Publisher name: Oxford University Press PY - 2015/1/1 Y1 - 2015/1/1 N2 - Motivation: MS2-GFP-tagging of RNA is currently the only method to measure intervals between consecutive transcription events in live cells. For this, new transcripts must be accurately detected from intensity time traces. Results: We present a novel method for automatically estimating RNA numbers and production intervals from temporal data of cell fluorescence intensities that reduces uncertainty by exploiting temporal information. We also derive a robust variant, more resistant to outliers caused e.g. by RNAs moving out of focus. Using Monte Carlo simulations, we show that the quantification of RNA numbers and production intervals is generally improved compared with previous methods. Finally, we analyze data from live Escherichia coli and show statistically significant differences to previous methods. The new methods can be used to quantify numbers and production intervals of any fluorescent probes, which are present in low copy numbers, are brighter than the cell background and degrade slowly. Availability: Source code is available under Mozilla Public License at http://www.cs.tut.fi/%7ehakkin22/jumpdet/. Contact: AB - Motivation: MS2-GFP-tagging of RNA is currently the only method to measure intervals between consecutive transcription events in live cells. For this, new transcripts must be accurately detected from intensity time traces. Results: We present a novel method for automatically estimating RNA numbers and production intervals from temporal data of cell fluorescence intensities that reduces uncertainty by exploiting temporal information. We also derive a robust variant, more resistant to outliers caused e.g. by RNAs moving out of focus. Using Monte Carlo simulations, we show that the quantification of RNA numbers and production intervals is generally improved compared with previous methods. Finally, we analyze data from live Escherichia coli and show statistically significant differences to previous methods. The new methods can be used to quantify numbers and production intervals of any fluorescent probes, which are present in low copy numbers, are brighter than the cell background and degrade slowly. Availability: Source code is available under Mozilla Public License at http://www.cs.tut.fi/%7ehakkin22/jumpdet/. Contact: UR - http://www.scopus.com/inward/record.url?scp=84922352843&partnerID=8YFLogxK U2 - 10.1093/bioinformatics/btu592 DO - 10.1093/bioinformatics/btu592 M3 - Article VL - 31 SP - 69 EP - 75 JO - Bioinformatics JF - Bioinformatics SN - 1367-4803 IS - 1 ER - TY - JOUR T1 - Characterizing rate limiting steps in transcription from RNA production times in live cells AU - Häkkinen, Antti AU - Ribeiro, Andre S. PY - 2016/5/1 Y1 - 2016/5/1 N2 - Motivation: Single-molecule measurements of live Escherichia coli transcription dynamics suggest that this process ranges from sub- to super-Poissonian, depending on the conditions and on the promoter. For its accurate quantification, we propose a model that accommodates all these settings, and statistical methods to estimate the model parameters and to select the relevant components. Results: The new methodology has improved accuracy and avoids overestimating the transcription rate due to finite measurement time, by exploiting unobserved data and by accounting for the effects of discrete sampling. First, we use Monte Carlo simulations of models based on measurements to show that the methods are reliable and offer substantial improvements over previous methods. Next, we apply the methods on measurements of transcription intervals of different promoters in live E. coli, and show that they produce significantly different results, both in low- and high-noise settings, and that, in the latter case, they even lead to qualitatively different results. Finally, we demonstrate that the methods can be generalized for other similar purposes, such as for estimating gene activation kinetics. In this case, the new methods allow quantifying the inducer uptake dynamics as opposed to just comparing them between cases, which was not previously possible. We expect this new methodology to be a valuable tool for functional analysis of cellular processes using single-molecule or single-event microscopy measurements in live cells. AB - Motivation: Single-molecule measurements of live Escherichia coli transcription dynamics suggest that this process ranges from sub- to super-Poissonian, depending on the conditions and on the promoter. For its accurate quantification, we propose a model that accommodates all these settings, and statistical methods to estimate the model parameters and to select the relevant components. Results: The new methodology has improved accuracy and avoids overestimating the transcription rate due to finite measurement time, by exploiting unobserved data and by accounting for the effects of discrete sampling. First, we use Monte Carlo simulations of models based on measurements to show that the methods are reliable and offer substantial improvements over previous methods. Next, we apply the methods on measurements of transcription intervals of different promoters in live E. coli, and show that they produce significantly different results, both in low- and high-noise settings, and that, in the latter case, they even lead to qualitatively different results. Finally, we demonstrate that the methods can be generalized for other similar purposes, such as for estimating gene activation kinetics. In this case, the new methods allow quantifying the inducer uptake dynamics as opposed to just comparing them between cases, which was not previously possible. We expect this new methodology to be a valuable tool for functional analysis of cellular processes using single-molecule or single-event microscopy measurements in live cells. U2 - 10.1093/bioinformatics/btv744 DO - 10.1093/bioinformatics/btv744 M3 - Article VL - 32 SP - 1346 EP - 1352 JO - Bioinformatics JF - Bioinformatics SN - 1367-4803 IS - 9 ER - TY - JOUR T1 - Hypermonogenic solutions and plane waves of the Dirac operator in Rp×Rq AU - Guzmán Adán, Alí AU - Orelma, Heikki AU - Sommen, Franciscus PY - 2019/4/1 Y1 - 2019/4/1 N2 - In this paper we first define hypermonogenic solutions of the Dirac operator in Rp×Rq and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function class in classical Clifford analysis. After that, we define the corresponding hypermonogenic plane wave solutions and deduce explicit methods to compute these functions. AB - In this paper we first define hypermonogenic solutions of the Dirac operator in Rp×Rq and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function class in classical Clifford analysis. After that, we define the corresponding hypermonogenic plane wave solutions and deduce explicit methods to compute these functions. KW - Cauchy's formula KW - Hypermonogenic solution KW - Plane wave U2 - 10.1016/j.amc.2018.09.058 DO - 10.1016/j.amc.2018.09.058 M3 - Article VL - 346 SP - 1 EP - 14 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 ER - TY - GEN T1 - Resilient Cooperative Voltage Control for Distribution Network with High Penetration Distributed Energy Resources AU - Gusrialdi, Azwirman AU - Xu, Ying AU - Qu, Zhihua AU - Simaan, Marwan A. PY - 2020 Y1 - 2020 N2 - This paper considers the problem of designing a resilient distributed voltage control algorithm for distribution systems with high penetration of distributed energy resources in the presence of an unknown cyber-attack. The purpose of the attack is to force the system to violate the operating voltage limit by intercepting its communication channels and inserting exogenous signals to perturb and/or modify the information being exchanged. We first review the cooperative voltage control proposed in our previous work and provide a new stability analysis for it. Next, we present a resilient cooperative voltage control algorithm by introducing a virtual system interconnected with the original system such that the voltage can be maintained within the operational limit under unknown attacks. The resiliency of the proposed algorithm is demonstrated via simulations on the IEEE 8500-node system when subjected to an attack which consists of corrupting the data being exchanged in the communication network between two generation units. AB - This paper considers the problem of designing a resilient distributed voltage control algorithm for distribution systems with high penetration of distributed energy resources in the presence of an unknown cyber-attack. The purpose of the attack is to force the system to violate the operating voltage limit by intercepting its communication channels and inserting exogenous signals to perturb and/or modify the information being exchanged. We first review the cooperative voltage control proposed in our previous work and provide a new stability analysis for it. Next, we present a resilient cooperative voltage control algorithm by introducing a virtual system interconnected with the original system such that the voltage can be maintained within the operational limit under unknown attacks. The resiliency of the proposed algorithm is demonstrated via simulations on the IEEE 8500-node system when subjected to an attack which consists of corrupting the data being exchanged in the communication network between two generation units. KW - cooperative control KW - cyber attacks KW - distribution network KW - resilient control KW - Voltage control M3 - Conference contribution SN - 978-1-7281-8813-3 SP - 1533 EP - 1539 BT - European Control Conference 2020, ECC 2020 PB - IEEE ER - TY - JOUR T1 - Unite and conquer T2 - Univariate and multivariate approaches for finding differentially expressed gene sets AU - Glazko, Galina V. AU - Emmert-Streib, Frank PY - 2009/9 Y1 - 2009/9 N2 - Motivation: Recently, many univariate and several multivariate approaches have been suggested for testing differential expression of gene sets between different phenotypes. However, despite a wealth of literature studying their performance on simulated and real biological data, still there is a need to quantify their relative performance when they are testing different null hypotheses. Results: In this article, we compare the performance of univariate and multivariate tests on both simulated and biological data. In the simulation study we demonstrate that high correlations equally affect the power of both, univariate as well as multivariate tests. In addition, for most of them the power is similarly affected by the dimensionality of the gene set and by the percentage of genes in the set, for which expression is changing between two phenotypes. The application of different test statistics to biological data reveals that three statistics (sum of squared t-tests, Hotelling's T2, N-statistic), testing different null hypotheses, find some common but also some complementing differentially expressed gene sets under specific settings. This demonstrates that due to complementing null hypotheses each test projects on different aspects of the data and for the analysis of biological data it is beneficial to use all three tests simultaneously instead of focusing exclusively on just one. AB - Motivation: Recently, many univariate and several multivariate approaches have been suggested for testing differential expression of gene sets between different phenotypes. However, despite a wealth of literature studying their performance on simulated and real biological data, still there is a need to quantify their relative performance when they are testing different null hypotheses. Results: In this article, we compare the performance of univariate and multivariate tests on both simulated and biological data. In the simulation study we demonstrate that high correlations equally affect the power of both, univariate as well as multivariate tests. In addition, for most of them the power is similarly affected by the dimensionality of the gene set and by the percentage of genes in the set, for which expression is changing between two phenotypes. The application of different test statistics to biological data reveals that three statistics (sum of squared t-tests, Hotelling's T2, N-statistic), testing different null hypotheses, find some common but also some complementing differentially expressed gene sets under specific settings. This demonstrates that due to complementing null hypotheses each test projects on different aspects of the data and for the analysis of biological data it is beneficial to use all three tests simultaneously instead of focusing exclusively on just one. U2 - 10.1093/bioinformatics/btp406 DO - 10.1093/bioinformatics/btp406 M3 - Article VL - 25 SP - 2348 EP - 2354 JO - Bioinformatics JF - Bioinformatics SN - 1367-4803 IS - 18 ER - TY - JOUR T1 - The watching system as a generalization of identifying code AU - Ghorbani, Modjtaba AU - Dehmer, Matthias AU - Maimani, Hamidreza AU - Maddah, Sheyda AU - Roozbayani, Maryam AU - Emmert-Streib, Frank PY - 2020 Y1 - 2020 N2 - The watching system, as a generalization of identifying code, has been defined by Auger in 2010. The identifying code has been used to wireless networks and it has been also applied to locate objects in the sensor networks. On the other hand, the graph product is employed in most of the mathematic branches such as network design to study the structure of network elements. In this paper, we give some upper bounds for the watching number of well-know product graphs. AB - The watching system, as a generalization of identifying code, has been defined by Auger in 2010. The identifying code has been used to wireless networks and it has been also applied to locate objects in the sensor networks. On the other hand, the graph product is employed in most of the mathematic branches such as network design to study the structure of network elements. In this paper, we give some upper bounds for the watching number of well-know product graphs. KW - Domination number KW - Graph products KW - Identifying code KW - Watching system U2 - 10.1016/j.amc.2020.125302 DO - 10.1016/j.amc.2020.125302 M3 - Article VL - 380 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 M1 - 125302 ER - TY - JOUR T1 - On k-Hypermonogenic Functions and Their Mean Value Properties AU - Eriksson, Sirkka-Liisa AU - Orelma, Heikki PY - 2016 Y1 - 2016 N2 - We study a hyperbolic version of holomorphic functions to higher dimensions. In this frame work, a generalization of holomorphic functions are called (Formula presented.)-hypermonogenic functions. These functions are depending on several real variables and their values are in a Clifford algebra. They are defined in terms of hyperbolic Dirac operators. They are connected to harmonic functions with respect to the Riemannian metric (Formula presented.) in the same way as the usual harmonic function to holomorphic functions. We present the mean value property for (Formula presented.)-hypermonogenic functions and related results. Earlier the mean value properties has been proved for hypermonogenic functions. The key tools are the invariance properties of the hyperbolic metric. AB - We study a hyperbolic version of holomorphic functions to higher dimensions. In this frame work, a generalization of holomorphic functions are called (Formula presented.)-hypermonogenic functions. These functions are depending on several real variables and their values are in a Clifford algebra. They are defined in terms of hyperbolic Dirac operators. They are connected to harmonic functions with respect to the Riemannian metric (Formula presented.) in the same way as the usual harmonic function to holomorphic functions. We present the mean value property for (Formula presented.)-hypermonogenic functions and related results. Earlier the mean value properties has been proved for hypermonogenic functions. The key tools are the invariance properties of the hyperbolic metric. KW - Dirac operator KW - Hyperbolic metric KW - Hypermonogenic KW - Monogenic U2 - 10.1007/s11785-015-0445-z DO - 10.1007/s11785-015-0445-z M3 - Article VL - 10 SP - 311 EP - 325 JO - Complex Analysis and Operator Theory JF - Complex Analysis and Operator Theory SN - 1661-8254 IS - 2 ER - TY - JOUR T1 - Hypermonogenic Functions of Two Vector Variables AU - Eriksson, S. L. AU - Orelma, H. AU - Vieira, N. N1 - EXT="Eriksson, S. L." PY - 2018 Y1 - 2018 N2 - In this paper we introduce the modified Dirac operators (Formula presented.) and (Formula presented.), where (Formula presented.) is differentiable function, and (Formula presented.) is the Clifford algebra generated by the basis vectors of (Formula presented.). We look for solutions (Formula presented.) of the system (Formula presented.), where the first and third variables are invariant under rotations. These functions are called (Formula presented.)-hypermonogenic functions. We discuss about axially symmetric functions with respect to the symmetric group (Formula presented.). Some examples of axially symmetric (Formula presented.)-hypermonogenic functions generated by homogeneous functions and hypergeometric functions are presented. AB - In this paper we introduce the modified Dirac operators (Formula presented.) and (Formula presented.), where (Formula presented.) is differentiable function, and (Formula presented.) is the Clifford algebra generated by the basis vectors of (Formula presented.). We look for solutions (Formula presented.) of the system (Formula presented.), where the first and third variables are invariant under rotations. These functions are called (Formula presented.)-hypermonogenic functions. We discuss about axially symmetric functions with respect to the symmetric group (Formula presented.). Some examples of axially symmetric (Formula presented.)-hypermonogenic functions generated by homogeneous functions and hypergeometric functions are presented. KW - Axially symmetric functions KW - Hypermonogenic functions KW - Modified Dirac operator KW - Several vector variables U2 - 10.1007/s11785-017-0728-7 DO - 10.1007/s11785-017-0728-7 M3 - Article VL - 12 SP - 555 EP - 570 JO - Complex Analysis and Operator Theory JF - Complex Analysis and Operator Theory SN - 1661-8254 IS - 2 ER - TY - JOUR T1 - A microscopic view of the mechanisms of active transport across the cellular membrane AU - Enkavi, Giray AU - Li, Jing AU - Wen, Pochao AU - Thangapandian, Sundarapandian AU - Moradi, Mahmoud AU - Jiang, Tao AU - Han, Wei AU - Tajkhorshid, Emad PY - 2014 Y1 - 2014 N2 - Membrane transporters are molecular machines that couple active transport of their specific substrates to various sources of cellular energy through a set of highly coordinated protein conformational changes. The alternating-access mechanism of transport in these proteins, which ensures that the substrate is only accessible from one side of the membrane at any given time, relies on complex and global protein conformational changes that are also closely coupled to molecular events such as substrate binding and translocation. In this review, we describe the application of advanced molecular modeling and simulation technologies to a number of membrane transport proteins studied in our laboratory. The goal is to demonstrate the power of the methods in describing functionally relevant molecular events ranging from more localized events such as substrate binding and gating motions to large, global protein conformational changes governing the transition of the protein between major functional states. AB - Membrane transporters are molecular machines that couple active transport of their specific substrates to various sources of cellular energy through a set of highly coordinated protein conformational changes. The alternating-access mechanism of transport in these proteins, which ensures that the substrate is only accessible from one side of the membrane at any given time, relies on complex and global protein conformational changes that are also closely coupled to molecular events such as substrate binding and translocation. In this review, we describe the application of advanced molecular modeling and simulation technologies to a number of membrane transport proteins studied in our laboratory. The goal is to demonstrate the power of the methods in describing functionally relevant molecular events ranging from more localized events such as substrate binding and gating motions to large, global protein conformational changes governing the transition of the protein between major functional states. KW - Conformational changes KW - Membrane transporters KW - Molecular dynamics KW - Nonequilibrium simulation KW - Primary transporters KW - Secondary transporters KW - Substrate binding UR - http://www.scopus.com/inward/record.url?scp=84919386963&partnerID=8YFLogxK U2 - 10.1016/B978-0-444-63378-1.00004-5 DO - 10.1016/B978-0-444-63378-1.00004-5 M3 - Article VL - 10 SP - 77 EP - 125 JO - Annual Reports in Computational Chemistry JF - Annual Reports in Computational Chemistry SN - 1574-1400 ER - TY - JOUR T1 - Universal construction mechanism for networks from one-dimensional symbol sequences AU - Emmert-Streib, Frank PY - 2012/10/15 Y1 - 2012/10/15 N2 - In this paper we introduce construction mechanisms to generate directed networks from one-dimensional symbol sequences. We prove that any of these construction mechanism leads to the same undirected network. Further, we prove that the introduced construction mechanisms are universal in the sense that any undirected network can be generated by such a mechanism. In addition, we provide various numerical examples to demonstrate the applicability of the introduced mechanism. AB - In this paper we introduce construction mechanisms to generate directed networks from one-dimensional symbol sequences. We prove that any of these construction mechanism leads to the same undirected network. Further, we prove that the introduced construction mechanisms are universal in the sense that any undirected network can be generated by such a mechanism. In addition, we provide various numerical examples to demonstrate the applicability of the introduced mechanism. KW - Complex networks KW - Network construction KW - Random networks KW - Symbol sequences KW - Universal network construction UR - http://www.scopus.com/inward/record.url?scp=84867336661&partnerID=8YFLogxK U2 - 10.1016/j.amc.2012.07.006 DO - 10.1016/j.amc.2012.07.006 M3 - Article VL - 219 SP - 1020 EP - 1030 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 IS - 3 ER - TY - JOUR T1 - Evolutionary dynamics of the spatial Prisoner's Dilemma with self-inhibition AU - Emmert-Streib, Frank PY - 2012/2/5 Y1 - 2012/2/5 N2 - In this paper we study the influence of interventions on self-interactions in a spatial Prisoner's Dilemma on a two-dimensional grid with periodic boundary conditions and synchronous updating of the dynamics. We investigate two different types of self-interaction modifications. The first type (FSIP) is deterministic, effecting each self-interaction of a player by a constant factor, whereas the second type (PSIP) performs a probabilistic interventions. Both types of interventions lead to a reduction of the payoff of the players and, hence, represent inhibiting effects. We find that a constant but moderate reduction of self-interactions has a very beneficial effect on the evolution of cooperators in the population, whereas probabilistic interventions on self-interactions are in general counter productive for the coexistence of the two different strategies. AB - In this paper we study the influence of interventions on self-interactions in a spatial Prisoner's Dilemma on a two-dimensional grid with periodic boundary conditions and synchronous updating of the dynamics. We investigate two different types of self-interaction modifications. The first type (FSIP) is deterministic, effecting each self-interaction of a player by a constant factor, whereas the second type (PSIP) performs a probabilistic interventions. Both types of interventions lead to a reduction of the payoff of the players and, hence, represent inhibiting effects. We find that a constant but moderate reduction of self-interactions has a very beneficial effect on the evolution of cooperators in the population, whereas probabilistic interventions on self-interactions are in general counter productive for the coexistence of the two different strategies. KW - Evolutionary dynamics KW - Evolutionary game theory KW - Game theory KW - Prisoner's dilemma UR - http://www.scopus.com/inward/record.url?scp=84855904251&partnerID=8YFLogxK U2 - 10.1016/j.amc.2011.12.018 DO - 10.1016/j.amc.2011.12.018 M3 - Article VL - 218 SP - 6482 EP - 6488 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 IS - 11 ER - TY - JOUR T1 - Topological mappings between graphs, trees and generalized trees AU - Emmert-Streib, Frank AU - Dehmer, Matthias PY - 2007/3/15 Y1 - 2007/3/15 N2 - We present novel topological mappings between graphs, trees and generalized trees that means between structured objects with different properties. The two major contributions of this paper are, first, to clarify the relation between graphs, trees and generalized trees, a graph class recently introduced. Second, these transformations provide a unique opportunity to transform structured objects into a representation that might be beneficial for a processing, e.g., by machine learning techniques for graph classification. AB - We present novel topological mappings between graphs, trees and generalized trees that means between structured objects with different properties. The two major contributions of this paper are, first, to clarify the relation between graphs, trees and generalized trees, a graph class recently introduced. Second, these transformations provide a unique opportunity to transform structured objects into a representation that might be beneficial for a processing, e.g., by machine learning techniques for graph classification. KW - Applied graph theory KW - Graph transformation KW - Hierarchical graphs UR - http://www.scopus.com/inward/record.url?scp=33947616843&partnerID=8YFLogxK U2 - 10.1016/j.amc.2006.07.162 DO - 10.1016/j.amc.2006.07.162 M3 - Article VL - 186 SP - 1326 EP - 1333 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 IS - 2 ER - TY - JOUR T1 - Information theoretic measures of UHG graphs with low computational complexity AU - Emmert-Streib, Frank AU - Dehmer, Matthias PY - 2007/7/15 Y1 - 2007/7/15 N2 - We introduce a novel graph class we call universal hierarchical graphs (UHG) whose topology can be found numerously in problems representing, e.g., temporal, spacial or general process structures of systems. For this graph class we show, that we can naturally assign two probability distributions, for nodes and for edges, which lead us directly to the definition of the entropy and joint entropy and, hence, mutual information establishing an information theory for this graph class. Furthermore, we provide some results under which conditions these constraint probability distributions maximize the corresponding entropy. Also, we demonstrate that these entropic measures can be computed efficiently which is a prerequisite for every large scale practical application and show some numerical examples. AB - We introduce a novel graph class we call universal hierarchical graphs (UHG) whose topology can be found numerously in problems representing, e.g., temporal, spacial or general process structures of systems. For this graph class we show, that we can naturally assign two probability distributions, for nodes and for edges, which lead us directly to the definition of the entropy and joint entropy and, hence, mutual information establishing an information theory for this graph class. Furthermore, we provide some results under which conditions these constraint probability distributions maximize the corresponding entropy. Also, we demonstrate that these entropic measures can be computed efficiently which is a prerequisite for every large scale practical application and show some numerical examples. KW - Entropy KW - Graph classes KW - Graph measures KW - Hierarchical graphs KW - Information theory UR - http://www.scopus.com/inward/record.url?scp=34250623666&partnerID=8YFLogxK U2 - 10.1016/j.amc.2007.02.095 DO - 10.1016/j.amc.2007.02.095 M3 - Article VL - 190 SP - 1783 EP - 1794 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 IS - 2 ER - TY - JOUR T1 - Algorithmic computation of knot polynomials of secondary structure elements of proteins AU - Emmert-Streib, Frank PY - 2006/10/1 Y1 - 2006/10/1 N2 - The classification of protein structures is an important and still outstanding problem. The purpose of this paper is threefold. First, we utilize a relation between the Tutte and homfly polynomial to show that the Alexander-Conway polynomial can be algorithmically computed for a given planar graph. Second, as special cases of planar graphs, we use polymer graphs of protein structures. More precisely, we use three building blocks of the three-dimensional protein structure - α-helix, antiparallel β-sheet, and parallel β-sheet - and calculate, for their corresponding polymer graphs, the Tutte polynomials analytically by providing recurrence equations for all three secondary structure elements. Third, we present numerical results comparing the results from our analytical calculations with the numerical results of our algorithm - not only to test consistency, but also to demonstrate that all assigned polynomials are unique labels of the secondary structure elements. This paves the way for an automatic classification of protein structures. AB - The classification of protein structures is an important and still outstanding problem. The purpose of this paper is threefold. First, we utilize a relation between the Tutte and homfly polynomial to show that the Alexander-Conway polynomial can be algorithmically computed for a given planar graph. Second, as special cases of planar graphs, we use polymer graphs of protein structures. More precisely, we use three building blocks of the three-dimensional protein structure - α-helix, antiparallel β-sheet, and parallel β-sheet - and calculate, for their corresponding polymer graphs, the Tutte polynomials analytically by providing recurrence equations for all three secondary structure elements. Third, we present numerical results comparing the results from our analytical calculations with the numerical results of our algorithm - not only to test consistency, but also to demonstrate that all assigned polynomials are unique labels of the secondary structure elements. This paves the way for an automatic classification of protein structures. KW - Knot polynomial KW - Planar graph KW - Protein structure KW - Topological invariant KW - Tutte polynomial UR - http://www.scopus.com/inward/record.url?scp=34547671421&partnerID=8YFLogxK U2 - 10.1089/cmb.2006.13.1503 DO - 10.1089/cmb.2006.13.1503 M3 - Article VL - 13 SP - 1503 EP - 1512 JO - Journal of Computational Biology JF - Journal of Computational Biology SN - 1066-5277 IS - 8 ER - TY - JOUR T1 - Modeling probability densities with sums of exponentials via polynomial approximation AU - Dumitrescu, Bogdan AU - Şicleru, Bogdan C. AU - Avram, Florin PY - 2016 Y1 - 2016 N2 - Abstract We propose a method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on shape-constrained optimization with exponential functions. Each function is lower and upper bounded on sub-intervals by low-degree polynomials. Thus, the constraints can be approximated with polynomial inequalities that can be implemented with linear matrix inequalities. Convexity is preserved, but the problem has now a finite number of constraints. We show how to take advantage of the properties of the exponential function in order to build quickly accurate approximations. The problem used for illustration is the least-squares fitting of a positive sum of exponentials to an empirical probability density function. When the exponents are given, the problem is convex, but we also give a procedure for optimizing the exponents. Several examples show that the method is flexible, accurate and gives better results than other methods for the investigated problems. AB - Abstract We propose a method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on shape-constrained optimization with exponential functions. Each function is lower and upper bounded on sub-intervals by low-degree polynomials. Thus, the constraints can be approximated with polynomial inequalities that can be implemented with linear matrix inequalities. Convexity is preserved, but the problem has now a finite number of constraints. We show how to take advantage of the properties of the exponential function in order to build quickly accurate approximations. The problem used for illustration is the least-squares fitting of a positive sum of exponentials to an empirical probability density function. When the exponents are given, the problem is convex, but we also give a procedure for optimizing the exponents. Several examples show that the method is flexible, accurate and gives better results than other methods for the investigated problems. KW - Density fitting KW - Optimization KW - Polynomial approximation KW - Semi-infinite programming KW - Sum of exponentials U2 - 10.1016/j.cam.2015.07.032 DO - 10.1016/j.cam.2015.07.032 M3 - Article VL - 292 SP - 513 EP - 525 JO - Journal of Computational and Applied Mathematics JF - Journal of Computational and Applied Mathematics SN - 0377-0427 ER - TY - GEN T1 - Chipless graphene tag and dual-CP reader for Internet of Things AU - Dong, Guoqing AU - Shen, Yizhu AU - He, Han AU - Virkki, Johanna AU - Hu, Sanming PY - 2017/9/26 Y1 - 2017/9/26 N2 - This paper proposes a printable chipless tag that encodes more bits than a conventional tag, and also a dual circularly polarized (CP) reader that achieves high isolation as well as insensitive orientation. To demonstrate this concept, a radio-frequency identification (RFID) tag with a compact size of 12mm × 12mm is designed to encode 8 bits covering 6-9 GHz, and is investigated with dual-CP backscattering characteristics. Using conductive ink such as graphene, it is possible to directly print this kind of chipless tag on A4 papers, clothes, plastics, etc. This flexible low-cost tag and dual-CP reader are promising to significantly benefit the Internet of Things (IoT). AB - This paper proposes a printable chipless tag that encodes more bits than a conventional tag, and also a dual circularly polarized (CP) reader that achieves high isolation as well as insensitive orientation. To demonstrate this concept, a radio-frequency identification (RFID) tag with a compact size of 12mm × 12mm is designed to encode 8 bits covering 6-9 GHz, and is investigated with dual-CP backscattering characteristics. Using conductive ink such as graphene, it is possible to directly print this kind of chipless tag on A4 papers, clothes, plastics, etc. This flexible low-cost tag and dual-CP reader are promising to significantly benefit the Internet of Things (IoT). KW - Chipless tag KW - dual circular polarization KW - Internet of Things (IoT) KW - radar cross section (RCS) KW - radio-frequency identification (RFID) M3 - Conference contribution BT - 2017 International Applied Computational Electromagnetics Society Symposium in China, ACES-China 2017 PB - IEEE ER - TY - JOUR T1 - Graph distance measures based on topological indices revisited AU - Dehmer, Matthias AU - Emmert-Streib, Frank AU - Shi, Yongtang PY - 2015/6/18 Y1 - 2015/6/18 N2 - Graph distance measures based on topological indices have been already explored by Dehmer et al. Also, inequalities for those graph distance measures have been proved. In this paper, we continue studying such comparative graph measures based on the well-known Wiener index, graph energy and Randić index, respectively. We prove extremal properties of the graph distance measures for some special classes of graphs. To demonstrate useful properties of the measures, we also discuss numerical results. To conclude the paper we state some open problems. AB - Graph distance measures based on topological indices have been already explored by Dehmer et al. Also, inequalities for those graph distance measures have been proved. In this paper, we continue studying such comparative graph measures based on the well-known Wiener index, graph energy and Randić index, respectively. We prove extremal properties of the graph distance measures for some special classes of graphs. To demonstrate useful properties of the measures, we also discuss numerical results. To conclude the paper we state some open problems. KW - Distance measure KW - Edit distance KW - Extremal graph KW - Topological index U2 - 10.1016/j.amc.2015.05.072 DO - 10.1016/j.amc.2015.05.072 M3 - Article VL - 266 SP - 623 EP - 633 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 ER - TY - JOUR T1 - A comparative analysis of multidimensional features of objects resembling sets of graphs AU - Dehmer, Matthias AU - Emmert-Streib, Frank AU - Gesell, Tanja PY - 2008/2/15 Y1 - 2008/2/15 N2 - In the present paper, we introduce a notion of a style representing abstract, complex objects having characteristics that can be represented as structured objects. Furthermore, we provide some mathematical properties of such styles. As a main result, we present a novel approach to perform a meaningful comparative analysis of such styles by defining and using graph-theoretic measures. We compare two styles by comparing the underlying feature sets representing sets of graph structurally. To determine the structural similarity between the underlying graphs, we use graph similarity measures that are computationally efficient. More precisely, in order to compare styles, we map each feature set to a so-called median graph and compare the resulting median graphs. As an application, we perform an experimental study to compare special styles representing sets of undirected graphs and present numerical results thereof. AB - In the present paper, we introduce a notion of a style representing abstract, complex objects having characteristics that can be represented as structured objects. Furthermore, we provide some mathematical properties of such styles. As a main result, we present a novel approach to perform a meaningful comparative analysis of such styles by defining and using graph-theoretic measures. We compare two styles by comparing the underlying feature sets representing sets of graph structurally. To determine the structural similarity between the underlying graphs, we use graph similarity measures that are computationally efficient. More precisely, in order to compare styles, we map each feature set to a so-called median graph and compare the resulting median graphs. As an application, we perform an experimental study to compare special styles representing sets of undirected graphs and present numerical results thereof. KW - Classification KW - Object comparison KW - Similarity KW - Structural similarity KW - Structured objects U2 - 10.1016/j.amc.2007.05.058 DO - 10.1016/j.amc.2007.05.058 M3 - Article VL - 196 SP - 221 EP - 235 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 IS - 1 ER - TY - JOUR T1 - An efficient heuristic approach to detecting graph isomorphism based on combinations of highly discriminating invariants AU - Dehmer, Matthias AU - Grabner, Martin AU - Mowshowitz, Abbe AU - Emmert-Streib, Frank PY - 2013/8 Y1 - 2013/8 N2 - The search for an easily computable, finite, complete set of graph invariants remains a challenging research topic. All measures characterizing the topology of a graph that have been developed thus far exhibit some degree of degeneracy, i.e., an inability to distinguish between non-isomorphic graphs. In this paper, we show that certain graph invariants can be useful in substantially reducing the computational complexity of isomorphism testing. Our findings are underpinned by numerical results based on a large scale statistical analysis. AB - The search for an easily computable, finite, complete set of graph invariants remains a challenging research topic. All measures characterizing the topology of a graph that have been developed thus far exhibit some degree of degeneracy, i.e., an inability to distinguish between non-isomorphic graphs. In this paper, we show that certain graph invariants can be useful in substantially reducing the computational complexity of isomorphism testing. Our findings are underpinned by numerical results based on a large scale statistical analysis. KW - Graph isomorphism KW - Graph measures KW - Graph topology KW - Graphs KW - Uniqueness UR - http://www.scopus.com/inward/record.url?scp=84884974800&partnerID=8YFLogxK U2 - 10.1007/s10444-012-9281-0 DO - 10.1007/s10444-012-9281-0 M3 - Article VL - 39 SP - 311 EP - 325 JO - Advances in Computational Mathematics JF - Advances in Computational Mathematics SN - 1019-7168 IS - 2 ER - TY - JOUR T1 - Structural similarity of directed universal hierarchical graphs T2 - A low computational complexity approach AU - Dehmer, Matthias AU - Emmert-Streib, Frank PY - 2007/12/1 Y1 - 2007/12/1 N2 - In the present paper we mainly introduce an efficient approach to measure the structural similarity of so called directed universal hierarchical graphs. We want to underline that directed universal hierarchical graphs can be obtained from generalized trees which are already introduced. In order to classify these graphs, we state our novel graph similarity method. As a main result we notice that our novel algorithm has low computational complexity. AB - In the present paper we mainly introduce an efficient approach to measure the structural similarity of so called directed universal hierarchical graphs. We want to underline that directed universal hierarchical graphs can be obtained from generalized trees which are already introduced. In order to classify these graphs, we state our novel graph similarity method. As a main result we notice that our novel algorithm has low computational complexity. KW - Complexity analysis KW - Graph classes KW - Graph classification KW - Graph similarity KW - Hierarchical models KW - Structured objects UR - http://www.scopus.com/inward/record.url?scp=35648968162&partnerID=8YFLogxK U2 - 10.1016/j.amc.2007.04.006 DO - 10.1016/j.amc.2007.04.006 M3 - Article VL - 194 SP - 7 EP - 20 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 IS - 1 ER - TY - JOUR T1 - Comparing large graphs efficiently by margins of feature vectors AU - Dehmer, Matthias AU - Emmert-Streib, Frank PY - 2007/5/15 Y1 - 2007/5/15 N2 - Measuring the structural similarity of graphs is a challenging and outstanding problem. Most of the classical approaches of the so-called exact graph matching methods are based on graph or subgraph isomorphic relations of the underlying graphs. In contrast to these methods in this paper we introduce a novel approach to measure the structural similarity of directed and undirected graphs that is mainly based on margins of feature vectors representing graphs. We introduce novel graph similarity and dissimilarity measures, provide some properties and analyze their algorithmic complexity. We find that the computational complexity of our measures is polynomial in the graph size and, hence, significantly better than classical methods from, e.g. exact graph matching which are NP-complete. Numerically, we provide some examples of our measure and compare the results with the well-known graph edit distance. AB - Measuring the structural similarity of graphs is a challenging and outstanding problem. Most of the classical approaches of the so-called exact graph matching methods are based on graph or subgraph isomorphic relations of the underlying graphs. In contrast to these methods in this paper we introduce a novel approach to measure the structural similarity of directed and undirected graphs that is mainly based on margins of feature vectors representing graphs. We introduce novel graph similarity and dissimilarity measures, provide some properties and analyze their algorithmic complexity. We find that the computational complexity of our measures is polynomial in the graph size and, hence, significantly better than classical methods from, e.g. exact graph matching which are NP-complete. Numerically, we provide some examples of our measure and compare the results with the well-known graph edit distance. KW - Degree vectors KW - Directed and undirected graphs KW - Graph similarity KW - Similarity measures UR - http://www.scopus.com/inward/record.url?scp=34248165422&partnerID=8YFLogxK U2 - 10.1016/j.amc.2006.11.185 DO - 10.1016/j.amc.2006.11.185 M3 - Article VL - 188 SP - 1699 EP - 1710 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 IS - 2 ER - TY - JOUR T1 - A similarity measure for graphs with low computational complexity AU - Dehmer, Matthias AU - Emmert-Streib, Frank AU - Kilian, Jürgen PY - 2006/11/1 Y1 - 2006/11/1 N2 - We present and analyze an algorithm to measure the structural similarity of generalized trees, a new graph class which includes rooted trees. For this, we represent structural properties of graphs as strings and define the similarity of two graphs as optimal alignments of the corresponding property stings. We prove that the obtained graph similarity measures are so called Backward similarity measures. From this we find that the time complexity of our algorithm is polynomial and, hence, significantly better than the time complexity of classical graph similarity methods based on isomorphic relations. AB - We present and analyze an algorithm to measure the structural similarity of generalized trees, a new graph class which includes rooted trees. For this, we represent structural properties of graphs as strings and define the similarity of two graphs as optimal alignments of the corresponding property stings. We prove that the obtained graph similarity measures are so called Backward similarity measures. From this we find that the time complexity of our algorithm is polynomial and, hence, significantly better than the time complexity of classical graph similarity methods based on isomorphic relations. KW - Computational complexity KW - Dynamic programming KW - Graph similarity KW - Graph theory UR - http://www.scopus.com/inward/record.url?scp=33750819438&partnerID=8YFLogxK U2 - 10.1016/j.amc.2006.04.006 DO - 10.1016/j.amc.2006.04.006 M3 - Article VL - 182 SP - 447 EP - 459 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 IS - 1 ER - TY - JOUR T1 - On efficient network similarity measures AU - Dehmer, Matthias AU - Chen, Zengqiang AU - Shi, Yongtang AU - Zhang, Y. AU - Tripathi, Shailesh AU - Ghorbani, Modjtaba AU - Mowshowitz, Abbe AU - Emmert-Streib, F. PY - 2019/12/1 Y1 - 2019/12/1 N2 - This paper presents novel graph similarity measures which can be applied to simple directed and undirected networks. To define the graph similarity measures, we first map graphs to real numbers by utilizing structural graph measures. Then, we define measures of similarity between real numbers and prove that they can be used as proxies for graph similarity. Numerical results are derived to show the domain coverage of these measures as well as their clustering ability. The latter relates to the efficient grouping of graphs according to certain structural properties. Our numerical results are sensitive to these properties and offer insights useful for designing effective graph similarity measures. AB - This paper presents novel graph similarity measures which can be applied to simple directed and undirected networks. To define the graph similarity measures, we first map graphs to real numbers by utilizing structural graph measures. Then, we define measures of similarity between real numbers and prove that they can be used as proxies for graph similarity. Numerical results are derived to show the domain coverage of these measures as well as their clustering ability. The latter relates to the efficient grouping of graphs according to certain structural properties. Our numerical results are sensitive to these properties and offer insights useful for designing effective graph similarity measures. KW - Distance measures KW - Graphs KW - Inequalities KW - Networks KW - Similarity measures U2 - 10.1016/j.amc.2019.06.035 DO - 10.1016/j.amc.2019.06.035 M3 - Article VL - 362 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 M1 - 124521 ER - TY - JOUR T1 - Relations and bounds for the zeros of graph polynomials using vertex orbits AU - Dehmer, Matthias AU - Emmert-Streib, Frank AU - Mowshowitz, Abbe AU - Ilić, Aleksandar AU - Chen, Zengqiang AU - Yu, Guihai AU - Feng, Lihua AU - Ghorbani, Modjtaba AU - Varmuza, Kurt AU - Tao, Jin PY - 2020/9/1 Y1 - 2020/9/1 N2 - In this paper, we prove bounds for the unique, positive zero of OG ★(z):=1−OG(z), where OG(z) is the so-called orbit polynomial [1]. The orbit polynomial is based on the multiplicity and cardinalities of the vertex orbits of a graph. In [1], we have shown that the unique, positive zero δ ≤ 1 of OG ★(z) can serve as a meaningful measure of graph symmetry. In this paper, we study special graph classes with a specified number of orbits and obtain bounds on the value of δ. AB - In this paper, we prove bounds for the unique, positive zero of OG ★(z):=1−OG(z), where OG(z) is the so-called orbit polynomial [1]. The orbit polynomial is based on the multiplicity and cardinalities of the vertex orbits of a graph. In [1], we have shown that the unique, positive zero δ ≤ 1 of OG ★(z) can serve as a meaningful measure of graph symmetry. In this paper, we study special graph classes with a specified number of orbits and obtain bounds on the value of δ. KW - Data science KW - Graph measures KW - Graphs KW - Networks KW - Quantitative graph theory KW - Symmetry U2 - 10.1016/j.amc.2020.125239 DO - 10.1016/j.amc.2020.125239 M3 - Article VL - 380 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 M1 - 125239 ER - TY - JOUR T1 - Entropy bounds for dendrimers AU - Chen, Zengqiang AU - Dehmer, Matthias AU - Emmert-Streib, Frank AU - Shi, Yongtang PY - 2014/9/1 Y1 - 2014/9/1 N2 - Many graph invariants have been used for the construction of entropy-based measures to characterize the structure of complex networks. When considering Shannon entropy-based graph measures, there has been very little work to find their extremal values. A reason for this might be the fact that Shannon's entropy represents a multivariate function and all probability values are not equal to zero when considering graph entropies. Dehmer and Kraus proved some extremal results for graph entropies which are based on information functionals and express some conjectures generated by numerical simulations to find extremal values of graph entropies. Dehmer and Kraus discussed the extremal values of entropies for dendrimers. In this paper, we continue to study the extremal values of graph entropy for dendrimers, which has most interesting applications in molecular structure networks, and also in the pharmaceutical and biomedical area. Among all dendrimers with n vertices, we obtain the extremal values of graph entropy based on different well-known information functionals. Numerical experiments verifies our results. AB - Many graph invariants have been used for the construction of entropy-based measures to characterize the structure of complex networks. When considering Shannon entropy-based graph measures, there has been very little work to find their extremal values. A reason for this might be the fact that Shannon's entropy represents a multivariate function and all probability values are not equal to zero when considering graph entropies. Dehmer and Kraus proved some extremal results for graph entropies which are based on information functionals and express some conjectures generated by numerical simulations to find extremal values of graph entropies. Dehmer and Kraus discussed the extremal values of entropies for dendrimers. In this paper, we continue to study the extremal values of graph entropy for dendrimers, which has most interesting applications in molecular structure networks, and also in the pharmaceutical and biomedical area. Among all dendrimers with n vertices, we obtain the extremal values of graph entropy based on different well-known information functionals. Numerical experiments verifies our results. KW - Dendrimers KW - Extremal values KW - Graph entropy KW - Information theory KW - Shannon's entropy UR - http://www.scopus.com/inward/record.url?scp=84903150191&partnerID=8YFLogxK U2 - 10.1016/j.amc.2014.05.105 DO - 10.1016/j.amc.2014.05.105 M3 - Article VL - 242 SP - 462 EP - 472 JO - Applied Mathematics and Computation JF - Applied Mathematics and Computation SN - 0096-3003 ER - TY - JOUR T1 - Multichannel Blind Sound Source Separation using Spatial Covariance Model with Level and Time Differences and Non-Negative Matrix Factorization AU - Carabias Orti, Julio Jose AU - Nikunen, Joonas AU - Virtanen, Tuomas AU - Vera-Candeas, Pedro PY - 2018/9 Y1 - 2018/9 N2 - This paper presents an algorithm for multichannel sound source separation using explicit modeling of level and time differences in source spatial covariance matrices (SCM). We propose a novel SCM model in which the spatial properties are modeled by the weighted sum of direction of arrival (DOA) kernels. DOA kernels are obtained as the combination of phase and level difference covariance matrices representing both time and level differences between microphones for a grid of predefined source directions. The proposed SCM model is combined with the NMF model for the magnitude spectrograms. Opposite to other SCM models in the literature, in this work, source localization is implicitly defined in the model and estimated during the signal factorization. Therefore, no localization pre-processing is required. Parameters are estimated using complex-valued non-negative matrix factorization (CNMF) with both Euclidean distance and Itakura Saito divergence. Separation performance of the proposed system is evaluated using the two-channel SiSEC development dataset and four channels signals recorded in a regular room with moderate reverberation. Finally, a comparison to other state-of-the-art methods is performed, showing better achieved separation performance in terms of SIR and perceptual measures. AB - This paper presents an algorithm for multichannel sound source separation using explicit modeling of level and time differences in source spatial covariance matrices (SCM). We propose a novel SCM model in which the spatial properties are modeled by the weighted sum of direction of arrival (DOA) kernels. DOA kernels are obtained as the combination of phase and level difference covariance matrices representing both time and level differences between microphones for a grid of predefined source directions. The proposed SCM model is combined with the NMF model for the magnitude spectrograms. Opposite to other SCM models in the literature, in this work, source localization is implicitly defined in the model and estimated during the signal factorization. Therefore, no localization pre-processing is required. Parameters are estimated using complex-valued non-negative matrix factorization (CNMF) with both Euclidean distance and Itakura Saito divergence. Separation performance of the proposed system is evaluated using the two-channel SiSEC development dataset and four channels signals recorded in a regular room with moderate reverberation. Finally, a comparison to other state-of-the-art methods is performed, showing better achieved separation performance in terms of SIR and perceptual measures. KW - Covariance matrices KW - direction of arrival estimation KW - Direction-of-arrival estimation KW - interaural level difference KW - interaural time difference KW - Kernel KW - Microphones KW - multichannel source separation KW - non-negative matrix factorization KW - Source separation KW - spatial covariance model KW - Spectrogram KW - Time-frequency analysis U2 - 10.1109/TASLP.2018.2830105 DO - 10.1109/TASLP.2018.2830105 M3 - Article VL - 26 SP - 1512 EP - 1527 JO - Ieee-Acm transactions on audio speech and language processing JF - Ieee-Acm transactions on audio speech and language processing SN - 2329-9290 IS - 9 ER - TY - GEN T1 - The different levels of magneto-mechanical coupling in energy conversion machines and devices AU - Belahcen, A. AU - Kouhia, R. AU - Fonteyn, K. PY - 2011 Y1 - 2011 N2 - This paper reviews the methods for coupling the magnetic and mechanical problems in magnetic materials and their application to electrical machines. The reviewed methods include both the material models and the computing methods as well as the methods for computing the magnetic forces. The paper shows that there are different levels of coupling the magnetic system with the mechanical one and that the use of a method or another depends on the application and the level of accuracy aimed at. The paper also clarifies some terms and concepts related to the coupling terminology such as strong, weak, local, global, direct and indirect coupling and put these terms in a coherent context. Most of the examples are related to the two dimensional analysis but some three dimensional ones are also shown. AB - This paper reviews the methods for coupling the magnetic and mechanical problems in magnetic materials and their application to electrical machines. The reviewed methods include both the material models and the computing methods as well as the methods for computing the magnetic forces. The paper shows that there are different levels of coupling the magnetic system with the mechanical one and that the use of a method or another depends on the application and the level of accuracy aimed at. The paper also clarifies some terms and concepts related to the coupling terminology such as strong, weak, local, global, direct and indirect coupling and put these terms in a coherent context. Most of the examples are related to the two dimensional analysis but some three dimensional ones are also shown. KW - Computing Methods KW - Coupled problems KW - Electrical machines KW - Magnetic forces KW - Magneto-mechanics KW - Magnetostriction UR - http://www.scopus.com/inward/record.url?scp=84857432902&partnerID=8YFLogxK M3 - Conference contribution SN - 9788489925786 SP - 472 EP - 483 BT - Proceedings of the 4th International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2011 ER - TY - JOUR T1 - Optimal energy decay for the wave-heat system on a rectangular domain AU - Batty, Charles AU - Paunonen, Lassi AU - Seifert, David PY - 2019 Y1 - 2019 N2 - We study the rate of energy decay for solutions of a coupled wave-heat system on a rectangular domain. Using techniques from the theory of C 0 -semigroups, and in particular a well-known result due to Borichev and Tomilov, we prove that the energy of classical solutions decays like t - 2/ 3 as t \rightarrow \infty . This rate is moreover shown to be sharp. Our result implies in particular that a general estimate in the literature, which predicts at least logarithmic decay and is known to be best possible in general, is suboptimal in the special case under consideration here. Our strategy of proof involves direct estimates based on separation of variables and a refined version of the technique developed in our earlier paper for a one-dimensional wave-heat system. AB - We study the rate of energy decay for solutions of a coupled wave-heat system on a rectangular domain. Using techniques from the theory of C 0 -semigroups, and in particular a well-known result due to Borichev and Tomilov, we prove that the energy of classical solutions decays like t - 2/ 3 as t \rightarrow \infty . This rate is moreover shown to be sharp. Our result implies in particular that a general estimate in the literature, which predicts at least logarithmic decay and is known to be best possible in general, is suboptimal in the special case under consideration here. Our strategy of proof involves direct estimates based on separation of variables and a refined version of the technique developed in our earlier paper for a one-dimensional wave-heat system. KW - C -semigroups KW - Coupled KW - Energy KW - Heat equation KW - Rates of decay KW - Rectangular domain KW - Resolvent estimates KW - Wave equation U2 - 10.1137/18M1195796 DO - 10.1137/18M1195796 M3 - Article VL - 51 SP - 808 EP - 819 JO - SIAM JOURNAL ON MATHEMATICAL ANALYSIS JF - SIAM JOURNAL ON MATHEMATICAL ANALYSIS SN - 0036-1410 IS - 2 ER - TY - JOUR T1 - Revealing differences in gene network inference algorithms on the network level by ensemble methods AU - Altay, Gökmen AU - Emmert-Streib, Frank PY - 2010/5/25 Y1 - 2010/5/25 N2 - Motivation: The inference of regulatory networks from large-scale expression data holds great promise because of the potentially causal interpretation of these networks. However, due to the difficulty to establish reliable methods based on observational data there is so far only incomplete knowledge about possibilities and limitations of such inference methods in this context. Results: In this article, we conduct a statistical analysis investigating differences and similarities of four network inference algorithms, ARACNE, CLR, MRNET and RN, with respect to local network-based measures. We employ ensemble methods allowing to assess the inferability down to the level of individual edges. Our analysis reveals the bias of these inference methods with respect to the inference of various network components and, hence, provides guidance in the interpretation of inferred regulatory networks from expression data. Further, as application we predict the total number of regulatory interactions in human B cells and hypothesize about the role of Myc and its targets regarding molecular information processing. AB - Motivation: The inference of regulatory networks from large-scale expression data holds great promise because of the potentially causal interpretation of these networks. However, due to the difficulty to establish reliable methods based on observational data there is so far only incomplete knowledge about possibilities and limitations of such inference methods in this context. Results: In this article, we conduct a statistical analysis investigating differences and similarities of four network inference algorithms, ARACNE, CLR, MRNET and RN, with respect to local network-based measures. We employ ensemble methods allowing to assess the inferability down to the level of individual edges. Our analysis reveals the bias of these inference methods with respect to the inference of various network components and, hence, provides guidance in the interpretation of inferred regulatory networks from expression data. Further, as application we predict the total number of regulatory interactions in human B cells and hypothesize about the role of Myc and its targets regarding molecular information processing. UR - http://www.scopus.com/inward/record.url?scp=77954484005&partnerID=8YFLogxK U2 - 10.1093/bioinformatics/btq259 DO - 10.1093/bioinformatics/btq259 M3 - Article VL - 26 SP - 1738 EP - 1744 JO - Bioinformatics JF - Bioinformatics SN - 1367-4803 IS - 14 M1 - btq259 ER - TY - JOUR T1 - Magnetic origin of the chemical balance in alloyed Fe-Cr stainless steels T2 - First-principles and Ising model study AU - Airiskallio, E. AU - Nurmi, E. AU - Väyrynen, I. J. AU - Kokko, K. AU - Ropo, M. AU - Punkkinen, M. P J AU - Johansson, B. AU - Vitos, L. PY - 2014 Y1 - 2014 N2 - Iron-chromium is the base material for most of the stainless steel grades. Recently, new insights into the origins of fundamental physical and chemical characteristics of Fe-Cr based alloys have been achieved. Some of the new results are quite unexpected and call for further investigations. The present study focuses on the magnetic contribution in the atomic driving forces related to the chemical composition in Fe-Cr when alloyed with Al, Ti, V, Mn, Co, Ni, and Mo. Using the ab initio exact muffin-tin orbitals method combined with an Ising-type spin model, we demonstrate that the magnetic moment of the solute atoms with the induced changes in the magnetic moments of the host atoms form the main factor in determining the mixing energy and chemical potentials of low-Cr Fe-Cr based alloys. The results obtained in the present work are related to the designing and tuning of the microstructure and corrosion protection of low-Cr steels. AB - Iron-chromium is the base material for most of the stainless steel grades. Recently, new insights into the origins of fundamental physical and chemical characteristics of Fe-Cr based alloys have been achieved. Some of the new results are quite unexpected and call for further investigations. The present study focuses on the magnetic contribution in the atomic driving forces related to the chemical composition in Fe-Cr when alloyed with Al, Ti, V, Mn, Co, Ni, and Mo. Using the ab initio exact muffin-tin orbitals method combined with an Ising-type spin model, we demonstrate that the magnetic moment of the solute atoms with the induced changes in the magnetic moments of the host atoms form the main factor in determining the mixing energy and chemical potentials of low-Cr Fe-Cr based alloys. The results obtained in the present work are related to the designing and tuning of the microstructure and corrosion protection of low-Cr steels. KW - Al KW - Chemical potential KW - Co KW - Corrosion protection KW - Cr KW - Fe KW - First principles calculation KW - Ising model KW - Magnetic moment KW - Mixing energy KW - Mn KW - Mo KW - Ni KW - Stainless steel KW - Ti KW - V UR - http://www.scopus.com/inward/record.url?scp=84902660256&partnerID=8YFLogxK U2 - 10.1016/j.commatsci.2014.05.036 DO - 10.1016/j.commatsci.2014.05.036 M3 - Article VL - 92 SP - 135 EP - 140 JO - Computational Materials Science JF - Computational Materials Science SN - 0927-0256 ER -