Deep Local Minima Research Articles

Quantum optimization algorithm based on multistep quantum computation

We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation, and apply the algorithm for solving optimization problems with continuous variables. We construct the state space of the problem by discretizing the variables of the problem, and divide the state space according to the function values of the vectors of the state space. By comparing the function values of the vectors with a series of threshold values in decreasing order, we construct a sequence of Hamiltonians where the search space of a Hamiltonian is nested in that of the previous one. By applying a multistep quantum computation process for finding the ground state of the last Hamiltonian, the optimal vector of the state space of the problem is located in a small search space and can be determined efficiently. One of the most difficult problems in optimization algorithms is that a trial vector is trapped in a deep local minimum while the global minimum is missed, this problem can be alleviated in our algorithm and the run time is proportional to the number of the steps of the algorithm, provided that the reduction rate of the search spaces is polynomial large. We discuss the implementation of the algorithm and test the algorithm for some test functions.

Molecular Modeling of Cardiac Sodium Channel with Mexiletine.

A sodium channel blocker mexiletine (MEX) is used to treat chronic pain, myotonia and some arrhythmias. Mutations in the pore domain (PD) of voltage-gated sodium channels differently affect tonic block (TB) and use-dependent block (UDB) by MEX. Previous studies identified several MEX-sensing residues in the hNav1.5 channel and demonstrated that the channel block by MEX increases with activation of the voltage-sensing domain III (VSDIII), whereas MEX stabilizes the activated state of VSDIII. Structural rationales for these observations are unclear. Here, Monte Carlo (MC) energy minimizations were used to dock MEX and its more potent analog, Thio-Me2, into the hNav1.5 cryo-EM structure with activated VSDs and presumably inactivated PD. Computations yielded two ensembles of ligand binding poses in close contacts with known MEX-sensing residues in helices S6III, S6IV and P1IV. In both ensembles, the ligand NH3 group approached the cation-attractive site between backbone carbonyls at the outer-pore bottom, while the aromatic ring protruded ether into the inner pore (putative UDB pose) or into the III/IV fenestration (putative TB pose). In silico deactivation of VSDIII shifted helices S4-S5III, S5III, S6III and S6IV and tightened the TB site. In a model with activated VSDIII and three resting VSDs, MC-minimized energy profile of MEX pulled from the TB site towards lipids shows a deep local minimum due to interactions with 11 residues in S5III, P1III, S6III and S6IV. The minimum may correspond to an interim binding site for MEX in the hydrophobic path to the TB site along the lipid-exposed sides of repeats III and IV where 15 polar and aromatic residues would attract cationic blockers. The study explains numerous experimental data and suggests the mechanism of allosteric modification of the MEX binding site by VSDIII.

Universal hidden order in amorphous cellular geometries

Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties.

Electrically controlled dc and ac transport in bilayer WSe2

We investigate quantum transport in a bilayer ${\mathrm{WSe}}_{2}$ in the presence of an external potential $V$ and interlayer coupling. The dc and ac conductivities are evaluated in the framework of linear response theory. As functions of the Fermi energy, the dc ones exhibit a nonmonotonic behavior with a flat region in the band gap. A deep local minimum is visible in spin-Hall conductivity near the top of the valence band as a consequence of a large valence band splitting. On the other hand, the ac spin- and valley-Hall conductivities, as functions of the frequency, show two opposite peaks near the top of the valence band. The spin-Hall conductivity exhibits a minimum value at $V=0$ whereas the valley-Hall conductivity decreases monotonically upon varying $V$ from negative to positive values. Furthermore, we evaluate the power absorption spectrum and assess its dependence on the spin and valley degrees of freedom. The results are pertinent to the development of electrically controlled spintronic and valleytronic devices based on bilayer ${\mathrm{WSe}}_{2}$ and other group VI semiconductors.

Interpretation of a Variable Reflection Nebula Associated with HBC 340 and HBC 341 in NGC 1333

Abstract We present multi-epoch, R-band imaging obtained from the Palomar Transient Factory of a small, fan-shaped reflection nebula in NGC 1333 that experiences prominent brightness fluctuations. Photometry of HBC 340 (K7e) and HBC 341 (M5e), a visual pair of late-type, young stellar objects lying near the apex of the nebula, demonstrates that while both are variable, the former has brightened by more than two magnitudes following a deep local minimum in 2014 September. Keck high-dispersion (R ∼ 45,000–66,000), optical spectroscopy of HBC 340 suggests that the protostar is a spectroscopic binary (HBC 340Aa + HBC 340Ab). Both HBC 340 and HBC 341 exhibit strong Hα and forbidden line emission, consistent with accretion and outflow. We conclude that the brightness fluctuations in the reflection nebula represent light echos produced by varying incident radiation emanating from HBC 340. The short-term variability observed in the protostar is attributed to irregular accretion activity, while correlated, dipping behavior on a several hundred day timescale may be due to eclipse-like events caused by orbiting circumstellar material. Archival Hubble Space Telescope imaging of the region reveals a second, faint (F814W ∼ 20.3 mag) companion to HBC 340 that lies 1.″02 (∼235 au) east of the protostar. If associated, this probable substellar mass object (20–50 Jupiter masses), HBC 340B, is likely unrelated to the observed brightness variations. The sustained brightening of HBC 340 since late 2014 can be explained by an EXor-like outburst, the recovery from a long duration eclipse event caused by obscuring circumstellar dust, or by the gradual removal of extincting material from along the line of sight. Our analysis here favors one of the extinction scenarios.

Inclusion of the fitness sharing technique in an evolutionary algorithm to analyze the fitness landscape of the genetic code adaptability

BackgroundThe canonical code, although prevailing in complex genomes, is not universal. It was shown the canonical genetic code superior robustness compared to random codes, but it is not clearly determined how it evolved towards its current form.The error minimization theory considers the minimization of point mutation adverse effect as the main selection factor in the evolution of the code. We have used simulated evolution in a computer to search for optimized codes, which helps to obtain information about the optimization level of the canonical code in its evolution.A genetic algorithm searches for efficient codes in a fitness landscape that corresponds with the adaptability of possible hypothetical genetic codes. The lower the effects of errors or mutations in the codon bases of a hypothetical code, the more efficient or optimal is that code.The inclusion of the fitness sharing technique in the evolutionary algorithm allows the extent to which the canonical genetic code is in an area corresponding to a deep local minimum to be easily determined, even in the high dimensional spaces considered.ResultsThe analyses show that the canonical code is not in a deep local minimum and that the fitness landscape is not a multimodal fitness landscape with deep and separated peaks. Moreover, the canonical code is clearly far away from the areas of higher fitness in the landscape.ConclusionsGiven the non-presence of deep local minima in the landscape, although the code could evolve and different forces could shape its structure, the fitness landscape nature considered in the error minimization theory does not explain why the canonical code ended its evolution in a location which is not an area of a localized deep minimum of the huge fitness landscape.

Giant Rashba Splitting in CH_{3}NH_{3}PbBr_{3} Organic-Inorganic Perovskite.

As they combine decent mobilities with extremely long carrier lifetimes, organic-inorganic perovskites open a whole new field in optoelectronics. Measurements of their underlying electronic structure, however, are still lacking. Using angle-resolved photoelectron spectroscopy, we measure the valence band dispersion of single-crystal CH_{3}NH_{3}PbBr_{3}. The dispersion of the highest energy band is extracted applying a modified leading edge method, which accounts for the particular density of states of organic-inorganic perovskites. The surface Brillouin zone is consistent with bulk-terminated surfaces both in the low-temperature orthorhombic and the high-temperature cubic phase. In the low-temperature phase, we find a ring-shaped valence band maximum with a radius of 0.043 Å^{-1}, centered around a 0.16eV deep local minimum in the dispersion of the valence band at the high-symmetry point. Intense circular dichroism is observed. This dispersion is the result of strong spin-orbit coupling. Spin-orbit coupling is also present in the room-temperature phase. The coupling strength is one of the largest ones reported so far.

Efficient implementation and application of the artificial bee colony algorithm to low-dimensional optimization problems

We adapt a swarm-intelligence-based optimization method (the artificial bee colony algorithm, ABC) to enhance its parallel scaling properties and to improve the escaping behavior from deep local minima. Specifically, we apply the approach to the geometry optimization of Lennard-Jones clusters. We illustrate the performance and the scaling properties of the parallelization scheme for several system sizes (5–20 particles). Our main findings are specific recommendations for ranges of the parameters of the ABC algorithm which yield maximal performance for Lennard-Jones clusters and Morse clusters. The suggested parameter ranges for these different interaction potentials turn out to be very similar; thus, we believe that our reported values are fairly general for the ABC algorithm applied to chemical optimization problems.

A Robust Method for Shape from Shading Using Genetic Algorithm Based on Matrix Code

In this paper, a method for reconstructing a 3-D shape of an object from a 2-D shading image using a Genetic Algorithm (GA), which is an optimizing technique based on mechanisms of natural selection. The 3D-shape is recovered through the analysis of the gray levels in a single image of the scene. This problem is ill-posed except if some additional assumptions are made. In the proposed method, shape from shading is addressed as an energy minimization problem. The traditional deterministic approach provides efficient algorithms to solve this problem in terms of time but reaches its limits since the energy associated with shape from shading can contain multiple deep local minima. Genetic Algorithm is used as an alternative approach which is efficient at exploring the entire search space. The Algorithm is tested in both synthetic and real image and is found to perform accurate and efficient results.

From quantum chemical formation free energies to evaporation rates

Abstract. Atmospheric new particle formation is an important source of atmospheric aerosols. Large efforts have been made during the past few years to identify which molecules are behind this phenomenon, but the actual birth mechanism of the particles is not yet well known. Quantum chemical calculations have proven to be a powerful tool to gain new insights into the very first steps of particle formation. In the present study we use formation free energies calculated by quantum chemical methods to estimate the evaporation rates of species from sulfuric acid clusters containing ammonia or dimethylamine. We have found that dimethylamine forms much more stable clusters with sulphuric acid than ammonia does. On the other hand, the existence of a very deep local minimum for clusters with two sulfuric acid molecules and two dimethylamine molecules hinders their growth to larger clusters. These results indicate that other compounds may be needed to make clusters grow to larger sizes (containing more than three sulfuric acid molecules).

Multiple native states reveal persistent ruggedness of an RNA folding landscape

According to the “thermodynamic hypothesis”, the sequence of a biological macromolecule defines its folded, active structure as a global energy minimum on the folding landscape.1,2 But the enormous complexity of folding landscapes of large macromolecules raises a question: Is there indeed a unique global energy minimum corresponding to a unique native conformation, or are there deep local minima corresponding to alternative active conformations?3 Folding of many proteins is well described by two-state models, leading to highly simplified representations of protein folding landscapes with a single native conformation.4,5 Nevertheless, accumulating experimental evidence suggests a more complex topology of folding landscapes with multiple active conformations that can take seconds or longer to interconvert.6,7,8 Here we employ single molecule experiments to demonstrate that an RNA enzyme folds into multiple distinct native states that interconvert much slower than the time scale of catalysis. These data demonstrate that the severe ruggedness of RNA folding landscapes extends into conformational space occupied by native conformations.

Hybrid parallel tempering and simulated annealing method

In this paper, we propose a new hybrid scheme of parallel tempering and simulated annealing (hybrid PT/SA). Within the hybrid PT/SA scheme, a composite system with multiple conformations is evolving in parallel on a temperature ladder with various transition step sizes. The simulated annealing (SA) process uses a cooling scheme to decrease the temperature values in the temperature ladder to the target temperature. The parallel tempering (PT) scheme is employed to reduce the equilibration relaxation time of the composite system at a particular temperature ladder configuration in the SA process. The hybrid PT/SA method reduces the waiting time in deep local minima and thus leads to a more efficient sampling capability on high-dimensional complicated objective function landscapes. Compared to the approaches PT and parallel SA with the same temperature ladder, transition step sizes, and cooling scheme (parallel SA) configurations, our preliminary results obtained with the hybrid PT/SA method confirm the expected improvements in simulations of several test objective functions, including the Rosenbrock’s function and the “rugged” funnel-like function, and several instantiations of the traveling salesman problem. The hybrid PT/SA may have slower convergence than genetic algorithms (GA) with good crossover heuristics, but it has the advantage of tolerating “bad” initial values and displaying robust sampling capability, even in the absence of additional information. Moreover, the hybrid PT/SA has natural parallelization potential.

The hyperspherical acceleration effect particle swarm optimizer

This paper proposes Hyperspherical Acceleration Effect Particle Swarm Optimization (HAEPSO) for optimizing complex, multi-modal functions. The HAEPSO algorithm finds the particles that are trapped in deep local minima and accelerates them in the direction of global optima. This novel technique improves the efficiency by manipulating PSO parameters in hyperspherical coordinate system. Performance comparisons of HAEPSO are provided against different PSO variants on standard benchmark functions. Results indicate that the proposed algorithm gives robust results with good quality solution and faster convergence. The proposed algorithm is an effective technique for solving complex, higher dimensional multi-modal functions.

Improved transition path sampling methods for simulation of rare events

The free energy surfaces of a wide variety of systems encountered in physics, chemistry, and biology are characterized by the existence of deep minima separated by numerous barriers. One of the central aims of recent research in computational chemistry and physics has been to determine how transitions occur between deep local minima on rugged free energy landscapes, and transition path sampling (TPS) Monte-Carlo methods have emerged as an effective means for numerical investigation of such transitions. Many of the shortcomings of TPS-like approaches generally stem from their high computational demands. Two new algorithms are presented in this work that improve the efficiency of TPS simulations. The first algorithm uses biased shooting moves to render the sampling of reactive trajectories more efficient. The second algorithm is shown to substantially improve the accuracy of the transition state ensemble by introducing a subset of local transition path simulations in the transition state. The system considered in this work consists of a two-dimensional rough energy surface that is representative of numerous systems encountered in applications. When taken together, these algorithms provide gains in efficiency of over two orders of magnitude when compared to traditional TPS simulations.

Physicochemical and physiological basis of dichromatic colour

Out of three perceptual characteristics of the colour of any substance, the hue depends mostly on the spectral properties of a substance, while the brightness and saturation depend also on the concentration of a substance and its thickness. Here, we report that evident change of the hue of the colour (i.e., from green to red) is due to a change in concentration or the thickness of a layer in some exceptional substances such as pumpkin seed oil or an aqueous solution of bromophenol blue. In some regions of Central Europe, salad dressing is made preferably with the pumpkin seed oil, which has a strong characteristic nut-like taste and remarkable properties of the colour: it appears red in a bottle, but green when served as a salad dressing. The colour of the pumpkin seed oil was previously described as brownish yellow, dark green, dark green to red ochre or dark reddish brown to light yellow green. We elucidated the physicochemical and physiological basis of such dichromatism by Beer-Lambert law and by the characteristics of human colour perception. Our concept was corroborated by the outcome of calculations of colour from spectral properties using colour matching functions. We found that dichromatism is observed if the absorption spectrum of any substance has at least two local minima: one wide but shallow and one narrow but deep local minimum.

The island confinement method for reducing search space in local search methods

Typically local search methods for solving constraint satisfaction problems such as GSAT, WalkSAT, DLM, and ESG treat the problem as an optimisation problem. Each constraint contributes part of a penalty function in assessing trial valuations. Local search examines the neighbours of the current valuation, using the penalty function to determine a "better" neighbour valuation to move to, until finally a solution which satisfies all the constraints is found. In this paper we investigate using some of the constraints as "hard" constraints, that are always satisfied by every trial valuation visited, rather than as part of a penalty function. In this way these constraints reduce the possible neighbours in each move and also the overall search space. The treating of some constraints as hard requires that the space of valuations that are satisfied is "connected" in order to guarantee that a solution can be found from any starting position within the region; thus the concept of islands and the name "island confinement method" arises. Treating some constraints as hard provides new difficulties for the search mechanism since the search space becomes more jagged, and there are more deep local minima. A new escape strategy is needed. To demonstrate the feasibility and generality of our approach, we show how the island confinement method can be incorporated in, and significantly improve, the search performance of two successful local search procedures, DLM and ESG, on SAT problems arising from binary CSPs.

Driven polymer transport through a nanopore controlled by a rotating electric field: Off-lattice computer simulations

The driven translocation kinetics of a single strand polynucleotide chain through a nanopore is studied using off-lattice Monte Carlo simulations, by which the authors demonstrate a novel method in controlling the driven polymer transport through a nanopore by a rotating electric field. The recorded time series of blockade current from the driven polynucleotide transport are used to determine the sequence of polynucleotides by implementing a modified Monte Carlo algorithm, in which the energy landscape paving technique is incorporated to avoid trapping at deep local minima. It is found that only six-time series of block current are required to completely determine the polynucleotide sequence if the average missing rate (AMR) of current signals in these time series is smaller than 20%. For those time series with AMR greater than 20%, the error rate in sequencing an unknown polynucleotide decreases rapidly by increasing the number of time series. To find the most appropriate experimental conditions, the authors have investigated the dependence of AMR of current signals and qualified rate of measured time series of blockade current on various controllable experimental variables.

Structure and Dynamics of the Aniline−Argon Complex as Derived from its Potential Energy Surface

The structure and dynamics of the van der Waals (vdW) complex of aniline (An) with argon (Ar) are studied using ab initio methods. The inversion potential of the aniline-argon (AnAr) complex perturbed by the weak vdW interaction is calculated taking into account subtle corrections from the zero-point energy of the vdW modes and from the frequency shifts of the An normal modes modified by the complexation. The intermolecular potential energy surface (PES) of the AnAr complex is determined by performing a large-scale computation of the interaction energy and the fitting of the analytical many-body expansion to the set of single-point interaction energies. The PES determined shows two deep local minima corresponding to the anti and syn AnAr conformers. The difference in the energies of these two minima is only 15 cm-1, but it is sufficient to localize the inversion wave functions and to form the two conformers. In the conformer anti (syn) of lower (higher) energy, Ar is bound to the An ring opposite (adjacent) the amino-hydrogens. In the additional local minima higher in energy, Ar approaches the aniline ring between the C-H bonds near its plane. An additional local minimum is located opposite of nitrogen between the two N-H bonds. The high-energy minima are, however, too flat to form stable conformers. The perturbation of the interaction of Ar with the phenyl ring by the NH2 group is described by the vdW hole, which is responsible for unusually strong intermode mixing in the excited intermolecular vibrational states. The analysis of these states calculated for the ground (S0) as well as the first excited electronic state (S1) resolves difficulties faced earlier with the assignment of the observed vibronic bands of AnAr.

A HYBRID NEURAL LEARNING ALGORITHM USING EVOLUTIONARY LEARNING AND DERIVATIVE FREE LOCAL SEARCH METHOD

In this paper we investigate a hybrid model based on the Discrete Gradient method and an evolutionary strategy for determining the weights in a feed forward artificial neural network. Also we discuss different variants for hybrid models using the Discrete Gradient method and an evolutionary strategy for determining the weights in a feed forward artificial neural network. The Discrete Gradient method has the advantage of being able to jump over many local minima and find very deep local minima. However, earlier research has shown that a good starting point for the discrete gradient method can improve the quality of the solution point. Evolutionary algorithms are best suited for global optimisation problems. Nevertheless they are cursed with longer training times and often unsuitable for real world application. For optimisation problems such as weight optimisation for ANNs in real world applications the dimensions are large and time complexity is critical. Hence the idea of a hybrid model can be a suitable option. In this paper we propose different fusion strategies for hybrid models combining the evolutionary strategy with the discrete gradient method to obtain an optimal solution much quicker. Three different fusion strategies are discussed: a linear hybrid model, an iterative hybrid model and a restricted local search hybrid model. Comparative results on a range of standard datasets are provided for different fusion hybrid models.

Hybridization of Neural Learning Algorithms Using Evolutionary and Discrete Gradient Approaches

In this study we investigated a hybrid model based on the Discrete Gradient method and an evolutionary strategy for determining the weights in a feed forward artificial neural network. Also we discuss different variants for hybrid models using the Discrete Gradient method and an evolutionary strategy for determining the weights in a feed forward artificial neural network. The Discrete Gradient method has the advantage of being able to jump over many local minima and find very deep local minima. However, earlier research has shown that a good starting point for the discrete gradient method can improve the quality of the solution point. Evolutionary algorithms are best suited for global optimisation problems. Nevertheless they are cursed with longer training times and often unsuitable for real world application. For optimisation problems such as weight optimisation for ANNs in real world applications the dimensions are large and time complexity is critical. Hence the idea of a hybrid model can be a suitable option. In this study we propose different fusion strategies for hybrid models combining the evolutionary strategy with the discrete gradient method to obtain an optimal solution much quicker. Three different fusion strategies are discussed: a linear hybrid model, an iterative hybrid model and a restricted local search hybrid model. Comparative results on a range of standard datasets are provided for different fusion hybrid models.