Physical Amplitudes Research Articles

Physical states and transition amplitudes in piecewise flat quantum gravity

In this paper, we show how the path integral for gravity and matter on a piecewise flat spacetime can be used to define the physical quantum gravity states and the related transition amplitudes. The physical states are given by the path integrals for open manifolds from a certain topological class, while the corresponding transition amplitudes are obtained by gluing two such open manifolds into a closed one and calculating the corresponding path integral. We also solve the problem of how to associate a quantum gravity state to an effective action. This is done by using the path integral for a closed manifold from the transition-amplitude topological class so that the state which corresponds to the effective action can be chosen to be the Hartle–Hawking or the Vilenkin wavefunction for the vacuum manifold component of the transition-amplitude manifold.

Minimal exposure durations reveal visual processing priorities for different stimulus attributes

Human vision can detect a single photon, but the minimal exposure required to extract meaning from stimulation remains unknown. This requirement cannot be characterised by stimulus energy, because the system is differentially sensitive to attributes defined by configuration rather than physical amplitude. Determining minimal exposure durations required for processing various stimulus attributes can thus reveal the system’s priorities. Using a tachistoscope enabling arbitrarily brief displays, we establish minimal durations for processing human faces, a stimulus category whose perception is associated with several well-characterised behavioural and neural markers. Neural and psychophysical measures show a sequence of distinct minimal exposures for stimulation detection, object-level detection, face-specific processing, and emotion-specific processing. Resolving ongoing debates, face orientation affects minimal exposure but emotional expression does not. Awareness emerges with detection, showing no evidence of subliminal perception. These findings inform theories of visual processing and awareness, elucidating the information to which the visual system is attuned.

Integrative Modeling of Accelerometry-Derived Sleep, Physical Activity, and Circadian Rhythm Domains With Current or Remitted Major Depression

Accelerometry has been increasingly used as an objective index of sleep, physical activity, and circadian rhythms in people with mood disorders. However, most prior research has focused on sleep or physical activity alone without consideration of the strong within- and cross-domain intercorrelations; and few studies have distinguished between trait and state profiles of accelerometry domains in major depressive disorder (MDD). To identify joint and individual components of the domains derived from accelerometry, including sleep, physical activity, and circadian rhythmicity using the Joint and Individual Variation Explained method (JIVE), a novel multimodal integrative dimension-reduction technique; and to examine associations between joint and individual components with current and remitted MDD. This cross-sectional study examined data from the second wave of a population cohort study from Lausanne, Switzerland. Participants included 2317 adults (1164 without MDD, 185 with current MDD, and 968 with remitted MDD) with accelerometry for at least 7 days. Statistical analysis was conducted from January 2021 to June 2023. Features derived from accelerometry for 14 days; current and remitted MDD. Logistic regression adjusted for age, sex, body mass index, and anxiety and substance use disorders. Among 2317 adults included in the study, 1261 (54.42%) were female, and mean (SD) age was 61.79 (9.97) years. JIVE reduced 28 accelerometry features to 3 joint and 6 individual components (1 sleep, 2 physical activity, 3 circadian rhythms). Joint components explained 58.5%, 79.5%, 54.5% of the total variation in sleep, physical activity, and circadian rhythm domains, respectively. Both current and remitted depression were associated with the first 2 joint components that were distinguished by the salience of high-intensity physical activity and amplitude of circadian rhythm and timing of both sleep and physical activity, respectively. MDD had significantly weaker circadian rhythmicity. Application of a novel multimodal dimension-reduction technique demonstrates the importance of joint influences of physical activity, circadian rhythms, and timing of both sleep and physical activity with MDD; dampened circadian rhythmicity may constitute a trait marker for MDD. This work illustrates the value of accelerometry as a potential biomarker for subtypes of depression and highlights the importance of consideration of the full 24-hour sleep-wake cycle in future studies.

Electroweak three-body decays in the presence of two- and three-body bound states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements [formula omitted] and [formula omitted]

The non-first-order-factorizable contributions1 to the unpolarized and polarized massive operator matrix elements to three-loop order, AQg(3) and ΔAQg(3), are calculated in the single-mass case. For the F12-related master integrals of the problem, we use a semi-analytic method based on series expansions and utilize the first-order differential equations for the master integrals which does not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to O(ε5) in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable x∈]0,∞[ using highly precise series expansions to obtain the imaginary part of the physical amplitude for x∈]0,1] at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-x region. We also derive expansions in the region of small and large values of x. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.

Association between physical health and neurocognition in first-episode schizophrenia

IntroductionImpaired cognition is a core feature of schizophrenia that is evident early in the first episode and is frequently accompanied by compromised physical health. Although physical health confers benefits to cognition, it remains unclear whether physical activity, body mass index (BMI) and cardiorespiratory fitness are associated with neurocognition in first episode schizophrenia patients. The purpose of this study was to examine differences in stimulus categorization and motor response selection processes between first-episode schizophrenia patients compared to age-matched controls and explore associations between physical health and these stages of information processing.MethodsFourteen young adult patients receiving care following a first episode of psychosis and a matched sample of nonpsychiatric controls completed a visual oddball task from which the P3 and LRP (lateralized readiness potential) event-related potential (ERP) components were extracted to assess stimulus categorization and response selection processes, respectively. Physical activity, aerobic fitness, and BMI were correlated with ERP measures.ResultsCompared with controls, patients had lower physical activity levels and longer P3 and LRP latencies. Regardless of stimulus probability, patients had reduced accuracy and slower reaction times relative to controls. In patients, marginal associations were found between physical activity and P3 difference waveform amplitude, and BMI was negatively associated with parent P3 waveform amplitude.DiscussionThe present findings suggest that cognitive impairment in first-episode schizophrenia spans both stimulus- and response-related stages of information processing, and may be targeted through physical activity interventions.

From Pseudo to Real: Generalized Subspace Method for Power Spectrum Reconstruction

Subspace methods are widely used in statistical signal processing owing to their super-resolution. Conventional subspace methods, such as multiple signal classification (MUSIC) identify parameters containing frequency and direction of arrival by calculating pseudo-spectra without physical amplitudes. However, the real value of amplitude plays a significant role in fault diagnosis and condition monitoring. Additionally, due to hardware limitations and increased frequency, uniform (Nyquist) sampling becomes challenging. Nonuniform sampling, an alternative to high-rate sampling is common in practice. Consequently, Nonuniform (sub-Nyquist) signal processing methods are urgently required. In this paper, a generalized subspace method (GSM) is proposed to bridge the pseudo spectrum with the real spectrum. The proposed method is a supplement to the existing subspace methods and is applicable to both uniform and nonuniform sampling. In the GSM, the Fourier coefficient of the autocorrelation function is derived by signal subspace from the perspective of basis matching. Then, an alias-free real power spectrum is obtained by combining the power spectrum reconstructed by GSM with the classical pseudo spectrum. Finally, simulation and experiment demonstrate the performance of the proposed method in power spectrum reconstruction. Even under the dual influence of undersampled and nonuniform, the proposed method is still effective.

April-GCN: Adjacency Position-velocity Relationship Interaction Learning GCN for Human motion prediction

The Human Motion Prediction (HMP) task attempts to model human kinematics, which requires considering both the physical connections between joints and the continuity of the joints’ trajectories. To handle this complex task, some recent works have employed Graph Convolutional Networks (GCN) in learning dynamic relations among joints. However, HMP task is essentially a time series task, to model the temporal and spatial features of motion, some works extended the common adjacency matrix formulation to create a large-scale mixed adjacency matrix which introduces redundant connection relationships in single-path GCN. Other works proposed dual-path GCNs and multi-path GCNs to make feature representations more informative, while ignoring the significant differences of features. To tackle these issues, we propose a novel adjacency matrix interaction learning framework called Adjacency Position-velocity Relationship Interaction Learning GCN (April-GCN) which alleviates the differences between dual-path features and improves the feature fusion results. The proposed network utilizes a dual-path GCN structure to exploit the adjacency relationship between physical connections and movement amplitude by interactively learning the GCN adjacency matrices of the two paths. The network excavated closely aligned position-velocity correlations to obtain a more comprehensive and richer representation of joint connections. On three datasets, H3.6M, CMU, and 3DPW, it achieves state-of-the-art performance for both short-term and long-term predictions.

A Design Strategy for Surface Nanostructures to Realize Sensitive Refractive-Index Optical Sensors.

Refractive-index optical sensors have been extensively studied. Originally, they were surface plasmon resonance sensors using only a flat gold film. Currently, to develop practically useful label-free optical sensors, numerous proposals for refractive index sensors have been made using various nanostructures composed of metals and dielectrics. In this study, we explored a rational design strategy for sensors using surface nanostructures comprising metals or dielectrics. Optical responses, such as reflection and transmission, and resonant electromagnetic fields were computed using a numerical method of rigorous coupled-wave analysis combined with a scattering-matrix algorithm. As a result, good performance that almost reached the physical limit was achieved using a plasmonic surface lattice structure. Furthermore, to precisely trace the refractive-index change, a scheme using two physical quantities, resonant wavelength and reflection amplitude, was found to be valid for a 2D silicon metasurface.

On the gauge-invariance of SCET beyond leading power

We point out that the gauge-invariance of the subleading Lagrangian of soft-collinear effective theory is realised in an intricate way through momentum-conservation violating contributions. Although these terms are disregarded in diagrammatic calculations, the gauge invariance of any physical transition amplitude is preserved due to the soft equations of motion. When not working with gauge-invariant building blocks, individual manifestly gauge-invariant constituent terms in the Lagrangian may give rise to gauge-dependent matrix elements starting at mathcal{O} (λ2). Implications for a gauge-invariant definition of radiative jet functions are discussed.

Rest–activity rhythm as a clinical biomarker: what are the next steps?

Rest–activity rhythm as a clinical biomarker: what are the next steps?

Characterising the interior of five inner Saturnian moons using Cassini ISS data

Context. The Cassini-Huygens space mission provided a huge amount of data for the Saturnian system. While the mission ended in September 2017, there is still much information to be retrieved from the data. Aims. Here, from their orbital motion, we infer the interior of the five inner Saturnian moons, Atlas, Prometheus, Pandora, Janus, and Epimetheus. Our results benefit from a recent study of the shape of these moons, which provides a much better estimation of their 3D shape and volume. Methods. Using Cassini Imaging Science Subsystem (ISS) astrometric data, we again reduced the Cassini ISS images with an improved shape modelling. We then integrated the orbital motion of the inner Saturnian moons and solved for a large set of physical parameters for this system, including the masses and physical libration amplitudes of the moons. Results. We obtain a density value (in g cm−3 with a 1σ error bar based on the digital terrain models and spherical harmonics available today) of 0.3935 ± 0.0033, 0.4873 ± 0.0026, 0.5045 ± 0.0017, 0.6233 ± 0.0015, and 0.6413 ± 0.0002 for Atlas, Prometheus, Pandora, Epimetheus, and Janus, respectively. We were able to determine the physical libration amplitudes of Prometheus, Pandora, Epimetheus, and Janus to be 0.98 ± 0.08, −5.2 ± 0.7, −6.0 ± 0.6, and −0.39 ± 0.16 (degrees and 1σ error bar), respectively. Our solutions for Epimetheus and Janus are in full agreement with a former estimation performed directly from the measurement of the rotation of these two moons. Conclusions. We confirm the large porosity of these five moons and their increase in density as a function of their size. Our estimations of the physical librations of Prometheus, Pandora, Janus, and Epimetheus are consistent with a homogeneous interior, but for Pandora a heterogeneous interior is also plausible.

Direct CP violation in K → ππ decay on the lattice with periodic boundary conditions

Following our recent publication on direct CP violation and the ΔI = 1/2 rule in K → ππ decay, which was made with G-parity boundary conditions, we revisit this problem with a conventional lattice setup employing periodic boundary conditions and two lattice spacings to check our previous result and to improve the precision. We show that the physical amplitude, which corresponds to an excited state in this case, can be obtained reliably with the Generalized Eigenvalue Problem (GEVP) method. Not only are periodic boundary conditions cheaper and allow the use of existing ensembles to take the continuum limit, but they provide a straightforward path to introduce electromagnetism and strong isospin symmetry breaking, which will be needed in the near future. In this article we show our preliminary results and discuss the prospect of the high-precision calculation of K → ππ decay with periodic boundary conditions.

A Multi-Rate Approach for Nonlinear Pre-Distortion Using End-to-End Deep Learning in IM-DD Systems

Modern intra-data center (IDC) interconnects leverage robust and low-cost intensity modulation (IM) and direct detection (DD) optical links, based on multimode fibers (MMFs) and vertical-cavity surface-emitting lasers (VCSELs). Current solutions, based on on-off keying (OOK) modulations, reach up to 25-50 Gbps per lane over nearly 100 meters. The actual target for IDCs is to increase VCSEL-MMF links capacity up to 100 Gbps, using PAM-4 on the same devices. To counteract the consequent linear and nonlinear distortions affecting the transmitted signals, an effective solution is to exploit digital signal processing (DSP). In this manuscript, we propose a novel method to optimize a nonlinear artificial neural network (ANN) digital pre-distorter (DPD), based on End-to-end (E2E) learning, that, trained jointly with a Feed-Forward Equalizer (FFE), fulfills physical amplitude constraints and handles different ratio between the sampling rates incurring along with an optical IM-DD system. We indeed propose an E2E ANN system operating simultaneously at different sampling frequencies. We moreover propose in our training method a substitution to the time-domain injection of the receiver noise in the system with an additive regularization term in the FFE gradient loss. We experimentally show the advantages of our proposed DPD comparing the bit error rate (BER) performance against the same scenario without DPD. We assess the gain in terms of Gross Bit Rate and Optical Path Loss (OPL), at given BER targets, for different fiber lengths.

Topological Equivalence Theorem and Double-Copy for Chern-Simons Scattering Amplitudes.

We study the mechanism of topological mass generation for 3-dimensional Chern-Simons gauge theories and propose a brand-new topological equivalence theorem to connect scattering amplitudes of the physical gauge boson states to that of the transverse states under high-energy expansion. We prove a general energy cancelation mechanism for N-point physical gauge boson amplitudes, which predicts large cancelations of E4 - L → E(4 - L) - N at any L-loop level (L ⩾ 0). We extend the double-copy approach to construct massive graviton amplitudes and to study their structures. We newly uncovered a series of strikingly large energy cancelations E12 → E1 of the tree-level 4-graviton scattering amplitude under high-energy expansion and establish a new correspondence between the 2 energy cancelations in the topologically massive Yang-Mills gauge theory and the topologically massive gravity theory. We further study the scattering amplitudes of Chern-Simons gauge bosons and gravitons in the nonrelativistic limit.

The analysis of amplitude and phase angle of periodic mixed convective fluid flow across a non-conducting horizontal circular cylinder

The present contribution deals with the study of amplitude and phase angle of periodical mixed convective fluid flow along the non-conducting circular cylinder. The surface of cylinder is thermally and electrically conducting by keeping surface temperature as a time dependent variable. The developed dimensionless equations are transformed into analytical expressions for flow characteristics by using primitive variable formulation which converts nonlinear PDE’s into primitive form for numerical data. The graphical representations of physical properties phase angle and amplitude are obtained for various values of Prandtl number Pr, mixed-convection parameter λ , magnetic-Prandtl number γ and magnetic force parameter ξ respectively. To demonstrate important properties of the solution, a parametric study is conducted for governing parameters and a set of graphical and numerical outcomes is analyzed. The amplitude of time dependent skin friction τ w , heat transfer q w and current density j w has been observed on suitable positions of the non-conducting cylinder π / 6 , π / 4 , π / 2 , 3 π / 4 , 5 π / 6 and π numerically. It is noticed that the maximum amplitude of time dependent skin friction τ w , heat transfer q w and current density j w is noted at position α = π / 2 by increasing the various amount of physical pertinent parameters.

Comments on Computation of Free-Free Transitions in Atomic Physics

The amplitude T for ‘free-free’ processes such as bremsstrahlung or photoabsorption by an electron in the continuum in the presence of an external field, is usually written as the matrix element of the radiation operator taken between two continuum states. However, unlike the case when at least one of the states is bound, as in radiative transitions, electron capture or the photo-effect, this expression contains unphysical term, proportional to a delta function, and is not really the physical amplitude Tphys. We first give an a priori definition of Tphys in terms of the scattering parts of the continuum functions, which does not have this delta function term and has an obvious interpretation in terms of time-ordered diagrams. We then show that when the formal amplitude T is modified by a long-distance cutoff, the modified form Tα approaches Tphys as the cutoff is removed. The modified form may be used as the basis for calculation and approximations without the need to introduce further cutoffs at a later stage.

Positivity and geometric function theory constraints on pion scattering

This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with O(N) global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion relation in the z-variable, rather than the fixed channel dispersion relation. We have written down fully crossing symmetric dispersion relation for O(N) model in z-variable for three independent combinations of isospin amplitudes. We have presented three independent sum rules or locality constraints for the O(N) model arising from the fully crossing symmetric dispersion relations. We have derived three sets of positivity conditions. We have obtained two-sided bounds on Taylor coefficients of physical Pion amplitudes around the crossing symmetric point (for example, π+π−→ π0π0) applying the positivity conditions and the Bieberbach-Rogosinski inequalities from geometric function theory.

Three-loop helicity amplitudes for four-quark scattering in massless QCD

We compute the three-loop corrections to the helicity amplitudes for q overline{q} → Q overline{Q} scattering in massless QCD. In the Lorentz decomposition of the scattering amplitude we avoid evanescent Lorentz structures and map the corresponding form factors directly to the physical helicity amplitudes. We reduce the amplitudes to master integrals and express them in terms of harmonic polylogarithms. The renormalised amplitudes exhibit infrared divergences of dipole and quadrupole type, as predicted by previous work on the infrared structure of multileg scattering amplitudes. We derive the finite remainders and present explicit results for all relevant partonic channels, both for equal and different quark flavours.

A Recipe for the Geophysical Exploration of Enceladus

Abstract Orbital geophysical investigations of Enceladus are critical to understanding its energy budget. In this paper, we identified key science questions for the geophysical exploration of Enceladus, answering which would support future assessment of Enceladus’ astrobiological potential. Using a Bayesian framework, we explored how science requirements map to measurement requirements. We performed mission simulations to study the sensitivity of single-spacecraft and dual-spacecraft configurations to static gravity and tidal Love numbers of Enceladus. We find that mapping Enceladus’ gravity field, improving the accuracy of the physical libration amplitude, and measuring Enceladus’ tidal response would provide critical constraints on the internal structure and establish a framework for assessing Enceladus’ long-term habitability. This kind of investigation could be carried out as part of a life search mission at little additional resource requirements.