Module Of Rank Research Articles

Adaptive Framework for Multi-Feature Hybrid Object Tracking

Object tracking is a computer vision task deemed necessary for high-level intelligent decision-making algorithms. Researchers have merged different object tracking techniques and discovered a new class of hybrid algorithms that is based on embedding a meanshift (MS) optimization procedure into the particle filter (PF) (MSPF) to replace its inaccurate and expensive particle validation processes. The algorithm employs a combination of predetermined features, implicitly assuming that the background will not change. However, the assumption of fully specifying the background of the object may not often hold, especially in an uncontrolled environment. The first innovation of this research paper is the development of a dynamically adaptive multi-feature framework for MSPF (AMF-MSPF) in which features are ranked by a ranking module and the top features are selected on-the-fly. As a consequence, it improves local discrimination of the object from its immediate surroundings. It is also highly desirable to reduce the already complex framework of the MSPF to save resources to implement a feature ranking module. Thus, the second innovation of this research paper introduces a novel technique for the MS optimization method, which reduces its traditional complexity by an order of magnitude. The proposed AMF-MSPF framework is tested on different video datasets that exhibit challenging constraints. Experimental results have shown robustness, tracking accuracy and computational efficiency against these constraints. Comparison with existing methods has shown significant improvements in term of root mean square error (RMSE), false alarm rate (FAR), and F-SCORE.

Schur–Weyl duality over commutative rings

The classical case of Schur–Weyl duality states that the actions of the group algebras of GLn and Sd on the dth-tensor power of a free module of finite rank centralize each other. We show that Schur–Weyl duality holds for commutative rings where enough scalars can be chosen whose non-zero differences are invertible. This implies all the known cases of Schur–Weyl duality so far. We also show that Schur–Weyl duality fails for and for any finite field when d is sufficiently large.

Nearly Finite-Dimensional Jordan Algebras

Nearly finite-dimensional Jordan algebras are examined. Analogs of known results are considered. Namely, it is proved that such algebras are prime and nondegenerate. It is shown that the property of being nearly finite-dimensional is preserved in passing from an alternative algebra to an adjoint Jordan algebra. A similar result is established for associative nearly finite-dimensional algebras with involution. It is stated that a nearly finite-dimensional Jordan PI-algebra with unity either is a finite module over a nearly finite-dimensional center or is a central order in an algebra of a nondegenerate symmetric bilinear form. Also the following result holds: if a locally nilpotent ideal has finite codimension in a Jordan algebra with the ascending chain condition on ideals, then that algebra is finite-dimensional. In addition, E. Formanek’s result in [Comm. Alg., 1, No. 1, 79-86 (1974)], which says that associative prime PI-rings with unity are embedded in a free module of finite rank over its center, is generalized to Albert rings.

Software defect number prediction: Unsupervised vs supervised methods

Context: Software defect number prediction (SDNP) can rank the program modules according to the prediction results and is helpful for the optimization of testing resource allocation.Objective: In previous studies, supervised methods vs unsupervised methods is an active issue for just-in-time defect prediction and file-level defect prediction based on effort-aware performance measures. However, this issue has not been investigated for SDNP. To the best of our knowledge, we are the first to make a thorough comparison for these two different types of methods.Method: In our empirical studies, we consider 7 real open-source projects with 24 versions in total, use FPA and Kendall as our effort-aware performance measures, and consider three different performance evaluation scenarios (i.e., within-version scenario, cross-version scenario, and cross-project scenario).Result: We first identify two unsupervised methods with best performance. These two methods simply rank modules according to the value of metric LOC and metric RFC from large to small respectively. Then we compare 9 state-of-the-art supervised methods incorporating SMOTEND, which is used for handling class imbalance problem, with the unsupervised method based on LOC metric (i.e., LOC_D method). Final results show that LOC_D method can perform significantly better than or the same as these supervised methods. Later motivated by a recent study conducted by Agrawla and Menzies, we apply differential evolutionary (DE) to optimize parameter value of SMOTEND used by these supervised methods and find that using DE can effectively improve the performance of these supervised methods for SDNP too. Finally, we continue to compare LOC_D with these optimized supervised methods using DE, and LOC_D method still has advantages in the performance, especially in the cross-version and cross-project scenarios.Conclusion: Based on these results, we suggest that researchers need to use the unsupervised method LOC_D as the baseline method, which is used for comparing their proposed novel methods for SDNP problem in the future.

Gray codes over certain run-length sequences for local rank modulation

In the local rank modulation (LRM) scheme, a sliding window produces a sequence of permutations by moving over a sequence of variables. LRM has been presented as a method of storing data in flash memory, which represents a natural generalization of the classical rank modulation scheme. In this paper, we present a study on Gray codes over certain run-length sequences for the $(1,2,n)$-LRM scheme to simulate virtual multilevel flash memory cells while maintaining the advantages of LRM. Unlike previous studies on the LRM scheme, we present Gray codes over certain run-length sequences in the $(1,2,n)$-LRM scheme. This class of Gray codes can overcome the drawback of the many distinct charge levels required in the rank modulation scheme and in certain Gray codes for LRM. Furthermore, we demonstrate that the proposed codes have an asymptotically optimal rate.

The symplectic structure on the moduli space of line bundles on a noncommutative Azumaya surface

In this note we prove that the moduli space of torsion-free modules of rank one over an Azumaya algebra on a K3 surface is an irreducible symplectic variety deformation equivalent to a Hilbert scheme of points on the K3 surface.

Irreducible ℤ+-modules of near-group fusion ring K(ℤ3, 3)

The near-group rings are an important class of fusion rings in the theory of tensor categories. In this paper, the irreducible ℤ+-modules over the near-group fusion ring K(ℤ3, 3) are explicitly classified. It turns out that there are only four inequivalent irreducible ℤ+-modules of rank 2 and two inequivalent irreducible ℤ+-modules of rank 4 over K(ℤ3, 3).

Unimodular elements in projective modules and an analogue of a result of Mandal

(1) Let $R$ be a commutative Noetherian ring of dimension $n$ and $P$ a projective $R[X_1,\ldots ,X_m]$-module of rank $n$. In this paper, we associate an obstruction for $P$ to split off a free summand of rank one. (2) Let $R$ be a local ring and $R[X]\subset A\subset R[X,X^{-1}]$. Let $P$ and $Q$ be two projective $A$-modules with $\text {rank}(Q)\lt \text {rank}(P)$. If $Q_f$ is a direct summand of $P_f$ for some special monic polynomial $f\in R[X]$, then $Q$ is also a direct summand of $P$.

Galois ring codes and their images under various bases

In this paper we consider linear block codes B of length n over the Galois ring GR(pr, m) and obtain their images with respect to various bases of GR(pr, m) seen as a free module of rank m over the residue class ring ℤpr. Interesting new examples of dual, normal and self-dual bases of GR(pr, m) and their relationships are given. The image of B is a linear block code over ℤpr of length mn and its generator matrix is formed row-wise by the images of βiG, where is a chosen basis of GR(pr, m) and G is a generator matrix of B. Certain conditions in which the pr-ary image is distance-invariant after a change in basis are investigated. Consequently a new quaternary code endowed with a homogeneous metric that is optimal with respect to certain known bounds is constructed.

Domain-Adapted Convolutional Networks for Satellite Image Classification: A Large-Scale Interactive Learning Workflow

Satellite imagery often exhibits large spatial extent areas that encompass object classes with considerable variability. This often limits large-scale model generalization with machine learning algorithms. Notably, acquisition conditions, including dates, sensor position, lighting condition, and sensor types, often translate into class distribution shifts introducing complex nonlinear factors and hamper the potential impact of machine learning classifiers. This paper investigates the challenge of exploiting satellite images using convolutional neural networks (CNN) for settlement classification where the class distribution shifts are significant. We present a large-scale human settlement mapping workflow based-off multiple modules to adapt a pretrained CNN to address the negative impact of distribution shift on classification performance. To extend a locally trained classifier onto large spatial extents areas we introduce several submodules: First, a human-in-the-loop element for relabeling of misclassified target domain samples to generate representative examples for model adaptation; second, an efficient hashing module to minimize redundancy and noisy samples from the mass-selected examples; and third, a novel relevance ranking module to minimize the dominance of source example on the target domain. The workflow presents a novel and practical approach to achieve large-scale domain adaptation with binary classifiers that are based-off CNN features. Experimental evaluations are conducted on areas of interest that encompass various image characteristics, including multisensors, multitemporal, and multiangular conditions. Domain adaptation is assessed on source–target pairs through the transfer loss and transfer ratio metrics to illustrate the utility of the workflow.

Generalized Verma modules over [formula omitted] induced from [formula omitted]-free [formula omitted]-modules

A class of generalized Verma modules over sln+2 are constructed from sln+1-modules which are U(hn)-free modules of rank 1. The necessary and sufficient conditions for these sln+2-modules to be simple are determined. This leads to a class of new simple sln+2-modules.

Harmonic Analysis on the Space of $p$-adic Unitary Hermitian Matrices, Mainly for Dyadic Case

We are interested in the harmonic analysis on $p$-adic homogeneous spaces based on spherical functions. In the present paper, we investigate the space $X$ of unitary hermitian matrices of size $m$ over a ${\mathfrak p}$-adic field $k$ and give unified description including dyadic case, which is a continuation of our previous papers on non-dyadic case. The space becomes complicated when $e = v_\pi(2) > 0$. First we introduce a typical spherical function $\omega(x;z)$ on $X$, and study their functional equations, which depend on $m$ and $e$, we give an explicit formula for $\omega(x;z)$, where Hall-Littlewood polynomials of type $C_n$ appear as a main term with different specialization according as $m = 2n$ or $2n+1$, but independent of $e$. By spherical transform, we show the Schwartz space ${\mathcal S}(K \backslash X)$ is a free Hecke algebra ${\mathcal H}(G,K)$-module of rank $2^n$, and give parametrization of all the spherical functions on $X$ and the explicit Plancherel formula on ${\mathcal S}(K \backslash X)$. The Plancherel measure does not depend on $e$, but the normalization of $G$-invariant measure on $X$ depends.

Evaluation Approach to Rank Module Partition Schemes of Complex Products Based on Hybrid Fuzzy Multi-Attribute Decision Making

Evaluation Approach to Rank Module Partition Schemes of Complex Products Based on Hybrid Fuzzy Multi-Attribute Decision Making

Normal Sally modules of rank one

In this paper, we explore the structure of the normal Sally modules of rank one with respect to an m-primary ideal in a Nagata reduced local ring R which is not necessary Cohen–Macaulay. As an application of this result, when the base ring is Cohen–Macaulay analytically unramified, the extremal bound on the first normal Hilbert coefficient leads to the depth of the associated graded rings G‾ with respect to a normal filtration is at least dim⁡R−1 and G‾ turns in to Cohen–Macaulay when the third normal Hilbert coefficient is vanished.

The localized skein algebra is Frobenius

When $A$ in the Kauffman bracket skein relation is a primitive $2N$th root of unity, where $N\geq 3$ is odd, the Kauffman bracket skein algebra $K_N(F)$ of a finite type surface $F$ is a ring extension of the $SL_2\mathbb{C}$-characters $\chi(F)$ of the fundamental group of $F$. We localize by inverting the nonzero characters to get an algebra $S^{-1}K_N(F)$ over the function field of the character variety. We prove that if $F$ is noncompact, the algebra $S^{-1}K_N(F)$ is a symmetric Frobenius algebra. Along the way we prove $K(F)$ is finitely generated, $K_N(F)$ is a finite rank module over $\chi(F)$, and the simple closed curves that make up any simple diagram on $F$ generate a finite field extension of $S^{-1}\chi(F)$ inside $S^{-1}K_N(F)$.

Ranking Modules for Integrate Testing Based on PageRank Algorithm

The testing industry need to prioritize the limited resources and focus on testing modules whose failure is mostly likely to cause faults. This paper discusses a method that can rank modules in a software package for integrate testing using the PageRank algorithm. In this algorithm, a sequences of random walks iteratively can find a high likelihood of encountering a node, which is interpreted as it being an important performance resource. An experiment result prove that the proposed method actually can be used to prioritize testing of specific modules when testing resource are scarce.

Relational similarity-based model of data part 1: foundations and query systems

We present a general rank-aware model of data which supports handling of similarity in relational databases. The model is based on the assumption that in many cases it is desirable to replace equalities on values in data tables by similarity relations expressing degrees to which the values are similar. In this context, we study various phenomena which emerge in the model, including similarity-based queries and similarity-based data dependencies. Central notion in our model is that of a ranked data table over domains with similarities which is our counterpart to the notion of relation on relation scheme from the classical relational model. Compared to other approaches which cover related problems, we do not propose a similarity-based or ranking module on top of the classical relational model. Instead, we generalize the very core of the model by replacing the classical, two-valued logic upon which the classical model is built by a more general logic involving a scale of truth degrees that, in addition to the classical truth degrees 0 and 1, contains intermediate truth degrees. While the classical truth degrees 0 and 1 represent nonequality and equality of values, and subsequently mismatch and match of queries, the intermediate truth degrees in the new model represent similarity of values and partial match of queries. Moreover, the truth functions of many-valued logical connectives in the new model serve to aggregate degrees of similarity. The presented approach is conceptually clean, logically sound, and retains most properties of the classical model while enabling us to employ new types of queries and data dependencies. Most importantly, similarity is not handled in an ad hoc way or by putting a “similarity module” atop the classical model in our approach. Rather, it is consistently viewed as a notion that generalizes and replaces equality in the very core of the relational model. We present fundamentals of the formal model and two equivalent query systems which are analogues of the classical relational algebra and domain relational calculus with range declarations. In the sequel to this paper, we deal with similarity-based dependencies.

CONGRUENCE OF SYMMETRIC INNER PRODUCTS OVER FINITE COMMUTATIVE RINGS OF ODD CHARACTERISTIC

Let $R$ be a finite commutative ring of odd characteristic and let $V$ be a free $R$-module of finite rank. We classify symmetric inner products defined on $V$ up to congruence and find the number of such symmetric inner products. Additionally, if $R$ is a finite local ring, the number of congruent symmetric inner products defined on $V$ in each congruence class is determined.

Stark units in positive characteristic

We show that the module of Stark units associated to a sign-normalized rank one Drinfeld module can be obtained from Anderson's equivariant A-harmonic series. We apply this to obtain a class formula a la Taelman and to prove a several variable log-algebraicity theorem, generalizing Anderson's log-algebraicity theorem. We also give another proof of Anderson's log-algebraicity theorem using shtukas and obtain various results concerning the module of Stark units for Drinfeld modules of arbitrary rank.

Lattice map for Anderson t-motives: First approach

There exists a lattice map from the set of pure uniformizable Anderson t-motives to the set of lattices. It is not known what is the image and the fibers of this map. We prove a local result that sheds the first light to this problem and suggests that maybe this map is close to 1–1. Namely, let M(0) be a t-motive of dimension n and rank r=2n — the n-th power of the Carlitz module of rank 2, and let M be a t-motive which is in some sense “close” to M(0). We consider the lattice map M↦L(M), where L(M) is a lattice in C∞n. We show that the lattice map is an isomorphism in a “neighborhood” of M(0). Namely, we compare the action of monodromy groups: (a) from the set of equations defining t-motives to the set of t-motives themselves, and (b) from the set of Siegel matrices to the set of lattices. The result of the present paper gives that the size of a neighborhood, where we have an isomorphism, depends on an element of the monodromy group. We do not know whether there exists a universal neighborhood. Method of the proof: explicit solution of an equation describing an isomorphism between two t-motives by a method of successive approximations using a version of the Hensel lemma.