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The study of single streamflow recession events is receiving increasing attention following the presentation of novel theoretical explanations for the emergence of power law forms of the recession relationship, and drivers of its variability. Individually characterizing streamflow recessions often involves describing the similarities and differences between model parameters fitted to each recession time series. Significant methodological sensitivity has been identified in the fitting and parameterization of models that describe populations of many recessions, but the dependence of estimated model parameters on methodological choices has not been evaluated for event-by-event forms of analysis. Here, we use daily streamflow data from 16 catchments in northern California and southern Oregon to investigate how combinations of commonly used streamflow recession definitions and fitting techniques impact parameter estimates of a widely used power law recession model. Results are relevant to watersheds that are relatively steep, forested, and rain-dominated. The highly seasonal mediterranean climate of northern California and southern Oregon ensures study catchments explore a wide range of recession behaviors and wetness states, ideal for a sensitivity analysis. In such catchments, we show the following: (i) methodological decisions, including ones that have received little attention in the literature, can impact parameter value estimates and model goodness of fit; (ii) the central tendencies of event-scale recession parameter probability distributions are largely robust to methodological choices, in the sense that differing methods rank catchments similarly according to the medians of these distributions; (iii) recession parameter distributions are method-dependent, but roughly catchment-independent, such that changing the choices made about a particular method affects a given parameter in similar ways across most catchments; and (iv) the observed correlative relationship between the power-law recession scale parameter and catchment antecedent wetness varies depending on recession definition and fitting choices. Considering study results, we recommend a combination of four key methodological decisions to maximize the quality of fitted recession curves, and to minimize bias in the related populations of fitted recession parameters.

Many of the applied mathematics courses we teach touch upon a range of rich and important ethical issues -- issues that, for a number of reasons, are rarely openly discussed in class. In this work, we describe a sequence of activities co-designed and co-taught by philosophy and mathematics faculty in the hopes of bridging the divide between the application and implementation of modern cryptography and the ethical dilemmas it creates. Although we have specifically focused on one area of applied mathematics at one particular type of institution, we highlight throughout the work the areas in which our approach can be changed to suit different content areas and student populations.

Seasonally dry ecosystems exhibit periods of high water availability followed by extended intervals during which rainfall is negligible and streamflows decline. Eventually, such declining flows will fall below the minimum values required to support ecosystem functions or services. The time at which dry season flows drop below these minimum values (Q∗), relative to the start of the dry season, is termed the "persistence time" (). The persistence time determines how long seasonal streams can support various human or ecological functions during the dry season. In this study, we extended recent work in the stochastic hydrology of seasonally dry climates to develop an analytical model for the probability distribution function (PDF) of the persistence time. The proposed model accurately captures the mean of the persistence time distribution, but underestimates its variance. We demonstrate that this underestimation arises in part due to correlation between the parameters used to describe the dry season recession, but that this correlation can be removed by rescaling the flow variables. The mean persistence time predictions form one example of the broader class of streamflow statistics known as crossing properties, which could feasibly be combined with simple ecological models to form a basis for rapid risk assessment under different climate or management scenarios.

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.

The falling limb of the hydrograph - the streamflow recession - is frequently well approximated by power law functions, in the form dq/dt = -aqb, so that recessions are often characterized in terms of their power law parameters (a, b). The empirical determination and interpretation of the parameter a is typically biased by the presence of a ubiquitous mathematical artifact resulting from the scale-free properties of the power law function. This reduces the information available from recession parameter analysis and creates several heretofore unaddressed methodological "pitfalls." This letter outlines the artifact, demonstrates its genesis, and presents an empirical rescaling method to remove artifact effects from fitted recession parameters. The rescaling process reveals underlying climatic patterns obscured in the original data and, we suggest, could maximize the information content of fitted power laws.

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.

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 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. 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 [less than or equal to] 2 [??]=, then r = 2[??]. 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 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Index Terms--Generalized complex orthogonal design (GCOD), maximum rate, minimum decoding delay, multiple-input multiple-output (MIMO), space-time block code.

For a positive integer , a radio k-labeling of a graph is a function from its vertex set to the non-negative integers such that for all pairs of distinct vertices and , we have where is the distance between the vertices and in . The minimum span over all radio -labelings of is called the radio k-chromatic number and denoted by . The most extensively studied cases are the classic vertex colorings (), (2,1)-labelings (), radio labelings (, the diameter of ), and radio antipodal labelings (. Determining exact values or tight bounds for is often non-trivial even within simple families of graphs. We provide general lower bounds for for all cycles when and show that these bounds are exact values when . [ABSTRACT FROM AUTHOR]

For an integer $$d \ge 2$$ , an $$L(d$$ ,1) -labeling of a graph $$G$$ is a function $$f$$ from its vertex set to the non-negative integers such that $${\vert }f(x) - f(y){\vert } \ge d$$ if vertices $$x$$ and $$y$$ are adjacent, and $${\vert }f(x) - f(y){\vert } \ge $$ 1 if $$x$$ and $$y$$ are at distance two. The minimum span over all the L( $$d$$ ,1)-labelings of $$G$$ is denoted by $$\lambda _{d}(G)$$ . For a given integer $$k \ge 2$$ , the edge-path-replacement of $$G$$ or $$G(P_{k})$$ is the graph obtained from $$G$$ by replacing each edge with a path $$P_{k}$$ on $$k$$ vertices. We show that the edges of $$G$$ can be colored with $$\lceil \varDelta (G)/2\rceil $$ colors so that each monochromatic subgraph has maximum degree at most 2 and use this fact to establish general upper bounds on $$\lambda _{d}(G(P_{k}))$$ for $$k \ge 4$$ . As a corollary, we settle the following conjecture by Lü (J Comb Optim, ): for any graph $$G$$ with $$\varDelta (G) \ge $$ 2, $$\lambda _{2}(G(P_{4})) \le \varDelta (G)$$ + 2. Moreover, $$\lambda _{2}(G(P_{4})) = \varDelta (G) + 1$$ when $$\varDelta (G)$$ is even and different from 2. We also show that the class of graphs $$G(P_{k})$$ with $$k \ge $$ 4 satisfies a conjecture by Havet and Yu ( Discrete Math 308:498-513) in the related area of ( $$d,1$$ )-total labeling of graphs. [ABSTRACT FROM AUTHOR]

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]