Shape Theory Research Articles

Wavelength-Dependent Exciton-Vibrational Coupling in the Water-Soluble Chlorophyll Binding Protein Revealed by Multilevel Theory of Difference Fluorescence Line-Narrowing.

One of the most powerful line-narrowing techniques used to unravel the homogeneous lineshapes of inhomogeneously broadened systems is difference fluorescence line-narrowing spectroscopy. When this spectroscopy was applied to multichromophoric systems so far, the spectra were analyzed by an effective two-level system approach, composed of the electronic ground state and the lowest exciton state. An effective Huang-Rhys factor was assigned for the coupling of this state to the vibrations. Here, we extend this approach by including a multilevel line shape theory, which takes into account the excitonic coupling between pigments and thereby the effect of the delocalization of the excited states explicitly. In this way, it becomes possible to extract the spectral density of the local exciton-vibrational coupling. The theory is applied to the recombinant water-soluble chlorophyll binding protein reconstituted with chlorophyll a or b and reveals a significant decrease of the Huang-Rhys factor of the local exciton-vibrational coupling with decreasing transition energy of the chlorophylls. This decrease could be due to the increase in steric interactions reducing the flexibility of the environment and red-shifting the site energy of the pigments.

Challenges in Topological Object Data Analysis

Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes to vectorize object data and perform statistical analysis. We apply to this pipeline to some biological images that were previously shown to be challenging to study using shape theory. Surprisingly, the most persistent features are shown to be "topological noise" and the statistical analysis depends on the less persistent features which we refer to as the "geometric signal". We also describe the first steps to a new approach to using topology for object data analysis, which applies topology to distributions on object spaces.

Statistical design of chaotic waveforms with enhanced targeting capabilities

We develop a statistical theory of waveform shaping of incident waves that aim to efficiently deliver energy at weakly lossy targets which are embedded inside chaotic enclosures. Our approach utilizes the universal features of chaotic scattering -- thus minimizing the use of information related to the exact characteristics of the chaotic enclosure. The proposed theory applies equally well to systems with and without time-reversal symmetry.

Statistical Theory of Shape Under Elliptical Models via Polar Decompositions

A new model of statistical shape theory under elliptical models is proposed by using the polar decomposition. This work completes the group of SVD and QR shape densities obtained from the transpose of the square root of a non singular Wishart matrix. The associated non isotropic and non central polar shape distributions are set in the context of consistent computable series of zonal polynomials. Then the inference procedures with elliptical assumptions can be performed at the same computational cost of the published routines based on Gaussian models. As an example of the technique, a classical application in Biology is studied under three models, the usual Gaussian and two Kotz type models; then the best model is selected by a modified BIC∗ criterion, and a test for equality in polar shapes is performed. The published results for this landmark data under isotropic Gaussian models and procrustes theory are also discussed.

A Study of Gravity Flow Based on the Upside-Down Drop Shape Theory and Considering Rock Shape and Breakage

The cave mining method relies on gravity to fragment the rock mass into blocks that can be extracted out of drawpoints. Several discrete element method (DEM) models on gravity flow are presented in the literature; however, only a few of those consider rock shape and secondary fragmentation. In this paper, the reliability of the particle flow code (PFC) to model gravity flow of fragmented rock is validated against known experimental results. A new method to create complex shape clusters is proposed and then used to investigate the mechanisms of gravity flow and the influence of particle bond strength on the secondary fragmentation, and the evolutions of the movement zone and extraction zone. The model results are validated against the upside-down drop shape theory for two cases: (1) constant size of fragmented rock blocks and (2) changing size due to breakage of the fragmented rock blocks. For the latter case, the results show that secondary fragmentation of weaker rocks would result in a wider movement zone and extraction zone than that of stronger rocks.

The evolution and impacts of Graeme Hugo’s environmental migration research

Drawing on Graeme’s published and unpublished work, as well as his long-term collaborations with two of us, we identify strands of thought that Graeme kept returning to and refining over the course of his career. We trace the evolution of four key points that he often reiterated: (1) The migration-environment relationship is complex and oversimplified; (2) Migration is both a consequence and a cause of environmental change; (3) Migration is just one possible response to environmental change; and (4) Displacement is just one type of migration response. We briefly map his impact on environmental migration scholarship and policy by revealing how key publications have been used in different contexts to shape theory and practice.

The shape of the Julia set of an expanding rational map

In memory of Sibe Mardešić, our friend.Sibe Mardešić has enriched algebraic topology developing shape and strong shape theories with important constructions and theorems.This paper relates computational topology to shape theory. We have developed some algorithms and implementations that under some conditions give a shape resolution of some Julia sets.When a semi-flow is induced by a rational map g of degree d defined on the Riemann sphere, one has the associated Julia set J(g). The main objective of this paper is to give a computational procedure to study the shape of the compact metric space J(g).Our main contribution is to provide an inverse system of cubic complexes approaching J(g) by using implemented algorithms based in the notion of spherical multiplier. This inverse system of cubical complexes is used to: (i) obtain nice global visualizations of the fractal structure of the Julia set J(g); (ii) determine the shape of the compact metric space J(g).These techniques also give the possibility of applying overlay theory (introduced by R. Fox and developed among others by S. Mardešić) to study the symmetry properties of the fractal geometry of the Julia set J(g).

Proper homotopy types and [formula omitted]-boundaries of spaces admitting geometric group actions

We extend several techniques and theorems from geometric group theory so they apply to geometric actions on arbitrary proper metric ARs (absolute retracts). Previous versions often required actions on CW complexes, manifolds, or proper CAT(0) spaces, or else included a finite-dimensionality hypothesis. We remove those requirements, providing proofs that simultaneously cover all of the usual variety of spaces. A second way that we generalize earlier results is by eliminating a freeness requirement often placed on the group actions. In doing so, we allow for groups with torsion.The main theorems are new in that they generalize results found in the literature, but a significant aim is expository. Toward that end, brief but reasonably comprehensive introductions to the theories of ANRs (absolute neighborhood retracts) and Z-sets are included, as well as a much shorter introduction to shape theory. Here is a sampling of the theorems proved here.Theorem.If quasi-isometric groupsG andH act geometrically on proper metric ARsX andY, resp., thenX is proper homotopy equivalent toY.Theorem.If quasi-isometric groupsG andH act geometrically on proper metric ARsX andY, resp., andY can be compactified to aZ-structureY¯,Z forH, then the same boundary can be added toX to obtain aZ-structure forG.Theorem.If quasi-isometric groupsGandH admitZ-structuresX¯,Z1 andY¯,Z2, resp., thenZ1 andZ2 are shape equivalent.

Piers Plowman and the Poetics of Enigma: Riddles, Rhetoric, and Theology

Piers Plowman and the Poetics of Enigma: Riddles, Rhetoric, and Theology

Cartesian powers of shapes of FANR's and polyhedra

We show that a finite polyhedron P of nontrivial homotopy type cannot be homotopy equivalent to a proper Cartesian factor of itself. In other words, P≃P×K implies that K≃1. Consequently, if P is a finite polyhedron such that Pn≃P, for some integer n≥2, then the homotopy type of P is trivial. This answers positively the problem [1, Problem (34.10)] stated by K. Borsuk in 1971 (in an equivalent, shape-theoretical formulation) and a question from Borsuk's monograph “Theory of Shape” [2, Problem (7.13), p. 142].We also prove that if (X,x)∈FANR, then Shn(X,x)=Sh(X,x), for some integer n≥2, implies that Sh(X)=1. This resolves positively Problem (5.6) from [7] (1981). Similarly as for polyhedra, first we show that if X∈FANR and Sh(X)≠1, then X cannot have the shape of a proper Cartesian factor of itself.

Weak coarse shape equivalences and infinite dimensional Whitehead theorem in coarse shape theory

In this paper, we study the weak coarse shape equivalences. First, we define paradominations and then we give a characterization of them, for uniformly movable pointed continuum spaces. Also, we show that a weak coarse shape equivalence to a pointed movable space is a paradomination. Finally, we prove that a weak coarse shape equivalence F⁎:(X,x)→(Y,y) between pointed continuum spaces is a coarse shape equivalence, if (X,x) and (Y,y) are simultaneously movable according to F⁎.

First-Principles Models for Biological Light-Harvesting: Phycobiliprotein Complexes from Cryptophyte Algae.

There have been numerous efforts, both experimental and theoretical, that have attempted to parametrize model Hamiltonians to describe excited state energy transfer in photosynthetic light harvesting systems. The Frenkel exciton model, with its set of electronically coupled two level chromophores that are each linearly coupled to dissipative baths of harmonic oscillators, has become the workhorse of this field. The challenges to parametrizing such Hamiltonians have been their uniqueness, and physical interpretation. Here we present a computational approach that uses accurate first-principles electronic structure methods to compute unique model parameters for a collection of local minima that are sampled with molecular dynamics and QM geometry optimization enabling the construction of an ensemble of local models that captures fluctuations as these systems move between local basins of inherent structure. The accuracy, robustness, and reliability of the approach is demonstrated in an application to the phycobiliprotein light harvesting complexes from cryptophyte algae. Our computed Hamiltonian ensemble provides a first-principles description of inhomogeneous broadening processes, and a standard approximate non-Markovian reduced density matrix dynamics description is used to estimate lifetime broadening contributions to the spectral line shape arising from electronic-vibrational coupling. Despite the overbroadening arising from this approximate line shape theory, we demonstrate that our model Hamiltonian ensemble approach is able to provide a reliable fully first-principles method for computation of spectra and can distinguish the influence of different chromophore protonation states in experimental results. A key feature in the dynamics of these systems is the excitation of intrachromophore vibrations upon electronic excitation and energy transfer. We demonstrate that the Hamiltonian ensemble approach provides a reliable first-principles description of these contributions that have been detailed in recent broad-band pump-probe and two-dimensional electronic spectroscopy experiments.

In pursuit of a missing transition: the Mesolithic and Neolithic radiocarbon chronology at La Font-aux-Pigeons rockshelter

Abstract

Role of quantum coherence in shaping the line shape of an exciton interacting with a spatially and temporally correlated bath.

Kubo's fluctuation theory of line shape forms the backbone of our understanding of optical and vibrational line shapes, through such concepts as static heterogeneity and motional narrowing. However, the theory does not properly address the effects of quantum coherences on optical line shape, especially in extended systems where a large number of eigenstates are present. In this work, we study the line shape of an exciton in a one-dimensional lattice consisting of regularly placed and equally separated optical two level systems. We consider both linear array and cyclic ring systems of different sizes. Detailed analytical calculations of line shape have been carried out by using Kubo's stochastic Liouville equation (SLE). We make use of the observation that in the site representation, the Hamiltonian of our system with constant off-diagonal coupling J is a tridiagonal Toeplitz matrix (TDTM) whose eigenvalues and eigenfunctions are known analytically. This identification is particularly useful for long chains where the eigenvalues of TDTM help understanding crossover between static and fast modulation limits. We summarize the new results as follows. (i) In the slow modulation limit when the bath correlation time is large, the effects of spatial correlation are not negligible. Here the line shape is broadened and the number of peaks increases beyond the ones obtained from TDTM (constant off-diagonal coupling element J and no fluctuation). (ii) However, in the fast modulation limit when the bath correlation time is small, the spatial correlation is less important. In this limit, the line shape shows motional narrowing with peaks at the values predicted by TDTM (constant J and no fluctuation). (iii) Importantly, we find that the line shape can capture that quantum coherence affects in the two limits differently. (iv) In addition to linear chains of two level systems, we also consider a cyclic tetramer. The cyclic polymers can be designed for experimental verification. (v) We also build a connection between line shape and population transfer dynamics. In the fast modulation limit, both the line shape and the population relaxation, for both correlated and uncorrelated bath, show similar behavior. However, in slow modulation limit, they show profoundly different behavior. (vi) This study explains the unique role of the rate of fluctuation (inverse of the bath correlation time) in the sustenance and propagation of coherence. We also examine the effects of off-diagonal fluctuation in spectral line shape. Finally, we use Tanimura-Kubo formalism to derive a set of coupled equations to include temperature effects (partly neglected in the SLE employed here) and effects of vibrational mode in energy transfer dynamics.

Speech production planning affects phonological variability: a case study in French liaison

Connected speech processes have played a major role in shaping theories about phonological organization, and how phonology interacts with other components of the grammar (Selkirk, 1974; Kiparsky, 1982; Kaisse, 1985; Nespor and Vogel, 1986, among others). External sandhi is subject to locality conditions, and it is more variable compared to processes applying word-internally. We suggest that an important part of understanding these two properties of external sandhi is the locality of speech production planning. Presenting evidence from French liaison, we argue that the effect of lexical frequency on variability can be understood as a consequence of the narrow window of phonological encoding during speech production planning. This proposal complements both abstract, symbolic and gestural overlap-based accounts of phonological alternations. By connecting the study of phonological alternations with the study of factors influencing speech production planning, we can derive novel predictions about patterns of variability in external sandhi, and better understand the data that drive the development of phonological theories.

Enclosed mmWave Wearable Networks: Feasibility and Performance

This paper investigates the feasibility of mmWave frequencies for personal networks of wireless wearable devices in enclosed settings (e.g., commuter trains, subways, airplanes, airports, or offices). At these frequencies, specular reflections off surfaces are expected to contribute intended signal power and, simultaneously, to aggravate the interference at the receivers. Meanwhile, blockages by obstacles and people---including the individuals wearing the devices---are expected to shield receivers from interference. With the aid of stochastic geometry and random shape theory, we assess the interplay of surface reflections and blockages for dense deployments of wearable networks equipped with directional antenna arrays in relevant indoor settings.

Impact of temperature-velocity distribution on fusion neutron peak shape

Doppler broadening of the 14 MeV DT and 2.45 MeV DD fusion neutron lines has long been our best measure of temperature in a burning plasma. At the National Ignition Facility (NIF), yields are high enough and our neutron spectrometers accurate enough that we see finer details of the peak shape. For example, we can measure the shift of the peak due to the bulk motion of the plasma, and we see indications of non-thermal broadening, skew, and kurtosis of the peak caused by the variations of temperature and fluid velocity during burn. We can also distinguish spectral differences among several lines of sight. This paper will review the theory of fusion neutron line shape, show examples of non-Gaussian line shapes and directional variations in NIF data, and describe detailed spectral shapes we see in radiation-hydrodynamics simulations of implosions.

Thermally Activated Electron Exchange in Cu12–xFexSb4S13 (x = 1.3, 1.5) Tetrahedrites: A Mössbauer Study

Mixed-valence iron Fe(III/II) tetrahedrites Cu10.7Fe1.3Sb4S13 and Cu10.5Fe1.5Sb4S13 have been prepared, characterized, and studied by Mössbauer spectroscopy. The low-temperature Mössbauer spectra (T ≤ 13 K) of all samples confirm the valence-localized nature of the ground state for the distinct Fe2+ and Fe3+ sites. At elevated temperatures the spectral transformations are characterized by a coexistence of valence-localized states Fe3+/Fe2+ (iron surrounded only by copper ions in the second coordination sphere) and valence-averaged spectral components corresponding to the electron hopping (FeA2+FeB3+) ↔ (FeA3+FeB2+). Our experiments suggest that these tetrahedrites belong to Robin–Day class II mixed-valence systems that display thermally activated charge transfer. Hopping frequencies (Ωhop) have been determined from spectral simulations using the stochastic line shape theory. Analysis of the ⟨Ω⟩(T) temperature dependences reveals the existence of a thermally activated process between (quasi)degenerate iron sites. The activation energies for Cu10.7Fe1.3Sb4S13 (EA ≈ 5.3 meV) and Cu10.5Fe1.5Sb4S13 (EA ≈ 6.6 meV) differ and suggest an important influence of the local crystal surroundings of iron ions on electron hopping. The isomer shift and quadrupole splitting values for the Fe3+ sites reveal a relatively strong and nonmonotonic change with temperature that suggests the occurrence of intrinsic charge delocalization in addition to the intersite electron hopping.

Ship nonlinear-feedback course keeping algorithm based on MMG model driven by bipolar sigmoid function for berthing

Course keeping is hard to implement under the condition of the propeller stopping or reversing at slow speed for berthing due to the ship's dynamic motion becoming highly nonlinear. To solve this problem, a practical Maneuvering Modeling Group (MMG) ship mathematic model with propeller reversing transverse forces and low speed correction is first discussed to be applied for the right-handed single-screw ship. Secondly, a novel PID-based nonlinear feedback algorithm driven by bipolar sigmoid function is proposed. The PID parameters are determined by a closed-loop gain shaping algorithm directly, while the closed-loop gain shaping theory was employed for effects analysis of this algorithm. Finally, simulation experiments were carried out on an LPG ship. It is shown that the energy consumption and the smoothness performance of the nonlinear feedback control are reduced by 4.2% and 14.6% with satisfactory control effects; the proposed algorithm has the advantages of robustness, energy saving and safety in berthing practice.

Confirmation of the upside-down drop shape theory in gravity flow and development of a new empirical equation to calculate the shape

Understanding the flow rules of caved ore and rock is the foundation for efficiently applying the caving mining method, and studying the change trends in both extraction zone (EZ) and movement zone (MZ) is the basis for researching these rules and for optimizing structural parameters. Ellipsoid draw theory is one of the traditional theories for the shapes of the extraction zone and the movement zone, which has played an important role in investigating the draw problems in caving mining method for a very long time. The isolated draw tests conducted in this study confirmed the upside-down drop shape theory's prediction that the EZ's shape has obvious longitudinal asymmetry, and is not a standard ellipsoid. The MZ's shape was further studied according to model experiments conducted by Castro, resulting in the fact that the MZ's shape is also the upside down drop shape. On this basis, a new way was proposed to investigate the extraction zone and movement zone shapes and their change trends, and then new empirical equations were deduced for calculation of their shapes.