'Explicit Learning: an Effort towards Human Scheduling Algorithms'

Abstract Scheduling problems are generally NP-hard combinatorial problems, and a lot of research has been done to solve these problems heuristically. However, most of the previous approaches are problem-specific and research into the development of a general scheduling algorithm is still in its infancy. Mimicking the natural evolutionary process of the survival of the fittest, Genetic Algorithms (GAs) have attracted much attention in solving difficult scheduling problems in recent years. Some obstacles exist when using GAs: there is no canonical mechanism to deal with constraints, which are commonly met in most real-world scheduling problems, and small changes to a solution are difficult. To overcome both difficulties, indirect approaches have been presented (in [1] and [2]) for nurse scheduling and driver scheduling, where GAs are used by mapping the solution space, and separate decoding routines then build solutions to the original problem. In our previous indirect GAs, learning is implicit and is restricted to the efficient adjustment of weights for a set of rules that are used to construct schedules. The major limitation of those approaches is that they learn in a non-human way: like most existing construction algorithms, once the best weight combination is found, the rules used in the construction process are fixed at each iteration. However, normally a long sequence of moves is needed to construct a schedule and using fixed rules at each move is thus unreasonable and not coherent with human learning processes. When a human scheduler is working, he normally builds a schedule step by step following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not completed yet, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this research we intend to design more human-like scheduling algorithms, by using ideas derived from Bayesian Optimization Algorithms (BOA) and Learning Classifier Systems (LCS) to implement explicit learning from past solutions. BOA can be applied to learn to identify good partial solutions and to complete them by building a Bayesian network of the joint distribution of solutions [3]. A Bayesian network is a directed acyclic graph with each node corresponding to one variable, and each variable corresponding to individual rule by which a schedule will be constructed step by step. The conditional probabilities are computed according to an initial set of promising solutions. Subsequently, each new instance for each node is generated by using the corresponding conditional probabilities, until values for all nodes have been generated. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the Bayesian network is updated again using the current set of good rule strings. The algorithm thereby tries to explicitly identify and mix promising building blocks. It should be noted that for most scheduling problems the structure of the network model is known and all the variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus learning can amount to 'counting' in the case of multinomial distributions. In the LCS approach, each rule has its strength showing its current usefulness in the system, and this strength is constantly assessed [4]. To implement sophisticated learning based on previous solutions, an improved LCS-based algorithm is designed, which consists of the following three steps. The initialization step is to assign each rule at each stage a constant initial strength. Then rules are selected by using the Roulette Wheel strategy. The next step is to reinforce the strengths of the rules used in the previous solution, keeping the strength of unused rules unchanged. The selection step is to select fitter rules for the next generation. It is envisaged that the LCS part of the algorithm will be used as a hill climber to the BOA algorithm. This is exciting and ambitious research, which might provide the stepping-stone for a new class of scheduling algorithms. Data sets from nurse scheduling and mall problems will be used as test-beds. It is envisaged that once the concept has been proven successful, it will be implemented into general scheduling algorithms. It is also hoped that this research will give some preliminary answers about how to include human-like learning into scheduling algorithms and may therefore be of interest to researchers and practitioners in areas of scheduling and evolutionary computation. References 1. Aickelin, U. and Dowsland, K. (2003) 'Indirect Genetic Algorithm for a Nurse Scheduling Problem', Computer & Operational Research (in print). 2. Li, J. and Kwan, R.S.K. (2003), 'Fuzzy Genetic Algorithm for Driver Scheduling', European Journal of Operational Research 147(2): 334-344. 3. Pelikan, M., Goldberg, D. and Cantu-Paz, E. (1999) 'BOA: The Bayesian Optimization Algorithm', IlliGAL Report No 99003, University of Illinois. 4. Wilson, S. (1994) 'ZCS: A Zeroth-level Classifier System', Evolutionary Computation 2(1), pp 1-18.

'Explicit Learning: an Effort towards Human Scheduling Algorithms'

Abstract Scheduling problems are generally NP-hard combinatorial problems, and a lot of research has been done to solve these problems heuristically. However, most of the previous approaches are problem-specific and research into the development of a general scheduling algorithm is still in its infancy. Mimicking the natural evolutionary process of the survival of the fittest, Genetic Algorithms (GAs) have attracted much attention in solving difficult scheduling problems in recent years. Some obstacles exist when using GAs: there is no canonical mechanism to deal with constraints, which are commonly met in most real-world scheduling problems, and small changes to a solution are difficult. To overcome both difficulties, indirect approaches have been presented (in [1] and [2]) for nurse scheduling and driver scheduling, where GAs are used by mapping the solution space, and separate decoding routines then build solutions to the original problem. In our previous indirect GAs, learning is implicit and is restricted to the efficient adjustment of weights for a set of rules that are used to construct schedules. The major limitation of those approaches is that they learn in a non-human way: like most existing construction algorithms, once the best weight combination is found, the rules used in the construction process are fixed at each iteration. However, normally a long sequence of moves is needed to construct a schedule and using fixed rules at each move is thus unreasonable and not coherent with human learning processes. When a human scheduler is working, he normally builds a schedule step by step following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not completed yet, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this research we intend to design more human-like scheduling algorithms, by using ideas derived from Bayesian Optimization Algorithms (BOA) and Learning Classifier Systems (LCS) to implement explicit learning from past solutions. BOA can be applied to learn to identify good partial solutions and to complete them by building a Bayesian network of the joint distribution of solutions [3]. A Bayesian network is a directed acyclic graph with each node corresponding to one variable, and each variable corresponding to individual rule by which a schedule will be constructed step by step. The conditional probabilities are computed according to an initial set of promising solutions. Subsequently, each new instance for each node is generated by using the corresponding conditional probabilities, until values for all nodes have been generated. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the Bayesian network is updated again using the current set of good rule strings. The algorithm thereby tries to explicitly identify and mix promising building blocks. It should be noted that for most scheduling problems the structure of the network model is known and all the variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus learning can amount to 'counting' in the case of multinomial distributions. In the LCS approach, each rule has its strength showing its current usefulness in the system, and this strength is constantly assessed [4]. To implement sophisticated learning based on previous solutions, an improved LCS-based algorithm is designed, which consists of the following three steps. The initialization step is to assign each rule at each stage a constant initial strength. Then rules are selected by using the Roulette Wheel strategy. The next step is to reinforce the strengths of the rules used in the previous solution, keeping the strength of unused rules unchanged. The selection step is to select fitter rules for the next generation. It is envisaged that the LCS part of the algorithm will be used as a hill climber to the BOA algorithm. This is exciting and ambitious research, which might provide the stepping-stone for a new class of scheduling algorithms. Data sets from nurse scheduling and mall problems will be used as test-beds. It is envisaged that once the concept has been proven successful, it will be implemented into general scheduling algorithms. It is also hoped that this research will give some preliminary answers about how to include human-like learning into scheduling algorithms and may therefore be of interest to researchers and practitioners in areas of scheduling and evolutionary computation. References 1. Aickelin, U. and Dowsland, K. (2003) 'Indirect Genetic Algorithm for a Nurse Scheduling Problem', Computer & Operational Research (in print). 2. Li, J. and Kwan, R.S.K. (2003), 'Fuzzy Genetic Algorithm for Driver Scheduling', European Journal of Operational Research 147(2): 334-344. 3. Pelikan, M., Goldberg, D. and Cantu-Paz, E. (1999) 'BOA: The Bayesian Optimization Algorithm', IlliGAL Report No 99003, University of Illinois. 4. Wilson, S. (1994) 'ZCS: A Zeroth-level Classifier System', Evolutionary Computation 2(1), pp 1-18.

A Hardware Task-Graph Scheduler for Reconfigurable Multi-tasking Systems

Reconfigurable hardware can be used to build a multitasking system where tasks are assigned to HW resources at run-time according to the requirements of the running applications. These tasks are frequently represented as direct acyclic graphs and their execution is typically controlled by an embedded processor that schedules the graph execution. In order to improve the efficiency of the system, the scheduler can apply prefetch and reuse techniques that can greatly reduce the reconfiguration latencies. For an embedded processor all these computations represent a heavy computational load that can significantly reduce the system performance. To overcome this problem we have implemented a HW scheduler using reconfigurable resources. In addition we have implemented both prefetch and replacement techniques that obtain as good results as previous complex SW approaches, while demanding just a few clock cycles to carry out the computations. We consider that the HW cost of the system (in our experiments 3% of a Virtex-II PRO xc2vp30 FPGA) is affordable taking into account the great efficiency of the techniques applied to hide the reconfiguration latency and the negligible run-time penalty introduced by the scheduler computations.

Acyclic 5-Choosability of Planar Graphs Without Adjacent Short Cycles

The conjecture claiming that every planar graph is acyclic 5-choosable[Borodin et al., 2002] has been verified for several restricted classes of planargraphs. Recently, O. V. Borodin and A. O. Ivanova, [Journal of Graph Theory,68(2), October 2011, 169-176], have shown that a planar graph is acyclically 5-choosable if it does not contain an i-cycle adjacent to a j-cycle, where 3<=j<=5 if i=3 and 4<=j<=6 if i=4. We improve the above mentioned result and prove that every planar graph without an i-cycle adjacent to a j-cycle with3<=j<=5 if i=3 and 4<=j<=5 if i=4 is acyclically 5-choosable.

Scheduling dynamic dataflow graphs with model checking

With the shift towards many-core computer architectures, dataflow programming has been proposed as one potential solution for producing software that scales to a varying number of processor cores. Programming for parallel architectures is considered difficult as the current popular programming languages are inherently sequential and introducing parallelism is typically up to the programmer. Dataflow, however, is inherently parallel, describing an application as a directed graph, where nodes represent calculations and edges represent a data dependency in form of a queue. These queues are the only allowed communication between the nodes, making the dependencies between the nodes explicit and thereby also the parallelism. Once a node have the su cient inputs available, the node can, independently of any other node, perform calculations, consume inputs, and produce outputs. Data ow models have existed for several decades and have become popular for describing signal processing applications as the graph representation is a very natural representation within this eld. Digital lters are typically described with boxes and arrows also in textbooks. Data ow is also becoming more interesting in other domains, and in principle, any application working on an information stream ts the dataflow paradigm. Such applications are, among others, network protocols, cryptography, and multimedia applications. As an example, the MPEG group standardized a dataflow language called RVC-CAL to be use within reconfigurable video coding. Describing a video coder as a data ow network instead of with conventional programming languages, makes the coder more readable as it describes how the video dataflows through the different coding tools. While dataflow provides an intuitive representation for many applications, it also introduces some new problems that need to be solved in order for data ow to be more widely used. The explicit parallelism of a dataflow program is descriptive and enables an improved utilization of available processing units, however, the independent nodes also implies that some kind of scheduling is required. The need for efficient scheduling becomes even more evident when the number of nodes is larger than the number of processing units and several nodes are running concurrently on one processor core. There exist several data ow models of computation, with different trade-offs between expressiveness and analyzability. These vary from rather restricted but statically schedulable, with minimal scheduling overhead, to dynamic where each ring requires a ring rule to evaluated. The model used in this work, namely RVC-CAL, is a very expressive language, and in the general case it requires dynamic scheduling, however, the strong encapsulation of dataflow nodes enables analysis and the scheduling overhead can be reduced by using quasi-static, or piecewise static, scheduling techniques. The scheduling problem is concerned with nding the few scheduling decisions that must be run-time, while most decisions are pre-calculated. The result is then an, as small as possible, set of static schedules that are dynamically scheduled. To identify these dynamic decisions and to find the concrete schedules, this thesis shows how quasi-static scheduling can be represented as a model checking problem. This involves identifying the relevant information to generate a minimal but complete model to be used for model checking. The model must describe everything that may affect scheduling of the application while omitting everything else in order to avoid state space explosion. This kind of simplification is necessary to make the state space analysis feasible. For the model checker to nd the actual schedules, a set of scheduling strategies are de ned which are able to produce quasi-static schedulers for a wide range of applications. The results of this work show that actor composition with quasi-static scheduling can be used to transform data ow programs to t many different computer architecture with different type and number of cores. This in turn, enables dataflow to provide a more platform independent representation as one application can be fitted to a specific processor architecture without changing the actual program representation. Instead, the program representation is in the context of design space exploration optimized by the development tools to fit the target platform. This work focuses on representing the dataflow scheduling problem as a model checking problem and is implemented as part of a compiler infrastructure. The thesis also presents experimental results as evidence of the usefulness of the approach.

Fixed point results for multivalued contractions on graphs and their applications

Nous présentons dans cette thèse des théorèmes de point fixe pour des contractions multivoques définies sur des espaces métriques, et, sur des espaces de jauges munis d’un graphe. Nous illustrons également les applications de ces résultats à des inclusions intégrales et à la théorie des fractales. Cette thèse est composée de quatre articles qui sont présentés dans quatre chapitres. Dans le chapitre 1, nous établissons des résultats de point fixe pour des fonctions multivoques, appelées G-contractions faibles. Celles-ci envoient des points connexes dans des points connexes et contractent la longueur des chemins. Les ensembles de points fixes sont étudiés. La propriété d’invariance homotopique d’existence d’un point fixe est également établie pour une famille de Gcontractions multivoques faibles. Dans le chapitre 2, nous établissons l’existence de solutions pour des systèmes d’inclusions intégrales de Hammerstein sous des conditions de type de monotonie mixte. L’existence de solutions pour des systèmes d’inclusions différentielles avec conditions initiales ou conditions aux limites périodiques est également obtenue. Nos résultats s’appuient sur nos théorèmes de point fixe pour des G-contractions multivoques faibles établis au chapitre 1. Dans le chapitre 3, nous appliquons ces mêmes résultats de point fixe aux systèmes de fonctions itérées assujettis à un graphe orienté. Plus précisément, nous construisons un espace métrique muni d’un graphe G et une G-contraction appropriés. En utilisant les points fixes de cette G-contraction, nous obtenons plus d’information sur les attracteurs de ces systèmes de fonctions itérées. Dans le chapitre 4, nous considérons des contractions multivoques définies sur un espace de jauges muni d’un graphe. Nous prouvons un résultat de point fixe pour des fonctions multivoques qui envoient des points connexes dans des points connexes et qui satisfont une condition de contraction généralisée. Ensuite, nous étudions des systèmes infinis de fonctions itérées assujettis à un graphe orienté (H-IIFS). Nous donnons des conditions assurant l’existence d’un attracteur unique à un H-IIFS. Enfin, nous appliquons notre résultat de point fixe pour des contractions multivoques définies sur un espace de jauges muni d’un graphe pour obtenir plus d’information sur l’attracteur d’un H-IIFS. Plus précisément, nous construisons un espace de jauges muni d’un graphe G et une G-contraction appropriés tels que ses points fixes sont des sous-attracteurs du H-IIFS.

Rhodium-Catalyzed Hydroboration: Directed Asymmetric Desymmetrization

Rhodium-catalyzed asymmetric hydroboration in conjunction with directing groups can be used control relative and absolute stereochemistry. Hydroboration has the potential to create new C–C, C–O, and C–N bonds from an intermediate C–B bond with retention of stereochemistry. Desymmetrization resulting in the loss of one or more symmetry elements can give rise to molecular chirality, i.e., the conversion of a prochiral molecule to one that is chiral. Unsaturated amides and esters hold the potential for two-point binding to the rhodium catalyst and have been shown to direct the regiochemistry and impact stereochemistry in asymmetric hydroborations of acyclic β,γ-unsaturated substrates. In the present study, the pendant amide functionality directs the hydroboration cis in the cyclic substrates studied; the corresponding ester substrates do so to a lesser extent. The enantioselectivity is determined by regioselective addition to the re or si site of the rhodium-complexed alkene. The effect of catalyst, ligand and borane on the observed diastereoselectivity and enantioselectivity for a variety of cyclopentenyl ester and amide substrates is discussed.

Simplicial Complexes From Graphs Toward Graph Persistence

Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. This dissertation is an introductory study to link persistent homology and graph theory, the connection being represented by various methods to build simplicial complexes from a graph. The methods we consider are the complex of cliques, of independent sets, of neighbours, of enclaveless sets and complexes from acyclic subgraphs, each revealing several properties of the underlying graph. Moreover, we apply the core ideas of persistence theory in the new context of graph theory, we define the persistent block number and the persistent edge-block number.

Beam-energy Dependence Of The Directed Flow Of Protons, Antiprotons, And Pions In Au+au Collisions.

Rapidity-odd directed flow (v1) measurements for charged pions, protons, and antiprotons near midrapidity (y=0) are reported in sNN=7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV Au+Au collisions as recorded by the STAR detector at the Relativistic Heavy Ion Collider. At intermediate impact parameters, the proton and net-proton slope parameter dv1/dy|y=0 shows a minimum between 11.5 and 19.6 GeV. In addition, the net-proton dv1/dy|y=0 changes sign twice between 7.7 and 39 GeV. The proton and net-proton results qualitatively resemble predictions of a hydrodynamic model with a first-order phase transition from hadronic matter to deconfined matter, and differ from hadronic transport calculations.

Sub-telomere directed gene expression during initiation of invasive aspergillosis

Aspergillus fumigatus is a common mould whose spores are a component of the normal airborne flora. Immune dysfunction permits developmental growth of inhaled spores in the human lung causing aspergillosis, a significant threat to human health in the form of allergic, and life-threatening invasive infections. The success of A. fumigatus as a pathogen is unique among close phylogenetic relatives and is poorly characterised at the molecular level. Recent genome sequencing of several Aspergillus species provides an exceptional opportunity to analyse fungal virulence attributes within a genomic and evolutionary context. To identify genes preferentially expressed during adaptation to the mammalian host niche, we generated multiple gene expression profiles from minute samplings of A. fumigatus germlings during initiation of murine infection. They reveal a highly co-ordinated A. fumigatus gene expression programme, governing metabolic and physiological adaptation, which allows the organism to prosper within the mammalian niche. As functions of phylogenetic conservation and genetic locus, 28% and 30%, respectively, of the A. fumigatus subtelomeric and lineage-specific gene repertoires are induced relative to laboratory culture, and physically clustered genes including loci directing pseurotin, gliotoxin and siderophore biosyntheses are a prominent feature. Locationally biased A. fumigatus gene expression is not prompted by in vitro iron limitation, acid, alkaline, anaerobic or oxidative stress. However, subtelomeric gene expression is favoured following ex vivo neutrophil exposure and in comparative analyses of richly and poorly nourished laboratory cultured germlings. We found remarkable concordance between the A. fumigatus host-adaptation transcriptome and those resulting from in vitro iron depletion, alkaline shift, nitrogen starvation and loss of the methyltransferase LaeA. This first transcriptional snapshot of a fungal genome during initiation of mammalian infection provides the global perspective required to direct much-needed diagnostic and therapeutic strategies and reveals genome organisation and subtelomeric diversity as potential driving forces in the evolution of pathogenicity in the genus Aspergillus.

Comparative study of the hygienic behavior of Carniolan and Africanized honey bees directed towards grouped versus isolated dead brood cells

In Apis mellifera, hygienic behavior involves recognition and removal of sick, damaged or dead brood from capped cells. We investigated whether bees react in the same way to grouped versus isolated damaged capped brood cells. Three colonies of wild-type Africanized honey bees and three colonies of Carniolan honey bees were used for this investigation. Capped worker brood cells aged 12 to 14 days old were perforated with the pin-killing method. After making holes in the brood cells, the combs were placed back into the hives; 24 h later the number of cleaned cells was recorded in areas with pin-killed and control brood cells. Four repetitions were made in each colony. Isolated cells were more frequently cleaned than grouped cells, though variance analysis showed no significant difference (P = 0.1421). Carniolan bees also were somewhat, though not significantly more hygienic than Africanized honey bees (P = 0.0840). We conclude that honey bees can detect and remove both isolated and grouped dead brood. The tendency towards greater hygienic efficiency directed towards grouped pin-killed brood may be a consequence of a greater concentration of volatiles emanating from the wounds in the dead pupae.

System-Size Independence of Directed Flow Measured at the BNL Relativistic Heavy-Ion Collider

We measure directed flow (v(1)) for charged particles in Au + Au and Cu + Cu collisions at root s(NN) = 200 and 62.4 GeV, as a function of pseudorapidity (eta), transverse momentum (p(t)), and collision centrality, based on data from the STAR experiment. We find that the directed flow depends on the incident energy but, contrary to all available model implementations, not on the size of the colliding system at a given centrality. We extend the validity of the limiting fragmentation concept to v(1) in different collision systems, and investigate possible explanations for the observed sign change in v(1)(p(t)).

Directed flow at midrapidity in event-by-event hydrodynamics

Fluctuations in the initial geometry of a nucleus-nucleus collision have been recently shown to result in a new type of directed flow (v(1)) that, unlike the usual directed flow, is also present at midrapidity. We compute this new v(1) versus transverse momentum and centrality for Au-Au collisions at RHIC using the hydrodynamic code NeXSPheRIO. We find that the event plane of v(1) is correlated with the angle of the initial dipole of the distribution, as predicted, though with a large dispersion. It is uncorrelated with the reaction plane. Our results are in excellent agreement with results inferred from STAR correlation data.

Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

On the k-restricted structure ratio in planar and outerplanar graphs

A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for Maximum Weight Planar Subgraph, which motivates this work. The planar k-restricted ratio is the infimum, over simple planar graphs H, of the ratio of the number of edges in a maximum k-restricted structure subgraph of H to the number edges of H. We prove that, as k tends to infinity, the planar k-restricted ratio tends to 1/2. The same result holds for the weighted version. Our results are based on analyzing the analogous ratios for outerplanar and weighted outerplanar graphs. Here both ratios tend to 1 as k goes to infinity, and we provide good estimates of the rates of convergence, showing that they differ in the weighted from the unweighted case.