On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Eutrophication causes speciation reversal in whitefish adaptive radiations

Species diversity can be lost through two different but potentially interacting extinction processes: demographic decline and speciation reversal through introgressive hybridization. To investigate the relative contribution of these processes, we analysed historical and contemporary data of replicate whitefish radiations from 17 pre-alpine European lakes and reconstructed changes in genetic species differentiation through time using historical samples. Here we provide evidence that species diversity evolved in response to ecological opportunity, and that eutrophication, by diminishing this opportunity, has driven extinctions through speciation reversal and demographic decline. Across the radiations, the magnitude of eutrophication explains the pattern of species loss and levels of genetic and functional distinctiveness among remaining species. We argue that extinction by speciation reversal may be more widespread than currently appreciated. Preventing such extinctions will require that conservation efforts not only target existing species but identify and protect the ecological and evolutionary processes that generate and maintain species.

Vasectomy reversal with ultrasonography-guided spermatic cord block

Study Type--Therapy (case series) Level of Evidence 4. What's known on the subject? and What does the study add? Vasectomy reversal is often performed in general or neuraxial anaesthesia. Even though the site of vasectomy reversal is easily amenable to regional/local anaesthesia, spermatic cord blocks are rarely applied because of their risk of vascular damage within the spermatic cord. Recently, we described the technique of ultrasonography (US)-guided spermatic cord block for scrotal surgery, which, thanks to the US guidance, at the same time avoids the risk of vascular damage of blindly performed injections and the risks of general and neuraxial anaesthesia. Vasectomy reversal can easily be done in regional anaesthesia with the newly described technique of US-guided spermatic cord block without the risks of vascular damage by a blindly performed injection and the risks of standard general and neuraxial anaesthesia. In addition, this technique grants long-lasting postoperative pain relief and patients recover more quickly. Microsurgical conditions are excellent and patient satisfaction is high. Thanks to these advantages, more patients undergoing vasectomy reversal might avoid general or neuraxial anaesthesia.

A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

Genomic signatures of relaxed disruptive selection associated with speciation reversal in whitefish

Background: Speciation reversal: the erosion of species differentiation via an increase in introgressive hybridization due to the weakening of previously divergent selection regimes, is thought to be an important, yet poorly understood, driver of biodiversity loss. Our study system, the Alpine whitefish (Coregonus spp.) species complex is a classic example of a recent postglacial adaptive radiation: forming an array of endemic lake flocks, with the independent origination of similar ecotypes among flocks. However, many of the lakes of the Alpine radiation have been seriously impacted by anthropogenic nutrient enrichment, resulting in a collapse in neutral genetic and phenotypic differentiation within the most polluted lakes. Here we investigate the effects of eutrophication on the selective forces that have shaped this radiation, using population genomics. We studied eight sympatric species assemblages belonging to five independent parallel adaptive radiations, and one species pair in secondary contact. We used AFLP markers, and applied FST outlier (BAYESCAN, DFDIST) and logistic regression analyses (MATSAM), to identify candidate regions for disruptive selection in the genome and their associations with adaptive traits within each lake flock. The number of outlier and adaptive trait associated loci identified per lake were then regressed against two variables (historical phosphorus concentration and contemporary oxygen concentration) representing the strength of eutrophication. Results: Whilst we identify disruptive selection candidate regions in all lake flocks, we find similar trends, across analysis methods, towards fewer disruptive selection candidate regions and fewer adaptive trait/candidate loci associations in the more polluted lakes. Conclusions: Weakened disruptive selection and a concomitant breakdown in reproductive isolating mechanisms in more polluted lakes has lead to increased gene flow between coexisting Alpine whitefish species. We hypothesize that the resulting higher rates of interspecific recombination reduce either the number or extent of genomic islands of divergence surrounding loci evolving under disruptive natural selection. This produces the negative trend seen in the number of selection candidate loci recovered during genome scans of whitefish species flocks, with increasing levels of anthropogenic eutrophication: as the likelihood decreases that AFLP restriction sites will fall within regions of heightened genomic divergence and therefore be classified as FST outlier loci. This study explores for the first time the potential effects of human-mediated relaxation of disruptive selection on heterogeneous genomic divergence between coexisting species.

Real-time dynamics of open quantum spin systems driven by dissipative processes

We study the real-time evolution of large open quantum spin systems in two spatial dimensions, whose dynamics is entirely driven by a dissipative coupling to the environment. We consider different dissipative processes and investigate the real-time evolution from an ordered phase of the Heisenberg or XY model towards a disordered phase at late times, disregarding unitary Hamiltonian dynamics. The corresponding Kossakowski-Lindblad equation is solved via an efficient cluster algorithm. We find that the symmetry of the dissipative process determines the time scales, which govern the approach towards a new equilibrium phase at late times. Most notably, we find a slow equilibration if the dissipative process conserves any of the magnetization Fourier modes. In these cases, the dynamics can be interpreted as a diffusion process of the conserved quantity.

The Effects of Density, Spatial Pattern, and Competitive Symmetry on Size Variation in Simulated Plant Populations

Patterns of size inequality in crowded plant populations are often taken to be indicative of the degree of size asymmetry of competition, but recent research suggests that some of the patterns attributed to size‐asymmetric competition could be due to spatial structure. To investigate the theoretical relationships between plant density, spatial pattern, and competitive size asymmetry in determining size variation in crowded plant populations, we developed a spatially explicit, individual‐based plant competition model based on overlapping zones of influence. The zone of influence of each plant is modeled as a circle, growing in two dimensions, and is allometrically related to plant biomass. The area of the circle represents resources potentially available to the plant, and plants compete for resources in areas in which they overlap. The size asymmetry of competition is reflected in the rules for dividing up the overlapping areas. Theoretical plant populations were grown in random and in perfectly uniform spatial patterns at four densities under size‐asymmetric and size‐symmetric competition. Both spatial pattern and size asymmetry contributed to size variation, but their relative importance varied greatly over density and over time. Early in stand development, spatial pattern was more important than the symmetry of competition in determining the degree of size variation within the population, but after plants grew and competition intensified, the size asymmetry of competition became a much more important source of size variation. Size variability was slightly higher at higher densities when competition was symmetric and plants were distributed nonuniformly in space. In a uniform spatial pattern, size variation increased with density only when competition was size asymmetric. Our results suggest that when competition is size asymmetric and intense, it will be more important in generating size variation than is local variation in density. Our results and the available data are consistent with the hypothesis that high levels of size inequality commonly observed within crowded plant populations are largely due to size‐asymmetric competition, not to variation in local density.