Government Contracts-Judicial Review Under Disputes Clause

In a factual dispute arising under a standard government construction contract, the contractor followed the procedures required by the disputes clause. The contractor, after its claim was denied by the contracting officer, appealed to the Board of Claims and Appeals of the Corps of Engineers. The Board rejected the claim, and the contractor brought suit in the Court of Claims, alleging, in the words of the Wunderlich Act, that the Board\u27s decision was capricious or arbitrary or so grossly erroneous as necessarily to imply bad faith, or was not supported by substantial evidence. Over the Government\u27s objection, a commissioner of the court received evidence de novo and concluded that the contractor was entitled to recover. The court received further evidence on the issue of damages and entered judgment for the contractor. On certiorari, held, reversed, two Justices dissenting. In cases subject to the standard disputes clause, the court may look only to the administrative record in order to determine, with respect to any of the Wunderlich Act\u27s standards of finality except fraud, whether the administrative decision should retain its finality. United States v. Carlo Bianchi & Co., 373 U.S. 709 (1963)

A classification scheme for bin packing theory

Classifications of published research place new results in a historical context and in so doing identify open problems. An example in wide use classifies results in scheduling theory according to a scheme originated by Graham, Lawler, Lenstra and Rinnooy Kan [10]. A similar effort was made by Dyckhoff [6] for cutting and packing problems. Such classification schemes can be combined with comprehensive bibliographies, e.g., the one provided for scheduling theory by Bruckner 1. This paper describes a novel classification scheme for bin packing which is being applied by the authors to an extensive (and growing) bibliography of the theory. Problem classifications are supplemented by compact descriptions of the main results and of the corresponding algorithms. The usefulness of the scheme is extended by an online search engine. With the help of this software, one is easily able to determine whether results already exist for applications that appear to be new, and to assist in locating the cutting edge of the general theory

Portfolio Margining: Strategy vs Risk

This paper presents the results of a novel mathematical and experimental analysis of two approaches to margining customer accounts, strategy-based and risk-based. Building combinatorial models of hedging mechanisms of these approaches, we show that the strategy-based approach is, at this point, the most appropriate one for margining security portfolios in customer margin accounts, while the risk-based approach can work efficiently for margining only index portfolios in customer mar-gin accounts and inventory portfolios of brokers. We also show that the application of the risk-based approach to security portfolios in customer margin accounts is very risky and can result in the pyramid of debt in the bullish market and the pyramid of loss in the bearish market. The results of this paper support the thesis that the use of the risk-based approach to margining customer accounts with positions in stocks and stock options since April 2007 influenced and triggered the U.S. stock market crash in October 2008. We also provide recommendations on ways to set appropriate margin requirements to help avoid such failures in the future

New Algorithms for Position Heaps

We present several results about position heaps, a relatively new alternative to suffix trees and suffix arrays. First, we show that, if we limit the maximum length of patterns to be sought, then we can also limit the height of the heap and reduce the worst-case cost of insertions and deletions. Second, we show how to build a position heap in linear time independent of the size of the alphabet. Third, we show how to augment a position heap such that it supports access to the corresponding suffix array, and vice versa. Fourth, we introduce a variant of a position heap that can be simulated efficiently by a compressed suffix array with a linear number of extra bits

A Stochastic Model of Fragmentation in Dynamic Storage Allocation

We study a model of dynamic storage allocation in which requests for single units of memory arrive in a Poisson stream at rate λ and are accommodated by the first available location found in a linear scan of memory. Immediately after this first-fit assignment, an occupied location commences an exponential delay with rate parameter μ, after which the location again becomes available. The set of occupied locations (identified by their numbers) at time t forms a random subset St of {1,2, . . .}. The extent of the fragmentation in St, i.e. the alternating holes and occupied regions of memory, is measured by (St) - |St |. In equilibrium, the number of occupied locations, |S|, is known to be Poisson distributed with mean ρ = λ/μ. We obtain an explicit formula for the stationary distribution of max (S), the last occupied location, and by independent arguments we show that (E max (S) - E|S|)/E|S| → 0 as the traffic intensity ρ → ∞. Moreover, we verify numerically that for any ρ the expected number of wasted locations in equilibrium is never more than 1/3 the expected number of occupied locations. Our model applies to studies of fragmentation in paged computer systems, and to containerization problems in industrial storage applications. Finally, our model can be regarded as a simple concrete model of interacting particles [Adv. Math., 5 (1970), pp. 246–290]

Differential efficiencies of dip-net sampling versus sampling surface-floating pupal exuviae in a biodiversity survey of Chironomidae

Relative efficiencies of standard dip-net sampling (SDN) versus collections of surface-floating pupal exuviae (SFPE) were determined for detecting Chironomidae at catchment and site scales and at subfamily/tribe-, genus- and species-levels based on simultaneous, equal-effort sampling on a monthly basis for one year during a biodiversity assessment of Bear Run Nature Reserve. Results showed SFPE was more efficient than SDN at catchment scales for detecting both genera and species. At site scales, SDN sampling was more efficient for assessment of a first-order site. No consistent pattern, except for better efficiency of SFPE to detect Orthocladiinae genera, was observed at genus-level for two second-order sites. However, SFPE was consistently more efficient at detecting species of Orthocladiinae, Chironomini and Tanytarsini at the second order sites. SFPE was more efficient at detecting both genera and species at two third-order sites. The differential efficiencies of the two methods are concluded to be related to stream order and size, substrate size, flow and water velocity, depth and habitat heterogeneity, and differential ability to discriminate species among pupal exuviae specimens versus larval specimens. Although both approaches are considered necessary for comprehensive biodiversity assessments of Chironomidae, our results suggest that there is an optimal, but different, allocation of sampling effort for detecting Chironomidae across stream orders and at differing spatial and taxonomic scales. Article submitted 13. August 2014, accepted 31. October 2014, published 22. December 2014

Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing

We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$. We give a positive answer to the long-standing open question whether this problem is strongly $NP$-complete for $m=4$. As a second result, we improve the lower bound of $\frac{12}{11}$ for approximating pseudo-polynomial Strip Packing to $\frac{5}{4}$. Since the best known approximation algorithm for this problem has a ratio of $\frac{4}{3} + \varepsilon$, this result narrows the gap between approximation ratio and inapproximability result by a significant step. Both results are proven by a reduction from the strongly $NP$-complete problem 3-Partition

Entanglement in the One-dimensional Kondo Necklace Model

We discuss the thermal and magnetic entanglement in the one-dimensional Kondo necklace model. Firstly, we show how the entanglement naturally present at zero temperature is distributed among pairs of spins according to the strength of the two couplings of the chain, namely, the Kondo exchange interaction and the hopping energy. The effect of the temperature and the presence of an external magnetic field is then investigated, being discussed the adjustment of these variables in order to control the entanglement available in the system. In particular, it is indicated the existence of a critical magnetic field above which the entanglement undergoes a sharp variation, leading the ground state to a completely unentangled phase.Comment: 8 pages, 13 EPS figures. v2: four references adde

Asymptotic Expansions for the Conditional Sojourn Time Distribution in the M/M/1M/M/1-PS Queue

We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results of Morrison \cite{MO} and Flatto \cite{FL}.Comment: 30 pages, 3 figures and 1 tabl