The Control of a Mathematical Analog of a Tentacle

A 2-dimensional dynamic analog of squid tentacles was presented. The tentacle analog consists of a multi-cell structure, which can be easily replicated to a large scale. Each cell of the model is a quadrilateral with unit masses at the corners. Each side of the quadrilateral is a spring-damper system in parallel. The spring constants are the controls for the system. The dynamics are subject to the constraint that the area of each quadrilateral must remain constant. The system dynamics was analyzed, and various equilibrium points were found with different controls. Then these equilibrium points were further determined experimentally, demonstrated to be asymptotically stable. A simulation built in MATLAB was used to find the convergence rates under different controls and damping coefficients. Finally, a control scheme was developed and used to drive the system to several configurations observed in real tentacle.

Shape and chemically anisotropic colloidal particles: A theoretical study of their structure, phase behavior, and slow dynamics

A detailed non-equilibrium state diagram of shape-anisotropic particle fluids is constructed. The effects of particle shape are explored using Naive Mode Coupling Theory (NMCT), and a single particle Non-linear Langevin Equation (NLE) theory. The dynamical behavior of non-ergodic fluids are discussed. We employ a rotationally frozen approach to NMCT in order to determine a transition to center of mass (translational) localization. Both ideal and kinetic glass transitions are found to be highly shape dependent, and uniformly increase with particle dimensionality. The glass transition volume fraction of quasi 1- and 2- dimensional particles fall monotonically with the number of sites (aspect ratio), while 3-dimensional particles display a non-monotonic dependence of glassy vitrification on the number of sites. Introducing interparticle attractions results in a far more complex state diagram. The ideal non-ergodic boundary shows a glass-fluid-gel re-entrance previously predicted for spherical particle fluids. The non-ergodic region of the state diagram presents qualitatively different dynamics in different regimes. They are qualified by the different behaviors of the NLE dynamic free energy. The caging dominated, repulsive glass regime is characterized by long localization lengths and barrier locations, dictated by repulsive hard core interactions, while the bonding dominated gel region has short localization lengths (commensurate with the attraction range), and barrier locations. There exists a small region of the state diagram which is qualified by both glassy and gel localization lengths in the dynamic free energy. A much larger (high volume fraction, and high attraction strength) region of phase space is characterized by short gel-like localization lengths, and long barrier locations. The region is called the attractive glass and represents a 2-step relaxation process whereby a particle first breaks attractive physical bonds, and then escapes its topological cage. The dynamic fragility of fluids are highly particle shape dependent. It increases with particle dimensionality and falls with aspect ratio for quasi 1- and 2- dimentional particles. An ultralocal limit analysis of the NLE theory predicts universalities in the behavior of relaxation times, and elastic moduli. The equlibrium phase diagram of chemically anisotropic Janus spheres and Janus rods are calculated employing a mean field Random Phase Approximation. The calculations for Janus rods are corroborated by the full liquid state Reference Interaction Site Model theory. The Janus particles consist of attractive and repulsive regions. Both rods and spheres display rich phase behavior. The phase diagrams of these systems display fluid, macrophase separated, attraction driven microphase separated, repulsion driven microphase separated and crystalline regimes. Macrophase separation is predicted in highly attractive low volume fraction systems. Attraction driven microphase separation is charaterized by long length scale divergences, where the ordering length scale determines the microphase ordered structures. The ordering length scale of repulsion driven microphase separation is determined by the repulsive range. At the high volume fractions, particles forgo the enthalpic considerations of attractions and repulsions to satisfy hard core constraints and maximize vibrational entropy. This results in site length scale ordering in rods, and the sphere length scale ordering in Janus spheres, i.e., crystallization. A change in the Janus balance of both rods and spheres results in quantitative changes in spinodal temperatures and the position of phase boundaries. However, a change in the block sequence of Janus rods causes qualitative changes in the type of microphase ordered state, and induces prominent features (such as the Lifshitz point) in the phase diagrams of these systems. A detailed study of the number of nearest neighbors in Janus rod systems reflect a deep connection between this local measure of structure, and the structure factor which represents the most global measure of order.

Probabilistic approach of water residence time and connectivity using Markov Chains with application to tidal embayments

Markov Chain analysis was recently proposed to assess the time scales and preferential pathways into biological or physical networks by computing residence time, first passage time, rates of transfer between nodes and number of passages in a node. We propose to adapt an algorithm already published for simple systems to physical systems described with a high resolution hydrodynamic model. The method is applied to bays and estuaries on the Eastern Coast of Canada for their interest in shellfish aquaculture. Current velocities have been computed by using a 2 dimensional grid of elements and circulation patterns were summarized by averaging Eulerian flows between adjacent elements. Flows and volumes allow computing probabilities of transition between elements and to assess the average time needed by virtual particles to move from one element to another, the rate of transfer between two elements, and the average residence time of each system. We also combined transfer rates and times to assess the main pathways of virtual particles released in farmed areas and the potential influence of farmed areas on other areas. We suggest that Markov chain is complementary to other sets of ecological indicators proposed to analyse the interactions between farmed areas - e.g. depletion index, carrying capacity assessment. Markov Chain has several advantages with respect to the estimation of connectivity between pair of sites. It makes possible to estimate transfer rates and times at once in a very quick and efficient way, without the need to perform long term simulations of particle or tracer concentration.

Census of quadrangle groups inclusions

In a classical result of 1972 Singerman classifies the inclusions between triangle groups. We extend the classification to a broader family of triangle and quadrangle groups forming a particular subfamily of Fuchsian groups. With two exceptions, each inclusion determines a finite bipartite map (hypermap) on a 2-dimensional spherical orbifold that encodes the complete information and gives a graphical visualisation of the inclusion. A complete description of all the inclusions is contained in the attached tables.

POSE ESTIMATION AND 3D RECONSTRUCTION USING SENSOR FUSION

A camera maps 3-dimensional (3D) world space to a 2-dimensional (2D) image space. In the process it loses the depth information, i.e., the distance from the camera focal point to the imaged objects. It is impossible to recover this information from a single image. However, by using two or more images from different viewing angles this information can be recovered, which in turn can be used to obtain the pose (position and orientation) of the camera. Using this pose, a 3D reconstruction of imaged objects in the world can be computed. Numerous algorithms have been proposed and implemented to solve the above problem; these algorithms are commonly called Structure from Motion (SfM). State-of-the-art SfM techniques have been shown to give promising results. However, unlike a Global Positioning System (GPS) or an Inertial Measurement Unit (IMU) which directly give the position and orientation respectively, the camera system estimates it after implementing SfM as mentioned above. This makes the pose obtained from a camera highly sensitive to the images captured and other effects, such as low lighting conditions, poor focus or improper viewing angles. In some applications, for example, an Unmanned Aerial Vehicle (UAV) inspecting a bridge or a robot mapping an environment using Simultaneous Localization and Mapping (SLAM), it is often difficult to capture images with ideal conditions. This report examines the use of SfM methods in such applications and the role of combining multiple sensors, viz., sensor fusion, to achieve more accurate and usable position and reconstruction information. This project investigates the role of sensor fusion in accurately estimating the pose of a camera for the application of 3D reconstruction of a scene. The first set of experiments is conducted in a motion capture room. These results are assumed as ground truth in order to evaluate the strengths and weaknesses of each sensor and to map their coordinate systems. Then a number of scenarios are targeted where SfM fails. The pose estimates obtained from SfM are replaced by those obtained from other sensors and the 3D reconstruction is completed. Quantitative and qualitative comparisons are made between the 3D reconstruction obtained by using only a camera versus that obtained by using the camera along with a LIDAR and/or an IMU. Additionally, the project also works towards the performance issue faced while handling large data sets of high-resolution images by implementing the system on the Superior high performance computing cluster at Michigan Technological University.

Trajectory planning of single and dual-arm robots for time-optimal handling of liquids and objects

This Thesis studies the optimal control problem of single-arm and dual-arm serial robots to achieve the time-optimal handling of liquids and objects. The first topic deals with the planning of time-optimal anti-sloshing trajectories of an industrial robot carrying a cylindrical container filled with a liquid, considering 1-dimensional and 2-dimensional planar motions. A technique for the estimation of the sloshing height is presented, together with its extension to 3-dimensional motions. An experimental validation campaign is provided and discussed to assess the thoroughness of such a technique. As far as anti-sloshing trajectories are concerned, 2-dimensional paths are considered and, for each one of them, three constrained optimizations with different values of the sloshing-height thresholds are solved. Experimental results are presented to compare optimized and non-optimized motions. The second part focuses on the time-optimal trajectory planning for dual-arm object handling, employing two collaborative robots (cobots) and adopting an admittance-control strategy. The chosen manipulation approach, known as cooperative grasping, is based on unilateral contact between the cobots and the object, and it may lead to slipping during motion if an internal prestress along the contact-normal direction is not prescribed. Thus, a virtual penetration is considered, aimed at generating the necessary internal prestress. The stability of cooperative grasping is ensured as long as the exerted forces on the object remain inside the static-friction cone. Constrained-optimization problems are solved for 3-dimensional paths: the virtual penetration is chosen among the control inputs of the problem and friction-cone conditions are treated as inequality constraints. Also in this case experiments are presented in order to prove evidence of the firm handling of the object, even for fast motions.

Advanced X-ray techniques for the structural characterisation of Prussian Blue Analogue cathode materials

The thesis is dedicated to the implementation of advanced x-ray-based techniques for the investigation of the battery systems, more predominantly, the cathode materials. The implemented characterisation methods include synchrotron based x-ray absorption spectroscopy, powder x-ray diffraction, 2-dimensional x-ray fluorescence, full field transmission soft x-ray microscopy, and laboratory x-ray photoelectron spectroscopy. The research highlights the different areas of expertise for each described method, in terms of material characterisation, exploring their complementarities and intersections. The results are focused over manganese hexacyanoferrate and partially Ni substituted manganese hexacyanoferrate, through both organic and aqueous battery systems. In aqueous system, the modification of cathode composition has been observed with various techniques, indicating to the processes occurring in bulk, surface, locally or in long-range, including with the speciation by 2-dimensional scanning, and the time-resolution, by the implementation of the operando measurements. In organic media, the inhomogenisation of the cathode material during the aging process was investigated by the development of the special image treatment procedure for the maps, obtained from the transmission soft x-ray microscopy. It worth mentioning, that apart from the combination of the outcomes from the various x-ray measurements, the exploration of the new capabilities was also conducted, namely, probing the oxidation state of the element with the synchrotron-based 2-dimensional x-ray fluorescence technique, which, generally, with conventional set up, is not possible to achieve. The results and methodology from this thesis can, of course, be generalised on the characterisation of the other battery systems, and not only, as the x-ray techniques are one of the most informative and sophisticated methods for advanced structural investigation of the materials.

Poset associahedra as sections of graph associahedra

Poset associahedra are a family of convex polytopes recently introduced by Pavel Galashin in 2021. The associahedron An is an (n-2)-dimensional convex polytope whose facial structure encodes the ways of parenthesizing an n-letter word (among several equivalent combinatorial objects). Associahedra are deeply studied polytopes that appear naturally in many areas of mathematics: algebra, combinatorics, geometry, topology... They have many presentations and generalizations. One of their incarnations is as a compactification of the configuration space of n points on a line. Similarly, the P-associahedron of a poset P is a compactification of the configuration space of order preserving maps from P to R. Galashin presents poset associahedra as combinatorial objects and shows that they can be realized as convex polytopes. However, his proof is not constructive, in the sense that no explicit coordinates are provided. The main goal of this thesis is to provide an explicit construction of poset associahedra as sections of graph associahedra, thus solving the open problem stated in Remark 1.5 of Galashin's paper.

The Function and Three-Dimensional Structure of a Thromboxane A(2)/Cysteinyl Leukotriene-Binding Protein from the Saliva of a Mosquito Vector of the Malaria Parasite

The highly expressed D7 protein family of mosquito saliva has previously been shown to act as an anti-inflammatory mediator by binding host biogenic amines and cysteinyl leukotrienes (CysLTs). In this study we demonstrate that AnSt-D7L1, a two-domain member of this group from Anopheles stephensi, retains the CysLT binding function seen in the homolog AeD7 from Aedes aegypti but has lost the ability to bind biogenic amines. Unlike any previously characterized members of the D7 family, AnSt-D7L1 has acquired the important function of binding thromboxane A(2) (TXA(2)) and its analogs with high affinity. When administered to tissue preparations, AnSt-D7L1 abrogated Leukotriene C(4) (LTC(4))-induced contraction of guinea pig ileum and contraction of rat aorta by the TXA(2) analog U46619. The protein also inhibited platelet aggregation induced by both collagen and U46619 when administered to stirred platelets. The crystal structure of AnSt-D7L1 contains two OBP-like domains and has a structure similar to AeD(7). In AnSt-D7L1, the binding pocket of the C-terminal domain has been rearranged relative to AeD7, making the protein unable to bind biogenic amines. Structures of the ligand complexes show that CysLTs and TXA(2) analogs both bind in the same hydrophobic pocket of the N-terminal domain. The TXA(2) analog U46619 is stabilized by hydrogen bonding interactions of the omega-5 hydroxyl group with the phenolic hydroxyl group of Tyr 52. LTC(4) and occupies a very similar position to LTE(4) in the previously determined structure of its complex with AeD7. As yet, it is not known what, if any, new function has been acquired by the rearranged C-terminal domain. This article presents, to our knowledge, the first structural characterization of a protein from mosquito saliva that inhibits collagen mediated platelet activation.

Slavnov-Taylor identities for the 2+1 dimensional noncommutative CPN-1 model

In the context of the 1/N expansion, the validity of the Slavnov-Taylor identity relating three- and two-point functions for the 2 + 1-dimensional noncommutative CP(N-1) model is investigated, up to subleading 1/N order, in the Landau gauge.

A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

Conotoxin TVIIA, a novel peptide from the venom of Conus tulipa - 2. Three-dimensional solution structure

The three-dimensional solution structure of conotoxin TVIIA, a 30-residue polypeptide from the venom of the piscivorous cone snail Conus tulipa, has been determined using 2D H-1 NMR spectroscopy. TVIIA contains six cysteine residues which form a 'four-loop' structural framework common to many peptides from Conus venoms including the omega-, delta-, kappa-, and mu O-conotoxins. However, TVIIA does not belong to these well-characterized pharmacological classes of conotoxins, but displays high sequence identity with conotoxin GS, a muscle sodium channel blocker from Conus geographus. Structure calculations were based on 562 interproton distance restraints inferred from NOE data, together with 18 backbone and nine side-chain torsion angle restraints derived from spin-spin coupling constants. The final family of 20 structures had mean pairwise rms differences over residues 2-27 of 0.18 +/- 0.05 Angstrom for the backbone atoms and 1.39 +/- 0.33 Angstrom for all heavy atoms. The structure consists of a triple-stranded, antiparallel beta sheet with +2x, -1 topology (residues 7-9, 16-20 and 23-27) and several beta turns. The core of the molecule is formed by three disulfide bonds which form a cystine knot motif common to many toxic and inhibitory polypeptides. The global fold, molecular shape and distribution of amino-acid sidechains in TVIIA is similar to that previously reported for conotoxin GS, and comparison with other four-loop conotoxin structures provides further indication that TVIIA and GS represent a new and distinct subgroup of this structural family. The structure of TVIIA determined in this study provides the basis for determining a structure-activity relationship for these molecules and their interaction with target receptors.

Comparative analysis of two-dimensional electrophoresis maps (2-DE) of Helicobacter pylori from Brazilian patients with chronic gastritis and duodenal ulcer: a preliminary report

Helicobacter pylori is a bacterium recognized as the major cause of peptic ulcer and chronic gastritis. Recently, a proteome-based approach was developed to investigate pathogenic factors related to H. pylori. In this preliminary study, H. pylori strains were isolated from gastric biopsies of patients with chronic gastritis and duodenal ulcers. A partial proteomic analysis of H. pylori strains was performed by bacterial lyses and proteins were separated by two-dimensional gel electrophoresis (2-DE). A comparative analysis was performed to verify a differential protein expression between these two 2-DE maps. These data should be useful to clarify the role of different proteins related to bacterial pathogenesis. This study will be completed using a larger number of samples and protein identification of H. pylori by MALDI-TOF mass spectrometry.

Exact lower bounds to the ground-state energy of spin systems: The two-dimensional S=1/2 antiferromagnetic Heisenberg model

We present a very simple but fairly unknown method to obtain exact lower bounds to the ground-state energy of any Hamiltonian that can be partitioned into a sum of sub-Hamiltonians. The technique is applied, in particular, to the two-dimensional spin-1/2 antiferromagnetic Heisenberg model. Reasonably good results are easily obtained and the extension of the method to other systems is straightforward.