As reações químicas que resultam da expressão de genes são complexas e ainda não são total- mente compreendidas. Sabe-se que os genes enviam, recebem, e processam informações formando uma complexa rede de comunicação, mas a arquitetura e dinâmica destas redes não são totalmente conhecidas. Dessa forma, um problema importante é determinar como os genes se relacionam dentro da célula. Esse processo de determinar o relacionamento entre os genes é conhecido como inferência de redes gênicas. Uma das formas para representar o relacionamento entre os genes é usar modelos matemáticos e computacionais de Redes Gênicas. Em especial, um dos modelos de grande interesse é o de Redes Booleanas (BN - do inglês Boolean Networks), no qual os genes podem assumir dois estados, ativo ou inativo, se estão, respectivamente, expressos ou não. Estes estados podem variar ao longo do tempo, dependendo de como os genes se relacionam. Nosso interesse está em estudar um caso particular deste modelo, conhecido como Redes Booleanas Limiarizadas, onde apenas uma classe de funções booleanas é utilizada para construir as BNs. Para inferir as Redes Booleanas Limiarizadas, usamos um algoritmo constituído de dois passos. Primeiro, usamos o arcabouço do Problema de Satisfação de Restrições (CSP - do inglês Constraint Satisfaction Problem) para inferir conjuntos de soluções consistentes com uma dada série temporal de um conjunto de genes. Em seguida analisamos o comportamento dinâmico das soluções encon- tradas , filtrando conjuntos de soluções de maior interesse para testes práticos em laboratório. Usando o arcabouço do CSP, construímos um solver, usando a biblioteca Gecode,1 para inferência de redes consistentes, usando como entrada uma série temporal oriunda de dados de microarrays. Em seguida, através da simulação da dinâmica de uma amostra das redes encontradas no passo anterior, fomos capazes de determinar algumas restrições interessantes para filtrar o conjunto de redes. Aplicamos o nosso método para três conjuntos de dados: dois artificiais, e para validação, usamos uma série temporal de uma rede artificial conhecida na literatura. Com isso fomos capazes de inferir conjuntos de redes gênicas de possível interesse para testes em laboratório. / The chemical reactions that result in gene expression are complex and not yet fully understood. It is known that genes send, receive and process information to form a complex network of com- munication, but the architecture and dynamics of these networks are not fully known. Thus, one major problem is to determine how genes are linked within the cell. This process of determining the relationship between genes is known as inference of genetic networks. One way to represent the relationship between genes is to use mathematical and computer models of genetic networks. In particular, one of the models of great interest are Boolean Networks (BN), in which genes can take two states, active or inactive, if they are, respectively, expressed or not. These states may vary over time, depending on how genes are related. Our interest is in studying a case of this particular model, known as thresholded Boolean networks, where only one class of Boolean functions is used to build the GNs. To infer the thresholded Boolean networks, we use an algorithm that consists of two steps. First, we use the framework of Constraint Satisfaction Problem (CSP) to infer sets of solutions consistent with a time series of a given set of genes. Then analyze the dynamic behavior of the solutions, filtering sets of solutions with interest for practical tests in the laboratory. Using the framework of the CSP, we constructed a solver, using the library Gecode, 2 for in- ference of consistent networks, using as input a time series arising from microarrays data. Then, by simulating the dynamics of a sample of networks found in the previous step, we were able to determine some interesting constraints to filter the set of networks. We apply our method to three datasets: two artificial, and for validation, we use a time series of an artificial network known from literature. Thus we were able to infer genetic networks sets of possible interest for laboratory tests.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第23397号 / 情博第766号 / 新制||情||131(附属図書館) / 京都大学大学院情報学研究科知能情報学専攻 / (主査)教授 阿久津 達也, 教授 山本 章博, 教授 鹿島 久嗣 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

The high cost of processor fabrication plants and approaching physical limits have started a new wave research in alternative computing paradigms. As an alternative to the top-down manufactured silicon-based computers, research in computing using natural and physical system directly has recently gained a great deal of interest. A branch of this research promotes the idea that any physical system with sufficiently complex dynamics is able to perform computation. The power of networks in representing complex interactions between many parts make them a suitable choice for modeling physical systems. Many studies used networks with a homogeneous structure to describe the computational circuits. However physical systems are inherently heterogeneous. We aim to study the effect of heterogeneity in the dynamics of physical systems that pertains to information processing. Two particularly well-studied network models that represent information processing in a wide range of physical systems are Random Boolean Networks (RBN), that are used to model gene interactions, and Liquid State Machines (LSM), that are used to model brain-like networks. In this thesis, we study the effects of function heterogeneity, in-degree heterogeneity, and interconnect irregularity on the dynamics and the performance of RBN and LSM. First, we introduce the model parameters to characterize the heterogeneity of components in RBN and LSM networks. We then quantify the effects of heterogeneity on the network dynamics. For the three heterogeneity aspects that we studied, we found that the effect of heterogeneity on RBN and LSM are very different. We find that in LSM the in-degree heterogeneity decreases the chaoticity in the network, whereas it increases chaoticity in RBN. For interconnect irregularity, heterogeneity decreases the chaoticity in LSM while its effects on RBN the dynamics depends on the connectivity. For {K} < 2, heterogeneity in the interconnect will increase the chaoticity in the dynamics and for {K} > 2 it decreases the chaoticity. We find that function heterogeneity has virtually no effect on the LSM dynamics. In RBN however, function heterogeneity actually makes the dynamics predictable as a function of connectivity and heterogeneity in the network structure. We hypothesize that node heterogeneity in RBN may help signal processing because of the variety of signal decomposition by different nodes.

Unification modulo the theory of Boolean algebras has been investigated by several autors. Nevertheless, the exact complexity of the decision problem for unification with constants and general unification was not known. In this research note, we show that the decision problem is complete for unification with constants and PSPACE-complete for general unification. In contrast, the decision problem for elementary unification (where the terms to be unified contain only symbols of the signature of Boolean algebras) is 'only' NP-complete.

No description available.

Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics - which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equational theories. In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics. / This report has also appeared as Report No. 03-03, Department of Computer Science, The University of Iowa.

The past two decades have seen a surge in the number of applications requiring precise positioning data. Modern cellular networks offer many services based on the user's location, such as emergency services (e.g., E911), and emerging wireless sensor networks are being used in applications spanning environmental monitoring, precision agriculture, warehouse and manufacturing logistics, and traffic monitoring, just to name a few. In these sensor networks in particular, obtaining precise positioning data of the sensors gives vital context to the measurements being reported. While the Global Positioning System (GPS) has traditionally been used to obtain this positioning data, the deployment locations of these cellular and sensor networks in GPS-constrained environments (e.g., cities, indoors, etc.), along with the need for reliable positioning, requires a localization scheme that does not rely solely on GPS. This has lead to localization being performed entirely by the network infrastructure itself, or by the network infrastructure aided, in part, by GPS. In the literature, benchmarking localization performance in these networks has traditionally been done in a deterministic manner. That is, for a fixed setup of anchors (nodes with known location) and a target (a node with unknown location) a commonly used benchmark for localization error, such as the Cramer-Rao lower bound (CRLB), can be calculated for a given localization strategy, e.g., time-of-arrival (TOA), angle-of-arrival (AOA), etc. While this CRLB calculation provides excellent insight into expected localization performance, its traditional treatment as a deterministic value for a specific setup is limited. Rather than trying to gain insight into a specific setup, network designers are more often interested in aggregate localization error statistics within the network as a whole. Questions such as: "What percentage of the time is localization error less than x meters in the network?" are commonplace. In order to answer these types of questions, network designers often turn to simulations; however, these come with many drawbacks, such as lengthy execution times and the inability to provide fundamental insights due to their inherent ``block box'' nature. Thus, this dissertation presents the first analytical solution with which to answer these questions. By leveraging tools from stochastic geometry, anchor positions and potential target positions can be modeled by Poisson point processes (PPPs). This allows for the CRLB of position error to be characterized over all setups of anchor positions and potential target positions realizable within the network. This leads to a distribution of the CRLB, which can completely characterize localization error experienced by a target within the network, and can consequently be used to answer questions regarding network-wide localization performance. The particular CRLB distribution derived in this dissertation is for fourth-generation (4G) and fifth-generation (5G) sub-6GHz networks employing a TOA localization strategy. Recognizing the tremendous potential that stochastic geometry has in gaining new insight into localization, this dissertation continues by further exploring the union of these two fields. First, the concept of localizability, which is the probability that a mobile is able to obtain an unambiguous position estimate, is explored in a 5G, millimeter wave (mm-wave) framework. In this framework, unambiguous single-anchor localization is possible with either a line-of-sight (LOS) path between the anchor and mobile or, if blocked, then via at least two NLOS paths. Thus, for a single anchor-mobile pair in a 5G, mm-wave network, this dissertation derives the mobile's localizability over all environmental realizations this anchor-mobile pair is likely to experience in the network. This is done by: (1) utilizing the Boolean model from stochastic geometry, which statistically characterizes the random positions, sizes, and orientations of reflectors (e.g., buildings) in the environment, (2) considering the availability of first-order (i.e., single-bounce) reflections as well as the LOS path, and (3) considering the possibility that reflectors can either facilitate or block reflections. In addition to the derivation of the mobile's localizability, this analysis also reveals that unambiguous localization, via reflected NLOS signals exclusively, is a relatively small contributor to the mobile's overall localizability. Lastly, using this first-order reflection framework developed under the Boolean model, this dissertation then statistically characterizes the NLOS bias present on range measurements. This NLOS bias is a common phenomenon that arises when trying to measure the distance between two nodes via the time delay of a transmitted signal. If the LOS path is blocked, then the extra distance that the signal must travel to the receiver, in excess of the LOS path, is termed the NLOS bias. Due to the random nature of the propagation environment, the NLOS bias is a random variable, and as such, its distribution is sought. As before, assuming NLOS propagation is due to first-order reflections, and that reflectors can either facilitate or block reflections, the distribution of the path length (i.e., absolute time delay) of the first-arriving multipath component (MPC) is derived. This result is then used to obtain the first NLOS bias distribution in the localization literature that is based on the absolute delay of the first-arriving MPC for outdoor time-of-flight (TOF) range measurements. This distribution is shown to match exceptionally well with commonly assumed gamma and exponential NLOS bias models in the literature, which were only attained previously through heuristic or indirect methods. Finally, the flexibility of this analytical framework is utilized by further deriving the angle-of-arrival (AOA) distribution of the first-arriving MPC at the mobile. This distribution gives novel insight into how environmental obstacles affect the AOA and also represents the first AOA distribution, of any kind, derived under the Boolean model. In summary, this dissertation uses the analytical tools offered by stochastic geometry to gain new insights into localization metrics by performing analyses over the entire ensemble of infrastructure or environmental realizations that a target is likely to experience in a network. / Doctor of Philosophy / The past two decades have seen a surge in the number of applications requiring precise positioning data. Modern cellular networks offer many services based on the user's location, such as emergency services (e.g., E911), and emerging wireless sensor networks are being used in applications spanning environmental monitoring, precision agriculture, warehouse and manufacturing logistics, and traffic monitoring, just to name a few. In these sensor networks in particular, obtaining precise positioning data of the sensors gives vital context to the measurements being reported. While the Global Positioning System (GPS) has traditionally been used to obtain this positioning data, the deployment locations of these cellular and sensor networks in GPS-constrained environments (e.g., cities, indoors, etc.), along with the need for reliable positioning, requires a localization scheme that does not rely solely on GPS. This has lead to localization being performed entirely by the network infrastructure itself, or by the network infrastructure aided, in part, by GPS. When speaking in terms of localization, the network infrastructure consists of what are called anchors, which are simply nodes (points) with a known location. These can be base stations, WiFi access points, or designated sensor nodes, depending on the network. In trying to determine the position of a target (i.e., a user, or a mobile), various measurements can be made between this target and the anchor nodes in close proximity. These measurements are typically distance (range) measurements or angle (bearing) measurements. Localization algorithms then process these measurements to obtain an estimate of the target position. The performance of a given localization algorithm (i.e., estimator) is typically evaluated by examining the distance, in meters, between the position estimates it produces vs. the actual (true) target position. This is called the positioning error of the estimator. There are various benchmarks that bound the best (lowest) error that these algorithms can hope to achieve; however, these benchmarks depend on the particular setup of anchors and the target. The benchmark of localization error considered in this dissertation is the Cramer-Rao lower bound (CRLB). To determine how this benchmark of localization error behaves over the entire network, all of the various setups of anchors and the target that would arise in the network must be considered. Thus, this dissertation uses a field of statistics called stochastic geometry} to model all of these random placements of anchors and the target, which represent all the setups that can be experienced in the network. Under this model, the probability distribution of this localization error benchmark across the entirety of the network is then derived. This distribution allows network designers to examine localization performance in the network as a whole, rather than just for a specific setup, and allows one to obtain answers to questions such as: "What percentage of the time is localization error less than x meters in the network?" Next, this dissertation examines a concept called localizability, which is the probability that a target can obtain a unique position estimate. Oftentimes localization algorithms can produce position estimates that congregate around different potential target positions, and thus, it is important to know when algorithms will produce estimates that congregate around a unique (single) potential target position; hence the importance of localizability. In fifth generation (5G), millimeter wave (mm-wave) networks, only one anchor is needed to produce a unique target position estimate if the line-of-sight (LOS) path between the anchor and the target is unimpeded. If the LOS path is impeded, then a unique target position can still be obtained if two or more non-line-of-sight (NLOS) paths are available. Thus, over all possible environmental realizations likely to be experienced in the network by this single anchor-mobile pair, this dissertation derives the mobile's localizability, or in this case, the probability the LOS path or at least two NLOS paths are available. This is done by utilizing another analytical tool from stochastic geometry known as the Boolean model, which statistically characterizes the random positions, sizes, and orientations of reflectors (e.g., buildings) in the environment. Under this model, considering the availability of first-order (i.e., single-bounce) reflections as well as the LOS path, and considering the possibility that reflectors can either facilitate or block reflections, the mobile's localizability is derived. This result reveals the roles that the LOS path and the NLOS paths play in obtaining a unique position estimate of the target. Using this first-order reflection framework developed under the Boolean model, this dissertation then statistically characterizes the NLOS bias present on range measurements. This NLOS bias is a common phenomenon that arises when trying to measure the distance between two nodes via the time-of-flight (TOF) of a transmitted signal. If the LOS path is blocked, then the extra distance that the signal must travel to the receiver, in excess of the LOS path, is termed the NLOS bias. As before, assuming NLOS propagation is due to first-order reflections and that reflectors can either facilitate or block reflections, the distribution of the path length (i.e., absolute time delay) of the first-arriving multipath component (MPC) (or first-arriving ``reflection path'') is derived. This result is then used to obtain the first NLOS bias distribution in the localization literature that is based on the absolute delay of the first-arriving MPC for outdoor TOF range measurements. This distribution is shown to match exceptionally well with commonly assumed NLOS bias distributions in the literature, which were only attained previously through heuristic or indirect methods. Finally, the flexibility of this analytical framework is utilized by further deriving angle-of-arrival (AOA) distribution of the first-arriving MPC at the mobile. This distribution yields the probability that, for a specific angle, the first-arriving reflection path arrives at the mobile at this angle. This distribution gives novel insight into how environmental obstacles affect the AOA and also represents the first AOA distribution, of any kind, derived under the Boolean model. In summary, this dissertation uses the analytical tools offered by stochastic geometry to gain new insights into localization metrics by performing analyses over all of the possible infrastructure or environmental realizations that a target is likely to experience in a network.

A Probabilistically Checkable Proof (PCP) of a mathematical statement is a proof written in a special manner that allows for efficient probabilistic verification. The celebrated PCP Theorem states that for every family of statements in NP, there is a probabilistic verification procedure that checks the validity of a PCP proof by reading only 3 bits from it. This landmark theorem, and the works leading up to it, laid the foundation for many subsequent works in computational complexity theory, the most prominent among them being the study of inapproximability of combinatorial optimization problems. This thesis focuses on a broad class of combinatorial optimization problems called Constraint Satisfaction Problems (CSPs). In an instance of a CSP problem of arity k, we are given a set of variables taking values from some finite domain, and a set of constraints each involving a subset of at most k variables. The goal is to find an assignment that simultaneously satisfies as many constraints as possible. An alternative formulation of the goal that is commonly used is Gap-CSP, where the goal is to decide whether a CSP instance is satisfiable or far from satisfiable, where the exact meaning of being far from satisfiable varies depending on the problems.We first study Boolean CSPs, where the domain of the variables is {0,1}. The main question we study is the hardness of distinguishing satisfiable Boolean CSP instances from those for which no assignment satisfies more than some epsilon fraction of the constraints. Intuitively, as the arity increases, the CSP gets more complex and thus the hardness parameter epsilon should decrease. We show that for Boolean CSPs of arity k, it is NP-hard to distinguish satisfiable instances from those that are at most 2^{~O(k^{1/3})}/2^k-satisfiable. We also study coloring of graphs and hypergraphs. Given a graph or a hypergraph, a coloring is an assignment of colors to vertices, such that all edges or hyperedges are non-monochromatic. The gap problem is to distinguish instances that are colorable with a small number of colors, from those that require a large number of colors. For graphs, we prove that there exists a constant K_0&gt;0, such that for any K &gt;= K_0, it is NP-hard to distinguish K-colorable graphs from those that require 2^{Omega(K^{1/3})} colors. For hypergraphs, we prove that it is quasi-NP-hard to distinguish 2-colorable 8-uniform hypergraphs of size N from those that require 2^{(log N)^{1/4-o(1)}} colors. In terms of techniques, all these results are based on constructions of PCPs with perfect completeness, that is, PCPs where the probabilistic proof verification procedure always accepts a correct proof. Not only is this a very natural property for proofs, but it can also be an essential requirement in many applications. It has always been particularly challenging to construct PCPs with perfect completeness for NP statements due to limitations in techniques. Our improved hardness results build on and extend many of the current approaches. Our Boolean CSP result and GraphColoring result were proved by adapting the Direct Sum of PCPs idea by Siu On Chan to the perfect completeness setting. Our proof for hypergraph coloring hardness improves and simplifies the recent work by Khot and Saket, in which they proposed the notion of superposition complexity of CSPs. / Ett probabilistiskt verifierbart bevis (eng: Probabilistically Checkable Proof, PCP) av en matematisk sats är ett bevis skrivet på ett speciellt sätt vilket möjliggör en effektiv probabilistisk verifiering. Den berömda PCP-satsen säger att för varje familj av påståenden i NP finns det en probabilistisk verifierare som kontrollerar om en PCP bevis är giltigt genom att läsa endast 3 bitar från det. Denna banbrytande sats, och arbetena som ledde fram till det, lade grunden för många senare arbeten inom komplexitetsteorin, framförallt inom studiet av approximerbarhet av kombinatoriska optimeringsproblem. I denna avhandling fokuserar vi på en bred klass av optimeringsproblem i form av villkorsuppfyllningsproblem (engelska ``Constraint Satisfaction Problems'' CSPs). En instans av ett CSP av aritet k ges av en mängd variabler som tar värden från någon ändlig domän, och ett antal villkor som vart och ett beror på en delmängd av högst k variabler. Målet är att hitta ett tilldelning av variablerna som samtidigt uppfyller så många som möjligt av villkoren. En alternativ formulering av målet som ofta används är Gap-CSP, där målet är att avgöra om en CSP-instans är satisfierbar eller långt ifrån satisfierbar, där den exakta innebörden av att vara ``långt ifrån satisfierbar'' varierar beroende på problemet.Först studerar vi booleska CSPer, där domänen är {0,1}. Den fråga vi studerar är svårigheten av att särskilja satisfierbara boolesk CSP-instanser från instanser där den bästa tilldelningen satisfierar högst en andel epsilon av villkoren. Intuitivt, när ariten ökar blir CSP mer komplexa och därmed bör svårighetsparametern epsilon avta med ökande aritet. Detta visar sig vara sant och ett första resultat är att för booleska CSP av aritet k är det NP-svårt att särskilja satisfierbara instanser från dem som är högst 2^{~O(k^{1/3})}/2^k-satisfierbara. Vidare studerar vi färgläggning av grafer och hypergrafer. Givet en graf eller en hypergraf, är en färgläggning en tilldelning av färger till noderna, så att ingen kant eller hyperkant är monokromatisk. Problemet vi analyserar är att särskilja instanser som är färgbara med ett litet antal färger från dem som behöver många färger. För grafer visar vi att det finns en konstant K_0&gt;0, så att för alla K &gt;= K_0 är det NP-svårt att särskilja grafer som är K-färgbara från dem som kräver minst 2^{Omega(K^{1/3})} färger. För hypergrafer visar vi att det är kvasi-NP-svårt att särskilja 2-färgbara 8-likformiga hypergrafer som har N noder från dem som kräv minst 2^{(log N)^{1/4-o(1)}} färger. Samtliga dessa resultat bygger på konstruktioner av PCPer med perfekt fullständighet. Det vill säga PCPer där verifieraren alltid accepterar ett korrekt bevis. Inte bara är detta en mycket naturlig egenskap för PCPer, men det kan också vara ett nödvändigt krav för vissa tillämpningar. Konstruktionen av PCPer med perfekt fullständighet för NP-påståenden ger tekniska komplikationer och kräver delvis utvecklande av nya metoder. Vårt booleska CSPer resultat och vårt Färgläggning resultat bevisas genom att anpassa ``Direktsumman-metoden'' introducerad av Siu On Chan till fallet med perfekt fullständighet. Vårt bevis för hypergraffärgningssvårighet förbättrar och förenklar ett färskt resultat av Khot och Saket, där de föreslog begreppet superpositionskomplexitet av CSP. / <p>QC 20150916</p>

The evolution of metabolism regulation is an intertwined process, where different strategies are constantly being developed towards a cognitive ability to perceive and respond to an environment. Organisms depend on an orchestration of a complex set of chemical reactions: maintaining homeostasis with a changing environment, while simultaneously sending material and energetic resources to where they are needed. The success of an organism requires efficient metabolic regulation, highlighting the connection between evolution, population dynamics and the underlying biochemistry. In this work, I represent organisms as coupled information-processing networks, that is, gene-regulatory networks receiving signals from the environment and acting on chemical reactions, eventually affecting material flows. I discuss the mechanisms through which metabolism control is improved during evolution and how the nonlinearities of competition influence this solution-searching process. The propagation of the populations through the resulting landscapes generally point to the role of the rhythm of cell division as an essential phenotypic feature driving evolution. Subsequently, as it naturally follows, different representations of organisms as oscillators are constructed to indicate more precisely how the interplay between competition, maturation timing and cell-division synchronisation affects the expected evolutionary outcomes, not always leading to the \"survival of the fastest\".

<p>U radu je razmatran problem dizajna i minimizacije rekurzivne<br />Bulove formule konstruisane za proizvoljnu Bulovu funkciju y:BN<br />&rarr;B.<br />U cilju rešavanja ovog problema, predstavljene su dve algoritamske<br />heuristike za minimizaciju rekurzivne Bulove formule. Minimizacija<br />rekurzivne Bulove formule vrši se korišćenjem regularnih poredaka<br />pozitivnih proizvod termova. U disertaciji je dokazano kako je ova<br />regularnost poredaka zapravo potreban i dovoljan uslov da željena<br />Bulova funcija y bude korektno predstavljena rekurzivnom Bulovom<br />formulom konstruisanom na osnovu tih poredaka. Pokazano je i kako<br />predstavljeni algoritmi daju bolje rezultate za veći broj instanci<br />problema u poređenju sa algoritmima dostupnim u literaturi.</p> / <p>In this thesis, the problem of design and minimization of recursive Boolean<br />formula, based on an arbitrary Boolean function y:BN<br />&rarr;B , is considered. As a<br />solution of a problem, two heuristic algorithms that minimize the length of<br />recursive Boolean formula, were presented. Minimization, itself, is done by<br />using regular orders of positive product terms. In the thesis it was proved that<br />the regularity of orders represents necessary and sufficient condition for<br />correct representation of Boolean function y by recursive Boolean formula<br />based on such regular order. Developed algorithms are compared with other<br />heuristic algorithms for recursive Boolean formula minimization, available in<br />the literature, and it is shown how algorithms proposed in this thesis provide<br />better results for more problem instances.</p>