Specific Transformation Research Articles

SAVE: Encoding spatial interactions for vision transformers

Transformers have achieved impressive performance in visual tasks. Position encoding, which equips vectors (elements of input tokens, queries, keys, or values) with sequence specificity, effectively alleviates the lack of permutation relation in transformers. In this work, we first clarify that both position encoding and additional position-specific operations will introduce positional information when participating in self-attention. On this basis, most existing position encoding methods are equivalent to special affine transformations. However, this encoding method lacks the correlation of vector content interaction. We further propose Spatial Aggregation Vector Encoding (SAVE) that employs transition matrices to recombine vectors. We design two simple yet effective modes to merge other vectors, with each one serving as an anchor. The aggregated vectors control spatial contextual connections by establishing two-dimensional relationships. Our SAVE can be plug-and-play in vision transformers, even with other position encoding methods. Comparative results on three image classification datasets show that the proposed SAVE performs comparably to current position encoding methods. Experiments on detection tasks show that the SAVE improves the downstream performance of transformer-based methods. Code is available at https://github.com/maxiao0234/SAVE.

Comprehensive Insight into Regular Damped Oscillatory Structures from Effective Electromagnetic Form Factor Data of Some Mesons and Nucleons

Regular damped oscillatory structures from the “effective” electromagnetic form factors of the hadrons h=π±,K±,K0,p,n were investigated. The “effective” electromagnetic form factor behaviors were calculated from the experimental data on the total cross-sections σtot(e+e−→hh¯) with errors. The apparent oscillations were observed for the first time for the proton, and we show, also taking other hadrons into consideration, that they are an arbitrary artifact resulting from a very simplistic theoretical description based on an elementary three-parameter model. If the data are described by a more appropriate and physically well-founded Unitary and Analytic model, then the oscillations disappear. In spite of this, if the three-parameter model is used to describe the “effective” electromagnetic form factor data, an interesting phenomenon is observed. The oscillations are opposite for particles which form an isospin doublet. By using the physically well-founded Unitary and Analytic model, it is demonstrated that this feature originates from the special transformation properties of the electromagnetic current of the corresponding particles in the isotopic space.

Integrated Jacobi elliptic function solutions to the [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation by utilizing new solutions of the elliptic equation of order six

In this research, the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation ((3+1)-GKPE) that expresses various nonlinear phenomena was studied. An extended Jacobi elliptic function expansion method (JEFEM) was developed by considering new solutions for the Jacobi elliptic equation of order six. Then the extended method was applied to the (3+1)-GKPE, where new exact Jacobi elliptic function solutions were obtained. This equation is of particular interest as it required a special transformation in order to apply the JEFEM. Moreover, some of the solutions are shown graphically.

Adaptive Sampling for Signals Associated with the Special Affine Fourier Transform

Adaptive sampling is inspired by the working principle of biological neurons, which converts the amplitude information of the received signal into a time sequence through a time encoding machine (TEM). The article mainly studies uniform sampling and adaptive sampling of non-bandlimited signals in two kinds of function spaces associated with the special affine Fourier transform (SAFT). Firstly, based on the stability characterization of the basis functions, we prove the existence of orthogonal projection operators in function spaces associated with the canonical convolution and the SAFT-convolution, respectively. Secondly, uniform sampling theorems are established for two kinds of signals living in the proposed function spaces. Finally, adaptive sampling schemes based on the crossing TEM and the integrate-and-fire TEM are studied. Moreover, the corresponding iterative reconstruction algorithms with exponential convergence are provided.

Optical solitons and their propagations in a time-varying coefficient modified nonlinear Schrödinger equation with non-zero boundary conditions via Riemann–Hilbert method

In this article, a time-varying coefficient modified nonlinear Schrödinger equation (tvcmNLSE) with non-zero boundary conditions (NZBCs) at infinity, phase term of which contains time-varying coefficients, is proposed to describe the nonlinear propagation behavior of optical pulses in non-uniform optical fibre. Meanwhile, the Riemann–Hilbert method (RHM) for the tvcmNLSE with NZBCs is presented for the first time. Specifically, a special transformation is constructed to convert the tvcmNLSE with NZBCs into the case with constant NZBCs, and the associated asymptotic spectral problem (ASP) is obtained. By introducing a suitable two-piece Riemann surface to map the original spectral parameter into a single-valued one, and analyzing the ASP, we construct the corresponding Jost solutions and spectral matrix, and sequentially analyze their analytical, symmetric, and asymptotic properties. Then, a generalized Riemann–Hilbert problem (RHP) is established that relates to the converted tvcmNLSE with constant NZBCs. Using the reconstruction formula, we further derive N-soliton solution with NZBCs in the absence of reflection potential, and analyze the dynamic characteristics of single and double solitons. Most notably, by modulating discrete spectral points (DSPs) and time-varying coefficients, we discover some previously unreported new waveforms, such as parabolic and periodic solitons with NZBCs. These waveforms have important implications in both theory and practice. In addition, the influences of different time-varying coefficients, NZBCs, and DSPs on soliton solutions are also discussed and analyzed. This study shows that the selection of time-varying coefficients, distribution of DSPs, and constraints from NZBCs all have significant impacts on the properties of soliton solutions.

A Very Fast Reasoning in Favor of the Poincare Group, or of Minkowskian Rather than Euclidean Line Elements

1. We present a very fast derivation of Minkowski’s line element which is the geometric foundation not only of the special Lorentz transformation but of the whole Poincar’e group aka inhomogeneous Lorentz group [1]. The Euclidean line element is excluded using the wave equation and Einstein’s special principle of relativity (Einstein’s first postulate) [2]. For doing so, it is not necessary, 1. to assume the speed of light to be independent of the motion of the observer (Einstein’s second postulate [2], 2. to synchronize watches, 3. to interrelate the coordinate systems of the inertial frames involved; their relative velocity (and hence reciprocity [3]) even plays not any role in the derivation. 4. to make any assumption about the properties of the underlying coordinate transformation such as linearity, uniqueness etc

TransURL: Improving malicious URL detection with multi-layer Transformer encoding and multi-scale pyramid features

While machine learning progress is advancing the detection of malicious URLs, advanced Transformers applied to URLs face difficulties in extracting local information, character-level information, and structural relationships. To address these challenges, we propose a novel approach for malicious URL detection, named TransURL, that is implemented by co-training the character-aware Transformer with three feature modules—Multi-Layer Encoding, Multi-Scale Feature Learning, and Spatial Pyramid Attention. This special Transformer allows TransURL to extract embeddings that contain character-level information from URL token sequences, with three feature modules contributing to the fusion of multi-layer Transformer encodings and the capture of multi-scale local details and structural relationships. The proposed method is evaluated across several challenging scenarios, including class imbalance learning, multi-classification, cross-dataset testing, and adversarial sample attacks. The experimental results demonstrate a significant improvement compared to the best previous methods. For instance, it achieved a peak F1-score improvement of 40% in class-imbalanced scenarios, and exceeded the best baseline result by 14.13% in accuracy in adversarial attack scenarios. Additionally, we conduct a case study where our method accurately identifies all 30 active malicious web pages, whereas two pior SOTA methods miss 4 and 7 malicious web pages respectively. The codes and data are available at: https://github.com/Vul-det/TransURL/.

Nonlinear oscillators dynamics using optimal and modified homotopy perturbation method

This study investigates the several strongly nonlinear oscillators (Van der Pol, Duffing and Rayleigh) for which we have applied the most powerful and advanced optimal semi-analytical technique: optimal and modified homotopy perturbation method (OM-HPM) for the convergent semi-analytical series solution. The numerical simulation demonstrates the high accuracy of the OM-HPM, which is straightforward, does not require any domain decomposition, special transformation, or pade approximations to get the convergent series solution. The key features for the high accuracy of the OM-HPM lies on the best optimal auxiliary linear operator. Therefore, OM-HPM offering a valuable tool for engineers and researcher to analyze the complex nonlinear oscillator.

Methods to mitigate voltage-rise issues in transmission systems

This paper proposes some novel methods for mitigating undesired voltage rises in modern-day power systems. Some older approaches are also revisited in the light of new developments including the proliferation of power-electronic interfaced equipment. The analysis is performed using both power flow technique as well as long-term simulation employing quasi-steady-state approximation of short-term dynamics. Guidelines and mitigation countermeasures that may be utilized during either system planning or operation are investigated, such as optimal placement of new reactor installations, special transformer load-tap-changer (LTC) controls and reactive power absorption by renewable energy sources, such as wind farms connected through power converters in distribution feeders. Several case studies are investigated in two test systems: a sub-transmission area of the French Transmission Grid, and the Hellenic transmission power system, for which a number of different operating points is considered.

Random walk algorithms for solving nonlinear chemotaxis problems

Abstract Random walk based stochastic simulation methods for solving a nonlinear system of coupled transient diffusion and drift-diffusion equations governing a two-component chemotaxis process are developed. The nonlinear system is solved by linearization, the system is evolved in time, by small time steps, where on each step a linear system of equations is solved by using the solution from the previous time step. Three different stochastic algorithms are suggested, (1) the global random walk on grid (GRWG), (2) a randomized vector algorithm (RVA) based on a special transformation of the original matrix to a stochastic matrix, and (3) a stochastic projection algorithm (SPA). To get high precision results, these methods are combined with an iterative refinement method.

Two-Sided Clifford-Valued Special Affine Fourier Transform: Properties and Associated Convolution

The primary focus of the present study is to analyse the Clifford-valued functions by introducing the notion of a two-sided Clifford-valued special affine Fourier transform in L2(Rn,Cl0,n). Firstly we propose the novel definition of the Clifford-valued special affine Fourier transform and derive its fundamental properties which include inversion formula, translation covariance, scaling covariance and Plancherel formula. Subsequently we introduce the boundedness, continuity and differentiation theorems for the proposed transform. Finally we culminate our investigation by deriving the convolution for this newly proposed transform.

Conformally related vacuum gravitational waves and their symmetries

A special conformal transformation which carries a vacuum gravitational wave into another vacuum one is built by using Möbius-redefined time. It can either transform a globally defined vacuum wave into a vacuum sandwich wave, or carry the gravitational wave into itself. The first type, illustrated by linearly and circularly polarised vacuum plane gravitational waves, permutes the symmetries and the geodesics. Our second type is a pp wave with conformal O(1, 2) symmetry. An example inspired by molecular physics which seems to have escaped attention so far is an anisotropic generalisation of the familiar inverse-square profile and is reminiscent of Aichelburg-Sexl ultraboosts. The particle can escape, or perform circular periodic motion, or fall into the singularity.

A Sinc Rule for the Hankel Transform

This paper deals with the computation of the Hankel transform by means of the sinc rule applied after a special exponential transformation. An error analysis, particularly suitable for meromorphic functions, together with the parameter selection strategy, is considered. A prototype algorithm for automatic integration is also presented.

Special affine Fourier transform of tempered distributions and pseudo-differential operators

The primary aim is to develop a new class of pseudo-differential operators by incorporating the Special Affine Fourier Transform (SAFT) and some of its fundamental properties in Schwartz and tempered distribution space. The secondary aim is to explore the utility of the SAFT in constructing a new generalized heat equation and derive its analytical solution. Further, we have investigated particular cases of the proposed generalized heat equation. Furthermore, we have visually illustrated solutions of this equation via MATLAB R2023b.

First-order quantum phase transition in the two-qubit squeezed Rabi model

We study the ground state of the two-qubit squeezed Rabi model. Two special transformations are found to diagonalize the system Hamiltonian when each qubit’s frequency is close to the field frequency, where both the squeezing and counterrotating-wave interactions are removed, leading to an effective integrable Hamiltonian. The analytical ground state is determined and matches with numerical solutions well for a range of squeezing strengths and qubit-field detunings in the ultrastrong-coupling regime. We demonstrate that the ground state exhibits a first-order quantum phase transition at a phase boundary linearly induced by the squeezed light. We characterize the two-qubit negativity analytically and find that its two-qubit entanglement increases with the increasing squeezing strength nonlinearly. The average photon numbers of the field mode and variances of position and momentum quadratures are also analyzed and discovered to have a nonlinear relation with the squeezing strength. Finally, we discuss the experimental scheme and realization possibility of the predicted results.

Nonuniform Sampling in Lp-Subspaces Associated with the Multi-Dimensional Special Affine Fourier Transform

In this paper, the sampling and reconstruction problems in function subspaces of Lp(Rn) associated with the multi-dimensional special affine Fourier transform (SAFT) are discussed. First, we give the definition of the multi-dimensional SAFT and study its properties including the Parseval’s relation, the canonical convolution theorems and the chirp-modulation periodicity. Then, a kind of function spaces are defined by the canonical convolution in the multi-dimensional SAFT domain, the existence and the properties of the dual basis functions are demonstrated, and the Lp-stability of the basis functions is established. Finally, based on the nonuniform samples taken on a dense set, we propose an iterative reconstruction algorithm with exponential convergence to recover the signals in a Lp-subspace associated with the multi-dimensional SAFT, and the validity of the algorithm is demonstrated via simulations.

An electrophoretic mobility shift assay using the protein isolated from host plants

BackgroundThe electrophoretic mobility shift assay (EMSA) is a common technology to detect DNA-protein interactions. However, in most cases, the protein used in EMSA is obtained via prokaryotic expression, and rarely from plants. At the same time, the proteins expressed from prokaryotic systems usually cannot fold naturally and have no post translationally modification, which may affect the binding of proteins to DNA.ResultsHere, we develop a technique to quickly isolate proteins of interest from host plants and then analyze them using fluorescent EMSA. This technology system is called: protein from plants fluorescent EMSA method (PPF-EMSA). In PPF-EMSA, a special transient transformation method is employed to transiently deliver genes into the plant, enabling efficient synthesis the encoded proteins. Then, the target protein is isolated using immunoprecipitation, and the DNA probes were labeled with cyanine 3 (Cy3). Both fluorescent EMSA and super-shift fluorescent EMSA can be performed using the proteins from plants. Three kinds of plants, Betula platyphylla, Populus. davidiana×P. bolleana and Arabidopsis thaliana, are used in this study. The proteins isolated from plants are in a natural state, can fold naturally and are posttranslationally modified, enabling true binding to their cognate DNAs.ConclusionAs transient transformation can be performed quickly and not depended on whether stable transformation is available or not, we believe this method will have a wide application, enabling isolation of proteins from host plant conveniently.

Bubble universe from flat spaces

We show by matching two flat spaces one in Minkowski coordinates ( empty space) and the other in Minkowski coordinates after a special conformal transformation (also empty space) through a bubble with positive and constant surface tension, that the motion of the bubble is hyperbolic. If the surface tension is very big the initial size of the bubble is as small as we wish, so that we can indeed obtain an infinite universe out of empty spaces. The induced space in the bubble is de Sitter type.

The new kink type and non-traveling wave solutions of (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

In this paper, the new solitary wave solutions of the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation are obtained by Lie group symmetry method and the extended homoclinic test approach. Firstly, the equation can be reduced to (1+1)-dimensional partial differential equation by Lie group symmetry, and corresponding bilinear forms of the equation are given by symmetry functions. Secondly, the extended homoclinic test approach is employed to obtain the new kink type and singular solitary wave solutions. In addition, some new traveling and non-traveling wave solutions with arbitrary functions and oscillating tail are investigated through the special transformations for the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation.

A Proposal for method of cold nuclear fusion, based on new Axioms and Laws

It is known that the Classical field theory is based on 1 basic Axiom set by Maxwell (1864). This basic Axiom describes a field with movement along a closed loop and with constant speed. It is an ideal foundation for describing an Electromagnetic Field, but it is not suitable for other more complex fields with variable speed and different accelerations. The author has proposed a more general Theory of Extended Field which consists of 2 Axioms and 8 Laws. New Axiom1 describes a structure of field with movement along open loop or open vortex with variable speed. New Axiom2 describes two mutual orthogonal structures of fields which work in resonance. This new Theory leads to the following results: movement in a closed loop is replaced with movement in an open loop or vortex; evenly movement is replaced with unevenly movement (decelerated or accelerated) ; during its movement decelerating vortex emits primary free cross vortices, while accelerating vortices suck in of this same primary free cross vortices; movement in 2D is transformed into the movement in 3D; a transverse vortex in 2D generates a longitudinal vortex in 3D through a special transformation and vice versa - a longitudinal vortex in 3D through another special transformation generates the cross vortex in 2D. Now the author proposes to use a longitudinal accelerating vortex for cold fusion. With a force proportional to the positive acceleration, it will suck in both vortices and atoms - in this case the isotope of hydrogen (deuterium). The accelerator vortex sucks in and sticks two of all the deuterium, which will form helium in an exothermic reaction with the release of a lot of heat. A longitudinal acceleration vortex can be generated by applying Law 2. A decelerating transverse vortex in plane 2D (moving outside-inward) generates at its center a longitudinal accelerating vortex in 3D perpendicular to the 2D plane. This perpendicular accelerating vortex at the center pulls the transverse decelerating vortex up (against the Gravitational Force) or has quality of Anti-Gravity Force.