Coherent Measures Research Articles

10 W super-wideband ultra-low-intensity-noise single-frequency fiber laser at 1 µm.

A 10 W super-wideband ultra-low-intensity-noise single-frequency fiber laser (SFFL) at 1 µm is experimentally demonstrated, based on dual gain saturation effects from semiconductors and optical fibers, together with an analog-digital hybrid optoelectronic feedback loop. Three intensity-noise-inhibited units synergistically work, which actualizes a connection of effective bandwidth and enhancement of noise-suppressing amplitude. With the cascade action of the semiconductor optical amplifier and optical fiber amplifier, the laser power is remarkably boosted. Eventually, an SFFL with an output power of 10.8 W and a relative intensity noise (RIN) below -150 dB/Hz at the frequency range over 1 Hz is realized. More meaningfully, within the total frequency range of 10 Hz to 10 GHz exceeding 29 octaves, the RIN is controlled to below -160 dB/Hz, approaching the shot-noise limit (SNL) level. To the best of our knowledge, this is the lowest RIN result of SFFL within such an extensive frequency range, and this is the highest output power of the near-SNL super-wideband SFFL. Furthermore, a linewidth of less than 0.8 kHz, a long-term stable polarization extinction ratio of 20 dB, and an optical signal-to-noise ratio of over 60 dB are obtained simultaneously. This start-of-the-art SFFL has provided a systematic solution for high-power and low-noise light sources, which is competitive for sophisticated applications, such as free-space laser communication, space-based gravitational wave detection, and super-long-distance space coherent velocity measurement and ranging.

Hypergraph of Functional Connectivity Based on Event-Related Coherence: Magnetoencephalography Data Analysis

We construct hypergraphs to analyze functional brain connectivity, leveraging event-related coherence in magnetoencephalography (MEG) data during the visual perception of a flickering image. Principal network characteristics are computed for the delta, theta, alpha, beta, and gamma frequency ranges. Employing a coherence measure, a statistical estimate of correlation between signal pairs across frequencies, we generate an edge time series, depicting how an edge evolves over time. This forms the basis for constructing an edge-to-edge functional connectivity network. We emphasize hyperedges as connected components in an absolute-valued functional connectivity network. Our coherence-based hypergraph construction specifically addresses functional connectivity among four brain lobes in both hemispheres: frontal, parietal, temporal, and occipital. This approach enables a nuanced exploration of individual differences within diverse frequency bands, providing insights into the dynamic nature of brain connectivity during visual perception tasks. The results furnish compelling evidence supporting the hypothesis of cortico–cortical interactions occurring across varying scales. The derived hypergraph illustrates robust activation patterns in specific brain regions, indicative of their engagement across diverse cognitive contexts and different frequency bands. Our findings suggest potential integration or multifunctionality within the examined lobes, contributing valuable perspectives to our understanding of brain dynamics during visual perception.

Stackelberg equilibria with multiple policyholders

We examine Pareto-efficient contracts and Stackelberg Equilibria (SE) in a sequential-move insurance market in which a central monopolistic insurer on the supply side contracts with multiple policyholders on the demand side. We obtain a representation of Pareto-efficient contracts when the monopolistic insurer's preferences are represented by a coherent risk measure. We then obtain a representation of SE in this market, and we show that the contracts induced by an SE are Pareto-efficient. However, we note that SE do not induce a welfare gain to the policyholders in this case, echoing the conclusions of recent work in the literature. The social welfare implications of this finding are examined through an application to the flood insurance market of the United States of America, in which we find that the central insurer has a strong incentive to raise premia to the detriment of the policyholders. Accordingly, we argue that monopolistic insurance markets are problematic, and must be appropriately addressed by external regulation.

Grid Turbulence Measurements with an Acoustic Doppler Current Profiler

The motivation for this study is to investigate the abilities and limitations of a Nortek Signature1000 acoustic Doppler current profiler (ADCP) regarding fine-scale turbulence measurements. Current profilers offer the advantage of gaining more coherent measurement data than available with point acoustic measurements, and it is desirable to exploit this property in laboratory and field applications. The ADCP was tested in a towing tank, where turbulence was generated from a grid towed under controlled conditions. Grid-induced turbulence is a well-studied phenomenon and a good approximation for isotropic turbulence. Several previous experiments are available for comparison and there are developed theories within the topic. In the present experiments, a Nortek Vectrino acoustic Doppler velocimeter (ADV), which is an established instrument for turbulence measurements, was applied to validate the ADCP. It was found that the mean flow measured with the ADCP was accurate within 4% of the ADV. The turbulent variance was reasonably well resolved by the ADCP when large grid bars were towed at a high speed, but largely overestimated for lower towing speed and smaller grid bars. The effective cutoff frequency and turbulent eddy size were characterized experimentally, which provides detailed guidelines for when the ADCP data can be trusted and will allow future experimentalists to decide a priori if the Nortek Signature can be used in their setup. We conclude that the ADCP is not suitable for resolving turbulent spectra in a small-scale grid-induced flow due to the intrinsic Doppler noise and the low spatial and temporal sample resolution relative to the turbulent scales.

Quantifying coherence via the generalized Wigner–Yanase–Dyson skew information

Quantum coherence is an important feature that distinguishes quantum mechanics from classical physics. In this paper, we study the coherence of a quantum state with respect to a quantum channel, and introduce a coherence measure in terms of the generalized Wigner–Yanase–Dyson skew information. The basic properties and operational significance of the measure are expounded in detail, which shows that it is indeed a veritable quantity and satisfies many desirable conditions intuitively required for the coherence measures. We illustrate the significance of characterizing channels from the coherence perspective through some examples. Finally, we consider the average coherence of a state based on the generalized Wigner–Yanase–Dyson skew information with respect to any complete mutually unbiased bases in prime power dimensional systems, as well as with respect to all orthonormal bases, and show that these two averages are equivalent since they both can be seen as the coherence of the quantum state with respect to the depolarizing quantum channel.

A HeartMath intervention, focusing on coherence, resilience and faith, following a trauma

Traumatic experiences can have an impact on faith. HeartMath, which focuses on coherence and resilience, is one approach utilised to help overcome traumatic experiences. This study focused on a HeartMath intervention, emphasising psychophysiological coherence, sense of coherence, resilience and faith following a traumatic experience. A quasi-experimental, single, within-sample design was used. The purposeful sample consisted of 10 participants. A 12-week HeartMath intervention was undertaken. Related quantitative and qualitative coherence, resilience and faith measures were used at pre-test, re-test and, after intervention, post-test, with participant diaries completed. Quantitatively, there were significant post-intervention positive improvements in physiological average coherence, achievement, and low, medium and high coherence level scores. Although not significant, there were improvements in the resilience scale and faith scale. However, there was no improvement in the sense of coherence scale total score. Qualitatively, there were positive integrative thematic changes in experiences of the sense of coherence, resilience and faith. Recommended next research steps were a case study on causal, correlational and relationship mechanisms of change, followed by an appreciative inquiry evaluating HeartMath as a pastoral care and counselling intervention.Contribution: This article contributes to the area of practical theology, specifically pastoral care and counselling, as it quasi-experimentally explores a HeartMath intervention and faith following a traumatic experience.

A computable quantification of multi-mode Gaussian coherence and complete monogamy relation

We propose a quantification CνGn of n-mode Gaussian coherence. The value of CνGn only depends on the covariance matrices and displacement vectors of continuous-variable states without any optimization procedures, and thus is easily calculated. For n=1, CνG1 is a proper Gaussian coherence measure of single-mode CV system. For n≥2, CνGn is invariant under any permutation of submodes, nonincreasing under any n-mode local incoherent Gaussian channels, vanishes at incoherent Gaussian states, and, satisfies the unification condition and the hierarchy condition that a multi-partite quantum correlation measure should obey. Thus CνGn is a multi-partite Gaussian correlation measure, which reveals, though the quantum coherence lives in single-partite systems, that the multi-mode coherence for continuous-variable systems can be regarded as a multipartite Gaussian correlation between modes, and such multi-partite Gaussian correlation is also a quantum resource. Moreover, we show that CνGn is completely monogamous as a multipartite Gaussian correlation measure. This means that the n-mode Gaussian coherence subjects to the principles of resource allocation. In addition, CνGn is an upper bound of the geometric-based single-mode Gaussian coherence measure CBu by the Bures distance at pure Gaussian states of mode ≤2 and can be used to detect coherence in any n-mode Gaussian states more efficiently.

Conceptualizing Discussions on the Dark Web: An Empirical Topic Modeling Approach

Social networks on the Internet have become a home that attracts all types of human thinking to exchange knowledge and ideas and share businesses. On the other hand, it has also become a source for researchers to analyze this knowledge and frame it in patterns that define types of thoughts circulating on these networks and representing the communities around them. In particular, some social networks on the Dark Web attract a special kind of thinking centered around the malicious and illegal activities disseminated on websites and marketplaces on the Dark Web. These networks involve discussions to exchange and discourse information, tips, and advice on performing such business. Studying social networks on the Dark Web is still in its infancy. In this paper, we present a methodology for analyzing the content of social networks on the Dark Web using topic modeling methods. We demonstrate the needed stages for the topic modeling process, beginning with data preprocessing and feature extraction to topic modeling algorithms. We utilize and discuss the following four topic models: LDA, CTM, PAM, and PTM. We discuss the following four topic coherence measures as evaluation metrics: UMass, UCI, CNPMI, and CV, demonstrating the selection of the best number of topics for each model according to the most coherent produced topics. Furthermore, we discuss the limitations, challenges, and future work. Our proposed approach highlights the ability to discover the latent thematic patterns in conversations and messages in the common language used in social networks on the Dark Web, constructing topics as groups of terms and their associations. This paper provides researchers with a leading methodology for analyzing thought patterns on the Dark Web.

Convex approximations of two-stage risk-averse mixed-integer recourse models

AbstractWe consider two-stage risk-averse mixed-integer recourse models with law invariant coherent risk measures. As in the risk-neutral case, these models are generally non-convex as a result of the integer restrictions on the second-stage decision variables and hence, hard to solve. To overcome this issue, we propose a convex approximation approach. We derive a performance guarantee for this approximation in the form of an asymptotic error bound, which depends on the choice of risk measure. This error bound, which extends an existing error bound for the conditional value at risk, shows that our approximation method works particularly well if the distribution of the random parameters in the model is highly dispersed. For special cases we derive tighter, non-asymptotic error bounds. Whereas our error bounds are valid only for a continuously distributed second-stage right-hand side vector, practical optimization methods often require discrete distributions. In this context, we show that our error bounds provide statistical error bounds for the corresponding (discretized) sample average approximation (SAA) model. In addition, we construct a Benders’ decomposition algorithm that uses our convex approximations in an SAA-framework and we provide a performance guarantee for the resulting algorithm solution. Finally, we perform numerical experiments which show that for certain risk measures our approach works even better than our theoretical performance guarantees suggest.

Generalized GHZ entanglement states for optimal rotation detection of quantum spin systems using majorana representation

A multitude of engineering and scientific applications require the estimation of an unknown axis’ rotation, known as the reference frame alignment problem. These problems can be categorized using the quantum Cramer–Rao bound. Detecting rotations is typically focused on smaller angles, as errors are more significant in this range. Therefore, selecting the optimal combination of measurement techniques based on a quantum entangled state for a particular setup is a critical step. This paper proposes a linear combination of anticoherence and coherence measures based on the generalized GHZ entanglement states. The anticoherence measures, optimizes the spin system’s average fidelity in detecting rotated states, while the overlap between states in any spin number is minimal. The optimal quantum rotosensors are characterized by the minimal average fidelity given by the overlap before and after averaging over all directions. The individual subsystems’ states have substantial overlap with GHZ states, making the generalized GHZ state the entanglement quantum spin-j state with coherence decay rate ϵ beneficial in finding the optimal rotation detection on noncoherent entanglement state.

Integrated self-injection-locked narrow linewidth laser based on thin-film lithium niobate.

Narrow linewidth lasers have a wide range of applications in the fields of coherent optical communications, atomic clocks, and measurement. Lithium niobate material possesses excellent electro-optic and thermo-optic properties, making it an ideal photonic integration platform for a new generation. The light source is a crucial element in large-scale photonic integration. Therefore, it is essential to develop integrated narrow linewidth lasers based on low-loss LNOI. This study is based on the multimode race-track type add-drop microring resonator with multimode interferometric coupler (MMRA-MRR) of the DFB laser self-injection-locked, to achieve the narrowing of linewidth to the laser. The microring external cavity was used to narrow the linewidth of the laser to 2.5 kHz. The output power of the laser is 3.18 mW, and the side-mode suppression ratio is 60 dB. This paper presents an integrated low-noise, narrow-linewidth laser based on thin-film lithium niobate material for the communication band. This is significant for achieving all-optical device on-chip integration of lithium niobate material in the future. It has great potential for use in high-speed coherent optical communication.

Robust valley quantum coherence in synthetic 3R-phase MoS2: A material for future valley based devices

Two-dimensional layered transition metal dichalcogenides (TMDCs) offer the ideal platform to optically initialize the qubits utilizing the superposition of valley polarized photons. However, in the commonly available 2H phase TMDCs, thickness sensitive crystal inversion symmetry demands the precise control over the number of layers, which makes the study of valley physics challenging. On the other hand, 3R-polymorphic phase TMDCs are non-centrosymmetric irrespective of the number of layers and therefore retain valley degree of freedom for all the thicknesses. Here, using polarization resolved photoluminescence measurements under linearly polarized excitations, we demonstrate the coherent superposition of the valley photons (known as valley coherence) in synthetic 3R-phase MoS2 with different numbers of layers ranging from 3 layers to 11 layers. With near-resonant excitation (633 nm for AX0), the degree of linear polarization (a measure of the valley coherence) is observed up to 70% at 80 K measurement temperatures and is found to be layer thickness independent. Robust valley coherence is attributed to the high optical quality and the 3R crystal symmetry of the MoS2. Using angle resolved polarization dependent measurements, it is established that the net dipolar emission aligns with the polarization orientations of the incident laser, which signifies the valley coherence to be independent of the crystal orientation. This study paves the way toward using 3R-phase MoS2 as a key material for the development of future quantum technologies utilizing valley polarized photons.

Uncertainty Relation of Quantum Coherence Measure Based on Hellinger Distance

Uncertainty Relation of Quantum Coherence Measure Based on Hellinger Distance

Cooperative Investment Problem With an Authoritative Risk Determined by Central Bank

In this paper, we are interested in providing an analytic solution for cooperative investment risk. We reformulate cooperative investment risk by writing dual representations for each risk preference (Coherent risk measure). Finding an analytic solution for this problem for both cases individual and cooperative investment by using dual representation for each risk preference has a strong effect on the financial market. In addition, we formulate a problem that covers the risk minimization with an expected return maximization problem with risk constraint, for the general case of an arbitrary joint distribution for the asset return under certain conditions and assuming that all coherent risk measure is continuous from below. Thus, the optimal portfolio is written as the optimal Lagrange multiplier associated with an equality-constrained dual problem. Furthermore, a unique equilibrium allocation as a fair optimal allocation solution in terms of equilibrium price density function for each agent is also shown.

A New Coherent Risk Measure of Entropic Value at Risk for Uncertain Systems

Uncertain risk analysis was initially explored by Liu, who introduced the concepts of loss function and risk index within uncertainty theory. Various risk measures, such as value at risk (VaR), tail VaR (TVaR), expected loss and entropic VaR (EVaR), have been proposed within probability theory. To date, Peng extended the concepts of VaR and TVaR, while Liu and Ralescu extended the notion of expected loss for uncertain systems. This paper mainly extends the concept of EVaR as a novel uncertain coherent risk measure. It will be demonstrated as the tightest upper bound one can find using Chernoff inequality for the VaR. In addition, we verify the properties of EVaR under uncertain measure, including positive homogeneity, translation invariance, monotonicity and subadditivity under independence. Furthermore, this paper provides a comparison of VaR, TVaR and EVaR under uncertain measure. Two examples will be given to illustrate this comparison.

On the Role of Alfvénic Fluctuations as Mediators of Coherence within Interplanetary Coronal Mass Ejections: Investigation of Multi-spacecraft Measurements at 1 au

Interplanetary coronal mass ejections (ICMEs) are defined as “coherent” if they are capable of responding to external perturbations in a collective manner. This implies that information must be able to propagate across ICME structures, and if this is not the case, single-point in situ measurements cannot be considered as indicative of global ICME properties. Here, we investigate the role of Alfvénic fluctuations (AFs) as mediators of ICME coherence. We consider multipoint magnetic field and plasma measurements of 10 ICMEs observed by the ACE and Wind spacecraft at 1 au at longitudinal separations of 0.5°–0.7°. For each event, we analyze the Alfvénicity in terms of the residual energy and cross helicity of fluctuations, and the coherence in terms of the magnetic correlation between Wind and ACE. We find that ∼65% and 90% of ICME sheaths and magnetic ejecta (MEs), respectively, present extended AFs covering at least 20% of the structure. Cross helicity suggests AFs of solar and interplanetary origin may coexist in the ICME population at 1 au. AFs are mainly concentrated downstream of shocks and in the back of MEs. The magnetic field is poorly correlated within sheaths, while the correlation decreases from the front to the back of the MEs for most magnetic field components. AFs are also associated with lower magnetic field correlations. This suggests either that ICME coherence is not mediated by Alfvén waves, implying that the coherence scale may be smaller than previously predicted, or that the magnetic field correlation is not a measure of coherence.

Risk-Averse Decision Making Under Uncertainty

A large class of decision making under uncertainty problems can be described via Markov decision processes (MDPs) or partially observable MDPs (POMDPs), with application to artificial intelligence and operations research, among others. In this paper, we consider the problem of designing policies for MDPs and POMDPs with objectives and constraints in terms of dynamic coherent risk measures rather than the traditional total expectation, which we refer to as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">constrained risk-averse problem</i> . Our contributions can be described as follows: For MDPs, under some mild assumptions, we propose an optimization-based method to synthesize Markovian policies. We then demonstrate that such policies can be found by solving difference convex programs (DCPs). We show that our formulation generalize linear programs for constrained MDPs with total discounted expected costs and constraints; For POMDPs, we show that, if the coherent risk measures can be defined as a Markov risk transition mapping, an infinite-dimensional optimization can be used to design Markovian belief-based policies. For POMDPs with stochastic finite-state controllers (FSCs), we show that the latter optimization simplifies to a (finite-dimensional) DCP. We incorporate these DCPs in a policy iteration algorithm to design risk-averse FSCs for POMDPs. We demonstrate the efficacy of the proposed method with numerical experiments involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) risk measures.

Measurement of Beta and Theta Brain Wave Coherence with Cardiac Wave Rhythm in Managers with Rational Decision-Making Style Based on Emotional Intelligence through ERT Cognitive Task

Objective: Since human life and society depend on brain functions, our understanding of the brain and mind can significantly impact all dimensions of human life. Therefore, the main objective of this study was to assess the coherence of brain waves (EEG) and cardiac wave rhythms (HRV) based on neuroscientific and neurocardiology principles. Methods and Materials: This research utilized an experimental design, specifically a quasi-experimental approach without a control group, and was applied in nature. The statistical population consisted of managers (90 individuals) from both public and private sectors in Gilan Province in 2022. From this population, 30 individuals were randomly selected. Their brain waves and cardiac rhythms were simultaneously recorded in both resting and decision-making states from the CZ region of the brain and triangular regions around the heart using the ProComp 2 neurofeedback tool while performing the emotional intelligence assessment test. The research instrument included the ERT cognitive test (Emotional Recognition Task) designed by Cambridge University in 1980 and administered through the Cantab software and BioGraph Infiniti version 0.6 software. For the purposes of this study, the cognitive task was provided to participants via software. The data were analysed using analysis of variance and mean comparison test via SPSS-26. Findings: The correlation test of brain waves and cardiac waves in resting and cognitive task states showed significant differences. No coherence between EEG and ECG was observed in the resting state compared to the cognitive task state. Conclusion: The results indicate that changes in brain waves and cardiac waves, and the coherence between these waves, vary among managers with similar decision-making styles. These variations depend on the environmental, mental, and emotional conditions of the individuals.

Properties of the entropic risk measure EVaR in relation to selected distributions

Entropic Value-at-Risk (EVaR) measure is a convenient coherent risk measure. Due to certain difficulties in finding its analytical representation, it was previously calculated explicitly only for the normal distribution. We succeeded to overcome these difficulties and to calculate Entropic Value-at-Risk (EVaR) measure for Poisson, compound Poisson, Gamma, Laplace, exponential, chi-squared, inverse Gaussian distribution and normal inverse Gaussian distribution with the help of Lambert function that is a special function, generally speaking, with two branches.

Experimental Analysis of Coherent Velocity Measurement Based on Near-infrared Single-element SPAD Detector

Experimental Analysis of Coherent Velocity Measurement Based on Near-infrared Single-element SPAD Detector