Independent Codes Research Articles

TRUST

The radiative transport of photons through arbitrary three-dimensional (3D) structures of dust is a challenging problem due to the anisotropic scattering of dust grains and strong coupling between different spatial regions. The radiative transfer problem in 3D is solved using Monte Carlo or Ray Tracing techniques as no full analytic solution exists for the true 3D structures. We provide the first 3D dust radiative transfer benchmark composed of a slab of dust with uniform density externally illuminated by a star. This simple 3D benchmark is explicitly formulated to provide tests of the different components of the radiative transfer problem including dust absorption, scattering, and emission. This benchmark includes models with a range of dust optical depths fully probing cases that are optically thin at all wavelengths to optically thick at most wavelengths. This benchmark includes solutions for the full dust emission including single photon (stochastic) heating as well as two simplifying approximations: One where all grains are considered in equilibrium with the radiation field and one where the emission is from a single effective grain with size-distribution-averaged properties. A total of six Monte Carlo codes and one Ray Tracing code provide solutions to this benchmark. Comparison of the results revealed that the global SEDs are consistent on average to a few percent for all but the scattered stellar flux at very high optical depths. The image results are consistent within 10%, again except for the stellar scattered flux at very high optical depths. The lack of agreement between different codes of the scattered flux at high optical depths is quantified for the first time. We provide the first 3D dust radiative transfer benchmark and validate the accuracy of this benchmark through comparisons between multiple independent codes and detailed convergence tests.

Energy levels and radiative rates for transitions in Cr-like Kr XIII, Tc XX and Xe XXXI

Energy levels, radiative transition probabilities, Landé g-factors, and radiative lifetimes are reported for 144 levels of the 3p63d6 and 3p53d7 configurations of the Cr-like ions Kr XIII, Tc XX and Xe XXXI. Since to our knowledge no prior data for energy levels or A-values, experimental or theoretical, are available in the literature for these ions, calculations have been performed with three independent atomic structure codes, namely GRASP, FAC and a code implementing the QR approach, with increasing configuration interaction (CI) basis with each code. This is to establish the accuracy of the calculated results so that data can be confidently applied in the modeling of plasmas. Our recommended data are determined within the QR approach, because not only has the largest CI basis been included in this calculation, the reliability has already been established in our earlier work for other Cr-like ions, for which some experimental and theoretical data were available for comparison. Results for radiative rates (A-values) and transition wavelengths (λ) are listed for all strong E1, E2 and M1 transitions among the 144 levels of each ion.

The Sirius System and Its Astrophysical Puzzles: Hubble Space Telescope and Ground-based Astrometry∗

Abstract Sirius, the seventh-nearest stellar system, is a visual binary containing the metallic-line A1 V star Sirius A, the brightest star in the sky, orbited in a 50.13 year period by Sirius B, the brightest and nearest white dwarf (WD). Using images obtained over nearly two decades with the Hubble Space Telescope (HST), along with photographic observations covering almost 20 years and nearly 2300 historical measurements dating back to the 19th century, we determine precise orbital elements for the visual binary. Combined with the parallax and the motion of the A component, these elements yield dynamical masses of and for Sirius A and B, respectively. Our precise HST astrometry rules out third bodies orbiting either star in the system, down to masses of ∼15– . The location of Sirius B in the Hertzsprung–Russell diagram is in excellent agreement with theoretical cooling tracks for WDs of its dynamical mass, and implies a cooling age of ∼126 Myr. The position of Sirius B on the mass–radius plane is also consistent with WD theory, assuming a carbon–oxygen core. Including the pre-WD evolutionary timescale of the assumed progenitor, the total age of Sirius B is about 228 ± 10 Myr. We calculated evolutionary tracks for stars with the dynamical mass of Sirius A, using two independent codes. We find it necessary to assume a slightly subsolar metallicity, of about , to fit its location on the luminosity–radius plane. The age of Sirius A based on these models is about 237–247 Myr, with uncertainties of ±15 Myr, consistent with that of the WD companion. We discuss astrophysical puzzles presented by the Sirius system, including the probability that the two stars must have interacted in the past, even though there is no direct evidence for this and the orbital eccentricity remains high.

The Application of Computer Technology in Mongolian College English Teaching

Based on the demand of modern teaching, this paper researches the application of and problems faced by Mongolian information processing and computer multimedia technology in computer-assisted instruction. It also sets the teaching software content and learning goal and further designs the teaching software according to the English learning features and characteristics of choosing the medium of information of Mongolian college students. This software is suitable for use in learning and teaching bilingualism second language to Mongolian students, and teachers and can realize the independent code of bilingual characters, Mongolian input and output, Mongolian character handling and bilingual inter-translation functions. Manufacture and development of bilingual teaching software facilitates the enthusiasm of Mongolian college students to learn English, improve the language learning environment and plays a positive facilitation role in multilanguage integration and cultural development of the Mongolian area.

Nuclear genetic codes with a different meaning of the UAG and the UAA codon

BackgroundDepartures from the standard genetic code in eukaryotic nuclear genomes are known for only a handful of lineages and only a few genetic code variants seem to exist outside the ciliates, the most creative group in this regard. Most frequent code modifications entail reassignment of the UAG and UAA codons, with evidence for at least 13 independent cases of a coordinated change in the meaning of both codons. However, no change affecting each of the two codons separately has been documented, suggesting the existence of underlying evolutionary or mechanistic constraints.ResultsHere, we present the discovery of two new variants of the nuclear genetic code, in which UAG is translated as an amino acid while UAA is kept as a termination codon (along with UGA). The first variant occurs in an organism noticed in a (meta)transcriptome from the heteropteran Lygus hesperus and demonstrated to be a novel insect-dwelling member of Rhizaria (specifically Sainouroidea). This first documented case of a rhizarian with a non-canonical genetic code employs UAG to encode leucine and represents an unprecedented change among nuclear codon reassignments. The second code variant was found in the recently described anaerobic flagellate Iotanema spirale (Metamonada: Fornicata). Analyses of transcriptomic data revealed that I. spirale uses UAG to encode glutamine, similarly to the most common variant of a non-canonical code known from several unrelated eukaryotic groups, including hexamitin diplomonads (also a lineage of fornicates). However, in these organisms, UAA also encodes glutamine, whereas it is the primary termination codon in I. spirale. Along with phylogenetic evidence for distant relationship of I. spirale and hexamitins, this indicates two independent genetic code changes in fornicates.ConclusionsOur study documents, for the first time, that evolutionary changes of the meaning of UAG and UAA codons in nuclear genomes can be decoupled and that the interpretation of the two codons by the cytoplasmic translation apparatus is mechanistically separable. The latter conclusion has interesting implications for possibilities of genetic code engineering in eukaryotes. We also present a newly developed generally applicable phylogeny-informed method for inferring the meaning of reassigned codons.

The Global Relationship between Chromatin Physical Topology, Fractal Structure, and Gene Expression

Most of what we know about gene transcription comes from the view of cells as molecular machines: focusing on the role of molecular modifications to the proteins carrying out transcriptional reactions at a loci-by-loci basis. This view ignores a critical reality: biological reactions do not happen in an empty space, but in a highly complex, interrelated, and dense nanoenvironment that profoundly influences chemical interactions. We explored the relationship between the physical nanoenvironment of chromatin and gene transcription in vitro. We analytically show that changes in the fractal dimension, D, of chromatin correspond to simultaneous increases in chromatin accessibility and compaction heterogeneity. Using these predictions, we demonstrate experimentally that nanoscopic changes to chromatin D within thirty minutes correlate with concomitant enhancement and suppression of transcription. Further, we show that the increased heterogeneity of physical structure of chromatin due to increase in fractal dimension correlates with increased heterogeneity of gene networks. These findings indicate that the higher order folding of chromatin topology may act as a molecular-pathway independent code regulating global patterns of gene expression. Since physical organization of chromatin is frequently altered in oncogenesis, this work provides evidence pairing molecular function to physical structure for processes frequently altered during tumorigenesis.

Linux OS integrated modular avionics application development framework with apex API of ARINC653 specification

The framework is made to provide tools to develop the integrated modular avionics (IMA) applications, which could be launched on the target platform LynxOs-178 without modifying their source code. The framework usage helps students to form skills for developing modern modules of the avionics. In addition, students obtain deeper knowledge for the development of competencies in the field of technical creativity by using of the framework. The article describes the architecture and implementation of the Linux OS framework for ARINC653 compliant OS application development. The proposed approach reduces ARINC-653 application development costs and gives a unified tool to implement OS vendor independent code that meets specification. To achieve import substitution free and open-source Linux OS is used as an environment for developing IMA applications. The proposed framework is applicable for using as the tool to develop IMA applications and as the tool for development of the following competencies: the ability to master techniques of using software to solve practical problems, the ability to develop components of hardware and software systems and databases, using modern tools and programming techniques, the ability to match hardware and software tools in the information and automated systems, the readiness to apply the fundamentals of informatics and programming to designing, constructing and testing of software products, the readiness to apply basic methods and tools of software development, knowledge of various technologies of software development.

The model of disadvantages? The choice-of-law provisions of the Commonwealth of Independent States Model Civil Code and their impact on national legislations

The article describes the distinctive features and main disadvantages of the Commonwealth of Independent States Model Civil Code’s provisions of general parts of private international law, which found reception in the national legislation of the member states. The Code was accepted as a model for codification by the majority of the CIS states. An analysis of the Code’s provisions can help interpret the unclear national rules, will allow to predict courts’ modus operandi in conflict-of-laws cases and can provide an opportunity to estimate further development prospects of private international law in the post-Soviet area.

Modeling the source of GW150914 with targeted numerical-relativity simulations

In fall of 2015, the two LIGO detectors measured the gravitational wave signal GW150914, which originated from a pair of merging black holes (Abbott et al Virgo, LIGO Scientific 2016 Phys. Rev. Lett. 116 061102). In the final 0.2 s (about 8 gravitational-wave cycles) before the amplitude reached its maximum, the observed signal swept up in amplitude and frequency, from 35 Hz to 150 Hz. The theoretical gravitational-wave signal for merging black holes, as predicted by general relativity, can be computed only by full numerical relativity, because analytic approximations fail near the time of merger. Moreover, the nearly-equal masses, moderate spins, and small number of orbits of GW150914 are especially straightforward and efficient to simulate with modern numerical-relativity codes. In this paper, we report the modeling of GW150914 with numerical-relativity simulations, using black-hole masses and spins consistent with those inferred from LIGO’s measurement (Abbott et al LIGO Scientific Collaboration, Virgo Collaboration 2016 Phys. Rev. Lett. 116 241102). In particular, we employ two independent numerical-relativity codes that use completely different analytical and numerical methods to model the same merging black holes and to compute the emitted gravitational waveform; we find excellent agreement between the waveforms produced by the two independent codes. These results demonstrate the validity, impact, and potential of current and future studies using rapid-response, targeted numerical-relativity simulations for better understanding gravitational-wave observations.

Micron-sized surface enhanced Raman scattering reporter/fluorescence probe encoded colloidal microspheres for sensitive DNA detection

A new type of optical probes, featuring surface enhanced Raman scattering (SERS) and fluorescence spectra dual-mode encoding, has been reported in this article. Based on the uniform micrometer-sized melamine resin/Ag nanoparticles (MRM/Ag-NPs) composite microspheres, the SERS reporters and fluorescent probes were successfully fixed onto the different layers of the MEM/Ag-NPs microspheres, which supported the sensitive DNA detecton. The two spectroscopic methods commonly considered to be contradictive to each other, yet the optical signals were separable in the experiments. The dual-encoding strategy and single microsphere detecton method put the number of available independent codes to be rough the multiple of those available in the two optical detection channels, which increases far more rapidly than the summation of the two channels. As a proof of cencept, the utility of this dual spectrum mode SERS-fluoresecence encoded microsphere (SFEM) was demonstrated in a specific DNA detection using complimentary ssDNA functionalized magnetic beads as the DNA capturing and separation agents. Excellent encoding results were demonstrated from the decoding of the SERS and fluorescence signals of the SFEM. The method appears to be general in scope and we expect that the SERS-fluoresecence encoded microspheres system is applicable to multiplex bioassays of a variety of biomolecules.

BWR loss of coolant accident simulation by means of RELAP5

Application of best estimate codes and methodologies for LOCA simulation can provide the high level of details of the real plant response necessary to assess the adequacy of an emergency core cooling system.The current KKM RELAP5 model developed for the KKM plant (Mühleberg nuclear power station) has been demonstrated to be valid for simulating a wide range of transients including loss of coolant type accidents. Using this model, KKM LOCA analyses have been performed for the recirculation line break. The simulations have been done for the full break size spectrum. The sensitivity to the most important physics phenomena, e.g. CCFL, and model parameters, e.g. nodalization, has also been assessed.Results from the KKM RELAP5 LOCA analyses have been compared to the KKM LOCA results obtained with TRACG code by GEH. The RELAP5 and the TRACG models were both validated and showed very good agreement with the measured plant data. Regarding the LOCA calculations, the plant behavior and PCT results predicted by the RELAP5 model are consistent with those reported by GEH using the TRACG model. The differences observed can firstly be attributed to the diversity in the basic modeling of physical phenomena in the two codes. In addition, differences may originate from varying details in modeling the KKM plant and core parameters. However, considering that completely independent codes and models of the KKM plant predict similar PCT and plant behaviors during a LOCA, both KKM RELAP5 and KKM TRACG models can confidently be used for comparison against safety criteria.

A SPECTROSCOPICALLY CONFIRMED DOUBLE SOURCE PLANE LENS SYSTEM IN THE HYPER SUPRIME-CAM SUBARU STRATEGIC PROGRAM

ABSTRACT We report the serendipitous discovery of HSC J142449−005322, a double source plane lens system in the Hyper Suprime-Cam Subaru Strategic Program. We dub the system Eye of Horus. The lens galaxy is a very massive early-type galaxy with stellar mass of ∼ 7 × 10 11 M ⊙ located at z L = 0.795 . The system exhibits two arcs/rings with clearly different colors, including several knots. We have performed spectroscopic follow-up observations of the system with FIRE on Magellan. The outer ring is confirmed at z S 2 = 1.988 with multiple emission lines, while the inner arc and counterimage is confirmed at z S 1 = 1.302 . This makes it the first double source plane system with spectroscopic redshifts of both sources. Interestingly, redshifts of two of the knots embedded in the outer ring are found to be offset by Δ z = 0.002 from the other knots, suggesting that the outer ring consists of at least two distinct components in the source plane. We perform lens modeling with two independent codes and successfully reproduce the main features of the system. However, two of the lensed sources separated by ∼0.7 arcsec cannot be reproduced by a smooth potential, and the addition of substructure to the lens potential is required to reproduce them. Higher-resolution imaging of the system will help decipher the origin of this lensing feature and potentially detect the substructure.

Simulations of inspiraling and merging double neutron stars using the Spectral Einstein Code

We present results on the inspiral, merger, and post-merger evolution of a neutron star - neutron star (NSNS) system. Our results are obtained using the hybrid pseudospectral-finite volume Spectral Einstein Code (SpEC). To test our numerical methods, we evolve an equal-mass system for $\approx 22$ orbits before merger. This waveform is the longest waveform obtained from fully general-relativistic simulations for NSNSs to date. Such long (and accurate) numerical waveforms are required to further improve semi-analytical models used in gravitational wave data analysis, for example the effective one body models. We discuss in detail the improvements to SpEC's ability to simulate NSNS mergers, in particular mesh refined grids to better resolve the merger and post-merger phases. We provide a set of consistency checks and compare our results to NSNS merger simulations with the independent BAM code. We find agreement between them, which increases confidence in results obtained with either code. This work paves the way for future studies using long waveforms and more complex microphysical descriptions of neutron star matter in SpEC.

Integrated Software Fingerprinting via Neural-Network-Based Control Flow Obfuscation

Dynamic software fingerprinting has been an important tool in fighting against software theft and pirating by embedding unique fingerprints into software copies. However, the existing work uses the methods from dynamic software watermarking as direct solutions, in which the secret marks are inside rather independent code modules attached to the software. This results in an intrinsic weakness against targeted collusive attacks, since differences among the software copies correspond directly to the fingerprint-related components. In this paper, we suggest a novel mode of the dynamic fingerprinting called integrated fingerprinting, of which the goal is to ensure all the fingerprinted software copies possess identical behaviors at semantic level. We then provide the first implementation of integrated fingerprinting called Neuroprint on top of a control flow obfuscator that replaces program’s conditional structures with neural networks trained to simulate their branching behaviors. Leveraging the rich entropy in the outputs of these neural networks, Neuroprint embeds the software fingerprints, such that a one-time construction of the networks serves both the purposes of obfuscation and fingerprinting. Evaluations show that due to the incomprehensibility of neural networks, it is infeasible to de-obfuscate the software transformed by Neuroprint or attack the fingerprint using even the latest program analysis techniques. Revealing information regarding the hidden fingerprints via collusive attacks on Neuroprint is difficult as well. Finally, Neuroprint also demonstrates negligible runtime overhead.

A genetic algorithm based approach for multi-objective hardware/software co-optimization

We develop a genetic algorithm based autotuning strategy in this paper. Autotuning is a platform independent code optimization process in which different hardware and software parameters of the code being optimized are identified and the parameter space explored to arrive at an alternative implementation that optimizes characteristics such as performance and energy consumption. The main advantage of our approach is that the number of possible compilations and executions that are explored in the configuration space is substantially smaller than exhaustive search. We demonstrate the usefulness of our approach to the underlying small matrix multiplication routines in spectral element solvers. The latter are an important class of higher order methods that are expected to be computationally intensive portion of the next generation of large scale CFD simulations. Our experimental results were conducted on a variety of existing platforms as well as on gem5 simulator platform with different cache configurations. On an existing platform, AMD Fusion, the genetic algorithm is able obtain 34% improvement in performance and 37% reduction in energy consumption over existing versions of the code. The fact that a very small fraction of the entire configuration space needs to be explored becomes very useful as algorithmic exploration is combined with exploration of cache configuration resulting in hardware/software co-optimization. We used the micro-architectural simulator, gem5, to evaluate different cache configurations for energy and performance trade-offs for out-of-order x86 cores at the micro-architectural level for small matrix multiplications. Our results show how genetic algorithm based autotuning strategy can come up with a close to optimal variant analyzing only about 0.25% of the exploration space.

Evaluation of a coupling interface for solving fluid–structure interaction problems

This research work evaluates the performance of a Fluid–Structure Interaction (FSI) solver, which is created using a generic interface to couple two independent software packages. The basic idea is to combine the advantages of the two independent codes to create a powerful FSI solver for two and three dimensional FSI analysis using the concept of modular programming. A detailed description about the implementation of an interface to couple a three-field system involved in the analysis is given, and this developed interface can be generalized to others codes. Since solving complex FSI problems is very time consuming, the focus of this work is placed on the performance of the coupled solver, for which a FSI benchmark will be solved on a computer cluster in order to measure speed up and efficiency.

NLO QCD corrections to triple collinear splitting functions

In this article, we study the triple-collinear limit of scattering amplitudes, focusing the discussion in processes which include at least one photon. To deal with infrared divergences we applied dimensional regularization (DREG) and we worked in the time-like (TL) kinematical region in order to ensure the validity of strict-collinear factorization. Both polarized and unpolarized splitting functions were obtained using independent codes, which allowed to implement a first cross-check among them. The divergent structure of all the triple-collinear splittings was compared with the Catani's formula, and we found a complete agreement. Moreover, in the polarized case, this comparison imposed additional constraints in the finite part of some master integrals (MI). The analysis of photon-started splittings led to very compact expressions, because of gauge invariance. These contributions were identified with the Abelian terms of the remaining splitting functions, which constitutes another cross-check of the results.

Numerical computation of the effective-one-body potentialqusing self-force results

The effective-one-body theory (EOB) describes the conservative dynamics of compact binary systems in terms of an effective Hamiltonian approach. The Hamiltonian for moderately eccentric motion of two non-spinning compact objects in the extreme mass-ratio limit is given in terms of three potentials: $a(v), \bar{d}(v), q(v)$. By generalizing the first law of mechanics for (non-spinning) black hole binaries to eccentric orbits, [\prd{\bf92}, 084021 (2015)] recently obtained new expressions for $\bar{d}(v)$ and $q(v)$ in terms of quantities that can be readily computed using the gravitational self-force approach. Using these expressions we present a new computation of the EOB potential $q(v)$ by combining results from two independent numerical self-force codes. We determine $q(v)$ for inverse binary separations in the range $1/1200 \le v \lesssim 1/6$. Our computation thus provides the first-ever strong-field results for $q(v)$. We also obtain $\bar{d}(v)$ in our entire domain to a fractional accuracy of $\gtrsim 10^{-8}$. We find to our results are compatible with the known post-Newtonian expansions for $\bar{d}(v)$ and $q(v)$ in the weak field, and agree with previous (less accurate) numerical results for $\bar{d}(v)$ in the strong field.

Validation of flexible multibody dynamics beam formulations using benchmark problems

As the need to model flexibility arose in multibody dynamics, the floating frame of reference formulation was developed, but this approach can yield inaccurate results when elastic displacements becomes large. While the use of three-dimensional finite element formulations overcomes this problem, the associated computational cost is overwhelming. Consequently, beam models, which are one-dimensional approximations of three-dimensional elasticity, have become the workhorse of many flexible multibody dynamics codes. Numerous beam formulations have been proposed, such as the geometrically exact beam formulation or the absolute nodal coordinate formulation, to name just two. New solution strategies have been investigated as well, including the intrinsic beam formulation or the DAE approach. This paper provides a systematic comparison of these various approaches, which will be assessed by comparing their predictions for four benchmark problems. The first problem is the Princeton beam experiment, a study of the static large displacement and rotation behavior of a simple cantilevered beam under a gravity tip load. The second problem, the four-bar mechanism, focuses on a flexible mechanism involving beams and revolute joints. The third problem investigates the behavior of a beam bent in its plane of greatest flexural rigidity, resulting in lateral buckling when a critical value of the transverse load is reached. The last problem investigates the dynamic stability of a rotating shaft. The predictions of eight independent codes are compared for these four benchmark problems and are found to be in close agreement with each other and with experimental measurements, when available.

High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin code

The recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit numerical diffusion, they are considered a promising alternative to more traditional semi-Lagrangian schemes (which are usually based on polynomial or spline interpolation).In this paper, we consider a parallel implementation of a semi-Lagrangian discontinuous Galerkin method for distributed memory systems (so-called clusters). Both strong and weak scaling studies are performed on the Vienna Scientific Cluster 2 (VSC-2). In the case of weak scaling we observe a parallel efficiency above 0.8 for both two and four dimensional problems and up to 8192 cores. Strong scaling results show good scalability to at least 512 cores (we consider problems that can be run on a single processor in reasonable time). In addition, we study the scaling of a two dimensional Vlasov–Poisson solver that is implemented using the framework provided. All of the simulations are conducted in the context of worst case communication overhead; i.e., in a setting where the CFL (Courant–Friedrichs–Lewy) number increases linearly with the problem size.The framework introduced in this paper facilitates a dimension independent implementation of scientific codes (based on C++ templates) using both an MPI and a hybrid approach to parallelization. We describe the essential ingredients of our implementation. Program summaryProgram title: sldgCatalogue identifier: AEZO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEZO_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 320111No. of bytes in distributed program, including test data, etc.: 5725614Distribution format: tar.gzProgramming language: C++03.Computer: PC, HPC systems.Operating system: POSIX compatible (extensively tested on various Linux systems). Only the timing class requires POSIX routines; all other parts of the program can be run on any system where a C++ compiler, Boost, and FFTW is available.RAM: Megabytes to Terabytes (depending on the problem size)Classification: 6.5, 4.3, 19.8.External routines: Boost, FFTWNature of problem: An approximate solution of the advection equation is computed using the semi-Lagrangian discontinuous Galerkin method. This procedure is used as the fundamental building block in a splitting based Vlasov solver.Solution method: The semi-Lagrangian discontinuous Galerkin approach is employed. For the Vlasov–Poisson problem we, in addition, use a splitting approach in time and the FFT to solve Poisson’s equation.Restrictions: We assume that the hyperbolic part of the problem under consideration can be (for example, using a splitting approach) decomposed into a sequence of one-dimensional advections.Unusual features: The framework is independent of the dimension of the problem under consideration. This is accomplished using template techniques.Running time: From minutes to weeks (depending on the problem size).