Data centers are often equipped with multiple cooling units. Here, an aquifer thermal energy storage (ATES) system has shown to be efficient. However, the usage of hot and cold-water wells in the ATES must be balanced...
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Data centers are often equipped with multiple cooling units. Here, an aquifer thermal energy storage (ATES) system has shown to be efficient. However, the usage of hot and cold-water wells in the ATES must be balanced for legal and environmental reasons. Reinforcement Learning has been proven to be a useful tool for optimizing the cooling operation at data centers. Nonetheless, since cooling demand changes continuously, balancing the ATES usage on a yearly basis imposes an additional challenge in the form of a delayed reward. To overcome this, we formulate a return decomposition, Cool-RUDDER, which relies on simple domain knowledge and needs no training. We trained a proximal policy optimization agent to keep server temperatures steady while minimizing operational costs. Comparing the Cool-RUDDER reward signal to other ATES-associated rewards, all models kept the server temperatures steady at around 30 °C. An optimal ATES balance was defined to be 0% and a yearly imbalance of −4.9% with a confidence interval of [−6.2, −3.8]% was achieved for the Cool 2.0 reward. This outperformed a baseline ATES-associated reward of 0 at −16.3% with a confidence interval of [−17.1, −15.4]% and all other ATES-associated rewards. However, the improved ATES balance comes with a higher energy consumption cost of 12.5% when comparing the relative cost of the Cool 2.0 reward to the zero reward, resulting in a trade-off. Moreover, the method comes with limited requirements and is applicable to any long-term problem satisfying a linear state-transition system.
The augmented ribbon model of a protein provides a way of describing features of its primary, secondary, and super-secondary structure. Associated with the model is a graph obtained by an ambient isotopy in space foll...
The augmented ribbon model of a protein provides a way of describing features of its primary, secondary, and super-secondary structure. Associated with the model is a graph obtained by an ambient isotopy in space followed by a projection into the plane. This projection graph is shown to be independent of the ambient isotopy.
In this paper an algorithm to numerically invert two-dimensional Laplace transforms is presented. This two-dimensional inverse Laplace transforms technique is an extension of the one-dimensional methods based on the r...
In this paper an algorithm to numerically invert two-dimensional Laplace transforms is presented. This two-dimensional inverse Laplace transforms technique is an extension of the one-dimensional methods based on the representation of the inverse function in terms of Fourier series. In particular, it extends the one-dimensional methods of Dubner and Abate [3] and Crump [1].
We consider random graphs with edge probability beta-n(-alpha), where n is the number of vertices of the graph, beta > 0 is fixed, and alpha = 1 or alpha = (l + 1)/l for some fixed positive integer l. We prove that...
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We consider random graphs with edge probability beta-n(-alpha), where n is the number of vertices of the graph, beta > 0 is fixed, and alpha = 1 or alpha = (l + 1)/l for some fixed positive integer l. We prove that for every first-order sentence, the probability that the sentence is true for the random graph has an asymptotic limit.
A method is described which is suitable for on-line query term expansion. By using an efficient version of the N-gram method for similarity matching, a small set of strings from the dictionary is selected. From this s...
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A method is described which is suitable for on-line query term expansion. By using an efficient version of the N-gram method for similarity matching, a small set of strings from the dictionary is selected. From this set, all the strings relevant to the query term are then identified using the Boyer-Moore pattern matching algorithm. Tests show that the method is both efficient and effective.
A set partition is called "gap-free" if its block sizes form an interval. In other words, there is at least one block of each size between the smallest and largest block sizes. Let B(n) and G(n), respectivel...
A set partition is called "gap-free" if its block sizes form an interval. In other words, there is at least one block of each size between the smallest and largest block sizes. Let B(n) and G(n), respectively, denote the number of partitions and the number of gap-free partitions of the set [n]. We prove that [GRAPHICS]
Let chi be an irreducible character of the symmetric group S(n). For an n-by-n matrix A = (a(ij)), define [GRAPHICS] If G is a graph, let D(G) be the diagonal matrix of its vertex degrees and A(G) its adjacency matrix...
Let chi be an irreducible character of the symmetric group S(n). For an n-by-n matrix A = (a(ij)), define [GRAPHICS] If G is a graph, let D(G) be the diagonal matrix of its vertex degrees and A(G) its adjacency matrix. Let y and z be independent indeterminates, and define L(G) = yD(G) + zA(G). Suppose t(n) is the number of trees on n vertices and s(n) is the number of such trees T for which there exists a nonisomorphic tree T such that d(chi)(xI - L(T)) = d(chi)(xI - L(T)) for every irreducible character chi of S(n). Then lim(n-->infinity)s(n)/t(n) = 1. (C) 1993 John Wiley & Sons, Inc.
Let X be a metric space. A family H of continuous functions of several variables of X with values in X is said to be generating if, whenever A ⊂ C ( K , X ) separates points and H operates on A , then A is dense in C ...
Let X be a metric space. A family H of continuous functions of several variables of X with values in X is said to be generating if, whenever A ⊂ C ( K , X ) separates points and H operates on A , then A is dense in C ( K , X ). (For example, the family H = { x + y , xy , constants} in C ( R 2 , R ) is generating (for R ) by the Stone-Weierstrass theorem.) We identify metric spaces which admit generating families (not all do), and among those, we search for spaces X that admit generating families in C ( X 2 , X )—such as R . (This may be considered a topological version of Hilbert's 13th problem.) Once we know this, we try to identify some (small) generating families in C ( X 2 , X ). (This is done in particular when X = R .) As a fringe benefit we obtain a “topological” proof of the Stone-Weierstrass theorem.
We discuss and explain the issues present in implementing a fast algorithm for discrete monomial transforms (DMTs) in the context of certain applications in MRI and data analysis. The DMT of a sequence f = (f(0),..., ...
We discuss and explain the issues present in implementing a fast algorithm for discrete monomial transforms (DMTs) in the context of certain applications in MRI and data analysis. The DMT of a sequence f = (f(0),..., f(m)) with respect to sample points {z0 ..., z(m)) subset-of C(m+1) is the sequence of sums (f(0),...,f(m)) where f(j) = SIGMA(k=0)(m)f(k)z(k)j. For different sets of sample points the DMT is an important component of many applications. Driscoll, Healy, and Rockmore described a fast [O(m log2 m) operations] algorithm via matrix factorization for computing the DMT. While the asymptotic complexity of the algorithm is guaranteed for any choice of the sample points, the numerical stability is not. In this paper we present a heuristic for stabilizing the fast DMT which makes its implementation feasible numerically for certain sets of sample points, while retaining its computational advantages even for moderate problem sizes, where it is shown to be more efficient than implementations using Horner's rule.
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