Modelling and solving central cycle problems with integer programming

We consider the problem of identifying a central subgraph of a given simple connected graph. The case where the subgraph comprises a discrete set of vertices is well known. However, the concept of eccentricity can be extended to connected subgraphs such as: paths, trees and cycles. Methods have been reported which deal with the requirement that the subgraph is a path or a constrained tree. We extend this work to the case where the subgraph is required to be a cycle. We report on computational experience with integer programming models of the problems of identifying cycle centres, cycle medians and cycle centroids, and also on a heuristic based on the first model. The problems have applications in facilities location, particularly the location of emergency facilities, and service facilities

Generalized Buneman pruning for inferring the most parsimonious multi-state phylogeny

Accurate reconstruction of phylogenies remains a key challenge in evolutionary biology. Most biologically plausible formulations of the problem are formally NP-hard, with no known efficient solution. The standard in practice are fast heuristic methods that are empirically known to work very well in general, but can yield results arbitrarily far from optimal. Practical exact methods, which yield exponential worst-case running times but generally much better times in practice, provide an important alternative. We report progress in this direction by introducing a provably optimal method for the weighted multi-state maximum parsimony phylogeny problem. The method is based on generalizing the notion of the Buneman graph, a construction key to efficient exact methods for binary sequences, so as to apply to sequences with arbitrary finite numbers of states with arbitrary state transition weights. We implement an integer linear programming (ILP) method for the multi-state problem using this generalized Buneman graph and demonstrate that the resulting method is able to solve data sets that are intractable by prior exact methods in run times comparable with popular heuristics. Our work provides the first method for provably optimal maximum parsimony phylogeny inference that is practical for multi-state data sets of more than a few characters.Comment: 15 page

ZARAMIT: A System for the Evolutionary Study of Human Mitochondrial DNA

Abstract. ZARAMIT is an information system capable of fully auto-mated phylogeny reconstruction. Methods have been tailored to mito-chondrial DNA sequences, with focus on subproblem partitioning. We have built exhaustive human mitochondrial phylogenies (∼5500 sequences) and detected problems in existing haplogroup hierarchies through data-driven classification. Information on the project can be found on zaramit.org. 1 The case for mitochondrial DNA Mitochondria, organelles present in most eukaryotic cells, are responsible for the generation of most of the cell’s chemical energy. They are also remarkable for possessing their own, separate genome, which coexists with nuclear DNA and is inherited independently. Further, mitochondrial DNA (mtDNA) has several features which make it an ideal candidate for conducting evolutionary studies. Firstly, it is small in mammals (15000 to 17000 base pairs) and encodes a homogeneous set of gene

Search for the doubly heavy baryon Ξbc+\it{\Xi}_{bc}^{+} decaying to J/ψΞc+J/\it{\psi} \it{\Xi}_{c}^{+}

A first search for the $\it{\Xi}_{bc}^{+}\to J/\it{\psi}\it{\Xi}_{c}^{+}$ decay is performed by the LHCb experiment with a data sample of proton-proton collisions, corresponding to an integrated luminosity of $9\,\mathrm{fb}^{-1}$ recorded at centre-of-mass energies of 7, 8, and $13\mathrm{\,Te\kern -0.1em V}$. Two peaking structures are seen with a local (global) significance of $4.3\,(2.8)$ and $4.1\,(2.4)$ standard deviations at masses of $6571\,\mathrm{Me\kern -0.1em V\!/}c^2$ and $6694\,\mathrm{Me\kern -0.1em V\!/}c^2$, respectively. Upper limits are set on the $\it{\Xi}_{bc}^{+}$ baryon production cross-section times the branching fraction relative to that of the $B_{c}^{+}\to J/\it{\psi} D_{s}^{+}$ decay at centre-of-mass energies of 8 and $13\mathrm{\,Te\kern -0.1em V}$, in the $\it{\Xi}_{bc}^{+}$ and in the $B_{c}^{+}$ rapidity and transverse-momentum ranges from 2.0 to 4.5 and 0 to $20\,\mathrm{Ge\kern -0.1em V\!/}c$, respectively. Upper limits are presented as a function of the $\it{\Xi}_{bc}^{+}$ mass and lifetime.Comment: All figures and tables, along with machine-readable versions and any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-005.html (LHCb public pages

Measurement of CP asymmetries and branching fraction ratios of B− decays to two charm mesons

The $CP$ asymmetries of seven $B^-$ decays to two charm mesons are measured using data corresponding to an integrated luminosity of $9\text{fb}^{-1}$ of proton-proton collisions collected by the LHCb experiment. Decays involving a $D^{*0}$ or $D^{*-}_s$ meson are analysed by reconstructing only the $D^0$ or $D^-_s$ decay products. This paper presents the first measurement of $\mathcal{A}^{CP}(B^- \rightarrow D^{*-}_s D^0)$ and $\mathcal{A}^{CP}(B^- \rightarrow D^{-}_s D^{*0})$, and the most precise measurement of the other five $CP$ asymmetries. There is no evidence of $CP$ violation in any of the analysed decays. Additionally, two ratios between branching fractions of selected decays are measured.The CP asymmetries of seven B$^{−}$ decays to two charm mesons are measured using data corresponding to an integrated luminosity of 9 fb$^{−1}$ of proton-proton collisions collected by the LHCb experiment. Decays involving a D$^{*0}$ or ${D}_s^{\ast -}$ meson are analysed by reconstructing only the D$^{0}$ or ${D}_s^{-}$ decay products. This paper presents the first measurement of $\mathcal{A} ^{CP}$(B$^{−}$→${D}_s^{\ast -}$D$^{0}$) and $\mathcal{A} ^{CP}$(B$^{−}$→${D}_s^{-}$D$^{∗0}$), and the most precise measurement of the other five CP asymmetries. There is no evidence of CP violation in any of the analysed decays. Additionally, two ratios between branching fractions of selected decays are measured.[graphic not available: see fulltext]The $CP$ asymmetries of seven $B^-$ decays to two charm mesons are measured using data corresponding to an integrated luminosity of $9\text{ fb}^{-1}$ of proton-proton collisions collected by the LHCb experiment. Decays involving a $D^{*0}$ or $D^{*-}_s$ meson are analysed by reconstructing only the $D^0$ or $D^-_s$ decay products. This paper presents the first measurement of $\mathcal{A}^{CP}(B^- \rightarrow D^{*-}_s D^0)$ and $\mathcal{A}^{CP}(B^- \rightarrow D^{-}_s D^{*0})$, and the most precise measurement of the other five $CP$ asymmetries. There is no evidence of $CP$ violation in any of the analysed decays. Additionally, two ratios between branching fractions of selected decays are measured

Combinatorial optimization for undergraduate

xii, 227 p.; 24 cm

The general cell formation problem: manufacturing cell creation with machine modification costs

The general cell formation problem: manufacturing cell creation with machine modification cost

Approaches to the general cell formation problem

It has long been recognized that productivity in manufacturing plants can often be increased by producing similar products in manufacturing cells. This involves: (i) assigning parts to individual machines and (ii) forming machines into manufacturing cells. These two activities have traditionally been carried out separately. However most solution procedures for (i) above, utilize a solution to (ii), and vice versa. Here we present a new model that deals with (i) and (ii) simultaneously. We then extend this model to allow for the reassignment of operations to different machine types by incorporating machine type modification costs. Such modification enables additional machine types to process certain parts, with view to reducing inter-cell travel. The cost of such modifications must be balanced by the consequent reduction in inter-cell travel cost. The extended model specifies which individual machines should be modified to enable them to process additional part types, part-machine assignment, and the grouping of individual machines for cell formation. The objective is to minimize the sum of the machine modification costs and the inter-cell travel. We call this endeavour the General Cell Formation Problem. Computational experience with the models indicates that they are likely to be useful additions to the production engineer’s toolkit