Linear Map Research Articles

Hausdorff dimension of recurrence sets

We consider linear mappings on the 2-dimensional torus, defined by T(x)=Ax (mod 1) , where A is an invertible 2×2 integer matrix, with no eigenvalues on the unit circle. In the case detA=±1 , we give a formula for the Hausdorff dimension of the set {x∈T2:d(Tn(x),x)<e−αn for infinitely many n}.

Transmission Coefficient-Based Monitoring of Microwave Ablation: Development and Experimental Evaluation in Ex Vivo Tissue.

To assess the feasibility of monitoring transient evolution of thermal ablation zones with a microwave transmission coefficient-based technique. Microwave ablation was performed in ex vivo bovine liver with two 2.45 GHz directional antennas. A custom apparatus was developed to enable periodic switching between "heating mode" when power from the generator was coupled to the antennas, and "monitoring mode", when antennas were coupled to a network analyzer for broadband transmission coefficient ( s21) measurements. Experiments were performed with applied powers ranging between 30-50 W per antenna for 53-1219 s. Transient s21 spectra over the course of ablations were analyzed to determine feasibility of predicting extent of ablation zones and compared against ground truth assessment from images of sectioned tissue. A linear regression-based mapping between the two datasets was derived to predict ablation extent. Normalized average transmission coefficient initially rapidly decreased and then increased before asymptotically approaching steady state, with the transition time ranging between 53 s (45 W) and 109 s (30 W). Analysis of ground truth ablation zone images indicated time to complete ablation of 230-350 s. The relative prediction error for time to complete ablation derived from the s21 data was in the range of 1.6%-2.3% compared to ground truth. We have demonstrated the feasibility of monitoring transient evolution of thermal ablation zones using microwave transmission coefficient measurements in ex vivo tissue. The presented technique has potential to contribute towards addressing the clinical need for a method of monitoring evolution of thermal ablation zones.

Vector finite fields of characteristic two as algebraic support of multivariate cryptography

The central issue of the development of the multivariate public key algorithms is the design of reversible non-linear mappings of $n$-dimensional vectors over a finite field, which can be represented in a form of a set of power polynomials. For the first time, finite fields $GF\left((2^d)^m\right)$ of characteristic two, represented in the form of $m$-dimensional finite algebras over the fields $GF(2^d)$ are introduced for implementing the said mappings as exponentiation operation. This technique allows one to eliminate the use of masking linear mappings, usually used in the known approaches to the design of multivariate cryptography algorithms and causing the sufficiently large size of the public key. The issues of using the fields $GF\left((2^d)^m\right)$ as algebraic support of non-linear mappings are considered, including selection of appropriate values of $m$ and $d$. In the proposed approach to development of the multivariate cryptography algorithms, a superposition of two non-linear mappings is used to define resultant hard-to-reverse mapping with a secret trap door. The used two non-linear mappings provide mutual masking of the corresponding reverse maps, due to which the size of the public key significantly reduces as compared with the known algorithms-analogues at a given security level.

Prediction of Enterprise Human Resource Demand Based on Iot and Data Mining Technology

This paper analyzes the prediction model of enterprise human resource demand based on Internet of Things (IoT) technology and data mining technology. It also analyzes the impact of the company’s growth scale and other key factors on the demand for human resources, tries to establish a coupling factor model of enterprise development and economic benefits, and then analyzes and forecasts the enterprise’s personnel structure and quality structure. The experimental results show that the optimized human resource demand forecasting model integrates the advantages of the grey system model in data processing, can mine the inherent laws of unorganized data information, and provides a certain convenience for forecasting. Through the linear mapping and processing of sample data, the input and output reflect a kind of correlation, thus changing the fault tolerance of information, making the prediction in the calculation process more accurate, and its comprehensive accuracy can exceed 92.5%.

Remark on a theorem of Oguiso

For a Calabi–Yau variety X, Oguiso (Math Res Lett 25(1):181–198, 2018) gave a useful criterion for primitivity of a self-map of X in terms of the associated linear map on the Néron–Severi space of X. In this short note, we prove a variant of Oguiso’s criterion and use it to verify primitivity of a certain birational automorphism of a Calabi–Yau threefold, to which Oguiso’s original criterion does not apply.

DS-AL: A Dual-Stream Analytic Learning for Exemplar-Free Class-Incremental Learning

Class-incremental learning (CIL) under an exemplar-free constraint has presented a significant challenge. Existing methods adhering to this constraint are prone to catastrophic forgetting, far more so than replay-based techniques that retain access to past samples. In this paper, to solve the exemplar-free CIL problem, we propose a Dual-Stream Analytic Learning (DS-AL) approach. The DS-AL contains a main stream offering an analytical (i.e., closed-form) linear solution, and a compensation stream improving the inherent under-fitting limitation due to adopting linear mapping. The main stream redefines the CIL problem into a Concatenated Recursive Least Squares (C-RLS) task, allowing an equivalence between the CIL and its joint-learning counterpart. The compensation stream is governed by a Dual-Activation Compensation (DAC) module. This module re-activates the embedding with a different activation function from the main stream one, and seeks fitting compensation by projecting the embedding to the null space of the main stream's linear mapping. Empirical results demonstrate that the DS-AL, despite being an exemplar-free technique, delivers performance comparable with or better than that of replay-based methods across various datasets, including CIFAR-100, ImageNet-100 and ImageNet-Full. Additionally, the C-RLS' equivalent property allows the DS-AL to execute CIL in a phase-invariant manner. This is evidenced by a never-before-seen 500-phase CIL ImageNet task, which performs on a level identical to a 5-phase one. Our codes are available at https://github.com/ZHUANGHP/Analytic-continual-learning.

DTL: Disentangled Transfer Learning for Visual Recognition

When pre-trained models become rapidly larger, the cost of fine-tuning on downstream tasks steadily increases, too. To economically fine-tune these models, parameter-efficient transfer learning (PETL) is proposed, which only tunes a tiny subset of trainable parameters to efficiently learn quality representations. However, current PETL methods are facing the dilemma that during training the GPU memory footprint is not effectively reduced as trainable parameters. PETL will likely fail, too, if the full fine-tuning encounters the out-of-GPU-memory issue. This phenomenon happens because trainable parameters from these methods are generally entangled with the backbone, such that a lot of intermediate states have to be stored in GPU memory for gradient propagation. To alleviate this problem, we introduce Disentangled Transfer Learning (DTL), which disentangles the trainable parameters from the backbone using a lightweight Compact Side Network (CSN). By progressively extracting task-specific information with a few low-rank linear mappings and appropriately adding the information back to the backbone, CSN effectively realizes knowledge transfer in various downstream tasks. We conducted extensive experiments to validate the effectiveness of our method. The proposed method not only reduces a large amount of GPU memory usage and trainable parameters, but also outperforms existing PETL methods by a significant margin in accuracy, achieving new state-of-the-art on several standard benchmarks.

Epitope mapping of SARS-CoV-2 RBDs by hydroxyl radical protein footprinting reveals the importance of including negative antibody controls

Understanding protein-protein interactions is crucial for drug design and investigating biological processes. Various techniques, such as CryoEM, X-ray spectroscopy, linear epitope mapping, and mass spectrometry-based methods, can be employed to map binding regions on proteins. Commonly used mass spectrometry-based techniques are cross-linking and hydrogen‑deuterium exchange (HDX). Another approach, hydroxyl radical protein footprinting (HRPF), identifies binding residues on proteins but faces challenges due to high initial costs and complex setups.This study introduces a generally applicable method using Fenton chemistry for epitope mapping in a standard mass spectrometry laboratory. It emphasizes the importance of controls, particularly the inclusion of a negative antibody control, not widely utilized in HRPF epitope mapping. Quantification by TMT labelling is introduced to reduce false positives, enabling direct comparison between sample conditions and biological triplicates. Additionally, six technical replicates were incorporated to enhance the depth of analysis.Observations on the receptor-binding domain (RBD) of SARS-CoV-2 Spike Protein, Alpha and Delta variants, revealed both binding and opening regions. Significantly changed peptides upon mixing with a negative control antibody suggested structural alterations or nonspecific binding induced by the antibody alone. Integration of negative control antibody experiments and high overlap between biological triplicates led to the exclusion of 40% of significantly changed regions. The final identified binding region correlated with existing literature on neutralizing antibodies against RBD.The presented method offers a straightforward implementation for HRPF analysis in a generic mass spectrometry-based laboratory. Enhanced data reliability was achieved through increased technical and biological replicates alongside negative antibody controls.

Improving linear orthogonal mapping based cross-lingual representation using ridge regression and graph centrality

Orthogonal linear mapping is a commonly used approach for generating cross-lingual embedding between two monolingual corpora that uses a word frequency-based seed dictionary alignment approach. While this approach is found to be effective for isomorphic language pairs, they do not perform well for distant language pairs with different sentence structures and morphological properties. For a distance language pair, the existing frequency-aligned orthogonal mapping methods suffer from two problems - (i)the frequency of source and target word are not comparable, and (ii)different word pairs in the seed dictionary may have different contribution. Motivated by the above two concerns, this paper proposes a novel centrality-aligned ridge regression-based orthogonal mapping. The proposed method uses centrality-based alignment for seed dictionary selection and ridge regression framework for incorporating influential weights of different word pairs in the seed dictionary. From various experimental observations over five language pairs (both isomorphic and distant languages), it is evident that the proposed method outperforms baseline methods in the Bilingual Dictionary Induction(BDI) task, Sentence Retrieval Task(SRT), and Machine Translation. Further, several analyses are also included to support the proposed method.

Linear maps preserving the Lorentz spectrum of 3 × 3 matrices

Linear maps preserving the Lorentz spectrum of 3 × 3 matrices

Nonlinear acoustic echo cancellation based on pipelined Hermite filters

This paper introduces a new class of nonlinear filters for nonlinear acoustic echo cancellation (NLAEC) based on Hermite nonlinear filters (HNFs), which is a sub-class of linear-in-the-parameters nonlinear filters (LIPNFs). Specifically, the basis functions of HNFs include cross-terms of the expanded inputs at different time instants, and are mutually orthogonal for white normally distributed input signals. Although HNFs yield good performance for NLAEC, they suffer from high computational complexity. To tackle this problem, a computationally efficient pipelined variant of HNFs is introduced. The pipelined HNFs (PHNFs) include a nonlinear part followed by a linear one such that the input space is first expanded nonlinearly and then cast by a linear mapping to the output space. Experimental results using both synthesized and real data, and involving several nonlinear scenarios show the effectiveness of the proposed approach.

Smoothing algorithms for nonsmooth optimization over the Stiefel manifold with applications to the graph Fourier basis problem

In this paper, we consider a class of nonsmooth and nonconvex optimization problems over the Stiefel manifold where the objective function is the summation of a nonconvex smooth function and a nonsmooth Lipschitz continuous convex function composed with a linear mapping. Besides, we are interested in its application to the graph Fourier basis problem. We propose three numerical algorithms for solving this problem, by combining smoothing methods and some existing algorithms for smooth optimization over the Stiefel manifold. In particular, we approximate the aforementioned nonsmooth convex function by its Moreau envelope in our smoothing methods, and prove that the Moreau envelope has many favorable properties. Thanks to this and the scheme for updating the smoothing parameter, we show that any accumulation point of the solution sequence generated by the proposed algorithms is a stationary point of the original optimization problem. Numerical experiments on building graph Fourier basis are conducted to demonstrate the efficiency of the proposed algorithms.

Generalizing Choi map in M3 beyond circulant scenario

We introduce a family of positive linear maps in the algebra of 3 × 3 complex matrices, which generalizes the seminal positive non-decomposable map originally proposed by Choi. Necessary and sufficient conditions for decomposability are derived and demonstrated. Specifically, the proposed maps evolve the circulant structure with three parameters into a doubly stochastic structure with five parameters.

Functional and Immunologic Mapping of Domains of the Reticulocyte-Binding Protein Plasmodium vivax PvRBP2a.

We previously described a novel Plasmodium vivax invasion mechanism into human reticulocytes via the PvRBP2a-CD98 receptor-ligand pair. Using linear epitope mapping, we assessed the PvRBP2a epitopes involved in CD98 binding and recognized by antibodies from patients who were infected. We identified 2 epitope clusters mediating PvRBP2a-CD98 interaction. Cluster B (PvRBP2a431-448, TAALKEKGKLLANLYNKL) was the target of antibody responses in humans infected by P vivax. Peptides from each cluster were able to prevent live parasite invasion of human reticulocytes. These results provide new insights for development of a malaria blood-stage vaccine against P vivax.

Nice Error Basis and Quantum Channel

The Weyl operators give a convenient basis of [Formula: see text] which is also orthonormal with respect to the Hilbert-Schmidt inner product. The properties of such a basis can be generalised to the notion of a nice error basis (NEB), as introduced by E. Knill [3]. We can use an NEB of [Formula: see text] to construct an NEB for [Formula: see text], the space of linear maps on [Formula: see text]. Any linear map will then correspond to a [Formula: see text] coefficient matrix in the basis decomposition with respect to such an NEB of [Formula: see text]. Positivity, complete (co)positivity or other properties of a linear map can be characterised in terms of such a coefficient matrix.

CLASS Angular Power Spectra and Map-component Analysis for 40 GHz Observations through 2022

Measurement of the largest angular scale (ℓ < 30) features of the cosmic microwave background (CMB) polarization is a powerful way to constrain the optical depth to reionization and search for the signature of inflation through the detection of primordial B-modes. We present an analysis of maps covering 73.6% of the sky made from the 40 GHz channel of the Cosmology Large Angular Scale Surveyor (CLASS) from 2016 August to 2022 May. Taking advantage of the measurement stability enabled by front-end polarization modulation and excellent conditions from the Atacama Desert, we show this channel achieves higher sensitivity than the analogous frequencies from satellite measurements in the range 10 < ℓ < 100. Simulations show the CLASS linear (circular) polarization maps have a white noise level of 125(130)μKarcmin . We measure the Galaxy-masked EE and BB spectra of diffuse synchrotron radiation and compare to space-based measurements at similar frequencies. In combination with external data, we expand measurements of the spatial variations of the synchrotron spectral energy density (SED) to include new sky regions and measure the diffuse SED in the harmonic domain. We place a new upper limit on a background of circular polarization in the range 5 < ℓ < 125 with the first bin showing D ℓ < 0.023 μKCMB2 at 95% confidence. These results establish a new standard for recovery of the largest-scale CMB polarization from the ground and signal exciting possibilities when the higher sensitivity and higher-frequency CLASS channels are included in the analysis.

High-resolution epitope mapping of commercial antibodies to ANCA antigens by yeast surface display

Epitope mapping provides critical insight into antibody-antigen interactions. Epitope mapping of autoantibodies from patients with autoimmune diseases can help elucidate disease immunogenesis and guide the development of antigen-specific therapies. Similarly, epitope mapping of commercial antibodies targeting known autoantigens enables the use of those antibodies to test specific hypotheses. Anti-Neutrophil Cytoplasmic Autoantibody (ANCA) vasculitis results from the formation of autoantibodies to multiple autoantigens, including myeloperoxidase (MPO), proteinase-3 (PR3), plasminogen (PLG), and peroxidasin (PXDN). To perform high-resolution epitope mapping of commercial antibodies to these autoantigens, we developed a novel yeast surface display library based on a series of >5000 overlapping peptides derived from their protein sequences. Using both FACS and magnetic bead isolation of reactive yeast, we screened 19 commercially available antibodies to the ANCA autoantigens. This approach to epitope mapping resulted in highly specific, fine epitope mapping, down to single amino acid resolution in many cases. Our study also identified cross-reactivity between some commercial antibodies to MPO and PXDN, which suggests that patients with apparent autoantibodies to both proteins may be the result of cross-reactivity. Together, our data validate yeast surface display using maximally overlapping peptides as an excellent approach to linear epitope mapping.

C⁎-extreme entanglement breaking maps on operator systems

Let E denote the set of all unital entanglement breaking (UEB) linear maps defined on an operator system S⊂Md and, mapping into Mn. As it turns out, the set E is not only convex in the classical sense but also in a quantum sense, namely it is C⁎-convex. The main objective of this article is to describe the C⁎-extreme points of this set E. By observing that every EB map defined on the operator system S dilates to a positive map with commutative range and also extends to an EB map on Md, we show that the C⁎-extreme points of the set E are precisely the UEB maps that are maximal in the sense of Arveson ([1] and [2]) and that they are also exactly the linear extreme points of the set E with commutative range. We also determine their explicit structure, thereby obtaining operator system generalizations of the analogous structure theorem and the Krein-Milman type theorem given in [8]. As a consequence, we show that C⁎-extreme (UEB) maps in E extend to C⁎-extreme UEB maps on the full algebra. Finally, we obtain an improved version of the main result in [8], which contains various characterizations of C⁎-extreme UEB maps between the algebras Md and Mn.

Hardware-Accelerated YOLOv5 Based on MPSoC

This paper details the development of a hardware acceleration system for YOLOv5, focusing on flame detection as its primary application. The implementation leverages the APU and DPU functionalities integrated into the Zynq UltraScale+ MPSoC XCZU7EV core. The proposed solution addresses the challenge of achieving real-time target detection on mobile terminals, ensuring both real-time operation and ultralow power consumption of YOLOv5. Notably, our design approach facilitates the deployment of all target detection algorithms under TensorFlow for mobile devices. To optimize model efficiency, we employ saturated linear mapping quantization with calibration. This technique maps model weights, double bases, and activations from 32-bit to 8-bit, incurring only a 1.64% accuracy loss. The data flow design is realized through efficient data exchange between DDR, APU, and DPU, utilizing the AXI4 bus architecture. Image pre-processing and post-processing tasks are executed on the APU, while neural network inference occurs on the DPU. Our accelerated system demonstrates compelling experimental results: maintaining a detection speed of 56FPS, achieving an accuracy of 36.56% on the COCO2014 dataset, and exhibiting a total system power consumption of only 4.147W. Furthermore, the energy consumption ratio is measured at 15.41GOPS/W, surpassing the RTX A6000 graphics card by a factor of 55.

MULTI-PARAMETER MUELLER-MATRIX TOMOGRAPHY OF HISTOLOGICAL SAMPLES OF BIOLOGICAL TISSUES AS AN ACCURATE AND EFFECTIVE METHOD FOR DETERMINING THE DEGREE OF BLOOD LOSS

Establishing the volume of blood loss is extremely important in the context of forensic practice, as it can indicate various circumstances of death and is important in solving criminal cases. Consideration of modern methods of determining this parameter in the article is relevant and aims to reveal new opportunities and perspectives in this field of forensic medical examination.&#x0D; Aim of the work. To develop a set of new forensic criteria for accurate determination of the volume of blood loss using the method of multichannel polarization Muller-matrix tomography of histological sections of parenchymal organs and human blood samples.&#x0D; Materials and methods. Samples of parenchymal organs and human blood were collected from 76 corpses of both sexes with varying degrees of blood loss from 0 mm3 to 2500 mm3. The research was carried out using the method of multichannel polarization Muller-matrix linear dichroism tomography of biological tissue samples.&#x0D; Results. For all studied biological samples, a decrease in the level of circular birefringence (CB) of formed blood elements against the background of a gradual necrotic decrease in distributions of linear birefringence (LB) of the optical anisotropy of parenchymal tissues and blood films was established for the process of blood loss. The range of sensitivity of the method of differential Mueller-matrix tomography with algorithmic reproduction of linear dichroism maps to changes in blood loss volume of the deceased, which is (0±2000) mm3, is determined.&#x0D; Conclusions. The accuracy of the method of differential Mueller matrix mapping with algorithmic reproduction of linear dichroism maps of biological preparations was determined, which is 86-92 % in the range of the level of blood loss ΔV = (0±2000) mm3.