Robust network reconstruction in polynomial time

This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work [1] on robust reconstruction to provide a practical implementation with polynomial computational complexity. Following the same experimental protocol, the algorithm obtains a set of structurally-related candidate solutions spanning every level of sparsity. We prove the existence of a magnitude bound on the noise, which if satisfied, guarantees that one of these structures is the correct solution. A problem-specific model-selection procedure then selects a single solution from this set and provides a measure of confidence in that solution. Extensive simulations quantify the expected performance for different levels of noise and show that significantly more noise can be tolerated in comparison to the original method. © 2012 IEEE.

Recovering Three-Dimensional Structure from Motion with Surface Reconstruction

We address the computational role that the construction of a complete surface representation may play in the recovery of 3--D structure from motion. We present a model that combines a feature--based structure--from- -motion algorithm with smooth surface interpolation. This model can represent multiple surfaces in a given viewing direction, incorporates surface constraints from object boundaries, and groups image features using their 2--D image motion. Computer simulations relate the model's behavior to perceptual observations. In a companion paper, we discuss further perceptual experiments regarding the role of surface reconstruction in the human recovery of 3--D structure from motion.

The Coupled Depth/Slope Approach to Surface Reconstruction

Reconstructing a surface from sparse sensory data is a well known problem in computer vision. Early vision modules typically supply sparse depth, orientation and discontinuity information. The surface reconstruction module incorporates these sparse and possibly conflicting measurements of a surface into a consistent, dense depth map. The coupled depth/slope model developed here provides a novel computational solution to the surface reconstruction problem. This method explicitly computes dense slope representation as well as dense depth representations. This marked change from previous surface reconstruction algorithms allows a natural integration of orientation constraints into the surface description, a feature not easily incorporated into earlier algorithms. In addition, the coupled depth/ slope model generalizes to allow for varying amounts of smoothness at different locations on the surface. This computational model helps conceptualize the problem and leads to two possible implementations- analog and digital. The model can be implemented as an electrical or biological analog network since the only computations required at each locally connected node are averages, additions and subtractions. A parallel digital algorithm can be derived by using finite difference approximations. The resulting system of coupled equations can be solved iteratively on a mesh-pf-processors computer, such as the Connection Machine. Furthermore, concurrent multi-grid methods are designed to speed the convergence of this digital algorithm.

“Reconstruction of Gene Regulatory Network from Expression Profile of Plasma RNA Data of Colorectal Cancer Patients using Soft Computing Techniques”

Microarray data analysis is one of data mining tool which is used to extract meaningful information hidden in biological data. One of the major focuses on microarray data analysis is the reconstruction of gene regulatory network that may be used to provide a broader understanding on the functioning of complex cellular systems. Since cancer is a genetic disease arising from the abnormal gene function, the identification of cancerous genes and the regulatory pathways they control will provide a better platform for understanding the tumor formation and development. The major focus of this thesis is to understand the regulation of genes responsible for the development of cancer, particularly colorectal cancer by analyzing the microarray expression data. In this thesis, four computational algorithms namely fuzzy logic algorithm, modified genetic algorithm, dynamic neural fuzzy network and Takagi Sugeno Kang-type recurrent neural fuzzy network are used to extract cancer specific gene regulatory network from plasma RNA dataset of colorectal cancer patients. Plasma RNA is highly attractive for cancer analysis since it requires a collection of small amount of blood and it can be obtained at any time in repetitive fashion allowing the analysis of disease progression and treatment response.

Neuromantic : from semi-manual to semi-automatic reconstruction of neuron morphology

The ability to create accurate geometric models of neuronal morphology is important for understanding the role of shape in information processing. Despite a significant amount of research on automating neuron reconstructions from image stacks obtained via microscopy, in practice most data are still collected manually. This paper describes Neuromantic, an open source system for three dimensional digital tracing of neurites. Neuromantic reconstructions are comparable in quality to those of existing commercial and freeware systems while balancing speed and accuracy of manual reconstruction. The combination of semi-automatic tracing, intuitive editing, and ability of visualizing large image stacks on standard computing platforms provides a versatile tool that can help address the reconstructions availability bottleneck. Practical considerations for reducing the computational time and space requirements of the extended algorithm are also discussed.

Sequence-specific reconstruction from fragmentary databases using seed sequences: implementation and validation on SAGE, proteome and generic sequencing data

Motivation: DNA assembly programs classically perform an all-against-all comparison of reads to identify overlaps, followed by a multiple sequence alignment and generation of a consensus sequence. If the aim is to assemble a particular segment, instead of a whole genome or transcriptome, a target-specific assembly is a more sensible approach. GenSeed is a Perl program that implements a seed-driven recursive assembly consisting of cycles comprising a similarity search, read selection and assembly. The iterative process results in a progressive extension of the original seed sequence. GenSeed was tested and validated on many applications, including the reconstruction of nuclear genes or segments, full-length transcripts, and extrachromosomal genomes. The robustness of the method was confirmed through the use of a variety of DNA and protein seeds, including short sequences derived from SAGE and proteome projects.

3D face computational photography using PCA spaces

In this paper, we present a 3D face photography system based on a facial expression training dataset, composed of both facial range images (3D geometry) and facial texture (2D photography). The proposed system allows one to obtain a 3D geometry representation of a given face provided as a 2D photography, which undergoes a series of transformations through the texture and geometry spaces estimated. In the training phase of the system, the facial landmarks are obtained by an active shape model (ASM) extracted from the 2D gray-level photography. Principal components analysis (PCA) is then used to represent the face dataset, thus defining an orthonormal basis of texture and another of geometry. In the reconstruction phase, an input is given by a face image to which the ASM is matched. The extracted facial landmarks and the face image are fed to the PCA basis transform, and a 3D version of the 2D input image is built. Experimental tests using a new dataset of 70 facial expressions belonging to ten subjects as training set show rapid reconstructed 3D faces which maintain spatial coherence similar to the human perception, thus corroborating the efficiency and the applicability of the proposed system.

Visualisation and reconstruction in dentistry

Visualisation in the field of dentistry has nor, thus far, reached the same development as other medical fields. Potential applications of visualisation techniques in this area, however, are many, ranging from educational displays to training for delicate procedures. This paper reports on the investigation of techniques for handling three-dimensional models of teeth, aiming at investigation of dental structures. An algorithm was implemented for this purpose, which reconstructs three-dimensional teeth models from two-dimensional contour slices. Results employing various data sets are presented, including the output of VRML models for exploration.

Image Reconstruction Using Interval Simulated Annealing in Electrical Impedance Tomography

Electrical impedance tomography (EIT) is an imaging technique that attempts to reconstruct the impedance distribution inside an object from the impedance between electrodes placed on the object surface. The EIT reconstruction problem can be approached as a nonlinear nonconvex optimization problem in which one tries to maximize the matching between a simulated impedance problem and the observed data. This nonlinear optimization problem is often ill-posed, and not very suited to methods that evaluate derivatives of the objective function. It may be approached by simulated annealing (SA), but at a large computational cost due to the expensive evaluation process of the objective function, which involves a full simulation of the impedance problem at each iteration. A variation of SA is proposed in which the objective function is evaluated only partially, while ensuring boundaries on the behavior of the modified algorithm.

Computational methods for the analysis of protein structure and function

The vast majority of known proteins have not yet been experimentally characterized and little is known about their function. The design and implementation of computational tools can provide insight into the function of proteins based on their sequence, their structure, their evolutionary history and their association with other proteins. Knowledge of the three-dimensional (3D) structure of a protein can lead to a deep understanding of its mode of action and interaction, but currently the structures of <1% of sequences have been experimentally solved. For this reason, it became urgent to develop new methods that are able to computationally extract relevant information from protein sequence and structure. The starting point of my work has been the study of the properties of contacts between protein residues, since they constrain protein folding and characterize different protein structures. Prediction of residue contacts in proteins is an interesting problem whose solution may be useful in protein folding recognition and de novo design. The prediction of these contacts requires the study of the protein inter-residue distances related to the specific type of amino acid pair that are encoded in the so-called contact map. An interesting new way of analyzing those structures came out when network studies were introduced, with pivotal papers demonstrating that protein contact networks also exhibit small-world behavior. In order to highlight constraints for the prediction of protein contact maps and for applications in the field of protein structure prediction and/or reconstruction from experimentally determined contact maps, I studied to which extent the characteristic path length and clustering coefficient of the protein contacts network are values that reveal characteristic features of protein contact maps. Provided that residue contacts are known for a protein sequence, the major features of its 3D structure could be deduced by combining this knowledge with correctly predicted motifs of secondary structure. In the second part of my work I focused on a particular protein structural motif, the coiled-coil, known to mediate a variety of fundamental biological interactions. Coiled-coils are found in a variety of structural forms and in a wide range of proteins including, for example, small units such as leucine zippers that drive the dimerization of many transcription factors or more complex structures such as the family of viral proteins responsible for virus-host membrane fusion. The coiled-coil structural motif is estimated to account for 5-10% of the protein sequences in the various genomes. Given their biological importance, in my work I introduced a Hidden Markov Model (HMM) that exploits the evolutionary information derived from multiple sequence alignments, to predict coiled-coil regions and to discriminate coiled-coil sequences. The results indicate that the new HMM outperforms all the existing programs and can be adopted for the coiled-coil prediction and for large-scale genome annotation. Genome annotation is a key issue in modern computational biology, being the starting point towards the understanding of the complex processes involved in biological networks. The rapid growth in the number of protein sequences and structures available poses new fundamental problems that still deserve an interpretation. Nevertheless, these data are at the basis of the design of new strategies for tackling problems such as the prediction of protein structure and function. Experimental determination of the functions of all these proteins would be a hugely time-consuming and costly task and, in most instances, has not been carried out. As an example, currently, approximately only 20% of annotated proteins in the Homo sapiens genome have been experimentally characterized. A commonly adopted procedure for annotating protein sequences relies on the "inheritance through homology" based on the notion that similar sequences share similar functions and structures. This procedure consists in the assignment of sequences to a specific group of functionally related sequences which had been grouped through clustering techniques. The clustering procedure is based on suitable similarity rules, since predicting protein structure and function from sequence largely depends on the value of sequence identity. However, additional levels of complexity are due to multi-domain proteins, to proteins that share common domains but that do not necessarily share the same function, to the finding that different combinations of shared domains can lead to different biological roles. In the last part of this study I developed and validate a system that contributes to sequence annotation by taking advantage of a validated transfer through inheritance procedure of the molecular functions and of the structural templates. After a cross-genome comparison with the BLAST program, clusters were built on the basis of two stringent constraints on sequence identity and coverage of the alignment. The adopted measure explicity answers to the problem of multi-domain proteins annotation and allows a fine grain division of the whole set of proteomes used, that ensures cluster homogeneity in terms of sequence length. A high level of coverage of structure templates on the length of protein sequences within clusters ensures that multi-domain proteins when present can be templates for sequences of similar length. This annotation procedure includes the possibility of reliably transferring statistically validated functions and structures to sequences considering information available in the present data bases of molecular functions and structures.

Bioimaging of animal embryogenesis: mathematical methods and computational algorithms

Some fundamental biological processes such as embryonic development have been preserved during evolution and are common to species belonging to different phylogenetic positions, but are nowadays largely unknown. The understanding of cell morphodynamics leading to the formation of organized spatial distribution of cells such as tissues and organs can be achieved through the reconstruction of cells shape and position during the development of a live animal embryo. We design in this work a chain of image processing methods to automatically segment and track cells nuclei and membranes during the development of a zebrafish embryo, which has been largely validates as model organism to understand vertebrate development, gene function and healingrepair mechanisms in vertebrates. The embryo is previously labeled through the ubiquitous expression of fluorescent proteins addressed to cells nuclei and membranes, and temporal sequences of volumetric images are acquired with laser scanning microscopy. Cells position is detected by processing nuclei images either through the generalized form of the Hough transform or identifying nuclei position with local maxima after a smoothing preprocessing step. Membranes and nuclei shapes are reconstructed by using PDEs based variational techniques such as the Subjective Surfaces and the Chan Vese method. Cells tracking is performed by combining informations previously detected on cells shape and position with biological regularization constraints. Our results are manually validated and reconstruct the formation of zebrafish brain at 7-8 somite stage with all the cells tracked starting from late sphere stage with less than 2% error for at least 6 hours. Our reconstruction opens the way to a systematic investigation of cellular behaviors, of clonal origin and clonal complexity of brain organs, as well as the contribution of cell proliferation modes and cell movements to the formation of local patterns and morphogenetic fields.

Reconstruction and analysis of the NF-kB pathway interactome: a systems biology approach

Background. One of the phenomena observed in human aging is the progressive increase of a systemic inflammatory state, a condition referred to as “inflammaging”, negatively correlated with longevity. A prominent mediator of inflammation is the transcription factor NF-kB, that acts as key transcriptional regulator of many genes coding for pro-inflammatory cytokines. Many different signaling pathways activated by very diverse stimuli converge on NF-kB, resulting in a regulatory network characterized by high complexity. NF-kB signaling has been proposed to be responsible of inflammaging. Scope of this analysis is to provide a wider, systemic picture of such intricate signaling and interaction network: the NF-kB pathway interactome. Methods. The study has been carried out following a workflow for gathering information from literature as well as from several pathway and protein interactions databases, and for integrating and analyzing existing data and the relative reconstructed representations by using the available computational tools. Strong manual intervention has been necessarily used to integrate data from multiple sources into mathematically analyzable networks. The reconstruction of the NF-kB interactome pursued with this approach provides a starting point for a general view of the architecture and for a deeper analysis and understanding of this complex regulatory system. Results. A “core” and a “wider” NF-kB pathway interactome, consisting of 140 and 3146 proteins respectively, were reconstructed and analyzed through a mathematical, graph-theoretical approach. Among other interesting features, the topological characterization of the interactomes shows that a relevant number of interacting proteins are in turn products of genes that are controlled and regulated in their expression exactly by NF-kB transcription factors. These “feedback loops”, not always well-known, deserve deeper investigation since they may have a role in tuning the response and the output consequent to NF-kB pathway initiation, in regulating the intensity of the response, or its homeostasis and balance in order to make the functioning of such critical system more robust and reliable. This integrated view allows to shed light on the functional structure and on some of the crucial nodes of thet NF-kB transcription factors interactome. Conclusion. Framing structure and dynamics of the NF-kB interactome into a wider, systemic picture would be a significant step toward a better understanding of how NF-kB globally regulates diverse gene programs and phenotypes. This study represents a step towards a more complete and integrated view of the NF-kB signaling system.

Finite element 3D reconstruction of the pulmonary acinus imaged by synchrotron X-ray tomography

The alveolated structure of the pulmonary acinus plays a vital role in gas exchange function. Three-dimensional (3D) analysis of the parenchymal region is fundamental to understanding this structure-function relationship, but only a limited number of attempts have been conducted in the past because of technical limitations. In this study, we developed a new image processing methodology based on finite element (FE) analysis for accurate 3D structural reconstruction of the gas exchange regions of the lung. Stereologically well characterized rat lung samples (Pediatr Res 53: 72-80, 2003) were imaged using high-resolution synchrotron radiation-based X-ray tomographic microscopy. A stack of 1,024 images (each slice: 1024 x 1024 pixels) with resolution of 1.4 mum(3) per voxel were generated. For the development of FE algorithm, regions of interest (ROI), containing approximately 7.5 million voxels, were further extracted as a working subunit. 3D FEs were created overlaying the voxel map using a grid-based hexahedral algorithm. A proper threshold value for appropriate segmentation was iteratively determined to match the calculated volume density of tissue to the stereologically determined value (Pediatr Res 53: 72-80, 2003). The resulting 3D FEs are ready to be used for 3D structural analysis as well as for subsequent FE computational analyses like fluid dynamics and skeletonization.