result is given by **the** inhomogeneous **three**-**point** vertex, after **fixing** **the** inhomogeneities. We find that **the** integrands match, which is already a strong evidence that **the** corre- spondence with **the** string theory persists at one loop. Moreover, we reveal through this comparison **the** reason for **the** asymmetric form of **the** gauge theory structure constant, while **the** string theory result is completely symmetric with respect to permutations of **the** **three** operators. To complete **the** result one should also compare **the** integration contours. This is a subtle issue which is still lacking complete understanding, both in **the** gauge and in **the** string theory. At **the** present stage **the** contours of integration are chosen case by case by taking into account **the** analytic properties of **the** solution.

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are not invariant [R vacuum jn ¼ 0i]. Nevertheless results obey **the** conformal constraints.
For **the** two- and **three**-**point** functions an AdS 2 bulk dual can be identified [ 1 ]. We have not accomplished that for **the** four-**point** **function**. But **the** simplicity of **the** block structure—just one block is needed to reproduce **the** four- **point** **function**—gives **the** hope that a dual model in **the** AdS 2 bulk can be found. It is interesting to observe that **the** AdS 2 bulk propagator is given by a hypergeometric **function**, just as G 4 and its conformal block are.

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In this paper, we address one simple but intriguing example of such phenomena in **the** context of **the** AdS/CFT correspondence; namely **the** emergence of **the** classical string world- sheet from **the** **three**-**point** functions in **the** planar N = 4 super Yang-Mills theory (SYM). On **the** one hand, a non-perturbative framework to compute **the** **three**-**point** functions of N = 4 SYM, called **the** hexagon vertex, was put forward recently in [ 1 ]. It describes **the** **three**-**point** functions in terms of **the** dynamics of “magnons”, which are **the** elementary fields constituting **the** gauge-invariant operator. On **the** other hand, **the** AdS/CFT implies that **the** very same object in **the** strong coupling limit admits a totally different description in terms of **the** classical string worldsheet and that **the** **three**-**point** **function** is given by its area [ 2 – 5 ]. However, apart from some partial results given in [ 1 ], it is still not clear whether and how these two descriptions are consistent with each other.

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Acknowledgments
We acknowledge **the** crucial contribution of **the** ESO staff for **the** management of service observations. In particular, we are deeply grateful to M. Hilker for his constant help and support of this programme. Italian participation in VIPERS has been funded by INAF through PRIN 2008 and 2010 programmes. LG and BRG acknowledge support of **the** European Research Council through **the** Darklight ERC Advanced Research Grant (# 291521). OLF acknowledges support of **the** European Research Council through **the** EARLY ERC Advanced Research Grant (# 268107). AP, KM, and JK have been supported by **the** National Science Centre (grants UMO-2012/07/B/ST9/04425 and UMO- 2013/09/D/ST9/04030), **the** Polish-Swiss Astro Project (co- financed by a grant from Switzerland, through **the** Swiss Contribution to **the** enlarged European Union). KM was sup- ported by **the** Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation No. R2405. RT acknowledges financial support from **the** European Research Council under **the** European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement n. 202686. MM, EB, FM, and LM acknowledge **the** support from grants ASI-INAF I/023/12/0 and PRIN MIUR 2010-2011. LM also ac- knowledges financial support from PRIN INAF 2012. Research conducted within **the** scope of **the** HECOLS International Associated Laboratory, supported in part by **the** Polish NCN grant DEC-2013/08/M/ST9/00664. We thank Hong Guo for kindly providing **the** data of their paper for comparison.

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is its deformed length. **The** ε 2 scaling factor is **the** right one to obtain a finite nonzero limit energy (without rescaling). Then there is a two-**point**, Lennard-Jones type contribution of **the** form
R k ε (ϕ ε ) = ε 2 r (ε −1 |ϕ ε (b k )|), (3) where r : R + → ¯ R + is a Lennard-Jones type potential, i.e., a continuous **function** such that r (0) = +∞, r is decreasing on [0, 1], r(1) = 0, r is nondecreasing on [1, +∞[, and r(`) → c when ` → +∞ for some constant c ≥ 0. **The** sum of these two terms forms an energy for each bond that is minimum at **the** natural length ε. This energy is infinitely repulsive when **the** deformed length of a bond goes to 0 and tends to +∞ when **the** deformed length of a bond goes to +∞. While **the** former behavior is desirable from **the** atomistic modeling **point** of view, **the** latter one is more debatable, because interatomic forces should tend to 0 when **the** interatomic distance tends to +∞. It is mostly there for coercivity reasons. We refer to [4] for work in which such coercivity assumptions are not made.

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2.2. Proposed theoretical PSF model
Before we formulate **the** model for **the** PSF, it is important to review **the** assumptions that will be used in **the** following section. We will primarily assume that **the** light used for illu- minating **the** specimen is either circularly polarized or phase randomized. Secondly, from **the** experiments conducted in **the** context of our current application, we conclude that vecto- rial diffraction models offer limited improvement in accuracy than scalar diffraction models (especially for CLSM). This is true even when **the** difference between **the** refractive indices of **the** objective lens and immersion medium is large; like in **the** case of imaging from air objective lens into specimen em- bedded in oil or glycerol [6]. We thus justify our usage of scalar models to calculate **the** PSF as they are computation- ally less expensive (one integral each for illumination and de- tection PSF) to calculate than **the** vectorial models (**three** in- tegrals for each of **the** illumination and detection PSF). **The** model used here is an extension of P. A. Stokseth’s [1] work on deriving **the** Optical Transfer **Function** (OTF) for a de- focused system from **the** corresponding pupil **function**. For a microscope with a circular aperture, it is straight forward to show **the** equivalence between Stokseth’s, and Gibson and Lanni’s scalar model (see [6]).

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共Received 18 January 2000; revised manuscript received 27 April 2000兲
We present a paper of **the** critical phenomena around **the** **quantum** critical **point** in heavy-fermion systems. In **the** framework of **the** S ⫽1/2 Kondo lattice model, we introduce an extended decoupling scheme of **the** Kondo interaction, which allows one to treat **the** spin fluctuations and **the** Kondo effect on an equal footing. **The** calculations, developed in a self-consistent one-loop approximation, lead to **the** formation of a damped collective mode with a dynamic exponent z ⫽2 in **the** case of an antiferromagnetic instability. **The** system displays a **quantum**-classical crossover at finite temperature depending on how **the** energy of **the** mode, on **the** scale of **the** magnetic correlation length, compares to k B T. **The** low-temperature behavior, in **the** different regimes separated by **the** crossover temperatures, is then discussed for both two- and **three**-dimensional systems.

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Adel Abbout, Gabriel Lemari´e, and Jean-Louis Pichard
Service de Physique de l’ ´ Etat Condens´e (CNRS URA 2464), IRAMIS/SPEC, CEA Saclay, 91191 Gif-sur-Yvette, France
We study an electron interferometer formed with a **quantum** **point** contact and a scanning probe tip in a two-dimensional electron gas. **The** images giving **the** conductance as a **function** of **the** tip position exhibit fringes spaced by half **the** Fermi wavelength. For a contact opened at **the** edges of a quantized conductance plateau, **the** fringes are enhanced as **the** temperature T increases and can persist beyond **the** thermal length l T . This unusual effect is explained assuming a simplified

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ACCEPTED MANUSCRIPT
**the** **function** values at **the** fixed angles and, occasionally, **the** first derivatives of **the** functions at **the** ends of **the** entire angular interpolation range as **the** free parameters (or unknowns). As a result, **the** number of free parameters is large but manageable. **The** optimization method includes ingredients from simulated annealing methods (e.g., Press et al. 1992; also compare to MCMC or Markov-Chain Monte-Carlo methods, Gilks et al. 1996). **The** optimization of **the** basis-**function** values proceeds from a chosen starting **point** via a Monte Carlo method that proposes random moves based on Gaussian proposal prob- ability densities, but gives rise to a move only if **the** proposed new **point** in **the** parameter space results in improved fits to all **the** observational data. **The** data are grouped according to differing phase-curve shapes to allow for wide applicability of **the** new basis functions. In optimizing **the** basis functions, **the** data are properly weighted by **the** asteroid groups and number of members within each group.

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choices are more natural than others and, in particular, lead to some Y k with a direct
combinatorial interpretation.
As a natural extension of our result, we note that an expression for **the** slice generating **function** of planar Eulerian triangulations was given in [8] which incorporates more parame- ters by assigning different weights to **the** vertices of each (gray, black or white) color. Again this expression is **the** result of some educated guess and no constructive derivation was provided. It is easy to incorporate such color-dependent vertex weights in our approach. This then leads to **three** copies of **the** generating functions Φ and Ω, determined by **three** independent closed systems, each depending on **the** **three** vertex weights at hand. Unfortu- nately, although there is no fundamental obstacle in using our method to solve these systems, expressions become rather involved and we were not able to recover **the** expression of [8].

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In this paper, we model **the** **point**-spread **function** (PSF) of a fluo- rescence MACROscope with a field aberration. **The** MACROscope is an imaging arrangement that is designed to directly study small and large specimen preparations without physically sectioning them. However, due to **the** different optical components of **the** MACRO- scope, it cannot achieve **the** condition of lateral spatial invariance for all magnifications. For example, under low zoom settings, this field aberration becomes prominent, **the** PSF varies in **the** lateral field, and is proportional to **the** distance from **the** center of **the** field. On **the** other hand, for larger zooms, these aberrations become gradually ab- sent. A computational approach to correct this aberration often relies on an accurate knowledge of **the** PSF. **The** PSF can be defined either theoretically using a scalar diffraction model or empirically by ac- quiring a **three**-dimensional image of a fluorescent bead that approx- imates a **point** source. **The** experimental PSF is difficult to obtain and can change with slight deviations from **the** physical conditions. In this paper, we model **the** PSF using **the** scalar diffraction approach, and **the** pupil **function** is modeled by chopping it. By comparing our modeled PSF with an experimentally obtained PSF, we validate our hypothesis that **the** spatial variance is caused by two limiting optical apertures brought together on different conjugate planes.

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We measure I c as a **function** of magnetic field within each plateau and of gate voltage at fixed magnetic field. In each case we sweep I dc between ±100 nA, alternating directions, while stepping B or VG after each sweep. For each value of B or V G we calculate |I c | as described above; **the** spread in |I c | at each **point** is predominantly **the** result of hysteresis in **the** I dc sweep direction. We observe two different types of hysteresis, each of which seems to occur inconsistently. One is similar to that observed in previous experiments, 6,14,21 illustrated in Fig. 4(a). This type of hysteresis may be explained by **the** electron heating model of breakdown; 22 however, as discussed below, **the** electron heating model cannot explain our results in **the** fractional **quantum** Hall regime. We also observe a strange type of hysteresis illustrated in Fig. 4(b). In some cases, both types of hysteresis occur simultaneously. For all measurements, **the** I dc sweep rate is 0.7 nA/s. We have tested **the** dependence on sweep rate at filling factors 2 and 5, sweeping I dc with fixed B and V G , and find no significant differences for slower sweep rates down to ~1 × 10 -3 nA/s.

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for **the** Poisson noise model assumed here. In order to verify this, we study **the** case of low photon number in this subsection. In Figure 13 , we see **the** observed image with **three** different photon numbers per source, namely 500, 1000, and 2000. For **the** case of 500 photons per source, **the** image is very dim, and we can barely distinguish **the** rotating PSF signal from **the** background noise, so we do not consider this case any further. For **the** case of 1000 photons being emitted by each **point** source, **the** corresponding image follows a Poisson distribution with a mean of 1000 photons. We take each image to contain 15 **point** sources. As before, we first randomly generated 20 images, which were used for training parameters. Then we tested 50 different observed images by using **the** trained parameter values. We got 90.53% for **the** recall rate and 78.32% for **the** precision rate in **the** KL-NC algorithm, but only 81.33% and 64.24%, respectively, for **the** two rates in **the** ` 2 -NC algorithm. For evaluation of **the** flux

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number of pairs with these small separations is much smaller, **the** computation time is not a similar issue as for large separations.
**The** results of our analysis will have an impact also on **the** computationally more demanding task of covariance matrix esti- mation. However, since in that case **the** exact computational cost is determined by **the** balance of data catalogs and random cata- logs, which does not need to be **the** same as for **the** individual two-**point** correlation estimate, we postpone a quantitative anal- ysis to a future, dedicated study. **The** same kind of methods can be applied to higher-order statistics (**three**-**point** and four-**point** correlation functions) to speed up their estimation ( Slepian & Eisenstein 2015 ).

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In this paper, we develop a systematic approach to **the** Kondo-lattice model for S 51/2(N52) in which **the** Kondo- like and **the** spin degrees of freedom are treated on an equal footing. **The** presented approach shows some similarities with earlier works. 11,15 But while Refs. 11 and 15 essentially describe **the** phase diagram of **the** Kondo lattice at a mean- field level, we focus on **the** effects of spin fluctuations in **the** magnetically disordered phase hence bringing **the** spin- fluctuation and **the** Kondo-effect theories together. **The** saddle-**point** results and **the** Gaussian fluctuations in **the** charge channel are consistent with **the** standard 1/N theories. In addition, **the** Gaussian fluctuations in **the** spin channel restore **the** spin-fluctuation effects that were missing in **the** 1/N expansion. **The** general expression of **the** dynamical spin susceptibility that we derive reproduces some of **the** features postulated in **the** phenomenological models. It presents a two-component behavior: a quasielastic component superim- posed on an inelastic peak with renormalized values of **the** relaxation rates, susceptibilities and v max . In a very striking

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Let X be a smooth projective curve over C. A celebrated theorem of Belyi states that X can be defined over a number field K if and only if there exists a rational **function** f on X with exactly **three** critical values, see [3], [13]. If such a **function** f exists, we can normalize it in such a way that **the** critical values are 0, 1 and ∞. After this normalization, we may view f as a finite cover f : X → P 1 which is ´ etale over P 1 − {0, 1, ∞}. We call f a **three** **point** cover. Another common name for f is Belyi map. **The** monodromy group of f is defined as **the** Galois group of **the** Galois closure of f .

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All this shows that there is a gap between **the** economic and legal approaches to collusion. **The** economic approach highlights nor communication nor agreement to analyze **the** collusion. It is dynamic and strategic interdependence induces actors to seek a non-cooperative equilibrium in their favor. **The** legal approach is more ambiguous. Seeking traces of an agreement or exchange to prove **the** existence of collusion, it is cantilevered. On **the** one hand, this research is unnecessary and wrong in situations where there exist favorable conditions for collusion. On **the** other hand, this search for a favorable non-cooperative equilibrium can be made very difficult in situations where **the** conditions that favor collusion are not present. In **the** absence of hard evidence, it can be very difficult to prove that a given behavior can be explained only by a concerted practice. For example, after **the** Second World War, **the** two major producers ICI and Solvay of a variety of soda for **the** glass had shared **the** international market according to an explicit agreement (known as Page 1000 assigning continental Europe to Solvay and UK to ICI). At **the** request of **the** European Commission in 1972, this agreement was broken. Nevertheless, **the** market allocation between these two producers remained unchanged. Despite **the** fact that ICI provided in part from Solvay, **the** Belgian company has always refused to become an operator on **the** UK market, despite **the** price increases that could incite it. **The** Commission saw in **the** maintaining of **the** market’s distribution an evidence of **the** persistence of an implicit functioning of **the** Agreement Page 1000, even though every company justified its behavior by **the** fear of competitor’s retaliation if it were to enter **the** market. It is necessary to keep in mind that if Article 101 of **the** Treaty prohibits any form of collusion that hinders competition, it does not remove to economic agents **the** right to adapt themselves intelligently to **the** existing and anticipated conduct of their rivals (see Encaoua and Guesnerie, 2006, p. 70).

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ard deviation suggests motions occurring on a slower timescale. Those slower motions were confirmed and char- acterized (Figs S1 and S2). S 2 in those regions generally could not be characterized by NMR due to overlapping/
broad peaks, further demonstrating **the** value of **the** simulations.
Dynamics on **the** intermediate (ns- µs) timescale. To investigate **the** intermediate timescale of motions, we extracted **the** Cα root mean square fluctuation (RMSF) from **the** molecular dynamics simulations (Fig. S2 and Table S6). As observed for fast motions, **the** core of each β-lactamase was rigid, while **the** surface loops were more flexible (Fig. 3 ). TEM-1 and **the** chimeras showed significantly more ns-µs dynamic residues than PSE-4, in agreement with **the** higher sequence similarity of **the** chimeras to TEM-1. **The** substitution of up to 19 amino acids in TEM-1 did not markedly alter ns-µs dynamics.

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I. INTRODUCTION
**The** implication of **quantum** mechanics in plasticity of crys- tals has long been a matter of theoretical investigations. **The** main efforts were concentrated on accounting for interactions between phonons and dislocations [ 1 – 3 ] because they are **the** key physical ingredients in **the** process of conversion of plastic work into heat during deformation [ 4 , 5 ] as well as in **the** process of thermal activation of dislocation glide [ 1 , 6 ]. Modern simulation tools [ 7 , 8 ] have allowed us recently to sup- plement **the** theory and shed new light on **the** low-temperature deformation tests. Employing atomic scale simulations based on **the** embedded atom method (EAM) [ 9 , 10 ] it was found that along **the** dislocation glide **the** zero-**point** energy (ZPE), which in **the** harmonic approximation is merely **the** sum of phonon frequencies times half ¯h, varies with an amplitude of same order as **the** dislocation Peierls barrier but with an opposite sign. **The** variation of **the** ZPE was found to yield a significant Peierls stress reduction for **the** screw dislocation in body-centered-cubic (bcc) Fe [ 7 ]. This result showed how **quantum** fluctuations could be involved in **the** plasticity of certain metals even though they are constituted of atoms with some relatively heavy masses in comparison with conventional **quantum** crystals [ 11 ] as solid He or H 2 . A recent experimental

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