Complex Counterpart Research Articles

Efficacy of Keystroke Dynamics-Based User Authentication in the Face of Language Complexity

Introduction: This study investigates the impact of language complexity on Keystroke Dynamics (KD) and its implications for accurate KD-based user authentication system performance in smartphones. Method: This research meticulously analyzes keystroke patterns using 160 volunteers, including both frequently typed and infrequently typed texts. Our analysis of 12 anomaly detection algorithms reveals that a simple text-based KD system consistently outperforms its complex counterpart with superior Equal Error Rates (EERs). Results: As a result, the Scaled Manhattan anomaly detector achieves an EER of 2.48% for simple text and an improvement over 2.98% for complex text. The incorporation of soft biometrics further enhances algorithmic performance, emphasizing strategies to build resilience into KD-based user authentication systems. Conclusion: Throughout this study, the importance of text complexity is emphasized, and innovative pathways are introduced to strengthen KD-based user authentication paradigms.

A Matrix Li–Yau–Hamilton Estimate for the Green Function on Kähler Manifolds

Abstract We prove a matrix Li–Yau–Hamilton inequality for the Green function on complete Kähler manifolds with nonnegative holomorphic bisectional curvature. This estimate is an elliptic analogue of the matrix estimate of Cao and Ni for the heat equation on Kähler manifolds. It is also the complex counterpart of the matrix estimate on Riemannian manifolds obtained previously by the author.

Unraveling Balinese Binding

This paper discusses the logophoric properties of Balinese anaphors. This paper first presents evidence showing that the Balinese complex anaphor may be interpreted logophorically even in the presence of a syntactic coargument. This leads to a novel solution of the "Balinese Bind paradox." This proposal is better able to account for the interpretive constraints observed in raising constructions than previous proposals. In addition to this analysis, this paper discusses the implications of the properties of the Balinese simplex anaphor, which cannot be interpreted logophorically; only its complex counterpart can. This presents a pattern opposite to the one reported and predicted by the literature.

Approaches to Visualising Endocytosis of LDL-Related Lipoproteins.

Endocytosis is the process by which molecules are actively transported into cells. It can take on a variety of forms depending on the cellular machinery involved ranging from specific receptor-mediated endocytosis to the less selective and actin-driven macropinocytosis. The plasma lipoproteins, which deliver lipids and other cargo to cells, have been intensely studied with respect to their endocytic uptake. One of the first molecules to be visualised undergoing endocytosis via a receptor-mediated, clathrin-dependent pathway was low-density lipoprotein (LDL). The LDL molecule has subsequently been shown to be internalised through multiple endocytic pathways. Dissecting the pathways of lipoprotein endocytosis has been crucial to understanding the regulation of plasma lipid levels and how lipids enter cells in the arterial wall to promote atherosclerosis. It has also aided understanding of the dysregulation that occurs in plasma lipid levels when molecules involved in uptake are defective, as is the case in familial hypercholesterolemia (FH). The aim of this review is to outline the many endocytic pathways utilised for lipoprotein uptake. It explores the various experimental approaches that have been applied to visualise lipoprotein endocytosis with an emphasis on LDL and its more complex counterpart, lipoprotein(a) [Lp(a)]. Finally, we look at new developments in lipoprotein visualisation that hold promise for scrutinising endocytic pathways to finer detail in the future.

Asymptotic interplay of states and adaptive coupling gains in the Lohe Hermitian sphere model

<p style='text-indent:20px;'>We study emergent dynamics of the Lohe Hermitian sphere (LHS) model with the same free flows under the dynamic interplay between state evolution and adaptive couplings. The LHS model is a complex counterpart of the Lohe sphere (LS) model on the unit sphere in Euclidean space, and when particles lie in the Euclidean unit sphere embedded in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb C^{d+1} $\end{document}</tex-math></inline-formula>, it reduces to the Lohe sphere model. In the absence of interactions between states and coupling gains, emergent dynamics have been addressed in [<xref ref-type="bibr" rid="b23">23</xref>]. In this paper, we further extend earlier results in the aforementioned work to the setting in which the state and coupling gains are dynamically interrelated via two types of coupling laws, namely anti-Hebbian and Hebbian coupling laws. In each case, we present two sufficient frameworks leading to complete aggregation depending on the coupling laws, when the corresponding free flow is the same for all particles.</p>

Complex counterpart of variance in quantum measurements for pre- and postselected systems

The variance of an observable in a pre-selected quantum system, which is always real and non-negative, appears as an increase in the probe wave packet width in indirect measurements. Extending this framework to pre- and post-selected systems, we formulate a complex-valued counterpart of the variance called "weak variance." In our formulation, the real and imaginary parts of the weak variance appear as changes in the probe wave packet width in the vertical-horizontal and diagonal-antidiagonal directions, respectively, on the quadrature phase plane. Using an optical system, we experimentally demonstrate these changes in the probe wave packet width caused by the real negative and purely imaginary weak variances. Furthermore, we show that the weak variance can be expressed as the variance of the weak-valued probability distribution in pre- and post-selected systems. These operational and statistical interpretations support the rationality of formulating the weak variance as a complex counterpart of the variance in pre- and post-selected systems.

Emergent dynamics of the Lohe Hermitian sphere model with frustration

We study emergent dynamics of the Lohe Hermitian sphere (LHS) model, which can be derived from the Lohe tensor model [S.-Y. Ha and H. Park, SIAM J. Appl. Dyn. Syst. 13, 1312–1342 (2020)] as a complex counterpart of the Lohe sphere model. The LHS model describes aggregate dynamics of point particles on the Hermitian sphere HSd lying in Cd+1, and the coupling terms in the LHS model consist of two terms. For an identical ensemble with the same free flow dynamics, we provide a sufficient framework, leading to the complete aggregation in which all point particles form a giant one-point cluster asymptotically. In contrast, for a non-identical ensemble, we also provide a sufficient framework for the practical aggregation. Our sufficient framework is formulated in terms of coupling strengths and initial data. We also provide several numerical examples and compare them with analytical results.

Emergent behaviors of Lohe Hermitian sphere particles under time-delayed interactions

<p style='text-indent:20px;'>We study emergent behaviors of the Lohe Hermitian sphere(LHS) model with a time-delay for a homogeneous and heterogeneous ensemble. The LHS model is a complex counterpart of the Lohe sphere(LS) aggregation model on the unit sphere in Euclidean space, and it describes the aggregation of particles on the unit Hermitian sphere in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb C^d $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M2">\begin{document}$ d \geq 2 $\end{document}</tex-math></inline-formula>. Recently it has been introduced by two authors of this work as a special case of the Lohe tensor model. When the coupling gain pair satisfies a specific linear relation, namely the Stuart-Landau(SL) coupling gain pair, it can be embedded into the LS model on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb R^{2d} $\end{document}</tex-math></inline-formula>. In this work, we show that if the coupling gain pair is close to the SL coupling pair case, the dynamics of the LHS model exhibits an emergent aggregate phenomenon via the interplay between time-delayed interactions and nonlinear coupling between states. For this, we present several frameworks for complete aggregation and practical aggregation in terms of initial data and system parameters using the Lyapunov functional approach.</p>

Ni-β-diimine complex heterogenized in delaminated ITQ-2 zeolite as catalytic precursor for ethylene oligomerization

A heterogenized nickel catalytic precursor was synthesized and applied in ethylene oligomerization catalytic reactions. For this, a β-diimine ligand was covalently anchored to the delaminated ITQ-2 zeolite and the metal complexed. The homogeneous nickel complex was synthesized in order to compare the effect of catalyst heterogenization on the reaction. The synthesized materials were characterized by several techniques, such as 1H NMR, solid-state 29Si CP-MAS-NMR, FTIR, TGA, N2 adsorption, flame atomic absorption spectroscopy, elemental analysis and X-ray absorption spectroscopy (XAS). The heterogenized catalytic precursor showed similar catalytic activity and higher selectivity for the target products to its homogeneous complex counterpart. The higher stability of the nickel centers under oxidative handling conditions was demonstrated by the XAS measurements. It was possible to reuse the catalytic precursor twice in oligomerization reactions despite the loss of catalytic activity ascribed to the presence of an excess of co-catalyst. Notwithstanding, it was demonstrated that Al-containing delaminated zeolites are promising materials for anchoring β-diimine-based catalytic precursors in comparison with mesoporous materials due to their higher acidity, which improves the intrinsic catalytic activity (turnover frequency, TOF) due to the higher nickel electron withdrawing capacity provided by the acidic support.

Modulated Model Predictive Control for Four-Leg Inverters With Online Duty Ratio Optimization

Conventional finite control set (FCS) predictive load-voltage control for four-leg inverters features simplification in digital implementation compared to its complex counterpart, three-dimensional space vector modulation. However, the FCS approach is typically characterized by a variable switching frequency, low steady-state performance, and a higher average switching frequency in the neutral leg than the other three legs. To overcome these shortcomings, an online duty-cycle-optimization based model predictive control technique is proposed in this article. The performance of the inverter is evaluated experimentally in terms of load voltage tracking in different operating conditions such as nonlinear loads and balanced/unbalanced references. The proposed technique fulfills the requirement of a high-performance converter, constant switching frequency, and enhanced load voltage tracking at a lower sampling rate and, thus, solves the drawbacks of the conventional FCS model predictive control for a four-leg inverter. Furthermore, the proposed approach can facilitate the overmodulation operation, which is desirable for this type of power converters under nonlinear and unbalanced loading conditions.

On the Nullstellensatz for c-holomorphic functions with algebraic graphs

C-holomorphic functions defined on algebraic sets and having algebraic graphs can be considered as a complex counterpart of regulous functions introduced recently in real geometry. This note is a part of our study on the subject; we prove herein some effective Nullstellensatze.

The Kibble-Zurek mechanism at exceptional points

Exceptional points (EPs) are ubiquitous in non-Hermitian systems, and represent the complex counterpart of critical points. By driving a system through a critical point at finite rate induces defects, described by the Kibble-Zurek mechanism, which finds applications in diverse fields of physics. Here we generalize this to a ramp across an EP. We find that adiabatic time evolution brings the system into an eigenstate of the final non-Hermitian Hamiltonian and demonstrate that for a variety of drives through an EP, the defect density scales as τ−(d + z)ν/(zν + 1) in terms of the usual critical exponents and 1/τ the speed of the drive. Defect production is suppressed compared to the conventional Hermitian case as the defect state can decay back to the ground state close to the EP. We provide a physical picture for the studied dynamics through a mapping onto a Lindblad master equation with an additionally imposed continuous measurement.

Development of C-Means Clustering Based Adaptive Fuzzy Controller for a Flapping Wing Micro Air Vehicle

Abstract Advanced and accurate modelling of a Flapping Wing Micro Air Vehicle (FW MAV) and its control is one of the recent research topics related to the field of autonomous MAVs. Some desiring features of the FW MAV are quick flight, vertical take-off and landing, hovering, and fast turn, and enhanced manoeuvrability contrasted with similar-sized fixed and rotary wing MAVs. Inspired by the FW MAV’s advanced features, a four-wing Nature-inspired (NI) FW MAV is modelled and controlled in this work. The Fuzzy C-Means (FCM) clustering algorithm is utilized to construct the data-driven NIFW MAV model. Being model free, it does not depend on the system dynamics and can incorporate various uncertainties like sensor error, wind gust etc. Furthermore, a Takagi-Sugeno (T-S) fuzzy structure based adaptive fuzzy controller is proposed. The proposed adaptive controller can tune its antecedent and consequent parameters using FCM clustering technique. This controller is employed to control the altitude of the NIFW MAV, and compared with a standalone Proportional Integral Derivative (PID) controller, and a Sliding Mode Control (SMC) theory based advanced controller. Parameter adaptation of the proposed controller helps to outperform it static PID counterpart. Performance of our controller is also comparable with its advanced and complex counterpart namely SMC-Fuzzy controller.

Case valuation after scrambling: Nominative objects in Japanese

This paper provides new evidence for the claim that nominative objects in Japanese undergo overt movement without remaining at their base-generated positions, based on a variant of the construction which has not received as much attention as its complex predicate counterpart. It is then argued that the overt movement is scrambling. Departing from the general assumption, this paper investigates the hypothesis that an application of scrambling affects Case valuation, which was originally investigated by Fukui & Nishigauchi (1992) and Fukui (1995) (cf. Kuno 2002). Under the proposal, a nominative object is scrambled from its original position to the edge of vP, where nominative Case can be assigned. When scrambling does not take place, the object stays in-situ and receives accusative Case at its base-generated position. In other words, the Case alternation is contingent on the application of scrambling, which captures the optionality of the Case alternation in terms of that of scrambling. It is also proposed that the proposed mechanism of the Case alternation be restricted in such a way that the landing site and the base-generated position are included in the same transferred domain. Given this restriction, it is also possible to correctly capture cases where scrambling does not affect case valuation. The proposed analysis crucially adopts the hypothesis proposed by Chomsky (2001), where the transferred domain is the complement of a phase head. To the extent that the proposed analysis is successful, this paper lends support to this characterization of transferred domains.

Fisher Vectors for PolSAR Image Classification

In this letter, we study the application of the Fisher vector (FV) to the problem of pixelwise supervised classification of polarimetric synthetic aperture radar images. This is a challenging problem since information in those images is encoded as complex-valued covariance matrices. We observe that the real parts of these matrices preserve the positive semidefiniteness property of their complex counterpart. Based on this observation, we derive an FV from a mixture of real Wishart densities and integrate it with a Potts-like energy model in order to capture spatial dependencies between neighboring regions. Experimental results on two challenging data sets show the effectiveness of the approach.

High-performance room-temperature NO2 sensors based on microstructures self-assembled from n-type phthalocyanines: Effect of fluorine–hydrogen bonding and metal–ligand coordination on morphology and sensing performance

Abstract To investigate the effect of fluorine–hydrogen bonding and metal–ligand coordination on the morphology and gas sensing properties of self-assembled nanostructures, metal free 2,3,9,10,16,17,24,25-octakis(heptafluorobutoxy)phthalocyanine H2[Pc(OCH2C3F7)8] (1) and its zinc complex counterpart Zn[Pc(OCH2C3F7)8] (2) are synthesized and fabricated into organic microstructures by a phase-transfer method. The self-assembling properties have been comparatively investigated by electronic absorption and Fourier transform infrared spectroscopy (FT-IR), X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), X-ray diffraction (XRD) and current–voltage (I–V) measurements. Competition and cooperation between the inter-molecular π-π interaction and C-H⋯F-C hydrogen bonding in the direction perpendicular to the π-π interaction direction for metal-free phthalocyanine 1 lead to the formation of uniformed two-dimensional helical microribbons with an aspect ratio (length/width) of ca 20. The additional Zn-O coordination interactions between the central zinc ion and the oxygen atom of the adjacent molecule increases the intermolecular interaction, and results in the formation of long one-dimensional nanowires for 2 with an aspect ratio of more than 200. Notably, the resulting microstructures were revealed to show good semiconducting properties with the increasing conductivity from 5.99 × 10−5 S cm−1 for the nanowires of 2 to 1.68 × 10−4 S cm−1 for the helical ribbons of 1. Moreover, the excellently sensitive, stable and reproducible responses to NO2 in 50–900 ppb range are observed for the helical ribbons of 1 at room temperature, implying the excellent potential as the NO2 sensor for applications in practical environments. Both sensitivity and detection limit of the helical ribbons of 1 for NO2 gas at room temperature was found to be better than those of the nanowires of 2. This suggests that the analyte-phthalocyanine interaction is dominated by not only high conductivity and great surface area but more importantly binding strength of analyte to the central cavity of the phthalocyanine.

A representation of Weyl–Heisenberg Lie algebra in the quaternionic setting

Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart. With the aid of the so-obtained position and momentum operators, we study the Heisenberg uncertainty principle on the whole set of quaternions and on a quaternionic slice, namely on a copy of the complex plane inside the quaternions. For the quaternionic harmonic oscillator, the uncertainty relation is shown to saturate on a neighborhood of the origin in the case we consider the whole set of quaternions, while it is saturated on the whole slice in the case we take the slice-wise approach. In analogy with the complex Weyl–Heisenberg Lie algebra, Lie algebraic structures are developed for the quaternionic case. Finally, we introduce a quaternionic displacement operator which is square integrable, irreducible and unitary, and we study its properties.

Discrete Frames on Finite Dimensional Left Quaternion Hilbert Spaces

An introductory theory of frames on finite dimensional left quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.

Knowledge graph completion via complex tensor factorization

In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs--labeled directed graphs-- and predicting missing relationships--labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, and time and space complexity. We reconcile both expressiveness and complexity through the use of complex-valued embeddings and explore the link between such complex-valued embeddings and unitary diagonalization. We corroborate our approach theoretically and show that all real square matrices--thus all possible relation/adjacency matrices--are the real part of some unitarily diagonalizable matrix. This results opens the door to a lot of other applications of square matrices factorization. Our approach based on complex embeddings is arguably simple, as it only involves a Hermitian dot product, the complex counterpart of the standard dot product between real vectors, whereas other methods resort to more and more complicated composition functions to increase their expressiveness. The proposed complex embeddings are scalable to large data sets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.

Baire classes of complex L 1-preduals

Let X be a complex L 1-predual, non-separable in general. We investigate extendability of complex-valued bounded homogeneous Baire-α functions on the set ext B X* of the extreme points of the dual unit ball B X* to the whole unit ball B X*. As a corollary we show that, given α ∈ [1, ω 1), the intrinsic α-th Baire class of X can be identified with the space of bounded homogeneous Baire-α functions on the set ext B X* when ext B X* satisfies certain topological assumptions. The paper is intended to be a complex counterpart to the same authors’ paper: Baire classes of non-separable L 1-preduals (2015). As such it generalizes former work of Lindenstrauss and Wulbert (1969), Jellett (1985), and ourselves (2014), (2015).