Inversion of lattice models from the observations of microscopic **degrees**
**of** **freedom**: parameter estimation with uncertainty quantification

**degrees**

**of**

**freedom**remains a largely unresolved issue. Expand abstract.

**of**modern tools often sufficient to extract minute details

**of**symmetry-breaking distortions such as polarization, octahedra tilts, or other structure-coupled order parameters. The patterns

**of**observed distortions in turn contain the information on microscopic driving forces defining the development

**of**materials microstructure and associated thermodynamics. However, the analysis

**of**underpinning physical models from experimentally observed microscopic

**degrees**

**of**

**freedom**remains a largely unresolved issue. Here, we explore such an approach using the paradigmatic Ising model on a square lattice. We show that the microscopic parameters

**of**the Ising model both for ferromagnetic and antiferromagnetic case can be extracted from the spin configurations for temperatures an order

**of**magnitude higher than the phase transition and perform uncertainty analysis for such reconstructions. This suggests that microscopic observations

**of**materials with sufficiently high precision can provide information on generative physics at temperatures well above corresponding phase transition, opening new horizons for scientific exploration via high-resolution imaging.

5/10 relevant

arXiv

Four-Arm Manipulation via Feet Interfaces

**degrees**

**of**

**freedom**each. Expand abstract.

**of**high dexterity, while the feet-controlled arms perform tasks requiring lower dexterity, such as supporting a load. The robotic arms are tele-operated through two foot interfaces that transmit translation and rotation to the end effector

**of**the manipulator. Haptic feedback is provided for the human to perceive contact and change in load and to adapt the feet pressure accordingly. Existing foot interfaces have been used primarily for a single foot control and are limited in range

**of**motion and number

**of**

**degrees**

**of**

**freedom**they can control. This paper presents foot-interfaces specifically made for bipedal control, with a workspace suitable for two feet operation and in five

**degrees**

**of**

**freedom**each. This paper also presents a position-force teleoperation controller based on Impedance Control modulated through Dynamical Systems for trajectory generation. Finally, an initial validation

**of**the platform is presented, whereby a user grasps an object with both feet and generates various disturbances while the object is supported by the feet.

5/10 relevant

arXiv

Adiabatic Elimination and Sub-space Evolution **of** Open Quantum Systems

**degrees**

**of**

**freedom**and formulating effective operators for the slow

**degree**s of freedom in reduced dimensions. Expand abstract.

**of**open quantum systems can be obtained by performing an adiabatic elimination

**of**the fast

**degrees**

**of**

**freedom**and formulating effective operators for the slow

**degrees**

**of**

**freedom**in reduced dimensions. Here, we perform the construction

**of**effective operators in frequency space, and using the final value theorem or alternatively the Keldysh theorem, we provide a correction for the trace

**of**the density matrix which takes into account the non trace-preserving character

**of**the evolution. We illustrate our results with two different systems, ones where the eliminated fast subspace is constituted by a continuous set

**of**states and ones with discrete states. Furthermore, we show that the two models converge for very large dissipation and at coherent population trapping points. Our results also provide an intuitive picture

**of**the correction to the trace

**of**the density matrix as a detailed balance equation.

5/10 relevant

arXiv

Challenges in assessing voxel-wise single-subject level benefits **of** MB acceleration

**degree**

**of**

**freedoms**suggests that sequences without MB outperform sequences with MB acceleration. Expand abstract.

**of**parameter estimates meaningless. Directly comparing t-values

**of**participants across different acquisition sequences is meaningless because

**of**the difference in

**degrees**

**of**

**freedom**(df) introduced by the higher number

**of**volumes acquired at higher multiband. Z-transformation

**of**the t-statics to correct for the difference in

**degree**

**of**

**freedoms**suggests that sequences without MB outperform sequences with MB acceleration. However, this may be due to an excessive penalty caused by inappropriate df estimation. Thus with the current evidence presented in this and previous studies that tested the impact

**of**MB on task related-statistics, the field lacks empirical evidence for the effects

**of**MB on individual subject statistics. We discuss the possible alternatives such as use

**of**Bayesian statistics.

4/10 relevant

bioRxiv

Two-field mimetic gravity revisited and Hamiltonian analysis

**degrees**

**of**

**freedom**in this model in addition to two tensor modes. Expand abstract.

**of**

**degrees**

**of**

**freedom**and stabilities. We first study the model at the linear cosmological perturbation level by quadratic Lagrangian and Hamiltonian formulations. We show that there are actually two (instead

**of**one) scalar

**degrees**

**of**

**freedom**in this model in addition to two tensor modes. We then push on the study to the full non-linear level in terms

**of**the Hamiltonian analysis, and confirm our result from the linear perturbation theory. We also consider the case where the kinetic terms

**of**the two mimetic scalar fields have opposite signs in the constraint equation. We point out that in this case the model always suffers from the ghost instability problem.

5/10 relevant

arXiv

Dynamics and Transport at the Threshold **of** Many-Body Localization

**degrees**

**of**

**freedom**coupled to a heat bath (or baths) consisting of thermal

**degree**s of freedom; however, this putative bath is itself nontrivial, being either small or very slowly... Expand abstract.

**of**matter, separated by a phase transition at which equilibrium statistical mechanics breaks down. True MBL is known to occur only under certain stringent conditions for perfectly isolated one-dimensional systems, with Hamiltonians that have strictly short-range interactions and lack any continuous non-Abelian symmetries. However, in practice, even systems that are not strictly MBL can be nearly MBL, with equilibration rates that are far slower than their other intrinsic timescales; thus, anomalously slow relaxation occurs in a much broader class

**of**systems than strict MBL. In this review we address transport and dynamics in such nearly-MBL systems from a unified perspective. Our discussion covers various classes

**of**such systems: (i) disordered and quasiperiodic systems on the thermal side

**of**the MBL-thermal transition; (ii) systems that are strongly disordered, but obstructed from localizing because

**of**symmetry, interaction range, or dimensionality; (iii) multiple-component systems, in which some components would in isolation be MBL but others are not; and finally (iv) driven systems whose dynamics lead to exponentially slow rates

**of**heating to infinite temperature. A theme common to many

**of**these problems is that they can be understood in terms

**of**approximately localized

**degrees**

**of**

**freedom**coupled to a heat bath (or baths) consisting

**of**thermal

**degrees**

**of**freedom; however, this putative bath is itself nontrivial, being either small or very slowly relaxing. We discuss anomalous transport, diverging relaxation times, and other signatures

**of**the proximity to MBL in these systems. We also survey recent theoretical and numerical methods that have been applied to study dynamics on either side

**of**the MBL transition.

5/10 relevant

arXiv

General Composite Non-Abelian Strings and Flag Manifold Sigma Models

**of**composite non-Abelian strings: vortex strings in non-Abelian theories where different sets

**of**colours have different amounts

**of**flux. After spontaneous symmetry breaking, there remains some internal colour

**degrees**

**of**

**freedom**attached to these objects, which we argue must exist in a Flag manifold, a more general kind

**of**projective space than both $\mathbb{CP}(N)$ and the Grassmannian manifold. These strings are expected to be BPS, since its constituents are. We demonstrate that this is true and construct a low-energy effective action for the fluctuations

**of**the internal Flag moduli, which we then re-write it in two different ways for the dynamics

**of**these

**degrees**

**of**freedom: a gauged linear sigma model with auxiliary fields and a non-linear sigma model with an explicit target space metric for the Flag Manifolds, both

**of**which $\mathcal{N}=(2,2)$ supersymmetric. We finish by performing some groundwork analysis

**of**the resulting theory.

5/10 relevant

arXiv

Quantum liquid with strong orbital fluctuations: the case **of** a pyroxene
family

**degrees**

**of**

**freedom**become liberated so that the excitations become dispersive and the spectral weight shifts to energies much smaller than the exchange integral. Expand abstract.

**of**the pyroxene family where spin and orbital

**degrees**

**of**

**freedom**remain tightly bound. We analyze their excitation spectrum and outline the conditions under which the orbital

**degrees**

**of**

**freedom**become liberated so that the excitations become dispersive and the spectral weight shifts to energies much smaller than the exchange integral.

5/10 relevant

arXiv

State Space System Modelling **of** a Quad Copter UAV

**degrees**

**of**

**freedom**(3DOF) and six

**degree**s of freedom (6DOF) quad copter state-space models are developed starting from basic Newtonian equations. Expand abstract.

**degrees**

**of**

**freedom**(3DOF) and six

**degrees**

**of**

**freedom**(6DOF) quad copter state-space models are developed starting from basic Newtonian equations. These state space models are very important to control the quad copter system which is inherently dynamically unstable.

5/10 relevant

arXiv

Fully-resolved wave-structure interaction simulations of a submerged
cylindrical point absorber with three **degrees** **of** **freedom**

**degrees**

**of**

**freedom**(DOF). Expand abstract.

**of**a submerged cylindrical point absorber with three free

**degrees**

**of**

**freedom**(DOF). The submerged buoy is tethered using a power take off unit that restrains the heave, surge, and pitch motions

**of**the buoy and absorbs energy from the three modes

**of**motion. The FD/BP methodology is more versatile than the previously used fictitious domain distributed Lagrange multiplier (FD/DLM) method for modeling similar point absorbers in the literature. For the latter method, external torques are not straightforward to incorporate in the rigid body dynamics, and consequently, the rotational velocities

**of**the buoys are often ignored. We also compare the simulated heave, surge and pitch dynamics

**of**the buoy using FD/BP method to that obtained by using time-domain Cummins model. It is demonstrated that the potential theory over-predicts the amplitudes

**of**heave and surge motions, whereas it results in an insignificant pitch for a fully-submerged axisymmetric converter. Further, we use fully-resolved WSI simulations to study the performance

**of**a 3-DOF buoy under varying PTO coefficients, mass density

**of**the buoy, and incoming wave heights.

10/10 relevant

arXiv