Structured Dispersion Matrices From Division Algebra Codes for Space-Time Shift Keying

We propose a novel method of constructing Dispersion Matrices (DM) for Coherent Space-Time Shift Keying (CSTSK) relying on arbitrary PSK signal sets by exploiting codes from division algebras. We show that classic codes from Cyclic Division Algebras (CDA) may be interpreted as DMs conceived for PSK signal sets. Hence various benefits of CDA codes such as their ability to achieve full diversity are inherited by CSTSK. We demonstrate that the proposed CDA based DMs are capable of achieving a lower symbol error ratio than the existing DMs generated using the capacity as their optimization objective function for both perfect and imperfect channel estimation.

Burst error correction using partial fourier matrices and block sparse representation

There is a strong relation between sparse signal recovery and error control coding. It is known that burst errors are block sparse in nature. So, here we attempt to solve burst error correction problem using block sparse signal recovery methods. We construct partial Fourier based encoding and decoding matrices using results on difference sets. These constructions offer guaranteed and efficient error correction when used in conjunction with reconstruction algorithms which exploit block sparsity.

Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices

Given a metric space with a Borel probability measure, for each integer N, we obtain a probability distribution on N x N distance matrices by considering the distances between pairs of points in a sample consisting of N points chosen independently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.

Long-Term Sustained Release of Salicylic Acid from Cross-Linked Biodegradable Polyester Induces a Reduced Foreign Body Response in Mice

There has been a continuous surge toward developing new biopolymers that exhibit better in vivo biocompatibility properties in terms of demonstrating a reduced foreign body response (FBR). One approach to mitigate the undesired FBR is to develop an implant capable of releasing anti-inflammatory molecules in a sustained manner over a long time period. Implants causing inflammation are also more susceptible to infection. In this article, the in vivo biocompatibility of a novel, biodegradable salicylic acid releasing polyester (SAP) has been investigated by subcutaneous implantation in a mouse model. The tissue response to SAP was compared with that of a widely used biodegradable polymer, poly(lactic acid-co-glycolic acid) (PLGA), as a control over three time points: 2, 4, and 16 weeks postimplantation. A long-term in vitro study illustrates a continuous, linear (zero order) release of salicylic acid with a cumulative mass percent release rate of 7.34 x 10(-4) h(-1) over similar to 1.5-17 months. On the basis of physicochemical analysis, surface erosion for SAP and bulk erosion for PLGA have been confirmed as their dominant degradation modes in vivo. On the basis of the histomorphometrical analysis of inflammatory cell densities and collagen distribution as well as quantification of proinflammatory cytokine levels (TNF-alpha and IL-1 beta), a reduced foreign body response toward SAP with respect to that generated by PLGA has been unambiguously established. The favorable in vivo tissue response to SAP, as manifest from the uniform and well-vascularized encapsulation around the implant, is consistent with the decrease in inflammatory cell density and increase in angiogenesis with time. The above observations, together with the demonstration of long-term and sustained release of salicylic acid, establish the potential use of SAP for applications in improved matrices for tissue engineering and chronic wound healing.

LDPC Code Designs Based on root I Matrices

LDPC codes can be constructed by tiling permutation matrices that belong to the square root of identity type and similar algebraic structures. We investigate into the properties of such codes. We also present code structures that are amenable for efficient encoding.

Similarity of Matrices Over Local Rings of Length Two

Let R be a (commutative) local principal ideal ring of length two, for example, the ring R = Z/p(2)Z with p prime. In this paper, we develop a theory of normal forms for similarity classes in the matrix rings M-n (R) by interpreting them in terms of extensions of R t]-modules. Using this theory, we describe the similarity classes in M-n (R) for n <= 4, along with their centralizers. Among these, we characterize those classes which are similar to their transposes. Non-self-transpose classes are shown to exist for all n > 3. When R has finite residue field of order q, we enumerate the similarity classes and the cardinalities of their centralizers as polynomials in q. Surprisingly, the polynomials representing the number of similarity classes in M-n (R) turn out to have non-negative integer coefficients.

Determinantal point processes in the plane from products of random matrices

We show that the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of k independent n x n matrices with i.i.d. complex Gaussian entries with a few of matrices being inverted. In second example we calculate the same for (compatible) product of rectangular matrices with i.i.d. Gaussian entries and in last example we calculate for product of independent truncated unitary random matrices. We derive exact expressions for limiting expected empirical spectral distributions of above mentioned ensembles.