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Ultraconserved elements (UCEs) are stretches of hundreds of nucleotides with highly conserved cores flanked by variable regions. Although the selective forces responsible for the preservation of UCEs are unknown, they are nonetheless believed to contain phylogenetically meaningful information from deep to shallow divergence events. Phylogenetic applications of UCEs assume the same degree of rate heterogeneity applies across the entire locus, including variable flanking regions. We present a Wright-Fisher model of selection on nucleotides (SelON) which includes the effects of mutation, drift, and spatially varying, stabilizing selection for an optimal nucleotide sequence. The SelON model assumes the strength of stabilizing selection follows a position dependent Gaussian function whose exact shape can vary between UCEs. We evaluate SelON by comparing its performance to a simpler and spatially invariant GTR+Γ model using an empirical dataset of 400 vertebrate UCEs used to determine the phylogenetic position of turtles. We observe much improvement in model fit of SelON over the GTR+Γ model, and support for turtles as sister to lepidosaurs. Overall, the UCE specific parameters SelON estimates provide a compact way of quantifying the strength and variation in selection within and across UCEs. SelON can also be extended to include more realistic mapping functions between sequence and stabilizing selection as well as allow for greater levels of rate heterogeneity. By more explicitly modeling the nature of selection on UCEs, SelON and similar approaches can be used to better understand the biological mechanisms responsible for their preservation across highly divergent taxa and long evolutionary time scales.

The position dependent nonconservative forces are called curl forces introduced recently by M.V. Berry, P. Shukla, J. Phys. A 45, 305201 (2012). In this article, we elucidate the role of curl forces in classical and quantum optics. At first we review the work of A. Ashkin and demonstrate the existence of curl force. We then discuss the role of curl force in ion trapping theory and map it to rotating saddle potential. Finally we show the connection between the two level atom problem, curl forces and their connection to Pais-Uhlenbeck oscillator.

Direct covalent connections of porphyrinoids have been demonstrated as an effective way to expand their π-electronic networks and perturb their optical and electrochemical properties. Covalent connections are also useful for studies on the precise electronic interaction between two porphyrinoid units. However, the chemistry of covalently linked corrole oligomers lags far behind that of the porphyrin counterparts in spite of the importance of corrole as a ring-contracted porphyrinoid. The lower symmetry of corroles naturally leads to many possible corrole dimers, which have been found to display different optical and electrochemical properties depending on the linking position. In this review, we summarize the synthesis, structures, and properties of corrole oligomers such as singly linked oligomers and fused dimers as well as their metal complexes with a particular focus on their linking position dependent electronic properties.

The study of physical systems endowed with a position-dependent mass (PDM) remains a fundamental issue of quantum mechanics. In this paper we use a new approach, recently developed by us for building the quantum kinetic energy operator (KEO) within the Schrodinger equation, in order to construct a new class of exactly solvable models with a position varying mass, presenting a harmonic-oscillator-like spectrum. To do so we utilize the formalism of supersymmetric quantum mechanics (SUSY QM) along with the shape invariance condition. Recent outcomes of non-Hermitian quantum mechanics are also taken into account.

Cutters with high flexibility, e.g. side-and-face cutters and band saw cutters, are widely used in industries for finishing of narrow and deep grooves or parting operations. However, because of this flexibility, chatter vibration tends to occur, and it is unique in that the mode shape along the teeth affects the present vibration, the regenerative vibration, and the compliance at the present cutting tooth in both magnitude and phase, which is new to the literature. Hence, a novel regenerative chatter stability model is developed where the position-dependent modal displacement ratio in the cutting direction is considered. The experimental results show agreement with the proposed model, and unique characteristics are extracted., Available online 16 May 2019. ファイル公開：2021-05-16

We construct higher-order Darboux transformations for Dirac equations in two dimensions that feature a position-dependent mass. Our method allows to generate closed-form expressions for both a transformed potential and a transformed position-dependent mass function.

Hyper-Kamiokande detector is proposed as a next generation underground water Cherenkov detector in Japan, and is planned to be an order of magnitude bigger than its predecessor, Super-Kamiokande. In order to further improve the detector capabilities in both low and high energy sectors, the multi-PMT modules instrumented with multiple 3-inch PMTs are being developed, in addition to the improved high quantum efficiency 20-inch PMTs. We developed a moveable laser system that can illuminate different positions on the photocathode to measure the characterization of the 3-inch PMTs as a function of the position on the photocathode.

The present theoretical study deals with microparticles (beads) that contain an immobilized Belousov-Zhabotinsky (BZ) reaction catalyst. In the theoretical experiment, a BZ bead is immersed in a small water droplet that contains all of the BZ reaction reagents but no catalyst. Such heterogeneous reaction-diffusion BZ systems with the same BZ reactant concentrations demonstrate various dynamic modes, including steady state and low-amplitude, high-amplitude, and mixed-mode oscillations (MMOs). The emergence of such dynamics depends on the sizes of the bead and water droplet, as well as on the location of the bead inside the droplet. MMO emergence is explained by time-delayed positive feedback in combination with a canard phenomenon. If two identical BZ beads are immersed in the same droplet, many different dynamic modes including chaos are observed.

More recently, we have proposed a set of noncommutative space that describes the quantum gravity at the Planck scale [J. Phys. A: Math. Theor. 53, 115303 (2020)]. The interesting significant result we found is that, the generalized uncertainty principle induces a maximal measurable length of quantum gravity. This measurement revealed strong quantum gravitational effects at this scale and predicted a detection of gravity particles with low energies. In the present paper, to make evidence this prediction, we study in this space, the dynamics of a particle with position-dependent mass (PDM) trapped in an infinite square well. We show that, by increasing the quantum gravitational effect, the PDM of the particle increases and induces deformations of the quantum energy levels. These deformations are more pronounced as one increases the quantum levels allowing, the particle to jump from one state to another with low energies and with high probability densities., Comment: 18 pages

We present a brief introduction to braids, in particular simple positive braids, with a double emphasis: first, we focus on term rewriting techniques, in particular, reduction diagrams and decreasing diagrams. The second focus is our employment of the colored braid notation next to the more familiar Artin notation. Whereas the latter is a relative, position dependent, notation, the former is an absolute notation that seems more suitable for term rewriting techniques such as symbol tracing. Artin's equations translate in this notation to simple word inversions. With these points of departure we treat several basic properties of positive braids, in particular related to the word problem, confluence property, projection equivalence, and the congruence property. In our introduction the beautiful diamond known as the permutohedron plays a decisive role.

Geometric errors measurement and identification for rotary table are important. However, precisely adjustment for the setup position of a double ball bar in each measurement pattern is inconvenient. This study proposes a novel optimization identification method using a double ball bar to recognize the position-dependent geometric errors (PDGEs) of rotary axis. A mathematical model for ball bar measurement is firstly constructed to map the relationship between measurement direction and position of the double ball bar. And then, the setup positions of the double ball bar for PDGEs identification are analyzed. According to analysis for setup positions of the double ball bar, simplified measurement patterns would be conducted by adjusting only two setup positions for the ball bar and thus reduce the procedure of accurate adjustment for the ball bar. The PDGEs can be fitted as an nth B-spline curve, on the account of its being smooth and continuous. To identify the PDGEs, an optimization method, by computing the suitable value of control points of nth B-spline curve of errors to minimize the optimal value of the target function between the actual measured value and the value derived from a theoretical measurement model, is proposed. Moreover, in order to obtain the accurate value of control points of the error curve, the sensitivity analysis is conducted to acquire the sensitivity matrix with respect to control points of errors. The PDGEs are able to be identified simultaneously after calculating the appropriate values of control points of errors. The proposed identification method is validated by simulation and experiment. The results prove the effectiveness of the proposed method.

This study proposes a continuous measurement method of 12 position-dependent geometric errors for rotary axes on five-axis machine tools with a tilting rotary table. Firstly, an algorithm for calculating the three-dimensional position deviations of the standard sphere is presented. The target points on the sphere surface are pre-distributed for the measurements. Then, the single setup continuous measurement method implemented by the standard spheres and a laser displacement sensor is designed. Before performing the measurements, the installation error of the laser displacement sensor is controlled in an acceptance range by an adjustment device with simple procedures. To expand this measurement idea, the application of this continuous measurement method on five-axis machine tools with one rotary axis on the spindle and another one on the worktable is illustrated. The standard uncertainties and the range of the uncertainty contributors are also provided. Finally, an experiment is performed to validate the identification accuracy and efficiency of the proposed method.

Thin-walled parts with curved surfaces are widely used in industrial applications, and the surface quality is a basic requirement to ensure the functional performance. Due to the thin-walled and curved geometric features, the rigidity for this kind of parts is not only low but also position-dependent. In this way, the deformation of such parts is easy to vary and complex along the toolpath in the machining process, which results in a poor dimensional quality for the thin-walled parts with curved surfaces. However, it is a novel idea that when the machining deformation is homogeneous, the deformation compensation is easily carried out and the improved machining quality can be obtained for the thin-walled curved surface parts. For the machining deformation is affected by the cutting force and the cutting force is affected by the instantaneous cutting-amount in essence, an instantaneous cutting-amount planning approach based on the position-dependent rigidity of thin-walled curved surface parts is proposed in this study, so as to homogenize the machining deformation thus improving the machining quality. Inspired by the generalized Hooke law, the instantaneous cutting-amount is planned here to be harmonious with the rigidity variation along the toolpath, so that the ratio between the cutting force and the rigidity, i.e. the deformation at certain cutting-position, can be kept as a constant value. For this sake, the instantaneous cutting-amount of thin-walled curved surface parts during the five-axis machining process is first modeled, and then, the position-depended rigidity of the parts is calculated. Finally, the instantaneous cutting-amount is scheduled according to the position-dependent rigidity. Experimental results verify the effectiveness of the presented method in homogenizing of the machining deformation. Achievements of this study are significant for enriching the high-quality machining technique of thin-walled parts with curved surfaces.

The Laser Methane Detector (LMD) technique has proven to be reliable for estimating enteric methane (CH4) output in ruminants. The number of peer-reviewed publications related to LMD measurements in ruminants is still small. Studies are largely limited to measurements of animals in controlled research environment and respiration chambers, while measurements on animals outside respiration chambers are rare. Most studies focused on cattle or sheep, but the LMD has not yet been applied to goats. Finally, no systematic measurement protocol is available for different livestock species. Thus, the experimental setup of studies varies considerably, making a comparison of results difficult, although previous papers have provided guidance. In the present study, the LMD technique was applied in two experiments with goats to evaluate the effect of; the position of goats, the time after feeding, CH4 peaks and troughs, the recording interval and the proportion of concentrate feed and hay in the diet on enteric CH4 emission. Measurements were taken on four (Experiment 1) and 12 (Experiment 2) 1-year old female Boer goats. The position affected the mean enteric CH4 emission, with higher values for lying than for standing goats. However, results across goats differ. In contrast, a day effect was observed that was consistent across positions and goats, with highest CH4 emissions obtained for day 3 (Experiment 1). As could be expected, the time after feeding strongly influenced the CH4 concentrations that were highest directly after morning feeding. CH4 concentrations gradually decreased with increasing time after feeding and were lowest early in the morning. No diet effect (quality and quantity) was observed (Experiment 2). This indicates a high individual variation of enteric CH4 emissions that could be exploited to select and breed animals with lower CH4 output. For subsequent experiments utilizing the LMD technique, it is recommended to use a 0.1-s interval for recording point measurements of CH4 concentrations, and for analysis to consider peaks only. A reduction of the recording interval to 1 s and 4 s only using CH4 peaks led to high deviances from the reference (0.1-s records, CH4 peaks and troughs), whereas the 0.1-s recording interval cleaned from CH4 troughs and using only CH4 peaks showed good accordance with the reference. Ongoing studies will verify the present results in view of developing a standardized protocol for measuring CH4 output in the major ruminant livestock species.

Objectives: To quantify, and compare, the whole- half- and peak-match running demands of professional club and international under-16 rugby league match-play. Methods: Four professional Club (n = 30) and two International (n = 23) under-16 matches were analysed using 10-Hz micro-technology units, with players analysed according to positional groups. Absolute (m) and relative (RD; m.min–1) total, high speed (>5 m·s–1; HSR) and sprint (>7 m·s–1) distance were analysed for whole- and half-match alongside maximum velocity (VMAX; m.s–1). Peak running demands were determined via moving averages of RD for 10, 30, and 60- to 600-seconds. Results: International forwards had most likely higher whole match relative sprint and VMAX, and 1st half RD than club level, and had very likely higher peak running demands at 60-, 180- and 600-second durations. For backs, whole game RD was most likely higher and total and sprint distance was likely higher at club level matches. Peak RD was also very likely higher for club backs at 10- and 60-seconds. Conclusions: The running demand differences between club and international level at the under-16 age group are position dependent, with greater running demands at club level match play for backs, but at the international level of forwards.

The supersymmetry (SUSY) formalism for a position dependent mass problem with a more general ordering is yet to be formulated. In this paper, we present an unified SUSY approach for PDM problems of any ordering. Highlighting all non-Hermitian Hamiltonians of PDM problems are of quasi-Hermitian nature, the SUSY operators of these problems are constructed using similarity transformation. The methodology that we propose here is applicable for even more general cases where the kinetic energy term is represented by linear combination of infinite number of possible orderings. We illustrate the method with an example, namely Mathews-Lakshmanan (ML) oscillator. Our results show that the latter system is shape invariant for all possible orderings. We derive eigenvalues and eigenvectors of this nonlinear oscillator for all possible orderings including Hermitian and non-Hermitian ones.

Producción Científica, The construction of position dependent mass Scarf Hamiltonians of the trigonometric as well as the hyperbolic types is addressed by means of the factorization method and the Riccati equation. These Hamiltonians are shown to be independent of the ordering parameter of the kinetic term. Additionally, new families of Hamiltonians with the Scarf spectrum are also determined by supersymmetry. Some examples for masses with and without singularities are considered to illustrate our results.

Variable-mass problems do not as a rule fit into the cardinal formulation of mechanics; therefore, new formalism has been constructed to treat variable-mass dynamics. We aim to situate a class of position-dependent mass problems in the level of classically conservative dynamics. The issue is that, by nature, the sum of kinetic and potential energies of a position-dependent mass point is not preserved. Given that, we demonstrate a theorem which establishes the mathematical equivalence between position-dependent mass dynamics and classically conservative dynamics. Meshchersky’s equation is herein assumed to be in scalar form. In applying the theorem, a counterintuitive situation arises. To our very best knowledge, our contribution is novel in the field of variable-mass dynamics.

We study the scheduling problem of minimizing total load on a proportionate flowshop. We consider position-dependent job processing times in the most general way. We show that this problem is solved in O ( n 4 ) time, where n is the number of jobs. We then extend the setting to allow job-rejection, where the scheduler may decide to process only a subset of the jobs, and the rejected jobs are penalized. This extension is shown to be solved in O ( n 5 ) time.

We propose new models of position-dependent processing times for single-machine group scheduling problems. The two objectives of the scheduling problems are to minimize the makespan and the total completion time, respectively. We present polynomial-time algorithms to solve the problems.

The modification of the sine–Gordon model with explicitly broken translational invariance is studied. Different simplified descriptions of the kink motion are applied and compared. The main problem of the collective coordinate descriptions is identified and a solution is proposed. Some modification of the known collective coordinate approaches is proposed and a new treatment is suggested. The results are compared with the results of the exact field model.

In a recent paper by Jafarov, Nagiyev, Oste and Van der Jeugt (2020 {\sl J.\ Phys.\ A} {\bf 53} 485301), a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent on the position, was constructed and it was shown that the confinement parameter gets quantized. By using a point canonical transformation starting from the constant-mass Schr\"odinger equation for the Rosen-Morse II potential, it is shown here that similar results can be easily obtained without quantizing the confinement parameter. In addition, an extension to a confined shifted harmonic oscillator directly follows from the same point canonical transformation., Comment: 7 pages, no figure

Motivation Current read-mapping software uses a singular specification of alignment parameters with respect to the reference. In the presence of varying reference structures (such as the repetitive regions of the human genome), alignments can be improved if those parameters are allowed vary. Results To that end, the C++ program ProDerAl was written to refine previously generated alignments using varying parameters for these problematic regions. Synthetic benchmarks show that this realignment can result in an order of magnitude fewer misaligned bases. Availability and implementation *Nix users can retrieve the source from GitHub (https://github.com/Benjamin-Crysup/proderal.git). Windows binary available at https://github.com/Benjamin-Crysup/proderal/releases/download/v1.1/proderal.zip. Supplementary information Supplementary data are available at Bioinformatics online.

In this note, single machine scheduling with concurrent resource allocation and position-dependent workloads is studied. The aim is to find jointly the optimal sequence and the optimal resource allocation. A bicriteria analysis of the problem is provided where the first criterion is to minimize the scheduling cost (i.e. makespan, total completion time, total absolute differences in completion times, total absolute differences in waiting times) and the second criterion is to minimize the total resource consumption cost. It is proved that four bicriteria problems can be solved efficiently.

This paper addresses one-machine scheduling with maintenance restrictions. A maintenance operation is position dependent in a sequence of normal jobs if the maintenance has to be performed after at most some defined number of job changes on the machine. We show that several problems with objective functions Cmax and Lmax are still solvable in polynomial time if position-dependent maintenance is considered. We then consider the problem of preemptive scheduling with ready times and due dates on one machine with the Lmax criterion. We show that this problem is computationally hard and present the characteristics of this problem—for example, the fact that optimum schedules may be nonactive. After determining a set of dominance properties, branch-and-bound and local search algorithms are proposed. The performance of the algorithms is evaluated using a series of computational experiments.

Accuracy identification of geometric errors of rotary axis is important for error compensation of the multi-axis machine tool. However, it is not easy because of the influence of setup error of measurement instrument, and there exists angular errors and displacement errors need to be identified simultaneously. In this paper, a decoupled method based on double ball bar is proposed to identify the geometric errors of rotary axis including both position independent geometric error (PIGE) and position dependent geometric error (PDGE). A formulation for ball bar measurement is derived from kinematic analysis to reveal the relationship between sensitivity direction and setup position of ball bar. The angular errors and displacement errors can be identified separately when choosing the appropriate setup position and direction of ball bar. It can effectively reduce the interaction influence between them and improve the accuracy. To identify the 4 PIGEs, a method by averaging the measured results of ball bar to compute the eccentricity and slant of rotary axis is proposed. And, the PDGEs are leaved to mainly describe the oscillation of geometric errors of rotary axis. It is useful to correct the deviation error resulting from setup error of ball bar. For the identification of 6 PDGEs, by means of adjusting setup position and direction of ball bar, they can be identified one by one along the sensitivity direction of ball bar. Furthermore, in order to reduce the influence of setup error of ball bar, the sensitivity analysis is performed to obtain the sensitivity of measured results of ball bar with respect to setup error. According to the sensitivity characteristics of setup error, a method is presented to correct the PDGEs. Finally, several numerical simulations and experiments are conducted to verify the theoretical model and the proposed identification method. The results from the simulations and experiments demonstrate that the method can identify the geometric errors of rotary axis effectively and accurately.

Many control applications, including feedforward and learning control, involve the inverse of a dynamical system. For nonminimum-phase systems the response of the inverse system is unbounded. For linear time-invariant (LTI), nonminimum-phase systems a bounded, noncausal inverse response can be obtained through an exponential dichotomy. For general linear time-varying (LTV) systems such a dichotomy does not exist in general. The aim of this paper is to develop an inversion approach for an important class of LTV systems, namely linear periodically time-varying (LPTV) systems, which occur in, e.g., position-dependent systems with periodic tasks and non-equidistantly sampled systems. The proposed methodology exploits the periodicity to determine a bounded inverse for general LPTV systems. Conditions for existence are provided. The method is successfully demonstrated in several application cases, including position-dependent and non-equidistantly sampled systems.

Following the history of mechanics (Dugas in A history of mechanics, Dover, New York, 1988), we read that Poisson’s theorem figured in the 1811 edition of the celebrated Mecanique Analytique. Indeed, as it can be observed in the classical textbooks, Poisson brackets formulation is one of the cardinal chapters of analytical mechanics. Given the natural motivation to accommodate variable-mass systems at the level of classical analytical mechanics, we will herein direct our attention toward Poisson brackets formulation. To wit, considering the case of a position-dependent mass particle, in which we will assume that the absolute velocity of mass ejection or aggregation is a linear function of the generalized velocity, we will endeavor to provide such position-dependent mass problems with an appropriate Poisson brackets formulation. To our very best knowledge, this means an original contribution to the research field of the analytical mechanics of variable-mass systems. We will start establishing the Poisson brackets definition for the dynamics of a position-dependent mass particle, which will be posited in harmony with the classical mathematical portrait of analytical mechanics. Therefrom, we will demonstrate consequent results which give rise to the required formulation, namely, Jacobi’s identity, canonical equations expressed by means of such Poisson brackets and Poisson’s theorem. Last, we will apply Poisson’s theorem to evaluate the relationship between the conservation laws which are at our disposal in the domain of position-dependent mass problems.

Delta-type robots are commonly used for positioning purposes in medical surgery. In such applications, the loading position accuracy of the end effector is of critical importance. However, the positioning accuracy is determined by the loading deflection, which depends in turn on the link flexibility and joint clearance within the system. Importantly, the loading deflection is posture/position dependent. This characteristic greatly complicates the task of improving the positioning accuracy using traditional compensation control methods. Accordingly, the present study proposes a non-spherical ball-socket joint design to improve the loading stiffness of the robot over the entire workspace. An analytical model is derived to quantify the loading deflection as a function of the link flexibility and joint clearance. The experimental results show that the non-spherical ball-socket joint design reduces the total variation in the loading deflection of the end effector by up to 81.04% compared to that of a traditional robot with spherical ball-socket joints when performing positioning over the entire workspace at the assigned height.

The study on the position-dependent dynamic characteristics of a vertical ball screw feed system without counterweight is an important step in the enhancement of the structural performance of mini-type vertical milling machines. The ball screw is generally driven by a servomotor, which converts a rotary motion into a linear motion through a screw–nut pair. To assess the position-dependent dynamic characteristics of a vertical ball screw feed system subjected to the influence of the screw–nut joint stiffness, a variable-coefficient lumped parameter model of the system is developed. This model is established taking into account the screw–nut joint stiffness under three different strategies: (1) considering the preload and the weight of the spindle system, (2) considering the elastic deformation but ignoring the effect of the weight, and (3) a perfectly rigid model. The differences between the three models in predicting the position-dependent dynamic characteristics of the system are compared, revealing that the stiffness of screw–nut joint greatly affects the vibratory behavior of the spindle system in the transmission direction. A set of conducted experimental results demonstrate that the stiffness model under the preload and the weight of the spindle system is the most accurate model for the prediction of the position-dependent natural frequency and displacement response of the system with the spindle system position. Therefore, it is more suitable for structure design, performance simulation, and evaluation of a vertical ball screw feed system without counterweight.

We study extensions of a minmax due-date assignment problem with a bound on due-dates.The first extension is to position-dependent processing times.A further extension is to a setting of due-window for acceptable lead-times.Theses extensions are shown to be solved in polynomial time.The option of job rejection is considered, and shown to be ordinary NP-hard. We focus on a due-date assignment model where due-dates are determined by penalties for jobs exceeding pre-specified (job-dependent, different) deadlines. The underlying assumption of this model, denoted by DIF, is that there are "lead times that customers consider to be reasonable and expected". In a minmax DIF model, the value of the objective function is that of the largest job/due-date cost. The goal is to find both the job sequence and the due-dates, such that this value is minimized.In this paper we study several extensions of the minmax DIF model. First, we consider general position-dependent job processing times. Then we extend the model to a setting of a due-window for acceptable lead-times. Here, the assumption is that a time interval exists, such that due-dates assigned to be within this interval are not penalized. The last extension of the DIF model is to a setting allowing job-rejection. This option reflects many real-life situations, where the scheduler may decide to process only a subset of the jobs, and the rejected jobs are penalized. The first two extensions are shown to be polynomially solvable: we introduce solution algorithms requiring O(n3) and O(n4) time, respectively, where n is the number of jobs. The last extension (assuming job-rejection) is proved to be NP-hard in the ordinary sense, and an efficient pseudo-polynomial dynamic programming algorithm is introduced.

To understand the role of ribose G-quartets and how they affect the properties of G-quadruplex structures, we studied three systems in which one, two, three, or four deoxyribose G-quartets were substituted with ribose G-quartets. These systems were a parallel DNA intramolecular G-quadruplex, d(TTGGGTGGGTTGGGTGGGTT), and two tetramolecular G-quadruplexes, d(TGGGT) and d(TGGGGT). Thermal denaturation experiments revealed that ribose G-quartets have position-dependent and cumulative effects on G-quadruplex stability. An unexpected destabilization was observed when rG quartets were presented at the 5'-end of the G stack. This observation challenges the general belief that RNA residues stabilize G-quadruplexes. Furthermore, in contrast to past proposals, hydration is not the main factor determining the stability of our RNA/DNA chimeric G-quadruplexes. Interestingly, the presence of rG residues in a central G-quartet facilitated the formation of additional tetramolecular G-quadruplex topologies showing positive circular dichroism signals at 295 nm. 2D NMR analysis of the tetramolecular TGgGGT (lowercase letter indicates ribose) indicates that Gs in the 5'-most G-quartet adopt the syn conformation. These analyses highlight several new aspects of the role of ribose G-quartets on G-quadruplex structure and stability, and demonstrate that the positions of ribose residues are critical for tuning G-quadruplex properties.

Visual scenes are initially processed via segregated neural pathways dedicated to either of the two visual hemifields. Although higher-order visual areas are generally believed to utilize invariant object representations (abstracted away from features such as stimulus position), recent findings suggest they retain more spatial information than previously thought. Here, we assessed the nature of such higher-order object representations in human cortex using high-resolution fMRI at 7T, supported by corroborative 3T data. We show that multi-voxel activation patterns in both the contra- and ipsilateral hemisphere can be exploited to successfully classify the object category of unilaterally presented stimuli. Moreover, robustly identified rank order-based response profiles demonstrated a strong contralateral bias which frequently outweighed object category preferences. Finally, we contrasted different combinatorial operations to predict the responses during bilateral stimulation conditions based on responses to their constituent unilateral elements. Results favored a max operation predominantly reflecting the contralateral stimuli. The current findings extend previous work by showing that configuration-dependent modulations in higher-order visual cortex responses as observed in single unit activity have a counterpart in human neural population coding. They furthermore corroborate the emerging view that position coding is a fundamental functional characteristic of ventral visual stream processing.

Using stated choice data collected by experimental design with repeated choice tasks, this study developed an approach to quantify the position-dependent order effects on the prediction of ...

In this paper, we consider the Bohr–Mottelson Hamiltonian in γ-rigid version with position dependent mass. The separation of variables has been done for the related wave equation. The obtained radial wave equation is solved for Kratzer potential. Then, the corresponding wave function, energy spectra and transition rates have been obtained for some nuclei. In addition, our results have been compared with experimental data.

An approach for obtaining a Schrodinger equation for a spinless nonrelativistic particle with a position-dependent mass is proposed. Rather than starting with the nonrelativistic hamiltonian for a free particle, we begin with its relativistic completion in the form of a Klein–Gordon equation and then reduce it to obtain the nonrelativistic limit. This type of procedure avoids the usual ordering ambiguities that commonly arise in obtaining a Schrodinger equation for a particle with position-dependent mass.

This paper is concerned with the monotonicity of the period function for closed orbits of systems of the Lienard II type equation given by $${\ddot{x}} + f(x){\dot{x}}^{2} + g(x) = 0$$ . We generalize Chicone’s result regarding the monotonicity of the period function to planar Hamiltonian vector fields in the presence of a position dependent mass. Sufficient conditions are also given for the isochronicity of the potential in case of such a system.

A 70-year-old woman, who had received mechanical aortic and mitral valve replacement for rheumatic valvular disease and implanted cardiac defibrillator (ICD) implantation for ventricular arrhythmia, underwent radiofrequency catheter ablation for symptomatic atrial fibrillation (AF). During the

In this paper, we provide unified methods for solving scheduling problems with convex resource allocation, concentrating on objective functions that can be expressed as a scalar product of the actual processing times vector and a job-independent and position-dependent penalties vector. We assume general position-dependent workloads, i.e., the workloads are not restricted to be either monotone functions of the job positions or to specific functions. The first unified method focuses on minimizing a scheduling measure subject to a constraint on the resource consumption, whereas the second addresses the complementary problem of minimizing the consumed resource given an upper bound on the scheduling measure. For each unified approach, we provide a methodical analysis and consequently provide a $$O\left( {n^{3} } \right)$$ solution algorithm. Furthermore, to demonstrate the unified schemes, we solve several scheduling measures that involve earliness and tardiness penalties.

This paper studies single-machine due-window assignment scheduling problems with truncated learning effect and resource allocation simultaneously. Linear and convex resource allocation functions under common due-window (CONW) assignment are considered. The goal is to find the optimal due-window starting (finishing) time, resource allocations and job sequence that minimize a weighted sum function of earliness and tardiness, due window starting time, due window size, and total resource consumption cost, where the weight is position-dependent weight. Optimality properties and polynomial time algorithms are proposed to solve these problems.

A classical single machine minmax common due-date assignment (CON) problem is studied. The problem is extended (independently) to the following settings: (1) general position-dependent job processing times are assumed, and an efficient O(n4) solution procedure is introduced; (2) the option of job rejection is allowed, and this case is shown to be solved in O(n5); (3) a deterioration effect is considered, and an O(n2) solution algorithm is proposed; (4) parallel uniform machines are considered; and (5) the machine setting is that of a permutation flowshop. The last two settings are known to be NP hard, and efficient heuristic procedures are introduced and shown numerically to produce very small optimality gaps.

In this paper, we introduce a group scheduling model with time-dependent and position-dependent DeJong’s learning effect. The objectives of scheduling problems are to minimize makespan, the total completion time, and the total weighted completion time, respectively. We show that the problems remain solvable in polynomial time under the proposed model.