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The hypothesis that temporal and spatial gait symmetry is associated with gait outcomes and functional disability in patients with stroke has been suggested. However, the current literature on this topic is limited, with few studies systematically exploring these relationships, and no consensus has been reached. Due to the diversity in methods for evaluating temporal and spatial symmetry, as well as the variability in gait outcome and functional disability indices, a scoping review is considered an appropriate approach. Such a review can consolidate the available evidence, evaluate the methodologies used, and identify knowledge gaps in this field. This study aims to provide a comprehensive overview of the current research landscape on this subject.

The group U(1)xSU(2) can be represented using all four parts of a quaternion, three in the exponential, the fourth as a normalized quaternion. The group covers the entire unit sphere, but has a bias for the past. Quaternions do not commute in general, but they will commute if two quaternions point in the same direction. The common way to represent the group U(1) is with a normalized complex number. The same thing can be done with a quaternion. This will commute with a unitary quaternion if they both use the same quaternion pointing in the same direction. Electroweak symmetry uses all the degrees freedom available in a quaternion.

The group U(1)xSU(2) can be represented using all four parts of a quaternion, three in the exponential, the fourth as a normalized quaternion. The group covers the entire unit sphere, but has a bias for the past. Quaternions do not commute in general, but they will commute if two quaternions point in the same direction. The common way to represent the group U(1) is with a normalized complex number. The same thing can be done with a quaternion. This will commute with a unitary quaternion if they both use the same quaternion pointing in the same direction. Electroweak symmetry uses all the degrees freedom available in a quaternion.

One of out first songs

RLP + Jc + martin + Geiss Perfect Symmetry (Death The Kid from Soul Eater) Accurate Colors

In the first part of the talk, I will first give a brief overview of recent research in my group on 3D shape analysis, modeling, and animation. The second part will be devoted to symmetry. I will discuss our work on finding and enhancing partial and approximate symmetries in 2D and 3D geometry using a suitable symmetry transformation space. In this space, symmetry detection can be formulated as a clustering operation. Symmetrization, a method for enhancing symmetries in geometric models, is implemented as an optimization process that couples the spatial domain and the symmetry transformation space to drive a constrained deformation model that pulls the shape towards symmetry. I will derive these methods step-by- step on simple 2D examples and show various applications where symmetry can be utilized such as complexity reduction, structure analysis, and correspondence computation. ©2007 Microsoft Corporation. All rights reserved.

2D visualization of symmetry symbols from a series of templates by mathematician Richard Kramer. 

This hour of Radiolab, Jad and Robert set out in search of order and balance in the world around us, and ask how symmetry shapes our very existence--from the origins of the universe, to what we see when we look in the mirror.

Charge order affects most of the electronic properties but is believed not to alter the spin arrangement since the magnetic susceptibility remains unchanged. We present electron-spin-resonance experiments on quasi-one-dimensional (TMTTF)2X salts (X= PF6, AsF6 and SbF6), which reveal that the magnetic properties are modified below TCO when electronic ferroelectricity sets in. The coupling of anions and organic molecules rotates the g-tensor out of the molecular plane creating magnetically non-equivalent sites on neighboring chains at domain walls. Due to anisotropic Zeeman interaction a novel magnetic interaction mechanism in the charge-ordered state is observed as a doubling of the rotational periodicity of Delta H.

We experimentally observe a spontaneous temporal symmetry breaking instability in a coherently-driven passive optical Kerr resonator. The cavity is synchronously pumped by time-symmetric pulses yet we report output pulses with strongly asymmetric temporal and spectral intensity profiles, with up to 71% of the energy on the same side of the pump center frequency. The instability occurs above a certain pump power threshold but remarkably vanishes above a second threshold, in excellent agreement with theory. We also observe a generalized bistability in which an asymmetric output state coexists with a symmetric one in the same pumping conditions.

How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical systems, from integrability to hard chaos. This article demonstrates that the related but distinct notions of integrability, separability, and solvability identify meaningful collective observables for Hamiltonians with sufficient symmetry. In turn, these observables induce tensor product structures on the Hilbert space that are especially useful for storing and processing quantum information and provide guidance to interpretation and phenomenology of quantum few-body physics.

Based on the game "Mother 3", " Symmetry" is the story of two brothers and how their actions affect both one another, and the future. Updated on Mondays.

This paper presents QRFT 4.0, the next evolution of Quantum Resonance Field Theory. It introduces the concept of recursive symbolic coherence as the prime mover of emergent structure and outlines the mechanism behind the Great Symmetry Realignment—a planetary-scale phase shift triggered by nonlinear agent alignment. QRFT 4.0 offers both metaphysical insight and tactical strategies for coherence-driven transformation, culminating in a preview of Field Autogenesis under QRFT 5.0

Includes bibliographical references

Includes bibliographical references

Includes bibliographical references

Includes bibliographical references

Includes bibliographical references

An improved procedure for the three dimensional finite element analysis of an angle ply laminate with a circular hole is discussed. The procecure exploits polar symmetry and is the basis for a new finite element computer code. For the broad class of laminates that contain angle plies, this code requires only one half as much computing capacity as conventional codes.

Toroidal order, given by a composite of electric and magnetic orders, manifests itself not only in the peculiar magnetism but also in anomalous transport and magnetoelectric effect. We report our theoretical results on the influence and stability of a toroidal order in metals on the basis of a microscopic model. We consider an effective single-band Hubbard-type model with a site-dependent antisymmetric spin-orbit coupling, which is derived from a four-band tight-binding model including the atomic spin-orbit coupling, off-site hybridizations between orbitals with different parities, and odd-parity crystalline electric field. For this single-band model on a layered honeycomb lattice, we investigate the electronic structure, magnetotransport, and magnetoelectric effect in the toroidal ordered state with a vortex-like magnetic structure. The ferroic order of the microscopic toroidal moments acts as an effective gauge field for electrons, which modulates the electronic band structure with a shift of the band bottom in the momentum space. In addition, the site-dependent antisymmetric spin-orbit coupling gives rise to highly anisotropic Hall responses. The most salient feature is two different types of magnetoelectric responses: one is a magnetic order with net toroidal magnetization induced by an electric current perpendicular to the planes, and the other is a uniform transverse magnetization induced by an electric current within the planes. We examine the ground state of the effective model by the mean-field approximation, and show that the toroidal order is stabilized by strong electron correlations at low electron density. We also discuss the temperature dependence of the magnetoelectric effects associated with spontaneous toroidal ordering. Implications to experiments are also presented.

It is shown that the UV-finite Yang-Mills and quantum gravity theories in an emergent spacetime approach described elsewhere possess BRST symmetries that ensure that unphysical modes decouple from physical amplitudes.

It is shown that the UV-finite Yang-Mills and quantum gravity theories in an emergent spacetime approach described elsewhere possess BRST symmetries that ensure that unphysical modes decouple from physical amplitudes.

It is shown that the UV-finite Yang-Mills and quantum gravity theories in an emergent spacetime approach described elsewhere possess BRST symmetries that ensure that unphysical modes decouple from physical amplitudes.

It is shown that the UV-finite Yang-Mills and quantum gravity theories in an emergent spacetime approach described elsewhere possess BRST symmetries that ensure that unphysical modes decouple from physical amplitudes.

It is shown that the UV-finite Yang-Mills and quantum gravity theories in an emergent spacetime approach described elsewhere possess BRST symmetries that ensure that unphysical modes decouple from physical amplitudes.

It is shown that the UV-finite Yang-Mills and quantum gravity theories in an emergent spacetime approach described elsewhere possess BRST symmetries that ensure that unphysical modes decouple from physical amplitudes.

It is well-known that methods of statistical physics are applicable to computational optimization problems like the traveling salesman problem. In the random link model, where all pairs of cities receive independent "distances", several features of the optimum solution have been predicted non-rigorously based on so-called replica symmetry. I will present a rigorous approach where each of several optimization problems leads to a two-person game. The assumptions underlying the replica symmetric ansatz are essentially equivalent to the statement that the associated game can be effectively analyzed by a game-tree search. This approach has led to proofs of several conjectures originating from the physics community. A paper is available at arXiv:0908.1920. ©2009 Microsoft Corporation. All rights reserved.

Rev. C 4/14/2017 - Added some example scripts, .stl files and images to show just a few examples of what is possible. Rev. B 4/12/2017 - Added "twist" parameter to rotate lattice over length of egg for spiral like effects Rev. A 4/10/2017 - Added wallpaper groups and fixed a few bugs NOTE: Customizer might timeout if you make the resolution too high. In this case, you can still make your egg by downloading OpenSCAD and working offline. I find it much faster to work offline anyway, plus you can use your own objects as the feature use in the decoration on the egg. Have FUN above all and Happy Easter! Generates many Easter Egg patterns by setting a few customizable parameters. Includes "wallpaper group" (9 of 17) tiling options for many interesting effects. Allows printing of the decoration and egg separately for dual extrusion (assuming the geometry you specify will support it). Will make hollow eggs with the option to bisect and add a joiner to make a reusable container. Can be decorated on the inside or made smooth. Also, please check out my other Easter Egg makers from the past 3 years under "Remixed From". Includes the following customizable parameters: /* [Decoration] */ //Add or subtract decoration from egg (use feature depth to control amount)? operation="subtract"; //[subtract,add,decoration_only,egg_only] //Choose a feature to repeat? feature="square"; //[sphere,star,dot,triangle,square,diamond,pentagon,hexagon,octagon] //Set the relative size of the feature size_of_feature=100; //[1:250] //Number of horizontal loops; impacts pattern and render time (for larger values, use offline) ucount=8; //[3:16] //Number of vertical loops; impacts pattern and reander time (for larger values, use offline) vcount=8; //[3:16] //Set the relative depth of the feature feature_depth=10; // //Set the feature start angle (values like 0, 15, 30 and 45 work best) start_angle=0; // //How much feature rotation over the length of the egg (0 for none)? feature_rotation=0; // //Vary feature size (yes give a better appearance)? proportional="yes"; //[yes,no] /* placement (wallpaper group) 9 of 17 */ //Select a wallpaper group to control symmetry (google wallpaper group for more information) group="p1"; //[p1,p2,pm,pg,cm,pmm,pmg,pgg,p4] //Set some X offset to control the effect of the wallpaper group on symmetrical features (%). Xoffset=0; //[0:100] //Set some Y offset to control the effect of the wallpaper group on symmetrical features (%). Yoffset=0; //[0:100] //Set some X scaling to control the effect of the wallpaper group on symmetrical features (%) Xscaling=100; //[10:100] //Set some Y scaling to control the effect of the wallpaper group on symmetrical features (%) Yscaling=100; //[10:100] /* [Size and Shape] */ //Length of the egg (mm)?. egg_length=60; //[30:200] //What shape egg? (use 7 for a hen egg; 0 for a sphere; 100 for a blimp) egg_shape=7; //[0:100] //What percentage of the interior should be hollow (0 for totally solid) interior=85; //[0:95] //Do you want the inside to be smooth or decorated? (hollow bisected eggs only) inside="smooth"; //[smooth,decorated] /* [Printing] */ //Do you want it bisected? (IMPORTANT: YES for printing, NO during preview.) bisect="no"; //[yes,no] //Do you want to add a joiner to hold the egg together? (hollow bisected eggs only) joiner="attached"; //[attached,detached,none] //Set the spacing between parts on the build plate in mm spacing=2; //[2:10]

Customized version of http://www.thingiverse.com/thing:2239001 Created with Customizer! http://www.thingiverse.com/apps/customizer/run?thing_id=2239001

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

Here are another versions: https://www.thingiverse.com/thing:5195805 (original) https://www.thingiverse.com/thing:5195809 (compact version) In Japan, special trays are sometimes used to give change in stores. Especially after COVID-19, the use of trays is compulsory in most stores because of complaints if trays are not used. Coins often stick to the tray and are difficult to pickup, so I designed a shape that is easy to pickup. This version allows you to grab coins and carry tray from both side. [Japanese] 別バージョンもあります。 https://www.thingiverse.com/thing:5195805 (オリジナル) https://www.thingiverse.com/thing:5195809 (コンパクト版) 店でお金を受け渡す際に使うトレー(コイントレー/キャッシュトレー/カルトン)です。 コロナの影響でよく使われるようになりましたが、特に皮革製のものは硬貨が張り付いて取りにくいことがあるので、取りやすい形状を考えて作成しました。 レジによく付いている硬貨用のくぼみをヒントに、トレーを置いたまま上からまとめてつかみ取りやすい構造にしています。 この前後対称版ではどちら側でもコインの受け取り・トレーの持ち運びができるようにしました。 また、底面を前後に出っ張らせることで、手をのせて硬貨をつかみ取れることが分かるようにしたつもりです。(オリジナル版が実際に使われているのを観察すると、皆さん硬貨を指先でつまみ取っていて、なかなかつかみ取ってくれなかったので)

Dr. Ali Ataie gives insights into the linguistic subtleties that could only have a Divine source. This clip in the MCC Gems Series is from a sermon Dr. Ataie gave about the sacred narratives in the Qur'an: https://youtu.be/xpt0kLHZYfY - More from MCC gems series: http://mcceastbay.org/gems - More from Dr. Ataie: http://mcceastbay.org/ali-ataie The Gems Series is a youth-initiated effort at the MCC aimed at providing viewers with bite-sized nuggets of wisdom and memorable anecdotes from the hundreds of hours of talks, sermons, panels, and lectures at the MCC to help you cultivate a more deeper love, understanding, and connection with your Creator and your faith. The talks span a range of topics from spiritual knowledge to current events from MCC's vast video library. If you enjoy this youth-run effort, please like and share and watch more at https://www.mcceastbay.org/gems More Dr. Ataie: http://mcceastbay.org/ali-ataie About Ustadh Ataie: Ali Ataie is a perennial student and researcher who has been involved in interfaith activities for over two decades. He holds a Masters in biblical studies with a focus on New Testament and biblical languages. He also holds a PhD in cultural and historical studies in religion from the Graduate Theological Union. His doctoral work focused on Muslim hermeneutics of Biblical texts, especially the Gospel of John. He lives in San Ramon, CA with his wife Roya and three daughters. - More Dr. Ataie: http://mcceastbay.org/ali-ataie This sermon was delivered via at Muslim Community Center - East Bay (MCC East Bay) in Pleasanton, California on July 22, 2022. Watch the complete Khutba: https://youtu.be/xpt0kLHZYfY More MCC East Bay: Events & Activities: http://www.mcceastbay.org/calendar Weekly Updates: http://www.mcceastbay.org/newsletter Support MCC: https://www.mcceastbay.org/sadaqa Facebook: http://www.facebook.com/MCCPleasanton Instagram: https://www.instagram.com/mcceastbay

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Check the rest out later, they've just settled in nice and are about to explode. I watered them up and imma come back in a week and these things are gonna double in size, Sunny EVERYDAY recently with the odd bit of overnight rain. Source: https://www.youtube.com/watch?v=YBWgj21zesw Uploader: Captain Richard Sensi-ble ⚓️

As most materials available in macroscopic quantities, graphene appears in a polycrystalline form and thus contains grain boundaries. In the present work, the effect of uniaxial strain on the electronic transport properties through graphene grain boundaries is investigated using atomistic simulations. A systematic picture of the transport properties with respect to the strain and the lattice symmetry of graphene domains on both sides of the boundary is provided. In particular, it is shown that the strain engineering can be used to open a finite transport gap in all graphene systems where two domains exhibit different orientations. This gap value is found to depend on the strain magnitude, on the strain direction and on the lattice symmetry of graphene domains. By choosing appropriately the strain direction, a large transport gap of a few hundred meV can be achieved when applying a small strain of only a few percents. For a specific class of graphene grain boundary systems, the strain engineering can also be used to reduce the scattering on defects and hence to significantly enhance the conductance. With a large strain-induced gap, these graphene heterostructures are proposed to be possible candidates for highly sensitive strain sensors, flexible transistors and p-n junctions with a strong non-linear I-V characteristics.

The proposed algorithm by Philippe D'Arco et al. 2013 J. Phys.: Condens. Matter 25 355401 was not well compared with other possible solutions for symmetry independent configuration (SIC) generation. In this comment, three well known solutions of SIC searching are discussed: exhaustive explorations, pure random sampling and "symmetry imposed" approaches. It is shown, that the advantages of the algorithm published by Philippe D'Arco et al. are questionable.

This item represents a case in PACER, the U.S. Government's website for federal case data. If you wish to see the entire case, please consult PACER directly.

symmetry

symmetry

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On 9/11/01, at 5:20pm, World Trade Center 7, a 570 ft. tall, 47-story building, suffering from scattered, uneven diffuse-flame fires and a gash to its lower south-western corner, drops from its 81-vertical-steel-column-reinforced position in the sky at near free-fall speed and symmetry with virtually no resistance from the still-intact, structurally-bound-to-column floors below the scattered diffuse-flame fires within, with no evidence that ANY portion of ANY of the 81 vertical steel columns remained standing, all while falling neatly into its own footprint. World Trade Center 7 was never hit by a plane. According to the officially-endorsed Department of Homeland Security's (DHS) Federal Emergency Management Agency (FEMA) report, flaming debris from the Twin Towers caused fires on multiple floors of the building - possibly igniting fuel-tanks in the basement and ultimately leading to its collapse. However, FEMA makes no attempt to illustrate that their hypothesis has any real data to support it whatsoever. They reach no final conclusions - choosing, rather, to call for a more extensive and thorough examination of the Building 7's apparent "collapse." "The specifics of the fires in WTC 7 and how they caused the building to collapse remain unknown at this time. Although the total diesel fuel on the premises contained massive potential energy, the best hypothesis has only a LOW PROBABILITY of occurrence. Further research, investigation, and analyses are needed to resolve this issue" (FEMA, World Trade Center Building Performance Study, 5/2002, Chapter 5.7). The Department of Commerce's (DOC) National Institute of Standards in Technology (NIST) has published NCSTAR 1: Federal Building and Fire Safety Investigation of the World Trade Center Disaster - Final Report on the Collapse of the World Trade Center Towers, but have yet to put out a conclusive report on WTC7. In a New York magazine article published in March 2006, Dr. S. Shyam Sunder, NIST's lead WTC disaster investigator, said, of World Trade Center 7, "We are studying the horizontal movement east to west, internal to the structure, on the fifth to seventh floors...But truthfully, I don't really know. We've had trouble getting a handle on Building No. 7." *Sigh* While the lack of a solid conclusion on what caused WTC7 to "collapse" is maintained by both the FEMA report and the lack of a NIST report, this fact is actively being ignored by those who would say that these reports are complete and that the investigation into 9/11 is therefore closed. Good people are being attacked by proponents of the official story for simply taking the advice within the FEMA report and attempting to further research, investigate and analyze the events surrounding the fall of WTC 7.

We study the critical collapse of a massless scalar field with angular momentum in spherical symmetry. In order to mimic the effects of angular momentum we perform a sum of the stress-energy tensors for all the scalar fields with the same eigenvalue, l, of the angular momentum operator and calculate the equations of motion for the radial part of these scalar fields. We have found that the critical solutions for different values of l are discretely self-similar (as in the original l=0 case). The value of the discrete, self-similar period, Delta_l, decreases as l increases in such a way that the critical solution appears to become periodic in the limit. The mass scaling exponent, gamma_l, also decreases with l.

We review and investigate different aspects of scalar fields in supergravity theories both when they parametrize symmetric spaces and when they parametrize spaces of special holonomy which are not necessarily symmetric (Kahler and Quaternionic-Kahler spaces): their role in the definition of derivatives of the fermions covariant under the R-symmetry group and (in gauged supergravities) under some gauge group, their dualization into (d-2)-forms, their role in the supersymmetry transformation rules (via fermion shifts, for instance) etc. We find a general definition of momentum map that applies to any manifold admitting a Killing vector and coincides with those of the holomorphic and tri-holomorphic momentum maps in Kahler and Quaternionic-Kahler spaces and with an independent definition that can be given in symmetric spaces. We show how the momentum map occurs ubiquitously: in gauge-covariant derivatives of fermions, in fermion shifts, in the supersymmetry transformation rules of (d-2)-forms etc. We also give the general structure of the Noether-Gaillard-Zumino conserved currents in theories with fields of different ranks in any dimension.

It has been found in numerical experiments that when one removes a sector from an elastic sheet and glues the edges of the sector back together, the resulting configuration is radially symmetric and nearly conical. We make a rigorous analysis of this setting under two simplyfying assumptions: Firstly, we only consider radially symmetric configurations. Secondly, we consider the so-called von-K\'arm\'an limit, where the size of the removed region as well as the deformations are small. We choose free boundary conditions for a sheet of infinite size. We show existence of minimizers of the suitably renormalized free energy functional. As a by-product, we obtain a lower bound for the elastic energy that has been conjectured in the related context of d-cones. Moreover, we determine the shape of minimizers at infinity up to exponentially decaying terms.

We start with the relation between the chiral symmetry breaking and gauge field topology. New lattice result further enhance the notion of Zero Mode Zone, a very narrow strip of states with quasizero Dirac eigenvalues. Then we move to the issue of "origin of mass" and Brown-RHo scaling: a number of empirical facts contradicts to the idea that masses of quarks and such hadrons as $\rho,N$ decrease near $T_c$. We argue that while at $T=0$ the main contribution to the effective quark mass is chirally odd $m_{\snchi}$, near $T_c$ it rotates to chirally-even component $m_\chi$, because "infinite clusters" of topological solitons gets split into finite ones. Recent progress in understanding of topology require introduction of nonzero holonomy $\neq 0$, which splits instantons into $N_c$ (anti)selfdual "instanton-dyons". Qualitative progress, as well as first numerical studios of the dyon ensemble are reported. New connections between chiral symmetry breaking and confinement are recently understood, since instanton-dyons generates holonomy potential with a minimum at confining value, if the ensemble is dense enough.

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Scenarios for baryon production are considered within the context of SU(5) and SO(10) grand unified theories where CP violation arises spontaneously. The spontaneous CP symmetry breaking then results in a matter-antimatter domain structure in the universe. Two possible, distinct types of theories of soft CP violation are defined. In the first type the CP nonconservation originates only from the breaking of SU(2) sub L X U(1) symmetry, and in the second type, even at the unification temperature scale, CP violation can emerge as a result of symmetry breaking by the vacuum expectation values of the superheavy Higgs sector scalars.

Detailed mean-flow and turbulence measurements have been made in the boundary layer in the plane of symmetry of a body of revolution at incidence. These data and the somewhat limited information available from previous experiments are utilized, together with extensive plane-of-symmetry boundary-layer calculations in laminar and turbulent flows, to determine the most important effects of mean-flow convergence and divergence. (Author)

Detailed mean-flow and turbulence measurements have been made in the boundary layer in the plane of symmetry of a body of revolution at incidence. These data and the somewhat limited information available from previous experiments are utilized, together with extensive plane-of-symmetry boundary-layer calculations in laminar and turbulent flows, to determine the most important effects of mean-flow convergence and divergence. (Author)