Low-temperature Simulated Annealing Research Articles

Scatter Search Applied to the Inference of a Development Gene Network

Efficient network inference is one of the challenges of current-day biology. Its application to the study of development has seen noteworthy success, yet a multicellular context, tissue growth, and cellular rearrangements impose additional computational costs and prohibit a wide application of current methods. Therefore, reducing computational cost and providing quick feedback at intermediate stages are desirable features for network inference. Here we propose a hybrid approach composed of two stages: exploration with scatter search and exploitation of intermediate solutions with low temperature simulated annealing. We test the approach on the well-understood process of early body plan development in flies, focusing on the gap gene network. We compare the hybrid approach to simulated annealing, a method of network inference with a proven track record. We find that scatter search performs well at exploring parameter space and that low temperature simulated annealing refines the intermediate results into excellent model fits. From this we conclude that for poorly-studied developmental systems, scatter search is a valuable tool for exploration and accelerates the elucidation of gene regulatory networks.

Atomistic simulations of nanoscale tungsten clusters: From structure and energetics to melting properties

Tungsten (W) dust generated from the interactions between the energetic edge plasma and W-based first-wall materials in future nuclear fusion reactors can significantly affect the plasma stability. As the precursor of dust, nanoscale clusters could aggregate and grow to become dust and are essential to the understanding of dust formation. Here, atomistic simulations have been used to explore the structure, energetics and melting properties of nanoscale W clusters. Comparisons of cluster configurations determined by two methods (high-temperature simulated annealing of a random configuration and low-temperature simulated annealing of a body-centered cubic configuration) reveal that the former technique gives more stable configurations for small clusters (N<77), while the latter method yields energetically more favorable configurations for large ones (N⩾77). Magic numbers corresponding to icosahedral, polyicosahedral and bcc structures are found. We further show that the melting points (Tm) of the clusters follow a well-established power-law correlation with the number of atoms (N) in the clusters, scaling as Tm∝(N/2)−1/3. This study will provide useful reference for the ongoing investigation of dust properties.

Solution Structures of Ca2+-CIB1 and Mg2+-CIB1 and Their Interactions with the Platelet Integrin αIIb Cytoplasmic Domain

The calcium- and integrin-binding protein 1 (CIB1) is a ubiquitous Ca(2+)-binding protein and a specific binding partner for the platelet integrin αIIb cytoplasmic domain, which confers the key role of CIB1 in hemostasis. CIB1 is also known to be involved in apoptosis, embryogenesis, and the DNA damage response. In this study, the solution structures of both Ca(2+)-CIB1 and Mg(2+)-CIB1 were determined using solution-state NMR spectroscopy. The methyl groups of Ile, Leu, and Val were selectively protonated to compensate for the loss of protons due to deuteration. The solution structure of Ca(2+)-CIB1 possesses smaller opened EF-hands in its C-domain compared with available crystal structures. Ca(2+)-CIB1 and Mg(2+)-CIB1 have similar structures, but the N-lobe of Mg(2+)-CIB1 is slightly more opened than that of Ca(2+)-CIB1. Additional NMR experiments, such as chemical shift perturbation and methyl group solvent accessibility as measured by a nitroxide surface probe, were carried out to further characterize the structures of Ca(2+)-CIB1 and Mg(2+)-CIB1 as well as their interactions with the integrin αIIb cytoplasmic domain. NMR measurements of backbone amide proton slow motion (microsecond to millisecond) dynamics confirmed that the C-terminal helix of Ca(2+)-CIB1 is displaced upon αIIb binding. The EF-hand III of both Ca(2+)-CIB1 and Mg(2+)-CIB1 was identified to be directly involved in the interaction of CIB1 with αIIb. Together, these data illustrate that CIB1 behaves quite differently from related EF-hand regulatory calcium-binding proteins, such as calmodulin or neuronal calcium sensor proteins.

Cone-based placement for field programmable gate arrays

Deterministic greedy methods have been proposed to place the netlist of configurable logic blocks (CLBs) and primary input output blocks (IOBs) quickly on a two-dimensional (2D) island-style field programmable gate array (FPGA) consisting of either one or multiple 2D island-style arrays of CLBs and IOBs. The first method, ‘ConeCLBPlace’, starts with a random placement of the primary output blocks along the periphery of the 2D array of CLBs, then places the CLBs and primary input blocks in a greedy deterministic way. In the second method, ‘ConeIOBPlace’, the IOBs are first placed on the periphery of the FPGA chip using a deterministic heuristic, and then the CLBs are placed within the 2D array using a typical simulated annealing (SA) flow. The third method, ‘ConePlace’, combines the above two deterministic approaches by first placing the IOBs only using ConeIOBPlace, and then the CLBs using ConeCLBPlace deterministically. Finally, a low-temperature SA is executed in order to obtain a high-quality final placement. ConeCLBPlace and ConePlace produce placements 2.34× and 1.83× faster than the placement step of popular FPGA place-and-route tool VPR (versatile place and route) on the average. The bounding box costs of placement produced by ConeCLBPlace and ConePlace, after execution of the iterative SA steps, are 1.05× and 1.14× of VPR, respectively, on the average, whereas the critical path delay obtained after routing is 1.03× of VPR for both methods on the average, implying almost the same quality of VPR. This justifies the utility of the methods proposed.

Multilevel optimization for large-scale hierarchical FPGA placement

This paper proposes a multilevel placer targeted at hierarchical FPGA (Field Programmable Gate Array) devices. The placer is based on multilevel optimization method which combines the multilevel bottom-up clustering process and top-down placement process into a V-cycle. It provides superior wirelength results over a known heuristic high-quality placement tool on a set of large circuits, when restricted to a short run time. For example, it can generate a placement result for a circuit with 5000 4-LUTs (4-Input Look Up Tables) in 70 seconds, almost 30% decrease of wirelength compared with than the heuristic implementation that takes over 500 seconds. We have verified our algorithm yields good quality-time tradeoff results as a low-temperature simulated annealing refinement process can only improve the result by an average of 1.11% at the cost of over 25-fold runtime.

GENFOLD: a genetic algorithm for folding protein structures using NMR restraints.

We report the development and validation of the program GENFOLD, a genetic algorithm that calculates protein structures using restraints obtained from NMR, such as distances derived from nuclear Overhauser effects, and dihedral angles derived from coupling constants. The program has been tested on three proteins: the POU domain (a small three-helix DNA-binding protein), bovine pancreatic trypsin inhibitor (BPTI), and the starch-binding domain from Aspergillus niger glucoamylase I, a 108-residue beta-sheet protein. Structures were calculated for each protein using published NMR restraints. In addition, structures were calculated for BPTI using artificial restraints generated from a high-resolution crystal structure. In all cases the fittest calculated structures were close to the target structure, and could be refined to structures indistinguishable from the target structures by means of a low-temperature simulated annealing refinement. The effectiveness of the program is similar to that of distance geometry and simulated annealing methods, and it is capable of using a very wide range of restraints as input. It can thus be readily extended to the calculation of structures of large proteins, for which few NOE restraints may be available.

A new methodology of simulated annealing for the optimisation problems

Complex optimisation problems with many degrees of freedom are often characterised by the enormously large configuration space, typically O ( e N ) or O ( N!). The idea of simulated annealing (SA) proposed by Kirkpatrick has been applied to the complex optimisation problems, which can be treated as annealing a statistical mechanical system from high temperature to low temperature; however, the SA is terribly slow for large problem sizes in typically O ( N 3ln N) time. We discover the hybrid algorithm (HA), which is based on a hybrid mechanism which combines conventional heuristics with low temperature simulated annealing (LTSA), which could be parallelised easily. The HA is a new approach of resolving optimisation problems with O ( N) complexity where information propagation can be inhibited by restraining the range of searches in the configuration space. We use the HA to resolve several famous combinatorial optimisation problems, including the travelling salesman problem (TSP) of large sizes up to 1 000 000 cities within 3 to 5 percent of the optimal value in linear time and other nonuniformly distributed TSPs as well. We shall also discuss the applicability of the HA to the optimisation problems in general.

Standard-cell placement from functional descriptions

This paper presents a functional language for the unambiguous description of digital circuits, a method and algorithms to obtain a standard-cell layout, and a comparative evaluation of the developed functional standard-cell placement technique. The presented placement scheme is different from traditional methods because the complete layout geometry is specified and constructed automatically from a functional description. The construction relies on a translation that combines the simplicity of standard-cells with the elegance of functional programming. An evaluation of the method introduced shows that the quality of the resulting placement is close to the results achieved with simulated annealing while the computation time is significantly less. Furthermore, the evaluation suggests to employ the functional placement method in conjunction with low-temperature simulated annealing for running-time reduction and improved-results.