Heuristic optimisation in financial modelling

There is a large number of optimisation problems in theoretical and applied finance that are difficult to solve as they exhibit multiple local optima or are not ‘well-behaved’ in other ways (e.g., discontinuities in the objective function). One way to deal with such problems is to adjust and to simplify them, for instance by dropping constraints, until they can be solved with standard numerical methods. We argue that an alternative approach is the application of optimisation heuristics like Simulated Annealing or Genetic Algorithms. These methods have been shown to be capable of handling non-convex optimisation problems with all kinds of constraints. To motivate the use of such techniques in finance, we present several actual problems where classical methods fail. Next, several well-known heuristic techniques that may be deployed in such cases are described. Since such presentations are quite general, we then describe in some detail how a particular problem, portfolio selection, can be tackled by a particular heuristic method, Threshold Accepting. Finally, the stochastics of the solutions obtained from heuristics are discussed. We show, again for the example from portfolio selection, how this random character of the solutions can be exploited to inform the distribution of computations.     

Craig interpolation for semilinear substructural logics

The Craig interpolation property is investigated for substructural logics whose algebraic semantics are varieties of semilinear (subdirect products of linearly ordered) pointed commutative residuated lattices. It is shown that Craig interpolation fails for certain classes of these logics with weakening if the corresponding algebras are not idempotent. A complete characterization is then given of axiomatic extensions of the “R‐mingle with unit” logic (corresponding to varieties of Sugihara monoids) that have the Craig interpolation property. This latter characterization is obtained using a model‐theoretic quantifier elimination strategy to determine the varieties of Sugihara monoids admitting the amalgamation property.     

Cavitand-functionalized porous silicon as an active surface for organophosphorus vapor detection

This paper reports on the preparation of a porous silicon-based material covalently functionalized with cavitand receptors suited for the detection of organophosphorus vapors. Two different isomeric cavitands, both containing one acid group at the upper rim, specifically designed for covalent anchoring on silicon, were grafted on H-terminated porous silicon (PSi) by thermal hydrosilylation. The covalently functionalized surfaces and their complexation properties were characterized by combining different analytical techniques, namely X-ray photoelectron spectroscopy (XPS), Fourier transform infrared spectroscopy (FTIR), and mass spectroscopy analysis coupled with thermal desorption experiments. Complexation experiments were performed by exposing both active surfaces and a control surface consisting of PSi functionalized with a structurally similar but inactive methylene-bridged cavitand (MeCav) to dimethyl methylphosphonate (DMMP) vapors. Comparison between active and inactive surfaces demonstrated the recognition properties of the new surfaces. Finally, the nature of the involved interactions, the energetic differences between active and inactive surfaces toward DMMP complexation, and the comparison with a true nerve gas agent (sarin) were studied by DFT modeling. The results revealed the successful grafting reaction, the specific host-guest interactions of the PSi-bonded receptors, and the reversibility of the guest complexation.     

Time-division multiplexing of the orbital angular momentum of light

We present an optical setup for generating a sequence of light pulses in which the orbital angular momentum (OAM) degree of freedom is correlated with the temporal one. The setup is based on a single q plate within a ring optical resonator. By this approach, we demonstrate the generation of a train of pulses carrying increasing values of OAM, or, alternatively, of a controlled temporal sequence of pulses having prescribed OAM superposition states. Finally, we exhibit an "OAM-to-time conversion" apparatus that divides different input OAM states into different time bins. The latter application provides a simple approach to digital spiral spectroscopy of pulsed light.     

A general stereoselective enamine mediated alkylation of α-substituted aldehydes

We herein present a general enamine-mediated α-alkylation of α-substituted aldehydes with carbenium ions for the stereoselective construction of quaternary stereogenic centers.     

A versatile strategy for tuning the color of electrochemiluminescence using silica nanoparticles

Colour emission of core-shell silica-PEG nanoparticles in water is tuned with an electrochemically induced energy transfer approach. The lack of solubility problems, side electrochemical reactions involving donors and acceptors within the nanoparticle, and the possibility of using many classes of dyes in ECL applications confirm the validity of this strategy.     

Effect of organic matter on the in vitro photoeradication of Pseudomonas aeruginosa by means of a cationic tetraaryl-porphyrin

Photodynamic therapy is emerging as an antimicrobial alternative approach; the concomitant presence of a photosensitizer (PS), O(2) and visible light induces lethal oxidative damages to bacterial cells. Among Gram-negative bacteria, Pseudomonas aeruginosa seems to be one of the least susceptible to photodynamic treatment. In this study, we evaluated the influence of several experimental conditions on photoeradication of a planktonic culture of P. aeruginosa PAO1 by means of a tetracationic meso-arylsubstituted porphyrin (RM24). Our findings suggest that the photo-oxidative stress induced by RM24 is strictly correlated to the amount of PS bound to the cells that in turn decreases with the increasing concentrations of organic compounds in the medium. The photoeradication is dependent on PS concentrations, cellular density and light dose. RM24 was able to induce oxidative stress by means of singlet oxygen formation, although ROS formation cannot be ruled out. The standardized experimental conditions of the photospot test allowed us to evidence intraspecific PDT sensitivity differences among three strains of P. aeruginosa.     

Reference frames in harmonic coordinates: geometric and physical aspects

This work is focused on the geometrical and physical characteristics of the class of reference frames associated to harmonic coordinates. Precisely, we express in relative form the harmonicity conditions and consider the so called ??spatially harmonicity?? of a reference frame in spherical symmetry. The initial data problem is then analyzed in polar coordinates and the obtained results are applied to special cases of exact solutions.     

A column generation heuristic for the two-dimensional two-staged guillotine cutting stock problem with multiple stock size

We consider a two-dimensional cutting stock problem where stock of different sizes is available, and a set of rectangular items has to be obtained through two-staged guillotine cuts. We propose a heuristic algorithm, based on column generation, which requires as its subproblem the solution of a two-dimensional knapsack problem with two-staged guillotines cuts. A further contribution of the paper consists in the definition of a mixed integer linear programming model for the solution of this knapsack problem, as well as a heuristic procedure based on dynamic programming. Computational experiments show the effectiveness of the proposed approach, which obtains very small optimality gaps and outperforms the heuristic algorithm proposed by Cintra et al. [3].     

Fredholm Integral Equations of the First Kind and Topological Information Theory

The Fredholm integral equations of the first kind are a classical example of ill-posed problem in the sense of Hadamard. If the integral operator is self-adjoint and admits a set of eigenfunctions, then a formal solution can be written in terms of eigenfunction expansions. One of the possible methods of regularization consists in truncating this formal expansion after restricting the class of admissible solutions through a-priori global bounds. In this paper we reconsider various possible methods of truncation from the viewpoint of the ${\varepsilon}$ -coverings of compact sets.