Space Translation Research Articles

Accelerated reference systems in AdS space

We consider reference systems of uniformly accelerated observers in anti-de Sitter space. We construct coordinate transformations for the transition from an inertial reference system to a uniformly accelerated reference system for all acceleration values, both greater and less than critical. The basis for the construction are the Beltrami coordinates, natural coordinates for describing a uniformly accelerated motion because geodesics in anti-de Sitter space in these coordinates become straight lines, i.e., can be described by linear functions. Because translations of space–time coordinates in anti-de Sitter space are non-Abelian, a nontrivial problem of defining the comoving inertial reference system arises. Constructing the coordinate system of an accelerated observer using this auxiliary comoving inertial reference system requires additional transformations that not only equalize the velocities of the two systems but also equalize the system origins. The presence of a critical acceleration in anti-de Sitter space leads to a difference in explicit expressions in passing to an accelerated coordinate system for accelerations greater and less than critical.

Single-mode displacement sensor

We show that one can determine both parameters of a displacement acting on an oscillator with an accuracy which scales inversely with the square root of the number of photons in the oscillator. Our results are obtained by using a grid state as a sensor state for detecting small translations in phase space (displacements). Grid states were first proposed in (see https://doi.org/10.1103/PhysRevA.64.012310 ) for encoding a qubit into an oscillator: an efficient preparation protocol of such states, using a coupling to a qubit, was developed in (see https://doi.org/10.1103/PhysRevA.93.012315 ). We compare the performance of the grid state with the quantum compass or cat code state and place our results in the context of the two-parameter quantum Cram\'er-Rao lower bound on the variances of the displacement parameters. We show that the accessible information about the displacement for a grid state increases with the number of photons in the state when we measure and prepare the state using a phase estimation protocol. This is in contrast with the accessible information in the quantum compass state which we show is always upper bounded by a constant, independent of the number of photons. We present numerical simulations of a phase estimation based preparation protocol of a grid state in the presence of photon loss, nonlinearities and qubit measurement, using no post-selection, showing how the two effective squeezing parameters which characterize the grid state change during the preparation. The idea behind the phase estimation protocol is a simple maximal-information gain strategy.

Methods for monitoring and measurement of protein translation in time and space.

Regulation of protein translation constitutes a crucial step in control of gene expression. In comparison to transcriptional regulation, however, translational control has remained a significantly under-studied layer of gene expression. This trend is now beginning to shift thanks to recent advances in next-generation sequencing, proteomics, and microscopy based methodologies which allow accurate monitoring of protein translation rates, from single target messenger RNA molecules to genome-wide scale studies. In this review, we summarize these recent advances, and discuss how they are enabling researchers to study translational regulation in a wide variety of in vitro and in vivo biological systems, with unprecedented depth and spatiotemporal resolution.

Geometric inequalities from phase space translations

We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution operation: the latter maps a classical probability distribution on phase space and a quantum state to a quantum state. We show that this inequality also gives rise to several related inequalities whose counterparts are well-known in the classical setting: in particular, it implies an entropy power inequality for the mentioned convolution operation as well as the isoperimetric inequality and establishes concavity of the entropy power along trajectories of the quantum heat diffusion semigroup. As an application, we derive a Log-Sobolev inequality for the quantum Ornstein-Uhlenbeck semigroup and argue that it implies fast convergence towards the fixed point for a large class of initial states.

A computationally efficient 3D/2D registration method based on image gradient direction probability density function

Three-dimensional (3D) to two-dimensional (2D) registration is an essential problem in many medical applications. This problem aims at finding the rigid transformation parameters to match the projected image of a 3D model to the real one to estimate the 3D pose of the anatomical model. This class of image registration is computationally intensive due to the large number of solution assessments necessary to search the complex solution space. Moreover, the convergence of the solution process is contingent on a manual initialization of the solution close to the optimal solution. In this paper, we address both of these challenges by introducing a registration method which is significantly faster and less sensitive to initialization than existing methods. The method explores the properties of image gradient probability density function for registration and uses a weighted histogram of image gradient directions (WHGD) as the image feature. This simplifies the computation by searching the parameter space (rotations and translations) sequentially rather than simultaneously. Our experiments demonstrated that the proposed method was able to achieve sub-millimeter and sub-degree accuracy with 5% of the solution assessments needed by an established existing method. The accuracy was not sensitive to the initial solution as long as it was within 90° and 30mm of the true registration, which is a substantial improvement over the existing methods.

Equivalence Conditions of Two Bézier Curves in the Euclidean Geometry

Let G be the group M(n) generated by all orthogonal transformations and translations of the n-dimensional Euclidean space or G be the subgroup of M(n) generated by rotations and translations of \(R^{n}\). This paper presents the conditions of G-equivalence for two Bezier curves in \(R^{n}\) of degree m, where \(m\ge 1\). Moreover, two minimal complete systems of control G-invariants of a Bezier curve are obtained. The definition of a non-directional Bezier curve is introduced and a complete system of control G-invariants of this curve is obtained. Correlations between elements of the second minimal complete system of control M(n)-invariants are investigated.

Building Socio-Moral Behaviour in Romanian Middle-School Education

Moral and civic education is complex and achieved in time. Students are active subjects of society involved in community life by means of their families, groups of friends but also specific relationships they have with various institutions. Moral development theories are elements that support the illustration and translation of the educational space into the form of skills, moral habits, positive character traits expressed at the level of the school population. Our research demonstrates the importance of using moral and civic education strategies consistent with the curriculum objectives and content, to contribute to the formation of character traits and socio-moral behaviour of students. The theme was researched during the 2015-2016 school year at “G. M. Cancicov” Middle School Bacău and involved the support of 4 headmasters of 6th-grade classes, together with 2 teachers of Civic Culture and Religion teaching at these classes. The research group consisted of 90 students, aged 12-13, of whom 45 are girls and 45 boys. There were applied initial evaluation, formative evaluation and final evaluation tests. Comparing the results from the initial and final evaluations it was found that the students’ situation has improved, most students have translated into practice the theoretical elements accumulated, they built a sense of will and character, as well as moral feelings (friendship, comradeship, respect, etc). From the observations made in various situations it was found that all students have acquired certain moral norms, theoretical aspects were put into practice to a higher degree, students showed more respect towards older, vulnerable people and others, became more polite, with attitudes of openness towards others, regarding punctuality, sincerity and other features as compulsory character traits.

Virtual ring and quantum elements of a classical particle

The fractal equations of mechanics (quantum and classical) are clearly demonstrated to be definitions of an arbitrary potential on a fractal complex number valued surface. The developed approach helps us to show that a translational motion of any rotating compact object (point-like particle) can be equivalently represented by a specific rotation of a virtual ring described in terms of a fractal “wave function”, the model endowing the particle with a set of quantum characteristics including quantization of the ring’s space translation.

Stability, uniqueness and recurrence of generalized traveling waves in time heterogeneous media of ignition type

The present paper is devoted to the study of stability, uniqueness and recurrence of generalized traveling waves of reaction-diffusion equations in time heterogeneous media of ignition type, whose existence has been proven by the authors of the present paper in a previous work. It is first shown that generalized traveling waves exponentially attract wave-like initial data. Next, properties of generalized traveling waves, such as space monotonicity and exponential decay ahead of interface, are obtained. Uniqueness up to space translations of generalized traveling waves is then proven. Finally, it is shown that the wave profile of the unique generalized traveling wave is of the same recurrence as the media. In particular, if the media is time almost periodic, then so is the wave profile of the unique generalized traveling wave.

Analysis of Stability, Local Convergence, and Transformation Sensitivity of a Variant of the Particle Swarm Optimization Algorithm

In this paper, we investigate three important properties (stability, local convergence, and transformation invariance) of a variant of particle swarm optimization (PSO) called standard PSO 2011 (SPSO2011). Through some experiments, we identify boundaries of coefficients for this algorithm that ensure particles converge to their equilibrium. Our experiments show that these convergence boundaries for this algorithm are: 1) dependent on the number of dimensions of the problem; 2) different from that of some other PSO variants; and 3) not affected by the stagnation assumption. We also determine boundaries for coefficients associated with different behaviors, e.g., nonoscillatory and zigzagging, of particles before convergence through analysis of particle positions in the frequency domain. In addition, we investigate the local convergence property of this algorithm and we prove that it is not locally convergent. We provide a sufficient condition and related proofs for local convergence for a formulation that represents updating rules of a large class of PSO variants. We modify the SPSO2011 in such a way that it satisfies that sufficient condition; hence, the modified algorithm is locally convergent. Also, we prove that the original standard PSO algorithm is not sensitive to rotation, scaling, and translation of the search space.

Transformations of asymptotic gravitational-wave data

Gravitational-wave data is gauge dependent. While we can restrict the class of gauges in which such data may be expressed, there will still be an infinite-dimensional group of transformations allowed while remaining in this class, and almost as many different---though physically equivalent---waveforms as there are transformations. This paper presents a method for calculating the effects of the most important transformation group, the Bondi-Metzner-Sachs (BMS) group, consisting of rotations, boosts, and supertranslations (which include time and space translations as special cases). To a reasonable approximation, these transformations result in simple coupling between the modes in a spin-weighted spherical-harmonic decomposition of the waveform. It is shown that waveforms from simulated compact binaries in the publicly available SXS waveform catalog contain unmodeled effects due to displacement and drift of the center of mass, accounting for mode-mixing at typical levels of 1%. However, these effects can be mitigated by measuring the average motion of the system's center of mass for a portion of the inspiral, and applying the opposite transformation to the waveform data. More generally, controlling the BMS transformations will be necessary to eliminate the gauge ambiguity inherent in gravitational-wave data for both numerical and analytical waveforms. Open-source code implementing BMS transformations of waveforms is included along with this paper in the supplemental materials.

R3DG features: Relative 3D geometry-based skeletal representations for human action recognition

Recently introduced cost-effective depth sensors coupled with real-time skeleton extraction algorithms have generated a renewed interest in skeleton-based human action recognition. Most of the existing skeleton-based approaches use either the joint locations or the joint angles to represent the human skeleton. In this paper, we introduce and evaluate a new family of skeletal representations for human action recognition, which we refer to as R3DG features. The proposed representations explicitly model the 3D geometric relationships between various body parts using rigid body transformations, i.e., rotations and translations in 3D space. Using the proposed skeletal representations, human actions are modeled as curves in R3DG feature spaces. Finally, we perform action recognition by classifying these curves using a combination of dynamic time warping, Fourier temporal pyramid representation and support vector machines. Experimental results on five benchmark action datasets show that the proposed representations perform better than many existing skeletal representations. The proposed approach also outperforms various state-of-the-art skeleton-based human action recognition approaches.

PPM Translation, Rotation and Scale in D-Dimensional Space by the Discrete to Continuous Approach

Point pattern matching (PPM), is an important problem arises in many computer visions, pattern recognition and computational geometry fields. This paper presents an important amelioration and generalization of discrete to continuous approach. With a very fast running time, numerically stable, easy to implement and dealing with large PPM applications and fields in d-dimensional space. The power of this approach resides in the passage from the discrete to the continuous, considering the issue in its entity. The experimental results in 2D and 3D show that with these new amelioration, our approach becomes very efficient.

Narratives of Space in the Writing of Five Contemporary Canadian Women Writers of Italian Origin

The purpose of this essay is to analyze the English writing of five Canadian authors of Italian origin – Darlene Madott, Maria Ardizzi, Licia Canton, Rosanna Battigelli and Dorina Michelutti – in terms of how they represent personal and inner spaces as a meaningful focal point for interpreting and reflecting on the dislocated subject’s quest for identity. I will show how they use the idea of compensatory spaces as a literary strategy to portray personal, private or inner spaces to articulate their characters’ processes of accepting or resisting cultural hybridity and multiplicity. The works of fiction I consider here embody the shifting perception of inner or personal spaces in the characters’ lives, and how this defines their spatial relationships with the new country in different terms and at different stages of the migrant’s process of accepting his or her new country. My reading is based on Homi Bhabha’s notions of third space and cultural translation and Michel Foucault’s concept of heterotopic spaces; I define these as compensatory spaces, an idea also rooted in Foucault’s view that heterotopies of compensation represent differences that transcend dichotomies and are open to fluidity. In this paper, the idea of third space addresses the process of cultural translation – understood not only as the positive and dialogic creation of a hybridized subject, but also as a narrative of conflicting personal spaces that gives voice to experiences of cultural dislocation.

Solutions of the focusing nonradial critical wave equation with the compactness property

Consider the focusing energy-critical wave equation in 3, 4 or 5 space dimensions. In a previous paper, we proved that any solution which is bounded in the energy space converges, along a sequence of times and in some weak sense, to a solution with the compactness property, that is a solution whose trajectory stays in a compact subset of the energy space up to space translation and scaling. It is conjectured that the only solutions with the compactness properties are stationary solutions and solitary waves that are Lorentz transforms of the formers. In this note we prove this conjecture with an additional non-degeneracy assumption related to the invariances of the elliptic equation satisfied by stationary solutions. The proof uses a standard monotonicity formula, modulation theory, and a new channel of energy argument which is independent of the space dimension.

Monitoring Translation in Space and Time with Ribosome Profiling

Monitoring Translation in Space and Time with Ribosome Profiling

Encoding a qubit into a cavity mode in circuit QED using phase estimation

Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into an oscillator such that the qubit is protected against small shifts (translations) in phase space. The idea underlying this encoding is that error processes of low rate can be expanded into small shift errors. The qubit space is defined as an eigenspace of two mutually commuting displacement operators $S_p$ and $S_q$ which act as large shifts/translations in phase space. We propose and analyze the approximate creation of these qubit states by coupling the oscillator to a sequence of ancilla qubits. This preparation of the states uses the idea of phase estimation where the phase of the displacement operator, say $S_p$, is approximately determined. We consider several possible forms of phase estimation. We analyze the performance of repeated and adapative phase estimation as the simplest and experimentally most viable schemes given a realistic upper-limit on the number of photons in the oscillator. We propose a detailed physical implementation of this protocol using the dispersive coupling between a transmon ancilla qubit and a cavity mode in circuit-QED. We provide an estimate that in a current experimental set-up one can prepare a good code state from a squeezed vacuum state using $8$ rounds of adapative phase estimation, lasting in total about $4 \mu$ sec., with $94\%$ (heralded) chance of success.

Pictorial Calculus for Isometries

In this paper a new graphical calculus for operating with isometries of low dimensional spaces is proposed. It generalizes a well-known graphical representation of vectors and translations in an affine space. Instead of arrows, we use arrows framed with affine subspaces at their end points. The head to tail addition of vectors and translations is generalized to head to tail composition rules for isometries. The material of this paper is elementary and can be used even in the framework of high-school geometry.

Real-time implementation of various colour space models

The colour space translation plays a significant task in pre-processing stage of digital image processing. Colour conversion can improve the quality of images. The objective is to convert one colour space to another and the inverse of same. Various colour space conversions are used such as RGB ← → HSV, RGB ← → HSL, RGB ← → HSI, RGB ← → YUV and RGB ← → YCbCr. The conversion process can be done using colour space conversion algorithm. The colour space conversion is used in various applications such as commercial, multimedia, computer vision, visual tracking systems etc. The hardware realisation of colour space conversion models can be implemented by using Xilinx system generator on field programmable gate array spartan-6. Finally, the above colour space conversion models are implemented in real-time then tabulated in terms of percentage resources utilisation and power required. The recommended RGB ← → HSV colour space conversion utilises 21% of DSP48A1s chips and required 0.354 watts of power. By means of colour conversion, the efficiency and speed are increased.

Bosons with long-range interactions on two-leg ladders in artificial magnetic fields

Motivated by experiments exploring the physics of neutral atoms in artificial magnetic fields, we study the ground state of bosons interacting with long range dipolar interactions on a two-leg ladder. Using two complimentary variational approaches, valid for weak interactions, we find rich physics driven by the long range forces. Generically, long range interactions tend to destroy the Meissner phase in favor of modulated density wave phases. Nearest neighbor interactions produce a novel interleg charge density wave phase, where the total density remains uniform, but the density on each leg of the ladder is modulating in space, out-of-phase with one another. At weak magnetic fields, next nearest neighbor interactions lead to a fully modulated biased ladder phase, where all the particles are on one leg of the ladder, and the density is modulating in space. This state simultaneously breaks $Z_{2}$ reflection symmetry and $U(1)$ symmetry associated with translation in real space. For values of the flux near $\phi = \pi$, we find that a switching effect occurs for arbitrarily weak interactions, where the density modulates in space, but the chiral current changes sign on every plaquette. Arbitrarily weak attractive interactions along the rungs destroy the Meissner phase completely, in favor of a modulated density wave phase. Varying magnetic field produces a cascade of first order transitions between modulated density wave states with different wave-vectors, which manifests itself as discrete jumps in the chiral current. Polarizing the dipoles along the ladder direction yields a region of phase space where a stable biased ladder phase occurs even at arbitrarily weak magnetic fields. We discuss the experimental consequences of our work, in particular, how the interleg charge density wave can manifest itself in recent experiments on bosons in synthetic dimensions.