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Main Results Sample Clauses

Main Results. In a first step a literature study was performed to screen observed pollutant concentrations of organic acids (formic acid, acetic acid), formaldehyde and volatile organic compounds (VOCs) within museum enclosures used for exhibiting and storing movable assets. This research showed that there are still pollutant problems in showcases throughout Europe, as shown from the investigation done in the EU FP5 MASTER project, see Figure 15.
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Main Results. ‌ ^√ ^ In this paper we focus on two optimization problems, namely the sparse Minimum Bisection Problem (sMBP) and the Xxxxxx Quadratic Assignment Problem (LQAP). Formal definitions are given below. However, we should add that many of our results hold for a larger class of optimization problems as long as log m = o(N ) (see Xxxxxxxxxxx, 1995). In the rest of the paper we will utilize the temperature rescaling β = β log m/N with β = O(1) which together with log m = o(N ) explains β 0 limit. This rescaling was justified in (Xxxxxxx et al., 2014). ^ For these two problems we shall provide tight asymptotics for the free en- ergy (5), and compute asymptotically the log-posterior agreement as well as β∗ that maximizes the posterior kernel. 2.1. Minimum bisection and quadratic assignment optimization problems‌ This section introduces combinatorial optimization problems that will be used to describe our findings. These problems fall into the log m = o(N ) class specified in Sec. 1.2 and cover a wide range of practical applications in signal processing and neural information processing. Minimum bisection problem (MBP). Consider a complete undirected weighted graph G = (V, E, X) of n vertices, where n is an even number. The input data instance X is represented by (random) weights (Wi)i∈E of the graph edges. Σ ∈S
Main ResultsFigure 1 shows the fringe visibility loss resulting from the mirror vibrations in var- ious operational conditions and for three different observing wavelengths: visible (0.6 μm), near infrared (2.2 μm) and ther- mal infrared (10 μm). The VLTI error budgets call for a 1% visibility loss due to vibrations inside the telescope for any of these observing wavelengths. This cor- responds respectively to an OPL varia- tion of 14, 50 and 215 nanometers r.m.s.
Main Results. In this paper we prove the following theorem. Theorem 1.1. For k < n, there is no deterministic wait-free protocol in the shared atomic registers model which solves the k-set agreement problem in a system of n processors. (i) two schedules are “indistinguishable” if for any protocol they exhibit the same output behavior, (ii) a set S of schedules is “knowable” if there is a protocol which “recognizes” it, in the sense that for some specified output symbol, the protocol pro- duces that symbol during an execution if and only if the execution proceeds according to some schedule from S. ∈ − These two concepts lead naturally to the definition of a topology on the set of schedules, and Theorem 1.1 is proved by analyzing this topology. Our approach reveals and exploits a close analogy between the impossibility of wait-free k-set agreement and a lemma of Knaster, Xxxxxxxxxx, and Xxxxxxxxxxxx (KKM lemma) [1], which is equivalent to the fixed point theorem for the closed unit xxxx Xx in m-dimensional Euclidean space: if f is a continuous map from Bm to itself, then there exists a point x Bm such that f (x) = x. Very roughly, f corresponds to a distributed protocol Π, and the fixed point x corresponds to the schedule for which Π fails to solve the k-set agreement. The increase in difficulty of the k-set agreement proof in going from the case k = 1 to the case k > 1 corresponds to the increase in difficulty in going from the fixed point theorem for the interval [ 1, 1], which is very simple, to the theorem for balls in higher dimension, which, while elementary, is considerably harder. An additional obstacle in our work is that, while the topological structure of Bm is well understood, we must develop the topological structure for the set of schedules from scratch. While the explicit use of topology can be avoided, we have retained the topological structure of the proof, because this is what drove the proof and it provides important insight into what is going on. Our topological structure has an intuitive interpretation in terms of the information about an execution which is “public knowledge.” We believe that it will be worthwhile to explore the connection with the formal theory of distributed knowledge [14]. The inspiration for the topological approach came from Xxxxxxxxx’x work [10], in which the combinatorial properties of triangulations in Rk were used to obtain certain reductions among various decision problems. There is a considerable literature con- cerning topologies u...
Main Results. ‌ The following extends the single-letter upper bound (36) in Proposition 3 to the multi-user case.
Main Results. We will make use of the following alternative character- ization of the unconstrainted secrecy capacity in [11]: For the no-helper case, CS = I(ZV ) where I(ZV ) is called the multivariate mutual information (MMI) defined as RS := min{r(V ) | (CS, rV ) ∈ R} = min{R ≥ 0 | CS(R) = CS} ≤ RCO.
Main Results. ‌ For simplicity, in this work, we assume that the number of colours k and the total sum of weights w are constants. However, we state most of the intermediate results in terms of k and w , but we do not attempt to optimise the terms involving k or w .
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Main ResultsCase 1. We begin with the restricted dataset [(xi, y¯i), i = 1, . . . , n] (2) where only the means of the Y variable are provided. The likelihood func- tion can be based on the marginal likelihood of xi, which is univariate normal N (µx, σ2), and conditional likelihood of y¯i, given xi, which is again univariate normal with conditional mean linear in xi and conditional variance independent of xi, namely, y¯i|xi ∼ N [µy + ρ resulting into the overall likelihood (xi − µx), σ2(1 − ρ2) ] (3) L(µx, µy, σx, σy, ρ|data) ∝ (σxσy)−n(1 − ρ2)−n/2 ∑1 exp [ − 2 (xi µx)2 − 2σ2(1 − ρ2) ∑i=1 mi(y¯i − µy − ρ σy (x − µ ))2
Main Results j The algebraic Riccati equation can be written in the factorized form; let P¯j = H¯ F H¯j . The factor can be computed recursively, for j = 0, 1, ..., as H¯0 = P0 , H¯j = H¯j—1 D¯j ; D¯1 = L0 Cd0P¯0CF + r0 2 , D¯j = AD¯j—1 (167) d0 There, P0 is the solution of the algebraic Riccati equation for the unaugmented process model. Vector L0is the injection gain in 165 corresponding to P¯0. The recursive formula 167 corresponds to the Lyapunov difference equation run from P¯0. Vectors D¯j for j = 1, ..., nd max can be pre-computed off-line together with H¯0. The newly proposed representation of the state covariance matrix is as follows: + Dk+1|kDF |k k+1 There, the time-varying index i(k), also called ‘target delay’, is given by min {i(k — 1) + 1, nd max} if min J(k) > i(k — 1) or J(k) = {}.
Main Results. Key results are highlighted in the figures below. 94% 77% 48% 24% HTS_TST HTS_TST POS TX_NEW Annual Target 43,845 5,843 7,543 2019 Q1 20,425 1,400 828 2019 Q2 20,837 1,385 976 2019 Q1-Q2 41,262 2,785 1,804 % of Target 94% 48% 24% TX_CURR 22,003 17,011 16,997 16,997 77% 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 5,000 4,500 4,000 88% 83% 100% 90% 80% 3,500 3,000 2,500 2,000 61% 35% 70% 60% 50% 40% 1,500 30% Annual Target 2019 Q1 2019 Q2 2019 Q1-Q2
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