Nontrivial Factor Research Articles

New integrable RG flows with parafermions

We consider irrelevant deformations of massless RSOS scattering theories by an infinite number of higher [TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}]s operators which introduce extra non-trivial CDD factors between left-movers and right-movers. It is shown that the resulting theories can be UV complete after bypassing typical Hagedorn-like singularities if the coefficients of the deformations are fine-tuned. By classifying all integrable cases, we have discovered a new UV complete QFT associated to the Mp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{M}}_p $$\\end{document} (p ≥ 3) minimal CFT based on the integrable structure of the RSOS scattering theory. This new theory is the massless ℤp−1 parafermionic sinh-Gordon (PShG) model with a self-dual coupling constant. This correspondence is confirmed by showing that the scale-dependent vacuum energies computed by the thermodynamic Bethe ansatz derived from the S-matrices match those from the quantization conditions for the PShG models using the reflection amplitudes.

Analysis of mapping atomic models to coarse-grained resolution.

Low-resolution coarse-grained (CG) models provide significant computational and conceptual advantages for simulating soft materials. However, the properties of CG models depend quite sensitively upon the mapping, M, that maps each atomic configuration, r, to a CG configuration, R. In particular, M determines how the configurational information of the atomic model is partitioned between the mapped ensemble of CG configurations and the lost ensemble of atomic configurations that map to each R. In this work, we investigate how the mapping partitions the atomic configuration space into CG and intra-site components. We demonstrate that the corresponding coordinate transformation introduces a nontrivial Jacobian factor. This Jacobian factor defines a labeling entropy that corresponds to the uncertainty in the atoms that are associated with each CG site. Consequently, the labeling entropy effectively transfers configurational information from the lost ensemble into the mapped ensemble. Moreover, our analysis highlights the possibility of resonant mappings that separate the atomic potential into CG and intra-site contributions. We numerically illustrate these considerations with a Gaussian network model for the equilibrium fluctuations of actin. We demonstrate that the spectral quality, Q, provides a simple metric for identifying high quality representations for actin. Conversely, we find that neither maximizing nor minimizing the information content of the mapped ensemble results in high quality representations. However, if one accounts for the labeling uncertainty, Q(M) correlates quite well with the adjusted configurational information loss, Îmap(M), that results from the mapping.

Radiation force of a self-focused vortex beam on Rayleigh particles.

The radiation force of a partially coherent self-focusing vortex beam on Rayleigh particles is studied in this paper. According to the generalized Huygens-Fresnel principle and Rayleigh scattering theory, the effects of two main parameters of the beam, namely relative coherence length and non-trivial phase factor, on the self-focusing characteristics and radiation force are respectively researched. We have also conducted a brief analysis of the stability of particle capture using this self-focusing vortex beam. It has been found that changing the values of such parameters can flexibly regulate the self-focusing effect of the beam on propagation so as to effectively adjust the magnitude of the radiation force and trapping range. The results show that such beams can be used to trap and manipulate particles without using a focusing lens. In addition, this beam is able to capture two different refractive index particles, that is, high refractive index particles are captured near the focus, and low refractive index particles are captured on the z-axis. The research results establish a theoretical basis for the application of this novel partially coherent self-focusing vortex beams in optical tweezers technology.

Motion-Compensated MR CINE Reconstruction With Reconstruction-Driven Motion Estimation.

In cardiac CINE, motion-compensated MR reconstruction (MCMR) is an effective approach to address highly undersampled acquisitions by incorporating motion information between frames. In this work, we propose a novel perspective for addressing the MCMR problem and a more integrated and efficient solution to the MCMR field. Contrary to state-of-the-art (SOTA) MCMR methods which break the original problem into two sub-optimization problems, i.e. motion estimation and reconstruction, we formulate this problem as a single entity with one single optimization. Our approach is unique in that the motion estimation is directly driven by the ultimate goal, reconstruction, but not by the canonical motion-warping loss (similarity measurement between motion-warped images and target images). We align the objectives of motion estimation and reconstruction, eliminating the drawbacks of artifacts-affected motion estimation and therefore error-propagated reconstruction. Further, we can deliver high-quality reconstruction and realistic motion without applying any regularization/smoothness loss terms, circumventing the non-trivial weighting factor tuning. We evaluate our method on two datasets: 1) an in-house acquired 2D CINE dataset for the retrospective study and 2) the public OCMR cardiac dataset for the prospective study. The conducted experiments indicate that the proposed MCMR framework can deliver artifact-free motion estimation and high-quality MR images even for imaging accelerations up to 20x, outperforming SOTA non-MCMR and MCMR methods in both qualitative and quantitative evaluation across all experiments. The code is available at https://github.com/JZPeterPan/MCMR-Recon-Driven-Motion.

Factors of HOMFLY polynomials

We study factorizations of HOMFLY polynomials of certain prime knots and oriented links. We begin with a computer analysis of prime knots with at most 12 crossings, finding 17 non-trivial factorizations. Next, we give an irreducibility criterion for HOMFLY polynomials of oriented links associated to 2-connected plane graphs.

Examining the validity and factor structure of the ICD-11 trait domains.

The International Classification of Diseases, 11th Edition (ICD-11) includes a new personality disorder (PD) severity diagnosis that may be further characterized using up to five trait domain specifiers. Most of the previous studies have investigated the ICD-11 trait domains using self-report measures. The present study aimed to validate ICD-11 PD trait domains using a multimethod design in a community mental health sample (n = 336). We conducted two confirmatory factor analyses to examine the factor structure of the ICD-11 PD trait model, utilizing clinician-rating, self-report, and informant-report measures. Finally, we examined associations between clinician-rated, self-reported, and informant-reported ICD-11 trait domains with external criteria, specifically traditional PD symptoms and the five-factor model of normal personality. All clinician-rated, self-reported, and informant-reported domain scores loaded meaningfully on their expected factors when controlling for nontrivial method factors. Generally, the trait domains exhibited meaningful associations with conceptually relevant external criteria, although the anankastia domain exhibited more variability in its pattern of correlations across methods. Overall, the ICD-11 trait domain model shows promising reliability and validity, indicating good progress within the field of PD assessment toward a more useful PD operationalization. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

On Jordan algebras that are factors of Matsuo algebras

We describe all finite connected 3-transposition groups whose Matsuo algebras have nontrivial factors that are Jordan algebras. As a corollary, we show that if $\mathbb{F}$ is a field of characteristic 0, then there exist infinitely many primitive axial algebras of Jordan type $\frac{1}{2}$ over $\mathbb{F}$ that are not factors of Matsuo algebras. As an example, we prove this for an exceptional Jordan algebra over~$\mathbb{F}$.

Machine learning model (RG-DMML) and ensemble algorithm for prediction of students’ retention and graduation in education

Automated prediction of students' retention and graduation in education using advanced analytical methods such as artificial intelligence (AI), has recently attracted the attention of educators, both in theory and in practice. Whereas invaluable insights and theories for measuring and testing the topic have been proposed, most of the existing methods do not technically highlight the non-trivial factors behind the renowned challenges and attrition. To this effect, by making use of two categories of data collected in a higher education setting about students (i) retention (n = 52262) and (ii) graduation (n = 53639); this study proposes a machine learning model - RG-DMML (retention and graduation data mining and machine learning) and ensemble algorithm for prediction of students' retention and graduation status in education. This was done by training and testing key features that are technically deemed suitable for measuring the constructs (retention and graduation), such as (i) the Average grade of the previous high school, and (ii) the Entry/admission score. The proposed model (RG-DMML) is designed based on the cross industry standard process for data mining (CRISP-DM) methodology, implemented using supervised machine learning technique such as K-Nearest Neighbor (KNN), and validated using the k-fold cross-validation method. The results show that the executed model and algorithm based on the Bagging method and 10-fold cross-validation are efficient and effective for predicting the student's retention and graduation status, with Precision (retention = 0.909, graduation = 0.822), Recall (retention = 1.000, graduation = 0.957), Accuracy (retention = 0.909, graduation = 0.817), F1-Score (retention = 0.952, graduation = 0.885) showing significant high accuracy levels or performance rate, and low Error-rate (retention = 0.090, graduation = 0.182), respectively. In addition, by considering the individual features selected through the Wrapper method in predicting the outputs, the proposed model proved more effective for predicting the students' retention status in comparison to the graduation data. The implications of the models' output and factors that impact the effective prediction or identification of at-risk students, e.g., for timely intervention, counselling, decision-making, and sustainable educational practice are empirically discussed in the study.

Bounded rank perturbations of matrix pencils without nontrivial invariant factors

In this paper, we solve the bounded rank perturbation problem for matrix pencils without nontrivial homogeneous invariant factors, over arbitrary fields. The solution is based on reducing the problem to two minimal case matrix pencil completion problems. If there are no nontrivial homogeneous invariant factors involved, these two minimal completion problems allow treating column and row minimal indices separately. This is an example of the utility of completion tools in perturbation problems, when dealing with matrix pencils.

A nonperturbative approach to Hawking radiation and black hole quantum hair

We present a nonperturbative derivation of the subleading order in Hawking radiation based on diffeomorphism symmetry breaking during black hole evaporation. The diffeomorphism group of horizon admits a nontrivial phase factor which encodes information about infalling matter during formation. This nonintegrable phase represents the black hole quantum hair as it arises from the diffeomorphisms that change the physical state of the black hole. During evaporation, the decrease in total area breaks the diffeomorphism symmetry and leads to a dynamical shift in that phase factor. This shift affects the usual Hawking spectrum via dispersion relation and results in the subleading term in Hawking radiation. The higher order terms are locally insensitive to the Unruh radiation due to the lack of diffeomorphism groups on the local Rindler horizon at the low energy scale. This explains the generic difference between Hawking radiation and Unruh radiation. In addition, this phase shift indicates the decrease of the total number of degrees of freedom in horizon phase space during evaporation as past Page time. This enables us to escape from the firewall paradox and provide an account for the resolution to the information paradox.

Enrollment Forecast for Clinical Trials at the Planning Phase with Study-Level Historical Data.

Given progressive developments and demands on clinical trials, accurate enrollment timeline forecasting is increasingly crucial for both strategic decision-making and trial execution excellence. Naïve approach assumes flat rates on enrollment using average of historical data, while traditional statistical approach applies simple Poisson-Gamma model using time-invariant rates for site activation and subject recruitment. Both of them are lack of non-trivial factors such as time and location. We propose a novel two-segment statistical approach based on Quasi-Poisson regression for subject accrual rate and Poisson process for subject enrollment and site activation. The input study-level data are publicly accessible and it can be integrated with historical study data from user's organization to prospectively predict enrollment timeline. The new framework is neat and accurate compared to preceding works. We validate the performance of our proposed enrollment model and compare the results with other frameworks on 7 curated studies.

P System Design for Integer Factorization

Membrane computing is a natural computing branch inspired by the structure of biological cells. The mathematical abstract model of a membrane computing system is called a P System, which is one of the main topics in membrane computing research for the design and verification of a P System. Integer factorization is still a world-class problem and a very important research direction. If a fast method can be found to solve the integer factorization problem, several important cryptographic systems including the RSA public key algorithm will be broken. The aim of this paper is to design a P System capable of implementing integer decomposition, taking advantage of the characteristics of parallelism of P Systems. We construct a process with a main goal to study the modal exponential function f(x) = ax mod N and explore the possible periodic behavior for different values of a. We attempt to compute nontrivial prime factors by the period found and constrain the operation of the P System in polynomial time.

Characterizing absolutely irreducible integer-valued polynomials over discrete valuation domains

Rings of integer-valued polynomials are known to be atomic, non-factorial rings furnishing examples for both irreducible elements for which all powers factor uniquely (absolutely irreducibles) and irreducible elements where some power has a factorization different from the trivial one.In this paper, we study irreducible polynomials F∈Int(R) where R is a discrete valuation domain with finite residue field and show that it is possible to explicitly determine a number S∈N that reduces the absolute irreducibility of F to the unique factorization of FS.To this end, we establish a connection between the factors of powers of F and the kernel of a certain linear map that we associate to F. This connection yields a characterization of absolute irreducibility in terms of this so-called fixed divisor kernel. Given a non-trivial element v of this kernel, we explicitly construct non-trivial factorizations of Fk, provided that k≥L, where L depends on F as well as the choice of v. We further show that this bound cannot be improved in general. Additionally, we provide other (larger) lower bounds for k, one of which only depends on the valuation of the denominator of F and the size of the residue class field of R.

Improving the success rate of quantum algorithm attacking RSA encryption system

Shor’s factorization algorithm (SFA) aims at finding the non-trivial factor of a given composite number, but the algorithm does not always work. In some cases, it has to call back to the beginning of the algorithm to make recalculation. After the analysis of the principle of SFA and the characteristics of RSA public-key cryptography with a series of data calculations, it can be concluded that the random value selected by the algorithm is closely related to whether the obtained period is effective. Therefore, a new optimized scheme is proposed to tackle with this defect from two perspectives: (a) When the a value is a perfect square, the algorithm can be completed with an odd cycle r. (b) When the period r obtained by the randomly selected a value is a multiple of 3, the algorithm can be completed by modifying the decomposition method to relax the requirements for the period without affecting the complexity of the algorithm. Due to the limitations of hardware in applying the quantum algorithms, the classical algorithm is applied to simulate quantum algorithms to test the success rate of decomposition of some composite numbers. The result indicates the effectiveness of the improved algorithm, which significantly reduces the probability of repeated operations to save the quantum circuit resources.

An effective description of charge diffusion and energy transport in a charged plasma from holography

We discuss the physics of sound propagation and charge diffusion in a plasma with non-vanishing charge density. Our analysis culminates the program initiated in [1] to construct an open effective field theory of low-lying modes of the stress tensor and charge current in such plasmas. We model the plasma holographically as a Reissner-Nordström-AdSd+1 black hole, and study linearized fluctuations of longitudinally polarized scalar gravitons and photons in this background. We demonstrate that the perturbations can be decoupled and repackaged into the dynamics of two designer scalars, whose gravitational coupling is modulated by a non-trivial dilatonic factor. The holographic analysis allows us to isolate the phonon mode from the charge diffusion mode, and identify the combination of currents that corresponds to each of them. We use these results to obtain the real-time Gaussian effective action, which includes both the retarded response and the associated stochastic (Hawking) fluctuations, accurate to quartic order in gradients.

On oracle factoring of integers

We present an oracle factorisation algorithm, which in polynomial deterministic time, finds a nontrivial factor of almost all positive integers n based on the knowledge of the number of points on certain elliptic curves in residue rings modulo n.

Chemical diffusion master equation: Formulations of reaction–diffusion processes on the molecular level

The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction–diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112, 49 (2022)]; it can be considered as the master equation for reaction–diffusion processes. The CDME consists of an infinite ordered family of Fokker–Planck equations, where each level of the ordered family corresponds to a certain number of particles and each particle represents a molecule. The equations at each level describe the spatial diffusion of the corresponding set of particles, and they are coupled to each other via reaction operators—linear operators representing chemical reactions. These operators change the number of particles in the system and, thus, transport probability between different levels in the family. In this work, we present three approaches to formulate the CDME and show the relations between them. We further deduce the non-trivial combinatorial factors contained in the reaction operators, and we elucidate the relation to the original formulation of the CDME, which is based on creation and annihilation operators acting on many-particle probability density functions. Finally, we discuss applications to multiscale simulations of biochemical systems among other future prospects.

Foliar water uptake in Pinus species depends on needle age and stomatal wax structures.

Foliar water uptake (FWU) has been documented in many species and is increasingly recognized as a non-trivial factor in plant-water relationships. However, it remains unknown whether FWU is a widespread phenomenon in Pinus species, and how it may relate to needle traits such as the form and structure of stomatal wax plugs. In this contribution, these questions were addressed by studying FWU in current-year and 1-year-old needles of seven Pinus species. We monitored FWU gravimetrically and analysed the needle surface via cryo-scanning electron microscopy. Additionally, we considered the effect of artificial wax erosion by application of the surfactant Triton X-100, which is able to alter wax crystals. The results show for all species that (1) FWU occurred, (2) FWU is higher in old needles compared to young needles and (3) there is substantial erosion of stomatal wax plugs in old needles. FWU was highest in Pinus canariensis, which has a thin stomatal wax plug. Surfactant treatment enhanced FWU. The results of this study provide evidence for (1) widespread FWU in Pinus, (2) the influence of stomatal wax plugs on FWU and (3) age-related needle surface erosion.

Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups

A characterization is given for the factorizations of almost simple groups with a solvable factor. It turns out that there are only several infinite families of these nontrivial factorizations, and an almost simple group with such a factorization cannot have socle exceptional Lie type or orthogonal of minus type. The characterization is then applied to study s s -arc-transitive Cayley graphs of solvable groups, leading to a striking corollary that, except for cycles, a non-bipartite connected 3 3 -arc-transitive Cayley graph of a finite solvable group is necessarily a normal cover of the Petersen graph or the Hoffman-Singleton graph.

Fingerprints of freeze-in dark matter in an early matter-dominated era

We study the impact of an alternate cosmological history with an early matter-dominated epoch on the freeze-in production of dark matter. Such early matter domination is triggered by a meta-stable matter field dissipating into radiation. In general, the dissipation rate has a non-trivial temperature and scale factor dependence. Compared to the usual case of dark matter production via the freeze-in mechanism in a radiation-dominated universe, in this scenario, orders of magnitude larger coupling between the visible and the dark sector can be accommodated. Finally, as a proof of principle, we consider a specific model where the dark matter is produced by a sub-GeV dark photon having a kinetic mixing with the Standard Model photon. We point out that the parameter space of this model can be probed by the experiments in the presence of an early matter-dominated era.