Translation Length Research Articles

SHCT: segmented helical computed tomography based on multiple slant source-translation.

Micro-computed tomography (Micro-CT) is inevitably required to inspect long large objects with high resolution. It is well known that helical CT solves the so-called "long object" problem, but it requires that the measured object be strictly located in the lateral field of view (FOV). Therefore, developing a novel scanning method to extend the FOV in both the lateral and axial directions (i.e., the large helical FOV) is necessary. Recently, due to the application of linearly distributed source arrays and the characteristics of easy extension of the FOV and engineering implementation, straight-line scanning systems have attracted much attention. In this paper, we propose a segmented helical computed tomography (SHCT) based on multiple slant source-translation. SHCT can readily extend the helical FOV by adjusting the source slant translation (SST) length, pitch (or elevation of the SST trajectory), and number of scanning circles. In SHCT, each projection view is truncated laterally and axially, but the projection data set within the cylindrical FOV region is complete. To ensure reconstruction efficiency and avoid the lateral truncation, we propose a generalized backprojection-filtration (G-BPF) algorithm for SHCT approximate reconstruction. Experimental results verify the effectiveness of the proposed SHCT methods for imaging large and long objects. As the pitch decreases, the proposed SHCT methods can reconstruct competitive, high-quality volumes.

Structural properties of hard-disk fluids under single-file confinement.

The structural properties of confined single-file hard-disk fluids are studied analytically by means of a mapping of the original system onto a one-dimensional mixture of non-additive hard rods, the mapping being exact in the polydisperse limit. Standard statistical-mechanical results are used as a starting point to derive thermodynamic and structural properties of the one-dimensional mixture, where the condition that all particles have the same chemical potential must be taken into account. Analytical results are then provided for the nth neighbor probability distribution function, the radial distribution function, and the structure factor, a very good agreement being observed upon comparison with simulation data from the literature. Moreover, we have analyzed the scaling form for the disappearance of defects in the zigzag configuration for high pressure and have obtained the translational correlation length and the structural crossover in the oscillation frequency for asymptotically large distances.

Co-translational formation of disulfides guides folding of the SARS-CoV-2 receptor binding domain

Many secreted proteins, including viral proteins, contain multiple disulfide bonds. How disulfide formation is coupled to protein folding in the cell remains poorly understood at the molecular level. Here, we combine experiment and simulation to address this question as it pertains to the SARS-CoV-2 receptor binding domain (RBD). We show that the RBD can only refold reversibly if its native disulfides are present before folding. But in their absence, the RBD spontaneously misfolds into a nonnative, molten-globule-like state that is structurally incompatible with complete disulfide formation and that is highly prone to aggregation. Thus, the RBD native structure represents a metastable state on the protein’s energy landscape with reduced disulfides, indicating that nonequilibrium mechanisms are needed to ensure native disulfides form before folding. Our atomistic simulations suggest that this may be achieved via co-translational folding during RBD secretion into the endoplasmic reticulum. Namely, at intermediate translation lengths, native disulfide pairs are predicted to come together with high probability, and thus, under suitable kinetic conditions, this process may lock the protein into its native state and circumvent highly aggregation-prone nonnative intermediates. This detailed molecular picture of the RBD folding landscape may shed light on SARS-CoV-2 pathology and molecular constraints governing SARS-CoV-2 evolution.

Asymptotic translation lengths and normal generation for pseudo-Anosov monodromies of fibered 3–manifolds

Let $M$ be a hyperbolic fibered 3-manifold. We study properties of sequences $(S_{\alpha_n}, \psi_{\alpha_n})$ of fibers and monodromies for primitive integral classes in the fibered cone of $M$. The main tool is the asymptotic translation length $\ell_{\mathcal{C}} (\psi_{\alpha_n})$ of the pseudo-Anosov monodromy $ \psi_{\alpha_n}$ on the curve complex. We first show that there exists a constant $C>0$ depending only on the fibered cone such that for any primitive integral class $(S, \psi)$ in the fibered cone, $\ell_{\mathcal{C}} (\psi)$ is bounded from above by $C/|\chi(S)|$. We also obtain a moral connection between $\ell_{\mathcal{C}} (\psi)$ and the normal generating property of $\psi$ in the mapping class group on $S$. We show that for all but finitely many primitive integral classes $(S, \psi)$ in an arbitrary 2-dimensional slice of the fibered cone, $\psi$ normally generates the mapping class group on $S$. In the second half of the paper, we study if it is possible to obtain a continuous extension of normalized asymptotic translation lengths on the curve complex as a function on the fibered face. An analogous question for normalized entropy has been answered affirmatively by Fried and the question for normalized asymptotic translation length on the arc complex in the fully punctured case has been answered negatively by Strenner. We show that such an extension in the case of the curve complex does not exist in general by explicit computation for sequences in the fibered cone of the magic manifold.

End‐periodic homeomorphisms and volumes of mapping tori

AbstractGiven an irreducible, end‐periodic homeomorphism of a surface with finitely many ends, all accumulated by genus, the mapping torus, , is the interior of a compact, irreducible, atoroidal 3‐manifold with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of in terms of the translation length of on the pants graph of . This builds on work of Brock and Agol in the finite‐type setting. We also construct a broad class of examples of irreducible, end‐periodic homeomorphisms and use them to show that our bound is asymptotically sharp.

On the finiteness property of hyperbolic simplicial actions: the right-angled Artin groups and their extension graphs

We study the right-angled Artin group action on the extension graph. We show that this action satisfies a certain finiteness property, which is a variation of a condition introduced by Delzant and Bowditch. As an application we show that the asymptotic translation lengths of elements of a given right-angled Artin group are always rational and once the defining graph has girth at least 6, they have a common denominator. We construct explicit examples which show the denominator of the asymptotic translation length of such an action can be arbitrary. We also observe that if either an element has a small syllable length or the defining graph for the right-angled Artin group is a tree then the asymptotic translation lengths are integers.

Experimental Evaluation of Sensor Fusion of Low-Cost UWB and IMU for Localization under Indoor Dynamic Testing Conditions.

Autonomous systems usually require accurate localization methods for them to navigate safely in indoor environments. Most localization methods are expensive and difficult to set up. In this work, we built a low-cost and portable indoor location tracking system by using Raspberry Pi 4 computer, ultra-wideband (UWB) sensors, and inertial measurement unit(s) (IMU). We also developed the data logging software and the Kalman filter (KF) sensor fusion algorithm to process the data from a low-power UWB transceiver (Decawave, model DWM1001) module and IMU device (Bosch, model BNO055). Autonomous systems move with different velocities and accelerations, which requires its localization performance to be evaluated under diverse motion conditions. We built a dynamic testing platform to generate not only the ground truth trajectory but also the ground truth acceleration and velocity. In this way, our tracking system's localization performance can be evaluated under dynamic testing conditions. The novel contributions in this work are a low-cost, low-power, tracking system hardware-software design, and an experimental setup to observe the tracking system's localization performance under different dynamic testing conditions. The testing platform has a 1 m translation length and 80 μm of bidirectional repeatability. The tracking system's localization performance was evaluated under dynamic conditions with eight different combinations of acceleration and velocity. The ground truth accelerations varied from 0.6 to 1.6 m/s2 and the ground truth velocities varied from 0.6 to 0.8 m/s. Our experimental results show that the location error can reach up to 50 cm under dynamic testing conditions when only relying on the UWB sensor, with the KF sensor fusion of UWB and IMU, the location error decreases to 13.7 cm.

Covers of surfaces, Kleinian groups and the curve complex

We show that curve complex distance is coarsely equal to electric distance in hyperbolic manifolds associated to Kleinian surface groups, up to errors that are polynomial in the complexity of the underlying surface. We then use this to control the quasi-isometry constants of maps between curve complexes induced by finite covers of surfaces. This makes effective previously known results, in the sense that the error terms are explicitly determined, and allows us to give several applications. In particular, we effectively relate the electric circumference of a fibered manifold to the curve complex translation length of its monodromy, and we give quantitative bounds on virtual specialness for cube complexes dual to curves on surfaces.

Rotation sets and actions on curves

Building on work of [7], we study the action of the homeomorphism group of a surface S on the fine curve graph C†(S). While the definition of C†(S) parallels the classical curve graph for mapping class groups, we show that the dynamics of the action of Homeo(S) on C†(S) is much richer: homeomorphisms induce parabolic isometries in addition to elliptics and hyperbolics, and all positive reals are realized as asymptotic translation lengths.When the surface S is a torus, we relate the dynamics of the action of a homeomorphism on C†(S) to the dynamics of its action on the torus via the classical theory of rotation sets. We characterize homeomorphisms acting hyperbolically, show asymptotic translation length provides a lower bound for the area of the rotation set, and, while no characterisation purely in terms of rotation sets is possible, we give sufficient conditions for elements to be elliptic or parabolic.

Alterations in kinematics of temporomandibular joint associated with chronic neck pain.

Temporomandibular disorder (TMD) is an umbrella term for pain and dysfunction of the temporomandibular joint (TMJ) and its associated structures. Patients with TMD show changes in TMJ kinematics and masticatory muscle activation. TMD is commonly comorbid with non-specific chronic neck pain (NCNP), which may be one of the risk factors for TMD. This study aimed to investigate whether patients with NCNP have altered TMJ kinematics and masticatory muscle activity. This was a cross-sectional exploratory study including 19 healthy participants and 20 patients with NCNP but without TMD symptoms. TMJ kinematics was measured during mouth opening and closing, jaw protrusion and jaw lateral deviation. Surface electromyography was used to record the muscle activity of the anterior temporalis, masseter, sternocleidomastoid and upper trapezius while clenching. Furthermore, cervical posture, cervical range of motion (ROM) and pressure-pain threshold of the neck and masticatory muscles were measured. Compared with the healthy group, the NCNP group showed significantly reduced upper cervical rotation ROM (p=.041) and increased condylar path length (p=.02), condylar translation (opening p=.034, closing p=.011) and mechanical pain sensitivity of the upper trapezius (p=.018). Increased condylar translation was significantly correlated with reduced upper cervical mobility and poor cervical posture (r=-0.322 to -0.397; p=.012-.046). Increased condylar translation and path length in patients with NCNP may indicate poor control of TMJ articular movement, which may result from neck pain or may be a compensation for limited neck mobility. Evaluation of excessive TMJ translation may be considered in patients with NCNP.

Associations between range of motion, strength, tear size, patient-reported outcomes, and glenohumeral kinematics in individuals with symptomatic isolated supraspinatus tears.

Clinical failure associated with nonoperative treatment of rotator cuff tears may be due to inadequate characterization of the individual's functional impairments. Clinically, restricted passive range of motion (ROM) (restrictions imply capsular tightness), limitations in muscle strength, and larger rotator cuff tears are hypothesized to be related to altered glenohumeral kinematics. Understanding these relationships, as well as the relationship between glenohumeral kinematics and patient-reported outcomes (PROs) prior to exercise therapy, may help characterize functional impairments in individuals with rotator cuff tears. The objectives of the study were to describe the baseline presentation of individuals with an isolated supraspinatus tear, including passive ROM, rotator cuff muscle strength, tear size, PROs, and glenohumeral kinematics, and to determine associations among these variables. One hundred one individuals with symptomatic isolated supraspinatus tears were recruited for the study and underwent assessments of passive glenohumeral ROM, isometric muscle strength, and ultrasonography to assess anterior-posterior tear size. Glenohumeral kinematics during scapular-plane abduction were measured using biplane radiography. Furthermore, PROs including the American Shoulder and Elbow Surgeons (ASES) score and the Western Ontario Rotator Cuff Index (WORC) score were collected. Individuals presented with decreased ROM, external rotation weakness compared with the uninvolved side, and pain and disability as measured by the ASES and WORC scores. These findings were not associated with glenohumeral kinematics, with the exception of a weak positive association between glenohumeral contact path lengths and WORC scores (ρ=0.25, P=.03). Tear size was 11.7±5.7 mm, and maximum anterior translation, superior translation, and contact path length were 3.0%±3.8% of glenoid width, 3.5%±3.8% of glenoid height, and 38.2%±20.7% of glenoid size, respectively. Individuals with a symptomatic isolated supraspinatus tear presented with decreased ROM, external rotation weakness, and pain and disability as measured by the ASES and WORC scores. However, no abnormal kinematics associated with these limitations were observed. Thus, given that the tear is isolated to the supraspinatus tendon and no capsular restrictions are present, normal function of the glenohumeral joint may be possible during scapular-plane abduction.

Ultrasensitive Ribo-seq reveals translational landscapes during mammalian oocyte-to-embryo transition and pre-implantation development.

In mammals, translational control plays critical roles during oocyte-to-embryo transition (OET) when transcription ceases. However, the underlying regulatory mechanisms remain challenging to study. Here, using low-input Ribo-seq (Ribo-lite), we investigated translational landscapes during OET using 30-150 mouse oocytes or embryos per stage. Ribo-lite can also accommodate single oocytes. Combining PAIso-seq to interrogate poly(A) tail lengths, we found a global switch of translatome that closely parallels changes of poly(A) tails upon meiotic resumption. Translation activation correlates with polyadenylation and is supported by polyadenylation signal proximal cytoplasmic polyadenylation elements (papCPEs) in 3' untranslated regions. By contrast, translation repression parallels global de-adenylation. The latter includes transcripts containing no CPEs or non-papCPEs, which encode many transcription regulators that are preferentially re-activated before zygotic genome activation. CCR4-NOT, the major de-adenylation complex, and its key adaptor protein BTG4 regulate translation downregulation often independent of RNA decay. BTG4 is not essential for global de-adenylation but is required for selective gene de-adenylation and production of very short-tailed transcripts. In sum, our data reveal intimate interplays among translation, RNA stability and poly(A) tail length regulation underlying mammalian OET.

Curvature of the space of stability conditions

Motivated by the study of the autoequivalence group of triangulated categories via isometric actions on metric spaces, we consider curvature properties (CAT(0), Gromov hyperbolic) of the space of Bridgeland stability conditions with the canonical metric defined by Bridgeland. We then prove that the metric is neither CAT(0) nor hyperbolic, and the quotient metric by the natural $\mathbb{C}$-action is not CAT(0) in case of the Kronecker quiver. Moreover, we also show the hyperbolicity of pseudo-Anosov functors defined by Dimitrov-Haiden-Katzarkov-Kontsevich, which yields the lower-bound of entropy by the translation length. Finally, pseudo-Anosov functors in case of curves have been completely classified.

Automatic Recognition Method of Machine English Translation Errors Based on Multisignal Feature Fusion.

The current automatic recognition method of machine English translation errors has poor semantic analysis ability, resulting in low accuracy of recognition results. Therefore, this paper designs an automatic recognition method for machine English translation errors based on multifeature fusion. Manually classify and summarize the real error sentence pairs, falsify a large amount of data by means of data enhancement, enhance the effect and robustness of the machine translation error detection model, and add the source text to translation length ratio information and the translation language model PPL into the model input. The score feature information can further improve the classification accuracy of the error detection model. Based on this error detection scheme, the detection results can be used for subsequent error correction and can also be used for error prompts to provide translation user experience; it can also be used for evaluation indicators of machine translation effects. The experimental results show that the word posterior probability features calculated by different methods have a significant impact on the classification error rate, and adding source word features based on the combination of word posterior probability and linguistic features can significantly reduce the classification error rate, to improve the translation error detection ability.

Normal generators for mapping class groups are abundant

We provide a simple criterion for an element of the mapping class group of a closed surface to be a normal generator for the mapping class group. We apply this to show that every nontrivial periodic mapping class that is not a hyperelliptic involution is a normal generator for the mapping class group when the genus is at least 3. We also give many examples of pseudo-Anosov normal generators, answering a question of D. D. Long. In fact we show that every pseudo-Anosov mapping class with stretch factor less than \sqrt{2} is a normal generator. Even more, we give pseudo-Anosov normal generators with arbitrarily large stretch factors and arbitrarily large translation lengths on the curve graph, disproving a conjecture of Ivanov.

Translation lengths of outer automorphisms of finitely generated free-by-finite groups

Bestvina, Feighn and Handel proved that every subgroup of the outer automorphism group, of the free group of rank n is either virtually finitely generated abelian or contains a nonabelian free group. In this note we consider the more general situation of the outer automorphism group of a finitely generated free-by-finite group G. We show that is translation discrete and that every subgroup of is either virtually finitely generated abelian or contains a nonabelian free group.

Linear Motion Error Evaluation of Open-Loop CNC Milling Using a Laser Interferometer

Abstract The usage of computerised numerical control (CNC) machines requires accuracy verification to ensure the high accuracy of the processed products. This paper introduces an accuracy verification method of an open-loop CNC milling machine using a fringe counting of He–Ne laser interferometry to evaluate the best possible accuracy and functionality. The linear motion accuracy of open-loop CNC milling was evaluated based on the number of pulses from the controller against the actual displacement measured by the He–Ne fringe-counting method. Interval distances between two pulses are also precisely measured using the He–Ne interferometry. The linear motion error and controller error can be simultaneously evaluated in sub-micro accuracy. The linear positioning error due to the micro-stepping driver accuracy of the mini-CNC milling machine was measured with the expanded uncertainty of measurement and was estimated at 240 nm. The experimental results show that linear motion error of the open-loop CNC milling can reach up to 50 μm for 200 mm translation length.

Domination results in n$n$‐Fuchsian fibers in the moduli space of Higgs bundles

In this article, we show some domination results on the Hitchin fibration, mainly focusing on the $n$-Fuchsian fibers. More precisely, we show the energy density of associated harmonic map of an $n$-Fuchsian representation dominates the ones of all other representations in the same Hitchin fiber, which implies the domination of topological invariants: translation length spectrum and entropy. As applications of the energy density domination results, we obtain the existence and uniqueness of equivariant minimal (or maximal) surfaces in certain product Riemannian (or pseudo-Riemannian) manifold. Our proof is based on establishing an algebraic inequality generalizing a GIT theorem of Ness on the nilpotent orbits to general orbits.

Slug Flow Hydrodynamics Modeling for Gas–Liquid Two-Phase Flow in a Pipe

Gas–liquid flow in a pipeline is a very common. Slug two-phase flow is dominated in the case of slightly upward flow (+0.25°) and considered to be the comprehensive flow configuration, and can be in close contact with all the other flow patterns. The models of different flow patterns can be unified. Precise prediction of the slug flow is crucial for proper design and operation. In this paper, we develop hydrodynamics unified modeling for gas–liquid two-phase slug flow, and the bubble and droplet entrainment is optimized. For the important parameters (wall and interfacial friction factors, slug translational velocity and average slug length), the correlations of these parameters are optimized. Furthermore, the related parameters for liquid droplet and gas bubble entrainment are given. Accounting for the gas–liquid interface shape, hydrodynamics models, i.e., the flat interface model (FIM) and the double interface model (DIM), of liquid film in the slug body are applied and compared with the experimental data. The calculated results show that the predictions for the liquid holdup and pressure gradient of the DIM agree with experimental data better than those of the FIM. A comparison between the available experimental results and Zhang’s model calculations shows that the DIM model correctly describes the slug dynamics in gas–liquid pipe flow.

THE INFLUENCE OF SINGLY CHARGED IONS ON THE TRANSLATIONAL MOTION OF MOLECULES IN EXTREMELY DILUTE AMIDE SOLUTIONS

The type of short range solvation of Li+, Na+ K+, Rb+, Cs+, NH4+, Cl– , Br–, I–, ClO4– ions has been determined and analyzed in formamide (FA), N-methylformamide (MFA), N-dimethylformamide (DMF) at 298.15 K. In order to determine the type of ion solvation we used familiar-variable quantitative parameter (– ri), where is the translational displacement length of ion, ri is its structural radius. It was found that the difference (– ri) is equal to the coefficient of attraction friction (CAF) of ions normalized to the solvent viscosity and hydrodynamic coefficient. The sign of the CAF is determined by the sign of the algebraic sum of its ion-molecular and intermolecular components. In amide solutions the studied cations are cosmotropes (positively solvated ((– ri) > 0), structure-making ions) and anions are chaotropes (negatively solvated ((– ri) < 0 ), structure-breaking ions). In the amide series, regardless of the sign (– ri), the near-solvation enhances, which can be explained by the weakening of the specific interaction between the solvent molecules. The decrease of and respectively (– ri) with increasing cation radius in a given solvent is the result of weakening of its coordinating force due to the decrease of charge density in the series Li+–Na+–K+–Rb+–Cs+. The increase of (and (– ri), correspondingly) for the ions studied in the series FA- MFA-DMF can be explained by the weakening of intermolecular interactions in this series, which leads to the strengthening of solvation. It was found that for the halide ions in the series FA-MFA-DMF the regular growth of parameter is explained by the weakening of the solvent structure. It was shown that Li+ ion with the lowest diffusion coefficient among cations and the highest value forms kinetically stable complexes in amide solutions.