Enhanced angular tolerance of resonant waveguide grating reflectors

We introduce an approach to enhance the angular tolerance of resonant waveguide gratings by stacking two resonant structures on top of each other. It is shown that reflectivities close to unity can be retrieved over the entire angular spectrum by a double T-shaped grating configuration. Although a combination of silicon as the high-index and diamond as the low-index material is considered, the principles of our new approach can also be used to realize monolithic silicon structures with similar properties. We illustrate that the functionality of the device can be understood by a decomposition into separated elements. Our approach might have compelling applications as new diffractive-reflective optical components with low-coating thermal noise in the field of high-precision metrology.     

Widely tunable monolithic narrowband grating filter for near-infrared radiation

We propose a monolithic narrowband guided-mode grating filter in fused silica that is widely tunable in the near-IR wavelength region. Based on a recently demonstrated approach for a monolithic reflector comprising an encapsulated grating, we theoretically investigate such a device by means of rigorous modeling aimed at a narrow linewidth. It is demonstrated that upon a spatial variation of the filter's grating period its resonance wavelength can be tuned in a remarkably wide range of near-IR radiation with 800 nm<λ(res)< 1600 nm by translating the laser beam relative to the grating area. The filter performance in terms of linewidth and contrast is essentially preserved over the entire tuning interval.     

Loss analysis and increasing of the fabrication tolerance of resonant coupling by tapering the mode beating section

The film mode matching method was used to analyze the inter waveguide coupling losses in a passive asymmetric twin waveguide caused by waveguide width and refractive index variation for both resonant and adiabatic coupling at a wavelength of 1,550 nm. The reasons for power losses are shown. It is demonstrated that tapering the mode beating section of the resonant coupler can increase the fabrication tolerance of resonant coupling without increasing the coupling length.     

New Roses: Simple Symmetric Venn Diagrams with 11 and 13 Curves

A symmetric \(n\) -Venn diagram is one that is invariant under \(n\) -fold rotation, up to a relabeling of curves. A simple \(n\) -Venn diagram is an \(n\) -Venn diagram in which at most two curves intersect at any point. In this paper, we introduce a new property of Venn diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to diagrams with crosscut symmetry, we found many simple symmetric Venn diagrams with 11 curves. The question of the existence of a simple 11-Venn diagram has been open since the 1960s. The technique used to find the 11-Venn diagram is extended and a symmetric 13-Venn diagram is also demonstrated.     

Approximability results for the resource-constrained project scheduling problem with a single type of resources

In this paper, we consider the well-known resource-constrained project scheduling problem. We give some arguments that already a special case of this problem with a single type of resources is not approximable in polynomial time with an approximation ratio bounded by a constant. We prove that there exist instances for which the optimal makespan values for the non-preemptive and the preemptive problems have a ratio of O(logn), where n is the number of jobs. This means that there exist instances for which the lower bound of Mingozzi et al. has a bad relative error of O(logn), and the calculation of this bound is an NP-hard problem. In addition, we give a proof that there exists a type of instances for which known approximation algorithms with polynomial time complexity have an approximation ratio of at least equal to $O(\sqrt{n})$ , and known lower bounds have a relative error of at least equal to O(logn). This type of instances corresponds to the single machine parallel-batch scheduling problem 1|p?batch,b=∞|C _max.     

The Structuring Causes of Behavior: Has Dretske Saved Mental Causation?

Fred Dretske’s account of mental causation, developed in Explaining Behavior and defended in numerous articles, is generally regarded as one of the most interesting and most ambitious approaches in the field. According to Dretske, meaning facts, construed historically as facts about the indicator functions of internal states, are the structuring causes of behavior. In this article, we argue that Dretske’s view is untenable: On closer examination, the real structuring causes of behavior turn out to be markedly different from Dretske’s meaning facts. Our argument proceeds in three steps. First, we set forth the problem of meaning individuation: We argue that the proposal that meaning facts are structuring causes of behavior commits Dretske to a very fine-grained individuation of meanings that is deeply counterintuitive. In a second step, we show that even these finely individuated meaning facts cannot do the job that they are supposed to do, since information facts—which are constitutive of, but distinct from Dretske’s meaning facts—are better candidates for the role of structuring causes. Finally, we argue that it is not even information facts, but facts of co-instantiation which are the real structuring causes of behavior. In concluding, we briefly consider the options that are left for Dretske if our arguments succeed.     

60 Years of portfolio optimization: Practical challenges and current trends

The concepts of portfolio optimization and diversification have been instrumental in the development and understanding of financial markets and financial decision making. In light of the 60 year anniversary of Harry Markowitz’s paper “Portfolio Selection,” we review some of the approaches developed to address the challenges encountered when using portfolio optimization in practice, including the inclusion of transaction costs, portfolio management constraints, and the sensitivity to the estimates of expected returns and covariances. In addition, we selectively highlight some of the new trends and developments in the area such as diversification methods, risk-parity portfolios, the mixing of different sources of alpha, and practical multi-period portfolio optimization.     

Dynamic graph generation for the shortest path problem in time expanded networks

In discrete optimization problems the progress of objects over time is frequently modeled by shortest path problems in time expanded networks, but longer time spans or finer time discretizations quickly lead to problem sizes that are intractable in practice. In convex relaxations the arising shortest paths often lie in a narrow corridor inside these networks. Motivated by this observation, we develop a general dynamic graph generation framework in order to control the networks’ sizes even for infinite time horizons. It can be applied whenever objects need to be routed through a traffic or production network with coupling capacity constraints and with a preference for early paths. Without sacrificing any information compared to the full model, it includes a few additional time steps on top of the latest arcs currently in use. This “frontier” of the graphs can be extended automatically as required by solution processes such as column generation or Lagrangian relaxation. The corresponding algorithm is efficiently implementable and linear in the arcs of the non-time-expanded network with a factor depending on the basic time offsets of these arcs. We give some bounds on the required additional size in important special cases and illustrate the benefits of this technique on real world instances of a large scale train timetabling problem.     

Fluorescence detected circular dichroism (FDCD) for supramolecular host–guest complexes

Fluorescence-detected circular dichroism (FDCD) spectroscopy is applied for the first time to supramolecular host–guest and host–protein systems and compared to the more known electronic circular dichroism (ECD). We find that FDCD can be an excellent choice for common supramolecular applications, e.g. for the detection and chirality sensing of chiral organic analytes, as well as for reaction monitoring. Our comprehensive investigations demonstrate that FDCD can be conducted in favorable circumstances at much lower concentrations than ECD measurements, even in chromophoric and auto-emissive biofluids such as blood serum, overcoming the sensitivity limitation of absorbance-based chiroptical spectroscopy. Besides, the combined use of FDCD and ECD can provide additional valuable information about the system, e.g. the chemical identity of an analyte or hidden aggregation phenomena. We believe that simultaneous FDCD- and ECD-based chiroptical characterization of emissive supramolecular systems will be of general benefit for characterizing fluorescent, chiral supramolecular systems due to the higher information content obtained by their combined use.

Fluorescence-detected circular dichroism (FDCD) spectroscopy is applied for the first time to supramolecular host–guest and host–protein systems and compared to the more known electronic circular dichroism (ECD).