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.

Adsorption of CO₂ on α-Pu (020) surface nanolayers is investigated using GGA-DFT and the suite of software DMOL³ and WIEN2k. Completely dissociated configurations (C+O+O) exhibit the strongest binding with the surface (7.94 eV), followed by partially dissociated (CO+O) and molecular CO₂ configurations (5.18 and 1.90 eV, respectively). For initial vertically upright orientations, final configuration of the CO ₂ molecule does not change after optimization. For initial flat lying orientations, the final states correspond to bent geometry with a bond angle of ∼130°. For CO+O coadsorptions, the stable configurations correspond to CO dipole moment orientations of 105°-167° with respect to the normal surface.

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.

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.

In computational physics and materials science ground-state properties are often extracted from an equation of state fit to energy-volume data. Magnetic systems often have multiple magnetic phases present in the energy-volume data, which poses a challenge for the fitting approach because the results are sensitive to the selection of included fitting points. This is because practically all popular equation of state fitting functions, such as Murnaghan and Birch-Murnaghan, assume just one phase and therefore cannot correctly fit magnetic energy-volume data that contains multiple phases. When fitting magnetic energy-volume data it is therefore important to select the range of fitting points in such a way that only points from the one relevant phase are included. We present a simple algorithm that makes the point selection automatically. Selecting fitting points automatically removes human bias and should also be useful for large-scale projects where selecting all fitting points by hand is not feasible.

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.

In order to characterize the impact of demographics and intercity commuting between cities on epidemic propagation, we propose a novel two-city epidemic model, where the spreading process is depicted by using SIR (susceptible-infected-recovered) model. The infectious diseases can spread in two cities at the same time, and be taken from one city to the other through intercity commuters. Firstly, we take use of the spectral analysis method to obtain the basic reproduction number R₀ of the model. Then, the equilibria including the endemic equilibrium and disease-free one of the proposed model are analyzed and calculated, and the results indicate that they are globally asymptotic stable. Moreover, the degree distribution of the population changes over time, forming a complex dynamical networks before the system reaches a steady state. Finally, through a large number of numerical simulations, we show that demographics, intercity commuting rates and exposed individuals during commuting have great effects on the epidemic spreading behavior between two cities. The analysis of the proposed model can further help to understand the transmission behavior of epidemics in reality, and it is also of great practical significance to predict the epidemic trends among cities and design effective measures to curb the infectious diseases.

Motivation: One of the most widely used models to analyse genotype-by-environment data is the additive main effects and multiplicative interaction (AMMI) model. Genotype-by-environment data resulting from multi-location trials are usually organized in two-way tables with genotypes in the rows and environments (location-year combinations) in the columns. The AMMI model applies singular value decomposition (SVD) to the residuals of a specific linear model, to decompose the genotype-by-environment interaction (GEI) into a sum of multiplicative terms. However, SVD, being a least squares method, is highly sensitive to contamination and the presence of even a single outlier, if extreme, may draw the leading principal component towards itself resulting in possible misinterpretations and in turn lead to bad practical decisions. Since, as in many other real-life studies the distribution of these data is usually not normal due to the presence of outlying observations, either resulting from measurement errors or sometimes from individual intrinsic characteristics, robust SVD methods have been suggested to help overcome this handicap. Results: We propose a robust generalization of the AMMI model (the R-AMMI model) that overcomes the fragility of its classical version when the data are contaminated. Here, robust statistical methods replace the classic ones to model, structure and analyse GEI. The performance of the robust extensions of the AMMI model is assessed through a Monte Carlo simulation study where several contamination schemes are considered. Applications to two real plant datasets are also presented to illustrate the benefits of the proposed methodology, which can be broadened to both animal and human genetics studies. Availability and implementation: Source code implemented in R is available in the supplementary material under the function r-AMMI.

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.

Motivation: Identification of somatic DNA copy number alterations (CNAs) and significant consensus events (SCEs) in cancer genomes is a main task in discovering potential cancer-driving genes such as oncogenes and tumor suppressors. The recent development of SNP array technology has facilitated studies on copy number changes at a genome-wide scale with high resolution. However, existing copy number analysis methods are oblivious to normal cell contamination and cannot distinguish between contributions of cancerous and normal cells to the measured copy number signals. This contamination could significantly confound downstream analysis of CNAs and affect the power to detect SCEs in clinical samples. Results: We report here a statistically principled in silico approach, Bayesian Analysis of COpy number Mixtures (BACOM), to accurately estimate genomic deletion type and normal tissue contamination, and accordingly recover the true copy number profile in cancer cells. We tested the proposed method on two simulated datasets, two prostate cancer datasets and The Cancer Genome Atlas high-grade ovarian dataset, and obtained very promising results supported by the ground truth and biological plausibility. Moreover, based on a large number of comparative simulation studies, the proposed method gives significantly improved power to detect SCEs after in silico correction of normal tissue contamination. We develop a cross-platform open-source Java application that implements the whole pipeline of copy number analysis of heterogeneous cancer tissues including relevant processing steps. We also provide an R interface, bacomR, for running BACOM within the R environment, making it straightforward to include in existing data pipelines.

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.

Motivation: Digital pathology enables new approaches that expand beyond storage, visualization or analysis of histological samples in digital format. One novel opportunity is 3D histology, where a three-dimensional reconstruction of the sample is formed computationally based on serial tissue sections. This allows examining tissue architecture in 3D, for example, for diagnostic purposes. Importantly, 3D histology enables joint mapping of cellular morphology with spatially resolved omics data in the true 3D context of the tissue at microscopic resolution. Several algorithms have been proposed for the reconstruction task, but a quantitative comparison of their accuracy is lacking. Results: We developed a benchmarking framework to evaluate the accuracy of several free and commercial 3D reconstruction methods using two whole slide image datasets. The results provide a solid basis for further development and application of 3D histology algorithms and indicate that methods capable of compensating for local tissue deformation are superior to simpler approaches.

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.

A wealth of literature exists on computing and visualizing cuts for the magnetic scalar potential of a current carrying conductor via Finite Element Methods (FEM) and harmonic maps to the circle. By a cut we refer to an orientable surface bounded by a given current carrying path (such that the flux through it may be computed) that restricts contour integrals on a curl-zero vector field to those that do not link the current-carrying path, analogous to branch cuts of complex analysis. This work is concerned with a study of a peculiar contour that illustrates topologically unintuitive aspects of cuts obtained from a trivial loop and raises questions about the notion of an optimal cut. Specifically, an unknotted curve that bounds only high genus surfaces in its convex hull is analyzed. The current work considers the geometric realization as a current-carrying wire in order to construct a magnetic scalar potential. Moreover, we consider the problem of choosing an energy functional on the space of maps, suggesting an algorithm for computing cuts via minimizing a conformally invariant functional utilizing Newton iteration.

First-principles calculations have been conducted to investigate the properties of FePd_n (n = 2-14) clusters. In the lowest energy structures of FePd_n clusters, the Fe atom gradually moves from the convex to the surface, and then to the interior site with the number of Pd atoms increasing from 2 to 14. The magnetic moments of Pd_n clusters have been enhanced by the doping of Fe impurity. Furthermore, the adsorption of small molecules, including NH₃, H₂O, CO, H₂, and O₂, on the higher stability of FePd_n (n = 5, 7, 10, and 12) clusters were studied. The lowest energy adsorption structures are obtained for each molecule. On the whole, the adsorption energies vary as the order of E_a(H₂O) <E_a(H₂) <E _a(NH₃) <E_a(O₂) <E _a(CO). NH₃, CO and H₂ molecules prefer to adsorb on the FePd₁₀ cluster with the highest adsorption energy, while H₂O and O₂ are more like to adsorb on the FePd ₅. The magnetic moments of FePd_n clusters are reduced with the adsorption of molecules.

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.

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:

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.

Motivation: The analysis of differentially expressed gene sets became a routine in the analyses of gene expression data. There is a multitude of tests available, ranging from aggregation tests that summarize gene-level statistics for a gene set to true multivariate tests, accounting for intergene correlations. Most of them detect complex departures from the null hypothesis but when the null hypothesis is rejected the specific alternative leading to the rejection is not easily identifiable. Results: In this article we compare the power and Type I error rates of minimum-spanning tree (MST)-based non-parametric multivariate tests with several multivariate and aggregation tests, which are frequently used for pathway analyses. In our simulation study, we demonstrate that MST-based tests have power that is for many settings comparable with the power of conventional approaches, but outperform them in specific regions of the parameter space corresponding to biologically relevant configurations. Further, we find for simulated and for gene expression data that MST-based tests discriminate well against shift and scale alternatives. As a general result, we suggest a two-step practical analysis strategy that may increase the interpretability of experimental data: first, apply the most powerful multivariate test to find the subset of pathways for which the null hypothesis is rejected and second, apply MST-based tests to these pathways to select those that support specific alternative hypotheses.

Motivation: To date, gene set analysis approaches primarily focus on identifying differentially expressed gene sets (pathways). Methods for identifying differentially coexpressed pathways also exist but are mostly based on aggregated pairwise correlations or other pairwise measures of coexpression. Instead, we propose Gene Sets Net Correlations Analysis (GSNCA), a multivariate differential coexpression test that accounts for the complete correlation structure between genes.Results: In GSNCA, weight factors are assigned to genes in proportion to the genes' cross-correlations (intergene correlations). The problem of finding the weight vectors is formulated as an eigenvector problem with a unique solution. GSNCA tests the null hypothesis that for a gene set there is no difference in the weight vectors of the genes between two conditions. In simulation studies and the analyses of experimental data, we demonstrate that GSNCA captures changes in the structure of genes' cross-correlations rather than differences in the averaged pairwise correlations. Thus, GSNCA infers differences in coexpression networks, however, bypassing method-dependent steps of network inference. As an additional result from GSNCA, we define hub genes as genes with the largest weights and show that these genes correspond frequently to major and specific pathway regulators, as well as to genes that are most affected by the biological difference between two conditions. In summary, GSNCA is a new approach for the analysis of differentially coexpressed pathways that also evaluates the importance of the genes in the pathways, thus providing unique information that may result in the generation of novel biological hypotheses.

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.

Graph entropies have been introduced to quantitatively measure the structural information content of graphs and networks; they have plenty of applications in various fields. Utilizing the number of subgraphs to establish measures for determining the complexity of molecular graphs are also prevalent in the study of mathematical chemistry. In this paper, we develop a new graph entropy measure that is based on the number of spanning forests. We prove explicit expressions for the entropy for trees, unicyclic and bicyclic graphs, and show that the cycle graph C_n attains the maximal value of the entropy for unicyclic graphs with order n and large cycle lengths. Based on generating numerical results, we conjecture extremal unicyclic graphs with respect to the entropy as well as we compare the values of our entropy for c-cyclic graphs, and generate graphs of bicyclic graphs and tricyclic graphs with 6 vertices for performing further research.

The growth behavior and magnetic properties of spherical uranium oxide nanoclusters have been investigated using the generalized gradient approximation (GGA) to density functional theory (DFT). The geometries of U_nO _m clusters remain the O_h symmetry after DFT relaxation. The largest binding energy corresponds to the cluster with the smallest deviation from the bulk (UO₂) ratio. The electronic structures and magnetic properties of these nanoclusters are presented. We find the chemical bonding between the U and O atoms has a significant ionic character. The reduction of magnetism in the inner positions can be understood by the charge transfer and the hybridization between U atoms and the neighboring O atoms.

In this paper we study the fractional analogous of the Laplace–Beltrami equation and the hyperbolic Riesz system studied previously by H. Leutwiler, in (Formula presented.). In both cases we replace the integer derivatives by Caputo fractional derivatives of order (Formula presented.). We characterize the space of solutions of the fractional Laplace–Beltrami equation, and we calculate its dimension. We establish relations between the solutions of the fractional Laplace–Beltrami equation and the solutions of the hyperbolic fractional Riesz system. Some examples of the polynomial solutions will be presented. Moreover, the behaviour of the obtained results when (Formula presented.) is presented, and a final remark about the consideration of Riemann–Liouville fractional derivatives instead of Caputo fractional derivatives is made.

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.

In this paper we first define hypermonogenic solutions of the Dirac operator in R^p×R^q 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.

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.

We consider the modified Cauchy–Riemann operator (Formula presented.) in the universal Clifford algebra (Formula presented.) with the basis (Formula presented.). The null-solutions of this operator are called k-hypermonogenic functions. We calculate the k-hyperbolic harmonic fundamental solutions, i.e. solutions to (Formula presented.), and use these solutions to find k-hypermonogenic kernels for a Cauchy-type integral formula in the upper half-space.

The ensemble empirical mode decomposition (EEMD) and its complete variant (CEEMDAN) are adaptive, noise-assisted data analysis methods that improve on the ordinary empirical mode decomposition (EMD). All these methods decompose possibly nonlinear and/or nonstationary time series data into a finite amount of components separated by instantaneous frequencies. This decomposition provides a powerful method to look into the different processes behind a given time series data, and provides a way to separate short time-scale events from a general trend. We present a free software implementation of EMD, EEMD and CEEMDAN and give an overview of the EMD methodology and the algorithms used in the decomposition. We release our implementation, libeemd, with the aim of providing a user-friendly, fast, stable, well-documented and easily extensible EEMD library for anyone interested in using (E)EMD in the analysis of time series data. While written in C for numerical efficiency, our implementation includes interfaces to the Python and R languages, and interfaces to other languages are straightforward.

We examine possibilities for making advances in nanocomputing by bringing in ideas from the field of machine learning. The potential from combining machine learning with nanocomputing seems to be underutilized. We review three complementary approaches. Firstly, machine learning can be used in the different phases of developing complicated nanocomputing devices: in modeling, designing, constructing, and programming the devices. Secondly, machine learning methods implemented by nanocomputing hardware can be a competitive solution especially for specialized application areas like sensory information processing; working towards such implementations advances nanocomputing by guiding development of the nanocomponents and architectures required for such applications. Thirdly, nanotechnology enabled quantum computing can significantly increase our capacity to solve NP-complete optimization problems; although this increase is not specific to machine learning, several such problems occur in machine learning and artificial intelligence, hence solving such problems is a useful goal that partly motivates development of quantum computing. The main value of this paper is to provide new ideas for researchers working on nanocomputing, nanoarchitectures, development and design of nanoprocessors and other nanocomponents, or nanomanufacturing.

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.

Melting of icosahedral and Wulff polyhedral copper clusters are studied using molecular dynamics and effective medium theory. Icosahedral closed shell copper clusters are most stable up to a cluster size of ∼ 2500 atoms and their melting temperature is highest for small clusters, accordingly. Wulff polyhedra are most stable for larger clusters and, consequently, their melting temperature is highest for large clusters. The melting temperature decreases with decreasing cluster size and is proportional to the average coordination number of atoms. The whole icosahedral cluster melts simultaneously and can possibly be superheated. Icosahedral clusters with partially filled shells melt at lower temperatures than closed shell icosahedra, but no surface premelting is observed. (111) surface layers of large Wulff polyhedra are also solid up to the cluster melting temperatures, but (100) facets premelt at a lower temperature than the whole cluster.

The time domain-random walk method was developed further for simulating mass transfer in fracture flows together with matrix diffusion in surrounding porous media. Specifically, a time domain-random walk scheme was developed for numerically approximating solutions of the advection-diffusion equation when the diffusion coefficient exhibits significant spatial variation or even discontinuities. The proposed scheme relies on second-order accurate, central-difference approximations of the advective and diffusive fluxes. The scheme was verified by comparing simulated results against analytical solutions in flow configurations involving a rectangular channel connected on one side with a porous matrix. Simulations with several flow rates, diffusion coefficients, and matrix porosities indicate good agreement between the numerical approximations and analytical solutions.

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.

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.

NetBioV (Network Biology Visualization) is an R package that allows the visualization of large network data in biology and medicine. The purpose of NetBioV is to enable an organized and reproducible visualization of networks by emphasizing or highlighting specific structural properties that are of biological relevance.

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.

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.

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.

In this paper, we prove bounds for the unique, positive zero of O_G ^★(z):=1−O_G(z), where O_G(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 O_G ^★(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.

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.

Motivation: Data from RNA-seq experiments provide us with many new possibilities to gain insights into biological and disease mechanisms of cellular functioning. However, the reproducibility and robustness of RNA-seq data analysis results is often unclear. This is in part attributed to the two counter acting goals of (i) a cost efficient and (ii) an optimal experimental design leading to a compromise, e.g. in the sequencing depth of experiments. Results: We introduce an R package called samExploreR that allows the subsampling (m out of n bootstraping) of short-reads based on SAM files facilitating the investigation of sequencing depth related questions for the experimental design. Overall, this provides a systematic way for exploring the reproducibility and robustness of general RNA-seq studies. We exemplify the usage of samExploreR by studying the influence of the sequencing depth and the annotation on the identification of differentially expressed genes.

We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for the strict and another one for the lax semantics. Both problems turn out to be EXPTIME-complete on general structures. Finally,we showhowfor a specific class of structures NEXPTIME-completeness for these problems under strict semantics can be achieved.

Summary: Each cell is a phenotypically unique individual that is influenced by internal and external processes, operating in parallel. To characterize the dynamics of cellular processes one needs to observe many individual cells from multiple points of view and over time, so as to identify commonalities and variability. With this aim, we engineered a software, 'SCIP', to analyze multi-modal, multi-process, time-lapse microscopy morphological and functional images. SCIP is capable of automatic and/or manually corrected segmentation of cells and lineages, automatic alignment of different microscopy channels, as well as detect, count and characterize fluorescent spots (such as RNA tagged by MS2-GFP), nucleoids, Z rings, Min system, inclusion bodies, undefined structures, etc. The results can be exported into *mat files and all results can be jointly analyzed, to allow studying not only each feature and process individually, but also find potential relationships. While we exemplify its use on Escherichia coli, many of its functionalities are expected to be of use in analyzing other prokaryotes and eukaryotic cells as well. We expect SCIP to facilitate the finding of relationships between cellular processes, from small-scale (e.g. gene expression) to large-scale (e.g. cell division), in single cells and cell lineages. Availability and implementation: http://www.ca3-uninova.org/project_scip. Supplementary information: Supplementary data are available at Bioinformatics online.

Each edition of the challenge on Detection and Classification of Acoustic Scenes and Events (DCASE) contained several tasks involving sound event detection in different setups. DCASE 2017 presented participants with three such tasks, each having specific datasets and detection requirements: Task 2, in which target sound events were very rare in both training and testing data, Task 3 having overlapping events annotated in real-life audio, and Task 4, in which only weakly labeled data were available for training. In this paper, we present three tasks, including the datasets and baseline systems, and analyze the challenge entries for each task. We observe the popularity of methods using deep neural networks, and the still widely used mel frequency-based representations, with only few approaches standing out as radically different. Analysis of the systems behavior reveals that task-specific optimization has a big role in producing good performance; however, often this optimization closely follows the ranking metric, and its maximization/minimization does not result in universally good performance. We also introduce the calculation of confidence intervals based on a jackknife resampling procedure to perform statistical analysis of the challenge results. The analysis indicates that while the 95% confidence intervals for many systems overlap, there are significant differences in performance between the top systems and the baseline for all tasks.

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.

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.

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.

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.

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.

The interplay between electrostatic and van der Waals (vdW) interactions in porphyrin-C₆₀ dyads is still under debate despite its importance in influencing the structural characteristics of such complexes considered for various applications in molecular photovoltaics. In this article, we sample the conformational space of a porphyrin-C₆₀ dyad using Car-Parrinello molecular dynamics simulations with and without empirical vdW corrections. Long-range vdW interactions, which are poorly described by the commonly used density functional theory functionals, prove to be essential for a proper dynamics of the dyad moieties. Inclusion of vdW corrections brings porphyrin and C₆₀ close together in an orientation that is in agreement with experimental observations. The structural differences arising from the vdW corrections are shown to be significant for several properties and potentially less important for others. Additionally, our Mulliken population analysis reveals that contrary to the common belief, porphyrin is not the primary electron donating moiety for C₆₀. In the considered dyad, fullerene's affinity for electrons is primarily satisfied by charge transfer from the amide group of the linker. However, we show that in the absence of another suitable bound donor, C₆₀ can withdraw electrons from porphyrin if it is sufficiently close.