End-to-End BER Analysis of Space Shift Keying in Decode-and-Forward Cooperative Relaying

Space shift keying (SSK) is a special case of spatial modulation (SM), which is a relatively new modulation technique that is getting recognized to be attractive in multi-antenna communications. Our new contribution in this paper is an analytical derivation of exact closed-form expression for the end-to-end bit error rate (BER) performance of SSK in decode-and-forward (1)1,) cooperative relaying. An incremental relaying (IR) scheme with selection combining (SC) at the destination is considered. In SSK, since the information is carried by the transmit antenna index, traditional selection combining methods based on instantaneous SNRs can not be directly used. To overcome this problem, we propose to do selection between direct and relayed paths based on the Euclidean distance between columns of the channel matrix. With this selection metric, an exact analytical expression for the end-to-end BER is derived in closed-form. Analytical results are shown to match with simulation results.

Full-rate full-diversity finite feedback space-time schemes with minimum feedback and transmission duration

A Finite Feedback Scheme (FFS) for a quasi-static MIMO block fading channel with finite N-ary delay-free noise-free feedback consists of N Space-Time Block Codes (STBCs) at the transmitter, one corresponding to each possible value of feedback, and a function at the receiver that generates N-ary feedback. A number of FFSs are available in the literature that provably attain full-diversity. However, there is no known full-diversity criterion that universally applies to all FFSs. In this paper a universal necessary condition for any FFS to achieve full-diversity is given, and based on this criterion the notion of Feedback-Transmission duration optimal (FT-optimal) FFSs is introduced, which are schemes that use minimum amount of feedback N for the given transmission duration T, and minimum T for the given N to achieve full-diversity. When there is no feedback (N = 1) an FT-optimal scheme consists of a single STBC, and the proposed condition reduces to the well known necessary and sufficient condition for an STBC to achieve full-diversity. Also, a sufficient criterion for full-diversity is given for FFSs in which the component STBC yielding the largest minimum Euclidean distance is chosen, using which full-rate (N-t complex symbols per channel use) full-diversity FT-optimal schemes are constructed for all N-t > 1. These are the first full-rate full-diversity FFSs reported in the literature for T < N-t. Simulation results show that the new schemes have the best error performance among all known FFSs.

Higher spin cosmology

We construct cosmological solutions of higher spin gravity in 2 + 1 dimensional de Sitter space. We show that a consistent thermodynamics can be obtained for their horizons by demanding appropriate holonomy conditions. This is equivalent to demanding the integrability of the Euclidean boundary conformal field theory partition function, and it reduces to Gibbons-Hawking thermodynamics in the spin-2 case. By using the prescription of Maldacena, we relate the thermodynamics of these solutions to those of higher spin black holes in AdS(3).

Generalized scaling of misorientation angle distributions at meso-scale in deformed materials

Scaling behaviour has been observed at mesoscopic level irrespective of crystal structure, type of boundary and operative micro-mechanisms like slip and twinning. The presence of scaling at the meso-scale accompanied with that at the nano-scale clearly demonstrates the intrinsic spanning for different deformation processes and a true universal nature of scaling. The origin of a 1/2 power law in deformation of crystalline materials in terms of misorientation proportional to square root of strain is attributed to importance of interfaces in deformation processes. It is proposed that materials existing in three dimensional Euclidean spaces accommodate plastic deformation by one dimensional dislocations and their interaction with two dimensional interfaces at different length scales. This gives rise to a 1/2 power law scaling in materials. This intrinsic relationship can be incorporated in crystal plasticity models that aim to span different length and time scales to predict the deformation response of crystalline materials accurately.

An iterative framework for sparse signal reconstruction algorithms

It has been shown that iterative re-weighted strategies will often improve the performance of many sparse reconstruction algorithms. However, these strategies are algorithm dependent and cannot be easily extended for an arbitrary sparse reconstruction algorithm. In this paper, we propose a general iterative framework and a novel algorithm which iteratively enhance the performance of any given arbitrary sparse reconstruction algorithm. We theoretically analyze the proposed method using restricted isometry property and derive sufficient conditions for convergence and performance improvement. We also evaluate the performance of the proposed method using numerical experiments with both synthetic and real-world data. (C) 2014 Elsevier B.V. All rights reserved.

The Tetrablock as a Spectral Set

The tetrablock, roughly speaking, is the set of all linear fractional maps that map the open unit disc to itself. A formal definition of this inhomogeneous domain is given below. This paper considers triples of commuting bounded operators (A,B,P) that have the tetrablock as a spectral set. Such a triple is named a tetrablock contraction. The motivation comes from the success of model theory in another inhomogeneous domain, namely, the symmetrized bidisc F. A pair of commuting bounded operators (S,P) with Gamma as a spectral set is called a Gamma-contraction, and always has a dilation. The two domains are related intricately as the Lemma 3.2 below shows. Given a triple (A, B, P) as above, we associate with it a pair (F-1, F-2), called its fundamental operators. We show that (A,B,P) dilates if the fundamental operators F-1 and F-2 satisfy certain commutativity conditions. Moreover, the dilation space is no bigger than the minimal isometric dilation space of the contraction P. Whether these commutativity conditions are necessary, too, is not known. what we have shown is that if there is a tetrablock isometric dilation on the minimal isometric dilation space of P. then those commutativity conditions necessarily get imposed on the fundamental operators. En route, we decipher the structure of a tetrablock unitary (this is the candidate as the dilation triple) and a tertrablock isometry (the restriction of a tetrablock unitary to a joint invariant sub-space). We derive new results about r-contractions and apply them to tetrablock contractions. The methods applied are motivated by 11]. Although the calculations are lengthy and more complicated, they beautifully reveal that the dilation depends on the mutual relationship of the two fundamental operators, so that certain conditions need to be satisfied. The question of whether all tetrablock contractions dilate or not is unresolved.

Forgotten records of Chrysopelea taprobanica Smith, 1943 (Squamata: Colubridae) from India

The colubrid snake Chrysopelea taprobanica Smith, 1943 was described from a holotype from Kanthali (= Kantalai) and paratypes from Kurunegala, both localities in Sri Lanka (formerly Ceylon) (Smith 1943). Since its description, literature pertaining to Sri Lankan snake fauna considered this taxon to be endemic to the island (Taylor 1950, Deraniyagala 1955, de Silva 1980, de Silva 1990, Somaweera 2004, Somaweera 2006, de Silva 2009, Pyron et al. 2013). In addition, earlier efforts on the Indian peninsula (e.g. Das 1994, 1997, Das 2003, Whitaker & Captain 2004, Aengals et al. 2012) and global data compilations (e.g. Wallach et al. 2014, Uetz & Hošek 2015) did not identify any record from mainland India until Guptha et al. (2015) recorded a specimen (voucher BLT 076 housed at Bio-Lab of Seshachalam Hills, Tirupathi, India) in the dry deciduous forest of Chamala, Seshachalam Biosphere Reserve in Andhra Pradesh, India in November 2013. Guptha et al. (2015) further mentioned an individual previously photographed in 2000 at Rishi Valley, Andhra Pradesh, but with no voucher specimen collected. Guptha’s record, assumed to be the first confirmed record of C. taprobanica in India, is noteworthy as it results in a large range extension, from northern Sri Lanka to eastern India with an Euclidean distance of over 400 km, as well as a change of status, i.e., species not endemic to Sri Lanka. However, at least three little-known previous records of this species from India evaded most literature and were overlooked by the researchers including ourselves.

Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

On Locally Gabriel Geometric Graphs

Let be a set of points in the plane. A geometric graph on is said to be locally Gabriel if for every edge in , the Euclidean disk with the segment joining and as diameter does not contain any points of that are neighbors of or in . A locally Gabriel graph(LGG) is a generalization of Gabriel graph and is motivated by applications in wireless networks. Unlike a Gabriel graph, there is no unique LGG on a given point set since no edge in a LGG is necessarily included or excluded. Thus the edge set of the graph can be customized to optimize certain network parameters depending on the application. The unit distance graph(UDG), introduced by Erdos, is also a LGG. In this paper, we show the following combinatorial bounds on edge complexity and independent sets of LGG: (i) For any , there exists LGG with edges. This improves upon the previous best bound of . (ii) For various subclasses of convex point sets, we show tight linear bounds on the maximum edge complexity of LGG. (iii) For any LGG on any point set, there exists an independent set of size .

Fermionic edge states and new physics

We investigate the properties of the Dirac operator on manifolds with boundaries in the presence of the Atiyah-Patodi-Singer boundary condition. An exact counting of the number of edge states for boundaries with isometry of a sphere is given. We show that the problem with the above boundary condition can be mapped to one where the manifold is extended beyond the boundary and the boundary condition is replaced by a delta function potential of suitable strength. We also briefly highlight how the problem of the self-adjointness of the operators in the presence of moving boundaries can be simplified by suitable transformations which render the boundary fixed and modify the Hamiltonian and the boundary condition to reflect the effect of moving boundary.

Anomalous transport at weak coupling

We evaluate the contribution of chiral fermions in d = 2, 4, 6, chiral bosons, a chiral gravitino like theory in d = 2 and chiral gravitinos in d = 6 to all the leading parity odd transport coefficients at one loop. This is done by using finite temperature field theory to evaluate the relevant Kubo formulae. For chiral fermions and chiral bosons the relation between the parity odd transport coefficient and the microscopic anomalies including gravitational anomalies agree with that found by using the general methods of hydrodynamics and the argument involving the consistency of the Euclidean vacuum. For the gravitino like theory in d = 2 and chiral gravitinos in d = 6, we show that relation between the pure gravitational anomaly and parity odd transport breaks down. From the perturbative calculation we clearly identify the terms that contribute to the anomaly polynomial, but not to the transport coefficient for gravitinos. We also develop a simple method for evaluating the angular integrals in the one loop diagrams involved in the Kubo formulae. Finally we show that charge diffusion mode of an ideal 2 dimensional Weyl gas in the presence of a finite chemical potential acquires a speed, which is equal to half the speed of light.

A note on tetrablock contractions

A commuting triple of operators (A, B, P) on a Hilbert space H is called a tetrablock contraction if the closure of the set E = {(a(11),a(22),detA) : A = GRAPHICS] with parallel to A parallel to <1} is a spectral set. In this paper, we construct a functional model and produce a set of complete unitary invariants for a pure tetrablock contraction. In this construction, the fundamental operators, which are the unique solutions of the operator equations A - B* P = DPX1DP and B - A* P = DPX2DP where X-1, X-2 is an element of B(D-P) play a pivotal role. As a result of the functional model, we show that every pure tetrablock isometry (A, B, P) on an abstract Hilbert space H is unitarily equivalent to the tetrablock contraction (MG1*+G2z, MG2*+G1z, M-z) on H-DP*(2). (D), where G(1) and G(2) are the fundamental operators of (A*, B*, P*). We prove a Beurling Lax Halmos type theorem for a triple of operators (MF1*+F2z, MF2*+F1z, M-z), where epsilon is a Hilbert space and F-1, F-2 is an element of B(epsilon). We also deal with a natural example of tetrablock contraction on a functions space to find out its fundamental operators.

Geometria et Geometriae : e mathematica ad philosopiam

Resumen: Luego de exponer las posibilidades filosóficas que las geometrías abren a las orientaciones de nuevos espacios, el artículo considera los procedimientos euclidianos y la conexión con las geometrías no-euclidianas. Hay muchas posiciones acerca de las bases filosóficas de las distintas geometrías. Hay además formulaciones muy importantes, desde la gnoseología a la ontología, respecto de las extensiones métricas de la alta geometría.

Constant mean curvature hypersurfaces with constant δ-invariant

We completely classify constant mean curvature hypersurfaces (CMC) with constant δ-invariant in the unit 4-sphere S4 and in the Euclidean 4-space E4.

Projections in a normed linear space and a generalization of the pseudo-inverse

The concept of a "projection function" in a finite-dimensional real or complex normed linear space H (the function P_M which carries every element into the closest element of a given subspace M) is set forth and examined.

If dim M = dim H - 1, then P_M is linear. If P_N is linear for all k-dimensional subspaces N, where 1 ≤ k < dim M, then P_M is linear.

The projective bound Q, defined to be the supremum of the operator norm of P_M for all subspaces, is in the range 1 ≤ Q < 2, and these limits are the best possible. For norms with Q = 1, P_M is always linear, and a characterization of those norms is given.

If H also has an inner product (defined independently of the norm), so that a dual norm can be defined, then when P_M is linear its adjoint P_M^H is the projection on (kernel P_M)^⊥ by the dual norm. The projective bounds of a norm and its dual are equal.

The notion of a pseudo-inverse F⁺ of a linear transformation F is extended to non-Euclidean norms. The distance from F to the set of linear transformations G of lower rank (in the sense of the operator norm ∥F - G∥) is c/∥F⁺∥, where c = 1 if the range of F fills its space, and 1 ≤ c < Q otherwise. The norms on both domain and range spaces have Q = 1 if and only if (F⁺)⁺ = F for every F. This condition is also sufficient to prove that we have (F⁺)^H = (F^H)⁺, where the latter pseudo-inverse is taken using dual norms.

In all results, the real and complex cases are handled in a completely parallel fashion.