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We consider a particular class of n-dimensional homogeneous diffusions all of which have an identity diffusion matrix and a drift function that is piecewise constant and scale invariant. Abstract stochastic calculus immediately gives us general results about existence and uniqueness in law and invariant probability distributions when they exist. These invariant distributions are probability measures on the $n$-dimensional space and can be extremely resistant to a more detailed understanding. To have a better analysis, we construct a polyhedra such that the inward normal at its surface is given by the drift function and show that the finer structures of the invariant probability measure is intertwined with the geometry of the polyhedra. We show that several natural interacting Brownian particle models can thus be analyzed by studying the combinatorial fan generated by the drift function, particularly when these are simplicial. This is the case when the polyhedra is a polytope that is invariant under a Coxeter group action, which leads to an explicit description of the invariant measures in terms of iid Exponential random variables. Another class of examples is furnished by interactions indexed by weighted graphs all of which generate simplicial polytopes with $n !$ faces. We show that the proportion of volume contained in each component simplex corresponds to a probability distribution on the group of permutations, some of which have surprising connections with the classical urn models.

We consider auctions in which the players have very limited knowledge about their own valuations. Specifically, the only information that a Knightian player $i$ has about the profile of true valuations, $\theta^*$, consists of a set of distributions, from one of which $\theta_i^*$ has been drawn. The VCG mechanism guarantees very high social welfare both in single- and multi-good auctions, so long as Knightian players do not select strategies that are dominated. With such Knightian players, however, we prove that the VCG mechanism guarantees very poor social welfare in unrestricted combinatorial auctions.

The notion of treewidth plays an important role in theoretical and practical studies of graph problems. It has been recognized that, especially in practical environments, when computing the treewidth of a graph it is invaluable to first apply an array of preprocessing rules that simplify and shrink it. This work seeks to prove rigorous performance guarantees for such preprocessing rules, both known and new ones, by studying them in the framework of kernelization from parameterized complexity. It is known that the NP-complete problem of determining whether a given graph G has treewidth at most k admits no polynomial-time preprocessing algorithm that reduces any input instance to size polynomial in k, unless NP is in coNP/poly and the polynomial hierarchy collapses to its third level. In this paper we therefore consider structural graph measures larger than treewidth, and determine whether efficient preprocessing can shrink the instance size to a polynomial in such a parameter value. We prove that given an instance (G,k) of treewidth we can efficiently reduce its size to O(fvs(G)^4) vertices, where fvs(G) is the size of a minimum feedback vertex set in G. We can also prove a size reduction to O(vc(G)^3) vertices, where vc(G) is the size of a minimum vertex cover. Phrased in the language of parameterized complexity, we show that Treewidth has a polynomial kernel when parameterized by the size of a given feedback vertex set, and also by the size of a vertex cover. In contrast we show that Treewidth parameterized by the vertex-deletion distance to a single clique, and Weighted Treewidth parameterized by the size of a vertex cover, do not admit polynomial kernelizations unless NP is in coNP/poly.

Unique Sink Orientations (USOs) are an appealing abstraction of several major optimization problems of applied mathematics such as for instance Linear Programming (LP), Markov Decision Processes (MDPs) or 2-player Turn Based Stochastic Games (2TBSGs). A polynomial time algorithm to find the sink of a USO would translate into a strongly polynomial time algorithm to solve the aforementioned problems---a major quest for all three cases. In addition, we may translate MDPs and 2TBSGs into the problem of finding the sink of an acyclic USO of a cube, which can be done using the well-known Policy Iteration algorithm (PI). The study of its complexity is the object of this work. Despite its exponential worst case complexity, the principle of PI is a powerful source of inspiration for other methods. As our first contribution, we disprove Hansen and Zwick's conjecture claiming that the number of steps of PI should follow the Fibonacci sequence in the worst case. Our analysis relies on a new combinatorial formulation of the problem---the so-called Order-Regularity formulation (OR). Then, for our second contribution, we (exponentially) improve the $\Omega(1.4142^n)$ lower bound on the number of steps of PI from Schurr and Szab\'o in the case of the OR formulation and obtain an $\Omega(1.4269^n)$ bound.

A ``hybrid method'', dedicated to asymptotic coefficient extraction in combinatorial generating functions, is presented, which combines Darboux's method and singularity analysis theory. This hybrid method applies to functions that remain of moderate growth near the unit circle and satisfy suitable smoothness assumptions--this, even in the case when the unit circle is a natural boundary. A prime application is to coefficients of several types of infinite product generating functions, for which full asymptotic expansions (involving periodic fluctuations at higher orders) can be derived. Examples relative to permutations, trees, and polynomials over finite fields are treated in this way.

This research determined the costs, benefits and efficiency of the Post 9/11 Era GI Bill Transferability benefit by simulating four different retention mechanisms and comparing the cost of each to provide desired retention levels among a population of sailors who valued the Transferability benefit more than or less than the Cost of the mechanisms investigated were a purely monetary auction, a Universal Incentive Package (UIP) Auction, and the Combinatorial Retention Auction Mechanism (CRAM). All three mechanisms were simulated, data were analyzed and results were compared. The CRAM clearly showed it was the most efficient method for meeting retention objectives while constraining Costs to the Navy as much as possible. Cost savings to the Navy ranged from 27% to 51% over Cash Only Selective Reenlistment Bonuses (SRB). Furthermore, this report confirms that an across-the-board benefit such as GI Bill Transferability significantly reduces the positive surplus when sailors who have a Value of Transferability less than the Cost of Transferability nonetheless exploit this benefit. Maintaining the status quo SRB policy combined with the estimated negative retention effects of the GI Bill Transferability benefit only magnifies the cost ineffectiveness of the Post 9/11 Era GI Bill.

This research determined the costs, benefits and efficiency of the Post 9/11 Era GI Bill Transferability benefit by simulating four different retention mechanisms and comparing the cost of each to provide desired retention levels among a population of sailors who valued the Transferability benefit more than or less than the Cost of the mechanisms investigated were a purely monetary auction, a Universal Incentive Package (UIP) Auction, and the Combinatorial Retention Auction Mechanism (CRAM). All three mechanisms were simulated, data were analyzed and results were compared. The CRAM clearly showed it was the most efficient method for meeting retention objectives while constraining Costs to the Navy as much as possible. Cost savings to the Navy ranged from 27% to 51% over Cash Only Selective Reenlistment Bonuses (SRB). Furthermore, this report confirms that an across-the-board benefit such as GI Bill Transferability significantly reduces the positive surplus when sailors who have a Value of Transferability less than the Cost of Transferability nonetheless exploit this benefit. Maintaining the status quo SRB policy combined with the estimated negative retention effects of the GI Bill Transferability benefit only magnifies the cost ineffectiveness of the Post 9/11 Era GI Bill.

28 p. 28 cm

28 p. 28 cm

This thesis examines the combination of three algorithms: Graph Theoretic Tracker (GTT), Hough Transform, and Heuristic Search to enhance the detection of spectral tracks of underwater targets in LOFARGRAMS. Previous studies examined these algorithms separately. Here, GTT is used as a pre-processor of the LOFARGRAM display data to locat optimum paths of signals through noise. The line tonals in the output image from GTT are then manipulated by the Hough Transform into clusters of points in parameter space. A Heuristic Search sorting technique is employed to determine cluster centers. These cluster centers are then reconstructed back into line tonals using the inverse Hough Transform formula. The results of this thesis show improvements by taking the Hough Transform of the original LOFARGRAM masked by the output of GTT. The effect of background noise is offset by the accumulation in the parameter space. Subsequently, the recovery of desired tonals is improved.

We study the periods mapping from the moduli space of real hyperelliptic curves with marked point on an oriented oval to the euclidean space. The mapping arises in the analysis of Chebyshev construction used in the constrained optimization of the uniform norm of polynomials and rational functions. The decomposition of the moduli space into polyhedra labeled by planar graphs allows to investigate the global topology of low dimensional fibers of the periods mapping.

We study the periods mapping from the moduli space of real hyperelliptic curves with marked point on an oriented oval to the euclidean space. The mapping arises in the analysis of Chebyshev construction used in the constrained optimization of the uniform norm of polynomials and rational functions. The decomposition of the moduli space into polyhedra labeled by planar graphs allows to investigate the global topology of low dimensional fibers of the periods mapping.

This article is from BMC Bioinformatics , volume 15 . Abstract Background: Measuring the impact of combinations of genetic or chemical perturbations on cellular fitness, sometimes referred to as synthetic lethal screening, is a powerful method for obtaining novel insights into gene function and drug action. Especially when performed at large scales, gene-gene or gene-drug interaction screens can reveal complex genetic interactions or drug mechanism of action or even identify novel therapeutics for the treatment of diseases.The result of such large-scale screen results can be represented as a matrix with a numeric score indicating the cellular fitness (e.g. viability or doubling time) for each double perturbation. In a typical screen, the majority of combinations do not impact the cellular fitness. Thus, it is critical to first discern true "hits" from noise. Subsequent data exploration and visualization methods can assist to extract meaningful biological information from the data. However, despite the increasing interest in combination perturbation screens, no user friendly open-source program exists that combines statistical analysis, data exploration tools and visualization. Results: We developed TOPS (Tool for Combination Perturbation Screen Analysis), a Java and R-based software tool with a simple graphical user interface that allows the user to import, analyze, filter and plot data from double perturbation screens as well as other compatible data. TOPS was designed in a modular fashion to allow the user to add alternative importers for data formats or custom analysis scripts not covered by the original release.We demonstrate the utility of TOPS on two datasets derived from functional genetic screens using different methods. Dataset 1 is a gene-drug interaction screen and is based on Luminex xMAP technology. Dataset 2 is a gene-gene short hairpin (sh)RNAi screen exploring the interactions between deubiquitinating enzymes and a number of prominent oncogenes using massive parallel sequencing (MPS). Conclusions: TOPS provides the benchtop scientist with a free toolset to analyze, filter and visualize data from functional genomic gene-gene and gene-drug interaction screens with a flexible interface to accommodate different technologies and analysis algorithms in addition to those already provided here. TOPS is freely available for academic and non-academic users and is released as open source.

This article is from BMC Bioinformatics , volume 15 . Abstract Background: Measuring the impact of combinations of genetic or chemical perturbations on cellular fitness, sometimes referred to as synthetic lethal screening, is a powerful method for obtaining novel insights into gene function and drug action. Especially when performed at large scales, gene-gene or gene-drug interaction screens can reveal complex genetic interactions or drug mechanism of action or even identify novel therapeutics for the treatment of diseases.The result of such large-scale screen results can be represented as a matrix with a numeric score indicating the cellular fitness (e.g. viability or doubling time) for each double perturbation. In a typical screen, the majority of combinations do not impact the cellular fitness. Thus, it is critical to first discern true "hits" from noise. Subsequent data exploration and visualization methods can assist to extract meaningful biological information from the data. However, despite the increasing interest in combination perturbation screens, no user friendly open-source program exists that combines statistical analysis, data exploration tools and visualization. Results: We developed TOPS (Tool for Combination Perturbation Screen Analysis), a Java and R-based software tool with a simple graphical user interface that allows the user to import, analyze, filter and plot data from double perturbation screens as well as other compatible data. TOPS was designed in a modular fashion to allow the user to add alternative importers for data formats or custom analysis scripts not covered by the original release.We demonstrate the utility of TOPS on two datasets derived from functional genetic screens using different methods. Dataset 1 is a gene-drug interaction screen and is based on Luminex xMAP technology. Dataset 2 is a gene-gene short hairpin (sh)RNAi screen exploring the interactions between deubiquitinating enzymes and a number of prominent oncogenes using massive parallel sequencing (MPS). Conclusions: TOPS provides the benchtop scientist with a free toolset to analyze, filter and visualize data from functional genomic gene-gene and gene-drug interaction screens with a flexible interface to accommodate different technologies and analysis algorithms in addition to those already provided here. TOPS is freely available for academic and non-academic users and is released as open source.

This article is from BMC Bioinformatics , volume 15 . Abstract Background: Measuring the impact of combinations of genetic or chemical perturbations on cellular fitness, sometimes referred to as synthetic lethal screening, is a powerful method for obtaining novel insights into gene function and drug action. Especially when performed at large scales, gene-gene or gene-drug interaction screens can reveal complex genetic interactions or drug mechanism of action or even identify novel therapeutics for the treatment of diseases.The result of such large-scale screen results can be represented as a matrix with a numeric score indicating the cellular fitness (e.g. viability or doubling time) for each double perturbation. In a typical screen, the majority of combinations do not impact the cellular fitness. Thus, it is critical to first discern true "hits" from noise. Subsequent data exploration and visualization methods can assist to extract meaningful biological information from the data. However, despite the increasing interest in combination perturbation screens, no user friendly open-source program exists that combines statistical analysis, data exploration tools and visualization. Results: We developed TOPS (Tool for Combination Perturbation Screen Analysis), a Java and R-based software tool with a simple graphical user interface that allows the user to import, analyze, filter and plot data from double perturbation screens as well as other compatible data. TOPS was designed in a modular fashion to allow the user to add alternative importers for data formats or custom analysis scripts not covered by the original release.We demonstrate the utility of TOPS on two datasets derived from functional genetic screens using different methods. Dataset 1 is a gene-drug interaction screen and is based on Luminex xMAP technology. Dataset 2 is a gene-gene short hairpin (sh)RNAi screen exploring the interactions between deubiquitinating enzymes and a number of prominent oncogenes using massive parallel sequencing (MPS). Conclusions: TOPS provides the benchtop scientist with a free toolset to analyze, filter and visualize data from functional genomic gene-gene and gene-drug interaction screens with a flexible interface to accommodate different technologies and analysis algorithms in addition to those already provided here. TOPS is freely available for academic and non-academic users and is released as open source.

This article is from BMC Bioinformatics , volume 15 . Abstract Background: Measuring the impact of combinations of genetic or chemical perturbations on cellular fitness, sometimes referred to as synthetic lethal screening, is a powerful method for obtaining novel insights into gene function and drug action. Especially when performed at large scales, gene-gene or gene-drug interaction screens can reveal complex genetic interactions or drug mechanism of action or even identify novel therapeutics for the treatment of diseases.The result of such large-scale screen results can be represented as a matrix with a numeric score indicating the cellular fitness (e.g. viability or doubling time) for each double perturbation. In a typical screen, the majority of combinations do not impact the cellular fitness. Thus, it is critical to first discern true "hits" from noise. Subsequent data exploration and visualization methods can assist to extract meaningful biological information from the data. However, despite the increasing interest in combination perturbation screens, no user friendly open-source program exists that combines statistical analysis, data exploration tools and visualization. Results: We developed TOPS (Tool for Combination Perturbation Screen Analysis), a Java and R-based software tool with a simple graphical user interface that allows the user to import, analyze, filter and plot data from double perturbation screens as well as other compatible data. TOPS was designed in a modular fashion to allow the user to add alternative importers for data formats or custom analysis scripts not covered by the original release.We demonstrate the utility of TOPS on two datasets derived from functional genetic screens using different methods. Dataset 1 is a gene-drug interaction screen and is based on Luminex xMAP technology. Dataset 2 is a gene-gene short hairpin (sh)RNAi screen exploring the interactions between deubiquitinating enzymes and a number of prominent oncogenes using massive parallel sequencing (MPS). Conclusions: TOPS provides the benchtop scientist with a free toolset to analyze, filter and visualize data from functional genomic gene-gene and gene-drug interaction screens with a flexible interface to accommodate different technologies and analysis algorithms in addition to those already provided here. TOPS is freely available for academic and non-academic users and is released as open source.

This article is from BMC Bioinformatics , volume 15 . Abstract Background: Measuring the impact of combinations of genetic or chemical perturbations on cellular fitness, sometimes referred to as synthetic lethal screening, is a powerful method for obtaining novel insights into gene function and drug action. Especially when performed at large scales, gene-gene or gene-drug interaction screens can reveal complex genetic interactions or drug mechanism of action or even identify novel therapeutics for the treatment of diseases.The result of such large-scale screen results can be represented as a matrix with a numeric score indicating the cellular fitness (e.g. viability or doubling time) for each double perturbation. In a typical screen, the majority of combinations do not impact the cellular fitness. Thus, it is critical to first discern true "hits" from noise. Subsequent data exploration and visualization methods can assist to extract meaningful biological information from the data. However, despite the increasing interest in combination perturbation screens, no user friendly open-source program exists that combines statistical analysis, data exploration tools and visualization. Results: We developed TOPS (Tool for Combination Perturbation Screen Analysis), a Java and R-based software tool with a simple graphical user interface that allows the user to import, analyze, filter and plot data from double perturbation screens as well as other compatible data. TOPS was designed in a modular fashion to allow the user to add alternative importers for data formats or custom analysis scripts not covered by the original release.We demonstrate the utility of TOPS on two datasets derived from functional genetic screens using different methods. Dataset 1 is a gene-drug interaction screen and is based on Luminex xMAP technology. Dataset 2 is a gene-gene short hairpin (sh)RNAi screen exploring the interactions between deubiquitinating enzymes and a number of prominent oncogenes using massive parallel sequencing (MPS). Conclusions: TOPS provides the benchtop scientist with a free toolset to analyze, filter and visualize data from functional genomic gene-gene and gene-drug interaction screens with a flexible interface to accommodate different technologies and analysis algorithms in addition to those already provided here. TOPS is freely available for academic and non-academic users and is released as open source.

The paper is devoted to upper bounds on run-time of Non-Elitist Genetic Algorithms until some target subset of solutions is visited for the first time. In particular, we consider the sets of optimal solutions and the sets of local optima as the target subsets. Previously known upper bounds are improved by means of drift analysis. Finally, we propose conditions ensuring that a Non-Elitist Genetic Algorithm efficiently finds approximate solutions with constant approximation ratio on the class of combinatorial optimization problems with guaranteed local optima (GLO).

This article is from Molecular Systems Biology , volume 7 . Abstract A combinatorial depletion strategy is combined with biochemistry, quantitative proteomics and computational approaches to elucidate the structure of the SAGA/ADA complexes. The analysis reveals five connected functional modules capable of independent assembly.

Combinatorial Analysis. The Foundations of a New Theory. MacMahon, P Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Math. or Phys. Character (1896-1934). 1900-01-01. 194:361–386

In the principles-and-parameters model of language, the principle known as 'free indexation' plays an important part in the process of determining the referential properties of elements such as anaphors and pronominals. This paper addresses two issues. (1) We investigate the combinatorics of free indexation. By relating the problem to the n-set partitioning problem, we show that free indexation must produce an exponential number of referentially distinct phrase structures given a structure with n (independent) noun phrases. (2) We introduce an algorithm for free indexation that is defined compositionally on phrase structures. We show how the compositional nature of the algorithm makes it possible to incrementally interleave the computation of free indexation with phrase structure construction. Additionally, we prove the algorithm to be an 'optimal' procedure for free indexation. More precisely, by relating the compositional structure of the formulation to the combinatorial analysis, we show that the algorithm enumerates precisely all possible indexings, without duplicates.

Fomin and Mikhalkin give formulas for computing Severi degrees using long-edge graphs. We define \tau-graphs that generalize their graphs, and a closely related family of combinatorial objects (\tau, n)-words. By considering their generating functions, we prove a linearity conjecture of Block, Colley and Kennedy, which gives a combinatorial proof of the result that the polynomials appearing in the formal logarithm of the generating function for Severi degrees are quadratic.

This research determined the costs, benefits and efficiency of the Post 9/11 Era GI Bill Transferability benefit by simulating four different retention mechanisms and comparing the cost of each to provide desired retention levels among a population of sailors who valued the Transferability benefit more than or less than the Cost of the mechanisms investigated were a purely monetary auction, a Universal Incentive Package (UIP) Auction, and the Combinatorial Retention Auction Mechanism (CRAM). All three mechanisms were simulated, data were analyzed and results were compared. The CRAM clearly showed it was the most efficient method for meeting retention objectives while constraining Costs to the Navy as much as possible. Cost savings to the Navy ranged from 27% to 51% over Cash Only Selective Reenlistment Bonuses (SRB). Furthermore, this report confirms that an across-the-board benefit such as GI Bill Transferability significantly reduces the positive surplus when sailors who have a Value of Transferability less than the Cost of Transferability nonetheless exploit this benefit. Maintaining the status quo SRB policy combined with the estimated negative retention effects of the GI Bill Transferability benefit only magnifies the cost ineffectiveness of the Post 9/11 Era GI Bill.

Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backbones drawn horizontally on top of each other such that (1) intramolecular and intermolecular bonds are noncrossing and (2) there is no "zig-zag" configuration. This paper studies joint structures with arc-length at least four in which both, interior and exterior stack-lengths are at least two (no isolated arcs). The key idea in this paper is to consider a new type of shape, based on which joint structures can be derived via symbolic enumeration. Our results imply simple asymptotic formulas for the number of joint structures with surprisingly small exponential growth rates. They are of interest in the context of designing prediction algorithms for RNA-RNA interactions.

Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backbones drawn horizontally on top of each other such that (1) intramolecular and intermolecular bonds are noncrossing and (2) there is no "zig-zag" configuration. This paper studies joint structures with arc-length at least four in which both, interior and exterior stack-lengths are at least two (no isolated arcs). The key idea in this paper is to consider a new type of shape, based on which joint structures can be derived via symbolic enumeration. Our results imply simple asymptotic formulas for the number of joint structures with surprisingly small exponential growth rates. They are of interest in the context of designing prediction algorithms for RNA-RNA interactions.

Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backbones drawn horizontally on top of each other such that (1) intramolecular and intermolecular bonds are noncrossing and (2) there is no "zig-zag" configuration. This paper studies joint structures with arc-length at least four in which both, interior and exterior stack-lengths are at least two (no isolated arcs). The key idea in this paper is to consider a new type of shape, based on which joint structures can be derived via symbolic enumeration. Our results imply simple asymptotic formulas for the number of joint structures with surprisingly small exponential growth rates. They are of interest in the context of designing prediction algorithms for RNA-RNA interactions.

Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backbones drawn horizontally on top of each other such that (1) intramolecular and intermolecular bonds are noncrossing and (2) there is no "zig-zag" configuration. This paper studies joint structures with arc-length at least four in which both, interior and exterior stack-lengths are at least two (no isolated arcs). The key idea in this paper is to consider a new type of shape, based on which joint structures can be derived via symbolic enumeration. Our results imply simple asymptotic formulas for the number of joint structures with surprisingly small exponential growth rates. They are of interest in the context of designing prediction algorithms for RNA-RNA interactions.

This article is from BMC Plant Biology , volume 12 . Abstract Background: Lupulin glands of hop produce a specific metabolome including hop bitter acids valuable for the brewing process and prenylflavonoids with promising health-beneficial activities. The detailed analysis of the transcription factor (TF)-mediated regulation of the oligofamily of one of the key enzymes, i.e., chalcone synthase CHS_H1 that efficiently catalyzes the production of naringenin chalcone, a direct precursor of prenylflavonoids in hop, constitutes an important part of the dissection of the biosynthetic pathways leading to the accumulation of these compounds. Results: Homologues of flavonoid-regulating TFs HlMyb2 (M2), HlbHLH2 (B2) and HlWDR1 (W1) from hop were cloned using a lupulin gland-specific cDNA library from the hop variety Osvald's 72. Using a "combinatorial" transient GUS expression system it was shown that these unique lupulin-gland-associated TFs significantly activated the promoter (P) of chs_H1 in ternary combinations of B2, W1 and either M2 or the previously characterized HlMyb3 (M3). The promoter activation was strongly dependent on the Myb-P binding box TCCTACC having a core sequence CCWACC positioned on its 5' end region and it seems that the complexity of the promoter plays an important role. M2B2W1-mediated activation significantly exceeded the strength of expression of native chs_H1 gene driven by the 35S promoter of CaMV, while M3B2W1 resulted in 30% of the 35S:chs_H1 expression level, as quantified by real-time PCR. Another newly cloned hop TF, HlMyb7, containing a transcriptional repressor-like motif pdLNLD/ELxiG/S (PDLNLELRIS), was identified as an efficient inhibitor of chs_H1-activating TFs. Comparative analyses of hop and A. thaliana TFs revealed a complex activation of Pchs_H1 and Pchs4 in combinatorial or independent manners. Conclusions: This study on the sequences and functions of various lupulin gland-specific transcription factors provides insight into the complex character of the regulation of the chs_H1 gene that depends on variable activation by combinations of R2R3Myb, bHLH and WDR TF homologues and inhibition by a Myb repressor.

We give combinatorial descriptions of two stochastic growth models for series-parallel networks introduced by Hosam Mahmoud by encoding the growth process via recursive tree structures. Using decompositions of the tree structures and applying analytic combinatorics methods allows a study of quantities in the corresponding series-parallel networks. For both models we obtain limiting distribution results for the degree of the poles and the length of a random source-to-sink path, and furthermore we get asymptotic results for the expected number of source-to-sink paths.

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover, a type of integer programming (IP) problem. A lattice-gas model on the Erd\"os-R\'enyi random graphs of $\alpha$-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical-mechanical model with a one-parameter family. Statistical-mechanical analyses reveal for $\alpha=2$ that the LP optimal solution is typically equal to that given by the IP below the critical average degree $c=e$ in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result $c=1$, and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with $\alpha\geq 3$, minimum vertex covers on $\alpha$-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree $c=e/(\alpha-1)$ where the replica symmetry is broken.

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover, a type of integer programming (IP) problem. A lattice-gas model on the Erd\"os-R\'enyi random graphs of $\alpha$-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical-mechanical model with a one-parameter family. Statistical-mechanical analyses reveal for $\alpha=2$ that the LP optimal solution is typically equal to that given by the IP below the critical average degree $c=e$ in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result $c=1$, and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with $\alpha\geq 3$, minimum vertex covers on $\alpha$-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree $c=e/(\alpha-1)$ where the replica symmetry is broken.

We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then it would also be deleted. A player wins the game when the other player has no moves available. We study this game under various viewpoints: by finding specific strategies for certain families of graphs, through using properties of a graph's automorphism group, by writing a program to look at Sprague-Grundy numbers, and by studying the game when played on random graphs. When analyzing Grim played on paths, using the Sprague-Grundy function, we find a connection to a standing open question about Octal games.

The main objective of the project was to investigate phase transformations in high-temperature shape memory alloys (HTSMA) through use of combinatorial nanocalorimetry. Calorimetry is a powerful characterization tool that is used to study phase transformations and reactions in materials. Nanocalorimetry is a novel variant of this technique in which thin-film and micro-machining technologies are used to fabricate calorimeter sensors that are much more sensitive than traditional calorimeters, that can access a much broader range of heating and cooling rates, and that lend themselves well to combinatorial studies.

The effect of an organic solvent atmosphere on ink deposition and deposition transport rate was studied and quantified. Various chemical compounds spanning a range of hydrophobicities and meniscus solubilities were used as inks in DPN and deposited in a variety of solvent atmospheres such as ethanol, methanol, hexanes and methylene chloride. The data obtained in these experiments will improve our understanding of the factors that govern the rate of ink delivery from tip to substrate, especially for air or water sensitive adsorbates. Another interesting outcome of these studies was the observation that introduction of an organic solvent into an inert atmosphere will increase the diffusion rate of certain alkanethiols by orders of magnitude and hence increase the deposition rate of these materials onto solid surfaces. These studies are in the process of being written up for publication, and submission to Langmuir is planned.

244 p. 24 cm

This article is from International Journal of Molecular Sciences , volume 14 . Abstract Delivery of secretory immunoglobulin A (sIgA) to mucosal surfaces as a passive immunotherapy agent is a promising strategy to prevent infectious diseases. Recombinant sIgA production in plants requires the co-expression of four transcriptional units encoding the light chain (LC), heavy chain (HC), joining chain (JC) and secretory component (SC). As a way to optimize sIgA production in plants, we tested the combinatorial expression of 16 versions of a human sIgA against the VP8* rotavirus antigen in Nicotiana benthamiana, using the recently developed GoldenBraid multigene assembly system. Each sIgA version was obtained by combining one of the two types of HC (α1 and α2) with one of the two LC types (k and λ) and linking or not a KDEL peptide to the HC and/or SC. From the analysis of the anti-VP8* activity, it was concluded that those sIgA versions carrying HCα1 and LCλ provided the highest yields. Moreover, ER retention significantly increased antibody production, particularly when the KDEL signal was linked to the SC. Maximum expression levels of 32.5 μg IgA/g fresh weight (FW) were obtained in the best performing combination, with an estimated 33% of it in the form of a secretory complex.

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

Abstract: A series of genome-scale algorithms and high-performance implementations is described and shown to be useful in the genetic analysis of gene transcription. With them it is possible to address common questions such as: are the sets of genes coexpressed under one type of conditions the same as those sets co-expressed under another? A new noise-adaptive graph algorithm, dubbed paraclique, is introduced and analyzed for use in biological hypotheses testing. A notion of vertex coverage is also devised, based on vertex-disjoint paths within correlation graphs, and used to determine the identity, proportion and number of transcripts connected to individual phenotypes and quantitative trait loci (QTL) regulatory models. A major goal is to identify which, among a set of candidate genes, are the most likely regulators of trait variation. These methods are applied in an effort to identify multiple-QTL regulatory models for large groups of genetically co-expressed genes, and to extrapolate the consequences of this genetic variation on phenotypes observed across levels of biological scale through the evaluation of vertex coverage. This approach is furthermore applied to definitions of homology-based gene sets, and the incorporation of categorical data such as known gene pathways. In all these tasks discrete mathematics and combinatorial algorithms form organizing principles upon which methods and implementations are based. Keywords: Microarray Analysis, Putative Co-Regulation, Quantitative Trait Loci, Regulatory Models

This research project was concerned with probabilistic analysis of a class of discrete optimization problems whose underlying combinatorial structure is based on hypergraph matchings. The primary goal of was to provide theoretical insights into characteristic behavior and properties of this class of problems, which would furnish guidelines for development and tuning of solution algorithms, both exact and heuristic, as well as determine amenability of this class of problems to particular types of solution methods. We have established convergence limits for the optimal values of randomized hypergraph matching problems, along with the corresponding convergence rates, and proposed algorithms for finding solutions with guaranteed quality. For hypergraph matching problems with linear objectives, this task reduces to finding k-cliques in specially constructed k-partite graphs, for which a new branch-and-bound algorithm was developed that employs bit parallelism to achieve significant computational improvements over existing methods. In a related development, the behavior of quasi-cliques in random graphs was investigated, and it was ascertained that the size of the maximum quasi-clique undergoes a first-order phase transition, one of the first results of this kind.

The main objective of the project was to investigate phase transformations in high-temperature shape memory alloys (HTSMA) through use of combinatorial nanocalorimetry. Calorimetry is a powerful characterization tool that is used to study phase transformations and reactions in materials. Nanocalorimetry is a novel variant of this technique in which thin-film and micro-machining technologies are used to fabricate calorimeter sensors that are much more sensitive than traditional calorimeters, that can access a much broader range of heating and cooling rates, and that lend themselves well to combinatorial studies.

In modern biology, one of the most important research problems is to understand how protein sequences fold into their native 3D structures. To investigate this problem at a high level, one wishes to analyze the protein landscapes, i.e., the structures of the space of all protein sequences and their native 3D structures. Perhaps the most basic computational problem at this level is to take a target 3D structure as input and design a fittest protein sequence with respect to one or more fitness functions of the target 3D structure. We develop a toolbox of combinatorial techniques for protein landscape analysis in the Grand Canonical model of Sun, Brem, Chan, and Dill. The toolbox is based on linear programming, network flow, and a linear-size representation of all minimum cuts of a network. It not only substantially expands the network flow technique for protein sequence design in Kleinberg's seminal work but also is applicable to a considerably broader collection of computational problems than those considered by Kleinberg. We have used this toolbox to obtain a number of efficient algorithms and hardness results. We have further used the algorithms to analyze 3D structures drawn from the Protein Data Bank and have discovered some novel relationships between such native 3D structures and the Grand Canonical model.

Bell System Technical Journal, 50: 7. September 1971 pp 2465-2484. A Combinatorial Analysis of the Main Distributing Frame: Spare Requirements for Conversion to Preferential Assignment from Random Assignment. (Schumer, M.A.)

This talk will be a survey of some recent developments in average-case analysis of algorithms for combinatorial problems. I will focus on random distributions which seem to yield computationally challenging problems and where to find the 'easiest hard problems' and the 'hardest easy problems'. As a detailed example, I will describe the modular subset sum problem, where you are given n numbers, a modulus M, and a target number T, and the goal is to find a subset of the numbers which sum to T (mod M). Though this is a classic NP-hard problem, many particular instances are not too challenging computationally. When the n numbers are selected uniformly at random from {0, 1, ... , M-1}, the difficulty depends critically on the size of M (as a function of n). I will describe what is known about this complicated relationship, including results from [Flaxman and Przydatek, STACS 2005] which describe an algorithm that succeeds in expected polynomial time when M = n O(log n) . I will also talk about another combinatorial problem, which related to the minimum spanning tree. When the cost of the edges between n nodes are selected independently and uniformly from [0,1], the cost of the minimum spanning tree converges to a constant, and the constant is ζ(3) = 1/1 3 + 1/2 3 + 1/3 3 + ... [Frieze, Discrete Appl. Math.1985]. In the two-stage stochastic programming version of this problem [Flaxman, Frieze, and Krivelevich, SODA 2005/Random Structures Algorithms 2006], you know the costs of each edge on Monday and the distribution of the costs of each edge on Tuesday. The goal is to select a set of edges to buy on Monday so that when the tree is completed on Tuesday, the expected total cost is minimized. When the Monday and Tuesday costs are all selected independently and uniformly from [0,1], a simple threshold heuristic produces a solution with expected cost ζ(3) - 1/2. This is not the optimal two-stage solution, however. ©2006 Microsoft Corporation. All rights reserved.

Combinatorial Analysis.--The Foundations of a New Theory. MacMahon, P Proceedings of the Royal Society of London (1854-1905). 1899-01-01. 66:336–337

Combinatorial optimization is widely applied in a number of areas nowadays. Unfortunately, many combinatorial optimization problems are NP-hard which usually means that they are unsolvable in practice. However, it is often unnecessary to have an exact solution. In this case one may use heuristic approach to obtain a near-optimal solution in some reasonable time. We focus on two combinatorial optimization problems, namely the Generalized Traveling Salesman Problem and the Multidimensional Assignment Problem. The first problem is an important generalization of the Traveling Salesman Problem; the second one is a generalization of the Assignment Problem for an arbitrary number of dimensions. Both problems are NP-hard and have hosts of applications. In this work, we discuss different aspects of heuristics design and evaluation. A broad spectrum of related subjects, covered in this research, includes test bed generation and analysis, implementation and performance issues, local search neighborhoods and efficient exploration algorithms, metaheuristics design and population sizing in memetic algorithm. The most important results are obtained in the areas of local search and memetic algorithms for the considered problems. In both cases we have significantly advanced the existing knowledge on the local search neighborhoods and algorithms by systematizing and improving the previous results. We have proposed a number of efficient heuristics which dominate the existing algorithms in a wide range of time/quality requirements. Several new approaches, introduced in our memetic algorithms, make them the state-of-the-art metaheuristics for the corresponding problems. Population sizing is one of the most promising among these approaches; it is expected to be applicable to virtually any memetic algorithm.

Combinatorial optimization problems are problems that have a large number of discrete solutions and a cost function for evaluating those solutions in comparison to one another. With the vital need of solving the combinatorial problem, several research efforts have been concentrated on the biological entities behaviors to utilize such behaviors in population-based metaheuristic. This paper presents bee colony algorithms which is one of the sophisticated biological nature life. A brief detail of the nature of bee life has been presented with further classification of its behaviors. Furthermore, an illustration of the algorithms that have been derived from bee colony which are bee colony optimization, and artificial bee colony. Finally, a comparative analysis has been conducted between these algorithms according to the results of the traveling salesman problem solution. Where the bee colony optimization (BCO) rendered the best performance in terms of computing time and results.

Substantial changes in many parts of the paper. In particular, significantly expanded treatment of monomial ideals and of Castelnuovo-Mumford regularity. Also relation between delta-regularity and Noether normalisation now treated.

Substantial changes in many parts of the paper. In particular, significantly expanded treatment of monomial ideals and of Castelnuovo-Mumford regularity. Also relation between delta-regularity and Noether normalisation now treated.

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of NK landscapes as an example. In our case the inherent network is the graph whose vertices represent the local maxima in the landscape, and the edges account for the transition probabilities between their corresponding basins of attraction. We exhaustively extracted such networks on representative NK landscape instances, and performed a statistical characterization of their properties. We found that most of these network properties are related to the search difficulty on the underlying NK landscapes with varying values of K.