Unlabeled Structures Research Articles

FINITE RELATION ALGEBRAS

AbstractWe will show that almost all nonassociative relation algebras are symmetric and integral (in the sense that the fraction of both labelled and unlabelled structures that are symmetric and integral tends to $1$ ), and using a Fraïssé limit, we will establish that the classes of all atom structures of nonassociative relation algebras and relation algebras both have $0$ – $1$ laws. As a consequence, we obtain improved asymptotic formulas for the numbers of these structures and broaden some known probabilistic results on relation algebras.

The ‘hidden side’ of spin labelled oligonucleotides: Molecular dynamics study focusing on the EPR-silent components of base pairing

Nitroxide labels are combined with nucleic acid structures and are studied using electron paramagnetic resonance experiments (EPR). As X-ray/NMR structures are unavailable with the nitroxide labels, detailed residue level information, down to atomic resolution, about the effect of these nitroxide labels on local RNA structures is currently lacking. This information is critical to evaluate the choice of spin label. In this study, we compare and contrast the effect of TEMPO-based (NT) and rigid spin (Ç) labels (in both 2′-O methylated and not-methylated forms) on RNA duplexes. We also investigate sequence- dependent effects of NT label on RNA duplex along with the more complex G-quadruplex RNA. Distances measured from molecular dynamics simulations between the two spin labels are in agreement with the EPR experimental data. To understand the effect of labelled oligonucleotides on the structure, we studied the local base pair geometries and global structure in comparison with the unlabelled structures. Based on the structural analysis, we can conclude that TEMPO-based and Ç labels do not significantly perturb the base pair arrangements of the native oligonucleotide. When experimental structures for the spin labelled DNA/RNA molecules are not available, general framework offered by the current study can be used to provide information critical to the choice of spin labels to facilitate future EPR studies.

Comparing the expressiveness of downward fragments of the relation algebra with transitive closure on trees

Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add transitive closure, projections, coprojections, intersection, and difference; this for Boolean queries and path queries on labeled and unlabeled structures. In all cases, we present the complete Hasse diagram. In particular, we establish, for each query language fragment that we study on trees, whether it is closed under difference and intersection.

Extension of training set using mean shift procedure for aerospace images classification

An effective method of training set extension for aerospace images classification is proposed. The method is based on mean shift procedure with respect to spatial information. It allows considering the unlabeled data structure. The results of experimental study using the Salinas hyperspectral image are presented, proving the effectiveness of the proposed method.

Correlative microscopy approach for biology using X-ray holography, X-ray scanning diffraction and STED microscopy

We present a correlative microscopy approach for biology based on holographic X-ray imaging, X-ray scanning diffraction, and stimulated emission depletion (STED) microscopy. All modalities are combined into the same synchrotron endstation. In this way, labeled and unlabeled structures in cells are visualized in a complementary manner. We map out the fluorescently labeled actin cytoskeleton in heart tissue cells and superimpose the data with phase maps from X-ray holography. Furthermore, an array of local far-field diffraction patterns is recorded in the regime of small-angle X-ray scattering (scanning SAXS), which can be interpreted in terms of biomolecular shape and spatial correlations of all contributing scattering constituents. We find that principal directions of anisotropic diffraction patterns coincide to a certain degree with the actin fiber directions and that actin stands out in the phase maps from holographic recordings. In situ STED recordings are proposed to formulate models for diffraction data based on co-localization constraints.

Multi-structure Segmentation from Partially Labeled Datasets. Application to Body Composition Measurements on CT Scans.

Labeled data is the current bottleneck of medical image research. Substantial efforts are made to generate segmentation masks to characterize a given organ. The community ends up with multiple label maps of individual structures in different cases, not suitable for current multi-organ segmentation frameworks. Our objective is to leverage segmentations from multiple organs in different cases to generate a robust multi-organ deep learning segmentation network. We propose a modified cost-function that takes into account only the voxels labeled in the image, ignoring unlabeled structures. We evaluate the proposed methodology in the context of pectoralis muscle and subcutaneous fat segmentation on chest CT scans. Six different structures are segmented from an axial slice centered on the transversal aorta. We compare the performance of a network trained on 3,000 images where only one structure has been annotated (PUNet) against six UNets (one per structure) and a multi-class UNet trained on 500 completely annotated images, showing equivalence between the three methods (Dice coefficients of 0.909, 0.906 and 0.909 respectively). We further propose a modification of the architecture by adding convolutions to the skip connections (CUNet). When trained with partially labeled images, it outperforms statistically significantly the other three methods (Dice 0.916, p< 0.0001). We, therefore, show that (a) when keeping the number of organ annotation constant, training with partially labeled images is equivalent to training with wholly labeled data and (b) adding convolutions in the skip connections improves performance.

Relative merits and limiting factors for x-ray and electron microscopy of thick, hydrated organic materials

Electron and x-ray microscopes allow one to image the entire, unlabeled structure of hydrated materials at a resolution well beyond what visible light microscopes can achieve. However, both approaches involve ionizing radiation, so that radiation damage must be considered as one of the limits to imaging. Drawing upon earlier work, we describe here a unified approach to estimating the image contrast (and thus the required exposure and corresponding radiation dose) in both x-ray and electron microscopy. This approach accounts for factors such as plural and inelastic scattering, and (in electron microscopy) the use of energy filters to obtain so-called “zero loss” images. As expected, it shows that electron microscopy offers lower dose for specimens thinner than about 1 µm (such as for studies of macromolecules, viruses, bacteria and archaebacteria, and thin sectioned material), while x-ray microscopy offers superior characteristics for imaging thicker specimen such as whole eukaryotic cells, thick-sectioned tissues, and organs. The required radiation dose scales strongly as a function of the desired spatial resolution, allowing one to understand the limits of live and frozen hydrated specimen imaging. Finally, we consider the factors limiting x-ray microscopy of thicker materials, suggesting that specimens as thick as a whole mouse brain can be imaged with x-ray microscopes without significant image degradation should appropriate image reconstruction methods be identified.

Dual-modality endomicroscopy with co-registered fluorescence and phase contrast

We describe a dual-modality laser scanning endomicroscope that provides simultaneous fluorescence contrast based on confocal laser endomicroscopy (CLE) and phase-gradient contrast based on scanning oblique back-scattering microscopy (sOBM). The probe consists of a 2.6mm-diameter micro-objective attached to a 30,000-core flexible fiber bundle. The dual contrasts are inherently co-registered, providing complementary information on labeled and un-labeled sample structure. Proof of principle demonstrations are presented with ex-vivo mouse colon tissue.

Isotope-induced desymmetrization can mimic isotopic perturbation of equilibria. On the symmetry of bromonium ions and hydrogen bonds.

The desymmetrizing effect of isotopic substitution on the geometry of otherwise symmetrical structures can be surprisingly large when there is anharmonic coupling between a desymmetrizing mode and modes whose zero-point energies are strongly isotope-dependent. This phenomenon is found to account for experimental observations that had been previously interpreted as implying asymmetry in bromonium ions and in hydrogen phthalate ions in aprotic solvents. The unlabeled structures are concluded to have the higher symmetry found in computed structures. Great care must be taken in applying isotopic perturbation as a test of asymmetry.

Boltzmann Samplers, Pólya Theory, and Cycle Pointing

We introduce a general method to count unlabeled combinatorial structures and to efficiently generate them at random. The approach is based on pointing unlabeled structures in an “unbiased” way so that a structure of size $n$ gives rise to $n$ pointed structures. We extend Polya theory to the corresponding pointing operator and present a random sampling framework based on both the principles of Boltzmann sampling and Polya operators. All previously known unlabeled construction principles for Boltzmann samplers are special cases of our new results. Our method is illustrated in several examples: in each case, we provide enumerative results and efficient random samplers. The approach applies to unlabeled families of plane and nonplane unrooted trees, and tree-like structures in general, but also to families of graphs (such as cacti graphs and outerplanar graphs) and families of planar maps.

An optimal algorithm to generate rooted trivalent diagrams and rooted triangular maps

A trivalent diagram is a connected, two-colored bipartite graph (parallel edges allowed but not loops) such that every black vertex is of degree 1 or 3 and every white vertex is of degree 1 or 2, with a cyclic order imposed on every set of edges incident to the same vertex. A rooted trivalent diagram is a trivalent diagram with a distinguished edge, its root. We shall describe and analyze an algorithm giving an exhaustive list of rooted trivalent diagrams of a given size (number of edges), the list being non-redundant in that no two diagrams of the list are isomorphic. The algorithm will be shown to have optimal performance in that the time necessary to generate a diagram will be seen to be bounded in the amortized sense, the bound being independent of the size of the diagrams. We call this the CAT property. One objective of the paper is to provide a reusable theoretical framework for algorithms generating exhaustive lists of complex combinatorial structures with attention paid to the case of unlabeled structures and to those generators having the CAT property.

Using Tablet PCs and DyKnow Vision to Enhance Student Engagement in a Human Anatomy Class

Keeping students engaged in human anatomy classes is a significant challenge. To increase students' active learning and facilitate understanding of material, Tablet PCs running the software DyKnow Vision were introduced in a human anatomy class. Tablet PCs and DyKnow Vision were specifically used to create a virtual blackboard for the identification and discussion of anatomical structures. Anatomical illustrations from the primary text used in the class were routinely imported and saved as DyKnow Vision files. Students were then provided with DyKnow panels of unlabeled structures to identify and label using digital ink. The labeled panels were submitted, reviewed, corrected with the class' participation, and appended to the class session. To assess students' level of engagement, their attitudes and perceptions of the effectiveness of the Tablet PCs/DyKnow as a pedagogical tool, an anonymous survey using a 5 point Likert scale was completed by students. Results strongly suggest that the Tablet PCs/DyKnow combination made the class enjoyable, enhanced students' comprehension of content, and had an overall positive impact on their learning of human anatomy.Funding: DePauw University

A Complete Grammar for Decomposing a Family of Graphs into 3-Connected Components

Tutte has described in the book "Connectivity in graphs" a canonical decomposition of any graph into 3-connected components. In this article we translate (using the language of symbolic combinatorics) Tutte's decomposition into a general grammar expressing any family ${\cal G}$ of graphs (with some stability conditions) in terms of the subfamily ${\cal G}_3$ of graphs in ${\cal G}$ that are 3-connected (until now, such a general grammar was only known for the decomposition into $2$-connected components). As a byproduct, our grammar yields an explicit system of equations to express the series counting a (labelled) family of graphs in terms of the series counting the subfamily of $3$-connected graphs. A key ingredient we use is an extension of the so-called dissymmetry theorem, which yields negative signs in the grammar and associated equation system, but has the considerable advantage of avoiding the difficult integration steps that appear with other approaches, in particular in recent work by Giménez and Noy on counting planar graphs. As a main application we recover in a purely combinatorial way the analytic expression found by Giménez and Noy for the series counting labelled planar graphs (such an expression is crucial to do asymptotic enumeration and to obtain limit laws of various parameters on random planar graphs). Besides the grammar, an important ingredient of our method is a recent bijective construction of planar maps by Bouttier, Di Francesco and Guitter. Finally, our grammar applies also to the case of unlabelled structures, since the dissymetry theorem takes symmetries into account. Even if there are still difficulties in counting unlabelled 3-connected planar graphs, we think that our grammar is a promising tool toward the asymptotic enumeration of unlabelled planar graphs, since it circumvents some difficult integral calculations.

The Size of the rth Smallest Component in Decomposable Structures with a Restricted Pattern

In our previous work [paper1], we derived an asymptotic expression for the probability that a random decomposable combinatorial structure of size n in the \exp -\log class has a given restricted pattern. In this paper, under similar conditions, we provide the probability that a random decomposable combinatorial structure has a given restricted pattern and the size of its rth smallest component is bigger than k, for r,k given integers. Our studies apply to labeled and unlabeled structures. We also give several concrete examples.

Integrating High Resolution Light Microscopy and Real Time Observation of Fluorescent Labels

Abstract Fluorescence microscopy has experienced tremendous growth over the past four decades and has facilitated major advancements in science. The classic fluorescent techniques (which include epifluorescence and confocal) allow researchers to selectively observe labeled structures with great clarity and consistency. Historically, biological scientists have been the most prolific users of fluorescence imaging. However, growing numbers of nano-materials research initiatives are now incorporating quantum dots and other fluorescent labels into their imaging protocols. This is especially true in areas where nano-materials and biological research is overlapping such as drug delivery. This nano-bio convergence, along with other advancements, has generated the need to observe highly dynamic events involving labeled and unlabeled structures in real time.

The relationship between serotonin, dopamine beta hydroxylase and GABA immunoreactive inputs and spinal preganglionic neurones projecting to the major pelvic ganglion of wistar rats

Preganglionic neurones in the lumbosacral spinal cord give rise to nerves providing the parasympathetic and sympathetic innervation of pelvic organs. These neurones are modulated by neurotransmitters released both from descending supra-spinal pathways and spinal interneurones. Though serotonin has been identified as exerting a significant influence on these neurones, few studies have investigated the circuitry through which it achieves this particularly in relation to sympathetic preganglionic neurones. Using a combination of neuronal tracing and multiple immunolabeling procedures, the current study has shown that pelvic preganglionic neurones receive a sparse, and probably non-synaptic, axosomatic/proximal dendritic input from serotonin-immunoreactive terminals. This was in marked contrast to dopamine beta hydroxylase-immunoreactive terminals, which made multiple contacts. However, the demonstration of both serotonin, and dopamine beta hydroxylase immunoreactive terminals on both parasympathetic and sympathetic preganglionic neurones provides evidence for direct modulation of these cells by both serotonin and norepinephrine. Serotonin-containing terminals displaying conventional synaptic morphology were often seen to contact unlabeled somata and dendritic processes in regions surrounding the labeled preganglionic cells. It is possible that these unlabeled structures represent interneurones that might allow the serotonin containing axons to exert an indirect influence on pelvic preganglionic neurones. Since many spinal interneurones employ GABA as a primary fast acting neurotransmitter we examined the relationship between terminals that were immunoreactive for serotonin or GABA and labeled pelvic preganglionic neurones. These studies were unable to demonstrate any direct connections between serotonin and GABA terminals within the intermediolateral or sacral parasympathetic nuclei. Colocalization of serotonin and GABA was very rare but terminals immunoreactive for each were occasionally seen to contact the same unlabeled processes in close proximity. These results suggest that in the rat, the serotonin modulation of pelvic preganglionic neurones may primarily involve indirect connections via local interneurones.

Enumerative Problems Inspired by Mayer's Theory of Cluster Integrals

The basic functional equations for connected and 2-connnected graphs can be traced back to the statistical physicists Mayer and Husimi. They play an essential role in establishing rigorously the virial expansion for imperfect gases. We first review these functional equations, putting the emphasis on the structural relationships between the various classes of graphs. We then investigate the problem of enumerating some classes of connected graphs all of whose 2-connected components (blocks) are contained in a given class $B$. Included are the species of Husimi graphs ($B =$ "complete graphs"), cacti ($B =$ "unoriented cycles"), and oriented cacti ($B =$ "oriented cycles"). For each of these, we address the question of their labelled and unlabelled enumeration, according (or not) to their block-size distributions. Finally we discuss the molecular expansion of these species. It consists of a descriptive classification of the unlabelled structures in terms of elementary species, from which all their symmetries can be deduced.

The ‘Burnside Process’ Converges Slowly

We consider the problem of sampling ‘unlabelled structures’, i.e., sampling combinatorial structures modulo a group of symmetries. The main tool which has been used for this sampling problem is Burnside’s lemma. In situations where a significant proportion of the structures have no nontrivial symmetries, it is already fairly well understood how to apply this tool. More generally, it is possible to obtain nearly uniform samples by simulating a Markov chain that we call the Burnside process: this is a random walk on a bipartite graph which essentially implements Burnside’s lemma. For this approach to be feasible, the Markov chain ought to be ‘rapidly mixing’, i.e., converge rapidly to equilibrium. The Burnside process was known to be rapidly mixing for some special groups, and it has even been implemented in some computational group theory algorithms. In this paper, we show that the Burnside process is not rapidly mixing in general. In particular, we construct an infinite family of permutation groups for which we show that the mixing time is exponential in the degree of the group.

Constructing Finite Unlabeled Structures Using Group Actions

The aim of this review is to point to a particular aspect of the constructive enumeration of finite unlabeled structures: The use of group actions and of double cosets in finite groups. In order to do this we start with a brief list of unlabeled structures, i.e., of mathematical structures defined as equivalence classes on finite sets. Then it will be shown that in each case the equivalence relation can be replaced by a finite group action, and so the whole bunch of tools of finite group actions' theory can be applied in each of these cases. The finite structures in question will be introduced as orbits of finite groups on finite sets, and so they can be obtained from transversals of orbit sets by simple deleting the labels. Therefore the construction of representatives of orbits, using double cosets, as well as the generation of representatives uniformly at random will be briefly described.

Cycle index series of structures over digraphs

Recently, we introduced (Méndez, Adv. Math. 123 (1996) 243–275.) a generalization of Joyal (Adv. Math. 42 (1981) 1–82) species in order to enumerate structures constructed over arc-labeled directed graphs (species on digraphs). We introduce here the Z-series for species on digraphs, in analogy with Joyal Z-series for ordinary species. We apply the Z-series to obtain classical and new generating functions for unlabeled structures on digraphs.