techniques can help to **the** computer scientist to ”avoid **the** curse of dimensionality”. **The** **Proper** **Generalized** **Decomposition** (PGD) method has been recently proposed [1, 17, 21] **for** **the** a priori construction of separated representations of an element u in a tensor product space V = V 1 ⊗ . . . ⊗ V d , which is **the** solution of a problem of type

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There exists several approaches to **the** numerical analysis of PGD. Both combine **the** existence of a **best** **approximation** **and** a greedy algorithm. **The** idea of using greedy algorithms was introduced by Ammar, Mokdad, Chinesta **and** Keunings [2], in **the** context of high-dimensional PDEs. It can be applied to several **problems** including, among others, **the** stationary FokkerPlanck equation of **the** FENE bead-spring chain model [13]. In Ammar, Mokdad, Chinesta **and** Keunings [3], **the** approach is extended to time-dependent **problems**. One should note, however, **the** method in [2] can be interpreted as a greedy algorithm **for** solving elliptic **problems** associated with self-adjoint operators, because it is equivalent to a minimization problem related with an energy functional (see Le Bris, Leli` evre **and** Maday [4] **for** elliptic **problems** associated with self-adjoint operators **and** **for** general elliptic ones, see Falc´ o **and** Nouy [6],). **The** extension of **the** method to more general **problems**, like **the** non-stationary FokkerPlanck equation, is done merely by analogy. In particular, its convergence, in general, is not guaranteed (a recent result in this approach is given in **the** paper of Figueroa **and** S¨ uli [7]). A modification of **the** low-rank separation method, introduced in Ammar, Chinesta **and** Falc´ o [1], where one minimizes **on** each iteration an L 2

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equations) or quantum mechanics (e.g. Schrödinger equation), stochastic parametric partial dierential equations in uncertainty quantication with functional approaches, **and** many mechanical or physical models involving extra parameters (**for** parametric analyses) among others. **For** such **problems**, classical **approximation** methods based **on** **the** a priori selection of **approximation** bases suer from **the** so called curse of dimensionality associated with **the** exponential (or factorial) increase in **the** dimension of **approximation** spaces. Tensor-based methods consist in approximating **the** solution u ∈ V of a problem, where V is a tensor space generated by d vector spaces V j (assume

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optimal **decomposition** of a given rank r is not trivial **and** has led to various definitions **and** associated algorithms **for** **the** separated representations. In **the** context of **problems** of type (1), **the** solution is not known a priori, nor an **approximation** of it. An approximate solution is even unreachable with tra- ditional numerical techniques when dealing with high dimensions d. It is **the** so-called curse of dimensionality associated with **the** dramatic increase of **the** di- mension of **approximation** spaces when increasing d. **The** PGD method aims at constructing a **decomposition** of type (2) without knowing a priori **the** solution u. **The** aim of **the** PGD is to construct a sequence u **n** based **on** **the** knowledge

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• **The** compact urban model favours sustainable mobility, with 8 out of 10 trips within **the** city being done by public transport, bicycle or **on** foot. Other noteworthy areas include **the** reduction in household water use in **the** city (which has decreased from 133 to 110 litres per inhabitant in 10 years) **and** **the** technical plan to take advantage of alternative hydraulic resources.

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earth), sand, cerulean (from **the** Latin caeruleus: sky blue), sea-green, ultramarine, green (in old English grene, akin to **the** old **term** growan, to grow; green also means fresh, vigorous, new). Probably, in most cases, no difference was originally made between **the** object **and** **the** color, so that both things constituted one **and** **the** same cognitive unit, **and** it was not until later **on** that **the** color name was used making abstraction of **the** object that had given origin to it. Other colors have been designated with geographical names, be- cause **the** pigments were obtained in those places, or be- cause some circumstances associated **the** colors with **the** places as in **the** case of sienna, indigo, Nile green, Prussian blue, African brown, bordeaux (Bordeaux is a region of France famous **for** its wines), magenta (name given by a French chemist who synthesized **the** pigment in 1859, **and** who took **the** word from **the** name of a town in **the** zone of Lombardia, Italy, where Napoleon III won a battle 58 ). It has

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At **the** time this analysis was performed **the** usual approach was to use time series of risk variables. However, when quantitative data of operational risks do not exist or when are scarce then it is necessary to obtain qualitative data based **on** experts’ decision to understand **the** behavior of **the** OpR. **The** qualitative methods just started to be implemented seriously in **the** financial system after **the** global financial crash of 2008. Therefore this article introduces a financial innovation because it presents a study based **on** qualitative data from surveys that were made by experts.

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A widespread observation is that climate change will affect both **the** geographical distribution of **the** wine industry **and** **the** quality of **the** product. Although wine is not an essential agricultural product **for** survival, it is closely connected to human history **and** culture as a significant product of human ingenuity (Mozell **and** Thach, 2014). Viticulture contributes to **the** local economy, tourism, industry **and** natural habitat (Duchene, 2016; Resco et al., 2016). In recent years, China has joined **the** world’s wine world presenting significant suitable regions **and** diverse climatic sites (De Orduña, 2010 ; Hannah et al., 2013). A great expansion of Chinese domestic wineries in new regions with increasing capability may be observed (Mozell **and** Thach, 2014). While there have been continued improvements in **the** wine industry, it is necessary to recognize **the** impact of global climate change, which will bring both challenges **and** opportunities to China.

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Because all possible outcomes are equally likely here, we can also compute P(A|B) using a shortcut. We can bypass **the** calculation of P(B) **and** P(A∩B), **and** simply divide **the** number of elements shared by A **and** B (which is 3) with **the** number of elements of B (which is 4), to obtain **the** same result 3/4. Another example. Using **the** previous example about a new supermarket is to be built in City Town: If we need P(a customer spends at least Rwf 20, if it is known that he/she travelled by car)

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a‘ ūb ibn Is ā al- indī fī l-Radd ‘alā al- a ārā, in Augustin P ÉRIER ed. , “Un traité de Yaḥyā ibn Ad , défense du dogme de la Trinité contre les ob ections d’al-Kind ”, Revue de l’Orient Chrétien 22 (1920-1921), pp. 3–21; I BN AL -Ṭ AYYIB , a ālah fī l- tathlīth, in Gérard T ROUPEAU ed. , “Le traité sur l’unité et la trinité de Abd Allāh ibn al-Ṭayyib”, Parole de l’Orient 2 (1971), pp. 71–89; Adel Theodore K HOURY , Apologétique Byzantine contre l’Islam (VIIIe-XIIIe s.) (Altenberge: Verlag für Christlich-Islamisches Schriftum, 1982), pp. 13-14; Richard B ULLIET , Conversion to Islam in **the** medieval period: an essay in quantitative history (Cambridge: Harvard University Press, 1979), pp. 131; Philip J ENKINS , **The** Lost History of Christianity (New York: HarperOne, 2008), p. 111; Arthur Stanley T RITTON , Muslim Theology (London: Luzac & Co., 1947), p. 89. Bibliography of Arab Christian literature **and** Christian - Muslim relations: Georg G RAF , Geschichte der christlichen arabischen Literatur (Città del Vaticano: Biblioteca Apostolica Vaticana, 1944-1953), V vol.; Samir Khalil S AMIR , “Bibliographie du dialogue islamo-chrétien : Auteurs arabes chrétiens (XIe-XIIe siècles ”, Islamochristiana 2 (1976), pp. 201-249; Samir Khalil S AMIR , “Bibliographie

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In fact, the novel's use of Caddy as the absent element that always returns and that resists symbolisation confers on her (as popular culture text) the status of the real, at the same [r]

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Many inborn errors are chronic diseases with unpredictable but often long courses. **The** e¡ects of therapy may only be evident after many years. Examples of inborn errors where **the** start of intervention may precede a clinical end-point by up to 20 years or even more include childhood familial hypercholesterolaemia (McKusick 143890), homocystinuria (cystathionine b-synthase de¢ciency), **and** any mild organic acidaemia. This sort of time course makes it hard to embrace enthusiastically a suitably designed trial, **and** especially a randomized controlled trial. **And** **the** course may be quite unpredictable. Once again we turn to X-linked adrenoleukodystrophy as an example. Here, about half **the** a¡ected boys will have a devastating course with severe physical disability, dementia, **and** death during **the** ¢rst to second decade. **The** other half will have a much more prolonged **and** benign course, with more or less intact survival to adulthood, **the** ¢nal phenotype still not being fully known (Moser et al 2000). It has not so far proved possible to distinguish between these phenotypes at an early age. This is perhaps an extreme example, but many inborn errors have su¤ciently unpredictable courses to make **the** evaluation of a trial of treatment very di¤cult.

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Since Emancipation opened up a world of possibilities, travelling during **the** postbellum period provided African Americans with further chances to redefine **and** recreate themselves. In this sense, Elizabeth Keckley’s Behind **the** Scenes (1868) becomes a paradigmatic example of **the** new African American **and**, more precisely, of **the** new black woman who emerged from slavery. Her story—largely ignored **and** almost exclusively studied by most critics in terms of her relationship to Mary Todd Lincoln—is one of “unwavering determination to prove herself in whatever she undertook, particularly in those aspects of her life that involved career” (Andrews 2005: viii) **and** becomes **the** narrative of **the** first African American self-made woman. Keckley’s achievements **and** failures are shaped both by her “forced” **and** “voluntary” transits between three intermediate locations which determine a series of key phases in her life: **the** master’s house in which **the** young Elizabeth loses her innocence; **the** White House where she succeeds professionally; **and**, when going back to her origins, she makes peace with her past. Thus, by being in constant movement, **the** former slave is able to challenge racial **and** gender constraints, reinvent herself, **and** create a path towards full citizenship.

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Based **on** **the** use of certain financial ratios, this work focuses **on** **the** explanation of an alternative calculation used to obtain its value. **The** starting point **for** this work is **the** selection of **the** ratios to study **the** short-**term** solvency of a sector. Without sacrificing generality, three ratios have been chosen whose structure makes it possible to get an idea of **the** proposed alternative calculation methodology that is being presented. Specifically, **the** cash flow or acid test ratios, **the** liquidity or solvency ratios **and** **the** current asset ratio + **the** long-**term** financial asset, divided by current liabilities. Figure 1 shows its formulation with **the** customary abbreviations.

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In this paper we will focus mainly **on** three measures that can be efficiently computed using landscape theory. They are **the** autocorrelation, **the** fitness-distance correlation **and** **the** expected fitness after bit-flip mutation. **The** first two statistics have been considered as measures **for** problem hardness. None of them is a perfect measure of **the** hardness of a problem **and** both have been criticized in **the** past. How- ever, they are used even in some recent works. In this paper we will see how they can be efficiently computed using land- scape theory under some conditions **and** we provide software tools to do it. Regarding **the** expected fitness after bit-flip mutation, it has some links to runtime analysis, which is a direct measure of problem hardness. But, more interesting is **the** fact that **the** elementary **decomposition** of a combi- natorial **optimization** problem has a one-to-one relationship with **the** expectation curves (depending **on** **the** probability of mutation) of bit-flip.

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Understanding a second language is difficult especially when there are so many words **and** `phrases that don´t mean exactly what **the** words indicate. These expressions take **on** a whole new meaning when combined **and** it can add confusion to a conversation. Therefore, once again, listen intently **and** observe non-verbal cues including facial expressions **and** body language. This can help improve understanding. In most cases, people will understand that this is a second language learner, **and** they will make concessions to make a person feel comfortable. **The** ear **and** eyes have to adapt to hear a new language. A simple smile or a peculiar frown can tell a speaker if her message is being understood.

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As far as wireless scheduling is concerned, **the** first steps in this direction were taken with **the** introduction of proportional fair scheduling (PFS) V **the** AMC-based algo- rithm used in Qualcomm’s HDR (1xEV-DO) system [8], [81]. By exploiting opportunities **for** reliable connectivity provided by **the** multiuser fading channel, PFS effects multiuser diversity which enhances throughput while maintaining Bproportional fairness[ among users. **The** striking success of PFS prompted further studies **on** channel-aware Bopportunistic[ scheduling **for** **best** effort [3], [42], [73], non-real-time [6], [49], [50], **and** real-time traffic [2], [64], [65], [69], [74]. Built **on** cross-layer channel-adaptive approaches, **the** resultant algorithms broadened **the** scope of traditional schedulers by allowing a scheduler to perform not only user selection (channel assignment) but also rate allocation. In fact, going beyond channel **and** rate assignments, we contend that with sufficient CSIT available, **the** scheduler should also perform optimal power allocation. This augmentation brings scheduling design closer to **the** overall optimal resource allocation task, **the** fundamental limits of which have been explored by information theorists in **the** context of determining **the** capacity region (maximum achievable rates) of multiple access **and** broadcast fading channels [9], [32], [45], [46], [76].

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