Ising model on the generalized Bruhat-Tits tree

The partition function and the correlation functions of the Ising model on the generalized Bruhat-Tits tree are calculated. We computed also the averages of these correlation functions when the corresponding vertices are attached to the boundary of the generalized Bruhat-Tits tree.     

A one-step synthesis of a poly(iptycene) through an unusual Diels-Alder cyclization/dechlorination of tetrachloropentacene

We have discovered the first reaction of a substituted pentacene molecule as a dienophile. A surprisingly clean Diels-Alder self-coupling of Cl4Pn leads to a novel ladder polymer, poly(iptycene), which can be converted to a conducting carbon at relatively low temperature (600-900 degrees C). Theoretical calculations of the former reaction suggest a biradical asymmetric mechanism, despite highly symmetric reactants.     

PartiallyU(1) compactified scalar massless field on the compact Riemann surface and the bosonic string amplitudes

The theory of the partiallyU(1) compactified scalar massless field on the compact Riemann surface with Nambu-Goto action is defined. The partition function is determined completely by a choice of the finite-dimensional approximations. The correlation functions are the only correctly defined objects of the theory. The averages of the correlation function asymptotic values provide the amplitudes. For the compact Riemann surfaces of any genus the usual bosonic string amplitudes are the special cases of the above amplitudes.     

Resistivity of a non-galilean-invariant Fermi liquid near Pomeranchuk quantum criticality

We analyze the effect of the electron-electron interaction on the resistivity of a metal near a Pomeranchuk quantum phase transition (QPT). We show that umklapp processes are not effective near a QPT, and one must consider both interactions and disorder to obtain a finite and T dependent resistivity. By power counting, the correction to the residual resistivity at low T scales as AT((D+2)/3) near a Z=3 QPT. We show, however, that A=0 for a simply connected, convex Fermi surface in 2D, due to the hidden integrability of the electron motion. We argue that A>0 in a two-band (s-d) model and propose this model as an explanation for the observed T((D+2)/3) behavior.     

A hybrid approach for predicting the distribution of vibro-acoustic energy in complex built-up structures

Finding the distribution of vibro-acoustic energy in complex built-up structures in the mid-to-high frequency regime is a difficult task. In particular, structures with large variation of local wavelengths and/or characteristic scales pose a challenge referred to as the mid-frequency problem. Standard numerical methods such as the finite element method (FEM) scale with the local wavelength and quickly become too large even for modern computer architectures. High frequency techniques, such as statistical energy analysis (SEA), often miss important information such as dominant resonance behavior due to stiff or small scale parts of the structure. Hybrid methods circumvent this problem by coupling FEM/BEM and SEA models in a given built-up structure. In the approach adopted here, the whole system is split into a number of subsystems that are treated by either FEM or SEA depending on the local wavelength. Subsystems with relative long wavelengths are modeled using FEM. Making a diffuse field assumption for the wave fields in the short wave length components, the coupling between subsystems can be reduced to a weighted random field correlation function. The approach presented results in an SEA-like set of linear equations that can be solved for the mean energies in the short wavelength subsystems.     

Numerical block diagonalization of matrix *-algebras with application to semidefinite programming

Semidefinite programming (SDP) is one of the most active areas in mathematical programming, due to varied applications and the availability of interior point algorithms. In this paper we propose a new pre-processing technique for SDP instances that exhibit algebraic symmetry. We present computational results to show that the solution times of certain SDP instances may be greatly reduced via the new approach.     

Halogen bonds as stabilizing interactions in a chiral self-assembled molecular monolayer

We report the formation of highly-ordered self-assembled monolayers of an achiral organic semiconductor molecule. STM results show spontaneous formation of very large single domains of ordered chiral monolayers. DFT calculations support the identification of halogen bonds as the primary interactions that steer molecular self-assembly, leading to organizational chirality.     

Library enhancement through the wisdom of crowds

We present a novel approach for enhancing the diversity of a chemical library rooted on the theory of the wisdom of crowds. Our approach was motivated by a desire to tap into the collective experience of our global medicinal chemistry community and involved four basic steps: (1) Candidate compounds for acquisition were screened using various structural and property filters in order to eliminate clearly nondrug-like matter. (2) The remaining compounds were clustered together with our in-house collection using a novel fingerprint-based clustering algorithm that emphasizes common substructures and works with millions of molecules. (3) Clusters populated exclusively by external compounds were identified as "diversity holes," and representative members of these clusters were presented to our global medicinal chemistry community, who were asked to specify which ones they liked, disliked, or were indifferent to using a simple point-and-click interface. (4) The resulting votes were used to rank the clusters from most to least desirable, and to prioritize which ones should be targeted for acquisition. Analysis of the voting results reveals interesting voter behaviors and distinct preferences for certain molecular property ranges that are fully consistent with lead-like profiles established through systematic analysis of large historical databases.     

Efficient substructure searching of large chemical libraries: the ABCD chemical cartridge

Efficient substructure searching is a key requirement for any chemical information management system. In this paper, we describe the substructure search capabilities of ABCD, an integrated drug discovery informatics platform developed at Johnson & Johnson Pharmaceutical Research & Development, L.L.C. The solution consists of several algorithmic components: 1) a pattern mapping algorithm for solving the subgraph isomorphism problem, 2) an indexing scheme that enables very fast substructure searches on large structure files, 3) the incorporation of that indexing scheme into an Oracle cartridge to enable querying large relational databases through SQL, and 4) a cost estimation scheme that allows the Oracle cost-based optimizer to generate a good execution plan when a substructure search is combined with additional constraints in a single SQL query. The algorithm was tested on a public database comprising nearly 1 million molecules using 4,629 substructure queries, the vast majority of which were submitted by discovery scientists over the last 2.5 years of user acceptance testing of ABCD. 80.7% of these queries were completed in less than a second and 96.8% in less than ten seconds on a single CPU, while on eight processing cores these numbers increased to 93.2% and 99.7%, respectively. The slower queries involved extremely generic patterns that returned the entire database as screening hits and required extensive atom-by-atom verification.