context stringlengths 100 10.3k | A stringlengths 100 7.26k | B stringlengths 100 5.61k | C stringlengths 100 10.3k | D stringlengths 100 3.93k | label stringclasses 4
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Thus, the planet radius or envelope thickness is reduced by the factor (1−Z)1𝑍(1-Z)( 1 - italic_Z ). (Stevenson, 2017) also shows that Rpsubscript𝑅𝑝R_{p}italic_R start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT remains essentially unchanged if this much Z𝑍Zitalic_Z heavier elements all concentrate into a core. So Rps... | Hydrogen (H and H2) is thereby inferred as the dominant species in the upper atmosphere of many of the close-in exoplanets, due to (1) the availability/abundance of hydrogen and (2) its lightest weight and thus its largest scale height compared to the other atmospheric species. In any atmosphere above a certain critica... | Nebular gas disks typically remove on the 5-10 million years timescale (Armitage, 2010; Hartmann, 2008). On the other hand, the noble gas abundances sourced from the Earth’s deep mantle suggest an early existence of a massive H2-He proto-atmosphere/envelope of the order of ≳103greater-than-or-equivalent-toabsentsupersc... | In order for significant in-gassing to occur over a limited time duration of planet formation, it requires enough pressure built up at the interface between the molten magma ocean and the overlaying gaseous layer. To the first order approximation, the in-gassing rate is proportional to the number density of gaseous spe... | Thus, the overall noble gas abundances of the light versus the heavy noble gas species paint a general two-stage picture of Earth formation: First, a co-accretion of a massive H2-He proto-atmosphere/envelope with the proto-Earth, and Second, the subsequent removal and replacement of such proto-atmosphere/envelope. Like... | B |
The Hamiltonian we wish to in this section is Eq. 4 with t𝐛1=tsubscript𝑡subscript𝐛1𝑡t_{{\bf b}_{1}}=titalic_t start_POSTSUBSCRIPT bold_b start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT = italic_t, t𝐛2=t′subscript𝑡subscript𝐛2superscript𝑡′t_{{\bf b}_{2}}=t^{\prime}italic_t start_POSTSUBSCRIPT bold_b sta... | In this section, we present pair properties obtained from numerical solution of Eq. (4). We study square, quasi-2D tetragonal, 3D simple cubic (SC), and 3D body-centered cubic (BCC) lattices. Study of the tetragonal lattice is inspired by superconductivity in the cuprates while the BCC is inspired by superconductivity ... | In this section, we examine the effects of NNN hopping on real-space pairs in a square UV𝑈𝑉UVitalic_U italic_V model with NN attraction. The model serves as a good illustration of the physical ideas explored in this paper and is inspired by the unconventional superconductivity in the underdoped cuprates. Two-dimensi... | There are several physical mechanisms that can lead to light pairs. In some lattices, the pairs remain light for purely geometric reasons. Consider a triangular lattice with a strong NN attraction V𝑉Vitalic_V, Fig. 1(A). The pair members can hop in turn without ever breaking the attractive bond. The pair mass is limit... | The physical effects discussed below also occur in other lattices with NNN hopping, including the 1D chain and 3D simple cubic lattice. The square UV𝑈𝑉UVitalic_U italic_V model serves as a convenient proxy for all hyper-cubic UV𝑈𝑉UVitalic_U italic_V models. The non-interacting (one particle) dispersion of Eq. (4)... | D |
If PBHs exist, they should be present within our Milky Way galaxy (Chapline, 1975b) and observable via gravitational microlensing signals from local stars (e.g., Chapline & Frampton, 2016). Microlensing is the effect when a foreground object (the lens) passes in front of a luminous background object (the source), relat... | Microlensing imparts a characteristic photometric signal on the measured light curves of lensed stars, which can be used to detect and characterize foreground objects irrespective of their luminosity, or whether they are gravitationally bound to a companion. Unlike other probes, such as gravitational waves or X\hypray ... | In addition to photometric measurements, one can obtain astrometric measurements for microlensing events using the location and movement of stars. In the absence of lensing and parallax a source star would appear to make a straight line on the sky over most observable timescales, however, in the presence of lensing, th... | If PBHs exist, they should be present within our Milky Way galaxy (Chapline, 1975b) and observable via gravitational microlensing signals from local stars (e.g., Chapline & Frampton, 2016). Microlensing is the effect when a foreground object (the lens) passes in front of a luminous background object (the source), relat... | Approximately 85% of the matter in our universe is composed of dark matter, which is not well\hypunderstood. Dark matter cannot be observed via electromagnetic mechanisms (hence “dark”) and is only observable through gravitational interactions, making it challenging to detect. Primordial black holes (PBHs), hypothesize... | A |
Finally, we will discuss the astrophysical processes that can lead to the production of such an object. We will consider the mechanism based on progenitors having a mass in the range (8−10)M⊙810subscript𝑀direct-product(8-10)M_{\odot}( 8 - 10 ) italic_M start_POSTSUBSCRIPT ⊙ end_POSTSUBSCRIPT (Suwa et al., 2018) and w... | The analysis of the central compact object within the supernova (SN) remnant HESS J1731-347 suggests that it has a small radius and, even more interestingly, a mass of the order or smaller than one solar mass (Doroshenko et al., 2022). This raises the question of which astrophysical process could lead to such a small m... | In order to understand why QSs can be produced with a mass of the order or smaller than one solar mass, it is useful to recall that the total binding energy (BE) of compact stars is the sum of the gravitational BE and the nuclear BE, the latter being related to the microphysics of the interactions as discussed in the s... | We have shown that QSs can explain the existence of compact stars having very small or very large masses. On the other hand, it is unlikely that all compact stars are QSs: it is well known that magnetar oscillations pose challenges to QSs (Watts & Reddy, 2007). Also, the analysis of the energy released by the SN1987a i... | Concerning the first point, the density of DM in the galactic bulge can easily be 1-2 orders of magnitude larger than in the area where the Sun is located (Nesti & Salucci, 2013; Salucci, 2019), and this can be a relevant factor, as we already suggested in the case of accretion-induced collapse of strange dwarfs (Di Cl... | B |
\prime}))\phi_{b}(X)\phi_{b}(Y)(\int d^{d-1}zf(z)\phi_{b}(z))}_{\ket{\Omega}}.⟨ start_ARG italic_ϕ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_X ) italic_ϕ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_Y ) end_ARG ⟩ start_POSTSUBSCRIPT 1-particle state end_POSTSUBSCRIPT = ⟨ start_ARG ( ∫ italic_d ... | The normalized time-ordered correlation functions become singular in the limit where two of the points coincide and the corresponding singularity behaves like an OPE of primary fields in a CFT [42]. The ADS/CFT correspondence postulates that for any theory of quantum gravity, the normalized time-ordered correlations on... | As one can see from the above equation, such two-point functions can be reduced to higher-order correlation functions. However, when the two-point functions are delta functions, the correlation functions factorize and can be calculated using Wick’s theorem. For example, for the above correlation function we have | where 𝒯𝒯\mathcal{T}caligraphic_T is the time ordering operator and ∼similar-to\sim∼ is equality up to analytic terms. Note that we have assumed that ϕitalic-ϕ\phiitalic_ϕ is canonically normalized which means the kinetic terms of ϕitalic-ϕ\phiitalic_ϕ in the effective action takes the form −12(∂μϕ)212superscriptsubs... | Let us point out that the boundary correlators could be different if they are evaluated for a non-vacuum state in the bulk. In dS/CFT this corresponds to having some operator insertions at the past boundary, which can be expressed as operator insertions at the antipodal point in the future boundary. On the other hand, ... | B |
We consider a free complex massive scalar field, ϕitalic-ϕ\phiitalic_ϕ, of mass m𝑚mitalic_m the dynamics of which is described by the modified Klein-Gordon equation f(□+μ2)ϕ=0𝑓□superscript𝜇2italic-ϕ0f(\Box+\mu^{2})\phi=0italic_f ( □ + italic_μ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) italic_ϕ = 0. Here f𝑓fit... | We now analyze the implications of our results on a specific class of non-local modifications of quantum mechanics belen16 ; belen17 . These modifications are consistent with the low-energy predictions of non-local effective field theories arising in different approaches to quantum gravity. Examples are found in the co... | Similar nonlocal evolution equations are found in different quantum-gravity models. For example, in four dimensions string field theory predicts a nonlocal KG equation of the form sft | In conclusion, we demonstrated that for a wide class of modifications of quantum mechanics as, for instance, those expected as consequences of quantum gravitational effects, the quantum speed limit is increased. We derived generalized expressions for the Mandelstam-Tamm, the Margolus-Levitin and Cramér-Rao bounds and d... | On the other hand, these systems represent a natural platform to test fields on black-hole spacetime obeying modified quantum laws. At difference with quantum gravitational ultraviolet corrections to real black holes, the way in which such corrections emerge from the microscopic theory in analogue-models is reasonably ... | B |
S}^{(ijk)}\big{)}roman_Γ start_POSTSUBSCRIPT 1,2 end_POSTSUBSCRIPT = ∑ start_POSTSUBSCRIPT italic_i < italic_j : ↓ , italic_k : ↑ end_POSTSUBSCRIPT roman_Φ ( caligraphic_S start_POSTSUPERSCRIPT ( italic_i italic_j italic_k ) end_POSTSUPERSCRIPT ) the contribution from ↑↓↓↑↓↓\uparrow\downarrow\downarrow↑ ↓ ↓ triplets. | By antisymmetry, each ↑↑↓↑↑↓\uparrow\uparrow\downarrow↑ ↑ ↓ triplet gives the same contribution, so that | from triplets of particles of spins ↑↑↓↑↑↓\uparrow\uparrow\downarrow↑ ↑ ↓ (resp. ↑↓↓↑↓↓\uparrow\downarrow\downarrow↑ ↓ ↓), | coming from ↑↑↓↑↑↓\uparrow\uparrow\downarrow↑ ↑ ↓ and ↑↓↓↑↓↓\uparrow\downarrow\downarrow↑ ↓ ↓ spin configurations: | We find that the ↑↑↓↑↑↓\uparrow\uparrow\downarrow↑ ↑ ↓ and ↑↓↓↑↓↓\uparrow\downarrow\downarrow↑ ↓ ↓ three-body loss-rates are given by | A |
In Superconformal Quantum Field Theories (SQFTs), that emerge from the geometrical engineering with toric CY cone, we can consider the so-called orientifold projections Dudas:2006bj ; Bianchi:1990yu ; Sagnotti:1987tw that are reviewed in Paragraph 2.2. The action in the string theory side is to make open oriented stri... | Orientifold projections give the opportunity of new possibilities to the creation of field theory models from string background called unoriented models Dudas:2006bj . The appellation "unoriented" is mainly due to the action of the orientifold map on the string oscillators: the involution makes oriented string unorient... | Let us indicate orientifold with ΩΩ\Omegaroman_Ω, therefore quantities after orientifold projection will be labelled with the apex ΩΩ\Omegaroman_Ω. The theory before orientifold is often referred to as the "parent", "oriented", "pre-orientifold" or "unorientifolded" theory while the one after orientifold as "daughter",... | The scenario I orientifold occurs when the pre and post orientifold R𝑅Ritalic_R-charges of the theories are the same and the central charge post orientifold is half of that pre orientifold: | In the scenario III orientifold the pre and post orientifold R𝑅Ritalic_R-charges of theory are not the same and the post orientifold central charge is less than half of that pre orientifold 2020in ,2022su : | B |
\omega\,\,\cfrac{d^{3}\vec{k}}{(2\pi)^{3}\,2\omega}.continued-fraction start_ARG italic_κ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG start_ARG 4 end_ARG ∑ start_POSTSUBSCRIPT italic_ω start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT end_POSTSUBSCRIPT ∑ start_POSTSUBSCR... | The modulus squared piece of the integrand in Eq. (11) can be simplified using the polarisation sum relation, see Eq. (5), as follows: | The series sum over products of Bessel functions and their derivative, weighted by powers of n𝑛nitalic_n, can be expressed completely as functions of e𝑒eitalic_e, using the identities derived in the appendix of [85] and reproduced in Eq. (123). This enables the identification of the eccentricity dependent part of the... | The sum over n𝑛nitalic_n can be evaluated, using the identities given in Eq. (123), to obtain the coefficients Ci(e)subscript𝐶𝑖𝑒C_{i}(e)italic_C start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( italic_e ), i=0,2,4𝑖024i=0,2,4italic_i = 0 , 2 , 4: | Finally, using the result of Eq. (16), the expression for the energy radiated by a source in terms of the source stress-tensor can be obtained as a modification of Eq. (11) as | A |
\,(g_{\mu\sigma}g_{\nu\lambda}-g_{\mu\lambda}g_{\nu\sigma})=0.italic_A start_POSTSUBSCRIPT italic_μ italic_ν italic_σ italic_λ end_POSTSUBSCRIPT = italic_R start_POSTSUBSCRIPT italic_μ italic_ν italic_σ italic_λ end_POSTSUBSCRIPT + divide start_ARG 1 end_ARG start_ARG italic_l start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIP... | The above conditions along with g(0)abgab(1)=0superscriptsubscript𝑔0𝑎𝑏subscriptsuperscript𝑔1𝑎𝑏0g_{(0)}^{ab}\,g^{(1)}_{ab}=0italic_g start_POSTSUBSCRIPT ( 0 ) end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_a italic_b end_POSTSUPERSCRIPT italic_g start_POSTSUPERSCRIPT ( 1 ) end_POSTSUPERSCRIPT start_POSTSUBSCRIP... | To obtain chiral ΛΛ\Lambdaroman_Λ-𝔟𝔪𝔰4𝔟𝔪subscript𝔰4\mathfrak{bms}_{4}fraktur_b fraktur_m fraktur_s start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT algebra from AdS4 gravity, we will analyse the asymptotic symmetries of locally AdS4 geometries (lAdS4). We work in Newman-Unti (NU) gauge with the coordinates (u,r,z,z¯)𝑢�... | Equation (14) implies equation of motion (13). These lAdS4 solutions share the same boundary conditions with solutions to asymptotically locally AdS4 condition given by , | The boundary conditions that we employ in this paper form a subset of Neumann boundary conditions Compere:2008us . We consider locally AdS4 solutions for which the components associated with the holographic stress tensor go to zero and the boundary metric is conformally flat Skenderis:1999nb .333The necessary and suffi... | C |
Asymmetric reheating alleviates this, but known schemes generally require a broken ℤ2subscriptℤ2\mathbb{Z}_{2}blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT in the late universe [Foot:2000tp, Berezhiani:2000gw, Ignatiev:2000yy, Berezhiani:2003xm, Barbieri:2005ri, Barbieri:2016zxn, Craig:2016lyx, Chacko:2016hvu, C... | Asymmetric reheating alleviates this, but known schemes generally require a broken ℤ2subscriptℤ2\mathbb{Z}_{2}blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT in the late universe [Foot:2000tp, Berezhiani:2000gw, Ignatiev:2000yy, Berezhiani:2003xm, Barbieri:2005ri, Barbieri:2016zxn, Craig:2016lyx, Chacko:2016hvu, C... | Perhaps no theories have been more affected than the storied mirror models, which introduce a ℤ2subscriptℤ2\mathbb{Z}_{2}blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT-symmetric copy of the Standard Model (SM) fields and gauge groups [Lee:1956qn, Kobzarev:1966qya, Pavsic:1974rq, Blinnikov:1982eh, Foot:1991bp, Foo... | This includes the familiar phenomena of SM neutrinos [Foot:1993yp, Foot:1995pa, Berezhiani:1995yi, Silagadze:1995tr, Foot:1997jf, Collie:1998ty, Foot:1999ph, Blinnikov:1999ky] or photons [Foot:2000vy, Foot:2000aj, Foot:2002iy, Badertscher:2003rk, Berezhiani:2005ek, Berezhiani:2008gi, Foot:2012ai, Chacko:2019jgi, Curtin... | In particular, oscillations between neutrons and mirror neutrons have seen much study in light of neutron lifetime anomalies [Mohapatra:2005ng, Mohapatra:2017lqw, Babu:2021mjg, Berezhiani:2005hv, Berezhiani:2006je, Serebrov:2007gw, Sandin:2008db, Serebrov:2008her, Berezhiani:2009ldq, Berezhiani:2011da, Berezhiani:2012r... | C |
This result is implied by a stronger result on the (spatially) local dependence of the coupling constants on the renormalisation group flow. | Let τ∈𝔻h𝔱𝜏subscript𝔻subscriptℎ𝔱\tau\in\mathbb{D}_{h_{\mathfrak{t}}}italic_τ ∈ blackboard_D start_POSTSUBSCRIPT italic_h start_POSTSUBSCRIPT fraktur_t end_POSTSUBSCRIPT end_POSTSUBSCRIPT and β>0𝛽0\beta>0italic_β > 0 be sufficiently large and | Let τ∈𝔻h𝔱𝜏subscript𝔻subscriptℎ𝔱\tau\in\mathbb{D}_{h_{\mathfrak{t}}}italic_τ ∈ blackboard_D start_POSTSUBSCRIPT italic_h start_POSTSUBSCRIPT fraktur_t end_POSTSUBSCRIPT end_POSTSUBSCRIPT and β>0𝛽0\beta>0italic_β > 0 be sufficiently large. | To see this, let N′>Nsuperscript𝑁′𝑁N^{\prime}>Nitalic_N start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT > italic_N be sufficiently large and | Let L𝐿Litalic_L be sufficiently large and N⩾j0y+2𝑁subscript𝑗0𝑦2N\geqslant j_{0y}+2italic_N ⩾ italic_j start_POSTSUBSCRIPT 0 italic_y end_POSTSUBSCRIPT + 2. | C |
The observation of bi-stability and the single superconducting qubit coupling to the Kittel mode are interesting developments in this field [23, 24]. Li et al. illustrated how to create tripartite entanglement in a system of microwave cavity photons entangled to the magnon and phonon modes of a YIG sphere in a magnomec... | It was followed by a study of entanglement transfer from the inter-cavity photon-photon entanglement to an intracavity photon-phonon via two macroscopic mechanical resonators [36]. | This study was followed by an investigation of magnon-magnon entanglement between two YIG spheres in cavity magnomechanics [26]. | Later, Wu et al. investigated magnon-magnon entanglement between two YIG spheres in cavity optomagnonics [27]. | In an interesting study, Joshi et al. theoretically examined whether two spatially distant cavities connected by an optical fiber may produce quantum entanglement between mechanical and optical modes [32]. | B |
It is more difficult to propose possible scenario for FM component to phase transition, which remains fixed at T≈125𝑇125T\approx 125italic_T ≈ 125 K, almost unaffected by Ni doping. While we expect that some FM clusters may exist in our crystals, similar to situation observed in x=0𝑥0x=0italic_x = 0 experiments [34],... | Based on the above analysis we conclude that the main origin of the anomalies observed in magnetization is the incoherent-coherent transition, which increases the density of itinerant carriers at low T𝑇Titalic_T, leading to change of M𝑀Mitalic_M with temperature, and to short-range magnetic order. | The correlation between ΔMΔ𝑀\Delta Mroman_Δ italic_M and RHsubscript𝑅𝐻R_{H}italic_R start_POSTSUBSCRIPT italic_H end_POSTSUBSCRIPT supports the idea that the positive ΔMΔ𝑀\Delta Mroman_Δ italic_M observed in samples with small y𝑦yitalic_y, i.e. with hole-dominated transport, is a result of delocalization of carr... | Since magnetic correlations are known to persist in this system, it is natural to consider magnetic phase transition as the origin of the peak feature. While long-range magnetic order is expected to be absent in our crystals, low-T𝑇Titalic_T short-range ordering has been documented at low x𝑥xitalic_x [35, 36]. Enhanc... | While there is a broad agreement that the electron-phonon coupling cannot account for superconducting (SC) transition temperatures (Tcsubscript𝑇𝑐T_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT’s) in iron-based superconductors (IBS), the nature of the normal state, and it’s implications for superconductiv... | A |
Non-Markovian dynamics: the third-order term breaks the Markov property, leading to non-Markovian dynamics. | The classical FPE represents a second-order approximation derived from the Kramer-Moyal expansion using the Pawula theorem [4]. However, as indicated by [4], higher-order terms, specifically those with n≥3𝑛3n\geq 3italic_n ≥ 3, can influence the PDF. Consequently, in certain scenarios, it is necessary to retain these ... | Utilizing the infinite-order kinetic equation in real-world scenarios presents a formidable challenge. To date, our knowledge about this matter is restricted, and it is recommended from a practical standpoint that the terms of drift and diffusion should be maintained when applying the equation. Although this approximat... | Including third-order and higher terms significantly broadens the range of phenomena that can be described by the truncated kinetic equation, enabling it to model more complex stochastic systems. However, if third-order and higher terms are considered, it will also lead to significant difficulties, including computatio... | The kinetic equation formulated in this paper is of infinite order in its partial derivatives. A fundamental question arises concerning the number of terms that should be retained for practical applications. Determining where to truncate the infinite series of the kinetic equation has been an ongoing challenge yet to b... | C |
For each of the six subjects, both the first (scan) and second (rescan) scan images were registered to the first scan images of Subject 1 using inbuilt MATLAB (Mathworks, Version 2022a) functions (𝚒𝚖𝚛𝚎𝚐𝚝𝚏𝚘𝚛𝚖𝚒𝚖𝚛𝚎𝚐𝚝𝚏𝚘𝚛𝚖\verb'imregtform'typewriter_imregtform and 𝚒𝚖𝚠𝚊𝚛𝚙𝚒𝚖𝚠𝚊𝚛𝚙\verb'imwarp'typ... | For each voxel, the ICC measure was applied to assess scan-rescan reproducibility of mean kurtosis, as described by Duval et al. (Duval et al., 2017) and Fan et al. (Fan et al., 2021), | Less than 4 min 4 min 4\text{ min\,}4 min DW-MRI data acquisitions can potentially replace existing data acquisitions used to obtained DTI metrics, since even the estimation of the apparent diffusion coefficient improves by using DW-MRI data relevant to DKI (Veraart et al., 2011b; Wu and Cheung, 2010). Additionally, i... | DW-MRI allows the measurement of mean kurtosis, a metric for the deviation away from standard Brownian motion of water in tissue, which has been used to infer variations in tissue microstructure. Research on mean kurtosis has shown benefits in specific applications over other diffusion related measures derived from DW-... | Recent clinical benefits of using kurtosis metrics over other DW-MRI derived measures have been demonstrated for grading hepatocellular carcinoma (Li et al., 2022b), prognosing chronic kidney disease (Liu et al., 2021), differentiating parotid gland tumours (Huang et al., 2021a), measuring response to radiotherapy trea... | A |
σ=1N−1∑i=1N(xi−x¯)2𝜎1𝑁1superscriptsubscript𝑖1𝑁superscriptsubscript𝑥𝑖¯𝑥2\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_{i}-\overline{x})^{2}}italic_σ = square-root start_ARG divide start_ARG 1 end_ARG start_ARG italic_N - 1 end_ARG ∑ start_POSTSUBSCRIPT italic_i = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N e... | measurement is usually expressed as a¯z±σ(az¯)plus-or-minussubscript¯𝑎𝑧𝜎¯subscript𝑎𝑧\overline{a}_{z}\pm\sigma(\bar{a_{z}})over¯ start_ARG italic_a end_ARG start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT ± italic_σ ( over¯ start_ARG italic_a start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT end_ARG ) representing the ... | σ(az¯)=σaz/N𝜎¯subscript𝑎𝑧subscript𝜎subscript𝑎𝑧𝑁\sigma(\bar{a_{z}})=\sigma_{a_{z}}/\sqrt{N}italic_σ ( over¯ start_ARG italic_a start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT end_ARG ) = italic_σ start_POSTSUBSCRIPT italic_a start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT end_POSTSUBSCRIPT / square-root start_ARG ... | σ(az¯)𝜎¯subscript𝑎𝑧\sigma(\bar{a_{z}})italic_σ ( over¯ start_ARG italic_a start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT end_ARG ) is proportional to N−1/2superscript𝑁12N^{-1/2}italic_N start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT. According to our | resolution of the digital instrument: σ(az¯)=σaz/Nopt∼δ𝜎¯subscript𝑎𝑧subscript𝜎subscript𝑎𝑧subscript𝑁𝑜𝑝𝑡similar-to𝛿\sigma(\bar{a_{z}})=\sigma_{a_{z}}/\sqrt{N_{opt}}\sim\deltaitalic_σ ( over¯ start_ARG italic_a start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT end_ARG ) = italic_σ start_POSTSUBSCRIPT italic_a s... | B |
2}}{s-m_{4}^{2}-m_{5}^{2}+\Delta_{4,5}(s)}.italic_μ ( italic_y ) = roman_log | 1 - italic_y | + divide start_ARG italic_y roman_log | italic_y | end_ARG start_ARG 1 - italic_y end_ARG , italic_y start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT = divide start_ARG - 2 italic_m start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT... | As m3→0→subscript𝑚30m_{3}\to 0italic_m start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT → 0 with m1=m4subscript𝑚1subscript𝑚4m_{1}=m_{4}italic_m start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = italic_m start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT | At m3=0subscript𝑚30m_{3}=0italic_m start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT = 0, the three-particle cuts yield logarithms. For w>mj+mk𝑤subscript𝑚𝑗subscript𝑚𝑘w>m_{j}+m_{k}italic_w > italic_m start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT + italic_m start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT, let | with coefficients and arguments in (19,20) that are well behaved at m3=0subscript𝑚30m_{3}=0italic_m start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT = 0. | Next, consider cases with m3>0subscript𝑚30m_{3}>0italic_m start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT > 0 and one of the other masses vanishing. | D |
TrS[σSC]subscriptTr𝑆delimited-[]superscript𝜎𝑆𝐶\displaystyle\mathrm{Tr}_{S}\left[\sigma^{SC}\right]roman_Tr start_POSTSUBSCRIPT italic_S end_POSTSUBSCRIPT [ italic_σ start_POSTSUPERSCRIPT italic_S italic_C end_POSTSUPERSCRIPT ] | =τC.absentsuperscript𝜏𝐶\displaystyle=\tau^{C}.= italic_τ start_POSTSUPERSCRIPT italic_C end_POSTSUPERSCRIPT . | C(σSC)≤C(ρS)+C(τC)𝐶superscript𝜎𝑆𝐶𝐶superscript𝜌𝑆𝐶superscript𝜏𝐶C\left(\sigma^{SC}\right)\leq C\left(\rho^{S}\right)+C\left(\tau^{C}\right)italic_C ( italic_σ start_POSTSUPERSCRIPT italic_S italic_C end_POSTSUPERSCRIPT ) ≤ italic_C ( italic_ρ start_POSTSUPERSCRIPT italic_S end_POSTSUPERSCRIPT ) + italic_C ( ... | and a DIO ΛΛ\Lambdaroman_Λ acting on SC𝑆𝐶SCitalic_S italic_C such that the final state σSC=Λ(ρS⊗τC)superscript𝜎𝑆𝐶Λtensor-productsuperscript𝜌𝑆superscript𝜏𝐶\sigma^{SC}=\Lambda(\rho^{S}\otimes\tau^{C})italic_σ start_POSTSUPERSCRIPT italic_S italic_C end_POSTSUPERSCRIPT = roman_Λ ( italic_ρ start_POSTSUPERSCRIP... | \right)+C\left(\tau^{C}\right).italic_C ( italic_σ start_POSTSUPERSCRIPT italic_S italic_C end_POSTSUPERSCRIPT ) ≥ italic_C ( roman_Tr start_POSTSUBSCRIPT italic_C end_POSTSUBSCRIPT [ italic_σ start_POSTSUPERSCRIPT italic_S italic_C end_POSTSUPERSCRIPT ] ) + italic_C ( italic_τ start_POSTSUPERSCRIPT italic_C end_POSTSU... | A |
In the following, we will discuss the case of theories with Ncsubscript𝑁𝑐N_{c}italic_N start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT odd and Nfsubscript𝑁𝑓N_{f}italic_N start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT generic. | In this paper we provided a proof of Nfsubscript𝑁𝑓N_{f}italic_N start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT-independence by establishing an injective map between massless bound states of theories with different number of flavors. We made use of tensor notation and found that such map can be established only on bou... | In its original formulation, the Persistent Mass Condition asserts that any bound state containing massive constituents must also be massive Preskill and Weinberg (1981). It is however possible to give the following more precise statement that does not make reference to internal constituents of the bound states and rel... | More in detail, one can impose the following restriction on the spectrum of massless bound states (i.e. on the set of possible representations): only states (representations) that can be interpolated by a class-A tensor are assumed to have non-vanishing index. | An important step forward towards a general proof was made by Farrar in Ref. Farrar (1980). She considered the possible existence of exotic massless bound states in the spectrum, i.e. bound states with antiquark constituents, and was able to prove chiral symmetry breaking by assuming ‘Nfsubscript𝑁𝑓N_{f}italic_N start... | B |
{tikzpicture}={tikzpicture}.{tikzpicture}{tikzpicture}\begin{tikzpicture}\hskip 6.0pt=\hskip 6.0pt\begin{tikzpicture}\;.= . | Note that every state ω(m)superscript𝜔𝑚\omega^{(m)}italic_ω start_POSTSUPERSCRIPT ( italic_m ) end_POSTSUPERSCRIPT has dimensions d2D2×d2D2superscript𝑑2superscript𝐷2superscript𝑑2superscript𝐷2d^{2}D^{2}\times d^{2}D^{2}italic_d start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_D start_POSTSUPERSCRIPT 2 end_POST... | with W(l)superscript𝑊𝑙W^{(l)}italic_W start_POSTSUPERSCRIPT ( italic_l ) end_POSTSUPERSCRIPT a completely positive map that maps two (possibly already blocked) spins into one blocked spin, i.e. W(l)superscript𝑊𝑙W^{(l)}italic_W start_POSTSUPERSCRIPT ( italic_l ) end_POSTSUPERSCRIPT maps states on ℂDl−1⊗ℂDl−1tensor-p... | In this case the coarse-graining dimension χ𝜒\chiitalic_χ equals D2superscript𝐷2D^{2}italic_D start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT. | \mathbb{C}}^{\chi}italic_W start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT : blackboard_C start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT ⊗ blackboard_C start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT → blackboard_C start_POSTSUPERSCRIPT italic_χ end_POSTSUPERSCRIPT, which maps two spins of dimension d𝑑ditalic_d into on... | C |
Processing a significant amount of features can be resource-consuming and it remains impossible to exhaustively search the space of solutions at too large sizes. Therefore, the classical method uses a suboptimal shortcut to select relevant features. | where wQ0superscriptsubscript𝑤𝑄0w_{Q}^{0}italic_w start_POSTSUBSCRIPT italic_Q end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT is the best solution returned by a state-of-the-art SA algorithm given a large amount of repetitions (200 000200000200\,000200 000 here). This solution wQ0superscriptsubscript𝑤... | where wisubscript𝑤𝑖w_{i}italic_w start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT is the i𝑖iitalic_i-th binary weight, hi(xs→)∈[−1,1]subscriptℎ𝑖→subscript𝑥𝑠11h_{i}(\vec{x_{s}})\in[-1,1]italic_h start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( over→ start_ARG italic_x start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT ... | In Fig. 8 we also show the mean classification performance of the quantum classifier optimized with the TN and based on boosting (red line). This model being based on the boosting procedure leverages the optimization of QUBOs with negative off-diagonal values which cannot be currently directly optimized on neutral atom... | Finding the optimal weight for each predictor is an exponentially complex optimization problem as the number of predictors increases. Hence, the Random Forest model uses majority voting for classification, which is quite restrictive in terms of performance. | D |
=2(−|A+|2+|B+|2−|A−|2+|B−|2).absent2superscriptsubscript𝐴2superscriptsubscript𝐵2superscriptsubscript𝐴2superscriptsubscript𝐵2\displaystyle=2\left(-|A_{+}|^{2}+|B_{+}|^{2}-|A_{-}|^{2}+|B_{-}|^{2}\right).= 2 ( - | italic_A start_POSTSUBSCRIPT + end_POSTSUBSCRIPT | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + | itali... | Numerical results show that the Jr⊚superscriptsubscript𝐽𝑟⊚J_{r}^{\circledcirc}italic_J start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ⊚ end_POSTSUPERSCRIPT current never gets amplified for scatterings with only one ingoing mode; see Figure 10. This can actually be inferred analytically, thanks a... | as quoted in the main text.) For ω>0𝜔0\omega>0italic_ω > 0, the A+subscript𝐴A_{+}italic_A start_POSTSUBSCRIPT + end_POSTSUBSCRIPT and B+subscript𝐵B_{+}italic_B start_POSTSUBSCRIPT + end_POSTSUBSCRIPT part correspond to positive charges (outgoing and ingoing waves respectively), while the A−subscript𝐴A_{-}italic_A s... | (Since both one positive charge and one negative charge give rise to one particle number, the particle flux averaged over time and an annular region at large r𝑟ritalic_r is given by | Apart from the energy and angular momentum changes during the scattering, an additional quantity we can monitor is the radial charge flux into the Q-ball jrsubscript𝑗𝑟j_{r}italic_j start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT, where jrsubscript𝑗𝑟j_{r}italic_j start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT is the ... | C |
This subsection translates the measurement assignments for the NMQC⊕direct-sum{}_{\oplus}start_FLOATSUBSCRIPT ⊕ end_FLOATSUBSCRIPT model discussed in the paper into realizable computations. This analysis is pertinent because the previous works related to this precise model have discussed these computations at an abstra... | This will enable a more direct comparison with fully classical circuits for Boolean function evaluation, in particular with respect to depth, which is associated with the temporal extension of these circuits. | The proof compares these quantum circuits with the length of the classical Boolean formulas, which describe classical circuits without a memory. The comparison is indeed very strong in the sense that the quantum circuit also does not use any memory (see Figure 1 for a pictorial representation of this subclass of circui... | Although we identified a separation at an abstract level, it almost disappears when these measurement assignments are translated to circuits. The depth of the circuit has an additional term for functions with a degree equal to or greater than three (Lemma 9). This implies that the depth of the resulting circuits is at ... | With the architecture of the circuits defined, it is possible to characterize the relevant properties resulting from specific measurement assignments. In particular, the multi-linear polynomials associated with the measurement assignments completely determine the circuits’ depth, width, and number of gates. | A |
In order to optimize the connection between two distant parties, the number of repeater links is an additional factor to consider and will certainly depend on the parameters of the available quantum hardware. | For repeater setups with multiple repeater links (without entanglement purification) some expressions for average waiting times are known, e.g., with probabilistic entanglement swapping [22, 34, 42] or for specific loss models, e.g., suited for satellite-based repeaters [43]. For some setups even expressions for the ob... | Figure 9: Entanglement purification can extend achievable ranges for quantum repeaters with multiple links. Key rates without entanglement purification (circles) and with one step of entanglement purification at the lowest level (crosses) when using | Figure 6: Achievable key rates for two repeater links with a combination of strategies. Without entanglement purification and cut-off times | When considering entanglement purification as an additional tool for repeater protocols with multiple links, many variations of protocols are possible (e.g. an approach that is generally similar but differs in detail is analyzed in Ref. [25]). This is because in principle one can apply entanglement purification protoco... | A |
In conclusion, we have observed a two-fold increase in the dispersive interaction between a qubit and a BO at 5.5 dB of squeezing. A word of caution is however necessary. The BO, through its amplified field fluctuations, couples more strongly not only to the qubit but to all coupled modes, including its bath. The resul... | In conclusion, we have observed a two-fold increase in the dispersive interaction between a qubit and a BO at 5.5 dB of squeezing. A word of caution is however necessary. The BO, through its amplified field fluctuations, couples more strongly not only to the qubit but to all coupled modes, including its bath. The resul... | Yet, the future of BOs is not prescribed to the injection of squeezed vacuum. Regarding the BO alone, the new regime of amplification that evades the gain-bandwidth product constraint [31] is immediately applicable for broadband quantum limited amplification with no hardware overhead [54]. As for applications to enhanc... | A striking feature appears in the amplitude response of the oscillator, where gain is observed at both signal and idler frequencies. Indeed, in the resonant regime δa=0subscript𝛿a0\delta_{\mathrm{a}}=0italic_δ start_POSTSUBSCRIPT roman_a end_POSTSUBSCRIPT = 0, the 3 dB amplification bandwidth Δ3dBsubscriptΔ3dB\Delta_{... | The proposals [12, 11] consider a ubiquitous system in quantum optics: the degenerate parametric oscillator (DPO), albeit operated in a new regime (Fig. 1a). In the usual regime, widely employed for quantum-limited amplification [22, 23, 24, 25, 26, 27, 28, 29], a pump modulates the oscillator frequency at twice its re... | B |
It is important to remark that the only known exact solution of NLG is the trivial solution, namely, we recover Minkowski spacetime in the absence of the gravitational field. That is, with eμ=α^δαμe^{\mu}{}_{\hat{\alpha}}=\delta^{\mu}_{\alpha}italic_e start_POSTSUPERSCRIPT italic_μ end_POSTSUPERSCRIPT start_FLOATSUBSCR... | see, for instance Ferraro:2006jd ; Maluf:2011kf ; Bahamonde:2015zma ; Boehmer:2021aji ; Capozziello:2022zzh and the references cited therein. | This approach differs from other extensions of TEGR that involve, for instance, the introduction of scalar fields into the theory. That is, scalar-torsion theories of gravity, which are analogues of scalar-tensor theories that extend GR, have been studied by a number of authors; for recent reviews, see Bahamonde:2021gf... | There is a 4–5 σ𝜎\sigmaitalic_σ discrepancy between the measurement of the Hubble constant using local studies of the nearby supernovas, for instance, and the measurement of the recession rate using the CMB on the basis of the ΛΛ\Lambdaroman_ΛCDM model DiValentino:2021izs . This inconsistency has opened up a new arena... | There are many other nonlocal models of gravity and cosmology; see, for instance Woodard:2018gfj ; Deser:2019lmm ; Balakin:2022gjw ; BasiBeneito:2022wux ; Jusufi:2023ayv and the references cited therein. | D |
Automatic differentiation in general, and backpropagation in particular, are the commonly used techniques to take derivatives of machine learning models with respect to their parameters (weights and biases), which are then used by an optimization algorithm to train the model. In our case, we use the same infrastructure... | Subdominant QNMs can also be computed with the PINN, although higher overtones (n>0𝑛0n>0italic_n > 0) become increasingly difficult to obtain and usually require larger training times. The simplest approach is to initialize the frequency parameter ω𝜔\omegaitalic_ω to a value closer to the desired mode prior to the tr... | When the differential equation has one or multiple parameters to be computed, these can be fitted in the same manner as the weights and biases of the neural network, making the practical implementation remarkably straightforward. General boundary conditions and solution normalizations can be included in the loss functi... | We have used physics-informed neural networks [50] to solve the Teukolsky master equation and compute the first quasi-normal modes of the Kerr geometry for arbitrary black-hole masses and spins. Our results show an accuracy typically below the percentual level as compared to the accepted values in the literature [40]. ... | We have performed a hyperparameter study on the possible neural network architectures we could use. It revealed that moderately simple neural networks are enough for this problem. Figures 2 and 3 show the relative deviation of the real and imaginary parts of the mode (2,0,0) when compared to [40] as a function of the n... | B |
The final assertion of the lemma is trivial since 𝔇σζ=𝔇ση=Λsubscript𝔇𝜎𝜁subscript𝔇𝜎𝜂Λ\mathfrak{D}_{\sigma\zeta}=\mathfrak{D}_{\sigma\eta}=\Lambdafraktur_D start_POSTSUBSCRIPT italic_σ italic_ζ end_POSTSUBSCRIPT = fraktur_D start_POSTSUBSCRIPT italic_σ italic_η end_POSTSUBSCRIPT = roman_Λ exactly when ζ=σΛcηΛ=... | There is a boundary effect acting on the Λn↑𝕃↑subscriptΛ𝑛𝕃\Lambda_{n}\uparrow\mathbb{L}roman_Λ start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ↑ blackboard_L that affects the existence and/or uniqueness of the limits that determine the structural coefficients of the algebra; | The following examples highlight how 𝒞𝒞\mathscr{C}script_C affects the structural coefficients of the algebra considering two extreme cases. | Therefore, the structural coefficients of 𝒜(𝒞⊙,μ,Φ,Ω)𝒜subscript𝒞direct-product𝜇ΦΩ\mathcal{A}(\mathscr{C}_{\odot},\mu,\Phi,\Omega)caligraphic_A ( script_C start_POSTSUBSCRIPT ⊙ end_POSTSUBSCRIPT , italic_μ , roman_Φ , roman_Ω ) are precisely the Gibbs measures | It can be easily seen that the structural coefficients of the 𝒞𝒞\mathscr{C}script_C-genetic and evolution Gibbs algebras are correlated. The theorem below establishes a characterization of the evolution algebra via isomorphism derived from the tensor algebra 𝒜⊗𝒜tensor-product𝒜𝒜\mathcal{A}\otimes\mathcal{A}caligra... | B |
Moreover, note that the maximum robustness relative to dephasing (0.5) is much higher than the maximal robustness to depolarization (0.2). | A natural question is whether one can find scenarios where the contextual robustness to dephasing approaches its logical maximum, or whether (as for the contextual robustness to depolarization) this quantity is always bounded from above. | In the case of quantum theory (which is the case we study here) the linear program simply takes as input a set of density matrices (representing the preparations) and a set of POVM elements (representing the measurement-outcome pairs), and checks whether or not these are simplex-embeddable, and consequently, whether th... | The robustness to dephasing for this scenario as a function of θ𝜃\thetaitalic_θ is plotted in Figure 4. The most striking feature of this plot is that the robustness approaches 1111 as θ→0→𝜃0\theta\to 0italic_θ → 0, so that the scenario achieves the maximum logically possible robustness to dephasing. This is in stark... | Moreover, note that the maximum robustness relative to dephasing (0.5) is much higher than the maximal robustness to depolarization (0.2). | A |
We have presented time-dependent Rabi frequencies to decouple an atomic qutrit from both dephasing and amplitude-damping noises occurring together, while also executing intrinsically different quantum operations, including the case of random gates. We notice that the detunings involved in the protection scheme are cons... | We have presented time-dependent Rabi frequencies to decouple an atomic qutrit from both dephasing and amplitude-damping noises occurring together, while also executing intrinsically different quantum operations, including the case of random gates. We notice that the detunings involved in the protection scheme are cons... | The analysis we present here shows that, at least in principle, it is possible to realize an experiment to test our protection scheme if we are able to emulate the noise effects involved in our model, either by finding a naturally noisy system similar to our setup, or by artificially introducing the same kinds of pertu... | periodic time-dependent unitary evolution. It is worth emphasizing that, although here we address the qutrit model using a laser-atom system, the same analysis could be extended to qudit systems involving higher dimensions, as for example, another set of hyperfine levels of an atomic system, or to a treatment of more t... | If such an experiment is accomplished, the principles used in the present model could be translated to other systems with the same logical capabilities and even for qudits with d>3𝑑3d>3italic_d > 3. The latter condition could be also realised using atomic qudits based on an extension of our simple qutrit model. It is ... | B |
Summarizing the discussion in this section, the nonlinear phase space filling due to excitons localization can be divided qualitatively into three different regimes (Fig. 2). Particularly, as the excitons started to localize at a different region of the lattice, NPSF enters the fractured regime. In this regime, the Rab... | In this section, we concentrate on drawing a connection between the proposed microscopic modeling of polariton lattice saturation with the recent exciting results for bilayers of TMDC. In the case of TMDC bilayers, the lattice ordering appears naturally, and we consider several possible contributing effects. Specifical... | In summary, we developed a non-perturbative microscopic theory for describing nonlinear optical effects arising from the phase space filling. While the developed quantum theory can be applied for many systems at strong coupling, we concentrate on the lattice geometries in the limit of strong NPSF (deep saturation). We ... | We note the kink-like feature in the saturation curve appears in the higher density as compared to the density estimated in the experimental study. One possible reason may be that our calculation assumes a perfect correlation of exciton density with the laser power. In reality, the relation between them may be complica... | moiré excitons in a twisted heterobilayer TMDC is the subject of current intense research [106, 108, 111, 112, 113, 114]. In particular, the recent experiment [95] for the TMDC heterobilayers has found strong nonlinear saturation effects in moiré exciton-polariton. Experimental results suggest that there are several re... | A |
Equations (4) describe forced oscillations of the semi-infinite chain. The problem of the latter was solved analytically in [36, 37, 49, 50, 51, 52]. Kinematic loading was considered in the form of sinusoidal law in [36, 52] and in the form of the linear law in [51] (loading with constant velocity). In [37, 49, 50] for... | where λ𝜆\lambdaitalic_λ is the renormalized factor; u^^𝑢\hat{u}over^ start_ARG italic_u end_ARG is the direct DCT of the particle displacement, which, in general case (for arbitrary β𝛽\betaitalic_β), is unknown; | Applying inverse DCT to u^˙˙^𝑢\dot{\hat{u}}over˙ start_ARG over^ start_ARG italic_u end_ARG end_ARG yields expression for the particle velocity: | In order to solve Eqs. (4), we introduce the direct and inverse discrete cosine transforms (DCT) [53]: | In order to check the estimation (36), we perform numerical integration of Eqs. (4) in the same way as discussed in Sect. 4.2. The obtained particle velocities and displacements are used for calculation the total energy of the chain. Comparison of the expressions (36) with the numerical solution and (37) is shown in Fi... | C |
QY=23Qa−Qc.subscript𝑄𝑌23subscript𝑄𝑎subscript𝑄𝑐Q_{Y}=\frac{2}{3}Q_{a}-Q_{c}.italic_Q start_POSTSUBSCRIPT italic_Y end_POSTSUBSCRIPT = divide start_ARG 2 end_ARG start_ARG 3 end_ARG italic_Q start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT . | Since, the standard model hypercharge U(1)YUsubscript1𝑌{\rm U}(1)_{Y}roman_U ( 1 ) start_POSTSUBSCRIPT italic_Y end_POSTSUBSCRIPT is a linear combination of several U(1)U1{\rm U}(1)roman_U ( 1 )s, | We have displayed the perturbative particle spectra of all the five inequivalent representative models and also discussed the duality under the exchange of the left and the right sectors. In particular, one of models (Model 1) does not contain any filler O6-planes whereas the other four models contain a single stack of... | Therefore, the holomorphic gauge kinetic function for the hypercharge is also taken as a linear combination of the kinetic gauge functions from all of the stacks as [32, 22], | Among the five models, the highest number of Higgs pairs is found to be 4 for Model 1 whereas all other models either contain a double or a single pair each. Thus, Model 1 may be the only viable candidate to explain the Yukawa couplings and fermion masses. However, we note that the two exotic symmetric representations ... | C |
(c) Cross sections in the Pθsubscript𝑃𝜃P_{\theta}italic_P start_POSTSUBSCRIPT italic_θ end_POSTSUBSCRIPT plane. | As usual, we work in the Cartesian coordinate system with the origin at the point 𝗉𝗉\mathsf{p}sansserif_p. | we begin by defining a (u,v,w)𝑢𝑣𝑤(u,v,w)( italic_u , italic_v , italic_w ) coordinate system with the origin at 𝗉𝗉\mathsf{p}sansserif_p. | In each plane, we consider a u𝑢uitalic_u-v𝑣vitalic_v coordinate system defined such that its origin is at 𝗉𝗉\mathsf{p}sansserif_p and the centre of 𝖢𝖢\mathsf{C}sansserif_C lies along the positive half of the u𝑢uitalic_u-axis. | Since we can choose all planes in this set to include the v𝑣vitalic_v-axis, we can describe points in any Pθsubscript𝑃𝜃P_{\theta}italic_P start_POSTSUBSCRIPT italic_θ end_POSTSUBSCRIPT according to a (u~,v)~𝑢𝑣(\tilde{u},v)( over~ start_ARG italic_u end_ARG , italic_v ) Cartesian coordinate system with its origin a... | A |
ϵ𝑯𝒖,𝒅*bold-italic-ϵsuperscriptsubscript𝑯𝒖𝒅\displaystyle\epsilon H_{u,d}^{*}bold_italic_ϵ bold_italic_H start_POSTSUBSCRIPT bold_italic_u bold_, bold_italic_d end_POSTSUBSCRIPT start_POSTSUPERSCRIPT bold_* end_POSTSUPERSCRIPT | =(𝑯𝒖,𝒅+𝑯𝒖,𝒅𝟎),absentmatrixsuperscriptsubscript𝑯𝒖𝒅superscriptsubscript𝑯𝒖𝒅0\displaystyle=\begin{pmatrix}H_{u,d}^{+}\\ | 𝑯𝒖,𝒅subscript𝑯𝒖𝒅\displaystyle H_{u,d}bold_italic_H start_POSTSUBSCRIPT bold_italic_u bold_, bold_italic_d end_POSTSUBSCRIPT | =(𝑯𝒖,𝒅𝟎*−𝑯𝒖,𝒅−),absentmatrixsuperscriptsubscript𝑯𝒖𝒅0superscriptsubscript𝑯𝒖𝒅\displaystyle=\begin{pmatrix}H_{u,d}^{0*}\\ | forbid such rotations of (𝑯𝒖,𝑯𝒅)matrixsubscript𝑯𝒖subscript𝑯𝒅\begin{pmatrix}H_{u},H_{d}\end{pmatrix}bold_( start_ARG start_ROW start_CELL bold_italic_H start_POSTSUBSCRIPT bold_italic_u end_POSTSUBSCRIPT bold_, bold_italic_H start_POSTSUBSCRIPT bold_italic_d end_POSTSUBSCRIPT end_CELL end_ROW end_ARG bold_). | C |
Interestingly, the alignment time is nearly independent of the inclination in the low inclination limit. | Let us consider the case where the orbital energy of a star on an inclined orbit with respect to the disc does not significantly change during its alignment. In this case, the characteristic alignment timescale is the time to dissipate the vertical velocity through repeating, dissipative encounters with the disc, viz. | This relation can be used to estimate the final semimajor axis of orbits that become aligned with the disc. We also find a more accurate expression for the final angular momentum in the prograde, GDF for orbits of arbitrary orientation (see equation 44). | Above, we used the timescale to change the z-component of a star’s momentum as a proxy for the alignment time. This is an accurate estimate at low inclinations. However, it breaks down at high inclinations, since orbits inspiral significantly in semimajor axis before they align. For high inclinations, we find the times... | As discussed in § 4 we expect aligned orbits to become circular and prograde. From Appendix B, for low eccentricity, low inclination orbits the change in the orbit’s semimajor axis will be modest prior to alignment with the disc. For orbits that are initially at high inclinations the change in semimajor axis will be si... | C |
As mentioned, the surfaces of SiPM arrays were covered by TPB to improve the light yield. Theoretically, light yield could increase about ∼similar-to\sim∼100%percent\%% by using TPB, because QE of SiPM would increase from ∼similar-to\sim∼25%percent\%% at 340 nm to ∼similar-to\sim∼50%percent\%% at 420 nm. It is tested w... | In this paper, we describe the development of a kg-scale cryogenic pure-CsI crystal detector running at 77 Kelvin. Compared to the previous work in Ref. Zhang et al. (2018), scintillation photons were readout by two Hamamatsu S14161-6050HS-04 8×\times×8 SiPM arrays using cryogenic front-end electronics developed in Ref... | A promising way to overcome these limitations is to operate undoped CsI crystals with SiPM readout at low temperatures. As reported in many references and well summarized in Ref. Klein et al. (2022), the cryogenic undoped CsI/NaI crystal features a twice higher light yield than the doped crystal at room temperature. Op... | We compare our results with other crystal detectors in literature as shown in Fig. 14. Experiments using doped crystals featured light yields smaller than 20 p.e./keVee. Recent results in Ref. Ding et al. (2022) used a 0.6×\times×0.6×\times×1.0 cm3 cryogenic pure CsI crystal readout by SiPM chips and achieved about 43 ... | Motivated by the detection of the CEν𝜈\nuitalic_νNS process and the weak-interaction massive particles (WIMP), the low-threshold and low background detection techniques are quickly developing Klein et al. (2022). The detection threshold is reaching 1 keV of nuclear recoil (keVnr) in many detectors, such as cryogenic g... | C |
We prepared the synthetic nabokoite, KCu77{}_{7}start_FLOATSUBSCRIPT 7 end_FLOATSUBSCRIPT(TeO44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT)(SO44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT)55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPTCl, and observed peculiar behavior of its square kagomé magnetic system dec... | KCu77{}_{7}start_FLOATSUBSCRIPT 7 end_FLOATSUBSCRIPT(TeO44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT)(SO44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT)55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPTCl orders antiferromagnetically at TN=3.2subscript𝑇N3.2T_{\textrm{N}}=3.2italic_T start_POSTSUBSCRIPT N end_POS... | Acknowledgements.We acknowledge useful discussions with S. Li, L. Shvanskaya, S. Streltsov and J. Richter. The synthesis of the samples was supported by Russian Science Foundation grant 23-23-00205. The X-ray data collection was performed on the equipment supported by the Lomonosov Moscow State University development p... | Electron spin resonance (ESR) spectra were obtained on the mixture of non-oriented single crystals of KCu77{}_{7}start_FLOATSUBSCRIPT 7 end_FLOATSUBSCRIPT(TeO44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT)(SO44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT)55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPTCl by mean... | We prepared the synthetic nabokoite, KCu77{}_{7}start_FLOATSUBSCRIPT 7 end_FLOATSUBSCRIPT(TeO44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT)(SO44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT)55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPTCl, and observed peculiar behavior of its square kagomé magnetic system dec... | B |
0.04182−0.00074+0.00085superscriptsubscript0.041820.000740.000850.04182_{-0.00074}^{+0.00085}0.04182 start_POSTSUBSCRIPT - 0.00074 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT + 0.00085 end_POSTSUPERSCRIPT | 3.32×10−53.32superscript105\quad 3.32\times 10^{-5}3.32 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT | Fig. 2 shows a scatter plot between the effective parameters of our model for the quark sector, whose dependence can be seen in Appendix E. For all parameter values shown in Fig. 2, the mixing angles in the quark sector can be reproduced within the experimental range, where we obtain the following ranges of values for ... | \right)\times 10^{-10}\,{MeV},}( 3.334 ± 0.013 ) × 10 start_POSTSUPERSCRIPT - 10 end_POSTSUPERSCRIPT roman_MeV , ( roman_Δ roman_m start_POSTSUBSCRIPT roman_B start_POSTSUBSCRIPT roman_d end_POSTSUBSCRIPT end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT roman_SM end_POSTSUBSCRIPT = ( 3.653 ± 0.037 ± 0.019 ) × 10 start_POSTSUPER... | for flavor violating Yukawa couplings equal to 2.5×10−42.5superscript1042.5\times 10^{-4}2.5 × 10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT. | A |
In case of FePS3, in the heterostructure (HS-1), at/around 65 K, SP1-SP3 modes show deviation from the anharmonic fit for each of the phonon frequencies [see Figure 2(a),(c),(e)]. Note that antiferromagnetic ordering sets in (TNsubscript𝑇NT_{\mathrm{N}}italic_T start_POSTSUBSCRIPT roman_N end_POSTSUBSCRIPT) at 120 K, ... | In case of FePS3, in the heterostructure (HS-1), at/around 65 K, SP1-SP3 modes show deviation from the anharmonic fit for each of the phonon frequencies [see Figure 2(a),(c),(e)]. Note that antiferromagnetic ordering sets in (TNsubscript𝑇NT_{\mathrm{N}}italic_T start_POSTSUBSCRIPT roman_N end_POSTSUBSCRIPT) at 120 K, ... | Thickness dependent Raman measurements were done on Bi2Te3/FePS3 heterostructures (HS-2, HS-3) with temperature ranging from 5 K to 300 K. The coupling strength was observed to be high for the heterostructure consisting of thick-layer Bi2Te3 and FePS3. Strength of spin-phonon coupling of Raman modes of Bi2Te3 decreases... | Noticeably, in the Bi2Te3/FePS3 heterostructure (HS-1), the enhancement of the intensity in all the Raman modes of FePS3, compared to the isolated flake, can be explained by the electron transfer at the Bi2Te3/FePS3 interface. | In conclusion, we report a proximate AFM order in Bi2Te3, a topological insulator, by investigating the temperature-dependent Raman spectroscopy of Bi2Te3 (TI)- FePS3 (AFM with TNsubscript𝑇NT_{\mathrm{N}}italic_T start_POSTSUBSCRIPT roman_N end_POSTSUBSCRIPT ∼similar-to\sim∼ 120 K) stacked vdW heterostructure down to ... | C |
Motivated by the advantages shown by quantum cryptography and quantum computing respectively in improving transmission security and computing speed, scholars have attempted to utilize QIP to address the challenges faced by FL. In 2021, Li et al. focused on the security issue of FL [24]. They proposed a private single-p... | In this paper, we focus on the quantum algorithm running on ordinary quantum computers and present a quantum federated learning based on gradient descent (QFLGD). It aims to provide a unified, secure, and effective gradient distribution estimation scheme with distributed quantum networks. In QFLGD, we propose two data ... | In this section, we present the QFLGD, which focuses on the parallel and private computing architectures for data in distributed quantum networks. This distributed quantum network typically consists of a server and several clients with quantum computing capabilities. We first give ways to extract the data information t... | Motivated by the advantages shown by quantum cryptography and quantum computing respectively in improving transmission security and computing speed, scholars have attempted to utilize QIP to address the challenges faced by FL. In 2021, Li et al. focused on the security issue of FL [24]. They proposed a private single-p... | This work focuses on the design of the QFLGD for distributed quantum networks that can securely implement FL over an exponentially large data set. We first gave two methods of quantum data preparation, which can extract static data information and dynamic parameter information into logarithmic qubits. Then, we put fort... | A |
Most previous studies have focused on using localized FRBs to constrain the Hubble constant Hagstotz et al. (2022); Wu et al. (2022); Liu et al. (2023); Fortunato et al. (2023); Gao et al. (2023); Wei and Melia (2023), while another approach for unlocalized FRBs involves marginalizing the likelihood across the entire r... | This paper is organized as follows. In Sec. II, we briefly describe the galaxy catalog and FRB data. In Sec. III, the model of the likelihood and the Bayesian method are introduced. The constraints and relevant discussion are given in Sec. IV. Conclusions are given in Sec. V. | In this paper, we use the statistical galaxy catalog method similar to the dark siren method in GW cosmology and obtain the measurement of the Hubble constant H0subscript𝐻0H_{0}italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT using twelve unlocalized ASKAP FRB data as an example. We find all potential host galaxies in... | It should be noted that actually, above z∼0.5similar-to𝑧0.5z\sim 0.5italic_z ∼ 0.5, the galaxy catalog is incomplete Yang et al. (2021), thus some high-redshift galaxies are absent in our analysis. This leads to the constraints lower compared to the reality (i.e., with a complete galaxy catalog), because of the positi... | Figure 1: The sky positions of the FRB data (black circles) and the footprints of the galaxy catalog (the blue area) used in this paper. The left and right panels show the data in the south Galactic cap (SGC) and north Galactic cap (NGC), respectively. | A |
This last equation implies that the average of P(t,t)(W)𝑃𝑡𝑡𝑊P(t,t)(W)italic_P ( italic_t , italic_t ) ( italic_W ) is indistinguishable from the integral over U(d)𝑈𝑑U(d)italic_U ( italic_d ) with an uniform-Haar measure. | Figure 8: Behavior of a quantum neural network model during training as the number of qubits increases for different parameterization depths. In these numerical simulations, we use the parameterization shown in Fig. 3 with restrictions, which we call Not Free, and without restrictions, which we call Free. The imposed r... | Figure 9: Behavior of a quantum neural network model during training as the number of qubits increases for different parameterization depths. In these numerical simulations, we use the parameterization shown in Fig. 3 with restrictions, which we call Not Free, and without restrictions, which we call Free. The imposed r... | As we can see, the behavior of the cost function using the U𝑈Uitalic_U parameterization with and without restrictions is similar, especially when the size of the system used is large. Once again we observe a dependence on the depth of the parameterization. However, as we previously mentioned, this is due to the fact t... | For more details we suggest Ref. Symbolic_integration . With this we can state the following theorem. | D |
Also in the context of interacting QFTs, it would be interesting to investigate whether continuous tensor network techniques in the spirit of Fernandez-Melgarejo:2020fzw can be used to study Krylov complexity in generic interacting scalar field theories212121We thank Adolfo del Campo for pointing out this interesting ... | In Sec. 4, we considered a real scalar field with cubic or quartic interaction terms propagating in 4-dimensional flat spacetime, and numerically studied the effects of interactions on the Lanczos coefficients. The cubic (quartic) interaction term can be thought of as a relevant (marginally irrelevant) deformation of t... | The corresponding staggering effect does not depend on n𝑛nitalic_n. By contrast, in the case of cubic interactions, there is no mass gap, and the staggering decreases as we increase n𝑛nitalic_n. This suggests that the staggering produced by the cubic interaction term may not be present for sufficiently large values o... | In this paper, we discussed the behavior of the Lanczos coefficients bnsubscript𝑏𝑛b_{n}italic_b start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT and the Krylov complexity K𝒪(t)subscript𝐾𝒪𝑡K_{\mathcal{O}}(t)italic_K start_POSTSUBSCRIPT caligraphic_O end_POSTSUBSCRIPT ( italic_t ) for free and interacting scalar QFT... | Deformations of local QFTs due to interactions are represented by renormalization group flows. One may be able to classify the effects of the interactions on the Lanczos coefficient and Krylov complexity in terms of the renormalization group flows. In particular, we observed that the staggering produced by a relevant d... | D |
+χa(Ir,0+−Ir,0−)].\displaystyle\left.+\chi_{a}\left(I^{+}_{r,0}-I^{-}_{r,0}\right)\right].+ italic_χ start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT ( italic_I start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_r , 0 end_POSTSUBSCRIPT - italic_I start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT start_POSTS... | and similarly for anti-particles with f→f¯→𝑓¯𝑓f\to\bar{f}italic_f → over¯ start_ARG italic_f end_ARG and f0→f¯0→subscript𝑓0subscript¯𝑓0f_{0}\to\bar{f}_{0}italic_f start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT → over¯ start_ARG italic_f end_ARG start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT. The advantage of the above modificati... | To express the conserved net particle four-current and the energy-momentum tensor in terms of hydrodynamic variables in Eqs. (1) and (2), we chose Landau frame to define the fluid four-velocity. Additionally, the net-number density and energy density of a non-equilibrium system needs to be defined using the so called m... | It is important to note that the BGK or MBGK collision kernels are affected by the matching conditions, which in turn affects the dissipative processes in the system. Moreover, at finite chemical potential, two descriptions become identical. We identified a class of matching conditions for which the homogeneous part of... | We emphasize that the above equation along with Eq. (18) constitute the two matching conditions required to define temperature and chemical potential of the system. In order to compare with the usual Landau matching conditions, we express Eq. (6) using first order results obtained in Eqs. (41) and (42), | D |
Since the integral over θ𝜃\thetaitalic_θ forms for values O((logω0t)n/k−1)≫1much-greater-than𝑂superscriptsubscript𝜔0𝑡𝑛𝑘11O\left(\left(\log\omega_{0}t\right)^{n/k-1}\right)\gg 1italic_O ( ( roman_log italic_ω start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_t ) start_POSTSUPERSCRIPT italic_n / italic_k - 1 end_PO... | We here derive the expression for the first passage time distribution (FPTD) in a fluctuating potential landscape. As discussed in the main text, we consider the adiabatic limit in which the FPTD can be approximated by | Discarding subdominant terms, in all three cases we thus get the general expression we present in the main text, | We here derive the expression for the correlation function in a fluctuating potential landscape. In general, the autocorrelation function can be expressed as a sum over exponential functions [38, 59], | The θ∗superscript𝜃\sqrt{\theta^{*}}square-root start_ARG italic_θ start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT end_ARG, as well as the log(ω0t)1/k−1\log\left(\omega_{0}t\right)^{1/k-1}roman_log ( italic_ω start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_t ) start_POSTSUPERSCRIPT 1 / italic_k - 1 end_POSTSUPERSCRIPT comin... | B |
Observational data are taken from the raw second and third catalogs of the Cosmicflows project (Tully et al., 2013, 2016). The second catalog containing ∼similar-to\sim∼8000 galaxies, with a mean distance of ∼similar-to\sim∼90 Mpc, serves as the basis to build the constraint-catalog of ∼similar-to\sim∼5000 bias-minimiz... | Figure 3: Radial velocities of simulated dark matter (sub)halos (black and grey) and observed galaxies (orange, blue and red) as a function of the distance from the synthetic observer and us respectively. Error bars stand for uncertainties on observational distance and velocity estimates. Orange and light blue (red and... | Uncertainties on distances and radial peculiar velocities in these catalogs depend on the distance indicator used to derive the distance moduli. Error bar sizes need to be limited to see clearly velocity waves. Thus, to be able to compare with the simulated data, only galaxies with uncertainties on distance moduli smal... | Observational data are taken from the raw second and third catalogs of the Cosmicflows project (Tully et al., 2013, 2016). The second catalog containing ∼similar-to\sim∼8000 galaxies, with a mean distance of ∼similar-to\sim∼90 Mpc, serves as the basis to build the constraint-catalog of ∼similar-to\sim∼5000 bias-minimiz... | Assuming the synthetic observer at the box center and the simulated volume oriented similarly to the local volume, observed and simulated positions and lines-of-sight can be matched. We can only compare velocity waves born from local galaxy clusters for which infalling galaxy peculiar velocities, with uncertainties on ... | B |
To summarize, we have demonstrated the formulation, applicability and superiority of EPR to the benchmark and real biological examples over some existing approaches. Below we make some final remarks. First, concerning the use of the steady-state distribution π(𝒙)𝜋𝒙\pi(\bm{x})italic_π ( bold_italic_x ) in (3) and it... | Overall, we have presented the EPR-Net, a simple yet effective DNN approach, for constructing the non-equilibrium potential landscape of NESS systems. This approach is both elegant and robust due to its variational structure and | To summarize, we have demonstrated the formulation, applicability and superiority of EPR to the benchmark and real biological examples over some existing approaches. Below we make some final remarks. First, concerning the use of the steady-state distribution π(𝒙)𝜋𝒙\pi(\bm{x})italic_π ( bold_italic_x ) in (3) and it... | Overall, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics. Even its nice mathematical structure and connection with non-equilibrium statistical physics make it a unique object that deserves further theoretical and numerical exploration in the future. | In this work, we present a simple yet efficient DNN approach to construct the potential landscape of high-dimensional non-equilibrium steady state (NESS) systems in (T1) type with either moderate or small noise. Its intimate connection with non-equilibrium statistical mechanics, nice variational structure and superior ... | A |
In conclusion, we constructed several models for dynamic quantum state reduction based on the idea that the time inversion symmetry underlying unitarity in quantum dynamics can be spontaneously broken, like any other symmetry in nature. Although it has been known for some time that the unitary dynamics of Schrödinger’s... | The mathematically most straightforward extension of the two-state evolution can be found by first rewriting Eq. (5) in the form: | These equations define a model for DQSR starting from an N𝑁Nitalic_N-state superposition in the initial state. The spontaneous breakdown of unitarity takes place in a time scaling with ϵ𝒩italic-ϵ𝒩\epsilon\mathcal{N}italic_ϵ caligraphic_N, so that the collapse process for a vanishingly small non-unitary perturbation... | We first considered a mathematically straightforward generalization, in which just a single random variable chosen from a flat, uniform distribution leads to precisely Born’s rule for an initial superposition of an arbitrary finite number of pointer states. This model, however, does not have a straightforward physical ... | In the previous section, we generalized the description of SUV as a model for DQSR from initial superpositions over two pointer states to an arbitrary number of pointer states in the initial superposition. The generalization based on dividing the N𝑁Nitalic_N-particle phase space into regions of attraction for the N𝑁N... | C |
In b), we changed the test graph to a larger one, n=15,p=0.3formulae-sequence𝑛15𝑝0.3n=15,p=0.3italic_n = 15 , italic_p = 0.3 and contrast the true dynamics (solid lines) and the neural network forecasts (dotted lines) for a new set of initial values that are sampled from the training distribution. The insets contrast... | All in all, we underscore that a model can strive for various degrees of generalization, from approximation to predictions and, finally, forecasting. It is also important to consider the data which was used during training: a model trained using non-i.i.d. time series data may adopt biases that would lead to poorer pre... | Now we turn our attention to forecasting and training using more realistic data, derived from time series. In this section, we also study the d𝑑ditalic_d-statistic, and its potential to quantify the reliability of the forecasts. | Overall, the neural networks can approximate various dynamical models and extrapolate predictions even when statistical properties of the input data, or the graph structure change, transcending the formal boundaries of SLT and UAT. We also showed that training and generalization are also possible using time series data... | In this section, we detail the primary findings of this paper, focusing on neural approximation, prediction and forecasting of complex network dynamics. We commence by examining scenarios in Sec. V.1 under the premise that the function 𝓕𝓕\pmb{\mathcal{F}}bold_caligraphic_F is accessible for analytical estimation. In ... | B |
(a) {6,4}64\{6,4\}{ 6 , 4 } MeV α𝛼\alphaitalic_α-curve, zoomed in at the low area density component. Different α𝛼\alphaitalic_α-lines frequently overlap, corresponding to non-unique atomic number solutions. | At low material area densities, this effect is most pronounced due to the significant low energy component of the bremsstrahlung spectra. The high probability of photoelectric interactions causes α𝛼\alphaitalic_α-lines to frequently overlap in this regime, resulting in atomic number ambiguity. At larger area densities... | (a) {6,4}64\{6,4\}{ 6 , 4 } MeV α𝛼\alphaitalic_α-curve, zoomed in at the low area density component. Different α𝛼\alphaitalic_α-lines frequently overlap, corresponding to non-unique atomic number solutions. | One way to visualize the capabilities for atomic number discrimination is to consider the separation between different α𝛼\alphaitalic_α-lines on the α𝛼\alphaitalic_α-curves shown in Fig. 1. α𝛼\alphaitalic_α-lines that are close together indicate a more challenging inversion since a purer signal is necessary to diffe... | (b) {6,4}64\{6,4\}{ 6 , 4 } MeV α𝛼\alphaitalic_α-curve only showing high-Z𝑍Zitalic_Z elements. Material overlap occurs even for larger values of α𝛼\alphaitalic_α, demonstrating that the high-Z𝑍Zitalic_Z degeneracy is still present for thick targets. | D |
The trace power spectral densities of magnetic field and proton velocity (PB=PB,X+PB,Y+PB,Zsubscript𝑃𝐵subscript𝑃𝐵𝑋subscript𝑃𝐵𝑌subscript𝑃𝐵𝑍P_{B}=P_{B,X}+P_{B,Y}+P_{B,Z}italic_P start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT = italic_P start_POSTSUBSCRIPT italic_B , italic_X end_POSTSUBSCRIPT + italic_P start_... | It is worth noting that timing analysis determines the actual wavevectors of the Alfvénic magnetic field. In contrast, the SVD method determines the best estimate of the wavevector sum in three magnetic field components Santolík et al. (2003). Thus, 𝐤Asubscript𝐤𝐴\mathbf{k}_{A}bold_k start_POSTSUBSCRIPT italic_A end_... | Due to the homogeneous and stationary state of the turbulence (Supplementary Fig. 3), we can utilize frequency-wavenumber distributions of Alfvénic power, i.e. magnetic power PBA(k⟂,k∥,fsc)subscript𝑃subscript𝐵𝐴subscript𝑘perpendicular-tosubscript𝑘parallel-tosubscript𝑓𝑠𝑐P_{B_{A}}(k_{\perp},k_{\parallel},f_{sc})... | We calculate wavenumber-frequency distributions of Alfvénic magnetic field and proton velocity power by an improved Alfvén mode decomposition method. This method combines the linear decomposition method Cho & Lazarian (2003), singular value decomposition (SVD) method Santolík et al. (2003), and multi-spacecraft timing ... | We set a moving time window with a five-hour length and a five-minute moving step. The selection of a five-hour length ensures that we obtain measurements at low frequencies (large scales) while the mean magnetic field (𝐁0subscript𝐁0\mathbf{B}_{0}bold_B start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT) within the moving time ... | C |
In Definition 5.3, the following symmetries are either manifest or implied: (1) the switch of X↔X¯↔𝑋¯𝑋X\leftrightarrow\bar{X}italic_X ↔ over¯ start_ARG italic_X end_ARG, (2) the switch of Y↔Y¯↔𝑌¯𝑌Y\leftrightarrow\bar{Y}italic_Y ↔ over¯ start_ARG italic_Y end_ARG, and (3) the switch X↔Y↔𝑋𝑌X\leftrightarrow Yitalic_... | The fact that each of X𝑋Xitalic_X and Y𝑌Yitalic_Y cut the other into balls means that they hide (classical and quantum) information from each other completely. Each region is associated with a natural choice of vacuum by immersion into a large ball or a sphere (possibly upon removing a ball). As a consequence of thes... | pgfstrokecolor}{rgb}{0.560181,0.691569,0.194885}\CIRCLE}Yitalic_X ∪ start_POSTSUBSCRIPT ● end_POSTSUBSCRIPT italic_Y. The verification of the conditions for pairing is similar to the examples above. In particular, one can verify that X𝑋Xitalic_X and Y𝑌Yitalic_Y cut each other into balls, and the transverse intersecti... | It is clear that the “misguided” attempt shown in Fig. 45(b) cannot be the way to combine X𝑋Xitalic_X and Y𝑌Yitalic_Y. This is because X𝑋Xitalic_X did not cut Y𝑌Yitalic_Y into two balls. Furthermore, the attempt to combine X𝑋Xitalic_X and Y𝑌Yitalic_Y as Fig. 45(c) cannot work either. There, although X𝑋Xitalic_X ... | In fact, because X𝑋Xitalic_X and Y𝑌Yitalic_Y cut each other into balls, the natural partitions that appear in a pairing must have a special property, summarized in the following lemma: | D |
For a given measurement clique, we can associate it with one quantum circuit to perform projective measurement on simultaneous-eigenstates of all the operators in the measurement clique. | Repetitive execution of that circuit yields an estimate of an expectation value of any product of the operators in the measurement clique. | The number of copies of quantum states needed to estimate the expectation value of the Hamiltonian with sufficient accuracy becomes very large even for relatively small systems, due to the need to estimate expectation values of O(N4)𝑂superscript𝑁4O(N^{4})italic_O ( italic_N start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIP... | For a given measurement clique, we can associate it with one quantum circuit to perform projective measurement on simultaneous-eigenstates of all the operators in the measurement clique. | A central task in applying quantum computers to quantum chemistry calculations is to estimate an expectation value of the electronic structure Hamiltonian with 2N2𝑁2N2 italic_N spin orbitals (fermions) in the form of | A |
Then there is non-zero a∈S𝑎𝑆a\in Sitalic_a ∈ italic_S such that ax⊴ay𝑎𝑥normal-⊴𝑎𝑦ax\trianglelefteq ayitalic_a italic_x ⊴ italic_a italic_y. Conversely, if such a𝑎aitalic_a exists, then the above inequalities hold non-strictly. | The problem with this approach is, however, that the characterization of the test spectrum of the quantum majorization semiring remains, for now, intractable. For one thing, we cannot similarly decompose the additive maps in the quantum case as we did in Propositions 13 and 14, because the states in the d𝑑ditalic_d-tu... | As mentioned previously, majorization in large samples implies catalytic majorization and thus the conditions in (5) are sufficient for catalytic majorization as well (and they are still generically necessary). Strengthening this, we show in Theorem 22 of Section 3 that asymptotic catalytic majorization is possible if ... | To characterize ordering in large samples as well, we need some further conditions on the preordered semiring involved. It can be shown [13] that the conditions listed in the theorem below imply the conditions required in Theorem 7. | As we will see, majorization in large samples implies catalytic majorization, and this follows from a known general construction (see e.g., [10]). Sufficient and generically necessary conditions for majorization in large samples in the case d=2𝑑2d=2italic_d = 2 were determined by Mu et al. in [21], and analogous condi... | C |
\mathrm{d}\|s\|^{2}}{\|s\|^{2}}\wedge\omega\bigg{)}.roman_d italic_μ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT ( italic_ω ) = italic_μ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT ( roman_d italic_ω ) + italic_μ start_POSTSUBSCRIPT italic_j + 1 end_POSTSUBSCRIPT ( divide start_ARG roman_d ∥ italic_s ∥ start_POST... | It follows that μ0(ω)=ωsubscript𝜇0𝜔𝜔\mu_{0}(\omega)=\omegaitalic_μ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_ω ) = italic_ω as currents on X∖V𝑋𝑉X\setminus Vitalic_X ∖ italic_V. Thus μ0(ω)subscript𝜇0𝜔\mu_{0}(\omega)italic_μ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_ω ) is a current extension of ω�... | To begin with we consider the case where ω𝜔\omegaitalic_ω is of top degree and s𝑠sitalic_s defines a normal crossings divisor. We have the following lemma. | A priori Lemma 4.3 holds in the case when X𝑋Xitalic_X is smooth and s𝑠sitalic_s defines a normal crossings divisor. The corresponding statement in the general setting follows by Lemma 4.3 and 2.4. | To find a current extension of ω𝜔\omegaitalic_ω across V𝑉Vitalic_V, following a classical idea, we consider the function | B |
{x}}}.italic_A start_POSTSUBSCRIPT italic_μ end_POSTSUBSCRIPT ( bold_x , italic_t ) = divide start_ARG 1 end_ARG start_ARG italic_V end_ARG ∫ italic_d start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_k italic_a start_POSTSUBSCRIPT italic_μ end_POSTSUBSCRIPT ( bold_k , italic_t ) italic_e start_POSTSUPERSCRIPT italic_... | Since there are no spatial oscillations of the metric along the z−limit-from𝑧z-italic_z -direction, it is expected that there will not be any resonant growth of z−limit-from𝑧z-italic_z -component | of the monochromatic plane GW, propagating along the z−limit-from𝑧z-italic_z -direction. For simplicity, we ignore the back | In this section, we describe numerical simulations of the field equations and the results, for U(1)𝑈1U(1)italic_U ( 1 ) and SU(2)𝑆𝑈2SU(2)italic_S italic_U ( 2 ) gauge theories. In 3+1313+13 + 1 dimensions, space-time oscillations propagating in the z−limit-from𝑧z-italic_z -direction result in adjacent z−limit-fr... | In this section, so far, the fields are considered to be independent of z𝑧zitalic_z. However, since the space-time oscillations are propagating along the z−limit-from𝑧z-italic_z -direction, the metric depends on z𝑧zitalic_z along with time t𝑡titalic_t. Thus, in 3+1313+13 + 1 dimensions, even in the linear regime, t... | A |
∼Δ−5/2.similar-toabsentsuperscriptΔ52\displaystyle\sim\Delta^{-5/2}.∼ roman_Δ start_POSTSUPERSCRIPT - 5 / 2 end_POSTSUPERSCRIPT . | That is, the cross-section for the cusp decreases faster as a function of threshold than the fold cross-section. Therefore, it is a generic expectation of catastrophe theory that folds will contribute more to the observed density than cusps. This is also, notably, a precise and testable prediction of our model; the num... | Catastrophe theory describes the mathematics of such singularities. Powerfully, catastrophe theory shows that the topological structure of singularities must conform to a few fundamental forms (the “elementary catastrophes") regardless of the precise details of the map in which the singularities arise. Catastrophe theo... | Catastrophe theory is the mathematical classification of the stable singularities of continuous mappings. The power of catastrophe theory comes from the fact that the stable sinuglarities can be classified by a small number of canonical forms. In this paper we will focus on the A3subscript𝐴3A_{3}italic_A start_POSTSUB... | While this relative rarity of ESEs compared to scintillation might initially seem to pose an issue for any attempt to explain these two phenomena with a unified model, the doubly catastrophic framework actually provides a natural explanation. It is a well-known result of catastrophe theory that the cross-section for fo... | A |
For 0≤i,j≤n−1formulae-sequence0𝑖𝑗𝑛1{0\leq{i,j}\leq{n-1}}0 ≤ italic_i , italic_j ≤ italic_n - 1 and k≥0𝑘0k\geq{0}italic_k ≥ 0, we have | CIon(i)KIon(i)−1LIon(i)−1P~Ion(i)−1,jkζ−(k−1+Ion(i))j−KiLi−1P~i,jkζ−(k−1+i)jsubscript𝐶Ion𝑖subscript𝐾Ion𝑖1superscript𝐿Ion𝑖1superscriptsubscript~𝑃Ion𝑖1𝑗𝑘superscript𝜁𝑘1Ion𝑖𝑗subscript𝐾𝑖superscript𝐿𝑖1superscriptsubscript~𝑃𝑖𝑗𝑘superscript𝜁𝑘1𝑖𝑗\displaystyle C_{\mathrm{Ion}(i)}\frac{K_{{\ma... | P~Ion(i)−1,jk=P~i,jk+1LDP~i,jk−1+An−iP~i,jk−1.superscriptsubscript~𝑃Ion𝑖1𝑗𝑘superscriptsubscript~𝑃𝑖𝑗𝑘1𝐿𝐷superscriptsubscript~𝑃𝑖𝑗𝑘1subscript𝐴𝑛𝑖superscriptsubscript~𝑃𝑖𝑗𝑘1\widetilde{P}_{\mathrm{Ion}(i)-1,j}^{k}=\widetilde{P}_{i,j}^{k}+\frac{1}{L}D% | DPi,jk−1=CIon(i)PIon(i)−1,jk−Pi,jkLζj.𝐷superscriptsubscript𝑃𝑖𝑗𝑘1subscript𝐶Ion𝑖superscriptsubscript𝑃Ion𝑖1𝑗𝑘superscriptsubscript𝑃𝑖𝑗𝑘𝐿superscript𝜁𝑗DP_{i,j}^{k-1}=C_{\mathrm{Ion}(i)}P_{\mathrm{Ion}(i)-1,j}^{k}-P_{i,j}^{k}L% | CIon(i)PIon(i)−1,jk−Pi,jkLζj=subscript𝐶Ion𝑖superscriptsubscript𝑃Ion𝑖1𝑗𝑘superscriptsubscript𝑃𝑖𝑗𝑘𝐿superscript𝜁𝑗absent\displaystyle C_{\mathrm{Ion}(i)}P_{\mathrm{Ion}(i)-1,j}^{k}-P_{i,j}^{k}L\zeta% | C |
There are many successful deep learning models for different tasks, ranging from ResNet specialized for image recognition He et al. (2016) to attention based models for natural language Vaswani et al. (2017). However, to investigate the existence of 1/f1𝑓1/f1 / italic_f noise, we need a network that is used specifical... | Drawing inspiration from the analogy to the brain and the presence of 1/f1𝑓1/f1 / italic_f noise in a well-functioning brain, we investigated the exponents of the LSTM layer while varying the capacity of the layer. The greater the number of cells in the LSTM layer, the greater its capacity for storing useful informati... | Figure 1 shows the most basic form of an RNN, demonstrating the idea that these recurrent networks are deep through time, in contrast to the depth through layers of a simple feedforward network. However, this also means that the simple RNN suffers from the same problem as DNNs with large depths - the vanishing gradient... | RNNs are a type of network that preserve the state of an input across a temporal sequence by feeding the outputs of its nodes back into those same nodes. This is as opposed to feedforward networks, where data flows only from layer to layer. By retaining knowledge of previous inputs through this recurrence, RNNs are sig... | Figure 4 is a scatter plot relating the histograms shown in Figure 3, demonstrating the lack of correlation between the activation exponent and the input exponent with an R2superscript𝑅2R^{2}italic_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT value of 0.061. This further supports our hypothesis that the 1/f1𝑓1/f1 / ... | C |
SR=S11−S12,SA=S11−S21,SF=S11+S22.formulae-sequencesubscript𝑆𝑅subscript𝑆11subscript𝑆12formulae-sequencesubscript𝑆𝐴subscript𝑆11subscript𝑆21subscript𝑆𝐹subscript𝑆11subscript𝑆22\displaystyle S_{R}=S_{11}-S_{12},S_{A}=S_{11}-S_{21},S_{F}=S_{11}+S_{22}.italic_S start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT = ital... | The longitudinal bulk viscous correction is incorporated into the retarded/advanced gluon self-energy by just replacing the thermal equilibrium distribution functions in Eq. (II.1) with longitudinal bulk viscous modified ones. Consequently, the real part of the longitudinal bulk viscous modified retarded gluon self-ene... | with GR/A00subscriptsuperscript𝐺00𝑅𝐴G^{00}_{R/A}italic_G start_POSTSUPERSCRIPT 00 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_R / italic_A end_POSTSUBSCRIPT being the temporal component of bare retarded/advanced gluon propagator. The superscript “***” denotes the resummed effect gluon propagator. Consequently, th... | Therefore, the medium HLL quark-loop contribution to the real part of retarded gluon self-energy in the magnetized QGP medium is given as | Similarly, the retarded (R𝑅Ritalic_R), advanced (A𝐴Aitalic_A), and symmetric (F𝐹Fitalic_F) gluon self-energies are given as | D |
In Section 3 we present our numerical simulations in one and two space dimensions as well as discuss their potential extension to higher dimensions. | In this paper, we propose a quantum Monte Carlo algorithm to solve high-dimensional Black-Scholes PDEs with correlation and general payoff function which is continuous and piece-wise affine (CPWA), enabling to price most relevant payoff functions used in finance (see also Section 2.1.2). Our algorithm follows the idea ... | In Section 4, we introduce and analyze all relevant quantum circuits we need in our quantum Monte Carlo algorithm. | In this section, we first present our quantum Monte Carlo algorithm named Algorithm 1 to solve Black-Scholes PDEs (1) with corresponding CPWA payoff function (8). Moreover, we then outline Algorithm 1 and present our main result in Theorem 1, namely a convergence and complexity analysis of our algorithm. | In Section 5, we provide a detailed error analysis of the steps of our algorithm outlined in Section 2.4.1. | B |
The authors calculate the lifetime of the EW-breaking vacuum at finite temperature, starting from low temperature and ending at the temperature at which one of the vacua evaporates. In the right frame of Fig. 2, with increasing temperature, the transition probability of the desired EW-breaking vacuum increases, which m... | As a result, the universe always stays in the EW-restored minimum. In the zero-temperature potential, the desired EW-breaking vacuum is meta-stable with a lifetime much longer than the universe’s age, so it is acceptable in the traditional method. For this kind of situation, checking the history is time-saving, because... | We see that the traditional method accepts some regions of meta-stable EW-breaking vacuum, but checking the cosmological history proves that incorrect. The exclusion of such regions is computationally fast, because one only needs to trace the minima of the potential with temperature. On the other hard, it is more time-... | Thus, this method can also correctly exclude this situation. However, if there are more than one minima that the desired EW-breaking vacuum can transition into at finite temperature, this method becomes invalid. As shown later, the calculation of transition probability is fairly time consuming, while checking the therm... | In the early hot universe, in the global minimum of effective potential (shown by the green dot and red lines) the EW symmetry is restored. With decreasing temperature a new minimum appears in the potential (shown by the orange lines). In the left frame, the new minimum turns into the desired EW-breaking vacuum and glo... | C |
In this section, we explain how we generate graphs with a given chromatic number, introduce different local decision heuristics, and present a genetic algorithm that we use to generate networks with specific properties. | Having analyzed the interplay between the length of added links and the reasoning of the acting agents in small-world graphs, it is now natural to ask, whether this behavior can also be observed in more complex networks. As described in Sec. 2.2, we generated modular graphs (2 x 20 nodes, 40 edges each) with different ... | To assess how strongly the topology of a network (with a fixed number of shortcuts) affects the runtime, we use a genetic algorithm that evolves to easy-to-solve or hard-to-solve networks (with respect to a given heuristic). The algorithm starts with an ensemble of six randomly selected small-world networks with the gi... | The natural extension of our investigation is to increase the chromatic number of the graphs. For Fig. 7 we performed a similar analysis as for Fig. 3, but with a ring graph with 39 nodes and a chromatic number of χ=3𝜒3\chi=3italic_χ = 3. Depending on the length of the added shortcut the system takes longer or is fast... | In this analysis, we mainly focus on small-world networks with few inserted links as a toy model for graphs with high clustering and small shortest path length. The idea of the graph generation follows [26]. However, since the networks are supposed to be solvable with a given number of χ𝜒\chiitalic_χ colors (the chrom... | D |
It order test the observability of the GW-EMW interaction effects it will be important to perform numerical general relativistic magnetohydrodynamic (GRMHD) simulations to obtain precise theoretical predictions, and check the validity of the effective speed approach. | This definition of effective speed is model independent, and could be applied to obtain an effective description of the propagation in any medium, and in this paper we consider the effects of the total current given by the sum of the EM current and the effective gravitomagnetic current. | We thank Luca Baiotti, Sudipta Hensh, Filippo Vernizzi and Mairi Sakellariadou for interesting discussions. This work was supported by the UDEA projects 2021-44670, 2019-28270, 2023-63330. | where ΠAsubscriptΠ𝐴\Pi_{A}roman_Π start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT was given in eq.(2), and the sub-index A𝐴Aitalic_A stands for the two polarizations +++ and ×\times×. | In this paper we go beyond these approximations, and derive the equations accounting for the full interaction between GWs and EMWs, including the back-reaction of GWs on EMWs, and of EMWs on GWs. | B |
We present a method for simultaneously fitting models for the Tully-Fisher relation and the peculiar velocity field. The method uses the conditional probability for the observed magnitude as a function of the observed HI velocity width; it is thus a ‘direct’ fit of the Tully-Fisher relation between magnitude and veloci... | We first apply this method to the Cosmicflows-4 (CF4) catalogue of Tully-Fisher measurements. We modify the conventional linear Tully-Fisher relation to account for the observed curvature at the bright end of the relation and for the varying scatter along the relation. For the peculiar velocity model, we adopt the rela... | et al. (2015), but leaving free the velocity scaling parameter β𝛽\betaitalic_β and a residual bulk motion 𝐕extsubscript𝐕ext\mathbf{V}_{\textrm{ext}}bold_V start_POSTSUBSCRIPT ext end_POSTSUBSCRIPT that approximates the effect of the mass distribution external to the 2M++ volume. The full model for the Tully-Fisher r... | We present a method for simultaneously fitting models for the Tully-Fisher relation and the peculiar velocity field. The method uses the conditional probability for the observed magnitude as a function of the observed HI velocity width; it is thus a ‘direct’ fit of the Tully-Fisher relation between magnitude and veloci... | The paper is organised as follows. In Section 2 we describe the method used to simultaneously fit the Tully-Fisher relation and the peculiar velocity model; we also show how to optimally estimate distances and peculiar velocities for individual galaxies. In Section 3 we describe the CF4 Tully-Fisher data and the model ... | A |
Table 4: Marginalized constraints on the parameters of the cosmological models considered in Sec. 2 for eLISA using MCMC. | Figure 7: Markov Chain Monte Carlo contours with Delay source type for 10 years eLISA mission duration. | Figure 9: Markov Chain Monte Carlo contours with Pop III source type for 10 years eLISA mission duration. | Figure 8: Markov Chain Monte Carlo contours with No Delay source type for 10 years eLISA mission duration. | Figure 6: Dependence of errors estimated by Fisher analysis on the mean value of H0subscript𝐻0H_{0}italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT (km s-1 Mpc-1) for source type No Delay and eLISA mission duration of 10 years. | A |
\tau)H}S^{z}(\mathbf{k})^{\dagger}e^{-\tau H}S^{z}(\mathbf{k})|i\rangleitalic_S start_POSTSUPERSCRIPT italic_z italic_z end_POSTSUPERSCRIPT ( bold_k , italic_τ ) = divide start_ARG 1 end_ARG start_ARG italic_Z end_ARG ∑ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ⟨ italic_i | italic_e start_POSTSUPERSCRIPT - ( itali... | +∑i<j(e−(β−τ)Eie−τEj+e−(β−τ)Eje−τEi)|⟨i|Sz(𝐤)|j⟩|2)\displaystyle+\sum_{i<j}(e^{-(\beta-\tau)E_{i}}e^{-\tau E_{j}}+e^{-(\beta-\tau% | 1Z∑i,je−(β−τ)Eie−τEj|⟨i|Sz(𝐤)|j⟩|21𝑍subscript𝑖𝑗superscript𝑒𝛽𝜏subscript𝐸𝑖superscript𝑒𝜏subscript𝐸𝑗superscriptquantum-operator-product𝑖superscript𝑆𝑧𝐤𝑗2\displaystyle\frac{1}{Z}\sum_{i,j}e^{-(\beta-\tau)E_{i}}e^{-\tau E_{j}}|% | S0zz(𝐤)+1Z∑i<je−βEi|⟨i|Sz(𝐤)|j⟩|2(e−τΔEij+e−(β−τ)ΔEij)subscriptsuperscript𝑆𝑧𝑧0𝐤1𝑍subscript𝑖𝑗superscript𝑒𝛽subscript𝐸𝑖superscriptquantum-operator-product𝑖superscript𝑆𝑧𝐤𝑗2superscript𝑒𝜏Δsubscript𝐸𝑖𝑗superscript𝑒𝛽𝜏Δsubscript𝐸𝑖𝑗\displaystyle S^{zz}_{0}(\mathbf{k})+\frac{1}{Z}\sum_{i<j... | 1Z(∑ie−βEi|⟨i|Sz(𝐤)|i⟩|2\displaystyle\frac{1}{Z}(\sum_{i}e^{-\beta E_{i}}|\langle i|S^{z}(\mathbf{k})|% | B |
Note that other models describe non-standard diffusion, in particular, in terms of fractional derivatives (see [17], [18] for an exhaustive review and a detailed list of applications for which there is experimental evidence for the insufficiency of the usual Wiener process). For such models, in some cases, it is also p... | In the case of the density equation of the generalized Ornstein-Uhlenbeck process, more complex models can be considered, for example, with other jump distributions. However, it seems that with further modifications, it is impossible to obtain such results by practically elementary methods, as in this work. | The method we use can be generalized to the multidimensional case, including asymmetric diffusion. The method can also be modified for the case of anomalous diffusion by replacing the ΔΔ\Deltaroman_Δ operator with −−ΔΔ-\sqrt{-\Delta}- square-root start_ARG - roman_Δ end_ARG in the equation for the probability density (... | In this paper, a fundamental solution of the Kolmogorov-Feller equation is constructed for the case of a Laplacian distribution of jumps. In the general case, the fundamental solution can be written as a series; however, with a countable number of dependencies between the return force and the intensity of the jump proc... | It should be noted that fundamental solutions are known for various evolutionary integro-differential equations, including the density equation in the case of anomalous diffusion, for example, [14], [13]. As a rule, they have the form of an integral transform or can be written as a series of special functions, but with... | B |
Recent work proposed a quantum generative architecture that achieves non-linearity in the quantum state evolution using repeat-until-success (RUS) sub-routines containing mid-circuit measurements, similar to non-linear activations in a classical feed-forward network [gili_qnbm]. This work put forth a preliminary invest... | The deferred measurement principle states that an unconditioned qubit can be measured at any point in the computation and it’s probabilistic outcome will not change [Nielsen_Chuang_2010]. As the RUS non-linearity maps input qubits to the next layer of output qubits through a mid-circuit measurement protocol, it is poss... | In this work, we attempt to answer two follow-up questions to the insights revealed in Ref [gili_qnbm]. First, we look more closely as to whether introducing non-linearity into quantum circuits for generative modeling through RUS sub-routines makes the model efficiently classically simulatable. The RUS sub-routines int... | 3.1 Does the non-linearity make the learning model efficiently classically simulatable as a result of the deferred measurement principle? | In this work, we attempt to answer two follow-up questions about the utility of this particular kind of non-linearity:(1) Does the non-linearity make the learning model efficiently classically simulatable as a result of the deferred measurement principle of quantum mechanics [Nielsen_Chuang_2010]? This principle states... | D |
The IBIS data were analyzed with the software developed at the Space Research Institute of the Russian Academy of Sciences (see Krivonos et al., 2010, 2012, 2017; Churazov et al., 2014). We constructed the images of the cluster region in several bands from 20 to 120 keV based on the data from 2003 to 2009. The data set... | To determine whether the Ophiuchus cluster is a point or extended source for the IBIS telescope, we investigate the radial cluster flux profile. Figure 1 shows a map of the flux from the Ophiuchus cluster and the X-ray sources nearest to it in the 20–60 keV energy band. To construct the radial profile, we took into acc... | In this paper we presented the results of the observations of the Ophiuchus galaxy cluster with the IBIS telescope onboard the INTEGRAL observatory in a wide energy band, 20−1202012020-12020 - 120 keV, based on the observational data from 2003 to 2009. The source was shown to be an extended one in the hard X-ray band. | Figure 1: IBIS image of the Ophiuchus galaxy cluster region in the 20−60206020-6020 - 60 keV energy band (in mCrab). The yellow circles mark the positions of the known X-ray sources in the field of view, the circle size corresponds to the angular resolution of the telescope (12′). The red dashed circumference indicates... | The X-ray emission from the Ophiuchus galaxy cluster is known to be an extended one with a characteristic size of about 15 arcmin (Nevalainen et al., 2009; Werner et al., 2016), which is comparable to the angular resolution of the IBIS telescope (12 arcmin). Despite the fact that the coded-aperture telescopes are unabl... | D |
When we study our equations with the Ricci tensor, we observe the universe as a whole, but when we work with the extrinsic curvature tensor, we observe the universe as part of a whole; in both cases we consider the energy-momentum tensor as a perfect fluid, which already has the structure to also be treated as a scalar... | Subsection IV.3 deals with energy flows, where we mention that there are internal energy flows in the brane and because of this there can be geometric alterations both internal and external to the brane, in addition that there are external energy flows, all of this when working with extra dimensions and perturbations. | The equations seen in this section generally indicate how when the matter content inside the brane is altered, this implies an alteration in its normal vectors, having repercussions on the bulk. One of the most important repercussions when talking about extra dimensions is knowing if there is an energy flow, the (τ,i)�... | In that same line of thought and looking for a formulation of perturbations in extra dimensions, we present a development of perturbations for branes where we start from evolutionary equations and in where the geometry of space-time is determined by the extrinsic curvature tensor. We have that the bulk where the branes... | Another example where we could apply the equations that we developed is in the perturbations that are generated in the neighborhood of black holes. We can model this by imagining that the black hole is covered by a ”Gaussian Surface” that will be analogous to a brane with positive curvature, which could be located on t... | A |
For each disk type, we consider three values for the initial spin: a0=−1subscript𝑎01a_{0}=-1italic_a start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = - 1, a0=0subscript𝑎00a_{0}=0italic_a start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = 0, and a0=1subscript𝑎01a_{0}=1italic_a start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = 1. For any ini... | Whereas in low redshift AGN super-Eddington accretion episodes are rare, the conditions for super-Eddington accretion were favorable at higher redshifts (Aird et al., 2018). The gas content of early galaxies correlates with the accretion rate of the SMBH, implying that a BH will accrete above the Eddington rate given s... | For a given luminosity, the lower the BH mass, the less gas reservoir is needed to achieve the Eddington rate. It follows that high accretion rates will more likely be found in galaxies hosting low-mass SMBHs. Cosmological simulations from Anglés-Alcázar et al. (2017) showed that underweight BHs (those that lie below t... | Figure 2: Dimensionless spin a(m)𝑎𝑚a(m)italic_a ( italic_m ) and a(t)𝑎𝑡a(t)italic_a ( italic_t ) for different values of initial spin: a0=−1subscript𝑎01a_{0}=-1italic_a start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = - 1, 00, 1111. The lower x𝑥xitalic_x-axis gives the mass accreted over the initial BH mass: when m/M0... | We translate this timescale into physical units at the upper x𝑥xitalic_x-axis in Fig. 2. The Eddington accretion rate is given by | D |
This highly nontrivial theorem was proved by von Neumann in v1930algebra , with an English translation available in muraskin1995neumann . | Proofs of the spectral theorem in this form can be found in chapter 4 of douglas1998banach and chapter 12 of rudin1991functional , and further explanation of the algebraic framework for thinking about the spectral theorem is given in appendix A.2. | The third bullet point is nontrivial, and the proof is clever; a readable account is given as proposition 1.3 in chapter V.1 of takesaki2001theory . | This is straightforward to prove from the definitions, and an explicit proof can be found in the paragraph before proposition 1 in chapter I.1 of dixmier2011neumann . | It is given as exercise 3f in chapter I.7.3 of dixmier2011neumann , where some tips are given as to how it can be proved. | D |
Attractor-Merging Crises: Two or more chaotic attractors simultaneously collide with the stable manifold of an unstable periodic orbit along a shared boundary in the basin of attraction. The chaotic attractors then fuse together into one attractor. | where δ0subscript𝛿0\delta_{0}italic_δ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is a perturbation to an initial point of a trajectory and δ(t)𝛿𝑡\delta(t)italic_δ ( italic_t ) is the evolution of that perturbation under the linearized dynamics. In our model (3), the MLE is dictated by the chaotic Lorenz equations and ... | In their work Mehra and Ramaswamy use variations in the maximal Lyapunov exponent (MLE) as a guide as to whether an interior or attractor-merging crisis is likely to occur. The MLE is defined to be | Our experiments in which we forced the Stommel model with other strange attractors enable us to draw some conclusions as to the possible generality of our findings. We can replicate the approach of the first Stommel FTLE to the neutral strange attractor FTLE around critical transition times. The observations regarding ... | The behaviour depicted in Figure 2 is particularly interesting when viewed from a finite-time standpoint. While the asymptotic behaviour after the crisis is that of convergence to the TH attractor, the system spends a long period of time elsewhere in phase space tracing the previously existing SA attractor. If this pro... | B |
Finally, we anticipate that the class of matrices introduced in this article, possibly with some modification, by participating into the local pentagon equation [13, 56], could determine novel hexagon maps i.e. maps that satisfy the hexagon equation [57]. | Pentagon maps appeared in the context of Roger’s dilogarithm [21, 22] and are also related to the closure relation of the Lagrangian multiform theory in the setting of discrete integrable systems [23, 24], as well as to cluster algebras [25, 26]. For further connections and interrelations of the pentagon equation and m... | pentagon, higher polygon and simplex equations. Furthermore the author is thankful to Andrew Hone for the invitation and host at the University of Kent, where part of these studies were initiated by the support of London Mathematical Society LMS grant ref. 42110 and by additional funding from the University of Kent. | where the superscript (T)𝑇(T)( italic_T ) stands for the transpose of a matrix, turns equivalent to the reverse-pentagon map | The author would like to thank Igor G. Korepanov for the motivation to initiate with these studies and for the many valuable discussions on | D |
In [123], interesting mathematical relations are further found between the NHSE, knot theory and spectral winding topology in the context of 3D exceptional metals. In the later half of this article, we also review how the NHSE can non-perturbatively modify state dynamics as well as signatures of criticality, in both si... | Beyond significantly modifying the band structure and topology of a system, the NHSE also introduces a new length scale, the skin decay length κ−1superscript𝜅1\kappa^{-1}italic_κ start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT. This extra degree of freedom nontrivially affects the behavior of critical systems, as we wil... | We also note that while this review will mainly focus on theoretical aspects, we will devote the last section to reviewing experimental demonstrations and proposals of NHSE-related phenomena. | While the NHSE has aleady been observed in a select set of experiments, there are many other proposals for future experimental demonstration in a variety of physical platforms. Below, we briefly review some existing proposals, each suited for realizing different NHSE-related phenomena. We would omit an explicit discuss... | Ever since its discovery, tremendous progress has been made in various aspects of NHSE that differ drastically from Hermitian systems, which we will review at length in this article. To mention a few examples, essentially being a one-dimensional (1D) directional phenomenon, NHSE is responsible for several unidirectiona... | B |
We acknowledge conversations with Johannes Hauschild, Xiao-Yu Dong, Hui-Ke Jin and Hong-Hao Tu. The MPS calculations were performed using the TeNPy Library (version 0.9.0) [48]. L.M.C. and P.Y. were supported by NSFC Grant No. 12074438, Guangdong Basic and Applied Basic Research Foundation under Grant No. 2020B15151201... | We acknowledge conversations with Johannes Hauschild, Xiao-Yu Dong, Hui-Ke Jin and Hong-Hao Tu. The MPS calculations were performed using the TeNPy Library (version 0.9.0) [48]. L.M.C. and P.Y. were supported by NSFC Grant No. 12074438, Guangdong Basic and Applied Basic Research Foundation under Grant No. 2020B15151201... | In this work, we study the ℤ3subscriptℤ3\mathbb{Z}_{3}roman_ℤ start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT Kitaev model numerically using matrix product states to complement the symmetry considerations. Based on results on cylinder and strip geometries, we found evidences that the model at the ferromagnetic isotropic point ... | This work was also supported by the Fundamental Research Funds for Central Universities (22qntd3005). | Using the bulk-edge correspondence, the edge theory of this model would be given by a 1+1D chiral CFT with central charge equal to the chiral central charge of the topological order. This can be revealed by putting the system on a strip geometry, where the chiral and anti-chiral gapless modes at the two edges are weakl... | C |
Additionally, for depth-1-QAOA we can exploit the parameter estimate (37) which renders parameter optimization unnecessary. | In this work, we derive a different formula for weighted MaxCut by extending a result on unweighted MaxCut from [56] and [64]. | Figure 4: Visualized results for QAOA parameter-estimate on instances a, b and c from Fig. 3. The x- and y-axis represent values of the parameters β𝛽\betaitalic_β and γ𝛾\gammaitalic_γ, respectively. The red cross marks the estimate in (37). The color encodes the expectation value (left) or the average (right) of the ... | As a performance metric, we measure the average value of the produced cut size on different weighted MaxCut instances. | The authors of [57] derive an analytical expressions for the expectation value produced by depth-1 QAOA on general Ising models, which includes weighted MaxCut. | C |
ωx/ωysubscript𝜔𝑥subscript𝜔𝑦\omega_{x}/\omega_{y}italic_ω start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT / italic_ω start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT, weak magnetic fields, or variation in the strengths of the SOCs. | the strengths of the Rashba and Dresselhaus SOCs are g1subscript𝑔1g_{1}italic_g start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and | W.L. acknowledges Chao Hang and Yu Zhou for helpful discussions. This work is supported by the NSF-China under Grant Nos. 11804396. We are grateful to the High Performance Computing Center of Central South University for partial support of this work. | Colors represent for the density of the electron, n(𝐫)𝑛𝐫n(\mathbf{r})italic_n ( bold_r ). (a) The quantum | stands for σz(𝐫)subscript𝜎𝑧𝐫\sigma_{z}(\mathbf{r})italic_σ start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT ( bold_r ) and the arrows for the in-plane spin fields | B |
}^{*}}{2}\right)^{\beta\alpha}.- divide start_ARG italic_i italic_g start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_C start_POSTSUBSCRIPT italic_F end_POSTSUBSCRIPT italic_δ start_POSTSUPERSCRIPT italic_b italic_a end_POSTSUPERSCRIPT end_ARG start_ARG square-root start_... | A(c),Feynmanmod(ℓ−)superscriptsubscript𝐴(c),Feynmanmodsuperscriptℓ\displaystyle A_{\textrm{(c),Feynman}}^{\textrm{mod}}(\ell^{-})italic_A start_POSTSUBSCRIPT (c),Feynman end_POSTSUBSCRIPT start_POSTSUPERSCRIPT mod end_POSTSUPERSCRIPT ( roman_ℓ start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT ) | A(a),Feynmanmod(ℓ−)superscriptsubscript𝐴(a),Feynmanmodsuperscriptℓ\displaystyle A_{\textrm{(a),Feynman}}^{\textrm{mod}}(\ell^{-})italic_A start_POSTSUBSCRIPT (a),Feynman end_POSTSUBSCRIPT start_POSTSUPERSCRIPT mod end_POSTSUPERSCRIPT ( roman_ℓ start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT ) | A(a),Feynmanmod(ℓ−)+A(c),Feynmanmod(ℓ−)superscriptsubscript𝐴(a),Feynmanmodsuperscriptℓsuperscriptsubscript𝐴(c),Feynmanmodsuperscriptℓ\displaystyle A_{\textrm{(a),Feynman}}^{\textrm{mod}}(\ell^{-})+A_{\textrm{(c)% | A(c),Feynmanmod(ℓ−)=A(c),Feynman(ℓ−)superscriptsubscript𝐴(c),Feynmanmodsuperscriptℓsubscript𝐴(c),FeynmansuperscriptℓA_{\textrm{(c),Feynman}}^{\textrm{mod}}(\ell^{-})=A_{\textrm{(c),Feynman}}(% | D |
_{m,C}^{2})italic_V ( bold_x start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ) ∣ italic_Z start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT = italic_m ∼ caligraphic_M start_POSTSUBSCRIPT roman_Σ start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT end_POSTSUBSCRIPT = caligraphic_N ( 0 , italic_σ start_POSTSUBSCRIPT italic_m , it... | Recently, Li et al. (2022) developed a log-Gaussian Cox process (LGCP; Møller et al., 1998) to detect UDGs via the spatial clustering signals of their associated globular clusters (GCs). Globular clusters are compact, spherical collections of hundreds of thousands of stars, and are easily detected, even at large distan... | Ultra-diffuse galaxies (UDGs) are a class of extremely faint galaxies first found in abundance by van Dokkum et al. (2015). UDGs have garnered significant attention due to their peculiar nature: despite their faintness, their sizes and masses are comparable to luminous galaxies like the Milky Way (van Dokkum et al., 20... | The priors and hyper-priors for our model parameters and hyperparameters are listed in 1. We also provide the physically meaningful parameter space for these parameters. The choice of priors and hyper-prior is based on extensive previous astrophysical research (e.g. van Dokkum et al., 2017; Burkert, 2017; Forbes, 2017;... | Table 1: Prior and hyper-prior for our model components. The last column provides the reasoning for choosing such a prior. LN stands for log-normal. See the Section 4 of the Supplementary Material for detailed explanation and references. | C |
A strong spike of negative label points lying below the PRF=0.300subscript𝑃𝑅𝐹0.300P_{RF}=0.300italic_P start_POSTSUBSCRIPT italic_R italic_F end_POSTSUBSCRIPT = 0.300 threshold is present at periods 13−15131513-1513 - 15 days. This arises from the TESS satellite 13.7 day lunar-synchronous orbital period with a larg... | The tendency of TCF to identify much shorter periods than the injected period for injected planetary signals was not expected. This the cloud of gray points in the lower-right of Figure 15. Just over half of the 10,850 synthetic injected planetary transit signals were assigned periods <1absent1<1< 1 day by the TCF algo... | But for periods shorter than 0.50.50.50.5 day, DTARPS-S has only moderate recovery of DIAmante candidates. This is likely due to concentration of injected False Positives with TCF periods in this region and TCF radii consistent with planetary objects (Figure 16) that bias the classifier against short period planet tran... | The recall rate of the injected planetary signals across the range of the injected period and radii can quantitatively measure the ability of the RF classifier to recover planets in the DIAmante data set. It is important to understand how the classifier performs across the planetary radius-period distribution to evalua... | In contrast, although the injected exoplanet periods do not go shorter than 0.625 days (because the injections were based on Kepler planets based on a transit search truncated below 0.5 days), the optimized RF classifier does not appear strongly biased against short period transit signals. This is seen by the recovery ... | D |
This procedure has advantages of uniformity and objectivity. Once various analysis parameters and thresholds were chosen, the ∼1similar-toabsent1\sim 1∼ 1 million stars are processed in identical fashion without human judgment. The DTARPS-S Analysis List can thus be viewed as well-defined and ‘complete’; for instance, ... | Of the 7,377 DTARPS-S Analysis List objects that exceeded the Random Forest classifier threshold in Paper I, the 462 cases that pass the vetting tests in §2 are listed in Table 1. These are designated DTARPS-S Candidates and represent the principal result of this paper. Notes on previous published information on indivi... | In order to evaluate these restrictions on the DTARPS-S Candidate sample, we processed a sample of ∼similar-to\sim∼1,800 DTARPS-S Analysis List objects through every stage of the vetting process except centroid-crowding analysis. This sample has Galactic longitudes from 193−236193236193-236193 - 236 and latitudes mostl... | Our vetting procedure described in §2 reduces the list 7,377 promising cases nearly 10-fold, giving lists of 772 stars likely to be hosting short-period exoplanets: 462 in the spatially complete DTARPS-S Candidate catalog (Table 1) and 310 in the spatially incomplete DTARPS Galactic Plane List (Table 4). But the vettin... | We emerge here with a sample of 462 light curves that satisfy all of our vetting tests, and an additional 310 light curves from Galactic Plane targets that satisfy most of the vetting tests. We report the 462 stars as the DTARPS-S Candidate Catalog and the 310 stars as the DTARPS-S Galactic Plane list. Of these 772 sta... | C |
\bf{F}}_{i}\cdot{\bf{F}}_{j})_{m,b,t}\rangle=-\frac{4}{3}.⟨ ( bold_F start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ⋅ bold_F start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT ) start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT ⟩ = - divide start_ARG 2 end_ARG start_ARG 3 end_ARG , ⟨ ( bold_F start_POSTSUBSCRIPT italic_i end_... | We apply two newly proposed Regge trajectory relations (8) along with (12) and (14) along with (15) to analyze the heavy-light systems, presenting the numerical plots for clarity. We find that the heavy-light diquarks, the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks satisfy these two for... | the heavy-light diquarks can be well described by (8) with (12) and (14) with (15). The spectra of the heavy-light diquarks | In Ref. Chen:2023cws, we present the heavy-light diquark Regge trajectories. The proposed Regge trajectory relations can universally describe the heavy-light mesons and the heavy-light diquarks. | From Eqs. (1) and (3), we see that the heavy-light diquarks, the heavy-light mesons, the heavy-light baryons, and the heavy-light tetraquarks are described in an unified approach Ferretti:2019zyh; Bedolla:2019zwg. Therefore, it is expected that these heavy-light systems can be described universally by the Regge traject... | D |
The right panel of Fig. 6 compares these results (in blue) to the results obtained in Ref. [5] using the strongly parameterized power-law model for the black hole merger rate. | Our autoregressive result, however, suggests that this growth may not be well modeled by a power law but instead by a slowly growing or constant merger rate that begins to evolve more sharply only beyond z≳0.4greater-than-or-equivalent-to𝑧0.4z\gtrsim 0.4italic_z ≳ 0.4. | We see that both approaches recover similar merger rates at z≈0.3𝑧0.3z\approx 0.3italic_z ≈ 0.3 and z≈1𝑧1z\approx 1italic_z ≈ 1, and both indicate that the black hole merger rate systematically grows with redshift. | Both approaches yield consistent estimates of the merger rate at z≈0.3𝑧0.3z\approx 0.3italic_z ≈ 0.3 and z≈1𝑧1z\approx 1italic_z ≈ 1, but our autoregressive result suggests that the intervening evolution is not necessarily well modeled by a power law. | That work also recovered a largely constant merger rate density below z≈0.4𝑧0.4z\approx 0.4italic_z ≈ 0.4, followed by a steeper increase in the merger rate out to z≈1𝑧1z\approx 1italic_z ≈ 1; see their Fig. 8. | C |
I thank Matt McEwen for extensive discussions on the construction, and for encouragement to continue improving upon earlier versions of the circuit. | I thank Austin Fowler for writing the correlated minimum weight perfect matching decoder used by this paper. | I thank Austin Fowler, Alexis Morvan, Mike Newman, and Kevin Satzinger for giving feedback that improved the paper. | I thank Ben Brown and Cody Jones for discussions about S gates and |i⟩ket𝑖|i\rangle| italic_i ⟩ states that inspired the ideas that eventually turned into the Y basis measurement presented in this paper. | Decoding was done using an internal correlated minimum weight perfect matching decoder written by Austin Fowler. | A |
Two Pauli operators P(u),P(v)∈𝒫n𝑃𝑢𝑃𝑣subscript𝒫𝑛P(u),P(v)\in\mathcal{P}_{n}italic_P ( italic_u ) , italic_P ( italic_v ) ∈ caligraphic_P start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT are said to commute if and only if ⟦P(u),P(v)⟧d=0subscript𝑃𝑢𝑃𝑣𝑑0\llbracket P(u),P(v)\rrbracket_{d}=0⟦ italic_P ( italic_u... | We now introduce some key definitions that underlies much of our results. First, in Section 3, we determine the maximum size of collections of non-commuting pairs. | Non-commuting pairs. We say Paulis s0,…,sk−1subscript𝑠0…subscript𝑠𝑘1s_{0},\dots,s_{k-1}italic_s start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , … , italic_s start_POSTSUBSCRIPT italic_k - 1 end_POSTSUBSCRIPT and t0,…,tk−1subscript𝑡0…subscript𝑡𝑘1t_{0},\dots,t_{k-1}italic_t start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , … , i... | We now show that nm𝑛𝑚nmitalic_n italic_m is also the upper bound. The key result that underlies the proof is the following number-theoretic obstruction: | We will show in Section 4 that h=Ψ(d)≥d+1ℎΨ𝑑𝑑1h=\Psi(d)\geq d+1italic_h = roman_Ψ ( italic_d ) ≥ italic_d + 1 is the maximum size non-commuting set on a single qudit, where ΨΨ\Psiroman_Ψ is the Dedekind Psi function from number theory. The situation of non-commuting sets on more than one qudit is complicated, and we... | A |
λ±=1+NM±2NM.subscript𝜆plus-or-minusplus-or-minus1𝑁𝑀2𝑁𝑀\lambda_{\pm}=1+\frac{N}{M}\pm 2\sqrt{\frac{N}{M}}.italic_λ start_POSTSUBSCRIPT ± end_POSTSUBSCRIPT = 1 + divide start_ARG italic_N end_ARG start_ARG italic_M end_ARG ± 2 square-root start_ARG divide start_ARG italic_N end_ARG start_ARG italic_M end_ARG end_AR... | spectra of the Potts model. Significantly, these results highlight the versatility of the proposed methodology, | matrices of the N=L2𝑁superscript𝐿2N=L^{2}italic_N = italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT spins of the Ising model in the two-dimensional | exactly in the same conditions that we used to obtain the eigenvalues of 𝒢𝒢\mathcal{G}caligraphic_G. The results are summarized and reported in Figs. 11, 12, and 13. | In an exciting application of random matrices the authors in [26, 27, 28], and simultaneously and independently in [29, 30] using the results developed by Marcenko and Pastur [17, 31], showed that deviations from the bulk of spectra of | D |
The CLIC is a potential future collider that stands out due to its ability to test new physics scenarios through high-energy e−e+superscript𝑒superscript𝑒e^{-}e^{+}italic_e start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT italic_e start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT collisions in a clean experimental environment w... | The LHC offers exciting possibilities for new discoveries and important insights at high-energy scale. However, it is widely recognized that linear colliders, with their clean experimental conditions, are the ideal environment for exploring new physics beyond the SM. The ability to use polarized electron beams in linea... | On the other hand, CLIC experiment program provides an opportunity for ±%80\pm\%80± % 80 polarized electron beams and no positron polarization at the center-of-mass energy of 3 TeV with the integrated luminosity of 1 ab-1 and 4 ab-1, respectively. Here, polarized electron beams can play a crucial role in increasing the... | The CLIC is a potential future collider that stands out due to its ability to test new physics scenarios through high-energy e−e+superscript𝑒superscript𝑒e^{-}e^{+}italic_e start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT italic_e start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT collisions in a clean experimental environment w... | The final state ℓℓννℓℓ𝜈𝜈\ell\ell\nu\nuroman_ℓ roman_ℓ italic_ν italic_ν of the process e+e−→ZZ→superscript𝑒superscript𝑒𝑍𝑍e^{+}e^{-}\rightarrow ZZitalic_e start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT italic_e start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT → italic_Z italic_Z consists of a pair of charged leptons ... | B |
We simulated diffraction of 3,5,7,9,11 harmonics of data from MNIST database extended as a 128×128128128128\times 128128 × 128 image as shown in Fig 3(a) and (b). | The second step, both reference and sample are exposed to the beam. The pattern is recorded to reconstruct complex and fine structured sample. Using the information measured in the first step, by applying cross correlation constrain, fourier magnitude constrain and support constrain in sequence the image is reconstruct... | The reconstructed image with 1000 RAAR iterations and shrinking wrap each 20 iteration is shown in Fig 3(d). | The oversampling of λ=1𝜆1\lambda=1italic_λ = 1 is 2. The same recipes as Fig. 3(b-d) is shown in Fig 4(b-d). | The first step is referenced pattern zooming. Since most of the time, the reference is designed to be real and without fine structures, so it is easily reconstruced with conventional CDI algorithm such as HIO. In this step, we are able to measure slowly and precisely, meaning repeated measurement is possible to increas... | B |
(B) In the ‘Remove least-employees firms first’ strategy, firms are closed according to their ascending numbers of employees. | To empirically test our framework, we approximate hypothetical decarbonization efforts with the removal of firms from the Hungarian production network. A firm that is removed from the production network no longer supplies its customers nor does it place demand to its (former) suppliers in the subsequent time step. It a... | This leads to a very slowly increasing expected job and output loss, but 107 firms need to be closed to reach the benchmark. | This results in only a gradual increase of expected job and output loss in the beginning, but fails to anticipate the effects of a systemically very important firm which triggers widespread job and output losses. 102 firms need to be closed in this strategy to reach the benchmark. | The ‘Remove least-employees firms first’ strategy that aims at minimizing job loss at each individual firm, shown in Fig. 3B manages to keep expected job and output loss at low levels for the initially removed firms. But since this strategy focuses on job loss at the individual firm level, it fails to anticipate a high... | C |
}A}.italic_η start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_x italic_x italic_x end_POSTSUPERSCRIPT ∼ 10 start_POSTSUPERSCRIPT - 3 end_POSTSUPERSCRIPT µ roman_m start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / µ roman_A . | To estimate NHE in the fluctuation regime, let us consider ϵ∗subscriptitalic-ϵ\epsilon_{*}italic_ϵ start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT defined by | Let us first consider the rectification in the x𝑥xitalic_x direction, which is perpendicular to the magnetic field. | To estimate the rectification in the fluctuation regime, let us consider the reduced temperature ϵ∗subscriptitalic-ϵ\epsilon_{*}italic_ϵ start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT defined by | To see this, let us consider the electric current in the x𝑥xitalic_x direction for the Rashba system. | A |
Advanced computational methods of data analysis [70, 71] could extend the investigation including other parameters, such as the static bias. | The space of the parameters could be enlarged by optimizing both design and protocol. Optimal design could be systematically searched for by using the recipe of §III.1. | Finally, we observe that more elaborated measurement schemes allow faithful detection in ”borderline” regions of the space of parameters. | The specific question we ask is whether it is possible to overcome experimental challenges posed by available quantum hardware. This work shows that the answer is positive but not trivial. Indeed detecting VPs in an efficient and faithful way requires combining state-of-the-art technologies, such as a multilevel AA unc... | Faster protocols may be found by optimal control theory [koch2022quantum] also exploiting multipod transitions and integrated measurement. Measurement schemes with post-selection could allow the handling of multilevel systems with more complicated spectra. | D |
However, for rotating Q-balls Volkov:2002aj ; Campanelli:2009su ; Arodz:2009ye ; Shnir:2011gr ; Nugaev:2014iva ; Loiko:2018mhb (and the closely related boson stars Silveira:1995dh ; Kleihaus:2005me ; Kleihaus:2007vk ; Kleihaus:2011sx ; Liebling:2012fv ; Davidson:2016uok ; Herdeiro:2019mbz ; Collodel:2019ohy ; Delgado:... | This equation can be shown to have a solution when ω0<ω<mϕsubscript𝜔0𝜔subscript𝑚italic-ϕ\omega_{0}<\omega<m_{\phi}italic_ω start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT < italic_ω < italic_m start_POSTSUBSCRIPT italic_ϕ end_POSTSUBSCRIPT Coleman:1985ki . One way to see that the solutions are localized is to consider the l... | The first term in the energy scales like the volume of the Q-ball, while the second scales like the surface area and so is typically subleading for large Q-balls. | Naturally, the angular momentum is quantized in the quantum theory, but even so, one would expect that it should be possible to place a small number of particles in a state of nonzero angular momentum, so that the angular momentum of the Q-ball | This is, in fact, a puzzling scenario since one might expect that a large classical object like a Q-ball | D |
With increasing ω𝜔\omegaitalic_ω, λcsubscript𝜆𝑐\lambda_{c}italic_λ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT decreases towards an asymptotic value where the aqueous suspension and the density-matched suspension match. The measured λcsubscript𝜆𝑐\lambda_{c}italic_λ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT... | fraction, ϕitalic-ϕ\phiitalic_ϕ, can be calculated. An example is given in Fig. 1g-h, where both hℎhitalic_h and ϕitalic-ϕ\phiitalic_ϕ are measured. | Once the disturbance arises and grows in the flow direction, secondary instabilities may further develop [28, 41], and two-dimensional structures form [42]. In our experiments, the density waves self-organize into a hexagonal pattern as f𝑓fitalic_f increases (cf. Fig. 1 and 4 Inset). A comprehensive theoretical analys... | As reported by Oyarte Gálvez et al. [26], the interaction force profile shows a hysteresis when corn starch particles are pressed into contact. However, the inhomogeneity transition here is reversible, which implies that the dense regions in our experiments are not permanent aggregates of contacting particles. To revea... | Nevertheless, as seen in Fig. 1g, the local density, ϕitalic-ϕ\phiitalic_ϕ, can be as high as 0.449 for the developed density waves, leading to viscosity proliferation locally. | D |
Furthermore, since the estimation of the population of GW sources depends on the third power of the source distance, calibration uncertainties are also translated into uncertainties in the population estimation. [10, 11, 12] | The Pcal can give a modulation the mirror surface with photon pressure. In the joint observation run 3 (2020 April) with KAGRA and GEO600 (O3GK), [15, 6, 8, 16] KAGRA employs the photon calibrator as a primary calibrator. The summary of the calibration overview in O3GK is described in the summary paper. [8] The initial... | The development of new photon calibrator is expected to extend for the possibility of new technologies. In previous study, the laser power of photon calibrator in LIGO and Virgo are 2W and 3W, respectively. In this development, we achieve to increase the maximum power to be 20W. LIGO and Virgo have used photon calibrat... | Calibration uncertainties also affect coordinate reconstruction, particularly in the case that only up to three detectors in the worldwide GW detector network can detect the GW signal. This phenomenon often occurs because the sensitivity of the interferometer has directional dependence. The effect of calibration uncert... | Calibration uncertainties are directly translated to the errors in the absolute GW signal. The primary impact of calibration uncertainties on the parameters appears to be in the determination of the distance to the source. | C |
For each k=0,…,N𝑘0…𝑁k=0,\dots,Nitalic_k = 0 , … , italic_N, u|(xk,xk+1)∈H2(xk,xk+1)evaluated-at𝑢subscript𝑥𝑘subscript𝑥𝑘1superscript𝐻2subscript𝑥𝑘subscript𝑥𝑘1u|_{(x_{k},x_{k+1})}\in H^{2}(x_{k},x_{k+1})italic_u | start_POSTSUBSCRIPT ( italic_x start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT , italic_x start_PO... | until the points xksubscript𝑥𝑘x_{k}italic_x start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT are exhausted, we arrive at the solution w≡0𝑤0w\equiv 0italic_w ≡ 0 | The discontinuities of the derivative u′superscript𝑢′u^{\prime}italic_u start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT are located at the | Indeed, gf∈C[0,b]𝑔𝑓𝐶0𝑏\frac{g}{f}\in C[0,b]divide start_ARG italic_g end_ARG start_ARG italic_f end_ARG ∈ italic_C [ 0 , italic_b ], and the jump of the derivative at xksubscript𝑥𝑘x_{k}italic_x start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT is given by | The derivative (eℑNh)′(ρ,x)superscriptsuperscriptsubscript𝑒subscriptℑ𝑁ℎ′𝜌𝑥(e_{\mathfrak{I}_{N}}^{h})^{\prime}(\rho,x)( italic_e start_POSTSUBSCRIPT fraktur_I start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_h end_POSTSUPERSCRIPT ) start_POSTSUPERSCRIPT ′ end_POSTSUPERSC... | B |
To achieve this, we generate optimal quantum circuits that implement the steering operator, and experimentally reconstruct the density states via quantum state tomography to obtain the fidelity. | (a) Average fidelity of preparing stabilizer states versus the number of repetitions N𝑁Nitalic_N with different coupling strengths J𝐽Jitalic_J. For certains values of J𝐽Jitalic_J, the fidelity decreases at first before increasing. | Figure 10 takes that average number of repetitions (application of ancilla-system entanglement operation in Figure 2a) needed to obtain a fidelity ℱ>0.9ℱ0.9\mathcal{F}>0.9caligraphic_F > 0.9 and compares it against the active steering approach. Note that we end the protocol once the readout of the ancilla is a 1111. Ea... | We demonstrate that by utilizing the programmability of a digital quantum processor, arbitrary quantum state can be prepared via a simple protocol of repeatedly executing the same small set of quantum gates. The success of the protocol – achieving high state initialization fidelity – depends primarily on the fidelity o... | We explored the dependence of a tunable parameter that relates fidelity convergence with the number of repetitions of the protocol. | D |
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