Linear Set Research Articles

The Trace Field Theory of a Finite Tensor Category

Given a finite tensor category $\mathcal {C}$ , we prove that a modified trace on the tensor ideal of projective objects can be obtained from a suitable trivialization of the Nakayama functor as right $\mathcal {C}$ -module functor. Using a result of Costello, this allows us to associate to any finite tensor category equipped with such a trivialization of the Nakayama functor a chain complex valued topological conformal field theory, the trace field theory. The trace field theory topologically describes the modified trace, the Hattori-Stallings trace, and also the structures induced by them on the Hochschild complex of $\mathcal {C}$ . In this article, we focus on implications in the linear (as opposed to differential graded) setting: We use the trace field theory to define a non-unital homotopy commutative product on the Hochschild chains in degree zero. This product is block diagonal and can be described through the handle elements of the trace field theory. Taking the modified trace of the handle elements recovers the Cartan matrix of $\mathcal {C}$

A Partial Channel Reciprocity-Based Codebook for Wideband FDD Massive MIMO

The acquisition of channel state information (CSI) in Frequency Division Duplex (FDD) massive MIMO has been a formidable challenge. In this paper, we address this problem with a novel CSI feedback framework enabled by the partial reciprocity of uplink and downlink channels in the wideband regime. We first derive the closed-form expression of the rank of the wideband massive MIMO channel covariance matrix for a given angle-delay distribution. A low-rankness property is identified, which generalizes the well-known result of the narrow-band uniform linear array setting. Then we propose a partial channel reciprocity (PCR) codebook, inspired by the low-rankness behavior and the fact that the uplink and downlink channels have similar angle-delay distributions. Compared to the latest codebook in 5G, the proposed PCR codebook scheme achieves higher performance, lower complexity at the user side, and requires less feedback. We derive the feedback overhead necessary to achieve asymptotically error-free CSI feedback. Two low-complexity alternatives are also proposed to further reduce the complexity at the base station side. Simulations with the practical 3GPP channel model show the significant gains over the latest 5G codebook, which prove that our proposed methods are practical solutions for 5G and beyond.

New MCDM Algorithms with Linear Diophantine Fuzzy Soft TOPSIS, VIKOR and Aggregation Operators

In this paper, we focus on several ideas associated with linear Diophantine fuzzy soft sets (LDFSSs) along with its algebraic structure. We provide operations on LDFSSs and their specific features, elaborating them with real-world examples and statistical depictions to construct an inflow of linguistic variables based on linear Diophantine fuzzy soft (LDFSS) information. We offer a study of LDFSSs to the multi-criteria decision-making (MCDM) process of university determination, together with new algorithms and flowcharts. We construct LDFSS-TOPSIS, LDFSS-VIKOR and the LDFSS-AO techniques as robust extensions of TOPSIS (a technique for order preferences through the ideal solution), VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje) and AO (aggregation operator). We use the LDFSS-TOPSIS, LDFSS-VIKOR and LDFSS-AO techniques to solve a real-world agricultural problem. Moreover, we present a small-sized robotic agri-farming to support the proposed technique. A comparison analysis is also performed to examine the symmetry of optimal decision and to analyze the efficiency of the suggested algorithms.

The tadpole conjecture in asymptotic limits

The tadpole conjecture suggests that the complete stabilization of complex structure deformations in Type IIB and F-theory flux compactifications is severely obstructed by the tadpole bound on the fluxes. More precisely, it states that the stabilization of a large number of moduli requires a flux background with a tadpole that scales linearly in the number of stabilized fields. Restricting to the asymptotic regions of the complex structure moduli space, we give the first conceptual argument that explains this linear scaling setting and clarifies why it sets in only for a large number of stabilized moduli. Our approach relies on the use of asymptotic Hodge theory. In particular, we use the fact that in each asymptotic regime an orthogonal sl(2)-block structure emerges that allows us to group fluxes into sl(2)-representations and decouple complex structure directions. We show that the number of stabilized moduli scales with the number of sl(2)-representations supported by fluxes, and that each representation fixes a single modulus. Furthermore, we find that for Calabi-Yau four-folds all but one representation can be identified with representations occurring on two-folds. This allows us to discuss moduli stabilization explicitly and establish the relevant scaling constraints for the tadpole.

ROOTED TREE ANALYSIS OF AN EXPLICIT FOURTH-STAGE FOURTH ORDER RUNGE- KUTTA METHOD

This research paper is aimed at using Butcher’s rooted trees to separate the f(y) functional derivatives from the f(x,y) functional derivatives after applying Taylor series expansion on the general fourth stage fourth order Runge Kutta method. This approach revealed that the f(y) functional derivatives generated a set of linear/ nonlinear equations that gave birth to a fourth stage fourth order Runge Kutta formula. This idea is derivable from general graphs and combinatorics.

Learning-Based Robust Resource Allocation for D2D Underlaying Cellular Network

In this paper, we study the resource allocation in D2D underlaying cellular network with uncertain channel state information (CSI). For satisfying the minimum rate requirement for cellular user and the reliability requirement for D2D user, we attempt to maximize the cellular user’s throughput whilst ensuring a chance constraint for D2D. Then, a robust resource allocation framework is proposed for solving the highly intractable chance constraint, where the CSI uncertainties are represented as a deterministic set and the reliability requirement is enforced to hold for any CSI within it. Then, a symmetrical-geometry-based learning approach is developed to model the uncertain CSI into polytope, ellipsoidal and box. After that, the chance constraint under these uncertainty sets is transformed into computation convenient convex constraints. To overcome the conservatism of symmetrical-geometry-based approach, we develop a support vector clustering (SVC)-based approach to model uncertain CSI as a compact convex uncertainty set. Based on that, the chance constraint is converted into a linear convex set. Then, we develop a bisection search-based power allocation algorithm for solving the resource allocation in D2D underlaying cellular network with the obtained convex constraints. Finally, we conduct the simulation to compare the proposed robust optimization approaches with the non-robust one.

Sliding mode observers for robust fault estimation in linear parameter varying systems

AbstractA linear parameter varying sliding mode fault reconstruction scheme is proposed. Compared with other conventional sliding mode observer designs, the estimate emerges quite naturally from the equations governing the sliding motion, and although the process may be viewed as a filtering of the discontinuous injection, there is no phase lag introduced in the process. A semi‐analytic solution to the proposed linear parameter varying sliding mode observer is first discussed. This motivates the structure of the linear matrix inequality formulation which is proposed, and clarifies the class of systems to which the approach is applicable. The linear matrix inequality problem set up minimizes the induced gain between the fault estimate and external disturbances, whilst ensuring linear quadratic performance of the underpinning sliding motion. The proposed scheme has been validated using the Japan Aerospace Exploration Agency's Multi‐Purpose Aviation Laboratory aircraft‐in‐the‐loop platform to demonstrate the design efficacy.

Spherical Linear Diophantine Fuzzy TOPSIS Algorithm for Green Supply Chain Management System

Enhancing competitive pressure is one of the most significant roles of supply chain management. The competitive environment and customer perception have shifted in favour of an ecological mentality. As a result, green supplier selection (GSS) has emerged as a critical problem. The challenge of green supplier selection striving for agility, durability, ecological sensitivity, leanness, and sustainability is tackled in this paper. In terms of recycling applications, environmental applications, carbon footprint, and water consumption, the environmental parameters evaluated in GSS and traditional supplier selection differ. Because of the form of the problem, a resolution is defined, which comprises an algorithm entrenched in the spherical linear Diophantine fuzzy sets (SLDFSs) Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) technique. Before discussing the approach of the SLDF model, some background information on SLDF sets is provided. To assure the uniqueness of this robust extension, different operations on SLDFSs are described, along with some concise interpretations to help the reader comprehend these ideas. A robust TOPSIS approach has been utilized in the issue of GSS by taking into consideration the multicriteria decision-making (MCDM) technique particularly useful in several areas, like analyzing and choosing traditional and environmental conventionalities. Due to linguistic criteria and the inability to assess all criteria, the fuzzy technique must be used with the TOPSIS method to lessen the consequences of instability and ambiguity. The spherical linear Diophantine fuzzy TOPSIS approach is employed, as it simplifies the evaluation of decision-makers and criteria. The hybrid technique resulting from integrating the SLDFS and TOPSIS is extremely successful in selecting which provider is more suited among the alternatives established on the criteria set by the order of significance, and this method may also be incorporated into similar issues.

Exercise timing influences multi-tissue metabolome and skeletal muscle proteome profiles in type 2 diabetic patients – A randomized crossover trial

Aims/hypothesisMetabolic effects of exercise may partly depend on the time-of-day when exercise is performed. We tested the hypothesis that exercise timing affects the adaptations in multi-tissue metabolome and skeletal muscle proteome profiles in men with type 2 diabetes. MethodsMen fitting the inclusion (type 2 diabetes, age 45–68 years and body mass index 23–33 kg/m2) and exclusion criteria (insulin treatment, smoking, concurrent systemic disease, and regular exercise training) were included in a randomized crossover trial (n = 15). Participants included in this metabolomics and proteomics analysis fully completed all exercise sessions (n = 8). The trial consisted of two weeks of high-intensity interval training (HIT) (three sessions/week) either in the morning (08:00, n = 5) or afternoon (16:45, n = 3), a two-week wash-out period, and an additional two weeks of HIT at the opposing time. Participants and researchers were not blinded to group allocation. Blood, skeletal muscle and subcutaneous adipose tissue were obtained before the first, and after each training period. Broad-spectrum, untargeted proteomic analysis was performed on skeletal muscle, and metabolomic analysis was performed on all biosamples. Differential content was assessed by linear regression and pathway set enrichment analyses were performed. Coordinated metabolic changes across tissues were identified by Spearman correlation analysis. ResultsMetabolic and proteomic profiles remained stable after two weeks of HIT, and individual metabolites and proteins were not altered, irrespective of the time of day at which the training was performed. However, coordinated changes in relevant metabolic pathways and protein categories were identified. Morning and afternoon HIT similarly increased plasma diacylglycerols, skeletal muscle acyl-carnitines, and subcutaneous adipose tissue sphingomyelins and lysophospholipids. Acyl-carnitines were central to training-induced metabolic cross-talk across tissues. Plasma carbohydrates, via the penthose phosphate pathway, were increased and skeletal muscle lipids were decreased after morning compared to afternoon HIT. Skeletal muscle lipoproteins were higher, and mitochondrial complex III abundance was lower after morning compared to afternoon HIT. Conclusions/interpretationWe provide a comprehensive analysis of a multi-tissue metabolomic and skeletal muscle proteomic responses to training at different times of the day in men with type 2 diabetes. Increased circulating lipids and changes in adipose tissue lipid composition were common between morning and afternoon HIT. However, afternoon HIT increased skeletal muscle lipids and mitochondrial content to a greater degree than morning training. Thus, there is a diurnal component in the metabolomic and proteomic response to exercise in men with type 2 diabetes. The clinical relevance of this response warrants further investigation.

Addressing overdispersion and zero-inflation for clustered count data via new multilevel heterogenous hurdle models

ABSTRACT Unobserved heterogeneity causing overdispersion and the excessive number of zeros take a prominent place in the methodological development on count modeling. An insight into the mechanisms that induce heterogeneity is required for better understanding of the phenomenon of overdispersion. When the heterogeneity is sourced by the stochastic component of the model, the use of a heterogenous Poisson distribution for this part encounters as an elegant solution. Hierarchical design of the study is also responsible for the heterogeneity as the unobservable effects at various levels also contribute to the overdispersion. Zero-inflation, heterogeneity and multilevel nature in the count data present special challenges in their own respect, however the presence of all in one study adds more challenges to the modeling strategies. This study therefore is designed to merge the attractive features of the separate strand of the solutions in order to face such a comprehensive challenge. This study differs from the previous attempts by the choice of two recently developed heterogeneous distributions, namely Poisson–Lindley (PL) and Poisson–Ailamujia (PA) for the truncated part. Using generalized linear mixed modeling settings, predictive performances of the multilevel PL and PA models and their hurdle counterparts were assessed within a comprehensive simulation study in terms of bias, precision and accuracy measures. Multilevel models were applied to two separate real world examples for the assessment of practical implications of the new models proposed in this study.

Novel distance and entropy definitions for linear Diophantine fuzzy sets and an extension of TOPSIS (LDF‐TOPSIS)

AbstractThe literature of multiple attribute decision making (MADM) is fruitful since there are various and successful applications of different fuzzy set extensions such as intuitionistic, Pythagorean and q‐Rung orthopair fuzzy sets (IFS, PFS and q‐ROFS). Besides their powerful aspects, some definitional limitations are known. In order to eradicate these boundaries regarding the definitions of membership and non‐membership degrees, linear Diophantine fuzzy set (LDFS) concept has been recently emerged. By considering two parameters, LDFS extends the representation area of the previous fuzzy set definitions and provides more extensive human judgement coverage field. In this study, the first distance and entropy measures in the literature have been developed for LDFSs. Their axiomatic definitions are given, and the proofs are shown. Also, thanks to our extensive literature review, we became aware that there is no MADM extension dedicatedly proposed for LDFS. So, the first MADM method extension for LDFS environment has also been developed in this study. A very well‐known MADM approach, TOPSIS, has been extended into LDFS environment for the first time in the literature. The applicability is shown in a healthcare management decision problem and the validity is checked and approved by comparing the alternative rankings LDF‐TOPSIS and the aggregation operators that were obtained from the literature produced.

Linear cutting blocking sets and minimal codes in the rank metric

This work investigates the structure of rank-metric codes in connection with concepts from finite geometry, most notably the q-analogues of projective systems and blocking sets. We also illustrate how to associate a classical Hamming-metric code to a rank-metric one, in such a way that various rank-metric properties naturally translate into the homonymous Hamming-metric notions under this correspondence. The most interesting applications of our results lie in the theory of minimal rank-metric codes, which we introduce and study from several angles. Our main contributions are bounds for the parameters of a minimal rank-metric codes, a general existence result based on a combinatorial argument, and an explicit code construction for some parameter sets that uses the notion of a scattered linear set. Throughout the paper we also show and comment on curious analogies/divergences between the theories of error-correcting codes in the rank and in the Hamming metric.

On the Tuning of the Computation Capability of Spiking Neural Membrane Systems with Communication on Request.

Spiking neural P systems (abbreviated as SNP systems) are models of computation that mimic the behavior of biological neurons. The spiking neural P systems with communication on request (abbreviated as SNQP systems) are a recently developed class of SNP system, where a neuron actively requests spikes from the neighboring neurons instead of passively receiving spikes. It is already known that small SNQP systems, with four unbounded neurons, can achieve Turing universality. In this context, 'unbounded' means that the number of spikes in a neuron is not capped. This work investigates the dependency of the number of unbounded neurons on the computation capability of SNQP systems. Specifically, we prove that (1) SNQP systems composed entirely of bounded neurons can characterize the family of finite sets of numbers; (2) SNQP systems containing two unbounded neurons are capable of generating the family of semilinear sets of numbers; (3) SNQP systems containing three unbounded neurons are capable of generating nonsemilinear sets of numbers. Moreover, it is obtained in a constructive way that SNQP systems with two unbounded neurons compute the operations of Boolean logic gates, i.e., OR, AND, NOT, and XOR gates. These theoretical findings demonstrate that the number of unbounded neurons is a key parameter that influences the computation capability of SNQP systems.

An Oversampling Method of Unbalanced Data for Mechanical Fault Diagnosis Based on MeanRadius-SMOTE.

With the development of machine learning, data-driven mechanical fault diagnosis methods have been widely used in the field of PHM. Due to the limitation of the amount of fault data, it is a difficult problem for fault diagnosis to solve the problem of unbalanced data sets. Under unbalanced data sets, faults with little historical data are always difficult to diagnose and lead to economic losses. In order to improve the prediction accuracy under unbalanced data sets, this paper proposes MeanRadius-SMOTE based on the traditional SMOTE oversampling algorithm, which effectively avoids the generation of useless samples and noise samples. This paper validates the effectiveness of the algorithm on three linear unbalanced data sets and four step unbalanced data sets. Experimental results show that MeanRadius-SMOTE outperforms SMOTE and LR-SMOTE in various evaluation indicators, as well as has better robustness against different imbalance rates. In addition, MeanRadius-SMOTE can take into account the prediction accuracy of the overall and minority class, which is of great significance for engineering applications.

Importance Resampling Approach for Sensor Mutual Coupling Correction

To achieve accurate direction parameter estimation of sensor array, mutual coupling between sensor elements should be properly handled. This problem becomes more challenging when the sources are coherent. In this paper, we derive an importance resampling approach (IRA) for joint mutual coupling and DOA estimation. Aiming to DOA estimation of coherent sources using the spatial smoothing technique and MUSIC algorithm, error analysis is first provided for the estimate of the corresponding mutual coupling coefficient matrix in a uniform linear array setting. An optimization formulation based on MUSIC is then established for joint estimation of mutual coupling coefficients and DOAs. The proposed IRA framework, which solves this optimization problem, has the advantages of few parameters and low computational complexity. Four different importance resampling algorithms which are the position resampling algorithm, the number resampling algorithm, the number and position resampling algorithm and the zero forcing resampling algorithm are proposed for the implement of the IRA framework with different arrangement and combination according to the characteristic of the real coupling coefficients vector. The proposed approach is effective not only to the case of coherent sources, but also for independent sources, and it can work in both single- and multiple-snapshot scenarios. The excellent performance of our methods for mutual coupling correction and DOA estimation is demonstrated via extensive simulation results, which can also be applied to other sensor parameter estimation scenarios.

Linear Diophantine Fuzzy Set Theory Applied to BCK/BCI-Algebras

In this paper, we apply the concept of linear Diophantine fuzzy sets in BCK/BCI-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties are discussed. Additionally, characterizations of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are considered. Moreover, the associated results for linear Diophantine fuzzy subalgebras, linear Diophantine fuzzy ideals and linear Diophantine fuzzy commutative ideals are obtained.

Scattered linear sets in a finite projective line and translation planes

In [15], Lunardon and Polverino construct a translation plane starting from a scattered linear set of pseudoregulus type in PG(1,qt). In this paper a similar construction of a translation plane Af obtained from any scattered linearized polynomial f(x) in Fqt[x] is described and investigated. A class of quasifields giving rise to such planes is defined. Denote by Uf the Fq-subspace of Fqt2 associated with f(x). If f(x) and f′(x) are scattered, then Af and Af′ are isomorphic if and only if Uf and Uf′ belong to the same orbit under the action of ΓL(2,qt). This gives rise to the same number of distinct translation planes as the number of inequivalent scattered linearized polynomials. In particular, for any scattered linear set L of maximum rank in PG(1,qt) there are cΓ(L) pairwise non-isomorphic translation planes, where cΓ(L) denotes the ΓL-class of L, as defined in [5] by Csajbók, Marino and Polverino. A result by Jha and Johnson [8] allows to describe the automorphism groups of the planes obtained from the linear sets not of pseudoregulus type defined in [15].

Abstract 5720: Niraparib enhances radiosensitivity of glioblastoma cells with proficient BRCA1/2 through proliferation-related nucleolar protein DDX21

Abstract Background Intrinsic resistance to irradiation is one of important factors leading to recurrence of glioblastoma (GBM) patients underwent standard treatment. The radiosensitization by various poly-(ADP-ribose)-polymerase (PARP) inhibitors have been intensively investigated in many solid tumor models especially harboring deficient BRCA1/2. However, the impact of a PARP1/2 inhibitor niraparib on radiosensitivity of glioblastoma cell lines with proficient BRCA1/2 and underling mechanisms has yet not been fully elucidated. Methods GDSC dataset with IC50 of PARP inhibitors and transcriptome profiles as well as NCI-60 cell lines with known survival fraction at 2 Gy (SF2) were used to deduce potential pathways by which PARP inhibitors suppress cell viability and confer radiosensitization through linear regression and reactome gene set enrichment analysis. Two GBM cell lines with proficient BRCA1/2, A172 and U-87-MG were used to evaluate IC50 and radiation dose enhancement factor DEF37 of niraparib by CCK8 experiment and clonogenicity assay. Changes in the distribution of cell cycle and DDX21 protein expression were analyzed with flow cytometry and western blot respectively. The involvement of DDX21 in the mechanism mediating radiosensization of niraparib was performed with small inference RNA experiment. Results Pathways relevant to ribosome biosynthesis and functions such as eukaryotic translation initiation, rRNA processing was found to be responsible for cytotoxicity of niraparib in 519 tumor cell lines. Moreover, mRNA expression of PARP1/2, genes participated in ribosome biosynthesis and homologous recombination (HR) were all significantly negatively associated with SF2 in 44 NCI-60 cell lines. The IC50 of niraparib in A172 and U-87-MG cell lines were 10.77±3.31 and 32.37±2.84 μM respectively. The DEF37 was established as 1.99 at 348 nM, 2.17 at 1044 nM for A172 cell line and 1.10 at 1056 nM, 1.44 at 3169 nM for U-87-MG cell line, respectively. Treatment with niraparib alone and in the combination with radiation (4 Gy) resulted in significant increase in fraction of G2 phase in both cell lines. Treatment with niraparib alone did not change protein expression level of DDX21 in both cell lines. However, knockdown of DDX21 with siRNA significantly reduced proliferation in U-87-MG cells. Niraparib at 1056 nM further decreased clonogenic number in the combination with 4 Gy radiation in U-87-MG cells compared with those treated with radiation alone. Importantly, knockdown of DDX21 resulted in significant increasing in clonogenic number of U-87-MG cells treated with radiation alone or the combination of niraparib and radiation compared with control cells. Conclusions Niraparib has radiosensitization effect for GBM cells with proficient BRCA1/2 at low concentration. DDX21 may be involved in the radiosensitization mechanism of niraparib. Citation Format: Jia Luo, He Xiao, Qian Chen, Yanlan Li, Chuan Chen, Mingying Geng. Niraparib enhances radiosensitivity of glioblastoma cells with proficient BRCA1/2 through proliferation-related nucleolar protein DDX21 [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 5720.

50 Years of translation structures

In this paper the term translation structure will denote any geometric object canonically constructed from an elementary abelian group. Hence, translation weak affine spaces, translation planes, linear sets, translation ovoids of polar spaces, translation generalized quadrangles and linear MRD-codes are examples of translation structures. I will present my personal excursus in the theory of finite translation structures, from the pioneering times of B. Segre, A. Barlotti and G. Tallini to these days. My aim is not to give a complete survey of the known results but to describe the influence of translation structures in proofs or disproofs of some conjectures in different areas of Finite Geometries and how valuable tool they were giving significant contributions in different areas of Discrete Mathematics.

Diagnostic Tests for the Necessity of Weight in Regression With Survey Data

SummaryTo weight or not to weight in regression analyses with survey data has been debated in the literature. The problem is essentially a tradeoff between the bias and the variance of the regression coefficient estimator. An array of diagnostic tests for informative weights have been developed. Nonetheless, studies comparing the performance of the tests, especially for finite samples, are scarce, and the theoretical equivalence of some tests has not been investigated. Focusing on the linear regression setting, we review a collection of such tests and propose enhanced versions of some of them that require an auxiliary regression model for the weight. Further, the equivalence of two popular tests is established which has not been reported before. In contrast to existing reviews with no empirical comparison, we compare the sizes and powers of the tests in simulation studies. The reviewed tests are applied to a regression analysis of the family expenditure using the data from the China Family Panel Study.