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With the ease and automation of data collection and plummeting storage costs, organizations are faced with massive amounts of data that present two pressing challenges: technical analysis of the data themselves and communication of the analytics process and its products. Although a plethora of academic and practitioner literature have focused on the former call, the latter challenge has received less attention. Here, we present strategies that we have found effective for bolstering communication skills of both undergraduate students and masters candidates at a business school. These approaches are based on the case studies that provide ample opportunity for oral communication among students with strong backgrounds in mathematics and introductory statistics, and solid training in written communication among student populations with less homogeneous preparation. We provide detailed discussions motivated by concrete examples executed across three courses. [ABSTRACT FROM PUBLISHER]

A broad class of soil fungi form the annular patterns known as ‘fairy rings’ and provide one of the only means to observe spatio-temporal dynamics of otherwise cryptic fungal growth processes in natural environments. We present observations of novel spiral and rotor patterns produced by fairy ring fungi and explain these behaviors mathematically by first showing that a well known model of fairy ring fungal growth and the Gray-Scott reaction-diffusion model are mathematically equivalent. We then use bifurcation analysis and numerical simulations to identify the conditions under which spiral waves and rotors can arise. We demonstrate that the region of dimensionless parameter space supporting these more complex dynamics is adjacent to that which produces the more familiar fairy rings, and identify experimental manipulations to test the transitions between these spatial modes. These same manipulations could also feasibly induce fungal colonies to transition from rotor/spiral formation to a set of richer, as yet unobserved, spatial patterns. [ABSTRACT FROM AUTHOR]

Given a positive integer d, an L(d, 1)-labeling of a graph G is an assignment of nonnegative integers to its vertices such that adjacent vertices must receive integers at least d apart, and vertices at distance two must receive integers at least one apart. The λd-number of G is the minimum k so that G has an L(d, 1)-labeling using labels in {0, 1, ..., k}. Informally, an amalgamation of two disjoint graphs G1 and G2 along a fixed graph G0 is the simple graph obtained by identifying the vertices of two induced subgraphs isomorphic to G0, one in G1 and the other in G2. A flower is an amalgamation of two or more cycles along a single vertex. We provide the exact λ2-number of a generalized flower which is the Cartesian product of a path Pn and a flower, or equivalently, an amalgamation of cylindrical rectangular grids along a certain Pn. In the process, we provide general upper bounds for the λd-number of the Cartesian product of P n and any graph G, using circular L(d+1, 1)-labelings of G where the labels {0, 1, ..., k} are arranged sequentially in a circle and the distance between two labels is the shortest distance on the circle. [ABSTRACT FROM AUTHOR]

The spectrum allocation problem in wireless communications can be modeled through vertex labelings of a graph, wherein each vertex represents a transmitter and edges connect vertices whose corresponding transmitters are operating in close proximity. One well-known model is the L ( 2 , 1 ) -labeling of a graph G in which a function f maps the vertices of G to the nonnegative integers such that if vertices x and y are adjacent, then | f ( x ) − f ( y ) | ≥ 2 , and if x and y are at distance two, then | f ( x ) − f ( y ) | ≥ 1 . The λ -number of G is the minimum span over all L ( 2 , 1 ) -labelings of G . Informally, an amalgamation of two graphs G 1 and G 2 along a fixed graph G 0 is the simple graph obtained by identifying the vertices of two induced subgraphs isomorphic to G 0 , one in G 1 and the other in G 2 . In this work, we supply a tight upper bound for the λ -number of amalgamations of several Cartesian products of complete graphs along a complete graph and find the exact λ -numbers for certain infinite subclasses of amalgamations of this form. A surprising relationship between the former upper bound and the minimum makespan scheduling problem is highlighted. [ABSTRACT FROM AUTHOR]

Key distributions based on cover-free families have been recently proposed for secure rekeying in group communication systems after multiple simultaneous user ejections. Existing literature has not quantified how difficult this rekeying operation might be. This study provides upper bounds on the number messages necessary to rekey a key distribution based on symmetric combinatorial designs after one or two simultaneous user ejections. Connections are made to results from finite geometry to show that these bounds are tight for certain key distributions. It is shown that in general determining the minimal number of messages necessary to rekey a group communication system based on a cover-free family is NP-hard. [ABSTRACT FROM PUBLISHER]

Complex orthogonal designs (CODs) have been successfully implemented in wireless systems as complex orthogonal space-time block codes (COSTBCs). Certain properties of the underlying CODs affect the performance of the codes. In addition to the main properties of a COD's rate and decoding delay, a third consideration is whether the COD can achieve transceiver signal linearization, a property that facilitates practical implementation by, for example, significantly simplifying the receiver structure for iterative decoding. It has been shown that a COD can achieve this transceiver signal linearization if the nonzero entries in any given row of the matrix are either all conjugated or all nonconjugated. This paper determines the conditions under which maximum rate CODs can achieve this desirable property. For an odd number of transmit antennas, it is shown that maximum rate CODs that achieve the lower bound on decoding delay can also achieve transceiver signal linearization. In contrast, for an even number of transmit antennas, maximum rate CODs that achieve the lower bound on delay cannot achieve this linearization. In this latter case, linearization is possible only if the COD achieves at least twice the lower bound on delay. This work highlights the tradeoffs among these three important properties. [ABSTRACT FROM AUTHOR]

Complex orthogonal space-time block codes (COSTBCs) based on generalized complex orthogonal designs (CODs) have been successfully implemented in wireless systems with multiple transmit antennas and single or multiple receive antennas. It has been shown that for a maximum rate COD with 2m - 1 or 2m columns, a lower bound on decoding delay is (2m m-i) and this delay is achievable when the number of columns is congruent to 0, 1, or 3 modulo 4. In this paper, the final case is addressed, and it is shown that when the number of columns is congruent to 2 modulo 4, the lower bound on decoding delay cannot be achieved. In this case, the shortest decoding delay a maximum rate COD can achieve is twice the lower bound. New. techniques for analyzing CODs are introduced with connections to binary vector spaces. [ABSTRACT FROM AUTHOR]

The growing demand for efficient wireless transmissions over fading channels motivated the development of space-time block codes. Space-time block codes built from generalized complex orthogonal designs are particularly attractive because the orthogonality permits a simple decoupled maximum-likelihood decoding algorithm while achieving full transmit diversity. The two main research problems for these complex orthogonal space-time block codes (COSTBCs) have been to determine for any number of antennas the maximum rate and the minimum decoding delay for a maximum rate code. The maximum rate for COSTBCs was determined by Liang in 2003. This paper addresses the second fundamental problem by providing a tight lower bound on the decoding delay for maximum rate codes. It is shown that for a maximum rate COSTBC for 2m - 1 or 2m antennas, a tight lower bound on decoding delay is r = (m -1 2m). This lower bound on decoding delay is achievable when the number of antennas is congruent to 0, 1, or 3 modulo 4. This paper also derives a tight lower bound on the number of variables required to construct a maximum rate COSTBC for any given number of antennas. Furthermore, it is shown that if a maximum rate COSTBC has a decoding delay of r where r < r < 2r, then r = 2r. This is used to provide evidence that when the number of antennas is congruent to 2 modulo 4, the best achievable decoding delay is 2 (m-1, 2m). [ABSTRACT FROM AUTHOR]

Abstract: The problem of assigning frequencies to transmitters in a radio network can be modeled through vertex labelings of a graph, wherein each vertex represents a transmitter and edges connect vertices whose corresponding transmitters are operating in close proximity. In one such model, an -labeling of a graph G is employed, which is an assignment fof nonnegative integers to the vertices of G such that if vertices x and y are adjacent, , and if x and y are at distance two, . The -number of G is the minimum span over all -labelings of G. Informally, an amalgamation of two graphs and along a fixed graph is the simple graph obtained by identifying the vertices of two induced subgraphs isomorphic to , one of and the other of . We provide upper bounds for the -number of the amalgamation of graphs along a given graph by determining the exact -number of amalgamations of complete graphs along a complete graph. We also provide the exact -numbers of amalgamations of rectangular grids along a path, or more specifically, of the Cartesian products of a path and a star with spokes of arbitrary lengths. [Copyright &y& Elsevier]

Complex orthogonal designs (CODs) of rate 1/2 have been considered recently for use in analog transmissions and as an alternative to maximum rate CODs due to the savings in decoding delay as the number of antennas increases. While algorithms have been developed to show that an upper bound on the minimum decoding delay for rate 1/2 CODs with n=2m-1 or n=2m columns is \nu(n) = 2^m-1 or \nu(n) = 2^m, depending on the parity of n modulo 8, it remains open to determine the exact minimum delay. This paper shows that this bound \nu(n) is also a lower bound on minimum decoding delay for a major class of rate 1/2 CODs, named balanced complex orthogonal designs (BCODs), and that this is the exact minimum decoding delay for most BCODs. These rate 1/2 codes are conjugation-separated and thus permit a linearized description of the transceiver signal. BCODs also display other combinatorial properties that are expected to be useful in implementation, such as having no linear processing. An elegant construction is provided for a class of rate 1/2 CODs that have no zero entries, effectively no irrational coefficients, no linear processing, and have each variable appearing exactly twice per column. The resulting codes meet the aforementioned bound on decoding delay in most cases. This class of CODs will be useful in practice due to their low peak-to-average power ratio (PAPR) and other desirable properties. [ABSTRACT FROM AUTHOR]

Abstract: The success of applying generalized complex orthogonal designs as space–time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space–time-polarization block codes. This paper offers techniques for constructing quaternion orthogonal designs via combinations of specially chosen complex orthogonal designs. One technique is used to build quaternion orthogonal designs on complex variables for any even number of columns. A second related technique is applied to maximum rate complex orthogonal designs to generate an infinite family of quaternion orthogonal designs on complex variables such that the resulting designs have no zero entries. This second technique is also used to generate an infinite family of quaternion orthogonal designs defined over quaternion variables that display a regular redundancy. The proposed constructions are theoretically important because they provide the first known direct techniques for building infinite families of orthogonal designs over quaternion variables for any number of columns. [Copyright &y& Elsevier]