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**A**: The strength of the effect is proportional to ϵΔitalic-ϵΔ\epsilon\Deltaitalic_ϵ roman_Δ**B**: Thus, nonlinearity acts differently on the left (higher energy) and right (lower energy) sides of the barrier.
**C**: Indeed, that can be seen directly from the form of Eq. (26), where the difference between time evolution in the right and left wells is that in one case the ΔΔ\Deltaroman_Δ and ϵitalic-ϵ\epsilonitalic_ϵ terms contribute to the phase with the same sign, while in the other case they contribute with opposite signs
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**A**: The premise of the algorithm is to iteratively simulate the spectrum corresponding to different Hamiltonian parameters on quantum hardware and guess parameters that are closer to the target experimental spectrum using classical optimization techniques. After a sufficient number of iterations, the learned Hamiltonian parameters can be used to gain insight into the chemical structure of the sample that produced the given NMR spectrum. In Fig. 8, we demonstrate the benefit of feedforward correction in this inference algorithm**B**: Figure 8(a) shows the Hellinger distance between the average noisy Trotterized spectrum and a given target spectrum at each iteration of the protocol. We see that the feedforward correction allows the algorithm to converge faster, as the increased resolution in the simulated spectra allows the classical optimization to more easily guess better Hamiltonian parameters. In Fig. 8(b), we take the Hamiltonian parameters for the initial and last iterations of the noisy protocol with feedforward correction and compute the corresponding spectra without noise to compare how well the learned parameters correspond to the true parameters underlying the given target spectrum. We see that even though the quantum simulation is noisy, we are still able to iteratively infer the Hamiltonian parameters underlying the target spectrum.**C**:
This improvement in the quality of the Hamiltonian simulation can be helpful for practical applications, such as the NMR spectrum inference task discussed in Ref. Sels et al. (2020). In that work, a hybrid quantum-classical algorithm is used to infer the parameters of a Hamiltonian, Eq. (1), that models the system of nuclear spins which produce a given experimental NMR spectrum
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**A**: This is for one data frame that has a measured m50𝑚50m50italic_m 50 of 22.01, and shows the measured efficiency as a function of magnitude**B**:
An example showing the planting of SNe into a difference image and the measured efficiency are shown in Figure 4**C**: The case with a source magnitude of 22 is shown in the bottom left, where close to half of the synthetic sources are detected. The source detection software was set to agree with those objects which would have likely received close attention; which can be seen in Figure 4. Human searchers are expected to outperform this detection efficiency algorithm, so the resulting efficiency curves will be somewhat conservative.
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**A**: 6(a) marks the secondary vortex for the viscous regime (γ=100v/w𝛾100𝑣𝑤\gamma=100\,v/witalic_γ = 100 italic_v / italic_w). As discussed in Sec.V, the current in the viscous regime undergoes multiple sign reversals due to the presence of several vortices with opposite signs**B**: In general, viscous flows feature trains of infinitely many higher-order vortices (Moffatt vortices) [50, 51]. However, these vortices are extremely weak compared to the primary vortices, making them insignificant from a practical standpoint.**C**: This can be compared to Figs. 2 (a) and (b) which detail the backflow effect for these current distributions.
The circle in the left inset of Fig
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**A**: Next, we describe the entanglement monotone concentratable entanglement (CE) as defined in [6] and [8], and the experimentally implementable tests for estimating the CE of an ensemble of qubit states as described in [7] and [8].**B**: Section II provides a background on the states considered, namely qubit, qudit, coherent, and orbital angular momentum states**C**:
The paper proceeds as follows
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**A**: On the other hand, a data-driven approach based on this model should produce similar results to one based on the Standard Model. The normal data-driven approach assumes that all Standard-Model nonperturbative QCD interactions are incorporated into the low energy data used as input**B**: Changing the model just means changing that assumption (replacing Standard-Model with this model). But since the data are still the same, the hadronic contribution to the calculation would remain the same.
**C**: This model has both an additional quark and also quark couplings that are different from those in the Standard Model. Therefore, a lattice calculation using this model would produce a different result than one using the Standard Model
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**A**: We then recall the results of [23] that we will require in this paper regarding the law of the maximum oscillation inside a ceiling, conditionally on all walls outside that ceiling**B**: Throughout this, we will also introduce any notation that will be used throughout the paper.
**C**: In this section, we recall the decomposition of the interface into walls and ceilings and their groupings into wall clusters
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**A**: One way to determine whether a trajectory will remain within a contraction region based on the location of the trajectory’s starting point is to find a trapping region that is inside the contraction region. A trapping region N𝑁Nitalic_N is a compact subset of the state space such that the flow of the system is inward everywhere on the boundary of N𝑁Nitalic_N, and therefore every trajectory that starts within N𝑁Nitalic_N will remain there for all future time, details of which can be found in Section 4.**B**:
The limitation of applying the above propositions is that when the symmetric part of the Jacobian of the virtual system of a network is not uniformly negative definite on the entire state space, it is difficult to determine whether the trajectories of the oscillators in this network are confined in the contraction region of the virtual system**C**: Note that even if a trajectory starts in a contraction region, it may leave the region later
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**A**: Pan2 ; Pan3 ; Damour2009 **B**: However, these calculations are very tedious which we will present elsewhere.**C**: For a complete self-consistent EOB theory, we should carry out the concrete calculations for the radiation-reaction force by using the method proposed in Refs.
Ref:poisson ; CutlerPRD ; Sasaki17 ; TagoshiSasaki745 , and then rewrite the inspiral-plunge modes following Refs
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**A**: The peak positions of the probability distribution function (PDF) distribution of the FENE model depend on the macroscopic flow field and change in time under the large macroscopic flow effects [40]**B**:
As discussed in [41], to catch the hysteresis of the original FENE model, a coarse-grained model should be able to catch the spike-like behaviors of the probability density in the FENE model in the large extensional effect of the flow field**C**: We show the position of particles (blue markers) and their underlying distribution probability density (obtained by the kernel density estimation) in the configuration space
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**A**: Note that the observing times of the two catalogs do not overlap. However, some FRB repeaters (e.g**B**: Collaboration et al., 2021), on the other hand, have 1134450 neutrino events spanning ten years. The availability of these two large catalogs makes it possible to perform a direct search of associations between the two types of astrophysical events**C**: FRB 121102) have been known to persist for at least a decade and some recently detected repeaters do not show a significant evolution of burst rate on a timescale of years. Even for apparent non-repeating FRBs, rate arguments suggest that they likely do not originate from cataclysmic events (Ravi, 2019; Luo
et al., 2020) and the lack of multiple detection may be a result of low repetition rate or that most repeated bursts are below the radio detection sensitivity threshold. It is very likely that these “non-repeating” FRBs also emitted additional bursts in the past, but these other bursts were not detected.
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**A**:
In XENON1T, our standard, triggered data acquisition software, which was designed to look for interactions with both an S1 and an S2, did not form a trigger from the smallest S2s**B**: Due to the low trigger rate in XENON1T, this meaningfully reduced our overall livetime as described in Section II.1. However, we have access to several days of continuous data taking, described in Section II.2, in which our signal detection efficiency is essentially unity for signals of one or more electrons.**C**: Thus, we can only search for potential light DM interactions that occur in close time proximity to larger S2s
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**A**:
Magnetic charges, if they exist in the early Universe, will provide a hitherto unexplored window to probe fundamental physics in the Standard Model of particle physics and beyond**B**: Though no evidence of magnetic charges has been found yet [1, 2], magnetically charged black holes have attracted much attention not only in theoretical study but also in recent astronomical observations [3, 4, 5]**C**: Recently, restoration of the electroweak symmetry near the horizon of a magnetic charged black hole has been discussed in [3] and the phenomenology of low-mass magnetic black holes, which can have electroweak-symmetric coronas outside of the event horizon, has been comprehensively studied in [4]. Potential astrophysical signatures for magnetically charged black holes have also been investigated in [5].
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**A**:
We will not be at liberty to assume (3.24) when performing the local density approximation in the proof of our main theorem**B**: This is reminiscent of considerations from [28],**C**: In the following, we use elliptic estimates based on work by Fournais and Helffer [25] to circumvent the condition (3.24)
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**A**:
The non-relativistic counterpart of the Dirac equation should not be considered necessarily as its non-relativistic limit. There are external potentials in which the rest energy contribution is not trivial**B**: We can still change the reference point and shift the energy levels by a constant value. However, the rest energy effects are not erased by the shift**C**: With the rest energy included, the GLL equation leads to a physical picture some elements of which cannot be seen in the framework of the LL equation. We demonstrated this for a non-relativistic Fermi field in a spherical well type potential of finite depth.
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**A**: There will be some overlap between these conditions but we have not found a general simple theory which covers everything**B**: To be more precise, we will give a quantitative estimate on the support of minimizers
**C**: In this section we discuss several possible conditions on c2>0subscript𝑐20c_{2}>0italic_c start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT > 0 which imply that the support of minimizers is always compact
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**A**: The presence of the GHY is essential for this derivation, as we shall see below**B**: While the variation of the GHY term with respect to the metric is well-known, we shall derive the variation with respect to the hypersurface, thereby extending previous results.**C**:
Below we shall derive the equations as well as the boundary and junction conditions by extending the covariant reduced variational principle developed above to the action functional (5.6)
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**A**: (MacLeod et al., 2018a).
The HST composite from Cohen et al**B**: The jet produces a blue shift in Hα𝛼\alphaitalic_α emission, modulating the primary’s envelope emission.**C**: (2004) shows a bipolar axis length of ∼1.5×104similar-toabsent1.5superscript104\sim 1.5\times 10^{4}∼ 1.5 × 10 start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT au
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**A**: Consider the following problem:
**B**: Then, the solution of Problem (21) is primarily ν𝜈\nuitalic_ν-optimal and secondarily ν∗superscript𝜈\nu^{*}italic_ν start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT-optimal**C**: In practice, we use the perturbation method (Mangasarian and Meyer, 1979) to compute the solution at once
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**A**: The dependence of GW sources on the galaxy properties through the GW bias parameter is marginalized in this analysis. In the future, with the availability of a few hundred dark sirens, the cross-correlation technique will be able to infer the clustering redshift of sources more accurately, and this will be able to shed further light on the tension in the Hubble constant determinations (Verde et al., 2019; Di Valentino et al., 2021).
**B**: In the future, with the availability of z<0.8𝑧0.8z<0.8italic_z < 0.8 spectroscopic galaxy catalogs such as DESI (Aghamousa et al., 2016) and SPHEREx (Dore et al., 2018) (supplemented by z>0.8𝑧0.8z>0.8italic_z > 0.8 spectroscopy from Euclid (Blanchard et al., 2020) and photometric redshifts from Vera Rubin Observatory (LSST Science Collaboration et al., 2009)), cross-correlation of the GW sources with galaxies will be a powerful technique to measure the expansion history (Mukherjee & Wandelt, 2018; Mukherjee et al., 2021b; Cigarrán Díaz & Mukherjee, 2022) and testing the general theory of relativity (Mukherjee et al., 2021c)**C**: The measurement presented in this analysis reports a value of the Hubble constant which is not influenced by the choice of the pair-instability supernovae (PISN) mass gap (Farmer et al., 2019)
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**A**: resonances**B**: The**C**: With the above q2superscript𝑞2q^{2}italic_q start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT selection applied, the average number
of K∗μ+μ−superscript𝐾superscript𝜇superscript𝜇K^{*}\mu^{+}\mu^{-}italic_K start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT italic_μ start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT italic_μ start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT and K∗e+e−superscript𝐾superscript𝑒superscript𝑒K^{*}e^{+}e^{-}italic_K start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT italic_e start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT italic_e start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT decays in each fit is 4850
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**A**: Here the contribution of scattered light to the intensity outcome is neglected**B**: (2.1) by corresponding exponents:
**C**: The exponent in the integral may be approximately considered by multiplying intensities deposited in αβ𝛼𝛽\alpha\betaitalic_α italic_β reflection of ij𝑖𝑗ijitalic_i italic_j photomultiplier in Eq
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**A**: In other words, the lack of centrosymmetry is essential to meaningfully distinguish between phases that are topologically trivial vs nontrivial.
**B**: Aiming to forgo all supplemental conditions, this work introduces a new class of topological insulators for which wave-function topology is a sufficient condition for a nontrivial shift**C**: The introduced class contrasts from previous case studies in being essentially noncentric, meaning that the topologically nontrivial phase of matter exists only in crystal classes without a center of inversion, as illustrated in Fig. 1(b)
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**A**: (2003); Valencia et al. (2020)**B**: On average, our initial state is close but not exactly equal to a maximally entangled state (Extended Data Fig. 1). In order to determine the underlying quantum process we must invert the dependence on the initial state to recover the Choi state of the channel, i.e., an optical circuit. The initial state can be written as a linear operation, 𝒜𝒜\mathcal{A}caligraphic_A, acting only on party A of a maximally entangled state ρ+superscript𝜌\rho^{+}italic_ρ start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT,
**C**: A single, well-characterised, and sufficiently strongly correlated state supported on an extended Hilbert space, along with a tomographically complete measurement, can also achieve quantum process tomography. This process is known as ancilla-assisted quantum process tomography (AA-QPT) Altepeter et al
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**A**: Lu:2024bqw **B**: Γ(Ωbbb−→Ξbb0π−)Γ→superscriptsubscriptΩ𝑏𝑏𝑏superscriptsubscriptΞ𝑏𝑏0superscript𝜋\Gamma(\Omega_{bbb}^{-}\to\Xi_{bb}^{0}\pi^{-})roman_Γ ( roman_Ω start_POSTSUBSCRIPT italic_b italic_b italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT → roman_Ξ start_POSTSUBSCRIPT italic_b italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT italic_π start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT ), our results are
much smaller than those in Ref**C**: This is likely due
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**A**: This is because the Hamiltonian can be diagonalized by a unitary transformation, and there is no preferred basis.
**B**: 1)**C**: The spectrum of the Hamiltonian (including the multiplicities of the eigenvalues): “the laws of physics are determined solely by the energy eigenspectrum of the Hamiltonian” ([44], p
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**A**: We assume noiseless circuits, but in the presence of noise the performance of teleportation protocols depends directly on the fidelity of the required resource Bell pairs. We are primarily interested in ways to use teleportation for routing, and Bell pairs are necessary for this process**B**: If operating in a quantum network, we can make use of protocols generalizing entanglement swapping from Bell basis measurements to n𝑛nitalic_n-qubit GHZ states to improve the performance of repeater protocols in lossy quantum networks [39]. Alternatively, we can prepare a high-fidelity Bell pair by performing multiple repeater protocols along different paths in parallel [40] or using multiplexers on each edge [41].
**C**: Our current teleportation routing model does not distinguish between routing over long or short paths, but a more comprehensive model of routing could prioritize shorter paths as they will be less error prone without error correction. Alternatively, we could use a purification protocol [37] to prepare high-fidelity Bell pairs at the cost of additional ancillas and overhead, or we could encode our state in an error-correcting code [38] to suppress the error rate when operating between nodes
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**A**: First, we consider the normal stress balance across a fluid interface written as,**B**:
Substituting (8) in (5) we see that the viscous stress terms cancel**C**: This points to the fact the viscous stresses must enter the problem through the boundary conditions
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**A**: In a real system, however, manipulating the mass term is quite nontrivial**B**: The mass term does not commute with the rest of the Hamiltonian and thus results in intriguing new topological features Kane and Mele (2005a); *Kane2005a**C**: Physically, such non-commuting nature originates from a complex mixture of different degrees of freedom which makes their control quite challenging. A simple way to manipulate the magnitude and signature of the mass gap thus has an enormous potential in fabricating topologically non-trivial systems and exploring their applications.
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**A**: Having this in mind, we follow the approach we took in [5] and define:
**B**: The active local measurements that we perform to obtain the data for the problem have to account somehow for this gauge invariance**C**: One possibility would be to attempt some gauge fixing in order to define a suitable source-to-solution map; in fact we shall do that at a later point, but in order to formulate the result it seems more appropriate to find a presentation of the data that is amenable to the gauge invariance
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**A**:
We acknowledge financial support from Agence Nationale de la Recherche (ANR project “GraphSkyrm”) under Grant No**B**: ANR-17-CE30-0029**C**: We thank François Parmentier for fruitful discussions and his valuable scientific input. Finally, we thank Patrice Jacques for his assistance with our figures.
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**A**: For each model we focus on a the relevant experimental signature and use the experimental collaboration’s Monte Carlo prediction as the expected Poisson mean of the event sample. Given their observed data, we then set limits at the 95% confidence level on the number of allowed events in the energy range as defined by the experiment. We consider both systematics and statistically limited searches with a conservative estimate of a 5%percent55\%5 % systematic uncertainty on the collaboration’s Monte Carlo prediction for their sub-GeV sample of 0-decay-e events.
**B**: (2018)**C**: In what follows we describe a simple rate-only analysis based on the published results in Abe et al
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**A**: As a demonstration, we show basic PE results for Einstein Telescope (ET) in section III.4, which is a good example to understand the capabilities of gwfish, but also its limitations since single-detector scenarios are especially difficult to model in the Fisher-matrix formalism due to unavoidable degeneracies in the signal model. As a direct scientific conclusion of these analyses, we confirm that the ET configuration has unique capabilities for PE of compact-binary coalescences**B**: Other more detailed studies carried out with gwfish have been published in separate papers. These include the evaluation of the perspectives of multi-messenger observations for ET (as single observatory and in network of GW detectors) operating in synergy with γ𝛾\gammaitalic_γ and X-ray satellites using astrophysically motivated populations of BNS mergers [25], and very high-energy observatories (Banerjee et al**C**: 2022 in preparation). gwfish was also used for the simulation of an astrophysical background in the ET null-stream study [26].
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**A**: The relationship between agents, the number of fragmented or disconnected clusters, population density, and population heterogeneity are among environmental factors affecting information exchange [15, 16]. Modeling innovation in networks makes it possible to understand the impact of social interactions diffusion**B**:
Models of innovation have mostly focused on studying the adoption of innovative ideas or products by groups of agents [10, 11, 12, 13]. Diffusion of innovation is a social process governed by the impact of media and social interactions [14]**C**: Recent studies have shown how ideas spread and how diffusion depends on the network structure [17, 18, 19]. A simple model was proposed to study how the trade-off between acquiring new skills and improving existing skills shapes social networks [20], while the relation between network structure and product and process innovation was analysed using configurational terms [21]. The impact of the network structure in respect to population size and connectivity was studied by simulating innovation and diffusion of cultural traits in populations with stereotyped social structures [22]. These studies show that small, seemingly insignificant idiosyncrasies of their structures can heavily impact innovation’s diffusion among members of a social network [23, 24].
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**A**: Other orbits would need to be studied in depth. We do not consider this effect in-depth – we assume that if the decoherence and phase effects can be measured in a single shot, then their variance with time will also be measurable (but see Appendix A for a short description of how to include the daily modulation). Thus, we study here a necessary, but not sufficient, metric for detecting DM with atom interferometers.**B**:
There are many possible decoherence and phase shift mechanisms for atom interferometers [e.g., see Ref. 75]. To definitively make a DM detection, an atom interferometer would need to see a signal that varies with the expected DM flux [65]**C**: For a terrestrial experiment, this would give the so-called “daily modulation” caused by the Earth’s rotation with respect to the incoming DM flux. For a space-based experiment, like most of the ones we consider here, the exact modulation will depend on the orbit. Low-Earth orbits will lead to modulation signals with timescales on the order of the orbit (e.g., for an experiment on the International Space Station, the timescale is ∼90similar-toabsent90\sim{90}∼ 90 minutes)
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**A**: be constant for t≫τpmuch-greater-than𝑡subscript𝜏𝑝t\gg\tau_{p}italic_t ≫ italic_τ start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT**B**: The
panel confirms this and also quantifies Δℰ(E0)Δℰsubscript𝐸0\Delta\mathcal{E}(E_{0})roman_Δ caligraphic_E ( italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT )**C**: (b). The
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**A**: The non-zero coherence shows that these are indeed cooperative effects. At late times, radiation trapping emerges [59], a regime characterized by a slowdown of emission in the absence of atomic coherences**B**: Additionally, we demonstrate that observables such as the cooperative decay rate and the emission linewidth scale with the optical depth of the system. Finally, we investigate the slow decay in the subradiant regime, as well as the phase change of the radiated field during the cooperative decay.
**C**: In this article, we focus on the deceptively simple example of a homogeneous gas of two-level atoms and obtain the time-evolution of an initially fully inverted system. By calculating the radiated intensity and the off-diagonal coherence of the density matrix, we find a superradiant outburst at early times and subradiant emission immediately afterwards
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**A**: Our main tool will be the couplings between the continuous and discrete models from the previous section, that is Theorem 4.5 for excursions, Theorem 4.8 for loop soups, and Theorem 4.9 for sets of excursions plus loops**B**: We first recall the Beurling estimate, which will also be useful in Section 6.
**C**: In this section, we prove that the discrete percolation parameters are asymptotically the same as the critical values obtained for the continuous percolation in Appendix A
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**A**:
We show the distance matrices for the 16 airlines in Fig. 5**B**: The results indicate that there are similarities and differences in changes in the network structure of each airline.**C**: Recall that five airlines are FSCs (i.e., American, Alaska, Delta, Hawaiian, and United), five airlines are LCCs (i.e., JetBlue, Frontier, Allegiant, Spirit, and Southwest), and six airlines are RCs (i.e., Endeavor, Envoy, PSA, SkyWest, Mesa, and Republic) (see also Table 1)
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**A**:
It is important at this point to emphasise that the initial motivation of the consistent histories formalism is the description of closed quantum systems without measurements or external observers. This is achieved by replacing the process of measurement with the consistency condition that must be satisfied in order for a question to be (classically) answered**B**: As it was demonstrated, the same question can be answered by considering different partitions of the histories space. For each of those partitions, to calculate the amplitudes and their interference one needs to use projections and/or restrictions in the path integral**C**: Mathematically the different partitions appear as if different measurements took place, but in consistent histories there is no “real” measurement taking place, or external observer. The physical system (paths and true Hamiltonian) are identical in all partitions, therefore reaching a different conclusion about properties of the same classical system seems problematic and gives further evidence that consistent histories without a set-selection mechanism may not be a viable alternative.
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**A**: Such quantum algorithms are crucial for near-term noisy, intermediate-scale quantum computers (NISQ), since the design of noise-resilient algorithms may extend the computational power of NISQ devices [16].**B**:
In light of these fluctuations, recent study on state tomography extends to temporal quantum tomography [15] with changing quantum states**C**: Therefore, a fundamental question from our perspective of machine learning is learning changing quantum states, which naturally fits into the framework of adaptive online learning
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**A**: By optimal ratio, we simply imply that the ratio of couplings needs to be tuned such that we obtain linear-in-T resistivity. Here we will show that the fundamental origin of this feature in this model is the emergence of a universal form of the spectral function as a function of the frequency near the Fermi surface over a large range of temperatures. As discussed below, this universal behavior emerges at finite (non-vanishing) temperatures due to a competition between two different types of interactions, and this cannot be obtained from the self-energy contributions due to interactions with the critical sector alone. We also emphasize that the universal form is needed even at large frequencies to reproduce strange-metallic transport properties (although it is valid only near the Fermi surface) due to the underlying non-Fermi liquid nature of the system.
**B**: It incorporates lattice band electrons hybridizing with fermionic operators of a quantum critical sector, and can be viewed as an effective theory of the conducting electrons of the lower Hubbard band with only two couplings. It was shown that there always exists an optimal ratio of these two couplings at which the model exhibits universal transport properties, especially linear-in-T resistivity, over a very wide range of temperatures, irrespective of all parameters provided the critical exponent lies within a certain range**C**: In this work, we analyze a simple effective model of strange metallic behavior proposed in Doucot et al. (2021) that captures features of Mottness
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**A**: Ivan S. Novikov: Investigation, Visualization, Data Curation, Validation, Software, Writing - Original draft**B**: Edgar M. Makarov: Investigation, Data Curation**C**: Yury V. Suleimanov: Conceptualization, Methodology, Software, Writing - Review & Editing. Alexander V. Shapeev: Conceptualization, Methodology, Resources, Writing - Review & Editing, Project administration, Funding acquisition, Supervision.
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**A**:
Apart from modeling graphene sheets under mechanical strain, the model we analyze in this work has also been considered for low-energy electron diffraction (LEED) studies in surface reconstructions of metals**B**: This phenomenon where the crystal structure of the metal is broken up on the surface is known as surface reconstruction [Her12, VKS+81]. In addition, the existence of one-dimensional flat bands in twisted one-dimensional Germanium selenide lattices has been recently discovered in [KXCR20].**C**: More precisely, metals such as iridium, platinum, and gold are known to exhibit columns of honeycomb lattice structures on their surface with pits in between them
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**A**: The technical reason for this decision is that our argument requires consideration**B**: First, we do not treat admissable or Leray
weak solutions of the Navier-Stokes equations, but instead assume that all Navier-Stokes solutions are strong**C**: in space-time, we have had to make two key modifications
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**A**: We calculate a representative neutrino radiation field in a snapshot of a neutron star merger simulation using time-inedependent Monte Carlo radiation transport (Figure 1). We use the results to show that there are electron lepton number crossings, and hence flavor instability, everywhere on the domtain except in the central hypermassive neutron star (Figure 2)**B**: We then take angular moments of this radiation field and assess how well a number of proposed tests are able to correctly determine the presence of ELN crossings using only these moments (Figure 7). All of the methods predicted instability near the regions where significant flavor transformation is likely (Figure 6)**C**: The resonant trajectory test and the generalized maximum entropy test derived in this work predict instability in almost all locations where ELN crossings are present in the full Monte Carlo data. Many of the tests showed significant dependence on the choice of closure, but the resonant trajectory showed remarkably little dependence, and the maximum entropy tests and order-1 polynomial tests are independent of the closure choice by construction. We note that each of these tests has particular advantages, including simplicity of implementation, guarantees to not over-predict instability, and insight into the growing modes of the distribution, and the optimal test to use varies by the need for each of these. In addition, while we chose a challenging and rich environment in which to test these instability metrics, the reader should be cautioned that the successes and similarities of the metrics may not carry through to other realizations of NSMs or other systems like CCSNe.
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**A**: Initiative and the Institute for Advanced Study**B**: This work used the Extreme Science and Engineering Discovery Environment (XSEDE) (Towns et al., 2014) through Expanse at SDSC and Bridges-2 at PSC through allocations PHY210053 and PHY210074.
The simulations were also in part performed on computational resources managed and supported by Princeton Research Computing, a consortium of groups including the Princeton Institute for Computational Science and Engineering (PICSciE) and the Office of Information Technology’s High Performance Computing Center and Visualization Laboratory at Princeton University. ERM also acknowledges the use of high-performance computing at the Institute for Advanced Study.**C**: ERM acknowledges support for compute time allocations on the NSF Frontera supercomputer under grants AST21006
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**A**: However, none of the realizations demonstrated the same orbital angular momentum (OAM)**B**: At the same time, our developed model predicts that by changing the coupling between the cells one can potentially tune the system to vortex-vortex state, implying FM order instead of dominant AFM arrangement. To realize this experimentally, we first reproduce already expected vortex-antivortex pair using pump profile shown in Fig. S7A. As a result, above condensation threshold power we observe formation donut-shaped PL inside the cells (Fig. S7B), corresponding to a vortex-antivortex pair as confirmed by the extracted phase map in Fig. S7C.
**C**: Our experimental measurements of the single-shot realizations in 2-cell structure revealed that such system preferentially occupies vortex-antivortex or antivortex-vortex states
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**A**:
A possible test case concerns the forward–backward asymmetry in the same process, in which case radiative corrections arise from the interference of initial-state-radiation (ISR) and FSR diagrams Binner et al**B**: (1999); Czyż et al**C**: (2005b); Lees et al. (2015)
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**A**: The many-body physics presented here could be relevant to the community working on atomtronics [55] and metrology [56]. Further investigations are warranted.**B**: Moreover, dipolar bosonic crystal orders and the dynamics of bosons in two-dimensional optical lattices, including the impact of competition between longitudinal and transversal fragmentations, have the future scope to be investigated**C**:
As the four-well set-up considered here is a minimal substructure of a two-dimensional optical lattice, tunneling of different quantum phases, such as, superfluid, Mott insulator [52], and fermionized Tonks–Girardeau gas [53, 54], can be studied by tuning the barrier height and the strength of inter-particle interaction
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**A**: The imbalance between the helicity eigenstates, namely the difference between the number density in helicity eigenstates, which comes only from the LLL electrons 333The spin degeneracy in the higher Landau levels, n≠0𝑛0n\neq 0italic_n ≠ 0, will be slightly lifted by the Zeeman splitting due to the anomalous magnetic moment of electrons, giving rise to an additional helicity imbalance, quadratic in magnetic fields**B**: Therefore, only LLL electrons contribute to the CME, unless the higher Landau levels are partially occupied. We thank Ken Van Tilburg for discussions on this., is given as
**C**: The CME of higher Landau levels cancels out, however, because the spin up and down states contribute oppositely
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**A**: To accomplish this we use the method of frozen phonons. In this approach, the electronic bands are recalculated with the lattice shifted along a phonon eigendisplacement**B**: To quantify the coupling strength of a specific phonon to a particular electronic band we integrate the energy changes of the band in the presence of the phonon over the Brillouin zone as outlined in the supplementary material. We find that in the vicinity of 4.54.54.54.5 THz, relevant to the experimental observables, the 4.74.74.74.7 THz mode has roughly an order of magnitude larger electron-phonon coupling strength compared to the nearby phonons. In particular, as shown in Fig. 2(c), the 2nd and 3rd conduction bands (in this paper we number the conduction bands from lowest to highest in energy) are significantly renormalised in the presence of the 4.7 THz phonon. Since the phonon is mostly coupled to two electronic bands, the frozen phonon calculations are consistent with equation (13) leading to the two bands shifting in energy by an equal and opposite amount given by:
**C**: We compute the electron-phonon interaction between IR active phonons and electrons. This is to identify the phonons that dominate the interaction with the photo-excited electronic bands
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**A**:
In the last Section there are some comments on generalizations**B**: It is a challenge to properly formulate a generalization for loops into more general compact homogeneous or Einstein targets. In another direction, I originally thought the theory might extend to symmetrizable Kac-Moody algebras. This now seems doubtful, and it is enlightening to understand why.**C**: The basic existence result for invariant measures generalizes to (an appropriate completion of) loops into symmetric spaces
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**A**: Finally, Fig. 8 (b) shows the primary emissivity for the same temperatures, namely, 301.93301.93301.93301.93, 183.35183.35183.35183.35, and 74.6774.6774.6774.67 MeV for a∗=0,0.9,0.99subscript𝑎00.90.99a_{*}=0,0.9,0.99italic_a start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT = 0 , 0.9 , 0.99, respectively.
One may compare Fig**B**: Fig.2 of Arbey:2020yzj highlights how the rotation in a Kerr BH reinforces the emission of non-spin-less particles and decreases the emission of scalar particles. This is no longer valid for the Kerr-bounce BH. In fact its scalar particle emissivity peaks at higher values for values of the spin parameter close extremality.**C**: 8 with Fig. 2 of Arbey:2020yzj which describes the primary emission of a Kerr BH for different field spins
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Free parameters in modified gravity theories are trivial and hold significant role**B**: It allows a particular gravity model to be consistent with observational results**C**: In this work we tried to constrain the simplest f(R,T)𝑓𝑅𝑇f(R,T)italic_f ( italic_R , italic_T ) model with logarithmic correction, using Hubble parameter and dark energy density parameter. The analysis reveals that the model parameter α𝛼\alphaitalic_α can assume any non negative value.
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**A**: So let us discuss Lattice Euclidean QFT for scalar field with more intensity. The most widely spread technique for calculating correlation functions is Feynman Perturbation Theory, obtained by decomposition of an exponent with interaction in power series**B**: This usually raises a series in positive powers of coupling constant, which are often diverge and appear to be only the asymptotic expansions. Commonly they diverge quite aggressively, which make us using the ressummation techniques, e.g**C**: Borel resummation. We will refer to the described series as Weak Coupling Perturbation Series in this paper.
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**A**: For example, SGR that make**B**: “intermediate” outbursts of SGR, with total power ≲1042less-than-or-similar-toabsentsuperscript1042\lesssim 10^{42}\,≲ 10 start_POSTSUPERSCRIPT 42 end_POSTSUPERSCRIPTergs/s**C**: It is unclear how these may differ from the Galactic
SGR with much more energetic giant outbursts
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**A**: Also shown is the a posteriori Highland-Cousins method (here labeled ‘Posterior HC’ and drawn in pink) which can be considered as an intermediate option between Highland–Cousins and our profiling method, and yields an intermediate performance.
**B**: Figure 6: The coverage obtained using critical values using the Highland–Cousins procedure (light blue) and our proposed profiling procedure (dark blue) for our toy model, where the true sign of C𝐶Citalic_C is unknown at fit time, and profiled over, evaluated for true positive sign (solid) and true negative sign (dashed)**C**: In both cases the coverage averaged over δ𝛿\deltaitalic_δ and sign is correct, but the profiling procedure exhibits substantially smaller deviations from correct coverage where these occur
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**A**: The path to solve the Mathieu differential equation is to employ perturbation theory and obtain a perturbative series, but perturbative series are usually divergent in physics [20, 21, 22]. When the series is asymptotic, it is common to employ Borel summation to extract non-perturbative information**B**: Such divergence is related to the existence of singularities in the Borel complex plane, usually also associated with instantons [11, 22]. These are crucial parts in the construction of transseries, which are important manipulations of formal series that can cancel out ambiguities [11, 12, 22, 13, 23, 24].
**C**: However, a more difficult task is the reconstruction of functions from divergent perturbative expansions, as it generates incomplete information. This signals the need to include non-perturbative instanton effects
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**A**: Strong repulsive interactions would stabilize a chiral skyrmion crystal state, whereas strong fluctuations would lead to a chiral skyrmion liquid**B**: Overall, these phases are expected to have properties similar to those of the vortex lattice and vortex liquid phases in superconductors [60, 61, 62, 63].
Which of the two states—skyrmion crystal or skyrmion liquid—wins in the true ground state**C**: The emergence of skyrmions through the mechanism discussed above can lead to different ground states depending on the interactions between skyrmions and the strength of the spin order parameter zero-point or thermal fluctuations
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**A**: It is a spin-1 gauge boson associated with a new Abelian U(1) symmetry and is one of the simplest possible extensions to the Standard Model (SM) [8, 9, 10]**B**: The dark photon, having the same quantum numbers as the SM photon, generically interacts with the SM photon through kinetic mixing [11, 12] described by the Lagrangian**C**:
The dark photon (DP) is a compelling dark matter candidate
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**A**: For large-size problems, the Hybrid solver shows an impressive performance, clearly outperforming the ZF Approximate solver in terms of solution quality and runtime. In this region, the ZF Exact solver has no data points as it becomes prohibitively expensive in both runtime and memory, highlighting the benefits of the Hybrid solver.
**B**: In this region, these two algorithms yield similar results in terms of solution quality. In particular, we observe that the Hybrid solver finds solutions with slightly better standard deviation, whereas the ZF Exact solver finds solutions with a smaller range**C**: To rank the different solvers considered in this work, direct use of the Quantum Annealing solver is preferred for small problem sizes due to its capacity to find high-quality solutions in very short times. However, hardware limitations in that solver mean that both the Hybrid and ZF Exact solvers outperform it for medium-sized problems
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**A**: Partial solutions to this problem have been given by Pezze et al. (2017), Yang et al. (2019b) and Chen et al. (2022a, b) in the view of quantum metrology. We note that necessary and sufficient conditions for the full rank case were first stated by Amari and Nagaoka, see Sec**B**: We now turn to estimating more than two parameters. In this scenario, as the NCRB no longer applies, we shall use the NHCRB, 𝒞NHsubscript𝒞NH\mathcal{C}_{\text{NH}}caligraphic_C start_POSTSUBSCRIPT NH end_POSTSUBSCRIPT, to bound the precision attainable with separable measurements Conlon et al. (2021). We first examine the attainability of the SLDCRB in the single-copy setting, which has recently been recognised as one of five open problems in quantum information theory Horodecki et al. (2022)**C**: 7.4 of Ref. Amari and Nagaoka (2000). Furthermore, Suzuki, Yang and Hayashi (see Appendix B1 of Ref. Suzuki et al. (2020)) gave the necessary and sufficient condition for the more general rank-deficient case. In this sense, the open problem seems to be solved as far as the single-copy setting is concerned. However, this open problem may be extended beyond the single-copy scenario to any finite-copy setting. Using the gap persistence theorem, we provide the necessary and sufficient conditions for the attainability of the SLDCRB with collective measurements on any finite number of copies of the probe state. To do this, we first present a simple and alternative proof for the necessary and sufficient conditions in the single-copy setting.
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**A**: However, there is still no an accepted LFEPP for 3D Ising model, although for this purpose there have been lots of methods or approaches which are valid for 1D, 2D and/or high-dimensional (D>3𝐷3D>3italic_D > 3) model. The most famous ones are Mean-Field Theory (eg., Bragg and William, 1934, 1935; Williams, 1935; Landau, 1937), Transfer Matrix Method (Onsager, 1944), φ4−limit-fromsuperscript𝜑4\varphi^{4}-italic_φ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT - Theory (Ginzburg and Landau, 1950), Variational Calculation (Thompson, 1965)**B**: Especially the Transfer Matrix Method and the similar ones are popular in the later studies (eg., Zhang, 2007), although their results are questionable (eg., Wu et al., 2008; Fisher and Perk, 2016; Perk, 2013). Transfer Matrix Method requires specialized and abstract knowledge of spinor algebra or operator algebra, which is unfamiliar to most non-professionals**C**: In 2015, Kocharovsky and Kocharovsky (2015) presented a method of the recurrence equations for partial contractions for 3D model, and they said that ”Towards an exact solution for the three-dimensional Ising model”. However, it can also be found that their method is too complicated and specialized.
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**A**:
Given this peculiar situation, one of the earliest puzzles in quantum information science was to devise a quantum generalization of the concept of conditional entropy. In the classical case, conditional entropy is meant to capture the uncertainty about the state of one particle given access to a second particle that is potentially statistically dependent on the first [3]**B**: When generalizing the definition of conditional entropy in a straightforward way to the quantum case (by means of this reduction), one finds that quantum conditional entropy is negative when evaluated for the EPR state mentioned above [4]. Since conditional entropy is never negative in classical information science, this situation represents a radical departure from the classical case and has been popularly described as “knowing less than nothing” [5].**C**: If there is no statistical dependence whatsoever, then the conditional entropy reduces to the usual entropy. However, if there is dependence, then there is a reduction in the uncertainty of the first particle when given access to the second
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**A**: A sophisticated interplay of hadronic interactions, such as elastic and inelastic scattering, resonance production, decay, etc., characterizes the expanding hadronic phase**B**: To precisely interpret the experimental data and deduce the properties of the QGP and the nature of the QCD phase transition, a thorough understanding of this complex phase is essential**C**: It can provide unique insights into the fundamental properties of matter under extreme conditions, emphasizing the necessity for modeling this dynamic phase. Here, we employ hydrodynamics to study the evolution of the hadronic medium and its cooling rate under various scenarios.
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**A**: The quantum part of the procedure involves evaluating a parametrized quantum circuit for a given set of parameters in each iteration. The parameters are updated for the next iteration via a cost function optimization routine on a classical computer. The optimized parameters are the interaction strengths of the time-independent Hamiltonian that generate the target unitary. Further, we demonstrate the applicability of our approach to designing Toffoli and Parity gates.
**B**: VQAs can be employed to solve a variety of optimisation [17] and linear algebra problems [18], as well as a prospect to simulate quantum chemical systems [19, 20, 21, 22, 23, 24, 25]. In the current work, we use a VQA to optimize the values of the couplings that are required in realizing a given target multi-qubit quantum gate via a time-independent Hamiltonian**C**: In our work, we devise an attractive Noisy Intermediate-Scale Quantum (NISQ)-friendly approach to designing multi-qubit gate automata, via the quantum-classical hybrid variational quantum algorithms (VQAs). In recent times, VQAs [14, 15] have emerged as potential candidates to provide a quantum advantage in the NISQ era [16]
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**A**: Since enbτminsuperscript𝑒𝑛𝑏subscript𝜏e^{nb\tau_{\min}}italic_e start_POSTSUPERSCRIPT italic_n italic_b italic_τ start_POSTSUBSCRIPT roman_min end_POSTSUBSCRIPT end_POSTSUPERSCRIPT**B**: (4.8) (and the line above it), (4.9),
and (thrice) in the two lines after (4.14), and it would replace 4444 by (ab)−1superscript𝑎𝑏1(ab)^{-1}( italic_a italic_b ) start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT in (4.3), (4.6), and (4.7)**C**: Taking a𝑎aitalic_a and b𝑏bitalic_b close to 1111, this would give a larger value for s*subscript𝑠s_{*}italic_s start_POSTSUBSCRIPT * end_POSTSUBSCRIPT (up to taking κ𝜅\kappaitalic_κ smaller in (4.14))
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**A**: III we present the results. Firstly, we show a paradoxical effect in which the periodic structure not only does not hinder the directed velocity of the particle, but on the contrary, it is involved in inducing the giant transport which can be orders of magnitude greater than the velocity of the free particle. Secondly, we outline the mechanism of this phenomenon**B**: Thirdly, we discuss the role of breaking of the periodic potential and active fluctuations symmetry. The last section provides the summary and conclusions. In Appendix A we introduce the dimensionless units whereas in Appendix B we detail on the parametrization of active fluctuations amplitude distribution. Finally, in the last Appendix we discuss exemplary realizations of active fluctuations.
**C**: The paper is organized as follows. In the next section we discuss details of the studied model. In Sec
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**A**: The hits with multiple steps contribute to the platform before the peak. Moreover, the finite granularity of the ECAL causes an error in L𝐿Litalic_L. Consequently, there is a small fraction of shower hits whose projected time is before zero.**B**:
where t𝑡titalic_t denotes the raw hit times, L𝐿Litalic_L denotes the distance between the IP and the center of the hit. Since the magnetic field is set to zero, this subtraction approximately normalizes the propagation time from the IP to the ECAL hit**C**: Each distribution contains a fast component from 0 to 2 ps, followed by a slow tail extending beyond one ns. During the simulation, there are a large amount of hits including only one step and pausing a peak in the fast component
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**A**: This limits the achievable performance for this algorithm.**B**:
Both as an absolute value and relative to the A100 results, the Jacobian kernel has low arithmetic intensity (AI-HBM, computed as total FLOP / effective bandwidth) of 0.070.070.070.07 with respect to DRAM memory movement in 2V2𝑉2V2 italic_V**C**: The kernel is apparently suffering from the cost of the relatively smaller L1 cache of the MI250X, relatively low L2 hit rate, and register spilling to scratch despite the application of launch bounds
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**A**: A mechanism for suppressing power that is known to operate in nature is the Compton scattering of baryons (i.e. visible matter) with CMB photons in the early Universe**B**: For example, DM can be gauged under a symmetry group akin to the SM. If the symmetry is unbroken and the gauge coupling sufficiently small, the gauge fields are light or massless, and we end up with a dark sector with two components Lesgourgues:2015wza : an interacting dark matter (IDM) coupled with a new component of ultrarelativistic dark radiation (DR).
**C**: It is a plausible possibility that an analogous mechanism is responsible for a power suppression in (part of) the DM component
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**A**: Next, anharmonic VPT2 calculations were performed in the same fashion utilizing CFOUR**B**: The needed cubic and semi-diagonal quartic force constants can be obtained from Hessians of displaced structuresBoese, Klopper, and Martin (2005a, b); Barone (2005)**C**: Unless specified otherwise, we use herein the default displacement of 0.050.050.050.05 in reduced normal coordinatesYagi et al. (2004) q𝑞qitalic_q, which are related to the cartesian normal coordinates Q𝑄Qitalic_Q via
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**A**: In the end, we comment on this global Gaussian operator optimization idea.**B**: This section summarizes the basic ideas of gradient descent on Riemannian manifolds, particularly on the manifold of symplectic matrices and unitary matrices**C**:
We will concentrate then on detailing the update on the symplectic group 𝑺𝑺\bm{S}bold_italic_S, which is endowed in the Riemannian manifold
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**A**: roman_E . ⟩ = ⟨ roman_K **B**: roman_E . ⟩ = ( italic_n + italic_δ ) roman_ℏ italic_ω / 2, which immediately gives the exact**C**: term must be the average kinetic energy. By virial theorem
therefore ⟨P.E.⟩=⟨K.E.⟩=(n+δ)ℏω/2\langle{\rm P.E.}\rangle=\langle{\rm K.E.}\rangle=(n+\delta)\hbar\omega/2⟨ roman_P
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**A**:
The RMSE distribution across the locations is shown in Fig**B**: The plots show that error in the sampling-based model is uniformly distributed, whereas error in other models is much higher in some regions.**C**: 6, and we infer that the RMSE for a ConvLSTM is least, while others have nearly similar
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**A**: Algorithm 2 summarizes the solving and training procedures for ANIE**B**: Theoretical considerations on Fredholm generalized equations with general operators, integral operator approximation through self-attention, and existence of the solutions for these equations are given in Appendix B.4. Figure 13 gives a diagrammatic representation of the integration procedure implemented in this article, and Figure 14 gives a schematic representation of the solver procedure with space and time.
**C**: A detailed description of the meaning of 𝔄𝔱𝔱𝔄𝔱𝔱\mathfrak{Att}fraktur_A fraktur_t fraktur_t is found in Appendix D.2
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**A**: This is in contrast to the model in the present paper, where all anisotropies decay to a homogeneous and isotropic fixed point, in keeping with the cosmic no-hair theorem Wald:1983ky . Also, even though FLRW is stable in our setup, the possibility of a tilt instability in the FLRW geometry which could potentially evade detection through the cosmic no-hair theorem was raised**B**:
It is worthwhile to mention Krishnan:2022qbv , which have partial overlap, and of course are compatible with some of the results and statements presented in this paper**C**: However it is important to note that the authors of Krishnan:2022qbv considered so called flowing dark-energy cosmology, where the tilt parameter is non-zero at late times (for details see Section V of Krishnan:2022qbv )
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**A**: The proposed framework is detailed in Section 3, and specifically the proof for the optimality of the Duostra algorithm is provided in Section 4. We present the experiment results in Section 5, and conclude the paper in Section 6. The source code555https://github.com/DVLab-NTU/qsyn of our method is embedded in the tool Qsyn (Lau_Qsyn_2024, ).
**B**: The rest of the paper is organized as follows**C**: We first explain the qubit mapping problem in Section 2
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**A**: Remarkably, all of these models have been shown to share the same scaling limit. Some notable examples include the longest increasing subsequence [BDJ99], directed last passage percolation [Joh00], polynuclear growth models [Joh03], the asymmetric simple exclusion process (ASEP) [TW08, TW09, Vir20, QS22], directed random polymers [ACQ11, Sep12] and the KPZ equation itself [QS22, Vir20].
**B**: Over the past two decades, an extensive class of (1 + 1) spacetime dimension models, collectively referred to as the KPZ universality class, has been exactly solved**C**: Numerous papers in physics literature [FNS77, vBKS85] had previously predicted that the height function ℋ(t,x)ℋ𝑡𝑥\mathcal{H}(t,x)caligraphic_H ( italic_t , italic_x ), when appropriately scaled, should converge to a universal random field that is independent of the specific model
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**A**: Thus, in (2.6) there is a pair of primed spinor indices coming from the projection of the 2-form onto its ASD part, as well as the primed spinor indices that are labels of the different summands in F𝐹Fitalic_F. It is assumed that all the primed spinor indices are symmetrized in (2.6). Let us write down the first few equations contained in (2.6) explicitly. Thus,**B**:
(By convention the primed indices cannot be mixed with the unprimed ones. This has the effect that their relative positions are irrelevant**C**: For example, it does not matter whether or not the parenthesis denoting the symmetrization encompass a single primed index). The second terms is the ASD part of the 2-form B𝐵Bitalic_B
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ACB
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ACB
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ACB
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CAB
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Selection 4
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**A**:
Phenomenological and experimental implications of the GUP have been investigated in low and high-energy regimes**B**: These include atomic systems [9, 10], quantum optical systems [11], gravitational bar detectors [12], gravitational decoherence [13, 14], composite particles [15], astrophysical systems [16], condensed matter systems [17], and macroscopic harmonic oscillators [18]**C**: Reviews of the GUP, its phenomenology, and its experimental implications can be found in Refs. [19, 20].
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ACB
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ABC
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BCA
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BAC
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Selection 2
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**A**:
The high-precision measurement of parameters with midband detectors requires more accurate GW waveform modeling. Otherwise, systematic errors can significantly contaminate the parameter estimations of GW signals**B**: In Ref. Favata:2013rwa , the author showed that the quasicircular waveform model becomes inaccurate for eccentric mergers with e∼10−3similar-to𝑒superscript103e\sim 10^{-3}italic_e ∼ 10 start_POSTSUPERSCRIPT - 3 end_POSTSUPERSCRIPT at f=10Hz𝑓10Hzf=10~{}\text{Hz}italic_f = 10 Hz in the case of neutron star binary merger. It has been also noted that extending the low-frequency limit results in observing more GW cycles, consequently amplifying the systematic errors Favata:2021vhw . Therefore, we expect that the issue of systematic errors will be more pronounced in the midband detectors.**C**: Specifically, we test the accuracy of estimated parameters assuming the quasicircular waveform model for the eccentric merger of BBHs. This issue has been examined in the context of ground-based detectors Martel:1999tm ; Favata:2013rwa ; Favata:2021vhw ; Cho:2022cdy
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ACB
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BAC
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BAC
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BAC
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Selection 1
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**A**: The sign for l=0𝑙0l=0italic_l = 0 changes beyond
the BAO scale of ∼105h−1Mpcsimilar-toabsent105superscriptℎ1Mpc\sim 105\,h^{-1}\mathrm{Mpc}∼ 105 italic_h start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT roman_Mpc**B**: ξX22;4>0subscriptsuperscript𝜉224𝑋0\xi^{22;4}_{X}>0italic_ξ start_POSTSUPERSCRIPT 22 ; 4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_X end_POSTSUBSCRIPT > 0 in this example**C**:
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ACB
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BAC
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CAB
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ACB
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Selection 2
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**A**: Although in topic (2), i.e., in the non-restricted KSh-conjecture, the deformations come to the foreground, they still did not draw as much attention as I think they should have, except for the filtered deformations**B**: (A plausible, very probable, reason for this negligence: of the two types of simple Lie algebras, the non-filtered deforms — results of deformations — of the vectorial Lie algebras are isomorphic to the known simple Lie algebras, whereas the Lie algebras of the other type — the ones with Cartan matrix and their simple relatives — are rigid, at least for p>3𝑝3p>3italic_p > 3**C**: The situation is totally different if p=2𝑝2p=2italic_p = 2, see Shchepochkina’s exceptional example — the deform of the divergence-free algebra — in [BGLLS].)
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ABC
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BCA
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BAC
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BAC
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Selection 1
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**A**: Since the branches beyond the maximum of the mass have a lower binding energy (dotted curve in the inset), they are unstable.**B**: This suggests a change of stability**C**: In addition, we can see a cusp at the maximum
of the mass for both the scalarized and nonscalarized NSs
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CBA
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ABC
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CAB
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BCA
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Selection 1
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**A**: We are unable to probe on the narrow 689-nm transition because the high bending losses in our current setup prevent us from sending the light through the nanofiber. Thus, instead, we employ an external 689-nm shelving beam to characterize and measure the novel magic wavelength [see Fig. 2(b)]. In all experiments, to ensure spin-resolved spectroscopy, the quadrupole B-field is kept on for the duration of the experimental cycle and contributes a ≈\approx≈200 mG magnetic field in the vertical direction at the atoms.
**B**: Our experimental cycle starts by generating an ultracold MOT cloud of 8888{}^{88}start_FLOATSUPERSCRIPT 88 end_FLOATSUPERSCRIPTSr atoms, which we overlap with the waist region of the fiber, which is 5 mm long. This ultracold atomic cloud has a free-space optical depth (OD) of 3.5 and reaches temperatures of ≈\approx≈1 μ𝜇\muitalic_μK after MOT-cooling on the 689-nm transition [62, 63]**C**: The fiber-guided trapping fields are then switched on with the MOT present for 35 ms to load the trap with cooled atoms before the MOT beams are switched off. The trapped atoms are ultimately probed by measuring absorption on the strong 461-nm dipole transition through the fiber [see Fig. 2(a-b)]
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BCA
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ABC
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ABC
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CAB
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Selection 4
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**A**: L.M.: conceptualization, investigation, methodology, administration, resources, writing, review and editing. All authors give approval for publication.
**B**: A.H.: methodology, visualization, review and editing. A.G.: investigation, methodology, writing, review and editing**C**: A.R.: investigation, simulation, methodology, visualization, writing, review and editing. D.G.: simulation, visualization, writing
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BCA
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CAB
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CBA
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BCA
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Selection 3
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**A**: (Integrability of imaginary geometry coupled with LQG.) The aforementioned integrability of quantum triangles, and the welding results in this paper, and the mating of trees theory [DMS21] can together be used to study the integrablity of imaginary geometry coupled with LQG. For example, a class of permutons (i.e**B**: In a subsequent work we will derive an exact expression for this quantity. See [BGS22] for other applications of SLE/LQG to permutons.
**C**: scaling limit of permutation) called the skew Brownian permutons were recently introduced in [Bor21], with the Baxter permuton [BM22] as a special case. As shown in [BHSY22, Proposition 1.14], the expected portion of inversions for these permutons is related to a natural quantity in imaginary geometry coupled with LQG
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ACB
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ABC
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BCA
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CBA
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Selection 1
|
**A**: Furthermore, the number of measured outputs can be optimised to only record significantly uncorrelated outputs for each node. Optimisation of PNN architecture, and inter-node connectivity (i.e. combining multiple output channels as input to a particular node) will allow further improvements.**B**: This can be achieved by increasing the number of unique physical reservoirs thereby increasing the range of beneficial reservoir dynamics that each node has**C**:
Realising a device level PNN requires a reduction in the number of nodes and the number of measured outputs without sacrificing computational performance
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BAC
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ABC
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ACB
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CBA
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Selection 4
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**A**: The authors thank the Megamaser Cosmology Project researchers for making the observational data used in this work publicly available and CONACYT for support under grant No. CF-MG-2558591. A.G.-J**B**: A.V.-R acknowledges financial assistance from CONACYT through grant No. 1007718.
A.H.-A. was supported by VIEP-BUAP as well as by SNII.**C**: and M.M. thank SNII and were supported by CONACYT through the postdoctoral grants Nos. 446473 and 31155, respectively
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ABC
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ABC
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ACB
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BAC
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Selection 3
|
**A**: It trivially obeys Onsager reciprocal relations. However, the CM momentum density does affect the reactive part of the dynamics of the angular momentum density**B**: This, by itself is a manifestation of non-reciprocity.
Indeed, when writing the reactive part of the dynamics of the hydrodynamic momentum density, which includes both CM linear momentum density and SAM density, odd viscosity appears together with an odd pressure and two other terms that couple vorticity to shears involving the direction of ℓbold-ℓ{\bm{\ell}}bold_ℓ. We, therefore, conclude that the mere existence of a non-vanishing SAM density breaks Onsager reciprocal relations and gives rise to odd viscosity.**C**: In this paper we directly coarse-grain the kinetic energy which results in somewhat different results. The reactive part of the CM stress tensor does not contain any trace of the SAM density and therefore has no odd viscosity
|
BCA
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CBA
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ACB
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ABC
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Selection 1
|
**A**: For long-time physics, this point of view is expected equivalent to the p-spin dynamics with sharp spherical or hard spins constraints Dominicsbook ; Leticia1 ; Kristima ; Kristina1 ; Nishimori ; Cugliandolo1 ; Cugliandolo2 ; Cugliandolo3 , provided that the minimum of the potential is non-degenerate, that we consider in our work. Furthermore, as pointed out in Annibale ,**B**:
Besides the bibliographic line of the authors, this work finds a place in the general context of the dynamics of glassy systems**C**: It has been considered in Kristima for the quartic version, and for instance in Guionnet ; Sompolinsky1 ; Sompolinsky2 ; Kurchan
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BCA
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BAC
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CAB
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BAC
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Selection 3
|
**A**: We believe it is plausible that the SSLW approach to gated reactions has not been widely applied in subsequent literature because it takes a very general form that appears to be more difficult to apply than it actually is**B**: However, it can be appreciated that the more specialized relation in Eq**C**: (14) only requires plugging in the underlying spatial propagator of the specific problem at hand, and perhaps some algebraic simplifications. To demonstrate the strength of this “plug and play” result, we briefly consider the two examples below.
|
ABC
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ACB
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CAB
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ACB
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Selection 1
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**A**: It should however be kept in mind that the algorithms \acssiqwc and \acssifc will generally produce different groupings of**B**: The qubit-wise commutativity of two terms implies that the terms commute fully, although the converse is not true**C**: In that sense, \acqwc can be said to form
a subset of \acfc
|
CBA
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BCA
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CBA
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CAB
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Selection 4
|
**A**: However, in practice, a PCA basis may poorly represent the real-world continuum distribution, potentially yielding extremely poor performance for spectra outside the PCA space. To quantitatively assess each method’s robustness, we apply minor linear perturbations to the simulated quasar continua. More specifically, we assume a linear perturbation:**B**: (2011) is constructed based on a limited number of (78787878, SNR≳10greater-than-or-equivalent-toabsent10\gtrsim 10≳ 10) quasar spectra**C**:
As mentioned in Section 1, the PCA basis from Pâris et al
|
ACB
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ABC
|
CAB
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CBA
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Selection 4
|
**A**: Consequently, metallic nanostructures often lead to a decrease in the efficiency in the case of phosphor layers for instance[10]. This quenching, detrimental to the IQY, has to be avoided as much as possible for applications. However we underline that there is no universal rule for the optimal distance between the emitter and the MNP[11].**B**: The Internal Quantum Yield (IQY)
is increased in that case. However, an emitter located too close to a single MNP may excite resonances which do not radiate efficiently and light is then absorbed**C**: First, in the vicinity of the nanoparticles, the density of photonic states is much higher, which means an emitter is more likely to emit light if it can couple to a nanoparticle resonance[9]. This spontaneous emission enhancement, also called Purcell effect, is characterized by a shortening of the luminescent emitter’s lifetime
|
CBA
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CAB
|
ABC
|
ABC
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Selection 1
|
**A**: Vannitsem et al. [11] highlight the crucial role of statistical post-processing techniques, including ML methods, in national meteorological services. They discuss theoretical developments and operational applications, current challenges, and potential future directions, particularly focusing on translating research findings into operational practices.**B**: Haupt et al. [10] provides an overview of using ML methods for post-processing of numerical weather predictions**C**: The National Centers for Environmental Prediction (NCEP), part of the National Oceanic and Atmospheric Administration (NOAA), currently issues a “week 3-4 outlook” for the contiguous United States (CONUS).111https://www.cpc.ncep.noaa.gov/products/predictions/WK34/
The NCEP outlooks are constructed using a combination of dynamical and statistical forecasts, with statistical forecasts based largely on how conditions in the past have varied (linearly) with indices of the El Niño-Southern Oscillation (ENSO), Madden-Julian Oscillation (MJO), and global warming (i.e., the 30-year trend). There exists great potential to advance subseasonal forecasting (SSF) using machine learning (ML) techniques
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BCA
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CBA
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ABC
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CAB
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Selection 2
|
**A**: The GitHub dataset is from 1/1/2015 to 8/30/2017 including 2 million users and 13 million projects. We selected the 100 most popular repositories because we aimed to characterize top GitHub repositories, and the impact of influencers on the popularity of repositories using the TTERGM model. The number of repositories is a hyperparameter which can be adjusted, depending on the goal of the model**B**: The API can be used to stream GitHub repository interactions with customized formats. Optionally, meta data from user relation events can be retrieved as well. The dataset contains 14 types of events which are listed in Table 1.
**C**: We selected the top 10 users, in terms of number of followers, as the influencers in this study. This threshold was chosen because the number of followers drops off sharply after that point, but can be chosen arbitrarily for different datasets. The data was acquired using the API from GitHub [Gousios and Spinellis, 2012]
|
CBA
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BCA
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BAC
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ACB
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Selection 4
|
**A**: (2003); Stovall et al. (2018); Gou et al. (2011); McClintock et al. (2011); Fabian et al. (2012); The LIGO Scientific Collaboration et al. (2021), and are described in detail in the following paragraphs.**B**: Fig. 2 shows the placement of the templates of the O4 template bank, which stores a total of ∼1.8×106similar-toabsent1.8superscript106\sim 1.8\times 10^{6}∼ 1.8 × 10 start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT templates.
The intrinsic parameter ranges chosen for the O4 template bank are motivated by observations and the GW detectors’ sensitivity Abbott et al. (2020); Legred et al. (2021); Dietrich et al**C**: (2020); Jiang et al. (2020); Abbott et al. (2018); Cromartie et al. (2019); Kalogera and Baym (1996); Kramer and Wex (2009); Burgay et al
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ABC
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BCA
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CAB
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CBA
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Selection 3
|
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