Non-abelian Littlewood-Offord inequalities

In 1943, Littlewood and Offord proved the first anti-concentration result for sums of independent random variables. Their result has since then been strengthened and generalized by generations of researchers, with applications in several areas of mathematics. In this paper, we present the first non-abelian analogue of Littlewood-Offord result, a sharp anti-concentration inequality for products of independent random variables.Comment: 14 pages Second version. Dependence of the upper bound on the matrix size in the main results has been remove

Lusztig Induction, Unipotent Supports, and Character Bounds

Recently, a strong exponential character bound has been established in [3] for all elements $g \in \mathbf{G}^F$ of a finite reductive group $\mathbf{G}^F$ which satisfy the condition that the centraliser $C_{\mathbf{G}}(g)$ is contained in a $(\mathbf{G},F)$-split Levi subgroup $\mathbf{M}$ of $\mathbf{G}$ and that $\mathbf{G}$ is defined over a field of good characteristic. In this paper, assuming a weak version of Lusztig's conjecture relating irreducible characters and characteristic functions of character sheaves holds, we considerably generalize this result by removing the condition that $\mathbf{M}$ is split. This assumption is known to hold whenever $Z(\mathbf{G})$ is connected or when $\mathbf{G}$ is a special linear or symplectic group and $\mathbf{G}$ is defined over a sufficiently large finite field.Comment: 35 pages; v2. minor improvements to abstract and introduction; v3. further improvements to the exposition; v4. significant changes. Main result now works for special linear and symplectic groups. Added results on groups of type A generalising results of Hildebrand; v5. post referee repor

International Fisheries Agreements: The Feasibility and Impacts of Partial Cooperation

This paper deals with partial cooperation among countries involved in the exploitation of straddling and highly migratory fish stocks.We analyse the feasibility of coalition structures and their impacts on fishing e.orts by means of games in partition function form.Furthermore, we demonstrate that the modified Shapley value is an appropriate device for the division of the gains from cooperation.international fisheries;overexploitation;partial cooperation;games in partition function form;competitive equilibrium;modified Shapley value.

Preduals of semigroup algebras

For a locally compact group G, the measure convolution algebra M(G) carries a natural coproduct. In previous work, we showed that the canonical predual C 0(G) of M(G) is the unique predual which makes both the product and the coproduct on M(G) weak*-continuous. Given a discrete semigroup S, the convolution algebra ℓ 1(S) also carries a coproduct. In this paper we examine preduals for ℓ 1(S) making both the product and the coproduct weak*-continuous. Under certain conditions on S, we show that ℓ 1(S) has a unique such predual. Such S include the free semigroup on finitely many generators. In general, however, this need not be the case even for quite simple semigroups and we construct uncountably many such preduals on ℓ 1(S) when S is either ℤ+×ℤ or (ℕ,⋅)

Efficient multi-standard cognitive radios on FPGAs

Cognitive radios that support multiple standards and modify operation depending on environmental conditions are becoming more important as the demand for higher bandwidth and efficient spectrum use increases. Traditional implementations in custom ASICs cannot support such flexibility, with standards changing at a faster pace, while software baseband implementations fail to achieve the performance required. Hence, FPGAs offer an ideal platform bringing together flexibility, performance, and efficiency. This work explores the possible techniques for designing multi-standard radios on FPGAs, and explores how partial reconfiguration can be leveraged in a way that is amenable for domain experts with minimal FPGA knowledge

Shaping spectral leakage for IEEE 802.11 p vehicular communications

IEEE 802.11p is a recently defined standard for the physical (PHY) and medium access control (MAC) layers for Dedicated Short-Range Communications. Four Spectrum Emission Masks (SEMs) are specified in 802.11p that are much more stringent than those for current 802.11 systems. In addition, the guard interval in 802.11p has been lengthened by reducing the bandwidth to support vehicular communication (VC) channels, and this results in a narrowing of the frequency guard. This raises a significant challenge for filtering the spectrum of 802.11p signals to meet the specifications of the SEMs. We investigate state of the art pulse shaping and filtering techniques for 802.11p, before proposing a new method of shaping the 802.11p spectral leakage to meet the most stringent, class D, SEM specification. The proposed method, performed at baseband to relax the strict constraints of the radio frequency (RF) front-end, allows 802.11p systems to be implemented using commercial off-the- shelf (COTS) 802.11a RF hardware, resulting in reduced total system cost

Transboundary Fishery Management: A Game Theoretic Approach

A basic issue in transboundary fishery management is the new member problem. In this paper we address the problem of allocating the profits between the charter members and the entrants, once the nations concerned have expressed an interest in achieving an agreement.Using game theory we argue that in the case of independent countries adjustment from the Nash equilibrium can be achieved by means of the proportional rule.Furthermore, we propose the population monotonic allocation scheme as management rule for division of profits within a coalition. Finally, we show that the equal division of the net gain value can be used to expand a coalition.game theory;fishing industry;Nash equilibrium