 12 are classified, and a number of interesting codes of greater length are constructed.     

On the classification and enumeration of self-dual codes

A complete classification is given of all [22, 11] and [24, 12] binary self-dual codes. For each code we give the order of its group, the number of codes equivalent to it, and its weight distribution. There is a unique [24, 12, 6] self-dual code. Several theorems on the enumeration of self-dual codes are used, including formulas for the number of such codes with minimum distance ? 4, and for the sum of the weight enumerators of all such codes of length n. Selforthogonal codes which are generated by code words of weight 4 are completely characterized.     

Can Coordination‐Driven Supramolecular Self‐Assembly Reactions Be Conducted from Fully Aliphatic Linkers?

The reaction between a preassembled Cu^I bimetallic molecular clip with a short intermetallic distance and a series of fully aliphatic cyano‐capped ditopic linkers with increasing lengths was investigated. It is shown that, depending on the length of the ditopic linkers, the rational design of unprecedented supramolecular compact metallacycles containing fully aliphatic walls is possible. The specific preorganized molecular arrangement of the molecular clip used favors stabilizing interlinker London dispersion interactions, which allow, as the length of the linkers increases, the selective formation of discrete compact metallacycles at the expense of 1D coordination polymers. The generalizability of this approach was demonstrated by the reaction of fully aliphatic cyano‐capped linkers with two other types of preassembled Cu^I bimetallic molecular clips that also had short intermetallic distances.