A Dollar for Your Thoughts: Determining Whether Nominal Damages Prevent an Otherwise Moot Case from Being an Advisory Opinion

This Note examines whether nominal damages should sustain an otherwise moot constitutional claim. A majority of circuit courts have held that a lone claim for nominal damages is sufficient. A minority of circuit courts have determined that nominal damages are insufficient because there is no practical effect in determining such a case. The courts in the minority analogize nominal damages to declaratory judgments and justify their rulings on the basis of judicial economy. This Note proposes that the minority rule is impermissible under current precedent from the U.S. Supreme Court. However, this Note also proposes that the majority rule be adjusted slightly to address the concerns and criticisms of the minority rule. This Note argues that courts should scrutinize the lone claim for nominal damages and require that plaintiffs allege a specific incident of constitutional deprivation to ensure that there is an ongoing case and controversy. Finally, this Note suggests that the Supreme Court provide more guidance to federal courts on the doctrine of mootness

Combinatorial batch codes

In this paper, we study batch codes, which were introduced by Ishai, Kushilevitz, Ostrovsky and Sahai in [4]. A batch code specifies a method to distribute a database of [n] items among [m] devices (servers) in such a way that any [k] items can be retrieved by reading at most [t] items from each of the servers. It is of interest to devise batch codes that minimize the total storage, denoted by [N] , over all [m] servers. We restrict out attention to batch codes in which every server stores a subset of the items. This is purely a combinatorial problem, so we call this kind of batch code a ''combinatorial batch code''. We only study the special case [t=1] , where, for various parameter situations, we are able to present batch codes that are optimal with respect to the storage requirement, [N] . We also study uniform codes, where every item is stored in precisely [c] of the [m] servers (such a code is said to have rate [1/c] ). Interesting new results are presented in the cases [c = 2, k-2] and [k-1] . In addition, we obtain improved existence results for arbitrary fixed [c] using the probabilistic method

Surface reactivity of amphibole asbestos. A comparison between crocidolite and tremolite

Among asbestos minerals, fibrous riebeckite (crocidolite) and tremolite share the amphibole structure but largely differ in terms of their iron content and oxidation state. In asbestos toxicology, iron-generated free radicals are largely held as one of the causes of asbestos malignant effect. With the aim of clarifying i) the relationship between Fe occurrence and asbestos surface reactivity, and ii) how free-radical generation is modulated by surface modifications of the minerals, UICC crocidolite and fibrous tremolite from Maryland were leached from 1 day to 1 month in an oxidative medium buffered at pH 7.4 to induce redox alterations and surface rearrangements that may occur in body fluids. Structural and chemical modifications and free radical generation were monitored by HR-TEM/EDS and spin trapping/EPR spectroscopy, respectively. Free radical yield resulted to be dependent on few specific Fe2+ and Fe3+ surface sites rather than total Fe content. The evolution of reactivity with time highlighted that low-coordinated Fe ions primarily contribute to the overall reactivity of the fibre. Current findings contribute to explain the causes of the severe asbestosinduced oxidative stress at molecular level also for iron-poor amphiboles, and demonstrate that asbestos have a sustained surface radical activity even when highly altered by oxidative leaching

Distinct difference configurations: multihop paths and key predistribution in sensor networks

A distinct difference configuration is a set of points in Z2 with the property that the vectors (difference vectors) connecting any two of the points are all distinct. Many specific examples of these configurations have been previously studied: the class of distinct difference configurations includes both Costas arrays and sonar sequences, for example. Motivated by an application of these structures in key predistribution for wireless sensor networks, we define the k-hop coverage of a distinct difference configuration to be the number of distinct vectors that can be expressed as the sum of k or fewer difference vectors. This is an important parameter when distinct difference configurations are used in the wireless sensor application, as this parameter describes the density of nodes that can be reached by a short secure path in the network. We provide upper and lower bounds for the k-hop coverage of a distinct difference configuration with m points, and exploit a connection with Bh sequences to construct configurations with maximal k-hop coverage. We also construct distinct difference configurations that enable all small vectors to be expressed as the sum of two of the difference vectors of the configuration, an important task for local secure connectivity in the application

Two-dimensional patterns with distinct differences; constructions, bounds, and maximal anticodes

A two-dimensional (2-D) grid with dots is called a configuration with distinct differences if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many applications such as radar, sonar, physical alignment, and time-position synchronization. Rather than restricting dots to lie in a square or rectangle, as previously studied, we restrict the maximum distance between dots of the configuration; the motivation for this is a new application of such configurations to key distribution in wireless sensor networks. We consider configurations in the hexagonal grid as well as in the traditional square grid, with distances measured both in the Euclidean metric, and in the Manhattan or hexagonal metrics. We note that these configurations are confined inside maximal anticodes in the corresponding grid. We classify maximal anticodes for each diameter in each grid. We present upper bounds on the number of dots in a pattern with distinct differences contained in these maximal anticodes. Our bounds settle (in the negative) a question of Golomb and Taylor on the existence of honeycomb arrays of arbitrarily large size. We present constructions and lower bounds on the number of dots in configurations with distinct differences contained in various 2-D shapes (such as anticodes) by considering periodic configurations with distinct differences in the square grid

Optimal constructions for ID-based one-way-function key predistribution schemes realizing specified communication graphs

We study a method for key predistribution in a network of n users where pairwise keys are computed by hashing users’ IDs along with secret information that has been (pre)distributed to the network users by a trusted entity. A communication graph G can be specified to indicate which pairs of users should be able to compute keys. We determine necessary and sufficient conditions for schemes of this type to be secure. We also consider the problem of minimizing the storage requirements of such a scheme; we are interested in the total storage as well as the maximum storage required by any user. Minimizing the total storage is NP-hard, whereas minimizing the maximum storage required by a user can be computed in polynomial time