Our main conclusion is that **fluctuations** are large: for both **the** energy loss at large angles and **the** gluon multiplicity N (x 0 ), **the** dispersion is parametrically as large as **the** respective average quantity. Such large **fluctuations** should be easy to observe **in** **event**-**by**-**event** studies of **the** di-**jet** asymmetry at **the** LHC. **In** particular, we predict that **the** multiplicity **fluctuations** should exhibit Koba-Nielsen- Olesen (KNO) scaling [ 43 ]. A similar scaling is known to hold for a **jet** branching **in** **the** vacuum [ 44 ], but **the** **medium**-**induced** gluon distribution is found to be considerably wider (see Sect. 4 for details). **The** physical picture emerging from our analysis can be summarized as follows. **In** a typical **event**, **the** leading particle evolves **by** emitting a number of order one of primary gluons with energy ω ∼ ω br (L) together with a large number ∼ [ω br (L)/ω] 1/2 of considerably softer gluons, with ω ω br (L). Here, ω br (L) ≡ ¯ α s qL ˆ 2 , with ¯ α s = α s N c /π and L **the** distance travelled **by** **the** **jet** through **the** **medium**, is **the** characteristic energy scale for **medium**-**induced** multiple branching. (We implicitly assume here that ω br (L) E, as this is **the** typical situation for high energy jets at **the** LHC; see **the** discussion at **the** end of Sect. 2.1 .) **The** primary gluons with ω . ω br (L) develop mini-jets via successive democratic branchings and thus transmit their whole energy to softer quanta with ω ∼ T that are expected to thermalize via collisions **in** **the** **medium** [ 42 ]. Harder emissions with ω ω br (L) occur only rarely, with a small probability ∼ [ω br (L)/ω] 1/2 , and moreover they do not contribute to **the** energy lost **by** **the** **jet** as a whole, since hard gluons propagate at small angles. **The** energy loss at large angles is rather controlled **by** **the** hardest typical emissions, those with energies ω ∼ ω br (L). As aforementioned, **the** number of such emissions is of order one and they occur independently from each other; accordingly, both **the** average energy loss **by** **the** **jet** and its dispersion are of order ω br (L) (see Eq. ( 3.15 )).

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Abstract
We study **the** gluon distribution produced via successive **medium**-**induced** branchings **by** an energetic **jet** propagating through a weakly-coupled quark-gluon plasma. We show that under suitable approximations, **the** **jet** **evolution** is a Markovian stochastic process, which is exactly solvable. For this process, we construct exact analytic solutions for all **the** n-point correlation functions describing **the** gluon distribution **in** **the** space of energy [1, 2]. Using these results, we study **the** **event**-**by**-**event** distribution of **the** energy lost **by** **the** **jet** at large angles and of **the** multiplicities of **the** soft particles which carry this energy. We ﬁnd that **the** **event**-**by**-**event** ﬂuctuations are huge: **the** standard deviation **in** **the** energy loss is parametrically as large as its mean value [1]. This has important consequences for **the** phenomenology of di-**jet** asymmetry **in** Pb +Pb collisions at **the** LHC: it implies that **the** ﬂuctuations **in** **the** branching process can contribute to **the** measured asymmetry on an equal footing with **the** geometry of **the** di-**jet** **event** (i.e. as **the** di ﬀerence between **the** **in**-**medium** path lengths of **the** two jets). We compute **the** higher moments of **the** multiplicity distribution and identify a remarkable regularity known as Koba-Nielsen-Olesen (KNO) scaling [2]. These predictions could be tested via **event**- **by**-**event** measurements of **the** di-**jet** asymmetry.

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[z(1 − z)] 3/2 = K(1 − z) , f (z) ≡ 1 − z(1 − z) 5/2
. (3.6)
It depends only upon **the** splitting fraction z since **the** corresponding dependence upon **the** energy (fraction) x of **the** leading particle, cf. Eq. ( 3.2 ), has been explicitly factored out **in** writing Eq. ( 3.4 ). We shall refer to **the** r.h.s. of Eq. ( 3.4 ) as **the** ‘branching term’ and denote it as ¯ α I[D]. This is **the** sum of two terms, which can be recognized as **the** familiar ‘gain’ and ‘loss’ terms characteristic of a branching process. **The** first term, which is positive and nonlocal **in** x, is **the** gain term : it describes **the** rise **in** **the** number of gluons at x due to emissions from gluons at larger x 0 = x/z. **The** respective integral over z is restricted to x < z < 1 **by** **the** support of D(x/z, τ ). **The** second, negative, term, which is local **in** x, represents **the** loss term and describes **the** reduction **in** **the** number of gluons at x due to their decay into gluons with smaller x 0 = zx. Taken separately, **the** gain term and **the** loss term **in** Eq. ( 3.4 ) have endpoint singularities at z = 1, but these singularities exactly cancel between **the** two terms and **the** overall equation is well defined.

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Abstract
Besides **the** emblematic studies of **the** Higgs boson and **the** search of new physics beyond **the** Standard Model, another goal of **the** LHC experimental program is **the** study of **the** quark- gluon plasma (QGP), a phase of nuclear matter that exists at high temperature or density, and **in** which **the** quarks and gluons are deconfined. This state of matter is now re-created **in** **the** laboratory **in** high-energy nucleus-nucleus collisions. To probe **the** properties of **the** QGP, a very useful class of observables refers to **the** propagation of energetic jets. A **jet** is a collimated spray of hadrons generated via successive parton branchings, starting with a highly energetic and highly virtual parton (quark or gluon) produced **by** **the** collision. When such a **jet** is produced **in** **the** dense environment of a nucleus-nucleus collision, its interactions with **the** surrounding **medium** lead to a modification of its physical properties, phenomenon known as **jet** quenching. **In** this thesis, we develop a new theory to describe **jet** quenching phenomena. Using a leading, double logarithmic approximation **in** perturbative QCD, we compute for **the** first time **the** effects of **the** **medium** on multiple vacuum-like emissions, that is emissions triggered **by** **the** virtuality of **the** initial parton. We show that, due to **the** scatterings off **the** plasma, **the** **in**- **medium** parton showers differ from **the** vacuum ones **in** two crucial aspects: their phase-space is reduced and **the** first emission outside **the** **medium** can violate angular ordering. A new physical picture emerges from these observations, with notably a factorisation **in** time between vacuum- like emissions and **medium**-**induced** parton branchings, **the** former constrained **by** **the** presence of **the** **medium**. This picture is Markovian, hence well suited for a Monte Carlo implementation. We develop then a Monte Carlo parton shower called JetMed which combines consistently both **the** vacuum-like shower and **the** **medium**-**induced** emissions.

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annually ( Fig. 2 ). Wine-growing developed here on a fault-
scarp relief **in** **the** Middle Ages ( Dion, 1959 ). These historical
hillslopes, **induced** **by** **the** Bressan rifting, form **the** eastern border of **the** Burgundy plateau. **The** hillslopes develop on Middle to Upper Jurassic limestones and marls, and are covered **by** colluvium soils of argillaceous-gravelly nature and formed **by** Weichselian cryoclastic deposits (“grèzes litées”) reaching up to 3 m thick ( Journaux, 1976 ). Soils were described fol- lowing **the** method of Baize and Girard (1995) . These deposits are draining, non-cohesive, easily erodible and display a low organic content (b1%) like all vineyard soils **in** Côte-d'Or ( Mériaux et al., 1981 ). Measured dry soil bulk density of **the** soil top layer varies between 1.25 and 1.5 t m-3. **The** texture is rather homogenous over **the** whole plot and is composed of 40% of clays and silts, 50% of gravels (2 mm to 10 mm) and a low sand and boulder content. **The** topsoil are ploughed ( Mériaux et al., 1981 ). **The** argillaceous aggregates with polyhedral blunted to grained form are slightly structured. No pedogenetic segrega- tion has been observed.

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Key words. Galaxies: **evolution** – Galaxies: kinematics and dynamics – Galaxies: interactions – Methods: N-body simulations
1. Introduction
**The** formation of disk galaxies remains an outstanding puzzle **in** contemporary astrophysics (see Mayer et al. 2008 for a re- view). According to hierarchical models of structure formation, mergers and interaction of galaxies are an essential ingredient of galaxy formation and **evolution**. Earlier works and numerical simulations show that **the** remnants of mergings of purely stel- lar progenitors are more likely to be elliptical galaxies (Toomre 1977; Barnes 1988; Barnes & Hernquist 1992; Hernquist 1992; Lima-Neto & Combes 1995; Balcells & Gonz´alez 1998; Naab et al. 1999 etc.) and recent studies extended this result to gas- rich progenitors (Springel & Hernquist 2005; Robertson et al. 2006; Hopkins et al. 2008). Whether this is compatible, or **in**- compatible, with **the** fraction of disk galaxies present **in** **the** lo- cal universe depends on **the** typical number of expected merg- ers **by** galaxy (see for instance Kazantzidis et al. 2007). Such predictions seems to be incompatible with observations which suggest that disk galaxies represent **the** majority (70%) of **the** galaxy population observed **in** **the** local universe (see Hammer et al. 2005; Nakamura et al. 2004 and references therein). To help resolve such issues, Hammer et al. (2005) suggested that disks can be rebuilt during **the** encounters of gas rich spirals. Indeed such proposition was guided **by** **the** remarkable coinci- dence of **the** redshift increase, up to z=1, of **the** merger rate,

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In p–Pb collisions with high event activity, the average medium-induced out-of-cone energy transport for jets with R = 0.4 and 15 < p ch < 50 GeV/c is T,jet measured to be less than 0.4 [r]

Q,l
(Q + l) 2 − l 2 K Q, l, z, xp + 0 ,
(4.8) where **the** lower limit x **in** **the** integral over z, which was a priori present only **in** **the** ‘gain’ term, has also been inserted **in** **the** ‘loss’ term, while at **the** same time multiplying **the** latter **by** a factor of 2, to account for its original singularities at both z = 0 and z = 1 (which is legitimate since, to **the** accuracy of interest, **the** integral is controlled **by** values z ' 1 x). **The** particular combination of momenta, (Q + l) 2 − l 2 , that emerges then **in** Eq. ( 4.8 ) can be given **the** following interpretation: when z ' 1, Q ≡ k − z(q + l) is **the** same as (minus) **the** transverse momentum q + l − k of **the** unmeasured daughter gluon. Hence Q + l ' k − q is **the** change **in** transverse momentum at **the** emission vertex, with two obvious components: **the** momentum l acquired via **medium** rescattering during **the** branching process and **the** momentum Q taken away **by** **the** unmeasured daughter gluon. **The** above applies to **the** ‘gain’ term. For **the** ‘loss’ term, there is no real emission, so **the** only source of momentum broadening is **the** momentum l transferred from **the** **medium**. **The** difference (Q + l) 2 − l 2 represents therefore **the** net change **in** **the** transverse momentum squared, and **the** average of this quantity over **the** (momentum dependent) splitting kernel yields **the** correction δ ˆ q.

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this odd mode is **the** small difference between **the** partic- ipant numbers of projectile and target nuclei **induced** **by** **fluctuations**, which creates a forward-backward asymme- try of **the** multiplicity [29, 30]. Since both **the** colliding system and **the** analysis window are symmetric around η = 0, principal components have definite parity **in** η, up to statistical **fluctuations**. Indeed, **the** next mode v 0 (3) (η) is even, suggesting that principal components typically have alternating parities. **The** corresponding eigenvalue is again much smaller, λ (3) ∼ λ (2) /5. v (4)

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Keywords:
Heavy-ion collisions, **fluctuations**, anisotropic flow
1. Introduction
It was recently realized that **the** understanding of **fluctuations**, **in** particular **fluctuations** **in** **the** initial state, is an essential ingredient **in** **the** analyses of ultra-relativistic heavy-ion collisions [1]. To characterize a fluctuating initial state theoretically, e ffective models have been proposed **by** properly introducing **fluctuations** on top of nucleus-nucleus collisions [2, 3]. However, despite some success of these models, **the** initial state of heavy-ion collisions still con- tributes a major fraction of **the** uncertainty of quantitative predictions [4, 5]. **In** experiments, initial state **fluctuations** can be revealed **by** **the** study of anisotropic flow v n . Defined as **the** Fourier harmonics of **the** corresponding particle spectrum, v n reflects **the** property of bulk **medium** expansion, and its response to **the** initial state anisotropy. Taking into account thus **the** direct mapping between v n and initial anisotropy, which is commonly formulated as eccentricity ε n , it is expected that **event**-**by**-**event** (EbyE) distribution of v n is largely determined **by** **fluctuations** of ε n . Indeed, many non-trivial observations have been made **in** heavy-ion experiments regarding flow **fluctuations**, among which **the** EbyE distribution of v n **in** Pb-Pb collisions [6], and cumulants of elliptic flow v 2 from p-Pb collisions [7, 8] will be discussed **in** this work. **In** this paper, without detailed modeling of initial state we propose a new parameterization to describe ε n **fluctuations**. As will be shown **in** Section 2, **the** crucial improvement of our new parameterization is rooted **in** **the** fact that |ε n | ≤ 1. **The** universality of parameterizing **fluctuations** of ε n will be addressed also **in** Section 2. **In** Section 3 we apply **the** parameterization to **the** measured flow cumulants and flow distribution.

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1 Introduction
What is **the** **event** B method? **In** **the** sequel, we refer to **the** original B method as classic B [ABR 96] and its **event**-based **evolution** as **event** B. **The** **event** B method [ABR 03a, ABR 98] reuses **the** set-theoretical and logical notations of **the** B method [ABR 96] and provides new notations for expressing abstract systems or simply models based on events. Moreover, **the** refinement over models is a key feature for incrementally de- veloping models from a textually-defined system, while preserving correctness; it im- plements **the** proof-based development paradigm. Each development. includes proofs for invariance and refinement. Operations of **the** B classical method do not exist **in** **the** **event** B method and are substituted **by** events. Events modify **the** system state (or state variables), **by** executing an action, but if a guard holds. An **event** is not called but observed. When refining machines **in** classic B, one should maintain **the** number of op- erations both **in** **the** abstract machine and **in** **the** refinement; on **the** contrary, new events may be introduced **in** **the** refinement model and they may modify only new variables. New events bring new proof obligations for ensuring a correct refinement. Finally, a B **event**-based model is a closed system with a finite list of state variables and a finite list of events. If **the** system reacts to its environment, **the** **event** B model should integrate events of **the** environment. **The** B classical chapter introduces useful notations for **the** **event** B method like set theory, generalised substitution, predicate calculus.

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2
IRIT, Toulouse, France Sergei.Soloviev@irit.fr
Abstract. This paper studies how dependent types can be employed for a refined treatment of **event** types, offering a nice improvement to Davidson’s **event** semantics. We consider dependent **event** types indexed **by** thematic roles and illustrate how, **in** **the** presence of refined **event** types, subtyping plays an essential role **in** semantic interpretations. We consider two extensions with dependent **event** types: first, **the** extension of Church’s simple type theory as employed **in** Montague semantics that is familiar with many linguistic semanticists and, secondly, **the** extension of a modern type theory as employed **in** MTT-semantics. **The** former uses subsumptive subtyping, while **the** latter uses coercive subtyping, to capture **the** subtyping relationships between dependent **event** types. Both of these extensions have nice meta-theoretic properties such as normalisation and logical consistency; **in** particular, we shall show that **the** former can be faithfully embedded into **the** latter and hence has expected meta-theoretic properties. As an example of applications, it is shown that dependent **event** types give a natural solution to **the** incom- patibility problem (sometimes called **the** **event** quantification problem) **in** combining **event** semantics with **the** traditional compositional seman- tics, both **in** **the** Montagovian setting with **the** simple type theory and **in** **the** setting of MTT-semantics.

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for fluence reaching 10 7 cm -2 . These positive results are
thought to be due to **the** doping of **the** epitaxial layer and **the** deep-well implants available and used **in** this technology, which prevents latchups. CIS1 devices are made using another process and are not immune to SELs. As can be seen **in** Fig. 17, CIS1 was studied **in** different operating modes. First, **the** device was biased and operated **in** nominal mode to take pictures. **The** number of SELs increases with LET, and **the** values can be fitted using **the** Weibull function. Several devices were irradiated to obtain this curve and provide a precise LET threshold of around 16 MeV. **The** threshold is higher than **the** maximum LET **the** protons can produce as a result of ionizing and **by** non-ionizing effects **in** silicon. However, layers of specific metals, such as copper and tungsten, are used **in** CIS leading to higher LET if **the** protons interact with these metals **by** displacement damage.

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Novosibirsk State University, Novosibirsk, Russia
**The** temperature **fluctuations** generated **by** viscous dissipation **in** an isotropic turbulent flow are studied using direct numerical simulation. It is shown that their scaling with Reynolds number is at odds with predictions from recent investigations. **The** origin of **the** discrepancy is traced back to **the** anomalous scaling of **the** dissipation rate **fluctuations**. Phenomenological arguments are presented which explain **the** observed results. **The** study shows that previously proposed models underpredict **the** variance of frictional temperature **fluctuations** **by** a factor proportional to **the** square of **the** Taylor-scale Reynolds number.

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– [[Γ, P true]] = [[Γ ]], x : Prf([[P ]] Γ ), where x does not occur free **in** [[Γ ]]. **The** following theorem shows that **the** embedding is well-defined and faithful (**in** **the** sense of **the** theorem) and hence C e has nice meta-theoretic properties (**the** corollary). Its proof is based on **the** embedding of Church’s simple type theory into **the** calculus of constructions [ 10 ]. We omit **the** discussion of technical details, for otherwise we would have to detail **the** syntax and rules of UTT and coercive subtyping [ 11 , 14 ], except remarking that a key reason that **the** proof goes through is because **the** coercions to model subtyping for dependent **event** types are constants and coherent (see Sect. 4.2 ) and hence model subsumptive subtyping **in** C e faithfully.

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allowed to continue execution until it needs the result of the faulting instruction. Instead of 'umping to an event handler, the handler is run on a separate thread. The [r]

and v 5 to v 2 v 3 [20]. Note that **the** last four-plane correla-
tor (Fig. 3(f)) is predicted to exceed unity when analyzed using **the** scalar-product method.
Conclusions.−We have argued that **event**-plane corre- lators **in** heavy-ion collisions can be analyzed with just two symmetric pseudorapidity windows. We have illus- trated **the** validity of our approach **by** analyzing events simulated within **the** AMPT model which reproduces for **the** first time **the** magnitude and centrality dependence of **the** measured correlators **in** Pb-Pb collisions at LHC. Much better agreement with data is achieved than **in** pre- vious hydrodynamic calculations using **the** **event**-plane method [16, 17]. This apparent discrepancy between data and hydrodynamic calculations may simply be due to **the** ambiguity of **the** **event**-plane method. It will then be re- solved once both experiment and theory switch from **the** **event**-plane method to **the** scalar-product method. We have presented predictions for new correlators, **in** partic- ular large four-plane correlators, which can be measured **in** forthcoming analyses. It would be interesting to study **the** correlators using **the** procedure presented here **in** **the** **event**-**by**-**event** hydrodynamical simulations to ascertain **the** sensitivity to initial-state models, namely **the** Monte- Carlo Glauber and **the** color-glass-condensate [42].

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Grand Challenge Initiative. Using an incremental proof-based approach, we model functionalities of **the** Pacemaker. **The** approach is illustrated **by** developing a new formal model of **the** cardiac pacemaker system. Our contribution are **in** this report to model **the** single electrode pacemaker system using **Event**-B and prove it. **The** incremental proof-based devel- opment is mainly driven **by** **the** refinement between an abstract model of **the** system and its detailed design through a series of refinements. A series of refinements is progressively added **the** functional and **the** timing prop- erties to **the** abstract system-level specifications using some intermediate models. **The** properties express system architecture, action-reaction and timing behavior. This paper uses all possible operational modes of a sin- gle electrode Pacemaker system that helps to develop better hardware. Every stage of refinement includes **the** detail information about oper- ating modes. **The** models are expressed **in** **Event**-B modeling language and validated primarily **by** **the** ProB tool **in** different situation such as hysteresis and rate adapting pacing under real-time constraints. **In** each stages of refinements include **the** detail information and more events are introduced. **The** final step of refinement completely localized **the** events and similar to implementation of single electrode pacemaker operating modes system. **The** stepwise refinement of **the** single electrode Pacemaker system contributes to achieve a high degree of automatic proof. Key words: Abstract model, **Event**-B, **Event**-driven approach, Proof- based development, Refinement, Pacemaker, Electrode, Heart

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