63,536 research outputs found
Theoretical Study of the Binding of Silane (SiH4) with Borane (BH3), Diborane (B2H6), and Boron Trichloride (BCl3): The Role of Core–Electron Correlation
Equilibrium structures and energies of gas-phase molecular complexes SiH4···BH3, SiH4···B2H6, and SiH4···BCl3 were determined using second-order Møller–Plesset perturbation theory (MP2) and the aug-cc-pVTZ basis set, with and without explicit core electron correlation. Single-point energies were calculated for the MP2-optimized structures using MP2 with the aug-cc-pVQZ basis set and using coupled cluster theory (CCSD(T)) with both the aug-cc-pVTZ and the aug-cc-pVQZ basis sets to extrapolate to the complete basis set (CBS). Partition functions were calculated using the harmonic oscillator/rigid rotorapproximation at the MP2/aug-cc-pVTZ level of theory. The explicit core electron correlation is demonstrated to have significant impact on the structures and binding energies and binding enthalpies of these complexes. The binding enthalpies were obtained at various temperatures ranging from 0 K to the dissociation temperatures of the complexes. The potential energy surfaces of the three complexes were explored, and no transition states were found along the pathways from separated species to the complexes
Cohen-Macaulay graphs and face vectors of flag complexes
We introduce a construction on a flag complex that, by means of modifying the
associated graph, generates a new flag complex whose -factor is the face
vector of the original complex. This construction yields a vertex-decomposable,
hence Cohen-Macaulay, complex. From this we get a (non-numerical)
characterisation of the face vectors of flag complexes and deduce also that the
face vector of a flag complex is the -vector of some vertex-decomposable
flag complex. We conjecture that the converse of the latter is true and prove
this, by means of an explicit construction, for -vectors of Cohen-Macaulay
flag complexes arising from bipartite graphs. We also give several new
characterisations of bipartite graphs with Cohen-Macaulay or Buchsbaum
independence complexes.Comment: 14 pages, 3 figures; major updat
RNA-RNA interaction prediction based on multiple sequence alignments
Many computerized methods for RNA-RNA interaction structure prediction have
been developed. Recently, time and space dynamic programming
algorithms have become available that compute the partition function of RNA-RNA
interaction complexes. However, few of these methods incorporate the knowledge
concerning related sequences, thus relevant evolutionary information is often
neglected from the structure determination. Therefore, it is of considerable
practical interest to introduce a method taking into consideration both
thermodynamic stability and sequence covariation. We present the \emph{a
priori} folding algorithm \texttt{ripalign}, whose input consists of two
(given) multiple sequence alignments (MSA). \texttt{ripalign} outputs (1) the
partition function, (2) base-pairing probabilities, (3) hybrid probabilities
and (4) a set of Boltzmann-sampled suboptimal structures consisting of
canonical joint structures that are compatible to the alignments. Compared to
the single sequence-pair folding algorithm \texttt{rip}, \texttt{ripalign}
requires negligible additional memory resource. Furthermore, we incorporate
possible structure constraints as input parameters into our algorithm. The
algorithm described here is implemented in C as part of the \texttt{rip}
package. The supplemental material, source code and input/output files can
freely be downloaded from \url{http://www.combinatorics.cn/cbpc/ripalign.html}.
\section{Contact} Christian Reidys \texttt{[email protected]}Comment: 8 pages, 9 figure
Thermodynamic Analysis of Interacting Nucleic Acid Strands
Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality
Tverberg's theorem with constraints
The topological Tverberg theorem claims that for any continuous map of the
(q-1)(d+1)-simplex to R^d there are q disjoint faces such that their images
have a non-empty intersection. This has been proved for affine maps, and if
is a prime power, but not in general.
We extend the topological Tverberg theorem in the following way: Pairs of
vertices are forced to end up in different faces. This leads to the concept of
constraint graphs. In Tverberg's theorem with constraints, we come up with a
list of constraints graphs for the topological Tverberg theorem.
The proof is based on connectivity results of chessboard-type complexes.
Moreover, Tverberg's theorem with constraints implies new lower bounds for the
number of Tverberg partitions. As a consequence, we prove Sierksma's conjecture
for , and .Comment: 16 pages, 12 figures. Accepted for publication in JCTA. Substantial
revision due to the referee
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