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We can apply the concepts of proper time oscillation outside quantum theory. If we neglect all quantum effects, a proper time oscillator can be treated as a ’stationary’ classical object, equivalent to a point mass at rest in general relativity. <|MaskedSetence|> <|MaskedSetence|> [6, 7]. The self-adjoint time operator, proper time uncertainty relation, and generation of a Schwarzschild field are properties that could reduce some of the differences between quantum theory and general relativity.
The paper is organized as follows: Section 2 introduces the concepts of proper time oscillation. <|MaskedSetence|> Section 5 further elaborates on the properties of a proper time oscillator and clarifies certain concepts. The last section is reserved for discussions and conclusions.. | **A**: Sections 3 and 4 provide an overview of a proper time oscillator’s quantum properties and gravitational field.
**B**: These results have been recently affirmed in refs.
**C**: Under this assumption, we expect the proper time oscillator to curve the surrounding spacetime and generate a gravitational field; its solution shall be the Schwarzschild metric.
| CBA | CBA | CBA | ABC | Selection 3 |
<|MaskedSetence|> Typically, in this context one assumes that weakly interacting bosons occupying different wells can be described with two independent single-particle orbitals and that the dynamics is governed by two mechanisms: contact two-body interactions acting locally and single-particle tunneling between wells. Then, in the mean-field limit, a corresponding Gross-Pitaevskii equation is introduced and numerically solved for different initial conditions Raghavan ; Ostrovskaya ; Ananikin . Generalized two-mode models, taking into account additional terms originating from long-range interactions or occupation-dependent tunnelings, are also considered in the literature and relevant corrections to the dynamics are studied Lahaye ; Adhikari ; Bruno . <|MaskedSetence|> <|MaskedSetence|> For example, it was shown that for initially imbalanced occupations the dynamics is heavily affected by strong interactions DuttaS . Unfortunately, the validity of the model used was not discussed and its predictions were not compared with the exact dynamics governed by a general model.
. | **A**:
In view of recent experimental progress with ultra-cold atoms forming a Bose-Einstein condensate, double-well systems are one of the most commonly exploited schemes studied Andrews ; Smerzi ; Milburn ; Menotti ; Meier ; Shin ; Albiez ; Levy ; Salgueiro ; Simon ; Liu .
**B**: Although the validity of these simplified two-mode models was confirmed experimentally for weak interactions between particles, they were extended beyond the range of their applicability and adopted for strongly interacting systems, i.e.
**C**: in situations when the local interaction energy is much larger than the single-particle tunneling energy.
| ABC | ABC | CBA | ABC | Selection 2 |
<|MaskedSetence|> Realizing Harmonic Oscillators With Coupled Supersymmetry
As previously noted, the quantum mechanical harmonic oscillator is a specific instance of a coupled supersymmetry, albeit a somewhat trivial case in which the two coupled SUSY equations are identical. This is not the only manner in which the two are connected. Indeed, a special class of coupled SUSYs may be realized as harmonic oscillator-like systems, i.e. <|MaskedSetence|> <|MaskedSetence|> | **A**: they satisfy the same Lie algebra and by virtue of Stone-von Neumann, may be realized in some way as harmonic oscillators.
**B**:
7.
**C**: If one takes γ=−δ𝛾𝛿\gamma=-\deltaitalic_γ = - italic_δ, then the coupled SUSY equations become
.
| BAC | ABC | BAC | BAC | Selection 1 |
unstable again however in a reversed way: unlike an ordinary matter
ball it performs an unbounded contraction. <|MaskedSetence|> E<0𝐸0E<0italic_E < 0 and is
already small i.e. 0<Rinitial<−Gm2/2E0subscript𝑅initial𝐺superscript𝑚22𝐸0<R_{\rm initial}<-Gm^{2}/2E0 < italic_R start_POSTSUBSCRIPT roman_initial end_POSTSUBSCRIPT < - italic_G italic_m start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 2 italic_E. <|MaskedSetence|> <|MaskedSetence|> | **A**: Applying (7)
we find again that R→0→𝑅0R\rightarrow 0italic_R → 0 i.e.
**B**: a sufficiently small bounded.
**C**: The second possibility is
that the ball is gravitationally bounded i.e.
| BAC | CAB | CAB | CAB | Selection 2 |
fails, in the sense that there can be no such simple decomposition as the group associated to the bulk space will include also a de-Sitter component. However, it is still possible to reconstruct a boundary theory by carefully restricting the doubled coordinates in the bulk region close to the boundary. There are several options by which such a restriction can be performed [43], [44], [45], each coming with advantages and disadvantages. The most important aspect is to keep the desirable effects of T-duality in the limit where the doubled coordinates become irrelevant. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> | **A**: Also, effects associated to the extended nature of the strings, from where double field theory extracts its stranger features, seem to be related to mixing of operators in the boundary and to a left-right symmetry which should not otherwise be present [46].
.
**B**: Heuristically speaking, it is possible to imagine that stringy modes encoded in the bulk double field theory may have the effect of violating associativity of the operators in the boundary.
**C**: It is currently not clear what precisely the boundary encoding map associated to the mixing terms found in the bulk due to the extended gauge symmetry.
| CBA | CBA | CBA | CBA | Selection 3 |
<|MaskedSetence|> The calculation presented here relies on properties of the exterior family of metrics. <|MaskedSetence|> It is not clear if one could define some timescale analogous to T𝑇Titalic_T that would have a meaning for an arbitrary exterior spacetime, therefore rendering the entire calculation not applicable. <|MaskedSetence|> Therefore, it would seem one would need to attempt to compare ‘different geometry transitions’ at the basis of their ‘absolute probabilities’.
In other words, the calculation presented here is not how the probability of some geometry X transitioning to a geometry Y compares to the probability of geometry X transitioning to some geometry Z, (or, to no transition). We have not here defined a probability in the sense that one transition is normalised against the sum of the probabilities of all possible geometry transitions. Rather, the spirit of the calculation is best understood as estimating how the probability of transition scales with the timescale T𝑇Titalic_T
and the mass scale m𝑚mitalic_m having assumed this transition to take place. Then, an implicit assumption is that, like in quantum mechanical tunneling, one may hope to estimate how the probability scales with time without needing to calculate its normalisation.. | **A**: It can be noted that it is not obvious to us how to do such a comparison in the first place, at least with the techniques we used here.
**B**: Indeed, as we have seen in Section III.5 here T𝑇Titalic_T is best thought of as a parameter of the specific exterior geometry we consider.
**C**: We have considered the exterior spacetime as given in all spacetime except a compact region.
| ACB | ACB | BCA | ACB | Selection 4 |
Let (Co,q→o)subscript𝐶𝑜subscript→𝑞𝑜(C_{o},\vec{q}_{o})( italic_C start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT , over→ start_ARG italic_q end_ARG start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT ) be a s𝑠sitalic_s-pointed ΓΓ\Gammaroman_Γ-curve such that ΓΓ\Gammaroman_Γ acts stably on Cosubscript𝐶𝑜C_{o}italic_C start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT (cf. Definition 5.1).
Let C~osubscript~𝐶𝑜\tilde{C}_{o}over~ start_ARG italic_C end_ARG start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT be the normalization of Cosubscript𝐶𝑜C_{o}italic_C start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT at the points Γ⋅r⋅Γ𝑟\Gamma\cdot rroman_Γ ⋅ italic_r, where r𝑟ritalic_r is a (stable) nodal point of Cosubscript𝐶𝑜C_{o}italic_C start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT. The nodal point r𝑟ritalic_r splits into two smooth points r′,r′′superscript𝑟′superscript𝑟′′r^{\prime},r^{\prime\prime}italic_r start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT , italic_r start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT in C~osubscript~𝐶𝑜\tilde{C}_{o}over~ start_ARG italic_C end_ARG start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> The following lemma shows that there exists a canonical smoothing deformation of (Co,q→o)subscript𝐶𝑜subscript→𝑞𝑜(C_{o},\vec{q}_{o})( italic_C start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT , over→ start_ARG italic_q end_ARG start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT ) over a formal disc 𝔻τ:=Specℂ[[τ]]assignsubscript𝔻𝜏Specℂdelimited-[]delimited-[]𝜏\mathbb{D}_{\tau}:={\rm Spec}\,\mathbb{C}[[\tau]]blackboard_D start_POSTSUBSCRIPT italic_τ end_POSTSUBSCRIPT := roman_Spec blackboard_C [ [ italic_τ ] ]. We denote by 𝔻τ×subscriptsuperscript𝔻𝜏\mathbb{D}^{\times}_{\tau}blackboard_D start_POSTSUPERSCRIPT × end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_τ end_POSTSUBSCRIPT the associated punctured formal disc Specℂ((τ))Specℂ𝜏{\rm Spec}\,\mathbb{C}((\tau))roman_Spec blackboard_C ( ( italic_τ ) ).
. | **A**: Let z′superscript𝑧′z^{\prime}italic_z start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT (resp.
**B**: r′′superscript𝑟′′r^{\prime\prime}italic_r start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT) for the curve C~osubscript~𝐶𝑜\tilde{C}_{o}over~ start_ARG italic_C end_ARG start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT.
**C**: z′′superscript𝑧′′z^{\prime\prime}italic_z start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT) be a local parameter at r′superscript𝑟′r^{\prime}italic_r start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT (resp.
| ACB | ACB | ACB | ABC | Selection 1 |
A pseudo-species is not a single type of anyons. Rather, the single-particle states of a pseudo-species correspond to different types of anyons (see Fig. 6).
This also answers the question 2) raised in the second paragraph in the introduction Section 1. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> | **A**: 4(e), a subsystem of any number of real anyons is characterized by the pseudo-species; the observables associated with the pseudo-species supply good quantum numbers (topological charges) of the subsystem.
**B**: Seen in Fig.
**C**: The single-particle states of the pseudo-species are precisely these topological charges.
.
| BCA | BAC | BAC | BAC | Selection 3 |
<|MaskedSetence|> The paper is organized as follows. <|MaskedSetence|> In Section 3, we give a concise example for the MSR of the mixed-spin (1/2,1/2)1212(1/2,1/2)( 1 / 2 , 1 / 2 ) systems. <|MaskedSetence|> A brief discussion and summary are given in Section 5.
. | **A**:
Our study provides an intuitive perspective of a two-spin (s𝑠sitalic_s and 1/2121/21 / 2) system and unveils the intrinsic property of the two-spin system on a Bloch sphere, which shall deepen our comprehension of the spin-(s,1/2)𝑠12(s,1/2)( italic_s , 1 / 2 ) system.
**B**: In Section 2, we study the fundamental theory of the MSR to describe an arbitrary pure state of spin-(s,1/2)𝑠12(s,1/2)( italic_s , 1 / 2 ), through coupling bases.
**C**: In Section 4, we show more applications of our method in the mixed-spin (s,1/2)𝑠12(s,1/2)( italic_s , 1 / 2 ) systems.
| CAB | ABC | ABC | ABC | Selection 3 |
<|MaskedSetence|> italic_e . <|MaskedSetence|> Similarly, the
element-to-node divergence operator produces valid results at the
boundary nodes only if the original continuous function 𝐩𝐩\mathbf{p}bold_p
has no component perpendicular to the boundary (i.e.,𝐩⟂|Γ=0)(i.e.,\,\mathbf{p_{\perp}}|_{\Gamma}=0)( italic_i . italic_e . <|MaskedSetence|> | **A**: is zero at the boundary (i.e.,u|Γ=0)(i.e.,\,u|_{\Gamma}=0)( italic_i .
**B**: , bold_p start_POSTSUBSCRIPT ⟂ end_POSTSUBSCRIPT | start_POSTSUBSCRIPT roman_Γ end_POSTSUBSCRIPT = 0 ).
In the following, we will refer to these conditions as the natural.
**C**: , italic_u | start_POSTSUBSCRIPT roman_Γ end_POSTSUBSCRIPT = 0 ).
| ACB | ACB | CAB | ACB | Selection 4 |
Since our identification will use a certain set of (framed) wild harmonic bundles, we remark that this set does not match any of the usual wild moduli spaces ℳHitsubscriptℳHit\mathcal{M}_{\text{Hit}}caligraphic_M start_POSTSUBSCRIPT Hit end_POSTSUBSCRIPT. In the usual story of moduli spaces of wild harmonic bundles over a punctured compact Riemann surface, one fixes the singular part of the Higgs field and the parabolic structure at the punctures. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> Hence our moduli space must a priori be different from the usual moduli spaces of wild harmonic bundles.
. | **A**: Under certain stability conditions, one obtains moduli spaces of these objects, with the natural hyperkähler metric [BB04].
**B**: Furthermore, we will have the additional data of a “framing”.
**C**: On the other hand, in our set of wild harmonic bundles we will allow the simple pole of the Higgs field and the parabolic structure to vary.
| ACB | ACB | ACB | BCA | Selection 1 |
<|MaskedSetence|> During the first two solar encounters, the reported AC power spectra are the mean of 16 individual power spectra calculated during the first 1/8 of each New York second (NYs = 217superscript2172^{17}2 start_POSTSUPERSCRIPT 17 end_POSTSUPERSCRIPT / 150,000 ≈\approx≈ 0.874 s (Bale et al., 2016)). <|MaskedSetence|> <|MaskedSetence|> For the second solar encounter, these channels were V12subscript𝑉12V_{12}italic_V start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT, V34subscript𝑉34V_{34}italic_V start_POSTSUBSCRIPT 34 end_POSTSUBSCRIPT, V5subscript𝑉5V_{5}italic_V start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT, and the single-axis high frequency SCM winding. For the first two encounters, the power spectral data were configured have 56 pseudo-logarithmically spaced frequency bins.
. | **A**:
This study utilizes power spectra calculated on-board by the FIELDS Digital Fields Board (DFB) (Malaspina et al., 2016).
**B**: AC power spectra are calculated for 4 channels.
**C**: For the first solar encounter, these channels were V12subscript𝑉12V_{12}italic_V start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT and the three low-frequency SCM𝑆𝐶𝑀SCMitalic_S italic_C italic_M axes.
| ABC | ABC | ABC | BCA | Selection 2 |
made non-negative (i.e. only zero in this case) for a single choice of
parameters. <|MaskedSetence|> <|MaskedSetence|> The both cases yield an isolated root ±12(1−𝐞3+𝐞12+𝐞123)plus-or-minus121subscript𝐞3subscript𝐞12subscript𝐞123\pm\frac{1}{2}(1-\mathbf{e}_{3}+\mathbf{e}_{12}+\mathbf{e}_{123})± divide start_ARG 1 end_ARG start_ARG 2 end_ARG ( 1 - bold_e start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT + bold_e start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT + bold_e start_POSTSUBSCRIPT 123 end_POSTSUBSCRIPT ). <|MaskedSetence|> | **A**: Alternatively, in the case s2=−12subscript𝑠212s_{2}=-\tfrac{1}{2}italic_s start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = - divide start_ARG 1 end_ARG start_ARG 2 end_ARG from
equation −4V22−(1−2V3)≥04superscriptsubscript𝑉2212subscript𝑉30-4V_{2}^{2}-(1-2V_{3})\geq 0- 4 italic_V start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT - ( 1 - 2 italic_V start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) ≥ 0 follows V2=0,V3=1/2formulae-sequencesubscript𝑉20subscript𝑉312V_{2}=0,V_{3}=1/2italic_V start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = 0 , italic_V start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT = 1 / 2.
**B**: Therefore, in this
algebra in fact there exist only isolated real square root of
𝖡=−𝐞3+𝐞12𝖡subscript𝐞3subscript𝐞12\mathsf{B}=-\mathbf{e}_{3}+\mathbf{e}_{12}sansserif_B = - bold_e start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT + bold_e start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT..
**C**: In particular, in the case s1=12subscript𝑠112s_{1}=\tfrac{1}{2}italic_s start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = divide start_ARG 1 end_ARG start_ARG 2 end_ARG, the requirement −4V22−(1+2V3)2≥04superscriptsubscript𝑉22superscript12subscript𝑉320-4V_{2}^{2}-(1+2V_{3})^{2}\geq 0- 4 italic_V start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT - ( 1 + 2 italic_V start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ≥ 0 yields V2=0,V3=−1/2formulae-sequencesubscript𝑉20subscript𝑉312V_{2}=0,V_{3}=-1/2italic_V start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = 0 , italic_V start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT = - 1 / 2.
| CAB | CAB | ACB | CAB | Selection 2 |
<|MaskedSetence|> <|MaskedSetence|> Before classifying an unlabeled sample, the recurrent pathway processes a sequence of labeled samples from the preceding batches to generate a context representation, which is fed into the skill processing layer. <|MaskedSetence|> The context system thus transforms samples of recently seen odors into a representation that helps classification on the next time period. This approach is similar to the context+skill technique for opponent modeling and enhanced extrapolation in games [26, 27]; the main difference is that in prior work the approach was based on neuroevolution of agent behavior, whereas in this paper it is implemented via backpropagation to generalize classification performance.. | **A**:
III-C2 The context+skill model
The context+skill NN model builds on the skill NN model by adding a recurrent processing pathway (Fig.
**B**: The recurrent layers are modified via backpropagation through time, and, in this manner, the recurrent pathway learns to generate representations that support classification.
**C**: 2D).
| ACB | ACB | CAB | ACB | Selection 4 |
It is well known that there are close relations between entanglement and spin squeezing, and a lot of effort has been devoted to unveiling it Ulam-Orgikh and Kitagawa (2001); Jin and Kim (2007); Jafarpour and Akhound (2008); Messikh et al. (2003); Wang (2004); Yin et al. (2010).
Because spin squeezing is relatively easy to be generated and measured experimentally Genes et al. <|MaskedSetence|> (2008); Takano et al. <|MaskedSetence|> (1992, 1994); Cronin et al. (2009); Bollinger et al. (1996); Döring et al. (2010), as well as in making high-precision atomic clocks Sørensen and Mølmer (1999); André et al. (2004); Meiser et al. (2008) and gravitational-wave interferometers Walls and Zoller (1981); Goda et al. <|MaskedSetence|> | **A**: (2003); Fernholz et al.
**B**: (2009), spin-squeezing parameters are promising candidates as measures of many-body correlations.
Improving the precision of measurements is another important application of spin squeezing.
For example, spin squeezing plays an important role in Ramsey spectroscopy Wineland et al.
**C**: (2008), etc.
.
| ABC | ABC | ABC | BAC | Selection 1 |
<|MaskedSetence|> Acknowledgements
During the writing of the paper, I was supported by the starter grant “Categorified Donaldson–Thomas theory” No. <|MaskedSetence|> I was also supported by a Royal Society university research fellowship. <|MaskedSetence|> Finally, I offer my heartfelt gratitude to Paul, Sophia, Sacha, Kristin and Nina, for their help and support throughout the writing of this paper.
. | **A**: 759967 of the European Research Council.
**B**: I would like to thank Andrei Okounkov and Olivier Schiffmann for helpful conversations, Tristan Bozec for patiently explaining his work on crystals to me, Lucien Hennecart and Shivang Jindal for helpful comments regarding an earlier version of the paper, and an anonymous referee for a careful reading of the paper and many helpful suggestions.
**C**: 1.7.
| CAB | CAB | CAB | BAC | Selection 1 |
The third study-case is the decay of Higgs to two Z𝑍Zitalic_Z bosons and their subsequent
decay into four leptons.
This final state has been extensively studied in the past as the golden decay mode of the Higgs boson and in searches for physics beyond the Standard Model Keung et al. <|MaskedSetence|> <|MaskedSetence|> (2012); Modak et al. <|MaskedSetence|> (2015).
We use this decay to validate the methodology and as an example of application of statistical methods to distinguish between different spin-parity hypotheses.
. | **A**: (2010); Bolognesi et al.
**B**: (2016); Berge et al.
**C**: (2008); Gao et al.
| CAB | CAB | CAB | BCA | Selection 2 |
<|MaskedSetence|> <|MaskedSetence|> Diagrammatically defined chains of algebras appear to have not been considered as objects whose representation category can be studied through the lens of representation stability. Diagrammatics and representation stability have, however, been uttered in the same breadth, but in a different sense: in [1] (Barter, Entova-Aizenbud, Heidersdorf) the authors produce a functor from the category of FIFI\operatorname{FI}roman_FI-modules modulo finite length FIFI\operatorname{FI}roman_FI-modules to the abelian envelope of the Deligne category. <|MaskedSetence|> Thus, representation stability with respect to a chain of diagrammatically defined algebras is not considered in [1] (Barter, Entova-Aizenbud, Heidersdorf).
. | **A**: It appears that much of the work in representation stability has focussed on algebraic objects which are either close to symmetric groups [5] [14] [8] (Wilson, Putman, Sam, Gunturkun, Snowden ) or are close to Lie groups [14] [17] (Sam, Snowden, Putman).
**B**:
To our knowledge, Temperley-Lieb algebras have not been studied in the representation stability literature, or within the broader context of representation stability and FIFI\operatorname{FI}roman_FI-modules.
**C**: The chain with respect to which one is considering representation stability there is of course still the chain of symmetric groups.
| CBA | BAC | BAC | BAC | Selection 4 |
Lemaître redshift formula, viz. 1+z=a−11𝑧superscript𝑎11+z=a^{-1}1 + italic_z = italic_a start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT. <|MaskedSetence|> <|MaskedSetence|> One such type of VSL exists in the form of
the velocity of light being dependent on the scale factor, e.g. <|MaskedSetence|> | **A**: We believe that
this is an oversight, however.
**B**: c∝a−ζproportional-to𝑐superscript𝑎𝜁c\propto a^{-\zeta}italic_c ∝ italic_a start_POSTSUPERSCRIPT - italic_ζ end_POSTSUPERSCRIPT,.
**C**: There are certain types of VSL in which
the classic Lemaître redshift formula is no longer applicable,
warranting a revision.
| CBA | ACB | ACB | ACB | Selection 3 |
For N𝑁Nitalic_N particles in each shot, the SQL, also known as the shot-noise limit, can be surpassed by using quantum effects such as entanglement Bollinger et al. (1996); Monz et al. (2011) and squeezing Muessel et al. (2015), reaching the so-called Heisenberg limit (HL), in which the sensitivity exceeds the SQL by 1/N1𝑁1/\sqrt{N}1 / square-root start_ARG italic_N end_ARG Bollinger et al. <|MaskedSetence|> (2002).
Many schemes have been proposed to achieve the SQL, such as quantum state transfer from light to atoms Agarwal and Puri (1990); Kuzmich et al. (1997); Moore et al. (1999), quantum nondemolition measurement Appel et al. (2009); Kuzmich et al. (1998); Louchet-Chauvet et al. (2010); Hammerer et al. (2010), one-axis twisting Schleier-Smith et al. (2010); Kitagawa and Ueda (1993); Sørensen and Mølmer (2001); Haine et al. (2014), two-axis countertwisting Kitagawa and Ueda (1993); Ma and Wang (2009), twist-and-turn squeezing Muessel et al. <|MaskedSetence|> (2001), spin changing collisions Lücke et al. (2011); Duan et al. (2000); Pu and Meystre (2000); Nolan et al. (2016), and adiabatically scanning through a quantum phase transition Lee (2006); Huang et al. (2018).
Furthermore, the concept of interaction-based readout resolves the dilemma that the states prepared via these schemes require the low-noise detection in order to see significant quantum enhancement Haine (2018); Demkowicz-Dobrzański et al. <|MaskedSetence|> | **A**: (2015); Law et al.
**B**: (2012).
.
**C**: (1996); Holland and Burnett (1993); Munro et al.
| CAB | CAB | BAC | CAB | Selection 2 |
<|MaskedSetence|> Factoring has a low-complexity quantum algorithm due to Shor [1], while it is believed to have only high-complexity classical algorithms. <|MaskedSetence|> Unlike factoring, oracle problems do have some lower bound proof methods: the polynomial [8], hybrid [9] and adversary [10, 11] methods. For example, the problem solved by Grover’s quantum algorithm [12] is an oracle problem. <|MaskedSetence|> In Grover’s quantum algorithm, the oracle is classical; it is a function on bit strings (representing classical computation). In phase estimation [7] the oracle is quantum; representing any quantum circuit, it is a unitary matrix. Additional versatile algorithms could be singled out by a new – possibly purely quantum – lower-bound method.
. | **A**: Rigorously proving complexity lower bounds is hard.
**B**:
Another advantage of oracles is the provability of limitations of computation.
**C**: It has a proven complexity lower bound in classical [12] as well as quantum [9, 8] circuits.
| BAC | BAC | CAB | BAC | Selection 2 |
Using this featurization approach (with 15 features) outperforms all benchmarking models (automatminer, in comparison, uses 200 features) even when a linear regression model is chosen, as seen in Figure 4a. <|MaskedSetence|> When a non-linear learning model is used (neural network or random forest model) the MAEs are significantly reduced. Our best model using random forests has a test-MAE of 0.09 eV, comparable to the accuracy of work function calculations employing DFT. This test performance is about 4–5 times better than the best benchmarking model and more than 6 times better than the baseline. Figure 5 shows the predicted work function for both the training and test sets in comparison to the DFT-calculated values. The kernel-density estimate distributions for both training and test sets are plotted for predicted and actual work functions showing that the predicted distribution is qualitatively faithful to the actual one. Notably, for the neural network and random forest models there is still a gap between training and test MAEs despite thorough hyperparameter tuning. The learning curves in Figure S8 indicate underfitting for the linear model and slight overfitting for the random forest model. <|MaskedSetence|> The database and model are available open-source (see data availability section) enabling other researchers to use this model for work function predictions and help experimentalists in their materials/synthesis choice.
Figure 5: Predicted work functions vs. <|MaskedSetence|> The kernel-density estimate distributions for both training and test sets are plotted for predicted work functions and the ground-truth at the top and right, respectively.. | **A**: This performance improvement is due to the superior implementation of how we featurize our slabs rather than the machine learning model itself.
**B**: The learning curve trend for the random forest model suggests that increasing the dataset size (by a factor of ∼10similar-toabsent10\sim 10∼ 10) could further improve the model performance and close the gap between training and cross-validated errors.
The prediction of the work function using this model is roughly 105superscript10510^{5}10 start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT times faster than DFT while having a MAE comparable to the accuracy of DFT.
**C**: DFT-calculated work functions.
| ABC | ABC | CBA | ABC | Selection 4 |
<|MaskedSetence|> <|MaskedSetence|> However, the error on the fitted amplitude in zero field is nearly as large as the value itself. <|MaskedSetence|> Due to the weak signal, not all parameters were fitted simultaneously. The peak center and width show no visible dependence on the magnetic field, and we have thus fixed these to the values obtained at 14.9 T.
. | **A**: We fitted the data using Gaussian peaks on a sloping background.
**B**: The intensity of the peak decreases with decreasing field, but a tiny signal may still be present at 2 K in zero field.
**C**: III Results
A selection of raw ND data is presented in Fig. 1 (a), showing a clear field-induced peak at 14.9 T.
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Section V describes how to compute multivoice signals in the frequency domain. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> We conclude this section by showing how to combine multiple voices to construct the full frequency-domain EMRI waveform.
In Sec. VI, we present various important technical details describing how we implement this framework for the results we present in this paper. We strongly emphasize that there is a great deal of room for improvement on the techniques described here. We have not, for example, carefully assessed the most effective method for laying out the grid of data on which we store information about adiabatic backreaction and waveform amplitudes, nor have we thoroughly investigated efficient methods for interpolating these data to off-grid points (e.g., [16]). These important points will be studied in future work, as we begin assessing how to take this framework and use it to develop EMRI waveforms in support of LISA data analysis and science studies.
. | **A**: We review the standard SPA Fourier transform and show how by including an additional derivative of the frequency it is straightforward to correct this artifact.
**B**: However, because the evolution of certain voices is not monotonic, the “standard” SPA calculation can fail, introducing singular artifacts at moments when a voice’s frequency evolution switches sign.
**C**: Because EMRI systems are slowly evolving, the stationary phase approximation (SPA) should accurately describe the Fourier transform of EMRI signals.
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3 CONCLUSION AND OUTLOOK
Thanks to the development of superconducting technology, MHz-level repetition-rate electron beam has come true. Seeded FELs have been proved to be convincing method to produce fully coherent EUV and soft X-ray radiation. However, limited by the average power of laser system today, seeded FEL mostly cannot run at the repetition-rate as high as the electron beam from superconducting linear accelerator. The huge challenges for reducing the required seed laser power while maintaining the great longitudinal coherence and mechanism simplicity of nominal seeded FELs has led to the invention of the proposed technique. The proposed technique, with its application either on HGHG or EEHG, reduces the requirement of the seed laser power by about three orders of magnitude and make CW seeded FELs possible for a commercially available fiber laser system. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> | **A**: The mechanical layout of the proposed technique is close to the that of nominal seeded FELs and this provides excellent conditions for subsequent proof-of-principle demonstrations and technical applications.
**B**: The achievable average power at EUV and soft X-ray range reaches about one hundred watts with a repetition rate of 1 MHz.
**C**: Progress made in this paper paves the way for the development of fully coherent EUV and soft X-ray FELs with a repetition rate of MHz.
.
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<|MaskedSetence|> 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. <|MaskedSetence|> <|MaskedSetence|> Chamblin:1999tk ; Chamblin:1999hg studied the thermodynamic associated to a charged AdS black holes in the holographic context, and then opening up a multitude of possibilities to connect string and gauge theories through various types of black hole and its thermodynamics. It is worthwhile to mention that within holography the thermodynamics quantities are derived from the holographic renormalization of the on-shell euclidian action or the thermodynamics potentials.
. | **A**:
A little bit more than twenty years after such studies in Refs.
**B**: Maldacena:1997re , relates the Hawking temperature achieved in a curved high-dimensional spacetime to the temperature of a super conformal Yang-Mills theory in a flat four-dimensional spacetime.
**C**: Soon after Witten’s work the authors in Refs.
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<|MaskedSetence|> At the very beginning of the test, the Maxwell demon will accompany the qubit carrier, for example, photons entering Bob’s device without being detected. The demon then secretly gains access to a specific part of Bob’s device and tries to obtain information about the measurement setting. <|MaskedSetence|> <|MaskedSetence|> The second one is to begin to choose one of the measurement settings after receiving the qubit sent by Alice and making the choice for every run. In the first case, the demon can directly memorize these classical data. For example in the case of two measurement settings, Bob’s quantum randomness generator would generate classical bitstring like 0110⋯0110⋯0110\cdots0110 ⋯, which corresponds to different measurement settings chosen in each experimental run. These classical data have to be stored in the local memory of Bob’s device. Since the classical bit can be cloned without changing its state, the demon can access the local memory and copy the bit information before Bob performs the qubit measurement.
For the second case, the demon could initially entangle with Bob’s quantum randomness generator, causing the composite state to becomes
. | **A**:
Suppose that Alice chooses to collaborate with a Maxwell demon, and they make an agreement on the cheating strategy as follows.
**B**: There are two situations in which Bob settles down his choice of measurement settings.
**C**: The first one is to settle down many run choices before Alice sends the qubit and these classical data are stored in the local memory.
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<|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> VI.Vidi.192.109). G.Q. thanks the support from Fundação para a Ciência e a Tecnologia (Portugal), namely through projects CEECIND/02474/2018 and project UIDB/50008/2020 and IT project QuantSat-PT. R.A. acknowledges support from the Doctoral Programme in the Physics and Mathematics of Information (DP-PMI) and the Fundação para a Ciência e Tecnologia (FCT) through Grant No. PD/BD/135011/2017.. | **A**: The authors are especially grateful to Jens Siewert, Andreas Osterloh, Barbara Kraus, and Karol Życzkowski for stimulating conversations which led to formal proof of Proposition 2 while staying at Centro de Ciencias de Benasque Pedro Pascual.
**B**: A.B acknowledges support from the National Science Center under grant number DEC-2015/18/A ST2/00274 and by NWO Vidi grant (Project No.
**C**:
Acknowledgements
The authors thank Andreas Osterloh, Karol Życzkowski, Rui Perdigão and Yasser Omar for fruitful discussions and correspondence.
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