scholarly journals Shape analysis via inconsistent surface registration

2020 ◽  
Vol 476 (2242) ◽  
pp. 20200147
Author(s):  
Gary P. T. Choi ◽  
Di Qiu ◽  
Lok Ming Lui
Keyword(s):  
Shape Analysis ◽  
Degrees Of Freedom ◽  
Surface Registration ◽  
Point Of View ◽  
Shape Classification ◽  
Surface Mapping ◽  
Conformal Theory ◽  
Global Consistency ◽  
Shed Light ◽  
Natural Way

In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometr- ics methods suffer from the limited degrees of freedom, while most of the more advanced non-rigid surface mapping methods rely on a strong assumption of the global consistency of two surfaces. From a practical point of view, given two anatomical surfaces with prominent feature landmarks, it is more desirable to have a method that automatically detects the most relevant parts of the two surfaces and finds the optimal landmark-matching alignment between these parts, without assuming any global 1–1 correspondence between the two surfaces. Our method is capable of solving this problem using inconsistent surface registration based on quasi-conformal theory. It further enables us to quantify the dissimilarity of two shapes using quasi-conformal distortion and differences in mean and Gaussian curvatures, thereby providing a natural way for shape classification. Experiments on Platyrrhine molars demonstrate the effectiveness of our method and shed light on the interplay between function and shape in nature.

scholarly journals From Loschmidt daemons to time-reversed waves

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150156 ◽  
Author(s):  
Mathias Fink
Keyword(s):  
Wave Propagation ◽  
Time Reversal ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Propagation Time ◽  
Reversal Invariance ◽  
Spatial Boundary ◽  
Dual Approaches ◽  
Spatio Temporal

Time-reversal invariance can be exploited in wave physics to control wave propagation in complex media. Because time and space play a similar role in wave propagation, time-reversed waves can be obtained by manipulating spatial boundaries or by manipulating time boundaries. The two dual approaches will be discussed in this paper. The first approach uses ‘time-reversal mirrors’ with a wave manipulation along a spatial boundary sampled by a finite number of antennas. Related to this method, the role of the spatio-temporal degrees of freedom of the wavefield will be emphasized. In a second approach, waves are manipulated from a time boundary and we show that ‘instantaneous time mirrors’, mimicking the Loschmidt point of view, simultaneously acting in the entire space at once can also radiate time-reversed waves.

ON ROBERTS’ PROOF OF THE TURAEV-WALKER THEOREM

1996 ◽  
Vol 05 (04) ◽  
pp. 427-439 ◽  
Author(s):  
RICCARDO BENEDETTI ◽  
CARLO PETRONIO
Keyword(s):  
Euler Characteristic ◽  
A Priori ◽  
Algebraic Approach ◽  
Fusion Rule ◽  
Point Of View ◽  
Witten Invariant ◽  
Manifolds With Boundary ◽  
3 Dimensional ◽  
Skein Theory ◽  
Natural Way

In this paper we discuss the beautiful idea of Justin Roberts [7] (see also [8]) to re-obtain the Turaev-Viro invariants [11] via skein theory, and re-prove elementarily the Turaev-Walker theorem [9], [10], [13]. We do this by exploiting the presentation of 3-manifolds introduced in [1], [4]. Our presentation supports in a very natural way a formal implementation of Roberts’ idea. More specifically, what we show is how to explicitly extract from an o-graph (the object by which we represent a manifold, see below), one of the framed links in S3 which Roberts uses in the construction of his invariant, and a planar diagrammatic representation of such a link. This implies that the proofs of invariance and equality with the Turaev-Viro invariant can be carried out in a completely “algebraic” way, in terms of a planar diagrammatic calculus which does not require any interpretation of 3-dimensional figures. In particular, when proving the “term-by-term” equality of the expansion of the Roberts invariant with the state sum which gives the Turaev-Viro invariant, we simultaneously apply several times the “fusion rule” (which is formally defined, strictly speaking, only in diagrammatic terms), showing that the “braiding and twisting” which a priori may exist on tetrahedra is globally dispensable. In our point of view the success of this formal “algebraic” approach witnesses a certain efficiency of our presentation of 3-manifolds via o-graphs. In this work we will widely use recoupling theory which was very clearly exposed in [2], and therefore we will avoid recalling notations. Actually, for the purpose of stating and proving our results we will need to slightly extend the class of trivalent ribbon diagrams on which the bracket can be computed. We also address the reader to the references quoted in [2], in particular for the fundamental contributions of Lickorish to this area. In our approach it is more natural to consider invariants of compact 3-manifolds with non-empty boundary. The case of closed 3-manifolds is included by introducing a correction factor corresponding to boundary spheres, as explained in §2. Our main result is actually an extension to manifolds with boundary of the Turaev-Walker theorem: we show that the Turaev-Viro invariant of such a manifold coincides (up to a factor which depends on the Euler characteristic) with the Reshetikhin-Turaev-Witten invariant of the manifold mirrored in its boundary.

DARK GEOMETRY

2004 ◽  
Vol 13 (10) ◽  
pp. 2275-2279 ◽  
Author(s):  
J. A. R. CEMBRANOS ◽  
A. DOBADO ◽  
A. L. MAROTO
Keyword(s):  
Dark Matter ◽  
Extra Dimensions ◽  
Degrees Of Freedom ◽  
Planck Scale ◽  
Point Of View ◽  
Missing Mass ◽  
Brane Worlds ◽  
Mass Problem ◽  
Extra Space ◽  
The Universe

Extra-dimensional theories contain additional degrees of freedom related to the geometry of the extra space which can be interpreted as new particles. Such theories allow to reformulate most of the fundamental problems of physics from a completely different point of view. In this essay, we concentrate on the brane fluctuations which are present in brane-worlds, and how such oscillations of the own space–time geometry along curved extra dimensions can help to resolve the Universe missing mass problem. The energy scales involved in these models are low compared to the Planck scale, and this means that some of the brane fluctuations distinctive signals could be detected in future colliders and in direct or indirect dark matter searches.

scholarly journals Control Systems and Number Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-28
Author(s):  
Fuhuo Li
Keyword(s):  
Zeta Functions ◽  
Feedback System ◽  
State Equation ◽  
The State ◽  
Point Of View ◽  
Pid Controllers ◽  
Primary Concern ◽  
Feedback Connection ◽  
Proper Understanding ◽  
Natural Way

We try to pave a smooth road to a proper understanding of control problems in terms of mathematical disciplines, and partially show how to number-theorize some practical problems. Our primary concern is linear systems from the point of view of our principle of visualization of the state, an interface between the past and the present. We view all the systems as embedded in the state equation, thus visualizing the state. Then we go on to treat the chain-scattering representation of the plant of Kimura 1997, which includes the feedback connection in a natural way, and we consider theH∞-control problem in this framework. We may view in particular the unit feedback system as accommodated in the chain-scattering representation, giving a better insight into the structure of the system. Its homographic transformation works as the action of the symplectic group on the Siegel upper half-space in the case of constant matrices. Both ofH∞- and PID-controllers are applied successfully in the EV control by J.-Y. Cao and B.-G. Cao 2006 and Cao et al. 2007, which we may unify in our framework. Finally, we mention some similarities between control theory and zeta-functions.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

scholarly journals Gastronomy unravelled by physics: Gastrophysics

2021 ◽  
Vol 6 (2) ◽  
pp. 153-180 ◽  
Author(s):  
Mie Thorborg Pedersen ◽  
Per Lyngs Hansen ◽  
Mathias Porsmose Clausen
Keyword(s):  
Scientific Literature ◽  
Full Range ◽  
Laws Of Nature ◽  
Well Being ◽  
Point Of View ◽  
Food Science ◽  
Scientific Disciplines ◽  
The Social ◽  
History Of ◽  
Shed Light

Useful attempts to shed light on the nature of gastronomy from a scientific point of view and to unravel the crucial connection between food, eating and well-being are currently underrepresented in the scientific literature. However, several scientific disciplines ranging from the natural to the social sciences offer valuable new perspectives on gastronomy. As one of the key disciplines in natural science, physics offers original and rigorous perspectives on all processes and structures constrained by the laws of nature. The emerging discipline called gastrophysics employs the full range of concepts, techniques and methods from physics to generate useful scientific input to the complex and holistic reflections on gastronomy. Relying on a review of the existing literature, this article illustrates how a science-based gastrophysics emerges, to a large extent from the convoluted history of food science as well as from various recent – and often overlapping – attempts to combine modern scientific methodology to questions from gastronomy. However, the present review also insists on a physics-inspired methodology to handle scale and complexity in food preparation and consumption across length scales from sub-molecular to entire foods. We exemplify how gastrophysics directly helps to develop gastronomy and how it adds to current approaches in traditional food science. We also suggest that gastrophysics may prove relevant in the context of the ongoing food transformation, which focuses strongly on sustainability, but where the importance of gastronomic aspects in this transformation is greatly needed.

scholarly journals An Introduction to Concept and Evolution of the Guardstone and Its Architectural Visualization of the Contemporary Religious and Cultural Diversities

2017 ◽  
Vol 6 (3) ◽  
pp. 52
Author(s):  
Sasni Amarasekara
Keyword(s):  
Sri Lanka ◽  
Developmental Stages ◽  
Logical Reasoning ◽  
Point Of View ◽  
Aesthetic Evaluation ◽  
Specific Study ◽  
Religious Buildings ◽  
Evolutionary Point ◽  
Shed Light ◽  
Academic Study

<p>This specific study deals with a unique piece of Buddhist architecture, the Guardstone found almost in every part of ancient kingdoms in Sri Lanka spanning from Anuradhapura to Kandy period significantly. The Guardstone is an excellent piece of structure placed on either side of the first step of the flight of stairs at the entrance of ancient religious buildings or palaces in Sri Lanka. The origin of this architectural masterpiece is still to determine. Nevertheless, it is widely accepted in an evolutionary point of view that the guardstone has passed through several developmental stages from a simple slab to a highly sophisticated artifact in its dimensions, complexity and artistry. The numerous inclusions as well as exclusions from time to time to this artifact still remain uncertain as to whether they were due to secular or ecclesiastical reasons or simply due to the creators own culture influenced imagination. This study will peruse all the possible evidence that are available architecturally and to develop a logical reasoning for any identifiable characteristic and to elucidate with reasonable legitimacy as to how and why such a character is present or absent in a particular guardstone. This study in no way has any intention of rejecting or amending any proposition available at present but will pursue its best to shed light only on the attributes of a guardstone and to concentrate on the diversities of this beautiful monastic artifact that deserves serious academic study and meticulous aesthetic evaluation.</p>

scholarly journals Viroporin activity of SARS-CoV-2 Orf3a and Envelope protein impacts viral pathogenicity

2021 ◽  
Author(s):  
Manish Sarkar ◽  
Paul Etheimer ◽  
Soham Saha
Keyword(s):  
Electrostatic Interactions ◽  
Inflammatory Responses ◽  
Water Channel ◽  
Point Of View ◽  
Alveolar Cells ◽  
E Protein ◽  
Ionic Imbalance ◽  
Cellular Compartments ◽  
Shed Light ◽  
Structural Point

COVID-19 is caused by SARS-CoV-2 which has affected nearly 220 million people worldwide and death toll close to 5 million as of present day. The approved vaccines are lifesaving yet temporary solutions to such a devastating pandemic. Viroporins are important players of the viral life cycle of SARS-Cov-2 and one of the primary determinants of its pathogenesis. We studied the two prominent viroporins of SARS-CoV-2 (i) Orf3a and (ii) Envelope (E) protein from a structural point of view. Orf3a has several hotspots of mutations which has been reported in SARS-CoV-2 with respect to SARS-CoV-1. Mutations in SARS-CoV-2 Orf3a channel forming residues enhances the formation of a prominent the inter-subunit channel, which was not present in the SARS-CoV-1 Orf3a. This enhanced structural feature can be correlated with higher channelling activity in SARS-CoV-2 than in SARS-CoV-1. On the other hand, E protein is one of the most conserved protein among the SARS-CoV proteome. We found that the water molecules form networks of electrostatic interactions with the polar residues in the E protein putative wetted condition while no water channel formation was observed in the putative dewetted condition. This aqueous medium mediates the non-selective translocation of cations thus affecting the ionic homeostasis of the host cellular compartments. This ionic imbalance leads to increased inflammatory response in the host cell. Our results shed light into the mechanism of viroporin action, which can be leveraged for the development of antiviral therapeutics. Furthermore, our results corroborate with previously published transcriptomic data from COVID-19 infected lung alveolar cells where inflammatory responses and molecular regulators directly impacted by ion channelling were upregulated. These observations overlap with transcript upregulation observed in diseases having acute lung injury, pulmonary fibrosis and Acute Respiratory Distress Syndrome (ARDS).

THREE-DIMENSIONAL COSSERAT CONTINUUM MODELING OF FRACTURED ROCK MASSES

2010 ◽  
Vol 02 (03n04) ◽  
pp. 217-234
Author(s):  
IOANNIS STEFANOU ◽  
JEAN SULEM
Keyword(s):  
Mechanical Properties ◽  
Discrete System ◽  
Degrees Of Freedom ◽  
Fractured Rock ◽  
Three Dimensional ◽  
Cosserat Continuum ◽  
Point Of View ◽  
Rock Masses ◽  
Homogenization Technique ◽  
Rock Structure

The behavior of rock masses is influenced by the existence of discontinuities, which divide the rock in joint blocks making it an inhomogeneous anisotropic material. From the mechanical point of view, the geometrical and mechanical properties of the rock discontinuities define the mechanical properties of the rock structure. In the present paper we consider a rock mass with three joint sets of different dip angle, dip direction, spacing and mechanical properties. The dynamic behavior of the discrete system is then described by a continuum model, which is derived by homogenization. The homogenization technique applied here is called generalized differential expansion homogenization technique and has its roots in Germain's (1973) formulation for micromorphic continua. The main advantage of the method is the avoidance of the averaging of the kinematic quotients and the derivation of a continuum that maps exactly the degrees of freedom of the discrete system through a one-to-one correspondence of the kinematic measures. The derivation of the equivalent continuum is based on the identification for any virtual kinematic field of the power of the internal forces and of the kinetic energy of the continuum with the corresponding quantities of the discrete system. The result is an anisotropic three-dimensional Cosserat continuum.

KINEMATICS FEATURES OF HAMMER PERFORATED TILLAGE ROLL

2020 ◽  
pp. 13-19
Author(s):  
I. А. Sharonov ◽  
◽  
Yu. М. Isaev ◽  
V. I. Kurdyumov ◽  
◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Soil Layer ◽  
Point Of View ◽  
Lagrange Equations ◽  
Middle Volga Region ◽  
Perforated Cylinder ◽  
Winter Crops ◽  
Combined Impact ◽  
The Impact

The task of improving the quality of agricultural tools by improving the technological processes of their functioning, taking into account the kinematic features of the combined impact of working elements of tools on the soil environment is important from a scientific and technical point of view. To form the required structure and density of the soil layer at the depth of sowing, a hammer perforated tillage roller (HPTR) has been developed. The study aim is to improve the quality of post-sowing compaction and structuring of the soil layer in the seed location zone based on the development of an innovative design of HPTR that combines different effects on the treated environment. The object of research is the kinematic mode of operation of the HPTR, equipped with cylindrical hammers installed at the ends of the rod, which, in turn, are radially and pivotally installed on the axis of the gunFeature of offered HPTR is the excitation of hammer vibrations, which changes the kinematic parameters of the tillage tool as a whole. Lagrange equations of the second kind are used to describe the process of HPTR operation, which is represented as a system of material objects with several degrees of freedom. The conducted studies revealed the periodic nature of changes in the strength of the impact of HPTR on the soil. The obtained equations allow us to determine the features of the HPTR movement at different masses of a hollow perforated cylinder and cylindrical hammers. This is of great importance for increasing the efficiency of soil bolster destruction and creating the soil structure recommended for winter crops sown in the Middle Volga region.

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