Nonequilibrium arrhythmic states and transitions in a mathematical model for diffuse fibrosis in human cardiac tissue

We present a comprehensive numerical study of spiral-and scroll-wave dynamics in a state-of-the-art mathematical model for human ventricular tissue with fiber rotation, transmural heterogeneity, myocytes, and fibroblasts. Our mathematical model introduces fibroblasts randomly, to mimic diffuse fibrosis, in the ten Tusscher-Noble-Noble-Panfilov (TNNP) model for human ventricular tissue; the passive fibroblasts in our model do not exhibit an action potential in the absence of coupling with myocytes; and we allow for a coupling between nearby myocytes and fibroblasts. Our study of a single myocyte-fibroblast (MF) composite, with a single myocyte coupled to N-f fibroblasts via a gap-junctional conductance G(gap), reveals five qualitatively different responses for this composite. Our investigations of two-dimensional domains with a random distribution of fibroblasts in a myocyte background reveal that, as the percentage P-f of fibroblasts increases, the conduction velocity of a plane wave decreases until there is conduction failure. If we consider spiral-wave dynamics in such a medium we find, in two dimensions, a variety of nonequilibrium states, temporally periodic, quasiperiodic, chaotic, and quiescent, and an intricate sequence of transitions between them; we also study the analogous sequence of transitions for three-dimensional scroll waves in a three-dimensional version of our mathematical model that includes both fiber rotation and transmural heterogeneity. We thus elucidate random-fibrosis-induced nonequilibrium transitions, which lead to conduction block for spiral waves in two dimensions and scroll waves in three dimensions. We explore possible experimental implications of our mathematical and numerical studies for plane-, spiral-, and scroll-wave dynamics in cardiac tissue with fibrosis.

Interplay of software bloat, hardware energy proportionality and system bottlenecks

In large flexible software systems, bloat occurs in many forms, causing excess resource utilization and resource bottlenecks. This results in lost throughput and wasted joules. However, mitigating bloat is not easy; efforts are best applied where savings would be substantial. To aid this we develop an analytical model establishing the relation between bottleneck in resources, bloat, performance and power. Analyses with the model places into perspective results from the first experimental study of the power-performance implications of bloat. In the experiments we find that while bloat reduction can provide as much as 40% energy savings, the degree of impact depends on hardware and software characteristics. We confirm predictions from our model with selected results from our experimental study. Our findings show that a software-only view is inadequate when assessing the effects of bloat. The impact of bloat on physical resource usage and power should be understood for a full systems perspective to properly deploy bloat reduction solutions and reap their power-performance benefits.

Reuse, recycle to de-bloat software

Most Java programmers would agree that Java is a language that promotes a philosophy of “create and go forth”. By design, temporary objects are meant to be created on the heap, possibly used and then abandoned to be collected by the garbage collector. Excessive generation of temporary objects is termed “object churn” and is a form of software bloat that often leads to performance and memory problems. To mitigate this problem, many compiler optimizations aim at identifying objects that may be allocated on the stack. However, most such optimizations miss large opportunities for memory reuse when dealing with objects inside loops or when dealing with container objects. In this paper, we describe a novel algorithm that detects bloat caused by the creation of temporary container and String objects within a loop. Our analysis determines which objects created within a loop can be reused. Then we describe a source-to-source transformation that efficiently reuses such objects. Empirical evaluation indicates that our solution can reduce upto 40% of temporary object allocations in large programs, resulting in a performance improvement that can be as high as a 20% reduction in the run time, specifically when a program has a high churn rate or when the program is memory intensive and needs to run the GC often.

USHA: unified software and hardware architecture for video decoding

Video decoders used in emerging applications need to be flexible to handle a large variety of video formats and deliver scalable performance to handle wide variations in workloads. In this paper we propose a unified software and hardware architecture for video decoding to achieve scalable performance with flexibility. The light weight processor tiles and the reconfigurable hardware tiles in our architecture enable software and hardware implementations to co-exist, while a programmable interconnect enables dynamic interconnection of the tiles. Our process network oriented compilation flow achieves realization agnostic application partitioning and enables seamless migration across uniprocessor, multi-processor, semi hardware and full hardware implementations of a video decoder. An application quality of service aware scheduler monitors and controls the operation of the entire system. We prove the concept through a prototype of the architecture on an off-the-shelf FPGA. The FPGA prototype shows a scaling in performance from QCIF to 1080p resolutions in four discrete steps. We also demonstrate that the reconfiguration time is short enough to allow migration from one configuration to the other without any frame loss.

Optimization of thermoacoustic refrigerator using response surface methodology

Thermoacoustic refrigerator (TAR) converts acoustic waves into heat without any moving parts. The study presented here aims to optimize the parameters like frequency, stack position, stack length, and plate spacing involving in designing TAR using the Response Surface Methodology (RSM). A mathematical model is developed using the RSM based on the results obtained from DeltaEC software. For desired temperature difference of 40 K, optimized parameters suggested by the RSM are the frequency 254 Hz, stack position 0.108 m, stack length 0.08 m, and plate spacing 0.0005 m. The experiments were conducted with optimized parameters and simulations were performed using the Design Environment for Low-amplitude ThermoAcoustic Energy Conversion (DeltaEC) which showed similar results.

Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as E-f, the fibroblast resting-membrane potential, the fibroblast conductance G(f), and the MF gap-junctional coupling G(gap). Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as G(gap), G(f), and E-f, and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity CV decreases as a function of G(gap), for zero-sided and one-sided couplings; however, for two-sided coupling, CV decreases initially and then increases as a function of G(gap), and, eventually, we observe that conduction failure occurs for low values of G(gap). In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling G(gap) or E-f. Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

Formulation of a mathematical approach to regional frequency analysis

Estimation of design quantiles of hydrometeorological variables at critical locations in river basins is necessary for hydrological applications. To arrive at reliable estimates for locations (sites) where no or limited records are available, various regional frequency analysis (RFA) procedures have been developed over the past five decades. The most widely used procedure is based on index-flood approach and L-moments. It assumes that values of scale and shape parameters of frequency distribution are identical across all the sites in a homogeneous region. In real-world scenario, this assumption may not be valid even if a region is statistically homogeneous. To address this issue, a novel mathematical approach is proposed. It involves (i) identification of an appropriate frequency distribution to fit the random variable being analyzed for homogeneous region, (ii) use of a proposed transformation mechanism to map observations of the variable from original space to a dimensionless space where the form of distribution does not change, and variation in values of its parameters is minimal across sites, (iii) construction of a growth curve in the dimensionless space, and (iv) mapping the curve to the original space for the target site by applying inverse transformation to arrive at required quantile(s) for the site. Effectiveness of the proposed approach (PA) in predicting quantiles for ungauged sites is demonstrated through Monte Carlo simulation experiments considering five frequency distributions that are widely used in RFA, and by case study on watersheds in conterminous United States. Results indicate that the PA outperforms methods based on index-flood approach.

Evaluating FuncSION: A software for automated synthesis of design solutions for stimulating ideation during mechanical conceptual design

The goal of the work reported in this paper is to use automated, combinatorial synthesis to generate alternative solutions to be used as stimuli by designers for ideation. FuncSION, a computational synthesis tool that can automatically synthesize solution concepts for mechanical devices by combining building blocks from a library, is used for this purpose. The objectives of FuncSION are to help generate a variety of functional requirements for a given problem and a variety of concepts to fulfill these functions. A distinctive feature of FuncSION is its focus on automated generation of spatial configurations, an aspect rarely addressed by other computational synthesis programs. This paper provides an overview of FuncSION in terms of representation of design problems, representation of building blocks, and rules with which building blocks are combined to generate concepts at three levels of abstraction: topological, spatial, and physical. The paper then provides a detailed account of evaluating FuncSION for its effectiveness in providing stimuli for enhanced ideation.

Discovering Math APIs by Mining Unit Tests

In today's API-rich world, programmer productivity depends heavily on the programmer's ability to discover the required APIs. In this paper, we present a technique and tool, called MATHFINDER, to discover APIs for mathematical computations by mining unit tests of API methods. Given a math expression, MATHFINDER synthesizes pseudo-code to compute the expression by mapping its subexpressions to API method calls. For each subexpression, MATHFINDER searches for a method such that there is a mapping between method inputs and variables of the subexpression. The subexpression, when evaluated on the test inputs of the method under this mapping, should produce results that match the method output on a large number of tests. We implemented MATHFINDER as an Eclipse plugin for discovery of third-party Java APIs and performed a user study to evaluate its effectiveness. In the study, the use of MATHFINDER resulted in a 2x improvement in programmer productivity. In 96% of the subexpressions queried for in the study, MATHFINDER retrieved the desired API methods as the top-most result. The top-most pseudo-code snippet to implement the entire expression was correct in 93% of the cases. Since the number of methods and unit tests to mine could be large in practice, we also implement MATHFINDER in a MapReduce framework and evaluate its scalability and response time.

Mining Unit Tests for Discovery and Migration of Math APIs

Today's programming languages are supported by powerful third-party APIs. For a given application domain, it is common to have many competing APIs that provide similar functionality. Programmer productivity therefore depends heavily on the programmer's ability to discover suitable APIs both during an initial coding phase, as well as during software maintenance. The aim of this work is to support the discovery and migration of math APIs. Math APIs are at the heart of many application domains ranging from machine learning to scientific computations. Our approach, called MATHFINDER, combines executable specifications of mathematical computations with unit tests (operational specifications) of API methods. Given a math expression, MATHFINDER synthesizes pseudo-code comprised of API methods to compute the expression by mining unit tests of the API methods. We present a sequential version of our unit test mining algorithm and also design a more scalable data-parallel version. We perform extensive evaluation of MATHFINDER (1) for API discovery, where math algorithms are to be implemented from scratch and (2) for API migration, where client programs utilizing a math API are to be migrated to another API. We evaluated the precision and recall of MATHFINDER on a diverse collection of math expressions, culled from algorithms used in a wide range of application areas such as control systems and structural dynamics. In a user study to evaluate the productivity gains obtained by using MATHFINDER for API discovery, the programmers who used MATHFINDER finished their programming tasks twice as fast as their counterparts who used the usual techniques like web and code search, IDE code completion, and manual inspection of library documentation. For the problem of API migration, as a case study, we used MATHFINDER to migrate Weka, a popular machine learning library. Overall, our evaluation shows that MATHFINDER is easy to use, provides highly precise results across several math APIs and application domains even with a small number of unit tests per method, and scales to large collections of unit tests.

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNPO4 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity theta and the wavelength lambda of a plane wave; we show that PD leads to a periodic, spatial modulation of theta and a temporally periodic modulation of lambda; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNPO4 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNPO4 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.

Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problem with Equilibrium Constraints

This article considers a semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC) defined as a semi-infinite mathematical programming problem with complementarity constraints. We establish necessary and sufficient optimality conditions for the (SIMPEC). We also formulate Wolfe- and Mond-Weir-type dual models for (SIMPEC) and establish weak, strong and strict converse duality theorems for (SIMPEC) and the corresponding dual problems under invexity assumptions.

How should biologists engage with controversial mathematical theory?

Mathematics is beautiful and precise and often necessary to understand complex biological phenomena. And yet biologists cannot always hope to fully understand the mathematical foundations of the theory they are using or testing. How then should biologists behave when mathematicians themselves are in dispute? Using the on-going controversy over Hamilton's rule as an example, I argue that biologists should be free to treat mathematical theory with a healthy dose of agnosticism. In doing so biologists should equip themselves with a disclaimer that publicly admits that they cannot entirely attest to the veracity of the mathematics underlying the theory they are using or testing. The disclaimer will only help if it is accompanied by three responsibilities - stay bipartisan in a dispute among mathematicians, stay vigilant and help expose dissent among mathematicians, and make the biology larger than the mathematics. I must emphasize that my goal here is not to take sides in the on-going dispute over the mathematical validity of Hamilton's rule, indeed my goal is to argue that we should refrain from taking sides.