The Home Care Crew Scheduling Problem: Preference-based visit clustering and temporal dependencies

In the Home Care Crew Scheduling Problem a staff of home carers has to be assigned a number of visits to patients’ homes, such that the overall service level is maximised. The problem is a generalisation of the vehicle routing problem with time windows. Required travel time between visits and time windows of the visits must be respected. The challenge when assigning visits to home carers lies in the existence of soft preference constraints and in temporal dependencies between the start times of visits.     

Ni(HF2)(3-Clpy)4]BF4 (py = pyridine): evidence for spin exchange along strongly distorted F···H···F- bridges in a one-dimensional polymeric chain

[Ni(HF(2))(3-Clpy)(4)]BF(4) (py = pyridine) is a simple one-dimensional (1D) coordination polymer composed of compressed NiN(4)F(2) octahedra that form chains with bridging HF(2)(-) ligands. In spite of significant distortion of the HF(2)(-) bridge, a quasi-1D antiferromagnetic (AFM) behavior was observed with J(FHF) = 4.86 K.     

Ruthenium Complexes Containing "Noninnocent" o-Benzoquinone Diimine/o-Phenylenediamide(2-) Ligands. Synthesis and Crystal Structure of the Nitrido-Bridged Complex [{LRu(o-C(6)H(4)(NH)(2))}(2)(&mgr;-N)](PF(6))(2).3CH(3)CN.C(6)H(5)CH(3)

Reaction of LRu(III)Cl(3) (L = 1,4,7-trimethyl-1,4,7-triazacyclononane) with 1,2-phenylenediamine (opdaH(2)) in H(2)O in the presence of air affords [LRu(II)(bqdi)(OH(2))](PF(6)) (1), where (bqdi) represents the neutral ligand o-benzoquinone diimine. From an alkaline methanol/water mixture of 1 was obtained the dinuclear species [{LRu(II)(bqdi)}(2)(&mgr;-H(3)O(2))](PF(6))(3) (1a). The coordinated water molecule in 1 is labile and can be readily substituted under appropriate reaction conditions by acetonitrile, yielding [LRu(II)(bqdi)(CH(3)CN)](PF(6))(2) (2), and by iodide and azide anions, affording [LRu(II)(bqdi)I](PF(6)).0.5H(2)O (3) and [LRu(bqdi)(N(3))](PF(6)).H(2)O (4), respectively. Heating of solid 4 in vacuum at 160 degrees C generates N(2) and the dinuclear, nitrido-bridged complex [{LRu(o-C(6)H(4)(NH)(2))}(2)(&mgr;-N)](PF(6))(2) (5). Complex 5 is a mixed-valent, paramagnetic species containing one unpaired electron per dinuclear unit whereas complexes 1-4 are diamagnetic. The crystal structures of 1, 1a.3CH(3)CN, 3, 4.H(2)O, and 5.3CH(3)CN.0.5(toluene) have been determined by X-ray crystallography: 1 crystallizes in the monoclinic space group P2(1)/m, Z = 2, with a = 8.412(2) ?, b = 15.562(3) ?, c = 10.025 ?, and beta = 109.89(2) degrees; 1a.3CH(3)CN, in the monoclinic space group C2/c, Z = 4, with a = 19.858(3) ?, b = 15.483(2) ?, c = 18.192(3) ?, and beta = 95.95(2) degrees; 3, in the orthorhombic space group Pnma, Z = 4, with a = 18.399(4) ?, b = 9.287(2) ?, and c = 12.052(2) ?, 4.H(2)O, in the monoclinic space group P2(1)/c, Z = 4, with a = 8.586(1) ?, b = 15.617(3) ?, c = 16.388(5) ?, and beta = 90.84(2) degrees; and 5.3CH(3)CN.0.5(toluene), in the monoclinic space group P2(1)/c, Z = 4, with a = 15.003(3) ?, b = 16.253(3) ?, c = 21.196(4) ?, and beta = 96.78(3) degrees. The structural data indicate that in complexes 1-4 the neutral o-benzoquinone diimine ligand prevails. In contrast, in 5 this ligand has predominantly o-phenylenediamide character, which would render 5 formally a mixed-valent Ru(IV)Ru(V) species. On the other hand, the Ru-N bond lengths of the Ru-N-Ru moiety at 1.805(5) and 1.767(5) ? are significantly longer than those in other crystallographically characterized Ru(IV)=N=Ru(IV) units (1.72-1.74 ?). It appears that the C(6)H(4)(NH)(2) ligand in 5 is noninnocent and that formal oxidation state assignments to the ligands or metal centers are not possible.     

3',4'-trans-linked bicyclic nucleosides locked in S-type conformations

A novel class of 3',4'-trans-linked bicyclic nucleosides with locked S-type furanose conformations is introduced by synthesis of two model derivatives; one was obtained by cyclic ether formation and the other by ring-closing metathesis methodology.     

Eigenvalue amplitudes of the Potts model on a torus

We consider the Q-state Potts model in the random-cluster formulation, defined on finite   two-dimensional lattices of size L×N$L\times N$ with toroidal boundary conditions. Due to the non-locality of the clusters, the partition function Z(L,N)$Z(L,N)$ cannot be written simply as a trace of the transfer matrix TL${\mathrm{T}}_L$. Using a combinatorial method, we establish the decomposition Z(L,N)=_∑l,Dkb(l,Dk)K_l,Dk$Z(L,N)={\sum }_{l,D_k}{b}^{(l,D_k)}{K}_{l,D_k}$, where the characters K_l,Dk=i_∑N(λi)$K_{l,D_k}={\sum }_i{({\lambda }_i)}^N$ are simple traces. In this decomposition, the amplitudes b(l,Dk)$b^{(l,D_k)}$ of the eigenvalues λi${\lambda }_i$ of TL${\mathrm{T}}_L$ are labelled by the number l=0,1,…,L$l=0,1,\dots ,L$ of clusters which are non-contractible with respect to the transfer (N  ) direction, and a representation Dk$D_k$ of the cyclic group Cl$C_l$. We obtain rigorously a general expression for b(l,Dk)$b^{(l,D_k)}$ in terms of the characters of Cl$C_l$, and, using number theoretic results, show that it coincides with an expression previously obtained in the continuum limit by Read and Saleur.     

Shell filling in closed single-wall carbon nanotube quantum dots

We observe twofold shell filling in the spectra of closed one-dimensional quantum dots formed in single-wall carbon nanotubes. Its signatures include a bimodal distribution of addition energies, correlations in the excitation spectra for different electron number, and alternation of the spins of the added electrons. This provides a contrast with quantum dots in higher dimensions, where such spin pairing is absent. We also see indications of an additional fourfold periodicity indicative of K-K' subband shells. Our results suggest that the absence of shell filling in most isolated nanotube dots results from disorder or nonuniformity.     

Gapmer Antisense Oligonucleotides Containing 2′,3′-Dideoxy-2′-fluoro-3′-C-hydroxymethyl-β-d-lyxofuranosyl Nucleotides Display Site-Specific RNase H Cleavage and Induce Gene Silencing

Off-target effects remain a significant challenge in the therapeutic use of gapmer antisense oligonucleotides (AONs). Over the years various modifications have been synthesized and incorporated into AONs, however, precise control of RNase H-induced cleavage and target sequence selectivity has yet to be realized. Herein, the synthesis of the uracil and cytosine derivatives of a novel class of 2′-deoxy-2′-fluoro-3′-C-hydroxymethyl-β-d -lyxo-configured nucleotides has been accomplished and the target molecules have been incorporated into AONs. Experiments on exonuclease degradation showed improved nucleolytic stability relative to the unmodified control. Upon the introduction of one or two of the novel 2′-fluoro-3′-C-hydroxymethyl nucleotides as modifications in the gap region of a gapmer AON was associated with efficient RNase H-mediated cleavage of the RNA strand of the corresponding AON:RNA duplex. Notably, a tailored single cleavage event could be engineered depending on the positioning of a single modification. The effect of single mismatched base pairs was scanned along the full gap region demonstrating that the modification enables a remarkable specificity of RNase H cleavage. A cell-based model system was used to demonstrate the potential of gapmer AONs containing the novel modification to mediate gene silencing.     

Enumerating maximal independent sets with applications to graph colouring

We give tight upper bounds on the number of maximal independent sets of size k (and at least k and at most k) in graphs with n vertices. As an application of the proof, we construct improved algorithms for graph colouring and computing the chromatic number of a graph.