Arbitrary Shift Research Articles

Multi-phase iterative learning control for high-order systems with arbitrary initial shifts

Aiming at the second-order tracking system with arbitrary initial shifts, this paper presents a multi-phase iterative learning control strategy. Firstly, utilizing the form of solution of the second-order non-homogeneous linear differential equation with constant coefficients and the initial shifts, we can select the appropriate control gain to ensure that the second-order systems are stable and reach the stable output after a fixed time. Secondly, on the premise that the second-order systems have reached the fixed output, two methods are proposed for rectifying the fixed shift, namely, shifts rectifying control and varied trajectory control. Theoretical analysis shows that the multi-stage iterative learning control strategy proposed in this paper can ensure that the second-order systems achieve complete tracking in the specified interval. Finally, the simulation examples affirm the validation of the designed algorithms.

Generalized Alder-Type Partition Inequalities

In 2020, Kang and Park conjectured a "level $2$" Alder-type partition inequality which encompasses the second Rogers-Ramanujan Identity. Duncan, Khunger, the fourth author, and Tamura proved Kang and Park's conjecture for all but finitely many cases utilizing a "shift" inequality and conjectured a further, weaker generalization that would extend both Alder's (now proven) as well as Kang and Park's conjecture to general level. Utilizing a modified shift inequality, Inagaki and Tamura have recently proven that the Kang and Park conjecture holds for level $3$ in all but finitely many cases. They further conjectured a stronger shift inequality which would imply a general level result for all but finitely many cases. Here, we prove their conjecture for large enough $n$, generalize the result for an arbitrary shift, and discuss the implications for Alder-type partition inequalities.

An optimally designed distribution‐free CUSUM procedure for tri‐aspect surveillance of continuous processes

AbstractIn the past few decades, research on nonparametric process monitoring schemes mainly dealt with the uni‐aspect or bi‐aspect schemes, focusing on monitoring process location or scale separately or jointly. Another critical process characteristic, namely, the process shape, is not explicitly dealt with in‐depth in most existing charting schemes. In classical hypothesis testing, some recent literature clearly showed that the multi‐aspect test statistics, although designed for very restrictive alternatives, often perform as well or better than many statistics for arbitrary distributional shifts. They are often better than Kolmogorov‐Smirnov or Cramér‐von Mises statistics and some empirical likelihood‐based test statistics. The current paper aims to use a tri‐aspect statistic to design a distribution‐free Phase‐II Cumulative Sum (CUSUM) charting scheme for monitoring any arbitrary process changes in the process. The proposal is nonparametric and is equivalent to an unknown standard case. It reflects, in addition, which parameters, among location, scale, or shape, are more responsible for a signal. The construction of the CUSUM scheme from an existing tri‐aspect Shewhart‐type chart is simple, so significant attention is devoted to determining a near‐optimal reference parameter of the chart in keeping an unknown shift type in mind. Comparisons of the optimal performance of various competitors are considered in terms of the median run length (MRL) metric. The proposed charting scheme designed with the tri‐aspect statistic compares highly favorably with many existing SPM schemes. The same is evident from our findings based on the Monte‐Carlo simulation. Finally, the proposed schemes are illustrated with a flow‐width measurement monitoring example.

Toward Comprehensive Shifting Fault Tolerance for Domain-Wall Memories With PIETT

Spintronic domain-wall memories (DWMs) offer improved memory density and energy compared to conventional memories but are susceptible to shifting faults. We propose PIETT (<b>P</b>inning, <b>I</b>nsertion, <b>E</b>rasure, and <b>T</b>ranslation-fault <b>T</b>olerance) for improved misalignment correction versus the state of the art. PIETT proposes a derived error correction combined with multi-domain access approach to detect and correct a minimum of three misalignment faults after an arbitrary shift distance. Moreover, we characterize the rate of both misalignment and pinning faults in DWM nanowires and demonstrate that pinning faults are a significant concern to DWM. As such, PIETT is the first method combine correction of misalignment and pinning faults in random access DWMs. It also introduces novel PIETT Transverse Access Points (TAPs) that utilize a novel write access mode which can set/reset multiple domains in a single intrinsic operation and can store shift distance detection codes. By allowing checks between shifts of the intrinsic shift distance (<i>e.g.,</i> 3 domains), using a single TAP per nanowire expands misalignment protection and determines the needed corrective shifts to correct faults in all nanowires. Two TAPs expands misalignment protection to correct misalignment by more than one position and detects pinning by detecting different shift distances at each extremity of the nanowire. PIETT leverages knowledge of pinned nanowire locations to guide a modified SECDED ECC with one additional parity bit stored in additional parity nanowires. Thus, PIETT in TAP mode can correct unlimited, potentially multi-position, misalignment faults and either up to three pinning faults or up to two pinning faults with up to one bit-flip fault using scrubbing. PIETT provides eight to 21 orders of magnitude improvement in mean-time-to-failure with similar or better area overhead and only a 1&#x0025; system performance degradation compared to state of the art DWM misalignment correction.

Spin-State Splittings in 3d Transition-Metal Complexes Revisited: Toward a Reliable Theory Benchmark

A new composite method for the calculation of spin-crossover energies in 3d transition-metal complexes based on multireference methods is presented. The method reduces to MRCISD+Q at the complete-basis-set (CBS) level for atomic ions, for which it gives excitation energies with a mean absolute error of only ca. 0.01 eV. For molecular complexes, the CASPT2+δMRCI composite approach corresponds to a CASPT2/CBS calculation augmented by a high-level MRCISD+Q-CASPT2 correction with a smaller ligand basis set. For a set of test complexes, the approach reproduces full MRCISD+Q/CBS results to within better than 0.04 eV, without depending on any arbitrary IPEA shifts. The high-quality CASPT2+δMRCI method has then been applied to a series of 3d transition-metal hexaqua complexes in aqueous solution, augmented by an elaborate 3D-RISM-SCF solvent treatment of the underlying structures. It provides unprecedented agreement with experiment for the lowest-lying vertical spin-flip excitation energies, except for the Fe3+ system. Closer examination of the latter case provides strong evidence that the observed lowest-energy excitation at 1.56 eV, which has been used frequently for evaluating quantum-chemical methods, does not arise from the iron(III) hexaqua complex in solution, but from its singly deprotonated counterpart, .

Fast algorithm for decoding phase images with arbitrary step shift

A numerical algorithm for fast search of the initial phase shift on phase images with arbitrary stepwise shifts is proposed. The algorithm is based on finding the minimum deviation of the model function from the measurement results. The interval search method used directly in the proposed approach made it possible to significantly reduce the computational complexity of the algorithm. The paper presents the results of measuring a three-dimensional profile by phase triangulation methods using the proposed algorithm. The obtained results confirm the efficiency and high practical value of the proposed phase image decoding algorithm.

On a Combinatorial Generation Problem of Knuth

The well-known middle levels conjecture asserts that for every integer $n\geq 1$, all binary strings of length $2(n+1)$ with exactly $n+1$ many 0s and 1s can be ordered cyclically so that any two consecutive strings differ in swapping the first bit with a complementary bit at some later position. In his book `The Art of Computer Programming Vol. 4A' Knuth raised a stronger form of this conjecture (Problem 56 in Chapter 7, Section 2.1.3), which requires that the sequence of positions with which the first bit is swapped in each step of such an ordering has $2n+1$ blocks of the same length, and each block is obtained by adding $s=1$ (modulo $2n+1$) to the previous block. In this work, we prove Knuth's conjecture in a more general form, allowing for arbitrary shifts $s\geq 1$ that are coprime to $2n+1$. We also present an algorithm to compute this ordering, generating each new bitstring in $\mathcal{O}(n)$ time, using $\mathcal{O}(n)$ memory in total.

Frequency Conversion Cascade by Crossing Multiple Space and Time Interfaces.

Time varying media recently emerged as promising candidates to fulfill the dream of controlling the wave frequency without nonlinear effects. However, frequency conversion remains limited by the dynamics of the variations of the propagation properties. Here we propose a new concept of space-time cascade to achieve arbitrary large frequency shifts by iterated elementary transformation steps. These steps use an intermediate medium in which wave packets enter and exit through noncommutative space and time interfaces. This concept avoids high frequency or subwavelength demanding metamaterials. Upward and downward frequency conversions are performed. The transmitted energy yield is given by the frequency ratio, regardless of impedence mismatch. We implement this concept with water waves controlled by electrostriction and achieve frequency conversion over 4 octaves.

Numerical Method for Fast Search of the Initial Phase Shift in Phase Images with Arbitrary Interframe Shifts

Numerical Method for Fast Search of the Initial Phase Shift in Phase Images with Arbitrary Interframe Shifts

Wannier Function Perturbation Theory: Localized Representation and Interpolation of Wave Function Perturbation

Thanks to the nearsightedness principle, the low-energy electronic structure of solids can be represented by localized states such as the Wannier functions. Wannier functions are actively being applied to a wide range of phenomena in condensed matter systems. However, the Wannier-functionbased representation is limited to a small number of bands and thus cannot describe the change of wavefunctions due to various kinds of perturbations, which require sums over an infinite number of bands. Here, we introduce the concept of the Wannier function perturbation, which provides a localized representation of wavefunction perturbations. Wannier function perturbation theory allows efficient calculation of numerous quantities involving wavefunction perturbation, among which we provide three applications. First, we calculate the temperature-dependent indirect optical absorption spectra of silicon near the absorption edge nonadiabatically, i.e., differentiating phonon-absorption and phonon-emission processes, and without arbitrary temperature-dependent shifts in energy. Second, we establish a theory to calculate the shift spin conductivity without any band-truncation error. Unlike the shift charge conductivity, an exact calculation of the shift spin conductivity is not possible within the conventional Wannier function methods because it cannot be obtained from geometric quantities for low-energy bands. We apply the theory to monolayer WTe$_2$. Third, we calculate the spin Hall conductivity of the same material again without any band-truncation error. Wannier function perturbation theory is a versatile method that can be readily applied to calculate a wide range of quantities related to various kinds of perturbations.

RELATIONAL STATISTICAL CONCEPT AND RANGE

This paper considers the introduction of relational space and time with the specification of simultaneity associated with the unity of the light signal for the whole world. In accordance with the ideas of some physicists, a concept is proposed, in fact, of absolute time, interpreted in a new way and consistent with the theory of action at a distance. This is ensured by the invariance of the increment of the relational time relative to arbitrary spatial shifts. This eliminates the ambiguity of the theory when using retarded and advanced potentials. The transition of these constructions to the description in the theory of relativity with the help of appropriate transformations is discussed.

Wave Functional of the Universe and Time

A version of the quantum theory of gravity based on the concept of the wave functional of the universe is proposed. To determine the physical wave functional, the quantum principle of least action is formulated as a secular equation for the corresponding action operator. Its solution, the wave functional, is an invariant of general covariant transformations of spacetime. In the new formulation, the history of the evolution of the universe is described in terms of coordinate time together with arbitrary lapse and shift functions, which makes this description close to the formulation of the principle of general covariance in the classical theory of Einstein’s gravity. In the new formulation of quantum theory, an invariant parameter of the evolutionary time of the universe is defined, which is a generalization of the classical geodesic time measured by a standard clock along time-like geodesics.

Competition of spatially inhomogeneous phases in systems with nesting-driven spin-density wave state

In this work we study zero-temperature phases of the anisotropic Hubbard model on a three-dimensional cubic lattice in a weak coupling regime. It is known that, at half-filling, the ground state of this model is antiferromagnetic (commensurate spin-density wave). For non-zero doping, various types of spatially inhomogeneous phases, such as phase-separated states and the state with domain walls ("soliton lattice"), can emerge. Using the mean-field theory, we evaluate the free energies of these phases to determine which of them could become the true ground state in the limit of small doping. Our study demonstrates that the free energies of all discussed states are very close to each other. Smallness of these energy differences suggests that, for a real material, numerous factors, unaccounted by the model, may arbitrary shift the relative stability of the competing phases. This further implies that purely theoretical prediction of the true ground state in a particular many-fermion system is unreliable.

Unlearning the ABCs of Tympanometry.

Interpretation of tympanometry commonly relies on the historical convention of classifying findings according to large and arbitrary threshold shifts of tympanometric peak pressure (TPP). This convention had value for prior generations of otolaryngologists in diagnosing severe, chronic middle ear disease requiring surgical intervention but may not be well suited for the present-day evaluation of less severe disease. The existing definition of a type C curve (less than -100 daPa) is likely insensitive to detect subtle abnormalities, including some presentations of obstructive eustachian tube dysfunction. The accuracy of clinical diagnosis may be improved by reporting the absolute values of TPP and moving beyond classification according to arbitrary thresholds.

Tunable Acoustic Metasurface for Three-Dimensional Wave Manipulations

Acoustic metasurfaces display unprecedented potential for their unique and flexible capabilities of wave front manipulations. Although rapid progress and significant developments have been achieved in this field, it still remains a significant challenge to obtain an acoustic metasurface that can perform different functions in three-dimensional (3D) space, as desired. Here, a tunable acoustic metasurface composed of Helmholtz-resonator-like digital-coding meta-atoms is presented to overcome the limitation and realize 3D dynamic wave manipulations. The digital meta-atom is constructed from two cylindrical cavities controlled by a motor. By changing the depth of the bottom cavity with the motor automatically, the reflection phase of the meta-atom can be adjusted continuously over the range of nearly 360\ifmmode^\circ\else\textdegree\fi{}, realizing the required digital states. To build the relationship between the digital-coding profiles and scattering patterns, convolution and addition operations are implemented. Based on such operations, various fascinating functionalities, such as arbitrary scattering-pattern shift and superposition of different scattering beams, are achieved. This study paves the way for studying acoustic metasurfaces from the digital perspective and provides efficient methods for realizing spatial acoustic wave control.

Prosociality in Majority Decisions: A Laboratory Experiment on the Robustness of the Uncovered Set

AbstractSocial choice theory demonstrates that majority rule is generically indeterminate. However, from an empirical perspective, large and arbitrary policy shifts are rare events in politics. The uncovered set (UCS) is the dominant preference-based explanation for the apparent empirical predictability of majority rule in multiple dimensions. Its underlying logic assumes that voters act strategically, considering the ultimate consequences of their actions. I argue that all empirical applications of the UCS rest on an incomplete behavioral model assuming purely egoistically motivated individuals. Beyond material self-interest, prosocial motivations offer an additional factor to explain the outcomes of majority rule. I test my claim in a series of committee decision-making experiments in which I systematically vary the fairness properties of the policy space while keeping the location of the UCS constant. The experimental results overwhelmingly support the prosociality explanation.

Optimal Third-Harmonic Current Injection for Asymmetrical Multiphase Permanent Magnet Synchronous Machines

This article proposes a modeling approach and an optimization strategy to exploit a third-harmonic current injection for the torque enhancement in multiphase isotropic permanent magnet synchronous machines with nonsinusoidal back electromotive forces. The modeling approach is based on a proper vector space decomposition and on the associated rotational transformation, aimed to properly select a set of stator current space vectors to be controlled. It is presented for a generic (i.e., asymmetrical, with an arbitrary angular shift) winding configuration. The injection strategy is related to the choice of a constant synchronous current set aimed at minimizing the average stator winding losses for a given reference torque by using the first and the third spatial harmonics of the air-gap flux density. The optimal solution has been found analytically and has been developed in detail for a selected set of asymmetrical winding configurations. Both the numerical and experimental results are in good agreement with the theoretical analysis.

Is it possible to detect a true rotation axis of the temporomandibular joint with common pantographic methods? A fundamental kinematic analysis

The location of the terminal hinge axis of the temporomandibular joint is still a very wide-spread procedure in dentistry in order to replicate the movement in various articulator devices. Especially pantographic methods are claimed to provide accurate measurements and, additionally, are seen to be able to separate a pure rotation of the joint from a movement with an arbitrary combined shift and rotation. In the latter application, these methods were used in a lot of studies as a reference standard. The aim of this study was to analyze, whether common pantographic methods in general are able to distinguish between a pure rotation and a movement with rotational and translational portions. The mathematical proof of this analysis was done with theoretical kinematic considerations and compared with computer simulations. The results show for the first time that there exist combinations of rotational and translational movements of the temporomandibular joint which cannot be separated from pure rotational movements using actual pantographic methods. Even more, the consequence is a shifted location of the (combined) finite center (axis) of rotation in comparison to the true center (axis) of rotation: in case of a translational portion of only 1 mm, this is a displacement of around ±6 mm and, in case of 2 mm translation, a displacement of ±12 mm. This finding necessitates a critical reinterpretation of former studies using pantographic methods as a reference standard. Further, under some circumstances it may also affect the applicability of articulator concepts and the interpretation of functional signs.

Pockels-effect-based adiabatic frequency conversion in ultrahigh-Q microresonators.

Adiabatic frequency conversion has some key advantages over nonlinear frequency conversion. No threshold and no phase-matching conditions need to be fulfilled. Moreover, it exhibits a conversion efficiency of 100 % down to the single-photon level. Adiabatic frequency conversion schemes in microresonators demonstrated so far suffer either from low quality factors of the employed resonators resulting in short photon lifetimes or small frequency shifts. Here, we present an adiabatic frequency conversion (AFC) scheme by employing the Pockels effect. We use a non-centrosymmetric ultrahigh-Q microresonator made out of lithium niobate. Frequency shifts of more than 5 GHz are achieved by applying just 20 V to a 70-µm-thick resonator. Furthermore, we demonstrate that with the same setup positive and negative frequency chirps can be generated. With this method, by controlling the voltage applied to the crystal, almost arbitrary frequency shifts can be realized. The general advances in on-chip fabrication of lithium-niobate-based devices make it feasible to transfer the current apparatus onto a chip suitable for mass production.

Iterative Learning Control for High-Order Systems With Arbitrary Initial Shifts

In this paper, two iterative learning control methods are proposed for the different high-order systems with arbitrary initial shifts. The tracking errors caused by nonzero initial shifts are easily detected when applying conventional learning algorithms. But this defect is overcome through applying a step-by-step rectifying controller with initial rectifying action introduced in a small interval. It demonstrates the improvement of tracking performance and shows the robustness with respect to the stochastic initial shifts. Finally, simulation results are presented to illustrate the effectiveness of the stated algorithms.