On good encodings for quantum annealer and digital optimization solvers.

Several optimization solvers inspired by quantum annealing have been recently developed, either running on actual quantum hardware or simulating it on traditional digital computers. Industry and academics look at their potential in solving hard combinatorial optimization problems. Formally, they provide heuristic solutions for Ising models, which are equivalent to quadratic unconstrained binary optimization (QUBO). Constraints on solutions feasibility need to be properly encoded. We experiment on different ways of performing such an encoding. As benchmark we consider the cardinality constrained quadratic knapsack problem (CQKP), a minimal extension of QUBO with one inequality and one equality constraint. We consider different strategies of constraints penalization and variables encoding. We compare three QUBO solvers: quantum annealing on quantum hardware (D-Wave Advantage), probabilistic algorithms on digital hardware and mathematical programming solvers. We analyze their QUBO resolution quality and time, and the persistence values extracted in the quantum annealing sampling process. Our results show that a linear penalization of CQKP inequality improves current best practice. Furthermore, using such a linear penalization, persistence values produced by quantum hardware in a generic way allow to match a specific CQKP metric from literature. They are therefore suitable for general purpose variable fixing in core algorithms for combinatorial optimization.

On the impact of resource relocation in facing health emergencies.

The outbreak of SARS-CoV-2 and the corresponding surge in patients with severe symptoms of COVID-19 put a strain on health systems, requiring specialized material and human resources, often exceeding the locally available ones. Motivated by a real emergency response system employed in Northern Italy, we propose a mathematical programming approach for rebalancing the health resources among a network of hospitals in a large geographical area. It is meant for tactical planning in facing foreseen peaks of patients requiring specialized treatment. Our model has a clean combinatorial structure. At the same time, it considers the handling of patients by a dedicated home healthcare service, and the efficient exploitation of resource sharing. We introduce mathematical programming heuristic based on decomposition methods and column generation to drive very large-scale neighborhood search. We evaluate its embedding in a multi-objective optimization framework. We experiment on real world data of the COVID-19 in Northern Italy during 2020, whose aggregation and post processing is made openly available to the community. Our approach proves to be effective in tackling realistic instances, thus making it a reliable basis for actual decision support tools.

Molecular dynamics and metadynamics simulations of electrosprayed water nanodroplets including sodium bis(2-ethylhexyl)sulfosuccinate micelles.

The behavior of aqueous solutions of sodium bis(2-ethylhexyl)sulfosuccinate (AOTNa) under conditions of electrospray ionization (ESI) has been investigated by molecular dynamics (MD) and well-tempered metadynamics (WTM) simulations at 300 K and 400 K. We have examined water droplets with initial fixed numbers of water molecules (1000) and AOT- anions (100), and with sodium cations in the range of 70-130. At 300 K, all charged droplets show the water evaporation rate increasing with the absolute value of the initial droplet charge state (Z), accompanied by ejection of an increasing number of solvated sodium ions or by expulsion of AOT- anions depending on the sign of Z and by fragmentation in the case of high |Z|. At 400 K, the water evaporation becomes more rapid and the fission process more extensive. In all cases, the AOTNa molecules, arranged as a direct micelle inside the aqueous system, undergo a rapid inversion in vacuo so that the hydrophilic heads and sodium ions surrounded by water molecules move toward the droplet interior. At the end of the 100-ns MD simulations, some water molecules remain within the aggregates at both temperatures. The subsequent metadynamics simulations accelerate the droplet evolution and show that all systems become anhydrous, in agreement with the experimental results of ESI mass spectrometry. This complete water loss is accompanied by sodium counterion emission for positively charged aggregates at 300 K. The analysis shows how the temperature and droplet charge state affect the populations of the generated surfactant aggregates, providing information potentially useful in designing future ESI experimental conditions.

Structure, stability, and fragmentation of sodium bis(2-ethylhexyl)sulfosuccinate negatively charged aggregates in vacuo by MD simulations.

Negatively charged supramolecular aggregates formed in vacuo by n bis(2-ethylhexyl)sulfosuccinate (AOT(-)) anions and n + n(c) sodium counterions (i.e., [AOT(n) Na(n+nc)](nc)) have been investigated by molecular dynamics (MD) simulations for n = 1 to 20 and n(c) = -1 to -5. By comparing the maximum excess charge values of negatively and positively charged AOTNa aggregates, it is found that the charge storage capability is higher for the latter systems, the difference decreasing as the aggregation number increases. Statistical analysis of physical properties like gyration radii and moment of inertia tensors of aggregates provides detailed information on their structural properties. Even for n(c) = -5, all stable aggregates show a reverse micelle-like structure with an internal core, including sodium counterions and surfactant polar heads, surrounded by an external layer consisting of the surfactant alkyl chains. Interestingly, the reverse micelle-like structure is retained also in proximity of fragmentation. Moreover, the aggregate shapes may be approximated by elongated ellipsoids whose longer axis increases with n and |n(c)|. The fragmentation patterns of a number of these aggregates have also been examined and have been found to markedly depend on the aggregate charge state. The simulated fragmentation patterns of a representative aggregate show good agreement with experimental data obtained using low collision voltages.

Molecular dynamics of electrosprayed water nanodroplets containing sodium bis(2-ethylhexyl)sulfosuccinate.

The behavior of aqueous solutions of sodium bis(2-ethylhexyl)sulfosuccinate (AOTNa) subject to electrospray ionization (ESI) has been investigated by molecular dynamics (MD) simulations at three temperatures (350, 500 and 800 K). We consider several types of water nanodroplets containing AOTNa molecules and composed of a fixed number of water molecules (1000), N(AOT)(0) AOT(-) anions (N(AOT)(0) = 0, 5, 10) and N(Na)(0) sodium ions (N(Na)(0) = 0, 5, 10, 15, 20): in a short time scale (less than 1 ns), the AOTNa molecules, initially forming direct micelles in the interior of the water nanodroplets, are observed in all cases to diffuse nearby the nanodroplet surface, so that the hydrophilic heads and sodium ions become surrounded by water molecules, whereas the alkyl chains lay at the droplet surface. Meanwhile, evaporation of water molecules and of solvated sodium ions occurs, leading to a decrease of the droplet size and charge. At 350 K, no ejection of neutral or charged surfactant molecules is observed, whereas at 500 K, some fragmentation occurs, and at 800 K, this event becomes more frequent. The interplay of all these processes, which depend on the values of temperature, N(AOT)(0) and N(Na)(0) eventually leads to anhydrous charged surfactant aggregates with prevalence of monocharged ones, in agreement with experimental results of ESI mass spectrometry. The quantitative analysis of the MD trajectories allows to evidence molecular details potentially useful in designing future ESI experimental conditions.

Algorithms for the design of maximum hydropathic complementarity molecules.

In this article, we address the problem of designing a string with optimal complementarity properties with respect to another given string according to a given criterion. The motivation comes from a drug design application, in which the complementarity between two sequences (proteins) is measured according to the values of the hydropathic coefficients associated with the sequence elements (amino acids). We present heuristic and exact optimization algorithms, and we report on some computational experiments on amino peptides taken from Semaphorin and human Interleukin-1ß, which have already been investigated in the literature using heuristic algorithms. With our techniques, we proved the optimality of a known solution for Semaphorin-3A, and we discovered several other optimal and near-optimal solutions in a short computing time; we also found in fractions of a second an optimal solution for human interleukin-1ß, whose complementary value is one order of magnitude better than previously known ones. The source code of a prototype C++ implementation of our algorithms is freely available for noncommercial use on the web. As a main result, we showed that in this context mathematical programming methods are more successful than heuristics, such as simulated annealing. Our algorithm unfolds its potential, especially when different measures could be used for scoring peptides, and is able to provide not only a single optimal solution, but a ranking of provable good ones; this ranking can then be used by biologists as a starting basis for further refinements, simulations, or in vitro experiments.

A molecular dynamics study of structure, stability and fragmentation patterns of sodium bis(2-ethylhexyl)sulfosuccinate positively charged aggregates in vacuo.

Positively charged supramolecular aggregates formed in vacuo by n AOTNa (sodium bis(2-ethylhexyl)sulfosuccinate) molecules and n(c) additional sodium ions, i.e. [AOT(n)Na(n+n(c))](n(c)), have been investigated by molecular dynamics (MD) simulations for n = 1-20 and n(c) = 0-5. Statistical analysis of physical quantities like gyration radii, atomic B-factors and moment of inertia tensors provides detailed information on their structural and dynamical properties. Even for n(c) = 5, all stable aggregates show a reverse micelle-like structure with an internal solid-like core including sodium counterions and surfactant polar heads surrounded by an external layer consisting of the surfactant alkyl chains. Moreover, the aggregate shapes may be approximated by rather flat and elongated ellipsoids whose longer axis increases with n and n(c). The fragmentation patterns of a number of these aggregates have also been examined and have been found to markedly depend on the aggregate charge state. In one particular case, for which experimental findings are available in the literature, a good agreement is found with the present fragmentation data.