Covariance Maps Research Articles

On Some Applications of P-Contraction Fixed Point Theorems in Bipolar Metric Spaces

In this paper, we have discussed the P-contraction type fixed point theorems of covariant mappings in bipolar metric spaces, and we have shown an example which supports our results. Also we discussed applications to integral equations and Homotopy theory.

Fragment Correlation Mass Spectrometry Enables Direct Characterization of Disulfide Bond Cleavage Pathways of Therapeutic Peptides.

Therapeutic peptides that are connected by disulfide bonds are often difficult to analyze by traditional tandem mass spectrometry without chemical modification. Using fragment correlation mass spectrometry, we analyzed 56 pairs of fragment ions generated from an equimolar (10 μM) mixture of three cyclic peptides, achieving sequence coverage of 86%, 100%, and 75% for octreotide, desmopressin, and the structural analogue of desmopressin, respectively. In all detected fragment ion pairs, only 20% of the fragment ions are terminal ions, with most of the measured ions only detected by fragment correlation mass spectrometry. From the peak volumes in the covariance map, we calculated branching ratios of each disulfide bond fragmentation pathway, providing a direct measurement of the probability of each fragmentation without requiring alteration of the chemical structure of the analytes.

([formula omitted])-contractive and ([formula omitted])-contractive mapping based fixed point theorems in fuzzy bipolar metric spaces and application to nonlinear Volterra integral equations

In this paper, we introduce some novel concepts within the realm of fuzzy bipolar metric spaces, namely (αη)-contractive type covariant mappings and contravariant mappings, and (βχ)-contractive type covariant mappings. We establish some fixed point theorems that demonstrate both the existence and uniqueness of fixed points for (αη)-contractive type covariant mappings and contravariant mappings, and for (βχ)-contractive type covariant mappings in complete fuzzy bipolar metric spaces utilizing the triangular property. Additionally, to substantiate the findings, some illustrative examples and consequential outcomes are presented. Furthermore, the proven results serve to extend, generalize, and enhance the corresponding outcomes documented in existing literature. A practical application of these findings in the context of non-linear Volterra integral equations is demonstrated, solidifying and reinforcing the credibility of the established results. Overall, this paper contributes to the understanding of fixed point theory in the context of fuzzy bipolar metric spaces and highlights the significance of (αη)-contractive mappings and (βχ)-contractive mappings in this domain.

A universal framework for entanglement detection under group symmetry

One of the fundamental questions in quantum information theory is determining entanglement of quantum states, which is generally an NP-hard problem. In this paper, we prove that all PPT (π―A⊗πB) -invariant quantum states are separable if and only if all extremal unital positive (πB,πA) -covariant maps are decomposable where πA,πB are unitary representations of a compact group and π A is irreducible. Moreover, an extremal unital positive (πB,πA) -covariant map L is decomposable if and only if L is completely positive or completely copositive. We then apply these results to prove that all PPT quantum channels of the form Φ(ρ)=aTr(ρ)dIdd+bρ+cρT+(1−a−b−c)diag(ρ) are entanglement-breaking, and that there is no A-BC PPT-entangled (U⊗U―⊗U) -invariant tripartite quantum state. The former strengthens some conclusions in (Vollbrecht and Werner 2001 Phys. Rev. A 64 062307; Kopszak et al 2020 J. Phys. A: Math. Theor. 53 395306), and the latter resolves some open questions raised in (Collins et al 2018 Linear Algebra Appl. 555 398–411).

K-Positivity and Schmidt number under orthogonal group symmetries

In this paper, we present a new application of group theory to develop a systematical approach to efficiently compute the Schmidt numbers. The Schmidt number is a natural quantification of entanglement in quantum information theory, but computing its exact value is generally a challenging task even for very concrete examples. We exhibit a complete characterization of all orthogonally covariant k-positive maps. This result generalizes earlier results by Tomiyama (Linear Algebra Appl 69:169–177, 1985). Furthermore, we optimize duality relations between k-positivity and Schmidt numbers under group symmetries. This new approach enables us to transfer the results of k-positivity to the computation of the Schmidt numbers of all orthogonally invariant quantum states.

Two-Dimensional Projected-Momentum Covariance Mapping for Coulomb Explosion Imaging.

We introduce projected-momentum covariance mapping, an extension of recoil-frame covariance mapping for 2D ion imaging studies. By considering the two-dimensional projection of the ion momenta as recorded by the detector, one opens the door to a complex suite of analysis tools adapted from three-dimensional momentum imaging studies. This includes the use of different frames of reference to unravel the dynamics of fragmentation and the application of fragment momentum constraints to isolate specific fragmentation channels. The technique is demonstrated on data from a two-dimensional ion imaging study of the Coulomb explosion of the cis and trans isomers of 1,2-dichloroethene, following strong-field ionization by an intense near-infrared femtosecond laser pulse. Classical simulations are used to guide the interpretation of projected-momentum covariance maps. The results offer a detailed insight into the distinct Coulomb explosion dynamics for this pair of isomers and lay the groundwork for future time-resolved studies of photoisomerization dynamics in this molecular system.

Boyd-Wong type contractions in generalized parametric bipolar metric space

In this manuscript, we introduce a new notion of generalized parametric bipolar metric space as a generalization of generalized parametric space and bipolar metric space. We also introduce Boyd-Wong type contractions for covariant and contravariant mappings to prove the fixed point results in the newly defined space. Some examples are also provided to illustrate the main results. Some corollaries are given of our results which shows the existence of fixed point for Banach type covariant and contravariant contractions. We solve integral and fractional differential equations with the help of proved results.

On some quadruple fixed points of covariant mappings in bipolar metric spaces with applications

On some quadruple fixed points of covariant mappings in bipolar metric spaces with applications

Organization of thalamocortical structural covariance and a corresponding 3D atlas of the mouse thalamus

For information from sensory organs to be processed by the brain, it is usually passed to appropriate areas of the cerebral cortex. Almost all of this information passes through the thalamus, a relay structure that reciprocally connects to the vast majority of the cortex. The thalamus facilitates this information transfer through a set of thalamocortical connections that vary in cellular structure, molecular profiles, innervation patterns, and firing rates. Additionally, corticothalamic connections allow for intracortical information transfer through the thalamus. These efferent and afferent connections between the thalamus and cortex have been the focus of many studies, and the importance of cortical connectivity in defining thalamus anatomy is demonstrated by multiple studies that parcellate the thalamus based on cortical connectivity profiles.Here, we examine correlated morphological variation between the thalamus and cortex, or thalamocortical structural covariance. For each voxel in the thalamus as a seed, we construct a cortical structural covariance map that represents correlated cortical volume variation, and examine whether high structural covariance is observed in cortical areas that are functionally relevant to the seed. Then, using these cortical structural covariance maps as features, we subdivide the thalamus into six non-overlapping regions (clusters of voxels), and assess whether cortical structural covariance is associated with cortical connectivity that specifically originates from these regions.We show that cortical structural covariance is high in areas of the cortex that are functionally related to the seed voxel, cortical structural covariance varies along cortical depth, and sharp transitions in cortical structural covariance profiles are observed when varying seed locations in the thalamus. Subdividing the thalamus based on structural covariance, we additionally demonstrate that the six thalamic clusters of voxels stratify cortical structural covariance along the dorsal–ventral, medial–lateral, and anterior–posterior axes. These cluster-associated structural covariance patterns are prominently detected in cortical regions innervated by fibers projecting out of their related thalamic subdivisions.Together, these results advance our understanding of how the thalamus and the cortex couple in their volumes. Our results indicate that these volume correlations reflect functional organization and structural connectivity, and further provides a novel segmentation of the mouse thalamus that can be used to examine thalamic structural variation and thalamocortical structural covariation in disease models.

Solving Integral Equation and Homotopy Result via Fixed Point Method

The aim of the present research article is to investigate the existence and uniqueness of a solution to the integral equation and homotopy result. To achieve our objective, we introduce the notion of (α,η,ψ)-contraction in the framework of F-bipolar metric space and prove some fixed point results for covariant and contravariant mappings. Some coupled fixed point results in F-bipolar metric space are derived as outcomes of our principal theorems. A non-trivial example is also provided to validate the authenticity of the established results.

Toward secret data location via fuzzy logic and convolutional neural network

Locating hidden data in digital images, otherwise called steganalysis, is a process of identifying the existence of secret messages within digital images. Steganalysis is used to manage digital data transmission by detecting the possible hidden information that can be used to violate the network policy; hence, it helps the development of policies and regulations aimed at strong protection from cyber threats to individuals’ and organizations’ data. The research works in the field of information security commonly focus on developing the locating approaches for non-adaptive steganography, which present a problem of less investigation of the complex challenge of locating the payload embedded with an adaptive steganographic algorithm. In this article, we propose a method to locate hidden data in a digital image in three stages: a) Identification of the modification maps between the carrier and final images. b) Using the modification maps as input to Mamdani fuzzy inference with four input membership functions: covariance map matrix, compass mean matrix, distance vector matrix, and pixel intensity matrix, and one output membership function, notably the fuzzy correlation maps. c) Feeding the fuzzy correlation maps to a convolutional neural network to identify the pixels with confidential data from the innocent pixels. By experimenting with our method against four steganographic algorithms, namely, HILL, HUGO-BD, WOW, and S-UNIWARD, the recall rates for the four algorithms initially increase in a similar range and improve with increasing payload capacity, which justifies the outperformance of the proposed strategy over the existing methods.

Brain network changes in adult victims of violence.

Stressful experiences such as violence can affect mental health severely. The effects are associated with changes in structural and functional brain networks. The current study aimed to investigate brain network changes in four large-scale brain networks, the default mode network, the salience network, the fronto-parietal network, and the dorsal attention network in self-identified victims of violence and controls who did not identify themselves as victims. The control group (n = 32) was matched to the victim group (n = 32) by age, gender, and primary psychiatric disorder. Sparse inverse covariance maps were derived from functional resting-state measurements and from T1 weighted structural data for both groups. Our data underlined that mostly the salience network was affected in the sample of self-identified victims. In self-identified victims with a current psychiatric diagnosis, the dorsal attention network was mostly affected underlining the potential role of psychopathological alterations on attention-related processes. The results showed that individuals who identify themselves as victim demonstrated significant differences in all considered networks, both within- and between-network.

Parkinson’s disease may disrupt overlapping subthalamic nucleus and pallidal motor networks

There is an ongoing debate about differential clinical outcome and associated adverse effects of deep brain stimulation (DBS) in Parkinson’s disease (PD) targeting the subthalamic nucleus (STN) or the globus pallidus pars interna (GPi). Given that functional connectivity profiles suggest beneficial DBS effects within a common network, the empirical evidence about the underlying anatomical circuitry is still scarce. Therefore, we investigate the STN and GPi-associated structural covariance brain patterns in PD patients and healthy controls.We estimate GPi’s and STN’s whole-brain structural covariance from magnetic resonance imaging (MRI) in a normative mid- to old-age community-dwelling cohort (n = 1184) across maps of grey matter volume, magnetization transfer (MT) saturation, longitudinal relaxation rate (R1), effective transversal relaxation rate (R2*) and effective proton density (PD*). We compare these with the structural covariance estimates in patients with idiopathic PD (n = 32) followed by validation using a reduced size controls’ cohort (n = 32).In the normative data set, we observed overlapping spatially distributed cortical and subcortical covariance patterns across maps confined to basal ganglia, thalamus, motor, and premotor cortical areas. Only the subcortical and midline motor cortical areas were confirmed in the reduced size cohort. These findings contrasted with the absence of structural covariance with cortical areas in the PD cohort.We interpret with caution the differential covariance maps of overlapping STN and GPi networks in patients with PD and healthy controls as correlates of motor network disruption. Our study provides face validity to the proposed extension of the currently existing structural covariance methods based on morphometry features to multiparameter MRI sensitive to brain tissue microstructure.

Some Common Fixed Point Theorems in Bipolar Metric Spaces

In this article, we introduce the notion of commutativity for covariant and contravariant mappings in bipolar metric spaces. Afterwards, by using this notion, we prove some common fixed point theorems which show the existence and uniqueness of common fixed point for covariant and contravariant mappings satisfying contractive type conditions.

A bivariant Yoneda lemma and (∞,2)–categories of correspondences

Everyone knows that if you have a bivariant homology theory satisfying a base change formula, you get an representation of a category of correspondences. For theories in which the covariant and contravariant transfer maps are in mutual adjunction, these data are actually equivalent. In other words, a 2-category of correspondences is the universal way to attach to a given 1-category a set of right adjoints that satisfy a base change formula. Through a bivariant version of the Yoneda paradigm, I give a definition of correspondences in higher category theory and prove an extension theorem for bivariant functors. Moreover, conditioned on the existence of a 2-dimensional Grothendieck construction, I provide a proof of the aforementioned universal property. The methods, morally speaking, employ the `internal logic' of higher category theory: they make no explicit use of any particular model.

Fixed Points on Covariant and Contravariant Maps with an Application

Fixed-point results on covariant maps and contravariant maps in a C★-algebra-valued bipolar metric space are proved. Our results generalize and extend some recently obtained results in the existing literature. Our theoretical results in this paper are supported with suitable examples. We have also provided an application to find an analytical solution to the integral equation and the electrical circuit differential equation.

Phase Covariant Channel: Quantum Speed Limit of Evolution

AbstractThe quantum speed of evolution for the phase covariant map is investigated. This involves absorption, emission, and dephasing processes. The maps under various combinations of the above processes are considered to investigate the effect of phase covariant maps on quantum speed limit time. For absorption‐free phase covariant maps, combinations of dissipative and CP‐(in)divisible (non)‐Markovian dephasing noises are considered. The role of coherence‐mixedness balance on the speed limit time is checked in the presence of both vacuum and finite temperature effects. The rate at which Holevo's information changes and the action quantum speed of evolution for specific cases of the phase covariant map are also investigated.

Multi-Prior Twin Least-Square Network for Anomaly Detection of Hyperspectral Imagery

Anomaly detection of hyperspectral imagery (HSI) identifies the very few samples that do not conform to an intricate background without priors. Despite the extensive success of hyperspectral interpretation techniques based on generative adversarial networks (GANs), applying trained GAN models to hyperspectral anomaly detection remains promising but challenging. Previous generative models can accurately learn the complex background distribution of HSI and typically convert the high-dimensional data back to the latent space to extract features to detect anomalies. However, both background modeling and feature-extraction methods can be improved to become ideal in terms of the modeling power and reconstruction consistency capability. In this work, we present a multi-prior-based network (MPN) to incorporate the well-trained GANs as effective priors to a general anomaly-detection task. In particular, we introduce multi-scale covariance maps (MCMs) of precise second-order statistics to construct multi-scale priors. The MCM strategy implicitly bridges the spectral- and spatial-specific information and fully represents multi-scale, enhanced information. Thus, we reliably and adaptively estimate the HSI label to alleviate the problem of insufficient priors. Moreover, the twin least-square loss is imposed to improve the generative ability and training stability in feature and image domains, as well as to overcome the gradient vanishing problem. Last but not least, the network, enforced with a new anomaly rejection loss, establishes a pure and discriminative background estimation.

The kinetic energy of PAH dication and trication dissociation determined by recoil-frame covariance map imaging.

We investigated the dissociation of dications and trications of three polycyclic aromatic hydrocarbons (PAHs), fluorene, phenanthrene, and pyrene. PAHs are a family of molecules ubiquitous in space and involved in much of the chemistry of the interstellar medium. In our experiments, ions are formed by interaction with 30.3 nm extreme ultraviolet (XUV) photons, and their velocity map images are recorded using a PImMS2 multi-mass imaging sensor. Application of recoil-frame covariance analysis allows the total kinetic energy release (TKER) associated with multiple fragmentation channels to be determined to high precision, ranging 1.94-2.60 eV and 2.95-5.29 eV for the dications and trications, respectively. Experimental measurements are supported by Born-Oppenheimer molecular dynamics (BOMD) simulations.

Multi-mass velocity map imaging study of the 805 nm strong field ionization of CF3I.

Multi-mass velocity map imaging studies of charged fragments formed by near infrared strong field ionization together with covariance map image analysis offer a new window through which to explore the dissociation dynamics of several different highly charged parent cations, simultaneously - as demonstrated here for the case of CF3IZ+ cations with charges Z ranging from 1 to at least 5. Previous reports that dissociative ionization of CF3I+ cations yields CF3+, I+ and CF2I+ fragment ions are confirmed, and some of the CF3+ fragments are deduced to undergo secondary loss of one or more neutral F atoms. Covariance map imaging confirms the dominance of CF3+ + I+ products in the photodissociation of CF3I2+ cations and, again, that some of the primary CF3+ photofragments can shed one or more F atoms. Rival charge symmetric dissociation pathways to CF2I+ + F+ and to IF+ + CF2+ products and charge asymmetric dissociations to CF3 + I2+ and CF2I2+ + F products are all also identified. The findings for parent cations with Z ≥ 3 are wholly new. In all cases, the fragment recoil velocity distributions imply dissociation dynamics in which coulombic repulsive forces play a dominant role. The major photoproducts following dissociation of CF3I3+ ions are CF3+ and I2+, with lesser contributions from the rival CF2I2+ + F+ and CF32+ + I+ channels. The CF32+ fragment ion images measured at higher incident intensities show a faster velocity sub-group consistent with their formation in tandem with I2+ fragments, from photodissociation of CF3I4+ parent ions. The measured velocity distributions of the I3+ fragment ions contain features attributable to CF3I5+ photodissociation to CF32+ + I3+ and the images of fragments with mass to charge (m/z) ratio ∼31 show formation of I4+ products that must originate from parent ions with yet higher Z.