Optimal control of flow in combined sewer systems

CER73-74PWWB46.May 1974.This study examines the development of a suitable control logic for the real time control of flow in combined sewer systems. The approach followed is based on continuous time optimal control theory. The combined sewer system is modelled as a series of interconnected reservoirs having both weir and orifice controls. Using this model as a basis the state equations and inequality constraints of the system are then presented. The objective function chosen is that of minimizing weighted flow diversions from the system. Application of the calculus of variations to the minimization problem yields necessary conditions for an optimal control. These necessary conditions are examined and solution forms for the optimal control strategies for several configurations and system inflows are derived. The problem of numerical solution of the necessary conditions is examined and it is concluded that in general their solution is too cumbersome for practical use. An alternative control solution is proposed, based on operating rules derived from the common factors shown to exist in the previously examined solution forms. When combined with a first order gradient search technique these operating rules yield an optimal control strategy. Results of application of this technique to systems of four reservoirs and ten reservoirs are presented. They show that a satisfactory control strategy for up to twenty control points can be obtained within the time limits imposed by real time operation. A further example is presented showing the effects of information errors on the true optimality of a computed control strategy. Finally the necessary modification to the necessary conditions for an optimal control in which there are time delays in the flow routing are presented. It is shown that the change in operating rules amounts to a shift in time scales between reservoirs. It appears that the approach outlined herein is a feasible solution to the problem of real time control of flow in combined sewers

An Exploration of HTML5, Flash, and Javascript - Building a Presentation Engine

Abstract HTML5 is an emerging standard that provides new features and capabilities that overlap with those traditionally provided by tools like Flash. Because the standard is still emerging there are no clear guidelines or trade-offs to help choose between using the different technologies. We demonstrate how HTML5 can be used to create a presentation engine, previously only possible in technologies like Flash. The presentations contain various rich and interactive media, including deep zoom viewing, videos, navigation control and sequencing of the presentation slides. These features demonstrate the capabilities of HTML5, combined with Javascript, and the techniques needed to use them

Morse theory and stable pairs

We study the Morse theory of the Yang-Mills-Higgs functional on the space of pairs (A; \Phi), where A is a unitary connection on a rank 2 hermitian vector bundle over a compact Riemann surface, and \Phi is a holomorphic section of (E; d_A). We prove that a certain explicitly defined substratification of the Morse stratification is perfect in the sense of G-equivariant cohomology, where G denotes the unitary gauge group. As a consequence, Kirwan surjectivity holds for pairs. It also follows that the twist embedding into higher degree induces a surjection on equivariant cohomology. This may be interpreted as a rank 2 version of the analogous statement for symmetric products of Riemann surfaces. Finally, we compute the G-equivariant Poincare polynomial of the space of semistable pairs. In particular, we recover an earlier result of Thaddeus. The analysis provides an interpretation of the Thaddeus flips in terms of a variation of Morse functions

Cohomology of U(2,1) representation varieties of surface groups

In this paper, we use the Morse theory of the Yang–Mills–Higgs functional on the singular space of Higgs bundles on Riemann surfaces to compute the equivariant cohomology of the space of semistable U(2, 1)‐ and SU(2, 1)‐Higgs bundles with fixed Toledo invariant. In the non‐coprime case, this gives new results about the topology of the U(2, 1) and SU(2, 1) character varieties of surface groups. The main results are a calculation of the equivariant Poincaré polynomials, a Kirwan surjectivity theorem in the non‐fixed determinant case, and a description of the action of the Torelli group on the equivariant cohomology of the character variety. This builds on earlier work for stable pairs and rank 2 Higgs bundles

Cohomology of SL(2,C) Character Varieties of Surface Groups and the Action of the Torelli Group

We determine the action of the Torelli group on the equivariant cohomology of the space of flat SL(2,C) connections on a closed Riemann surface. We show that the trivial part of the action contains the equivariant cohomology of the even component of the space of flat PSL(2,C) connections. The non-trivial part consists of the even alternating products of degree two Prym representations, so that the kernel of the action is precisely the Prym-Torelli group. We compute the Betti numbers of the ordinary cohomology of the moduli space of flat SL(2,C) connections. Using results of Cappell-Lee-Miller we show that the Prym-Torelli group, which acts trivially on equivariant cohomology, acts non-trivially on ordinary cohomology

Morse theory and hyperkähler Kirwan surjectivity for Higgs bundles

This paper uses Morse-theoretic techniques to compute the equivariant Betti numbers of the space of semistable rank two degree zero Higgs bundles over a compact Riemann surface, a method in the spirit of Atiyah and Bott’s original approach for semistable holomorphic bundles. This leads to a natural proof that the hyperkähler Kirwan map is surjective for the non-fixed determinant case

CONNECTING FINE- AND BROAD-SCALE SPECIES–AREA RELATIONSHIPS OF SOUTHEASTERN U.S. FLORA

Although the rate that species accumulate with area has long been regarded as an important component of fine-scale community structure and several studies have examined this rate in meta-analyses, few if any studies have systematically examined fine-scale species-area relationships using a consistent survey protocol over a large region. We examined fine-scale species-area relationships using the extensive database of the Carolina Vegetation Survey (North Carolina, South Carolina, Georgia, and Tennessee, USA), including 1472 plots wherein vascular plant richness was recorded for each of six subplot sizes regularly spaced on a log10 scale, from 0.01 to 1000 m2. Contrary to prevailing theory, our data closely and consistently fit an Arrhenius (power law) species-area model, echoing broader-scale patterns. Species accumulation rate (Z) values fell within a narrow range (95% between 0.2 and 0.5) despite a 30-fold range in 1000-m2 richness. When we added regional- and global-scale richness estimates to our results, a Preston-type triphasic curve emerged. We suggest that (1) fine-scale species-area relationships are remarkably consistent and (2) full-scale species-area curves reveal scale dependencies in diversity data that are not accounted for by current species-area theory

Benchmarking implementations of functional languages with ‘Pseudoknot', a float-intensive benchmark

Over 25 implementations of different functional languages are benchmarked using the same program, a floating-point intensive application taken from molecular biology. The principal aspects studied are compile time and execution time for the various implementations that were benchmarked. An important consideration is how the program can be modified and tuned to obtain maximal performance on each language implementation. With few exceptions, the compilers take a significant amount of time to compile this program, though most compilers were faster than the then current GNU C compiler (GCC version 2.5.8). Compilers that generate C or Lisp are often slower than those that generate native code directly: the cost of compiling the intermediate form is normally a large fraction of the total compilation time. There is no clear distinction between the runtime performance of eager and lazy implementations when appropriate annotations are used: lazy implementations have clearly come of age when it comes to implementing largely strict applications, such as the Pseudoknot program. The speed of C can be approached by some implementations, but to achieve this performance, special measures such as strictness annotations are required by non-strict implementations. The benchmark results have to be interpreted with care. Firstly, a benchmark based on a single program cannot cover a wide spectrum of ‘typical' applications. Secondly, the compilers vary in the kind and level of optimisations offered, so the effort required to obtain an optimal version of the program is similarly varie