Constraining the Number of Positive Responses in Adaptive, Non-Adaptive, and Two-Stage Group Testing

Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find all defectives by using as few tests as possible. We consider a variant of classical group testing in which one is concerned not only with minimizing the total number of tests but aims also at reducing the number of tests involving defective elements. The rationale behind this search model is that in many practical applications the devices used for the tests are subject to deterioration due to exposure to or interaction with the defective elements. In this paper we consider adaptive, non-adaptive and two-stage group testing. For all three considered scenarios, we derive upper and lower bounds on the number of "yes" responses that must be admitted by any strategy performing at most a certain number t of tests. In particular, for the adaptive case we provide an algorithm that uses a number of "yes" responses that exceeds the given lower bound by a small constant. Interestingly, this bound can be asymptotically attained also by our two-stage algorithm, which is a phenomenon analogous to the one occurring in classical group testing. For the non-adaptive scenario we give almost matching upper and lower bounds on the number of "yes" responses. In particular, we give two constructions both achieving the same asymptotic bound. An interesting feature of one of these constructions is that it is an explicit construction. The bounds for the non-adaptive and the two-stage cases follow from the bounds on the optimal sizes of new variants of d-cover free families and (p,d)-cover free families introduced in this paper, which we believe may be of interest also in other contexts

The multimarket contacts theory; an application to Italian banks

The multimarket contact hypothesis holds that more contacts between firms competing in the same markets may induce more collusion. This paper tests the hypothesis for the Italian banking market, analysing the behaviour of the largest Italian banks from 1990 to 1996. Market rivalry is gauged by changes in loan market shares and interest rates in each Italian province. Different measures of multimarket contacts are built. We estimate the effects of increasing multimarket contacts, concentration indicators, banksÂ’ costs and loan growth on variations in market shares and interest rates. No support is found for the multimarket contact hypothesis. Geographical overlap in banking is positively correlated with changes in market shares, confirming the thesis of an overall increase in competition within the Italian banking system. Greater multimarket links also seem to correspond to lower lending rates.banks, antitrust policy, multimarket contacts, panel data

Comparison of silver nanoparticles confined in nanoporous silica prepared by chemical synthesis and by ultra-short pulsed laser ablation in liquid

Hexagonally ordered mesoporous silica materials MCM-41 and SBA-15 have been synthesized and loaded with Ag nanoparticles, utilizing both chemical synthesis and ultra-short pulsed laser ablation in liquid. In laser ablation, a silver target, immersed in aqueous suspension of ordered mesoporous silica SBA-15, was irradiated by ultra-short laser pulses to generate silver nanoparticles. For comparison samples of similar silver contents were prepared either by incorporating silver into the SBA-15 during a hydrothermal synthesis or by introducing silver in MCM-41 by template ion-exchange. Samples were characterized by XRD, N2 physisorption, TEM and UV-vis spectroscopy. All preparations contained significant amount of 5-50 nm size silver agglomerates on the outer surface of the silica particles. The laser ablation process did not cause significant destruction of the SBA-15 structure and metallic silver (Ag0) nanoparticles were mainly generated. It is demonstrated that by laser ablation in aqueous silica suspension smaller and more uniform metallic silver particles can be produced and loaded on the surface of the silica support than by synthesis procedures. Catalytic properties of the samples have been tested in the total oxidation of toluene. Because of its favorable Ag dispersity the Ag/SBA-15 catalyst, generated by the laser ablation method, had better catalytic stability and, relative to its Ag load, higher activity than the conventional Ag/SBA-15 preparations

Generalized Selectors and Locally Thin Families with Applications to Conflict Resolution in Multiple Access Channels Supporting Simultaneous Successful Transmissions

We consider the Conflict Resolution Problem in the context of a multiple-access system in which several stations can transmit their messages simultaneously to the channel. We assume that there are n stations and that at most k, k ≤ n, stations are active at the same time, i.e, are willing to transmit a message over the channel. If in a certain instant at most d, d ≤ k, active stations transmit to the channel then their messages are successfully transmitted, whereas if more than d active stations transmit simultaneously then their messages are lost. In this latter case we say that a conflict occurs. The present paper investigates non-adaptive conflict resolution algorithms working under the assumption that active stations receive a feedback from the channel that informs them on whether their messages have been successfully transmitted. If a station becomes aware that its message has been correctly sent over the channel then it becomes immediately inactive, that is, stops transmitting. The measure to optimize is the number of time slots needed to solve conflicts among all active stations. The fundamental question is how much this measure decreases with the number d of messages that can be simultaneously transmitted with success. In this paper we prove that it is possible to achieve a speedup linear in d by providing a conflict resolution algorithm that uses a 1/d ratio of the number of time slots used by the optimal conflict resolution algorithm for the particular case d = 1 [20]. Moreover, we derive a lower bound on the number of time slots needed to solve conflicts non-adaptively which is within a log(k/d) factor from the upper bound. To the aim of proving these results, we introduce a new combinatorial structure that consists in a generalization of Komlós and Greenberg codes [20]. Constructions of these new codes are obtained via a new kind of selectors [11], whereas the non-existential result is implied by a non-existential result for a new generalization of the locally thin families of [1, 10]. We believe that the combinatorial structures introduced in this paper and the related results may be of independent interest

New selectors and locally thin families with applications to multi-access channels supporting simultaneous transmissions

We consider the Conflict Resolution Problem in the context of a multiple-access system in which several stations can transmit their messages with success simultaneously. We assume that there are n stations and at most k, k≤n, stations are active at the same time, i.e., are willing to transmit a message. If at most d, d≤k, active stations transmit simultaneously then their messages are successfully transmitted, whereas if more than d active stations transmit simultaneously then their messages are lost. The active stations receive a feedback from the channel that informs them on whether their messages have been successfully transmitted. The measure to optimize is the number of time slots needed to solve conflicts among all active stations, i.e., to make all active stations transmit their messages successfully. We prove that this measure decreases with the number d of messages that can be simultaneously transmitted with success by presenting a conflict resolution algorithm that uses a 1/d ratio of the number of time slots used by the optimal conflict resolution algorithm for the particular case d=1 [26]. We give a lower bound which is only a log(k/d) factor away from the number of time slots used by the algorithm. The algorithm is obtained via a new kind of the selectors of [13], whereas the lower bound is implied by a non-existential result for a new generalization of the locally thin families of [1,12]. We present also a randomized algorithm that allows to generate the above combinatorial structures in expected polynomial time when k=O(1)