Double Measurements Research Articles

A necessary and sufficient condition for double coset lumping of Markov chains on groups with an application to the random to top shuffle

Let Q Q be a probability measure on a finite group G G , and let H H be a subgroup of G G . We show that a necessary and sufficient condition for the random walk driven by Q Q on G G to induce a Markov chain on the double coset space H ∖ G / H H\backslash G/H is that Q ( g H ) Q(gH) is constant as g g ranges over any double coset of H H in G G . We obtain this result as a corollary of a more general theorem on the double cosets H ∖ G / K H \backslash G / K for K K an arbitrary subgroup of G G . As an application we study a variation on the r r -top to random shuffle which we show induces an irreducible, recurrent, reversible and ergodic Markov chain on the double cosets of S y m r × S y m n − r \mathrm {Sym}_r \times \mathrm {Sym}_{n-r} in S y m n \mathrm {Sym}_n . The transition matrix of the induced walk has remarkable spectral properties: we find its invariant distribution and its eigenvalues and hence determine its rate of convergence.

Intrinsic structure exploitation with dual alignment for universal visual recognition

This research explores the complex yet applicable domain of universal visual recognition, where unlabeled datasets may encompass additional, as-of-yet unidentified classes and present a skewed feature distribution within labeled datasets. The primary challenge lies in concurrently distinguishing instances of known classes and uncovering new classes within the unlabeled data. This difficulty is compounded by two factors: category shift and distribution shift. Current methodologies typically overlook the potential of harnessing the inherent structural relationship between labeled and unlabeled datasets, and they fail to effectively isolate the semantic variability of the newly identified classes from the established ones. To overcome these hurdles, we introduce an innovative framework, which we have termed MESA (short for Manifold structure Exploitation with double Spaces dual Alignment), to advance the field of universal visual recognition. Our approach begins by identifying geometrically and semantically related pairs of nearest neighbors between labeled and unlabeled data, which serve as anchor points to foster an intrinsic match between the two datasets. By integrating an affinity score for similarity, we establish a novel cross-view, anchor-guided, self-supervised learning paradigm. This model is designed to spread the learned labels’ information and to conjoin novel semantic insights within the predictive space. To intensify the matching accuracy for the known classes and enhance the differentiation of novel classes, we further implement a confident-prototype-driven, self-supervised learning paradigm in a cross-view manner. This strategy is aimed at revealing the macroscopic category configuration within the embedding space. MESA employs a pioneering bidirectional dual-alignment mechanism that operates simultaneously in the embedding and prediction spaces, hence providing a more robust approach to confronting challenges brought about by distribution and category shifts. Our exhaustive evaluation across several extensive image recognition benchmarks substantiates MESA’s superior performance over the latest cutting-edge methods, marking a significant leap forward in the sphere of universal visual recognition. Finally, MESA is implemented in Python using the Pytorch machine-learning library, and it is freely available at https://github.com/aimeeyaoyao/MESA.

Efficient preparation of non-Abelian topological orders in the doubled Hilbert space

Efficient preparation of non-Abelian topological orders in the doubled Hilbert space

A Selberg Trace Formula for GL3(Fp)∖GL3(Fq)/K

In this paper, we prove a discrete analog of the Selberg Trace Formula for the group GL3(Fq). By considering a cubic extension of the finite field Fq, we define an analog of the upper half-space and an action of GL3(Fq) on it. To compute the orbital sums, we explicitly identify the double coset spaces and fundamental domains in our upper half space. To understand the spectral side of the trace formula, we decompose the induced representation ρ=IndΓG1 for G=GL3(Fq) and Γ=GL3(Fp).

Double space T dualization and coordinate dependent RR field

In this article, we examine T dualization in the double space formalism of type II superstring theory in pure spinor formulation. All background fields are constant except the Ramond-Ramond field, which depends infinitesimally on bosonic coordinates xμ. In double space, T dual transformations are represented as permutations of the starting xμ and dual coordinates yμ. Combining these two sets of coordinates into the double coordinate ZM=(xμ,yμ), while demanding that the T dual double coordinate has the same T dual transformation law as the initial ones, we obtain how background fields transform under T duality. Comparing these results with ones obtained using the Buscher T dualization procedure, we conclude that these two approaches are equivalent for the considered choice of the background fields. Published by the American Physical Society 2024

Area law for steady states of detailed-balance local Lindbladians

We study steady-states of quantum Markovian processes whose evolution is described by local Lindbladians. We assume that the Lindbladian is gapped and satisfies quantum detailed balance with respect to a unique full-rank steady state σ. We show that under mild assumptions on the Lindbladian terms, which can be checked efficiently, the Lindbladian can be mapped to a local Hamiltonian on a doubled Hilbert space that has the same spectrum and a ground state that is the vectorization of σ1/2. Consequently, we can use Hamiltonian complexity tools to study the steady states of such open systems. In particular, we show an area-law in the mutual information for the steady state of such 1D systems, together with a tensor-network representation that can be found efficiently.

Rockburst classification based on cross reconstruction learning under small-sample condition

Rockburst is a prevalent geological hazard in deep geotechnical engineering, and its accurate prognostication is vital for prevention measures. Consequently, this research proffers a pioneering classification prediction methodology, namely Cross Reconstruction Learning (CR), underpinned by conventional machine learning algorithms and metric learning strategies. Initially, this technique partitions and restructures the original dataset, where each sample feature intersects and reconfigures with features from other samples within the set. During this amalgamation, new samples are assigned labels based on the degree of divergence or congruity between two sets of sample labels, thereby forming a new set of samples. Subsequently, an array of machine learning algorithms is utilized to train and test this new dataset. Ultimately, employing a universal class voting mechanism and decoding test set results through probability assignment, the predicted labels are converted back into rock burst outcomes, thereby determining the final prediction classification. The proposed model was trained on a database encompassing 239 instance samples, and its performance was validated against the currently proficient models (KNN, XGBoost, and Random Forest algorithms) employed in rock burst prediction. The outcome revealed a decline in the performance metrics of all three machine learning algorithms when interfaced with the Cross Reconstruction learning method, particularly the KNN algorithm, owing to the doubled feature dimensions in the combined dataset. However, the metrics of ensemble models, XGBoost and Random Forest, exhibited a notable improvement compared to the original classification models. On comparing multiple performance metrics, it was discovered that the CR-XGBoost model outperformed others across all evaluations, thereby offering significant guidance for practical engineering applications.

Linearizations of Cubic Two-Parameter Eigenvalue Problems and Its Vector Space

The paper considers the study of linearization techniques of cubic two-parameter matrix polynomial (CTMP). We analyze vector spaces of linearization of CTMP, namely ansatz vector space and double ansatz vector space. We also consider cubic two-parameter eigenvalue problem (CTEP) to study their linearization classes. A unified framework on linearization of CTMP will be established. The conditions under which a matrix pencil in the ansatz spaces is a linearization of CTMP will also be derived. Moreover, using these linearization techniques, CTEP is first converted into a singular linear two-parameter eigenvalue problem (2PEP) of larger size so that existing numerical method for (2PEP) can be applied.

Quasi-triangular pre-Lie bialgebras, factorizable pre-Lie bialgebras and Rota-Baxter pre-Lie algebras

In this paper, first we introduce the notions of quasi-triangular pre-Lie bialgebras and factorizable pre-Lie bialgebras. A factorizable pre-Lie bialgebra leads to a factorization of the underlying pre-Lie algebra. We show that the symplectic double of a pre-Lie bialgebra naturally enjoys a factorizable pre-Lie bialgebra structure. Then we give the Rota-Baxter characterization of factorizable pre-Lie bialgebras. More precisely, we introduce the notion of quadratic Rota-Baxter pre-Lie algebras and show that there is a one-to-one correspondence between factorizable pre-Lie bialgebras and quadratic Rota-Baxter pre-Lie algebras. Finally, we develop the theories of matched pairs, bialgebras and Manin triples of Rota-Baxter pre-Lie algebras. In particular, a factorizable pre-Lie bialgebra gives rise to a Rota-Baxter pre-Lie bialgebra, and conversely a Rota-Baxter pre-Lie bialgebra gives rise to a factorizable pre-Lie bialgebra structure on the double space.

Nontargeted metabolomics and enzyme inhibitory and antioxidant activities for chemical and biological characterization of jujube (Ziziphus jujuba) extracts

The chemical and biologically active characterization of jujube samples (fruits, cores, and leaves) were carried out by the integrated nontargeted metabolomics and bioassay. Firstly, collision cross-section values of active compounds in jujubes were determined by ultrahigh-performance liquid chromatography coupled with ion mobility quadrupole time-of-flight mass spectrometry. Then, a multidimensional statistical analysis that contained principal component analysis, partial least squares-discriminant analysis and hierarchical clustering analysis was employed to effectively cluster different tissues and types of jujubes, making identification more scientific. Furthermore, angiotensin-converting enzyme (ACE) and 2, 2-diphenyl-1-picrylhydrazyl (DPPH) were used to evaluate the quality of jujubes from a double activity dimension. The analytical results obtained by using ACE and DPPH to evaluate the quality of jujube were different from multivariate statistics, providing a reference for the application of jujube. Therefore, integrating chemical and biological perspectives to evaluate the quality of jujube provided a more comprehensive evaluation and effective reference for clinical needs.

Direct numerical simulations of turbulent channel flow with a rib-roughened porous wall

To describe the effects of porous roughness on turbulence, we have carried out direct numerical simulations using the lattice Boltzmann method. The simulated flows are fully developed turbulent flows in channels consisting of a solid smooth top wall and a porous bottom wall with transverse porous ribs whose heights are 10 % of the channel height. The considered ratios of the rib spacing to the rib height are $w/k\simeq 1$ and 9. The Kelvin-cell structure is applied to construct faithfully the porous media whose porosities are $\varphi \ge 0.79$ . Three kinds of porous media having different permeabilities are considered. The most permeable one has an approximately one order higher permeability than that of the least permeable one. The higher permeability case is designed to have a pore scale that is the same as the rib height so that it is the most permeable case for the rib roughness with the designed porosity. In the simulations, the bulk Reynolds number is set to $Re_b=5500$ , and the corresponding permeability Reynolds numbers are $Re_K=2.2\unicode{x2013}7.5$ . The simulated field data and the drag coefficient, which includes both the pressure drag by the ribs and the frictional drag over the porous wall, are analysed to understand the characteristics of the permeable roughness in terms of permeability. The decomposition of the drag coefficient into the integrated laminar, rib-drag, dispersion and turbulence parts elucidates the transition mechanism between the typical d-type to k-type roughness depending on $Re_K$ . By the double (time and space) averaged budget equations for the dispersion and Reynolds stresses, we explain how the energy generated by the roughness transfers to turbulence through dispersion resulting in the k-type characteristics. The nominal roughness sublayer thickness and the characteristic roughness height are introduced with the parameters obtained by fitting the velocity data to Best's and Nikuradse's logarithmic velocity formulae. Along with data in the literature, it is suggested that the ratio of the characteristic roughness height to the nominal roughness sublayer thickness becomes constant irrespective of the rib spacing in the full permeable-wall turbulence at $Re_K> 7$ .

Inertia I: The global MSp-SUSY induced uniform motion

In this communication our main emphasis is on the review of the foundations of standard Lorentz code (SLC) of a particle motion. To this aim, we develop the theory of global, so-called, `double space´- or master space (MSp)-supersymmetry, subject to certain rules, wherein the superspace is a 14D-extension of a direct sum of background spaces M4⊕ MSp by the inclusion of additional 8D fermionic coordinates. The latter is induced by the spinors θ and ¯θ referred to MSp. While all the particles are living on M4, their superpartners can be viewed as living on MSp. This is a main ground for introducing MSp, which is unmanifested individual companion to the particle of interest. Supersymmetry transformation is defined as a translation in superspace, specified by the group element with corresponding anticommuting parameters. The multiplication of two successive transformations induce the motion. As a corollary, we derive SLC in a new perspective of global double MSp-SUSY transformations in terms of Lorentz spinors (θ, ¯θ). This calls for a complete reconsideration of our ideas of Lorentz motion code, to be now referred to as the individual code of a particle, defined as its intrinsic property. In MSp-SUSY theory, obviously as in standard unbroken SUSY theory, the vacuum zero point energy problem, standing before any quantum field theory in M4, is solved. The particles in M4 themselves can be considered as excited states above the underlying quantum vacuum of background double spaces M4⊕ MSp, where the zero point cancellation occurs at ground-state energy, provided that the natural frequencies are set equal (q 2 0 ≡ νb = νf ), because the fermion field has a negative zero point energy while the boson field has a positive zero point energy. On these premises, we derive the two postulates on which the Special Relativity (SR) is based.

Optimizing SNARK networks via double metric dimension

<p>Doubly resolving sets (DRSs) provide a promising approach for source detection. They consist of minimal subsets of nodes with the smallest cardinality, referred to as the double metric dimension (DMD), that can uniquely identify the location of any other node within the network. Utilizing DRSs can improve the accuracy and efficiency of the identification of the origin of a diffusion process. This ability is crucial for early intervention and control in scenarios such as epidemic outbreaks, misinformation spreading in social media, and fault detection in communication networks. In this study, we computed the DMD of flower snarks $ J_{m} $ and quasi-flower snarks $ G_{m} $ by describing their minimal doubly resolving sets (MDRSs). We deduce that the DMD for the flower snarks $ J_{m} $ is finite and depends on the network's order, and the DMD for the quasi-flower snarks $ G_{m} $ is finite and independent of the network's order. Furthermore, our findings offer valuable insights into the structural features of complex networks. This knowledge can offer direction for future studies in network theory and its practical implementations.</p>

A new double series space derived by factorable matrix and four-dimensional matrix transformations

<p>In this study, we introduce a new double series space $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $ using the four dimensional factorable matrix $ F $ and absolute summability method for $ k\geq 1 $. Also, examining some algebraic and topological properties of $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $, we show that it is norm isomorphic to the well-known double sequence space $ \mathcal{L}_{k} $ for $ 1\leq k < \infty. $ Furthermore, we determine the $ \alpha $-, $ \beta \left(bp\right) $- and $ \gamma $-duals of the spaces $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $ for $ k\geq 1. $ Additionally, we characterize some new four dimensional matrix transformation classes on double series space $ \left\vert F_{a, b}^{u, \theta }\right\vert _{k} $. Hence, we extend some important results concerned on Riesz and Cesàro matrix methods to double sequences owing to four dimensional factorable matrix.</p>

Enriched multivalued contractions on double controlled metric type spaces with an application

Enriched multivalued contractions on double controlled metric type spaces with an application

Исследование влияния социально ориентированной скорости и кинетической энергии на убывающую аварийность в системе «человек – автомобиль – дорога – окружающая среда»

The study states that the “person - car - road - environment” system (PCRE system) is a poorly structured system. It is shown that the driver with his psychophysiological characteristics and temperament is the main participant influencing the safety of the PCRE system. The socially oriented speed chosen by drivers in a double dimension made it possible to perform experimental calculations of road safety parameters. The search for a possible decreasing accident rate in Moscow car traffic urged the extrapolation of existing road accident into an S-shaped theoretical model with an inflection point in 2026.

On geometries and monodromies for branes of codimension two

We study geometries for the NS5-, the KK5- and the 522-branes of codimension two in type II and heterotic string theories. The geometries are classified by monodromies that each brane has. They are the B-, the general coordinate and the β-transformations of the spacetime metric, the B-field and the dilaton (and the gauge fields). We show that the monodromy nature appears also in the geometric quantities such as the curvature and the complex structures of spacetime. They are linearly realized in the doubled (generalized) structures in the doubled space.

The βm – Homeomorphism in Double Fuzzy Topological Spaces

The purpose of this study is to introduce the concept of homeomorphism via βm – closed set and study its behavior and properties in double fuzzy topological spaces. This objective is achieved through the definitions of df- βm continuous functions and df- βm closed functions. The results of this study represent important relationships and proofs, in addition to providing some necessary examples.

Massively parallel and streaming algorithms for balanced clustering

Clustering is a fundamental problem with a wide range of applications. In this paper, we study a balanced version of the well-known k-center clustering problem, where the objective is to select k centers from a given set of points, and assign to each center at most L of the input points, so as to minimize the maximum distance from a point to the center to which it is assigned. We assume soft capacities, where points are allowed to be selected as center more than once. Motivated by applications involving massive datasets, we study the problem in the massively parallel computation (MPC) and streaming models. In particular, we present a two-round MPC algorithm for the balanced k-center problem, achieving an approximation factor of 5α+2, where α is the approximation factor of the corresponding sequential algorithm. This substantially improves the currently best approximation factor of 32α, available for the problem. We show that the approximation factor of our algorithm can be further improved to 5+ε in all spaces with bounded doubling dimension, including the Euclidean space. We also consider the balanced k-center problem in the streaming model, and present a constant-factor streaming algorithm in any metric space using O(knε) memory, and a factor 5+ε streaming algorithm using O(kpolylogn) memory in doubling metrics.

Training university teachers in an urban context to educate future teachers in rural Mayan environments: an international cooperation project

Training university teachers in an urban context to educate future teachers in rural Mayan environments: an international cooperation project