A Beta-Beta Achievability Bound with Applications

A channel coding achievability bound expressed in terms of the ratio between two Neyman-Pearson $\beta$ functions is proposed. This bound is the dual of a converse bound established earlier by Polyanskiy and Verd\'{u} (2014). The new bound turns out to simplify considerably the analysis in situations where the channel output distribution is not a product distribution, for example due to a cost constraint or a structural constraint (such as orthogonality or constant composition) on the channel inputs. Connections to existing bounds in the literature are discussed. The bound is then used to derive 1) an achievability bound on the channel dispersion of additive non-Gaussian noise channels with random Gaussian codebooks, 2) the channel dispersion of the exponential-noise channel, 3) a second-order expansion for the minimum energy per bit of an AWGN channel, and 4) a lower bound on the maximum coding rate of a multiple-input multiple-output Rayleigh-fading channel with perfect channel state information at the receiver, which is the tightest known achievability result.Comment: extended version of a paper submitted to ISIT 201

Beta-Beta Bounds: Finite-Blocklength Analog of the Golden Formula

It is well known that the mutual information between two random variables can be expressed as the difference of two relative entropies that depend on an auxiliary distribution, a relation sometimes referred to as the golden formula. This paper is concerned with a finite-blocklength extension of this relation. This extension consists of two elements: 1) a finite-blocklength channel-coding converse bound by Polyanskiy and Verd\'{u} (2014), which involves the ratio of two Neyman-Pearson $\beta$ functions (beta-beta converse bound); and 2) a novel beta-beta channel-coding achievability bound, expressed again as the ratio of two Neyman-Pearson $\beta$ functions. To demonstrate the usefulness of this finite-blocklength extension of the golden formula, the beta-beta achievability and converse bounds are used to obtain a finite-blocklength extension of Verd\'{u}'s (2002) wideband-slope approximation. The proof parallels the derivation of the latter, with the beta-beta bounds used in place of the golden formula. The beta-beta (achievability) bound is also shown to be useful in cases where the capacity-achieving output distribution is not a product distribution due to, e.g., a cost constraint or structural constraints on the codebook, such as orthogonality or constant composition. As an example, the bound is used to characterize the channel dispersion of the additive exponential-noise channel and to obtain a finite-blocklength achievability bound (the tightest to date) for multiple-input multiple-output Rayleigh-fading channels with perfect channel state information at the receiver.Comment: to appear in IEEE Transactions on Information Theor

Synthesis and Study of Olefin Metathesis Catalysts Supported by Redox-Switchable Diaminocarbene 3 Ferrocenophanes

A redox-switchable ligand, N,N'-dimethyldiaminocarbene[3]ferrocenophane (5), was synthesized and incorporated into a series of Ir- and Ru-based complexes. Electrochemical and spectroscopic analyses of (5) Ir(CO)(2)Cl (15) revealed that 5 displayed a Tolman electronic parameter value of 2050 cm(-1) in the neutral state and 2061 cm(-1) upon oxidation. Moreover, inspection of X-ray crystallography data recorded for (5) Ir(cis,cis-1,5-cyclooctadiene)Cl (13) revealed that 5 was sterically less bulky (%V-Bur = 28.4) than other known diaminocarbene[3]ferrocenophanes, which facilitated the synthesis of (5)(PPh3)Cl2Ru-(3-phenylindenylid-1-ene) (18). Complex 18 exhibited quasi-reversible electrochemical processes at 0.79 and 0.98 V relative to SCE, which were assigned to the Fe and Ru centers in the complex, respectively, based on UV-vis and electron pair resonance spectroscopic measurements. Adding 2,3-dichloro-5,6-dicyanoquinone over the course of a ring-opening metathesis polymerization of cis, cis-1,5-cyclooctadiene catalyzed by 18 ([monomer](0)/[18](0) = 2500) reduced the corresponding rate constant of the reaction by over an order of magnitude (pre-oxidation: k(obs) = 0.045 s(-1); post-oxidation: k(obs) = 0.0012 s(-1)). Subsequent reduction of the oxidized species using decamethylferrocene restored catalytic activity (post-reduction: k(obs) = up to 0.016 s(-1), depending on when the reductant was added). The difference in the polymerization rates was attributed to the relative donating ability of the redox-active ligand (i.e., strongly donating 5 versus weakly donating 5(+)) which ultimately governed the activity displayed by the corresponding catalyst.U. S. Army Research Office W911NF-09-1-0446Chemistr

GLOBAL ECONOMIC SYSTEM AND ECONOMIC INTEGRATION IN WEST AFRICA: A STUDY OF ECOWAS

The global economic system represents a trend in the contemporary global economic order that is anchored on the liberalization of trade as it affects economic interactions among states across the globe. This paper examines this trend of the contemporary global economic system with a view to ascertain its impact on ECOWAS efforts towards integration in the West African sub-region.  The paper argues that there is a relationship between the contemporary global system and the achievement or otherwise of ECOWAS objectives. This relationship lies in the trend and nature of the neoliberal global economic order that is pro-West, as championed by the United States and her Western Allies through the instrumentality of the Bretton Woods Institutions (International Monetary Fund (IMF) and World Bank), Multinational Corporations, World Trade Organization (WTO) and other similar institutions that have confined the states in the West African sub-region to dependent status, and the effects of this order on ECOWAS drove economic integration. In probing the proposition, the paper relies extensively on the qualitative approach of documentary sources of data generation and contents analysis as an analytical tool, while the integration theory of neo-functionalism serves as the explanatory framework underpinning the logic of the free trade mechanism of liberalization driven economic integration. The paper finds out that the unequal trade relationship and the anarchical nature of the neoliberal free trade order of the contemporary global economic system serve as the lubricants that oil the hub around which other issues of adversity of ECOWAS revolve.  This paper, among others, canvases for global economic democracy as it recommends that there is a dire need to renegotiate for better terms of trade in favor of Africa and equitable representation of Africans in the IMF, World Bank, WTO, and other similar institutions