Bounds for sorting by prefix reversal

For a permutation σ of the integers from 1 to n, let ?(σ) be the smallest number of prefix reversals that will transform σ to the identity permutation, and let ?(n) be the largest such ?(σ) for all σ in (the symmetric group) S_n. We show that $\text{?(n)?}\text{(5n+5)}\text{3}$, and that $\text{?(n)?}\text{17n}\text{16}$ for n a multiple of 16. If, furthermore, each integer is required to participate in an even number of reversed prefixes, the corresponding function g(n) is shown to obey $\text{3n}\text{2?1}\text{?g(n)?2n+3}$.     

On The Approximability Of The Traveling Salesman Problem

We show that the traveling salesman problem with triangle inequality cannot be approximated with a ratio better than when the edge lengths are allowed to be asymmetric and when the edge lengths are symmetric, unless P=NP. The best previous lower bounds were and respectively. The reduction is from H?stad’s maximum satisfiability of linear equations modulo 2, and is nonconstructive. * Supported in part by NSF ITR Grant CCR-0121555. † Supported by NSF award CCR-0307536 and a Sloan foundation fellowship.     

The Symmetric Group Action on Rank-selected Posets of Injective Words

The symmetric group \(\mathfrak {S}_{n}\) acts naturally on the poset of injective words over the alphabet {1, 2,…,n}. The induced representation on the homology of this poset has been computed by Reiner and Webb. We generalize their result by computing the representation of \(\mathfrak {S}_{n}\) on the homology of all rank-selected subposets, in the sense of Stanley. A further generalization to the poset of r-colored injective words is given.     

Resale price maintenance in supply chains with general multiplicative demand

We analyze a supply chain with a Resale Price Maintenance (RPM) contract in which the manufacturer sets the retail price with a general multiplicative price–demand function and prove the existence/uniqueness of an equilibrium. We also compare the equilibrium prices and quantities, consumer surplus and total system welfare for the RPM and wholesale price contracts. We conclude that a manufacturer may capture a smaller share of the total supply chain profit despite her ability to set the retail price.     

Cosmology with Gravitational Waves: A Review

Standard sirens have been the central paradigm in gravitational-wave cosmology so far. From the gravitational wave signature of compact star binaries, it is possible to measure the luminosity distance of the source directly, and if additional information on the source redshift is provided, a measurement of the cosmological expansion can be performed. This review article discusses several methodologies that have been proposed to use gravitational waves for cosmological studies. Methods that use only gravitational-wave signals and methods that use gravitational waves in conjunction with additional observations such as electromagnetic counterparts and galaxy catalogs will be discussed. The review also discusses the most recent results on gravitational-wave cosmology, starting from the binary neutron star merger GW170817 and its electromagnetic counterpart and finishing with the population of binary black holes, observed with the third Gravitational-wave Transient Catalog GWTC–3.     

On complete intersection toric ideals of graphs

We study the graphs G for which their toric ideals I _G are complete intersections. In particular, we prove that for a connected graph G such that I _G is a complete intersection all of its blocks are bipartite except for at most two. We prove that toric ideals of graphs which are complete intersections are circuit ideals. In this case, the generators of the toric ideal correspond to even cycles of G except of at most one generator, which corresponds to two edge disjoint odd cycles joint at a vertex or with a path. We prove that the blocks of these graphs satisfy the odd cycle condition. Finally, we characterize all complete intersection toric ideals of graphs which are normal.     

On the pivot structure for the weighing matrix W(12,11)

In the present article we concentrate our study on the growth problem for the weighing matrix W(12,11) and show that the unique W(12,11) has three pivot structures. An improved algorithm for extending a k?×?k (0,+,-) matrix to a W(n,n-1), if possible, has been developed to simplify the proof. For the implementation of the algorithm special emphasis is given to the notions of data structures and parallel processing.     

Sonochemical degradation of triclosan in water and wastewater

The sonochemical degradation of 5 μg l⁻¹ triclosan, a priority micro-pollutant, in various environmental samples (seawater, urban runoff and influent domestic wastewater) as well as in model solutions (pure and saline water) was investigated. Experiments were conducted with a horn-type sonicator operating at 80 kHz frequency and a nominal applied power of 135 W, while solid-phase microextraction coupled with gas chromatography–electron capture detector (SPME/GC–ECD) was employed to monitor triclosan degradation. The latter followed pseudo-first order kinetics with the rate constant being (min⁻¹): 0.2284 for seawater > 0.1051 for 3.5% NaCl in deionised water > 0.0597 for centrifuged urban runoff  0.0523 for untreated urban runoff > 0.0272 for deionised water > 0.0063 for wastewater influent. SPME/GC–ECD and SPME coupled with gas chromatography–mass spectrometry (SPME/GC–MS) were also used to check for the formation of chlorinated and other toxic by-products; at the conditions in question, the presence of such compounds was not confirmed.     

Protein‐Specific,Multicolor and 3D STED Imaging in Cells with DNA‐Labeled Antibodies

Photobleaching is a major challenge in fluorescence microscopy, in particular if high excitation light intensities are used. Signal‐to‐noise and spatial resolution may be compromised, which limits the amount of information that can be extracted from an image. Photobleaching can be bypassed by using exchangeable labels, which transiently bind to and dissociate from a target, thereby replenishing the destroyed labels with intact ones from a reservoir. Here, we demonstrate confocal and STED microscopy with short, fluorophore‐labeled oligonucleotides that transiently bind to complementary oligonucleotides attached to protein‐specific antibodies. The constant exchange of fluorophore labels in DNA‐based STED imaging bypasses photobleaching that occurs with covalent labels. We show that this concept is suitable for targeted, two‐color STED imaging of whole cells.