robench-2024b
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Table 2: Oscillation amplitudes of a neutrino with different projected energies with assumed mass m=2eV𝑚2𝑒𝑉m=2eVitalic_m = 2 italic_e italic_V. | 2.3×10−102.3superscript10102.3\times 10^{-10}2.3 × 10 start_POSTSUPERSCRIPT - 10 end_POSTSUPERSCRIPT | Let us consider an electron (ω0=7.6×1020s−1subscript𝜔07.6superscript1020superscript𝑠1\omega_{0}=7.6\times 10^{20}s^{-1}italic_ω start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = 7.6 × 10 start_POSTSUPERSCRIPT 20 end_POSTSUPERSCRIPT italic_s start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT), the lightest elementary particle apa... | 7.4×10−127.4superscript10127.4\times 10^{-12}7.4 × 10 start_POSTSUPERSCRIPT - 12 end_POSTSUPERSCRIPT | 4.0×10−234.0superscript10234.0\times 10^{-23}4.0 × 10 start_POSTSUPERSCRIPT - 23 end_POSTSUPERSCRIPT | C |
In addition we observe a number of further states for which likely assignments are shown in the figure. In particular we find two spin 3 F-wave states and another set of excited S-waves. | In addition we observe a number of further states for which likely assignments are shown in the figure. In particular we find two spin 3 F-wave states and another set of excited S-waves. | The results are listed in Table 5. In addition we take a look at the hyperfine splittings between spin-singlet and spin-triplet states | As a check, the kinetic masses for spin-averaged S-wave D𝐷Ditalic_D and Dssubscript𝐷𝑠D_{s}italic_D start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT mesons were also calculated. At our final choice κc=0.123subscript𝜅𝑐0.123\kappa_{c}=0.123italic_κ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = 0.123 the tuned kineti... | To disentangle spin-dependent from spin-independent contributions we further define spin-averaged masses | D |
))=f^{2}(t(r))g_{S}(\beta(r))\left(E_{k}(\beta(r)),\beta^{\prime}(r)\right).( ⟨ over¯ start_ARG italic_E end_ARG start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT , italic_V ⟩ start_POSTSUBSCRIPT italic_M ( italic_x , italic_f ) end_POSTSUBSCRIPT ∘ roman_θ start_POSTSUPERSCRIPT italic_V end_POSTSUPERSCRIPT ( italic_r ) ) ... | (w,z)∈(h,k)⟨β,β′⟩𝑤𝑧ℎ𝑘𝛽superscript𝛽′(w,z)\in(h,k)\langle\,\beta,\,\beta^{\prime}\,\rangle( italic_w , italic_z ) ∈ ( italic_h , italic_k ) ⟨ italic_β , italic_β start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ⟩. | of the velocity β′superscript𝛽′\beta^{\prime}italic_β start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT of the projection β=σ∘α𝛽𝜎𝛼\beta=\sigma\circ\alphaitalic_β = italic_σ ∘ italic_α. | Now we can use [20, Prp. 12.22(2)] to express β′superscript𝛽′\beta^{\prime}italic_β start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT | β′superscript𝛽′\beta^{\prime}italic_β start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT from the velocity α′superscript𝛼′\alpha^{\prime}italic_α start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT | C |
At present, not all processes of photon production in QGP and HG phase are amenable to a calculation of viscous (shear and bulk) corrections. | At present, not all processes of photon production in QGP and HG phase are amenable to a calculation of viscous (shear and bulk) corrections. | Take into account of the uncertainty of the system evolution, we ignored the viscous correction to the emission rate, which seems to work well in general. The calculated ptsubscript𝑝tp_{\rm t}italic_p start_POSTSUBSCRIPT roman_t end_POSTSUBSCRIPT spectra of direct photons from both initial conditions agree quite well ... | The elliptic flow v2subscript𝑣2v_{2}italic_v start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT of direct photons for all three centralities in this calculation coincide with experimental data! | For example, the AMY rate covers the processes of all orders according to the hard thermal loop calculation AMY , | D |
Note that the operators N^σsubscript^𝑁𝜎\hat{N}_{\sigma}over^ start_ARG italic_N end_ARG start_POSTSUBSCRIPT italic_σ end_POSTSUBSCRIPT are defined very differently to a common definition of a sum over occupations ∑ia^σi†a^σisubscript𝑖subscriptsuperscript^𝑎†𝜎𝑖subscript^𝑎𝜎𝑖\sum_{i}\hat{a}^{\dagger}_{\sigma i}... | In this article, we have studied the dynamical properties of two ultra-cold bosons confined in a one-dimensional double-well potential initially occupying the lowest state of a chosen site. We compare the exact dynamics governed by a full two-body Hamiltonian with two simplified two-mode models. In particular, we compa... | To study the dynamical properties of the system we assume that initially two bosons occupy the lowest state of a chosen (left) site of the double-well potential | Inspired by this simple observation, in this article we study the dynamical properties of two bosons confined in a one-dimensional double-well potential and initially occupying a chosen site. We numerically compare the exact, many-body dynamics of the system with the dynamics governed by simplified two-mode Hamiltonian... | This illusory conviction that a complete two-mode Hamiltonian (4) is sufficient to describe the dynamical properties of the system in the strong interaction limit has to be revisited when, instead of densities, inter-particle correlations are considered. For example, let us consider one of the simplest correlations – t... | B |
λc±=12(γ±γ2+4(σ+ζ))superscriptsubscript𝜆𝑐plus-or-minus12plus-or-minus𝛾superscript𝛾24𝜎𝜁\lambda_{c}^{\pm}=\frac{1}{2}\left(\gamma\pm\sqrt{\gamma^{2}+4(\sigma+\zeta)}\right)italic_λ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ± end_POSTSUPERSCRIPT = divide start_ARG 1 end_ARG start_ARG 2 e... | ζ>γ24𝜁superscript𝛾24\zeta>\frac{\gamma^{2}}{4}italic_ζ > divide start_ARG italic_γ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG start_ARG 4 end_ARG | Expanding (γ2−4ζ>0superscript𝛾24𝜁0\gamma^{2}-4\zeta>0italic_γ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT - 4 italic_ζ > 0) | Expanding (γ2−4ζ<0superscript𝛾24𝜁0\gamma^{2}-4\zeta<0italic_γ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT - 4 italic_ζ < 0) | γ2<4ζsuperscript𝛾24𝜁\gamma^{2}<4\zetaitalic_γ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT < 4 italic_ζ, the expanding eigenvalues λeR±iλeIplus-or-minussuperscriptsubscript𝜆𝑒𝑅𝑖superscriptsubscript𝜆𝑒𝐼\lambda_{e}^{R}\pm{i}\lambda_{e}^{I}italic_λ start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT start_POSTSUPERSCRI... | B |
LagoudakisNphys2008 ; RoumposNphys2011 ; NardinNphys2011 ; SanvittoNphot2011 ; DominiciSA2015 ; BoulierPRL2016 ; caputo2016topological ; caputo2019josephson | and f1subscript𝑓1f_{1}italic_f start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT is the spin-conserved and spin-exchange polariton-polariton | and f2subscript𝑓2f_{2}italic_f start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT are the same-spin and cross-spin nonradiative loss rates, respectively. | σ=±𝜎plus-or-minus\sigma=\pmitalic_σ = ± representing the spin state of polaritons with effective mass | In the absence of external magnetic field the “spin-up” and “spin-down” states σ=±𝜎plus-or-minus\sigma=\pmitalic_σ = ± of noninteracting polaritons, or their linearly | D |
Let {a,b,γ,δ}𝑎𝑏𝛾𝛿\{a,b,\gamma,\delta\}{ italic_a , italic_b , italic_γ , italic_δ } be an unbroken coupled SUSY, ℒℒ\mathcal{L}caligraphic_L and 𝒜𝒜\mathcal{A}caligraphic_A be as above, and, also as above, kera={ψi,0:i∈I}kernel𝑎conditional-setsubscript𝜓𝑖0𝑖𝐼\ker a=\{\psi_{i,0}:i\in I\}roman_ker italic_a = { it... | Let ψ𝜓\psiitalic_ψ be a normalized wavefunction. Note that Robertson’s uncertainty relation gives us that | That ℋ2=ℋ1+1subscriptℋ2subscriptℋ11\mathcal{H}_{2}=\mathcal{H}_{1}+1caligraphic_H start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = caligraphic_H start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT + 1 is a restatement of the commutation relation for a𝑎aitalic_a and a∗superscript𝑎a^{*}italic_a start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT... | The canonical uncertainty principle in quantum mechanics is the Heisenberg uncertainty principle which is an uncertainty principle between the position operator x𝑥xitalic_x and the momentum operator p𝑝pitalic_p. The Heisenberg uncertainty principle says that, in natural units, the standard deviation in | Let Ψ=(ψ1,ψ2)TΨsuperscriptsubscript𝜓1subscript𝜓2T\Psi=(\psi_{1},\psi_{2})^{\operatorname{T}}roman_Ψ = ( italic_ψ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , italic_ψ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT roman_T end_POSTSUPERSCRIPT be the state in which we are evaluating the expectation, then ... | A |
\frac{2}{3}v(t)\>\>.italic_w ( italic_t ) = divide start_ARG 1 end_ARG start_ARG 4 italic_π end_ARG ∫ start_POSTSUBSCRIPT italic_S start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_POSTSUBSCRIPT | bold_v start_POSTSUBSCRIPT italic_e start_POSTSUPERSCRIPT ± end_POSTSUPERSCRIPT end_POSTSUBSCRIPT ( italic_t ) - divide start... | where t1≈70.000subscript𝑡170.000t_{1}\approx 70.000italic_t start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ≈ 70.000 a and V1=V0⋅(t1/t0)3/2>0subscript𝑉1⋅subscript𝑉0superscriptsubscript𝑡1subscript𝑡0320V_{1}=V_{0}\cdot(t_{1}/t_{0})^{3/2}>0italic_V start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = italic_V start_POSTSUBSCRIPT 0 end_... | ⪅t0⪅10less-than-or-approximately-equalsabsentsubscript𝑡0less-than-or-approximately-equals10\lessapprox t_{0}\lessapprox 10⪅ italic_t start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ⪅ 10 s for the initial value of time and | ⪅t⪅1.38×1010less-than-or-approximately-equalsabsent𝑡less-than-or-approximately-equals1.38superscript1010\lessapprox t\lessapprox 1.38\times 10^{10}⪅ italic_t ⪅ 1.38 × 10 start_POSTSUPERSCRIPT 10 end_POSTSUPERSCRIPT a, then R(t)∼t2/3similar-to𝑅𝑡superscript𝑡23R(t)\sim t^{2/3}italic_R ( italic_t ) ∼ italic_t start_PO... | Consider first the radiation epoch 10101010 s ⪅t⪅70.000less-than-or-approximately-equalsabsent𝑡less-than-or-approximately-equals70.000\lessapprox t\lessapprox 70.000⪅ italic_t ⪅ 70.000 a (here “a” stands for “years” as usual). | D |
_{I}-U\left|\psi\right\rangle_{I})\left|1\right\rangle| italic_ψ ⟩ start_POSTSUBSCRIPT italic_F end_POSTSUBSCRIPT = divide start_ARG 1 end_ARG start_ARG 2 end_ARG ( | italic_ψ ⟩ start_POSTSUBSCRIPT italic_I end_POSTSUBSCRIPT + italic_U | italic_ψ ⟩ start_POSTSUBSCRIPT italic_I end_POSTSUBSCRIPT ) | 0 ⟩ + divide start_A... | We now measure the ancilla qubit in the computational basis. If the result is |0⟩ket0\left|0\right\rangle| 0 ⟩ then the input state becomes | while if the measured outcome of the ancilla is |1⟩ket1\left|1\right\rangle| 1 ⟩ then the input state becomes | A quantum circuit that would encode such a state with three qubits will start with three quantum states, the first encoding the original qubit state, and another two ancilla qubits initialised to |0⟩ket0\left|0\right\rangle| 0 ⟩. Two CNOT gates will couple the first qubit state to the second |0⟩ket0\left|0\right\rangle... | The error correction prescription on the other side will need some additional ancilla qubits, because we cannot directly measure the logical state without destroying it. Those ancilla qubits are used to extract the syndrome information related to possible errors without discriminating the state of any qubit. The error ... | A |
Note that the curvature tensor Rgsubscript𝑅𝑔R_{g}italic_R start_POSTSUBSCRIPT italic_g end_POSTSUBSCRIPT of an Einstein manifold | Rgsubscript𝑅𝑔R_{g}italic_R start_POSTSUBSCRIPT italic_g end_POSTSUBSCRIPT of (M,g)𝑀𝑔(M,g)( italic_M , italic_g ) as an operator in (5) is bounded which means that | Concerning the Einstein condition if Rgsubscript𝑅𝑔R_{g}italic_R start_POSTSUBSCRIPT italic_g end_POSTSUBSCRIPT comes from an Einstein metric | (M,g)𝑀𝑔(M,g)( italic_M , italic_g ) if bounded as an operator always solves the quantum vacuum Einstein | QM∈ℜsubscript𝑄𝑀ℜQ_{M}\in{\mathfrak{R}}italic_Q start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT ∈ fraktur_R satisfying the quantum vacuum Einstein equation as in | C |
The HR spacetime haggard_quantum-gravity_2015 ; de_lorenzo_improved_2016 constructed below provides a minimalistic model for a geometry where there is a transition of a trapped region (formed by collapsing matter) to an anti–trapped region (from which matter is released). The transition is assumed to happen through qu... | In this section we construct what we call here the Haggard-Rovelli spacetime. We follow a novel route for its construction that is adapted to the needs of the calculation and is more precise and conceptually clear. Note that the use of the word ‘spacetime’ here is an abuse of terminology as this spacetime has a region ... | Figure 1: Geometry transition as a path integral over geometries. The shaded region (pale green) is where the quantum transition occurs. Outside this compact spacetime region, quantum theory can be disregarded and the geometry is a solution of Einstein’s equations. This induces an intrinsic metric q𝑞qitalic_q and extr... | The transition region is excised from spacetime, by introducing a spacelike compact interior boundary, which surrounds the quantum region. Outside this region the metric solves Einstein’s field equations exactly everywhere, including on the interior boundary. | The key technical result in haggard_quantum-gravity_2015 is the discovery of an ‘exterior metric’ describing this process which solves Einstein’s field equations exactly everywhere, except for the transition region which is bounded by a compact boundary. The existence of this exterior metric, which we henceforth refer... | C |
(2) L→∞→𝐿L\to\inftyitalic_L → ∞ with fixed α≪1much-less-than𝛼1\alpha\ll 1italic_α ≪ 1 and fixed particle | Any increase in P2subscript𝑃2P_{2}italic_P start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT should be accompanied | momentum xeEsubscript𝑥𝑒𝐸x_{e}Eitalic_x start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT italic_E shown in the second diagram should be negative, | roughly speaking, related to the probability P2subscript𝑃2P_{2}italic_P start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT of one splitting | should be taken to be α(Q⟂)𝛼subscript𝑄perpendicular-to\alpha(Q_{\perp})italic_α ( italic_Q start_POSTSUBSCRIPT ⟂ end_POSTSUBSCRIPT ), where Q⟂subscript𝑄perpendicular-toQ_{\perp}italic_Q start_POSTSUBSCRIPT ⟂ end_POSTSUBSCRIPT is the | A |
In Section 2, we introduce the twisted affine Lie algebra L^(𝔤,σ)^𝐿𝔤𝜎\hat{L}(\mathfrak{g},\sigma)over^ start_ARG italic_L end_ARG ( fraktur_g , italic_σ ) attached to a finite order automorphism σ𝜎\sigmaitalic_σ of 𝔤𝔤\mathfrak{g}fraktur_g following [Ka, Chap. 8]. We prove some preparatory lemmas which is used l... | In Section 3, we define the space of twisted covacua attached to a Galois cover of an algebraic curve. We prove that this space is finite dimensional under the assumption given in Definition 3.5. | In this section we define the space of twisted covacua attached to a Galois cover of an algebraic curve. We prove that this space is finite dimensional. | The aim of this section is to prove the Factorization Theorem which identifies the space of covacua for a genus g𝑔gitalic_g nodal curve | As proved in Lemma 3.7, the space of twisted covacua is finite dimensional. We sheafify the notion of twisted covacua associated to a family of s𝑠sitalic_s-pointed ΓΓ\Gammaroman_Γ-curves as in Definition 7.7 and show that | A |
^{2}\Phi_{Q}\Bigg{\}}.+ 40 roman_Φ start_POSTSUBSCRIPT italic_Q end_POSTSUBSCRIPT roman_csc start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT roman_Φ start_POSTSUBSCRIPT italic_P end_POSTSUBSCRIPT roman_cot roman_Φ start_POSTSUBSCRIPT italic_Q end_POSTSUBSCRIPT [ 12 roman_Φ start_POSTSUBSCRIPT italic_P end_POSTSUBSCRIPT roma... | The integral over the three-dimensional angle θ𝜃\thetaitalic_θ can then be performed analytically, which yields a more manageable expression, | where x≡P/Q𝑥𝑃𝑄x\equiv P/Qitalic_x ≡ italic_P / italic_Q and θ𝜃\thetaitalic_θ is the angle between 𝒑𝒑\boldsymbol{p}bold_italic_p and 𝒒𝒒\boldsymbol{q}bold_italic_q. | We present here some details of the calculation discussed in the main text. In particular, to carry out the four-momentum integrations such as ∫d4Psuperscriptd4𝑃\int\operatorname{d}\!^{4}P∫ roman_d start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT italic_P, we find it very useful to change variables from (P0,|𝒑|)superscri... | As mentioned in the main text, the starting point in our N3LO computation is the two-loop HTL pressure as written down in eq. (34) of ref. [27], where we convert the sum-integrals into ordinary 3+1 dimensional integrals because we work at T=0𝑇0T=0italic_T = 0. The full expression is rather unwieldy when written in ful... | A |
=9(1+ττ¯)+16ττ¯+15(τ1¯+1τ¯),absent91𝜏¯𝜏16𝜏¯𝜏15𝜏¯11¯𝜏\displaystyle=9(1+\tau\bar{\tau})+16\tau\bar{\tau}+15(\tau\bar{1}+1\bar{\tau}),= 9 ( 1 + italic_τ over¯ start_ARG italic_τ end_ARG ) + 16 italic_τ over¯ start_ARG italic_τ end_ARG + 15 ( italic_τ over¯ start_ARG 1 end_ARG + 1 over¯ start_ARG italic_τ end_... | Comparing the equations above with Table 1, we find that the state counting in Table 1 actually counts the number of fusion channels to trivial fluxons 1111 and fluxons ττ¯𝜏¯𝜏\tau\bar{\tau}italic_τ over¯ start_ARG italic_τ end_ARG appearing on the RHS of each of the equations above. If we did the state counting in t... | The state counting using the extended Levin-Wen model therefore tells us which subspace of a multi-fluxon Hilbert space should be singled out as the physical Hilbert space. This result complies with that the gapped boundary of the disk is due to condensing ττ¯𝜏¯𝜏\tau\bar{\tau}italic_τ over¯ start_ARG italic_τ end_AR... | We compute using Eq. (16) and the precisely the lattice in Fig. 2, namely with P=5𝑃5P=5italic_P = 5, and obtain the state counting in Table 1. If we increase the plaquette number P𝑃Pitalic_P, we can obtain the state counting for larger Nττ¯subscript𝑁𝜏¯𝜏N_{\tau\bar{\tau}}italic_N start_POSTSUBSCRIPT italic_τ over¯... | Nevertheless, materials with boundaries are much easier to fabricate than closed ones. Understanding the anyonic exclusion statistics in topologically ordered states with boundaries is thus important. For such a system to have a well-defined, topologically protected, degenerate ground-state Hilbert space, which may sup... | A |
K(x)∈ℕ∪{+∞}𝐾𝑥ℕK(x)\in{\mathbb{N}}\cup\{+\infty\}italic_K ( italic_x ) ∈ blackboard_N ∪ { + ∞ } the Kolmogorov complexity of x∈ℝ𝑥ℝx\in{\mathbb{R}}italic_x ∈ blackboard_R. | famous ΩΩ\Omegaroman_Ω number [6, Section 14.8]) while K(x)<+∞𝐾𝑥K(x)<+\inftyitalic_K ( italic_x ) < + ∞ | whether K(x)=+∞𝐾𝑥K(x)=+\inftyitalic_K ( italic_x ) = + ∞ or K(x)<+∞𝐾𝑥K(x)<+\inftyitalic_K ( italic_x ) < + ∞ and in the latter case only the | Then K(x)=+∞𝐾𝑥K(x)=+\inftyitalic_K ( italic_x ) = + ∞ corresponds to the situation when no algorithms | stationary or single) black hole such that ∂M=Σ𝑀Σ\partial M=\Sigma∂ italic_M = roman_Σ corresponds to | C |
Firstly, we have the ones based on the ℒ∞subscriptℒ\mathcal{L}_{\infty}caligraphic_L start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT structure on linearized contact homology. | In the case that (X,ω)𝑋𝜔(X,\omega)( italic_X , italic_ω ) is a filling of (Y,α)𝑌𝛼(Y,\alpha)( italic_Y , italic_α ), we get an ℒ∞subscriptℒ\mathcal{L}_{\infty}caligraphic_L start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT augmentation | Suppose that (X,ω)𝑋𝜔(X,\omega)( italic_X , italic_ω ) is a symplectic filling of (Y,α)𝑌𝛼(Y,\alpha)( italic_Y , italic_α ). | Given (X,ω)𝑋𝜔(X,\omega)( italic_X , italic_ω ) a symplectic filling of (Y,α)𝑌𝛼(Y,\alpha)( italic_Y , italic_α ), | Let (Y,α)𝑌𝛼(Y,\alpha)( italic_Y , italic_α ) be a strict contact manifold, with symplectic filling (X,ω)𝑋𝜔(X,\omega)( italic_X , italic_ω ). As discussed in §3.4, the filling induces an ℒ∞subscriptℒ\mathcal{L}_{\infty}caligraphic_L start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT augmentation | C |
∘{}^{\circ}start_FLOATSUPERSCRIPT ∘ end_FLOATSUPERSCRIPT S+subscript𝑆S_{+}italic_S start_POSTSUBSCRIPT + end_POSTSUBSCRIPT means the star is on the south pole in the spin-(s+1/2𝑠12s+1/2italic_s + 1 / 2) sector. | ◇◇{}^{\Diamond}start_FLOATSUPERSCRIPT ◇ end_FLOATSUPERSCRIPT “Complex” means the stars’ distribution is complex. | ∙∙{}^{\bullet}start_FLOATSUPERSCRIPT ∙ end_FLOATSUPERSCRIPT E𝐸Eitalic_E means the star of the pseudo spin is on the equator. | ∘{}^{\circ}start_FLOATSUPERSCRIPT ∘ end_FLOATSUPERSCRIPT S+subscript𝑆S_{+}italic_S start_POSTSUBSCRIPT + end_POSTSUBSCRIPT means the star is on the south pole in the spin-(s+1/2𝑠12s+1/2italic_s + 1 / 2) sector. | ⋆⋆{}^{\star}start_FLOATSUPERSCRIPT ⋆ end_FLOATSUPERSCRIPT + (-) means the star is in the spin-(s+1/2𝑠12s+1/2italic_s + 1 / 2) (spin-(s−1/2𝑠12s-1/2italic_s - 1 / 2)) sector. | B |
\times\left(\eta\nabla\times\mathbf{B}\right),\,\,\nabla\cdot\mathbf{B}=0over˙ start_ARG bold_B end_ARG = ∇ × ( bold_v × bold_B ) - ∇ × ( italic_η ∇ × bold_B ) , ∇ ⋅ bold_B = 0 | Note that the five magnetic terms involving μ0subscript𝜇0\mu_{0}italic_μ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT in the final | ∂Ue∂rsuperscript𝑈𝑒𝑟\displaystyle\frac{\partial U^{e}}{\partial r}divide start_ARG ∂ italic_U start_POSTSUPERSCRIPT italic_e end_POSTSUPERSCRIPT end_ARG start_ARG ∂ italic_r end_ARG | Here, a dot above a symbol implies a partial time derivative, μ0subscript𝜇0\mu_{0}italic_μ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT | ∂Ue∂zsuperscript𝑈𝑒𝑧\displaystyle\frac{\partial U^{e}}{\partial z}divide start_ARG ∂ italic_U start_POSTSUPERSCRIPT italic_e end_POSTSUPERSCRIPT end_ARG start_ARG ∂ italic_z end_ARG | C |
Denote by θ𝜃\thetaitalic_θ any positive quantity that is small enough depending on δ𝛿\deltaitalic_δ (for example θ≪δ50much-less-than𝜃superscript𝛿50\theta\ll\delta^{50}italic_θ ≪ italic_δ start_POSTSUPERSCRIPT 50 end_POSTSUPERSCRIPT). This θ𝜃\thetaitalic_θ may take different values at different places. Let C𝐶Cital... | We now turn to the proof of Theorem 1.3. This proof consists of two parts: (a) proving almost sure local well-posedness for (1.1) on the support of the Gibbs measure, and (b) applying formal invariance to extend local solutions to global ones. Since part (b) is essentially an adaptation of Bourgain’s classical proof [1... | The heart of the proof of Proposition 3.3 is a collection of (probabilistic) multilinear estimates for 𝒩2l+1subscript𝒩2𝑙1\mathcal{N}_{2l+1}caligraphic_N start_POSTSUBSCRIPT 2 italic_l + 1 end_POSTSUBSCRIPT. We will state them in Proposition 3.4 below and show that they imply Proposition 3.3. We leave the proof of P... | The rest of the paper is organized as follows. In Section 2 we introduce the gauge transform and reduce to a favorable nonlinearity, and define the norms that will be used in the proof below. In Section 3 we identify the precise structure of the solution according to the ideas of Section 1.3, and reduce the local well-... | Proposition 3.4 will be proved in Section 5. In this section we make some preparations for the proof, namely we introduce two large deviation estimates and some counting estimates for integer lattice points. | C |
^{(3)}-\pi)+\pi\xi\overline{(-2\mathrm{i}m)})- italic_μ start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ( italic_γ ( 0 ) , italic_ξ ) = exp ( italic_π italic_ξ start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ( - 2 roman_i italic_m ) + roman_i ( 2 italic_π italic_m start_POSTSUPERSCRIPT ( 3 ) end_POSTSUPERSCRIPT - italic_π ... | We then conclude that the magnetic coordinate has the same jumps as the magnetic coordinate of the Ooguri-Vafa space. | where θmsubscript𝜃𝑚\theta_{m}italic_θ start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT is the angle parametrizing the U(1)𝑈1U(1)italic_U ( 1 ) fiber (we will call it the “magnetic angle”, hence the m𝑚mitalic_m subscript). | Notice that our definition of marked point uses a branch of the Arg function (with Arg(z)∈[−π,π)Arg𝑧𝜋𝜋\text{Arg}(z)\in[-\pi,\pi)Arg ( italic_z ) ∈ [ - italic_π , italic_π )), so the magnetic angle is not a priori a global continuous function of m𝑚mitalic_m. In the following, we will compute how the magnetic angle ... | Hence, we see that the magnetic angle has the same monodromy as the usual Ooguri-Vafa magnetic angle. | D |
The concept that the near-Sun solar wind is divided into ’quiet’ magnetic flux tubes (where near-fcesubscript𝑓𝑐𝑒f_{ce}italic_f start_POSTSUBSCRIPT italic_c italic_e end_POSTSUBSCRIPT waves are preferentially observed) and ’strong turbulence’ flux tubes where wave growth is suppressed is further supported by Figure... | Flux tubes where magnetic field turbulence is low contain a larger outward flux of strahl electrons. Those strahl electrons cause the sunward electron core drift (in the proton frame) to increase. The combination of larger strahl flux and more sunward electron core drift set up electron distribution functions unstable ... | The concept that the near-Sun solar wind is divided into ’quiet’ magnetic flux tubes (where near-fcesubscript𝑓𝑐𝑒f_{ce}italic_f start_POSTSUBSCRIPT italic_c italic_e end_POSTSUBSCRIPT waves are preferentially observed) and ’strong turbulence’ flux tubes where wave growth is suppressed is further supported by Figure... | However, this picture is incomplete. Why should flux tubes with ’quiet’ solar wind (lower magnetic turbulence, hewing closer to the Parker spiral direction) show larger strahl electron flux? Perhaps this indicates multiple coronal source region properties. Perhaps it indicates different strahl radial evolution (efficie... | The study of near-fcesubscript𝑓𝑐𝑒f_{ce}italic_f start_POSTSUBSCRIPT italic_c italic_e end_POSTSUBSCRIPT waves in the near-Sun solar wind has only just begun, and already it promises to provide insight into the regulation of electron heat flux (through improved understanding of electron population evolution and its ... | C |
1}\mathbf{e}_{1}=-1bold_e start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = bold_e start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT bold_e start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT = - bold_e start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT bold_e start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT bold_e start_... | 𝐶𝑙3,0subscript𝐶𝑙30\mathit{Cl}_{3,0}italic_Cl start_POSTSUBSCRIPT 3 , 0 end_POSTSUBSCRIPT and 𝐶𝑙1,2subscript𝐶𝑙12\mathit{Cl}_{1,2}italic_Cl start_POSTSUBSCRIPT 1 , 2 end_POSTSUBSCRIPT) or s2−S2=0superscript𝑠2superscript𝑆20s^{2}-S^{2}=0italic_s start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT - italic_S start_POSTSUP... | 3 Square roots in 𝐶𝑙3,0subscript𝐶𝑙30\mathit{Cl}_{3,0}italic_Cl start_POSTSUBSCRIPT 3 , 0 end_POSTSUBSCRIPT and 𝐶𝑙1,2subscript𝐶𝑙12\mathit{Cl}_{1,2}italic_Cl start_POSTSUBSCRIPT 1 , 2 end_POSTSUBSCRIPT algebras | However, in 𝐶𝑙1,2subscript𝐶𝑙12\mathit{Cl}_{1,2}italic_Cl start_POSTSUBSCRIPT 1 , 2 end_POSTSUBSCRIPT similar computation gives | 3.4 Examples for 𝐶𝑙3,0subscript𝐶𝑙30\mathit{Cl}_{3,0}italic_Cl start_POSTSUBSCRIPT 3 , 0 end_POSTSUBSCRIPT and 𝐶𝑙1,2subscript𝐶𝑙12\mathit{Cl}_{1,2}italic_Cl start_POSTSUBSCRIPT 1 , 2 end_POSTSUBSCRIPT | C |
This section describes the task of generalization of odor classification under sensor drift and defines several classifier models: the SVM ensemble, neural network ensemble, skill neural network, and context+skill neural network. | Two processing steps were applied to the data used by all models included in this paper. The first preprocessing step was to remove all samples taken for gas 6, toluene, because there were no toluene samples in batches 3, 4, and 5. Data was too incomplete for drawing meaningful conclusions. Also, with such data missing... | More specifically, natural odors consist of complex and variable mixtures of molecules present at variable concentrations [4]. Sensor variance arises from environmental dynamics of temperature, humidity, and background chemicals, all contributing to concept drift [5], as well as sensor drift arising from modification o... | Sensor drift in industrial processes is one such use case. For example, sensing gases in the environment is mostly tasked to metal oxide-based sensors, chosen for their low cost and ease of use [1, 2]. An array of sensors with variable selectivities, coupled with a pattern recognition algorithm, readily recognizes a br... | Experiments in this paper used the gas sensor drift array dataset [7]. The data consists of 10 sequential collection periods, called batches. Every batch contains between 161161161161 to 3,60036003{,}6003 , 600 samples, and each sample is represented by a 128-dimensional feature vector; 8 features each from 16 metal ox... | D |
In Fig. 7, I consider the same pulses that has large fidelity measurement in Fig. 6 but with different values of noise strength. Note that small value of noise strength, ΔΔ\Deltaroman_Δ is applicable for low temperature measurements while large value of ΔΔ\Deltaroman_Δ is applicable for high temperature measurements, p... | Finally in Fig. 7, I have shown that when π𝜋\piitalic_π pulse acts in x direction, CORPSE pulse acts in y direction and SCORPSE pulse acts in z-direction in presence of arbitrary low and high temperature measurements noise conditions, large fidelity recovery can be achieved and may consider for implementing in future ... | The paper is organized as follows. In section II, we provide a theoretical description of the model Hamiltonian for a qubit operating under several control pulses in a random telegraph noise environment. In section IV, we analyze two main results: (i) qubits driven by a pulse in the x-direction and RTN noise acts in z-... | Here I find that when π𝜋\piitalic_π pulse acts in x direction, CORPSE pulse acts in y direction and SCORPSE pulse acts in z-direction in presence of arbitrary low and high temperature measurements noise condition have large fidelity recovery and may consider for implementing in future for electronic circuits design to... | For a more general case, I consider the pulses acting in arbitrary in x, y and z directions and show that when π𝜋\piitalic_π pulse acts in x direction, CORPSE pulse acts in y direction and SCORPSE pulse acts in z-direction in presence of arbitrary low and high temperature measurements noise condition have large fideli... | C |
Now, let us consider the introduction of a covariant κ𝜅\kappaitalic_κ-deformation in the Horndeski theory. | In our case, the inclusion of κ𝜅\kappaitalic_κ-deformation produces a solution that does not necessarily impose a specific value of the critical exponent, and the κ𝜅\kappaitalic_κ-Horndeski-Einstein field equations (8) and (12) are satisfied by the equations (15)-(17) for any value of z𝑧zitalic_z. This is in contras... | The non-relativistic κ𝜅\kappaitalic_κ-deformation presented by daCosta:2020mbf ; Kaniadakis is derived through a kinetic interaction principle. In that context, the κ𝜅\kappaitalic_κ-derivative is defined in flat space by Kaniadakis | Here, we consider a generalization of the above flat space derivative to a curved spacetime κ𝜅\kappaitalic_κ-deformation of the relativistic covariant derivative Santos:2022fbq | Here, we reanalyse black brane thermodynamics in asymptotically AdS Lifshitz spacetimes within Horndeski gravity modified by the recently proposed κ𝜅\kappaitalic_κ-deformation Santos:2022fbq of the corresponding kinetic terms. We show that this proposal leads to a generalized entropy for black branes compatible with ... | B |
In the first place, one can find that the coherence decreases to zero (minimum, under the latter channel) and emerges certain peaks after the first Lee-Yang singularity, of which values decrease dramatically with the bath size increasing toward the thermodynamic limit. | Times in correspondence to the Lee-Yang zeros are the centers of all the vanishing domains of the rescaled concurrence at low temperature. | Furthermore, one can find that times in correspondence to the Lee-Yang zeros are also the zeros of the coherence. | Furthermore, one can find that times in correspondence to the Lee-Yang zeros are also the zeros of the coherence. | Times in correspondence to the Lee-Yang zeros are the centers of all the vanishing domains of the rescaled concurrence at low temperature. | B |
\tilde{Q},\tilde{W}}^{\tilde{\operatorname{\mathcal{S}}},\psi}=0fraktur_P start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_OPFUNCTION bold_H caligraphic_A end_OPFUNCTION start_POSTSUBSCRIPT over~ start_ARG italic_Q end_ARG , over~ start_ARG italic_W end_ARG end_POSTSUBSCRIPT start_POSTSUPERSCRIPT over~ start_ARG caligraph... | We call the filtration introduced in Theorem A the less perverse filtration, in order to distinguish it from a different perverse filtration, that was introduced in [DM20] on the way towards the definition of BPS sheaves, which recalled in (25). This is a perverse filtration on the critical CoHA 𝐇𝒜Q~,W~𝒮~subscripts... | We can generalise the results of this paper, incorporating deformed potentials as introduced in joint work with Tudor Pădurariu [DP22]. We indicate how this goes in this section. We will not use this generalisation of the less perverse filtration, except in the statement of Proposition 6.9 and the example of §7.2.1. | \operatorname{\mathcal{S}},G,\upzeta}start_OPFUNCTION bold_H caligraphic_A end_OPFUNCTION start_POSTSUBSCRIPT roman_Π start_POSTSUBSCRIPT italic_Q end_POSTSUBSCRIPT , roman_θ end_POSTSUBSCRIPT start_POSTSUPERSCRIPT caligraphic_S , italic_G , roman_ζ end_POSTSUPERSCRIPT carries a Hall algebra structure introduced by Sch... | In this subsection we give a curious example, which will not be used later in the paper. It is an example of how deforming the potential can modify the BPS Lie algebra. | B |
The distributions for JP=1−superscript𝐽𝑃superscript1J^{P}=1^{-}italic_J start_POSTSUPERSCRIPT italic_P end_POSTSUPERSCRIPT = 1 start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT are shown by the green lines. | The inset plots show distribution of the parameters β𝛽\betaitalic_β and ζ𝜁\zetaitalic_ζ for an ensemble of pseudoexperiments. The coloured lines indicate the true values corresponding to each hypothesis. | Far from the resonances the expected values of β𝛽\betaitalic_β and ζ𝜁\zetaitalic_ζ are determined for the continuum. | Bottom row: The angular distributions for β𝛽\betaitalic_β (left) and ζ𝜁\zetaitalic_ζ (right) for each scenario. | Moreover, interference effects modify the values of the angular asymmetries, β𝛽\betaitalic_β and ζ𝜁\zetaitalic_ζ. | A |
We denote the total statistical operator of the problem as ρ^(tot)superscript^𝜌(tot)\hat{\rho}^{\text{(tot)}}over^ start_ARG italic_ρ end_ARG start_POSTSUPERSCRIPT (tot) end_POSTSUPERSCRIPT | the initial matter state ρ^0,subscript^𝜌0\hat{\rho}_{0},over^ start_ARG italic_ρ end_ARG start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , and |⋅⟩ket⋅|\,\cdot\,\rangle| ⋅ ⟩ | We first highlight that the total energy of the system, formed by the matter and the gravitational field, is conserved in the derived QFT model. | (the matter-wave system and the gravitational field), and by ρ^^𝜌\hat{\rho}over^ start_ARG italic_ρ end_ARG | system, but only on graviton and matter-wave frequencies, ω𝒌subscript𝜔𝒌\omega_{\bm{k}}italic_ω start_POSTSUBSCRIPT bold_italic_k end_POSTSUBSCRIPT | C |
\}_{n\geq N}{ over∼ start_ARG roman_TL start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT end_ARG italic_H start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ( italic_X start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT , blackboard_k ) / [ italic_V start_POSTSUBSCRIPT italic_n , 1 end_POSTSUBSCRIPT ] , … , [ italic_V start_POSTSU... | The goal of this Subsection is to give a couple of examples of topological stability. This Section will likely not only be useful to a reader who is interested in topological stability, but will also be useful to a reader who wants to understand topological actions as in Section 3. | The definitions we provide assume that δ=1𝛿1\delta=1italic_δ = 1, and this is perhaps not a defect, but rather a feature of representation stability, at least from the viewpoint of actions on finite sets. With regard to topological actions, we are only interested in the δ=1𝛿1\delta=1italic_δ = 1 case and so we face n... | The goal of this Subsection is to make topological observations which are required to prove Theorem 5.16. We begin with a couple of simple but important observations. | Action of TLnsubscriptTL𝑛\operatorname{TL}_{n}roman_TL start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT on a topological space X𝑋Xitalic_X induces an action on each homology group Hk(X)subscript𝐻𝑘𝑋H_{k}(X)italic_H start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ( italic_X ). For the reader’s convenience, we will now... | A |
The renormalisation scale, μrsubscript𝜇𝑟\mu_{r}italic_μ start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT, is set to be the same value as μfsubscript𝜇𝑓\mu_{f}italic_μ start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT. | can reflect the relative magnitude of the cross sections for the hadroproduction of different states, | equivalently we set the values of the masses appeared in the cross sections in terms of the following approximation, | With the above parameter choice, we can compute the integrated cross sections for the states listed in Table 1 in the kinematic region, | In order to explore the relative magnitudes of the cross sections for the hadroproduction of different states, | C |
B−3Lτ𝐵3subscript𝐿𝜏B-3L_{\tau}italic_B - 3 italic_L start_POSTSUBSCRIPT italic_τ end_POSTSUBSCRIPT | 6.6×10−276.6superscript10276.6\times 10^{-27}6.6 × 10 start_POSTSUPERSCRIPT - 27 end_POSTSUPERSCRIPT | 7.0×10−277.0superscript10277.0\times 10^{-27}7.0 × 10 start_POSTSUPERSCRIPT - 27 end_POSTSUPERSCRIPT | 7.2×10−277.2superscript10277.2\times 10^{-27}7.2 × 10 start_POSTSUPERSCRIPT - 27 end_POSTSUPERSCRIPT | 7.3×10−277.3superscript10277.3\times 10^{-27}7.3 × 10 start_POSTSUPERSCRIPT - 27 end_POSTSUPERSCRIPT | D |
Here we present and prove a result that will be needed to demonstrate the excursion mimicry aspect of Theorem 7.2. | We now begin to implement the plan. The plan first claims, “low overlap entails a high cumulative duration for excursions”. However, though intuitive, this is not quite correct deterministically. In fact, a pair ϕitalic-ϕ\phiitalic_ϕ and ψ𝜓\psiitalic_ψ of n𝑛nitalic_n-zigzags from (0,0)00(0,0)( 0 , 0 ) and (0,1)01(0,1... | Let ϕitalic-ϕ\phiitalic_ϕ be an n𝑛nitalic_n-zigzag from (0,0)00(0,0)( 0 , 0 ) to (0,1)01(0,1)( 0 , 1 ). Let the parameters κ∈(0,e−1)𝜅0superscript𝑒1\kappa\in(0,e^{-1})italic_κ ∈ ( 0 , italic_e start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ) and R>0𝑅0R>0italic_R > 0 be given. | where the supremum is taken over all n𝑛nitalic_n-zigzags ψ𝜓\psiitalic_ψ from (0,0)00(0,0)( 0 , 0 ) to (0,1)01(0,1)( 0 , 1 ). | Let ϕitalic-ϕ\phiitalic_ϕ and ψ𝜓\psiitalic_ψ be n𝑛nitalic_n-zigzags between (0,0)00(0,0)( 0 , 0 ) and (0,1)01(0,1)( 0 , 1 ). | D |
ζ𝜁\zetaitalic_ζ (or equivalently μ𝜇\muitalic_μ in the relation 1+ζ=1/μ1𝜁1𝜇1+\zeta=1/\mu1 + italic_ζ = 1 / italic_μ); | to one parameter t0=14.7subscript𝑡014.7t_{0}=14.7italic_t start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = 14.7 Gy with χmin=1.1197subscript𝜒𝑚𝑖𝑛1.1197\chi_{min}=1.1197italic_χ start_POSTSUBSCRIPT italic_m italic_i italic_n end_POSTSUBSCRIPT = 1.1197. The long-dashed | VSL Formula (71) with t0=14.7subscript𝑡014.7t_{0}=14.7italic_t start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = 14.7 Gy. Long-dashed | in Figure 5 for t0≳14.8greater-than-or-equivalent-tosubscript𝑡014.8t_{0}\gtrsim 14.8italic_t start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ≳ 14.8, | Also note that this “optimal” value of t0=14.7subscript𝑡014.7t_{0}=14.7italic_t start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = 14.7 Gy is not | B |
In quantum metrology, the strong and collective atom-light interactions in cavity-QED systems exhibit prominent advantage in quantum-enhanced measurements. | and one can gain the sensitivity speeded up to attain the HL by a prefactor N2superscript𝑁2N^{2}italic_N start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT. | In summary, we study the time-reversal protocol to sense small displacements of the light field and corroborate the sensitivity of our scheme that can surpass the SQL and even attain the concrete HL. | Furthermore, we gain the sensitivities of the small displacements of the light field by choosing the optical part state as superposition of even and odd coherent state, and changing the atomic part state from the collective ground state to the superposed spin-coherent state in section 3 and section 4. | In this work, we study the time-reversal protocol to sense small displacements of the light field, and show the sensitivity of the scheme which could be speeded up to attain the HL. | D |
Mainly owing to its conceptual simplicity, gravitational lensing has developed into one of the most informative and reliable methods of observational cosmology (Bartelmann & | We have investigated how the power spectrum Cℓγsuperscriptsubscript𝐶ℓ𝛾C_{\ell}^{\gamma}italic_C start_POSTSUBSCRIPT roman_ℓ end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_γ end_POSTSUPERSCRIPT of weak cosmological gravitational lensing changes with the expansion function E(a)𝐸𝑎E(a)italic_E ( italic_a ) of the cosm... | The first term on the right-hand side reflects the variation of the density-fluctuation power spectrum Pδ(k,a)subscript𝑃𝛿𝑘𝑎P_{\delta}(k,a)italic_P start_POSTSUBSCRIPT italic_δ end_POSTSUBSCRIPT ( italic_k , italic_a ) in response to a change in the wave number k𝑘kitalic_k where it is to be evaluated, which is in ... | If the cosmic expansion function E(a)=H(a)/H0𝐸𝑎𝐻𝑎subscript𝐻0E(a)=H(a)/H_{0}italic_E ( italic_a ) = italic_H ( italic_a ) / italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is varied in an arbitrary way, how does the power spectrum of cosmological weak lensing change? Here, H(a)𝐻𝑎H(a)italic_H ( italic_a ) is t... | Schneider, 2001; Schneider, 2006; Bartelmann, 2010; Kilbinger, 2015; Mandelbaum, 2018). Expected weak-lensing power spectra depend on the cosmological background model in two ways: geometrically via the angular-diameter distances entering its geometrical weight function, and dynamically via the growth of density pertur... | D |
\right]}=t(U)\rho\,t(U)^{\dagger}divide start_ARG caligraphic_A ( italic_U ) ( italic_ρ ) end_ARG start_ARG roman_tr [ caligraphic_A ( italic_U ) ( italic_ρ ) ] end_ARG = italic_t ( italic_U ) italic_ρ italic_t ( italic_U ) start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT | The if-clause (m=1𝑚1m=1italic_m = 1) impossibility is immediate. In addition to the following full proof of Theorem 1, the appendix contains two more proofs for only the exact, ϵ=0italic-ϵ0\epsilon=0italic_ϵ = 0, impossibility. The “operational” proof in Appendix B reaches a contradiction by using the supposed cϕmsubs... | The rest of the paper is organized as follows. Section II defines oracle computation using functions on d𝑑ditalic_d-dimensional unitaries, U∈U(d)𝑈𝑈𝑑U\in U(d)italic_U ∈ italic_U ( italic_d ). Section III proves the if-clause impossibility and the process tomography limitation by exploiting the continuity of algorit... | The above results limit versatile quantum computation, and impact our understanding of tomography, measurements, linear optics and causality. Using process tomography for the if clause has a caveat: Instead of a superoperator estimate of ρ↦UρU†maps-to𝜌𝑈𝜌superscript𝑈†\rho\mapsto U\rho\,U^{\dagger}italic_ρ ↦ italic... | One direction of the equivalence is immediate from (5), the other follows from Theorem 2.3 of [67]. The theorem also relates the errors in the operator and superoperator languages. Here we continue with superoperators. | D |
The large database created by high-throughput DFT calculations forms the basis for a surrogate machine learning model that enables the prediction of the work function at a fraction of the computational cost. As a first step, we assess common models from the materials science machine learning community as a benchmark. F... | The large database created by high-throughput DFT calculations forms the basis for a surrogate machine learning model that enables the prediction of the work function at a fraction of the computational cost. As a first step, we assess common models from the materials science machine learning community as a benchmark. F... | It is not surprising that the model performance is poor when the bulk structure is used as an input as the database contains multiple surfaces of different work functions for any given bulk structure. While the performance of the benchmarking models improves when the surface slab is used as the input instead, the MAEs ... | Some statistical analyses have been carried out in literature showing that the electronegativity is linearly correlated with the work function both for elemental crystals and binary compounds.[59, 65] Additionally, for elemental crystals an inverse correlation with the atomic radius is pointed out. The work function of... | The observation that the distribution in work functions is near-Gaussian could indicate that the chemical space we chose was diverse enough to evenly sample work functions across possible values. The extended tail at the high work function end appears to be an artifact coming from ionically unrelaxed surfaces where a s... | B |
V𝑉Vitalic_V that intersects (𝒮0,ι0)subscript𝒮0subscript𝜄0\left(\mathcal{S}_{0},\iota_{0}\right)( caligraphic_S start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_ι start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ) | Let (𝒬,g,𝒪)𝒬𝑔𝒪\left(\mathcal{Q},g,\mathcal{O}\right)( caligraphic_Q , italic_g , caligraphic_O ) be a spacetime | Let (𝒬,g,𝒪)𝒬𝑔𝒪\left(\mathcal{Q},g,\mathcal{O}\right)( caligraphic_Q , italic_g , caligraphic_O ) be a spacetime, | Let (𝒬,g,𝒪)𝒬𝑔𝒪\left(\mathcal{Q},g,\mathcal{O}\right)( caligraphic_Q , italic_g , caligraphic_O ) be a spacetime. | Let (𝒬,g,𝒪)𝒬𝑔𝒪\left(\mathcal{Q},g,\mathcal{O}\right)( caligraphic_Q , italic_g , caligraphic_O ) be a spacetime. | A |
(for any λ∈ℝ∖{0}𝜆ℝ0\lambda\in\mathbb{R}\setminus\{0\}italic_λ ∈ blackboard_R ∖ { 0 } and K>0𝐾0K>0italic_K > 0). | L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-cutoff) for the Benjamin-Ono equation (1.19) with k=3𝑘3k=3italic_k = 3. | and thus are incompatible with the Wick-ordered L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-cutoff. | focusing Gibbs measure with an L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT-cutoff: | RNsubscript𝑅𝑁R_{N}italic_R start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT is as in (1.8) with λ∈ℝ∖{0}𝜆ℝ0\lambda\in\mathbb{R}\setminus\{0\}italic_λ ∈ blackboard_R ∖ { 0 } and k=3𝑘3k=3italic_k = 3. | A |
The observations of 2D superconductivity in the cuprates inspired the development of theories for pair-density wave (PDW) order Himeda et al. (2002); Berg et al. (2007); Agterberg et al. (2020) and more broadly the concept of intertwined orders in high-Tcsubscript𝑇𝑐T_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTS... | In conclusion, by combining neutron diffraction, muon spin rotation, and magnetization measurements in strong magnetic fields, we have found that La2-xSrxCuO4+y with x=0.06𝑥0.06x=0.06italic_x = 0.06 shows no magnetic order at low temperature, and that the application of a magnetic field induces stripe ordered regions.... | The superconducting coherence length in this sample has been estimated via the WHH model to be in the range ξ=2.5−4.5𝜉2.54.5\xi=2.5-4.5italic_ξ = 2.5 - 4.5 nm, which is in agreement with other La2-xSrxCuO4 compounds, e.g. Ref. Wang and Wen, 2008. We find the lower limit of the magnetic correlation length to be signifi... | It is evident that there is a rich interplay between the 2D SC, the stripe order, both structural and magnetic, and 3D SC in these cuprate compounds; And that there is a need to investigate the different phases in the cuprates in order to understand the competition, interplay, and phases separation of the different sta... | In panel (d) the rotation frequency of the muons in the non-magnetic regions is seen to be constant at high temperature, with a value that corresponds to the external magnetic field. The small negative shift of ωSCsubscript𝜔SC\omega_{\text{SC}}italic_ω start_POSTSUBSCRIPT SC end_POSTSUBSCRIPT below 38 K together with ... | C |
}](\lambda_{lmkn}^{2}+36am\omega_{mkn}-36a^{2}\omega_{mkn}^{2})[ ( italic_λ start_POSTSUBSCRIPT italic_l italic_m italic_k italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + 2 ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + 4 italic_a italic_m italic_ω start_POSTSUBSCRIPT italic_m italic_k italic_... | (2λlmkn+3)(96a2ωmkn2−48amωmkn)+144ωmkn2(M2−a2),2subscript𝜆𝑙𝑚𝑘𝑛396superscript𝑎2superscriptsubscript𝜔𝑚𝑘𝑛248𝑎𝑚subscript𝜔𝑚𝑘𝑛144superscriptsubscript𝜔𝑚𝑘𝑛2superscript𝑀2superscript𝑎2\displaystyle(2\lambda_{lmkn}+3)(96a^{2}\omega_{mkn}^{2}-48am\omega_{mkn})+144% | ∑lmkn|Zlmkn∞|24πωmkn2,(dEdt)H=∑lmknαlmkn|ZlmknH|24πωmkn2,subscript𝑙𝑚𝑘𝑛superscriptsubscriptsuperscript𝑍𝑙𝑚𝑘𝑛24𝜋superscriptsubscript𝜔𝑚𝑘𝑛2superscript𝑑𝐸𝑑𝑡Hsubscript𝑙𝑚𝑘𝑛subscript𝛼𝑙𝑚𝑘𝑛superscriptsubscriptsuperscript𝑍H𝑙𝑚𝑘𝑛24𝜋superscriptsubscript𝜔𝑚𝑘𝑛2\displaystyle\s... | 256(2Mr+)5(ωmkn−mΩH)[(ωmkn−mΩH)2+4ϵ2][(ωmkn−mΩH)2+16ϵ2]ωmkn3|Clmkn|2.256superscript2𝑀subscript𝑟5subscript𝜔𝑚𝑘𝑛𝑚subscriptΩHdelimited-[]superscriptsubscript𝜔𝑚𝑘𝑛𝑚subscriptΩH24superscriptitalic-ϵ2delimited-[]superscriptsubscript𝜔𝑚𝑘𝑛𝑚subscriptΩH216superscriptitalic-ϵ2superscriptsubscri... | [(λlmkn2+2)2+4amωmkn−4a2ωmkn2](λlmkn2+36amωmkn−36a2ωmkn2)delimited-[]superscriptsuperscriptsubscript𝜆𝑙𝑚𝑘𝑛2224𝑎𝑚subscript𝜔𝑚𝑘𝑛4superscript𝑎2superscriptsubscript𝜔𝑚𝑘𝑛2superscriptsubscript𝜆𝑙𝑚𝑘𝑛236𝑎𝑚subscript𝜔𝑚𝑘𝑛36superscript𝑎2superscriptsubscript𝜔𝑚𝑘𝑛2\displaystyle[(\l... | A |
Fig. 3(a, b) present the modulation depth as functions of the seed laser power and electron beam current. For nominal HGHG, the modulation depth is related to the seed laser intensity, but not to the electron beam current. For DEHG, however, the modulation depth is correlated with both the seed laser power and the elec... | Radiation at 6 nm was simulated to illustrate the capability of the proposed technique to generate soft X-ray pulses. In this case, the peak power of the seed laser is 0.2 MW, indicating average power of 70 mW under 350 fs pulse duration (FWHM) and 1 MHz repetition rate. Parameters of the electron beam and undulators a... | The long upstream modulator (two undulator segments) is used for seeding amplification and electron modulation, and the energy-modulated electron beam together with the amplified seed laser are then guided to the downstream elements for further beam manipulation and high harmonic generation through HGHG or EEHG process... | where the beam current profile is also presented as a reference coordinate. One can see clearly the enhancement of the seed laser intensity through the 1st modulator and the inheritance of the power profile to the electron beam current. The laser transport line introduces a 30 fs time delay of the laser to the electron... | The above simulation results demonstrate that the proposed technique is capable of generating stable, nearly full coherent and MHz-level repetition-rate EUV radiation. Nineteenth harmonic generation is almost the limit of HGHG with the above parameters. Shorter wavelengths are no longer at the scope of a single-stage H... | D |
\operatorname{QAC}}(M,\phi,-a)roman_WH start_POSTSUPERSCRIPT italic_q end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_QAC end_POSTSUBSCRIPT ( italic_M , italic_ϕ , italic_a ) → italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT caligraphic_H start_POSTSUPERSCRIPT italic_q end_POSTSUPERSCRIPT ( italic_M ∖ ∂ italic_M , i... | for all i𝑖iitalic_i allows us to take a=(0,…,0)𝑎0…0a=(0,\ldots,0)italic_a = ( 0 , … , 0 ) in Theorem 3.59, Corollary 3.10 and Corollary 3.11, giving in particular the identification | Finite dimensionality and Poincaré duality is a consequence of Proposition 5.3, Corollary 3.10 and Corollary 3.11. | Corollary 4.14 and Proposition 4.4 can then be combined to give a proof of the Vafa-Witten conjecture [43]. | When q=m2=4𝑞𝑚24q=\frac{m}{2}=4italic_q = divide start_ARG italic_m end_ARG start_ARG 2 end_ARG = 4, Poincaré duality follows from Corollary 3.11 and the fact that in middle degree | B |
Black hole thermodynamics is one of the most interesting topics in General Relativity. The history of the subject goes back to when Bekenstein proposed that the area of the black hole is proportional to its entropy Bekenstein:1973ur , followed by Hawking’s discovery that black holes radiate Hawking:1974sw . Since then,... | A little bit more than twenty years after such studies in Refs. Bekenstein:1973ur ; Hawking:1974sw the iconic work done by Witten, in Ref. Witten:1998zw , by using the new-found AdS/CFT correspondence, as proposed in Ref. Maldacena:1997re , relates the Hawking temperature achieved in a curved high-dimensional spacetim... | Black hole thermodynamics is one of the most interesting topics in General Relativity. The history of the subject goes back to when Bekenstein proposed that the area of the black hole is proportional to its entropy Bekenstein:1973ur , followed by Hawking’s discovery that black holes radiate Hawking:1974sw . Since then,... | Quantum corrections are relevant in the phenomenology of microscopic black holes. Its effects in a static black hole have been studied by Kazakov and Solodukhin Kazakov:1993ha , where the authors considered small deformations in the Schwarzschild metric due to the quantum fluctuations in the gravitational and matter fi... | Within general relativity context, some authors have proposed to associate mechanical pressure to black holes. For doing this, they considered that the cosmological constant is a thermodynamic variable that can be associated with the black hole pressure as shown in Refs. Kastor:2009wy ; Kubiznak:2012wp . In this way, a... | A |
We show that there exists a simple relation between the energy dissipated in the local environment due to the work of the demon and the violation of classical local correlation. | Our results provide a new approach to exploring and better understanding of relationships between quantum non-locality, information theory, and thermodynamics. | Quantum entanglement is a fundamental characteristic of quantum theory and plays an important role as a resource in quantum information tasks nonlocality1 ; nonlocality2 ; nonlocality3 . | Maxwell demon was first proposed by James Clark Maxwell in 1867 to demonstrate that the second law of thermodynamics is statistical rather than based on dynamical laws such as those of Newton demon . The Maxwell demon paradox was completely resolved by Landauer in 1961 when he introduced the concept of logical irrevers... | In conclusion, we have addressed the issue of simulating quantum non-locality through work. In the task of EPR steering, the Maxwell demon can be introduced in collaboration with Alice to deceive Bob using only local operations and classical communication. The existence of Maxwell demon-assisted EPR steering implies a ... | A |
In particular, we would like to understand the prediction of the quadrupole approximation, namely that the rate of gravitational energy loss along ℐ+superscriptℐ\mathcal{I}^{+}caligraphic_I start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT is given by −1/|u|41superscript𝑢4-1/|u|^{4}- 1 / | italic_u | start_POSTSUPERSCRIPT 4... | It would also be interesting to find a definitive answer to the question whether or not the rate (1.42) can be improved without assuming additional regularity. | We have thus established the uniform convergence of the sequence {ϕ1(k)}superscriptsubscriptitalic-ϕ1𝑘\{\phi_{1}^{(k)}\}{ italic_ϕ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( italic_k ) end_POSTSUPERSCRIPT }. In view of the uniformity of the convergence, the bounds from Propositions 5.1 and 5.5 car... | It may be instructive for the reader to keep the following solution to (3.11) in the case M=0𝑀0M=0italic_M = 0 in mind: | In view of the multipole structure of gravitational radiation, it thus seems to be necessary to first understand the answer to the following question: | D |
As a consequence, the action of SLOCC operators on the states |ψz⟩ketsubscript𝜓𝑧\ket{\psi_{z}}| start_ARG italic_ψ start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT end_ARG ⟩ would no longer be given by the corresponding Möbius transformation, and the statements in Theorem 1 would no longer hold. | Consider any SLIPnhsuperscriptsubscriptSLIP𝑛ℎ\text{SLIP}_{n}^{h}SLIP start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_h end_POSTSUPERSCRIPT measure and two (n+1)𝑛1(n+1)( italic_n + 1 )-qubit states. If both states have at least 3333 roots with respect to each subsystem, they are SLOCC-equiv... | The decomposition (4) can be performed with respect to any other subsystem, each with its own system of roots. Any local operator 𝒪k=(abcd)subscript𝒪𝑘matrix𝑎𝑏𝑐𝑑\mathcal{O}_{k}=\begin{pmatrix}a&b\\ | This system of four points can be mapped into a normal system (i.e. symmetrically related points z,−z,1/z,−1/z𝑧𝑧1𝑧1𝑧z,-z,1/z,-1/zitalic_z , - italic_z , 1 / italic_z , - 1 / italic_z) by a Möbius transformation. Similar local transformations can be performed with respect to other subsystems, transforming the states... | To study the effect of SLOCC operations on the system of roots we begin by acting on the first qubit of a state |ψ⟩ket𝜓\ket{\psi}| start_ARG italic_ψ end_ARG ⟩ written in the form of Eq. (4) with an invertible linear operator | B |
H. Gharibyan, C. Pattison, S. Shenker111Private communication via Stephen Shenker and Sourav Chatterjee in June 2020. and K. Wells who coined it as | so that for all H∈Ωi𝐻subscriptΩ𝑖H\in\Omega_{i}italic_H ∈ roman_Ω start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT the statistics of the i𝑖iitalic_i-th rescaled gap of the eigenvalues λixsuperscriptsubscript𝜆𝑖𝑥\lambda_{i}^{x}italic_λ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_x end_P... | The basic guiding principle for establishing quenched universality of Hxsuperscript𝐻𝑥H^{x}italic_H start_POSTSUPERSCRIPT italic_x end_POSTSUPERSCRIPT is to show that | The main universality result for the first mechanism (eigenbasis rotation) is the following quenched | Thus the main task is to show that eigenvectors of Hxsuperscript𝐻𝑥H^{x}italic_H start_POSTSUPERSCRIPT italic_x end_POSTSUPERSCRIPT become asymptotically orthogonal for different, sufficiently distant values of x𝑥xitalic_x. | B |
Fourth, the continuum assumption will break down near the wave front where the population is low. For the standard FKPP equation the resulting stochasticity introduces a speed reduction ∝ln−2(N)proportional-toabsentsuperscript2𝑁\propto\ln^{-2}(N)∝ roman_ln start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT ( italic_N ), w... | Our model cannot be tested in the usual environment of an agar plate: for such systems, where the phage are mobile rather than the bacteria, we predict that the asymptotic wave speed in populations of growing bacteria will vanish. A more suitable experimental setup for testing our theoretical predictions would therefor... | We focused here on the asymptotic wave speeds obtainable theoretically. Throughout, these wave speeds matched the predictions of FKPP theory, implying that these are pulled waves, i.e., driven by the infection dynamics in the very tip of the wave. This contrasts with recent work on bacteriophage plaques [29] where some... | Our main result is that the infected and uninfected bacteria form self-similar travelling waves, which retreat before the expanding phage front and which grow exponentially in time. The phage also form a self-similar front, which does not grow exponentially, but this is only in the case where superinfection (where a si... | Here, we will study the impact of exponential bacterial growth on the spread of bacteriophage infections. We will focus on the asymptotic wave speed of the infection and, as in ref. [30], allow for bacterial and bacteriophage mobility. In this paper, we want to stress the more mathematical and general aspects of this t... | A |
Robustness of quantum advantage, ΔΔ\Deltaroman_Δ, (ordinate) with the variation of noise strength, p𝑝pitalic_p (abscissa). In Gaussian noise, σ1=σ2=1subscript𝜎1subscript𝜎21\sigma_{1}=\sigma_{2}=1italic_σ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = italic_σ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = 1. In all cases, the... | The paper is organized in the following way. In Sec. 2, we provide the prerequisites which include the Chernoff bound (the upper bound on the efficiency of the illumination protocol), its classical limit, and the non-Gaussian states together with the noise models which we will use in our calculations. This is followed ... | In any experimental implementation, noise is inevitable, and in our work, the effects of different noisy probe states generated via different imperfections on the illumination procedure are investigated. Considering local noise modeled by Gaussian distributions, we found that, unlike a noiseless scenario, if the signal... | Instead of comparing the performance of noisy non-Gaussian states with the optimal classical scheme by coherent states, | We compare now the noisy non-Gaussian states with the corresponding noisy coherent state, i.e., noise affects both non-Gaussian and coherent states in a similar fashion, so that | D |
=π∧ω+du∧πabsent𝜋𝜔𝑑𝑢𝜋\displaystyle=\pi\wedge\omega+du\wedge\pi= italic_π ∧ italic_ω + italic_d italic_u ∧ italic_π | =dB(x)−B(x)dα+Aωabsent𝑑𝐵𝑥𝐵𝑥𝑑𝛼𝐴𝜔\displaystyle=dB(x)-B(x)d\alpha+A\omega= italic_d italic_B ( italic_x ) - italic_B ( italic_x ) italic_d italic_α + italic_A italic_ω | Now if we write Ω=ω−duΩ𝜔𝑑𝑢\Omega=\omega-duroman_Ω = italic_ω - italic_d italic_u and note that dΩ=dω𝑑Ω𝑑𝜔d\Omega=d\omegaitalic_d roman_Ω = italic_d italic_ω, we have the equation | =π∧ω+du∧πabsent𝜋𝜔𝑑𝑢𝜋\displaystyle=\pi\wedge\omega+du\wedge\pi= italic_π ∧ italic_ω + italic_d italic_u ∧ italic_π | =π∧(ω−du).absent𝜋𝜔𝑑𝑢\displaystyle=\pi\wedge(\omega-du).= italic_π ∧ ( italic_ω - italic_d italic_u ) . | D |
\sigma_{m}\geq 0\}=C_{i}.italic_C start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT = { ∑ start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT italic_a start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ⊗ italic_ϱ start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ; ∑ start_POSTSUBSCRI... | this claim is dual to the equivalence, in two dimensional case, of the tensor cone Cdsubscript𝐶𝑑C_{d}italic_C start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT determining decomposable maps with the tensor cone determining positive maps Cpsubscript𝐶𝑝C_{p}italic_C start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT. | The question of existence of product vectors in a subspace of the tensor product of two Hilbert spaces can be formulated in terms of algebraic geometry. In particular, properties of projective spaces as well as the Segre variety appeared to be crucial. For more information the reader may consult [14]. The following Pro... | As tensor cones are defined for the projective tensor product, the above tensor products ⊗tensor-product\otimes⊗ denote the projective tensor product ⊗πsubscripttensor-product𝜋\otimes_{\pi}⊗ start_POSTSUBSCRIPT italic_π end_POSTSUBSCRIPT. | super positive maps; they are determined by the largest tensor cone - the injective tensor cone Cisubscript𝐶𝑖C_{i}italic_C start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT. | C |
DM is free to propagate within the star and capture can, in principle, take place anywhere in the stellar interior. However, only a fraction of the DM flux traversing the star is effectively captured. | Figure 8: Capture rate in the optically thin limit for operators D1-D4 as a function of the DM mass mχsubscript𝑚𝜒m_{\chi}italic_m start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT for nucleons and exotic targets in the NS benchmark configuration QMC-4 (1.9M⊙1.9subscript𝑀direct-product1.9M_{\odot}1.9 italic_M start_POS... | Below, we derive general expressions for the capture rate in the optically thin limit, for various DM mass regimes, correctly incorporating the effects of baryon structure and strong interactions. | Figure 9: Capture rate in the optically thin limit for operators D5-D10 as a function of the DM mass mχsubscript𝑚𝜒m_{\chi}italic_m start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT for nucleons and exotic targets in the NS benchmark configuration QMC-4 (1.9M⊙1.9subscript𝑀direct-product1.9M_{\odot}1.9 italic_M start_PO... | Capture rate in the optically thin limit for the operators D5 (top) and D8 (bottom) as a function of the DM mass mχsubscript𝑚𝜒m_{\chi}italic_m start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT for neutron (left) and proton (right) targets, | B |
(1-x_{b})(x_{b}-x_{a})}]^{2}].- [ divide start_ARG italic_ω ( 1 - italic_x start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ) end_ARG start_ARG 2 italic_β start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_x start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_x start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT - italic_... | Here we did not give S explicitly, since it is given in the equation given above, and does not appear anymore. | We first write the metric as is given in [18], which is equivalent to the one given in [11]. We follow some of the work in [18] in the first part, and [6] in the second part of this section. | Here we start with the metric as given in [18] and try to write the wave equation, in the background of this metric, as given in [6], in the standard form given by [20]. How to perform this task is described in [21], as quoted by [22], and used meticulously by [23, 24]. The same method is recently used in [25, 36, 37, ... | Note that this last transformation is one of the transformations which does not change the Heun form of the differential equation. | A |
The expanders are physically realized as diffractive optical elements (DOE). Fabricating the DOEs consists of several stages. The first stage consists of etching the negative of the desired pattern onto a substrate. This etching is performed with laser beam lithography. The etched substrate forms a stamp which is then ... | While our experimental prototype was built for a HOLOEYE-PLUTO which possesses a 1K-pixel resolution, corresponding to a 1 mm eyebox with 75.6∘superscript75.675.6^{\circ}75.6 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT horizontal and vertical FOV, the improvement in hologram fidelity persists across resolutions. Irresp... | We used PyTorch to design and evaluate the neural étendue expanders. See Supplementary Notes 2 and 3 for details on the optimization framework, evaluation, and analysis. | We evaluated the neural étendue expanders using a prototype holographic display. The prototype consists of a HOLOEYE-PLUTO SLM, a 4F system, a DC block, and a camera for imaging the étendue expanded holograms. See Supplementary Notes 9 and 10 for details. | We validate neural étendue expansion experimentally with a holographic display prototype. See Fig. 2a for a schematic of the hardware prototype and Supplementary Notes 9 and 10 for further details on the experimental setup. | C |
(Thöne et al. 2011), to the establishment of the ultra-long-duration GRB class (Levan et al. 2014). GRB 111209A was found to be | (Thöne et al. 2011), to the establishment of the ultra-long-duration GRB class (Levan et al. 2014). GRB 111209A was found to be | To further explore this color-change in GRB-SNe, we need to collect more observations in the rest-frame UV. This can be done by observing rare nearby events in the UV, or with deep optical observations of the more distant GRB-SNe. | This discovery immediately opened multiple new lines of inquiry. We now question whether all ultra-long GRBs are associated with anomalous GRB-SNe, and | if so, whether they are similar to SN 2011kl or outliers in other aspects. Moreover, we would like to know if such peculiar, highly luminous GRB-SNe are exclusively | C |
In this tutorial review, we presented theory for reverse osmosis (RO) and electrodialysis (ED), explaining how both technologies are based on the same fundamental transport theory. This is the solution-friction (SF) theory, and for ED we solved it in the absence of convection, thus we did not discuss pressures. We used... | Water treatment generally refers to the removal of contaminants other than salts, such as organic micropollutants (OMPs), whereas desalination and deionization refer to the removal of salts, thus of ions. RO is a method that uses pressure to drive water through a membrane, keeping most of the ions and other solutes on ... | In general, for multi-ionic salt mixtures, and when we also include the partitioning coeffcient, ΦisubscriptΦ𝑖\Phi_{i}roman_Φ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT, possibly different between all ions, it is advisable to return to a Boltzmann equation for each ion, Eq. (34), and solve that in combination with... | Topics that we did not address in this tutorial review are first of all that both for RO and NF we must implement the Nernst-Planck equation for ions and a charged membrane in a full module calculation, and beyond that extend the theory from simple 1:1 salt solutions to multi-ionic solutions, also for electrodialysis. ... | An ED stack consists of many cell pairs, with electrodes on the two sides of the stack, where electronic current becomes ionic current. In this review we do not discuss the electrodes but we focus on the repeating unit of an ED stack, which is the membrane cell pair, see Fig. 1B, which consists of two membranes and two... | C |
QuantumNAT is fundamentally different from existing methods: (i) Prior work focuses on low-level numerical correction in inference only; QuantumNAT embraces more optimization freedom in both training and inference. It improves the intrinsic robustness and statistical fidelity of PQC parameters. (ii) PQC has a good buil... | To improve NN efficiency, extensive work has been explored to trim down redundant bit representation in NN weights and activations (Han | Figure 2. Quantum Neural Networks Architecture. QNN has multiple blocks, each has an encoder to encode classical values to quantum domain, quantum layers with trainable weights, and a measurement layer that obtains classical values. | et al., [n. d.]) 2-class (frog, ship). MNIST, Fashion, and CIFAR use 95% images in ‘train’ split as training set and 5% as the validation set. Due to the limited real QC resources, we use the first 300 images of ‘test’ split as test set. Vowel-4 dataset (990 samples) is separated to train:validation:test = 6:1:3 and te... | Moreover, by sparsifying the parameter space, quantization reduces the NN complexity as a regularization mechanism that mitigates potential overfitting issues. | A |
This work includes data products from the Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE), which is a project of the Jet Propulsion Laboratory/California Institute of Technology. NEOWISE is funded by the National Aeronautics and Space Administration. The Fermi-LAT Collaboration acknowledges support for ... | This work performed in part under DOE Contract DE-AC02-76SF00515. MG, PM and RS acknowledge the partial support of this research by grant 21-12-00343 from the Russian Science Foundation. KH has been supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Min... | AF received funding from the German Science Foundation DFG, within the Collaborative Research Center SFB1491 “Cosmic Interacting Matters - From Source to Signal”. YY thanks the Heising–Simons Foundation for financial support. SR was supported by the Helmholtz Weizmann Research School on Multimessenger Astronomy, funded... | This work performed in part under DOE Contract DE-AC02-76SF00515. MG, PM and RS acknowledge the partial support of this research by grant 21-12-00343 from the Russian Science Foundation. KH has been supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Min... | AF received funding from the German Science Foundation DFG, within the Collaborative Research Center SFB1491 “Cosmic Interacting Matters - From Source to Signal”. YY thanks the Heising–Simons Foundation for financial support. SR was supported by the Helmholtz Weizmann Research School on Multimessenger Astronomy, funded... | A |
{\rm D}_{5/2}(m=-1/2)| roman_g ⟩ ∼ 4 roman_S start_POSTSUBSCRIPT 1 / 2 end_POSTSUBSCRIPT ( italic_m = - 1 / 2 ) ↔ | roman_e ⟩ ∼ 3 roman_D start_POSTSUBSCRIPT 5 / 2 end_POSTSUBSCRIPT ( italic_m = - 1 / 2 ) electronic transition with frequencies ωbsubscript𝜔𝑏\omega_{b}italic_ω start_POSTSUBSCRIPT italic_b end_POSTSUBSC... | Figure 1: a) The mechanical oscillator corresponds to axial harmonic motion of a single 4040{}^{40}start_FLOATSUPERSCRIPT 40 end_FLOATSUPERSCRIPTCa+{}^{+}start_FLOATSUPERSCRIPT + end_FLOATSUPERSCRIPT ion localized in a linear Paul trap. The generation and analysis of states approaching idealized Fock states illustrated... | The genuine n𝑛nitalic_n-phonon quantum non-Gaussianity of pure states manifests itself by the proper number of negative annuli in the Wigner function. The topology of negative regions in the Wigner function exposes the genuine n𝑛nitalic_n-order quantum non-Gaussianity because each Fock state exhibits a specific numbe... | Fig. 1-c) analyses the exhibition of genuine n𝑛nitalic_n-phonon quantum non-Gaussianity using idealized and measured Fock states (yellow data points). | Figure S4: The thermal depth of the genuine n𝑛nitalic_n-phonon quantum non-Gaussianity (green points), the quantum non-Gaussianity (blue points) and negativity in the Wigner function (red points) that are exhibited by the ideal Fock states. The thermalization deteriorates the Fock states according to the map (S7). The... | C |
If Misubscript𝑀𝑖M_{i}italic_M start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT rejects, then fisubscript𝑓𝑖f_{i}italic_f start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT is uniformly random. | We may also construct oracles by joining other oracles together. For example, if we have a pair of oracles A,B:{0,1}∗→{0,1}:𝐴𝐵→superscript0101A,B:\{0,1\}^{*}\to\{0,1\}italic_A , italic_B : { 0 , 1 } start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT → { 0 , 1 }, then 𝒪=(A,B)𝒪𝐴𝐵\mathcal{O}=(A,B)caligraphic_O = ( italic_A... | Let 𝒟𝒟\mathcal{D}caligraphic_D be the resulting distribution over oracles 𝒪=(A,B)𝒪𝐴𝐵\mathcal{O}=(A,B)caligraphic_O = ( italic_A , italic_B ). | Let 𝒟𝒟\mathcal{D}caligraphic_D be the resulting distribution over oracles 𝒪=(A,B,C)𝒪𝐴𝐵𝐶\mathcal{O}=(A,B,C)caligraphic_O = ( italic_A , italic_B , italic_C ). We will show that the statement of the theorem holds with probability 1111 over 𝒪𝒪\mathcal{O}caligraphic_O sampled from 𝒟𝒟\mathcal{D}caligraphic_D. | 𝖯𝒪=𝖭𝖯𝒪superscript𝖯𝒪superscript𝖭𝖯𝒪\mathsf{P}^{\mathcal{O}}=\mathsf{NP}^{\mathcal{O}}sansserif_P start_POSTSUPERSCRIPT caligraphic_O end_POSTSUPERSCRIPT = sansserif_NP start_POSTSUPERSCRIPT caligraphic_O end_POSTSUPERSCRIPT with probability 1111 over 𝒪𝒪\mathcal{O}caligraphic_O. | B |
Network data analysis is an important research topic in a range of scientific disciplines in recent years, particularly in the biological science, social science, physics and computer science. Many researchers aim at analyzing these networks by developing models, quantitative tools and theoretical framework to have a d... | In this paper, we introduced the Degree-Corrected Distribution-Free Model (DCDFM), a model for community detection on weighted networks. The proposed model is an extension of previous Distribution-Free Models by incorporating node heterogeneity to model real-world weighted networks in which nodes degrees vary, and it a... | (a) DCDFM models weighted networks by allowing nodes within the same community to have different expectation degrees. Though the WSBM developed in [12] also considers node heterogeneity, it requires all elements of connectivity matrix to be nonnegative, and fitting it by spectral clustering is challenging. Our DCDFM in... | Network data analysis is an important research topic in a range of scientific disciplines in recent years, particularly in the biological science, social science, physics and computer science. Many researchers aim at analyzing these networks by developing models, quantitative tools and theoretical framework to have a d... | However, most works built under SBM and DCSBM require the elements of adjacency matrix of the network to follow Bernoulli distribution, which limits the network to being un-weighted. Modeling and designing methods to quantitatively detecting latent structural information for weighted networks are interesting topics. Re... | D |
Whereas, F(ℬηcF(\mathcal{B}^{\textrm{c}}_{\eta}italic_F ( caligraphic_B start_POSTSUPERSCRIPT c end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_η end_POSTSUBSCRIPT, ℬpr)=η<3(η+1)2η+4\mathcal{B}_{\textrm{pr}})=\eta<\frac{3(\eta+1)}{2\eta+4}caligraphic_B start_POSTSUBSCRIPT pr end_POSTSUBSCRIPT ) = italic_η < divide sta... | In this article, we first focus on state transformations which involve a single copy of a quantum state. We consider the intermediate regime between probabilistic and approximate transformations for which very few results have been presented so far [34, 35, 33, 36, 37]. Here, the goal is to convert a quantum state ρ𝜌\... | We now study the nature of our bounds in the asymptotic limit. As we show now, our single-copy bounds imply upper bounds on the asymptotic transformation rates in general resource theories. The deterministic rate for a transformation between ρ𝜌\rhoitalic_ρ and σ𝜎\sigmaitalic_σ is given by | Here, the infimum is taken over the set of deterministic free operations (ΛfsubscriptΛ𝑓\Lambda_{f}roman_Λ start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT). We now generalise the above definition to the probabilistic case where the probability of success is not allowed to decay too fast (exponentially in the number of c... | We investigated the problem of converting quantum states within general quantum resource theories, and within the theory of entanglement. In particular, we considered probabilistic transformations, allowing for a small error in the final state. For general resource theories, we obtained upper bounds on the conversion p... | D |
We selected some radionuclides of interest to test the predictions of the presented atomic models under different conditions: atomic number (Z=4−57𝑍457Z=4-57italic_Z = 4 - 57); transition nature (allowed: 7Be, 37Ar, 54Mn, 55Fe, 109Cd and 125I; first forbidden unique: 41Ca; second forbidden unique: 138La); and availabi... | Most often, experimental values are given as relative, i.e., as a ratio of capture probabilities between two shells, instead of absolute capture probabilities, which are much more difficult to measure precisely. To unify the presentation of their comparison with the theoretical predictions, we defined the following qua... | Table 2: Comparison of calculated and measured capture probabilities for different isotopes considered in the present work. The three models and the experimental values are described in the text. | Capture probabilities from BetaShape have been compared with a selection of measurements available in the literature, concluding to the need of new high-precision measurements to validate and constrain the theoretical models Mougeot (2018). This played a crucial role in the inception of the European metrology project M... | The theoretical capture probabilities of several transitions of interest have been compared with experimental values with relative uncertainties from 0.2% to 3.5%, except for 7Be (10%) and 41Ca (no existing measurement). Such a comparison covers a wide range of atomic numbers, 3≤Z≤573𝑍573\leq Z\leq 573 ≤ italic_Z ≤ 57... | A |
For US Top-500 Airport Network, it has 500×0.1400=705000.140070500\times 0.1400=70500 × 0.1400 = 70 highly mixed nodes and 500×0.7820=3915000.7820391500\times 0.7820=391500 × 0.7820 = 391 highly pure nodes. | For Political blogs, it has 1222×0.0393≈4812220.0393481222\times 0.0393\approx 481222 × 0.0393 ≈ 48 highly mixed nodes and 1222×0.8781≈107312220.878110731222\times 0.8781\approx 10731222 × 0.8781 ≈ 1073 highly pure nodes. | For US airports, it has 1572×0.0865≈13615720.08651361572\times 0.0865\approx 1361572 × 0.0865 ≈ 136 highly mixed nodes and 1572×0.8575≈134815720.857513481572\times 0.8575\approx 13481572 × 0.8575 ≈ 1348 highly pure nodes. | For Train bombing, it has 64×0.0938≈6640.0938664\times 0.0938\approx 664 × 0.0938 ≈ 6 highly mixed nodes and 64×0.7969≈51640.79695164\times 0.7969\approx 5164 × 0.7969 ≈ 51 highly pure nodes. | For Karate-club-weighted, it has 34×0.0588≈2340.0588234\times 0.0588\approx 234 × 0.0588 ≈ 2 highly mixed nodes and 34×0.7941≈27340.79412734\times 0.7941\approx 2734 × 0.7941 ≈ 27 highly pure nodes. | A |
ECR acknowledges the ThinkSwiss Research Scholarship, funded by the State Secretariat for Education, Research and Innovation (SERI) for the opportunity to spend three months at the University of Zürich Institute for Computational Science; travel support from the Alexander Vyssotsky Award from the University of Virginia... | We acknowledge PRACE for awarding us access to MareNostrum at the Barcelona Supercomputing Center (BSC), Spain. This research was partly carried out via the Frontera computing project at the Texas Advanced Computing Center. Frontera is made possible by National Science Foundation award OAC-1818253. This work was suppor... | RF acknowledges financial support from the Swiss National Science Foundation (grant no PP00P2_157591, PP00P2_194814, and 200021_188552). | MBK acknowledges support from NSF CAREER award AST-1752913, NSF grant AST-1910346, NASA grant NNX17AG29G, and HST-AR-15006, HST-AR-15809, HST-GO-15658, HST-GO-15901, HST-GO-15902, HST-AR-16159, and HST-GO-16226 from the Space Telescope Science Institute (STScI), which is operated by AURA, Inc., under NASA contract NAS5... | AW received support from NSF CAREER grant 2045928; NASA ATP grants 80NSSC18K1097 and 80NSSC20K0513; HST grants AR-15057, AR-15809, GO-15902 from STScI; a Scialog Award from the Heising-Simons Foundation; and a Hellman Fellowship. | B |
\uparrow}(\mathbb{R}_{+},\mathcal{M}(\mathbb{R}^{l}))( italic_φ , italic_μ ) ∈ caligraphic_C ( blackboard_R start_POSTSUBSCRIPT + end_POSTSUBSCRIPT , blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT ) × caligraphic_C start_POSTSUBSCRIPT ↑ end_POSTSUBSCRIPT ( blackboard_R start_POSTSUBSCRIPT + end_POSTSUB... | More precisely, let 𝕀^^𝕀\widehat{\mathbb{I}}over^ start_ARG blackboard_I end_ARG be a large deviations limit rate functions or | Now, let 𝕀^^𝕀\widehat{\mathbb{I}}over^ start_ARG blackboard_I end_ARG be a large deviations limit rate functions or (large deviations) LD limit points of | For any such a large deviation limit point 𝕀^^𝕀\widehat{\mathbb{I}}over^ start_ARG blackboard_I end_ARG, we aim to prove 𝕀^=𝕀*^𝕀superscript𝕀\widehat{\mathbb{I}}=\mathbb{I}^{*}over^ start_ARG blackboard_I end_ARG = blackboard_I start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT | Let 𝕀^^𝕀\widehat{\mathbb{I}}over^ start_ARG blackboard_I end_ARG be a large deviations limit point of | D |
In our analysis, these will be included in the δRsubscript𝛿𝑅\delta_{R}italic_δ start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT correction in Section 3.2. | For the GT one, since the matrix element is proportional to the unknown parameter r𝑟ritalic_r which has to be anyway fixed from experiment, the isospin breaking corrections do not play an important role. | For the subleading matrix elements, the isospin breaking corrections are not phenomenologically relevant, given the current experimental sensitivity. | Given the current precision of the beta decay experiments, isospin breaking effects must be taken into account in the case of the Fermi matrix element. | The parameter r𝑟ritalic_r, which is real by time-reversal invariance, is referred to as the ratio of GT and Fermi matrix elements in the literature. For the neutron decay r=3𝑟3r=\sqrt{3}italic_r = square-root start_ARG 3 end_ARG. | A |
\theta,\phi)\rho^{Z}(\mathbf{r}).italic_c start_POSTSUPERSCRIPT italic_Z end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_n italic_l italic_m end_POSTSUBSCRIPT ( bold_r ) = ∭ start_POSTSUBSCRIPT caligraphic_R start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT end_POSTSUBSCRIPT roman_d italic_V italic_g start_POSTSUBSCRIPT itali... | Here, we incorporate symmetries via the latter approach using Smooth Overlap of Atomic Positions (SOAP) descriptors that are invariant to rotation and translation. These atomic environment descriptors represent the electron density at some point r𝑟ritalic_r by the superposition of the Gaussian densities of atoms with ... | In this work, we use the Dscribe library Himanen et al. (2020) to obtain the descriptors. This library implements SOAP descriptors using a partial power spectrum that only includes real spherical harmonics. Because the density depends on the square of the distances between points, it is already invariant to translation... | The original SOAP descriptors compare the local atomic environments using a kernel that is the dot product of the normalized power spectra between different configurations | It is important to note that, when global descriptors are employed, the total energy is no longer the simple sum of local contributions. Now, it explicitly depends on quantities that interrelate features of the whole structure. This overall description of atomic structures implicitly removes the need for descriptors th... | B |
\scriptscriptstyle{Dol}}}_{r,0}(C),{\mathbb{Q}}_{\operatorname{vir}})bold_H start_POSTSUPERSCRIPT roman_BM end_POSTSUPERSCRIPT ( fraktur_M start_POSTSUPERSCRIPT roman_Dol end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_r , 0 end_POSTSUBSCRIPT ( italic_C ) , blackboard_Q start_POSTSUBSCRIPT roman_vir end_POSTSUBSCRIPT ) ... | }}}_{\bullet}(C))bold_U ( fraktur_g start_POSTSUPERSCRIPT roman_Dol end_POSTSUPERSCRIPT start_POSTSUBSCRIPT ∙ end_POSTSUBSCRIPT ( italic_C ) ). The following conjecture states that the images of these inclusions already generate. This is the Dolbeault version of Conjecture 4.7, and is motivated the same way, via Conjec... | In particular, the supports of the LHS and RHS of (51) are different, and so the morphism (51) is zero. This completes the proof of the g=1𝑔1g=1italic_g = 1 version of Conjecture 4.6. | Using the analogues of the above results for g(C)≤1𝑔𝐶1g(C)\leq 1italic_g ( italic_C ) ≤ 1, we deduce Theorem A. We split this up into two cases | In the remainder of this section we check appropriate modifications of Conjecture 5.6 for the cases g(C)≤1𝑔𝐶1g(C)\leq 1italic_g ( italic_C ) ≤ 1. | D |
Random walks are one of the most fundamental dynamical processes, and many studies have used random walks on networks (i.e., graphs) to gain insights into network structure and how such structure affects dynamical processes [25]. Much research has focused on standard random walks, in which the distribution of the occup... | Absorbing random walks have been used to develop centrality measures [14], other methods to rank the nodes of a network [46], transduction algorithms (which one can use to infer the labels of the nodes of a graph from the labels of a subset of the nodes) [7], and more. For example, Jaydeep et al. [7] proposed a transdu... | We now introduce adaptations of InfoMap that account for the absorption rates of the nodes of a network. Our approach uses absorption-scaled graphs, which arise naturally in the context of absorbing random walks [16]. | Figure 1: Consider an absorbing random walk on the depicted four-node network, and suppose that the absorption rate of node 2 is much larger than the absorption rates of the other nodes. Detecting communities via modularity maximization or the standard InfoMap algorithm produces a partition of the network into a single... | Random walks are one of the most fundamental dynamical processes, and many studies have used random walks on networks (i.e., graphs) to gain insights into network structure and how such structure affects dynamical processes [25]. Much research has focused on standard random walks, in which the distribution of the occup... | A |
Among our schemes, we use DP-OPT, DP-Approx and Balanced-Tree (see §IV-B) for the QNR-SP problem, and LP (Appendix A) and ITER schemes for the QNR problem. For ITER, we use three schemes: | ITER-DPA, ITER-Bal and ITER-SP, which iterate over DP-Approx, Balanced-Tree and SP respectively. To be comprehensive, | Among our schemes, we use DP-OPT, DP-Approx and Balanced-Tree (see §IV-B) for the QNR-SP problem, and LP (Appendix A) and ITER schemes for the QNR problem. For ITER, we use three schemes: | We observe that the performance gap between our proposed techniques and ITER-SP is higher than in the QNR-SP case, as SP picks paths based on just number of | the following schemes: ITER-DPA, ITER-Bal, ITER-SP, Delft-LP, and Q-Cast with the optimal LP as the benchmark for comparison (LP wasn’t feasible to run | A |
Note that each of these conditions jointly concerns the system energy, the time evolution law, the initial condition, and the choice of observables. | If we have enough information about the system to ensure that the system satisfies one of these sufficient conditions for the realizability condition, we can obtain the exact value of the true EP from Eq. (11b), and we can obtain additional information by the methods described below in Secs. V.2–V.4. | In this paper, we propose a method of thermodynamic inference for relaxation processes that uses measurements in tilted equilibrium, i.e., the equilibrium under the application of external fields to the system. Our approach combines the nonstationary measurement of a few observables with the tilted equilibrium measurem... | As discussed in Sec. III.3, the realizability condition [Eq. (12)] ensures that the inequality in Eq. (11a) holds with equality, allowing the inference of the exact value of EP. We discuss three situations where the realizability condition is satisfied in Sec. V.1. Moreover, assuming the realizability condition, we can... | In this paper, we have developed a method of thermodynamic inference that uses tilted equilibrium measurements. The method enables us to obtain the exact value of the minimum EP Δℋm(𝜼)Δsubscriptℋm𝜼\Delta{\mathcal{H}_{\mathrm{m}}}(\bm{\eta})roman_Δ caligraphic_H start_POSTSUBSCRIPT roman_m end_POSTSUBSCRIPT ( bold_i... | A |
Example file with an instance of Ising spin-glass. The Hamiltonian of the presented problem reads H(s0,s1,s2)=−1s0s1−3s0s2+1.5s1s2𝐻subscript𝑠0subscript𝑠1subscript𝑠21subscript𝑠0subscript𝑠13subscript𝑠0subscript𝑠21.5subscript𝑠1subscript𝑠2H(s_{0},s_{1},s_{2})=-1s_{0}s_{1}-3s_{0}s_{2}+1.5s_{1}s_{2}italic_H ... | the current directory. The input file comprises rows of the form “i j J_ij”. Here, i and j are indices of variables and J_ij is the | (required by the base class’ sample method) and an additional keyword parameter num_solutions indicating how many solutions should be returned. | plugins are responsible for implementing algorithms solving instances of Ising spin–glass or QUBO models (collectively known as Binary Quadratic | This work is supported by the project “Near-term quantum computers Challenges, optimal implementations and applications” under Grant Number POIR.04.04.00–00–17C1/18–00, which is carried out within the Team-Net programme of the Foundation for Polish Science co-financed by the European Union under the European Regional D... | D |
Coronaviruses constitute an extensive family of viruses typically responsible for causing mild to moderate upper-respiratory tract illnesses. Various coronaviruses circulate among animals, including pigs, cats, and bats. On occasion, these viruses can jump from animals to humans, leading to infections. Some of these in... | Numerical solutions of systems are invaluable in the study of epidemic models. This section presents the numerical results of our model, shedding light on how the parameters of the deterministic model (2) and the intensity of non-Gaussian noise in the stochastic model (4) impact the dynamics. We conduct numerical exper... | Environmental fluctuations have emerged as a significant factor in the study of diseases, particularly in the context of the coronavirus. Consequently, it becomes crucial to investigate the impact of random disturbances on epidemic models. Disease spread is inherently stochastic, and the introduction of stochastic nois... | To date, a multitude of mathematical models describing infectious diseases through differential equations have been formulated and scrutinized to understand the dynamics of infection spread, exemplified by research on [1, 2, 3, 4]. Recently, the mathematical modeling of the COVID-19 pandemic has captivated the attentio... | In this study, we explore a nonlinear stochastic COVID-19 system, incorporating the influence of non-Gaussian noise. The presence of non-Gaussian noise adds a layer of complexity to the modeling framework, allowing for a more realistic representation of the uncertainties and random fluctuations inherent in the dynamics... | C |