FTCS finite difference scheme GPGPU parallel computing for the heat conduction equation = Programación en paralelo GPGPU del método en diferencias finitas FTCS para la ecuación del calor

En el presente artículo se muestran las ventajas de la programación en paralelo resolviendo numéricamente la ecuación del calor en dos dimensiones a través del método de diferencias finitas explícito centrado en el espacio FTCS. De las conclusiones de este trabajo se pone de manifiesto la importancia de la programación en paralelo para tratar problemas grandes, en los que se requiere un elevado número de cálculos, para los cuales la programación secuencial resulta impracticable por el elevado tiempo de ejecución. En la primera sección se describe brevemente los conceptos básicos de programación en paralelo. Seguidamente se resume el método de diferencias finitas explícito centrado en el espacio FTCS aplicado a la ecuación parabólica del calor. Seguidamente se describe el problema de condiciones de contorno y valores iniciales específico al que se va a aplicar el método de diferencias finitas FTCS, proporcionando pseudocódigos de una implementación secuencial y dos implementaciones en paralelo. Finalmente tras la discusión de los resultados se presentan algunas conclusiones. In this paper the advantages of parallel computing are shown by solving the heat conduction equation in two dimensions with the forward in time central in space (FTCS) finite difference method. Two different levels of parallelization are consider and compared with traditional serial procedures. We show in this work the importance of parallel computing when dealing with large problems that are impractical or impossible to solve them with a serial computing procedure. In the first section a summary of parallel computing approach is presented. Subsequently, the forward in time central in space (FTCS) finite difference method for the heat conduction equation is outline, describing how the heat flow equation is derived in two dimensions and the particularities of the finite difference numerical technique considered. Then, a specific initial boundary value problem is solved by the FTCS finite difference method and serial and parallel pseudo codes are provided. Finally after results are discussed some conclusions are presented.

Neurite, a finite difference large scale parallel program for the simulation of the electrical signal propagation in neurites under mechanical loading

With the growing body of research on traumatic brain injury and spinal cord injury, computational neuroscience has recently focused its modeling efforts on neuronal functional deficits following mechanical loading. However, in most of these efforts, cell damage is generally only characterized by purely mechanistic criteria, function of quantities such as stress, strain or their corresponding rates. The modeling of functional deficits in neurites as a consequence of macroscopic mechanical insults has been rarely explored. In particular, a quantitative mechanically based model of electrophysiological impairment in neuronal cells has only very recently been proposed (Jerusalem et al., 2013). In this paper, we present the implementation details of Neurite: the finite difference parallel program used in this reference. Following the application of a macroscopic strain at a given strain rate produced by a mechanical insult, Neurite is able to simulate the resulting neuronal electrical signal propagation, and thus the corresponding functional deficits. The simulation of the coupled mechanical and electrophysiological behaviors requires computational expensive calculations that increase in complexity as the network of the simulated cells grows. The solvers implemented in Neurite-explicit and implicit-were therefore parallelized using graphics processing units in order to reduce the burden of the simulation costs of large scale scenarios. Cable Theory and Hodgkin-Huxley models were implemented to account for the electrophysiological passive and active regions of a neurite, respectively, whereas a coupled mechanical model accounting for the neurite mechanical behavior within its surrounding medium was adopted as a link between lectrophysiology and mechanics (Jerusalem et al., 2013). This paper provides the details of the parallel implementation of Neurite, along with three different application examples: a long myelinated axon, a segmented dendritic tree, and a damaged axon. The capabilities of the program to deal with large scale scenarios, segmented neuronal structures, and functional deficits under mechanical loading are specifically highlighted.

Localization of the N terminus of hepatitis B virus capsid protein by peptide-based difference mapping from cryoelectron microscopy

Recently, cryoelectron microscopy of isolated macromolecular complexes has advanced to resolutions below 10 Å, enabling direct visualization of α-helical secondary structure. To help correlate such density maps with the amino acid sequences of the component proteins, we advocate peptide-based difference mapping, i.e., insertion of peptides, ≈10 residues long, at targeted points in the sequence and visualization of these peptides as bulk labels in cryoelectron microscopy-derived difference maps. As proof of principle, we have appended an extraneous octapeptide at the N terminus of hepatitis B virus capsid protein and determined its location on the capsid surface by difference imaging at 11 Å resolution. Hepatitis B virus capsids are icosahedral particles, ≈300 Å in diameter, made up of T-shaped dimers (subunit Mr, 16–21 kDa, depending on construct). The stems of the Ts protrude outward as spikes, whereas the crosspieces pack to form the contiguous shell. The two N termini per dimer reside on either side of the spike-stem, at the level at which it enters the shell. This location is consistent with formation of the known intramolecular disulfide bond between the cysteines at positions 61 and −7 (in the residual propeptide) in the “e-antigen” form of the capsid protein and has implications for why this clinically important antigen remains unassembled in vivo.

Global air-sea flux of CO2: An estimate based on measurements of sea–air pCO2 difference

Approximately 250,000 measurements made for the pCO2 difference between surface water and the marine atmosphere, ΔpCO2, have been assembled for the global oceans. Observations made in the equatorial Pacific during El Nino events have been excluded from the data set. These observations are mapped on the global 4° × 5° grid for a single virtual calendar year (chosen arbitrarily to be 1990) representing a non-El Nino year. Monthly global distributions of ΔpCO2 have been constructed using an interpolation method based on a lateral advection–diffusion transport equation. The net flux of CO2 across the sea surface has been computed using ΔpCO2 distributions and CO2 gas transfer coefficients across sea surface. The annual net uptake flux of CO2 by the global oceans thus estimated ranges from 0.60 to 1.34 Gt-C⋅yr−1 depending on different formulations used for wind speed dependence on the gas transfer coefficient. These estimates are subject to an error of up to 75% resulting from the numerical interpolation method used to estimate the distribution of ΔpCO2 over the global oceans. Temperate and polar oceans of the both hemispheres are the major sinks for atmospheric CO2, whereas the equatorial oceans are the major sources for CO2. The Atlantic Ocean is the most important CO2 sink, providing about 60% of the global ocean uptake, while the Pacific Ocean is neutral because of its equatorial source flux being balanced by the sink flux of the temperate oceans. The Indian and Southern Oceans take up about 20% each.

A rat genetic map constructed by representational difference analysis markers with suitability for large-scale typing.

Representational difference analysis (RDA) was applied to isolate chromosomal markers in the rat. Four series of RDA [restriction enzymes, BamHI and HindIII; subtraction of ACI/N (ACI) amplicon from BUF/Nac (BUF) amplicon and vice versa] yielded 131 polymorphic markers; 125 of these markers were mapped to all chromosomes except for chromosome X. This was done by using a mapping panel of 105 ACI x BUF F2 rats. To complement the relative paucity of chromosomal markers in the rat, genetically directed RDA, which allows isolation of polymorphic markers in the specific chromosomal region, was performed. By changing the F2 driver-DNA allele frequency around the region, four markers were isolated from the D1Ncc1 locus. Twenty-five of 27 RDA markers were informative regarding the dot blot analysis of amplicons, hybridizing only with tester amplicons. Dot blot analysis at a high density per unit of area made it possible to process a large number of samples. Quantitative trait loci can now be mapped in the rat genome by processing a large number of samples with RDA markers and then by isolating markers close to the loci of interest by genetically directed RDA.

Isolation and characterization of a pseudoautosomal region-specific genetic marker in C57BL/6 mice using genomic representational difference analysis.

Representational difference analysis was used to identify strain-specific differences in the pseudoautosomal region (PAR) of mouse X and Y chromosomes. One second generation (C57BL/6 x Mus spretus) x Mus spretus interspecific backcross male carrying the C57BL/6 (B6) PAR was used for tester DNA. DNA from five backcross males from the same generation that were M. spretus-type for the PAR was pooled for the driver. A cloned probe designated B6-38 was recovered that is B6-specific in Southern analysis. Analysis of genomic DNA from several inbred strains of laboratory mice and diverse Mus species and subspecies identified a characteristic Pst I pattern of fragment sizes that is present only in the C57BL family of strains. Hybridization was observed with sequences in DBA/2J and to a limited extent with Mus musculus (PWK strain) and Mus castaneus DNA. No hybridization was observed in DNA of different Mus species, M. spretus, M. hortulanus, and M. caroli. Genetic analyses of B6-38 was conducted using C57BL congenic males that carry M. spretus alleles for distal X chromosome loci and the PAR and outcrosses of heterozygous congenic females with M. spretus. These analyses demonstrated that the B6-38 sequences were inherited with both the X and Y chromosome. B6-38 sequences were genetically mapped as a locus within the PAR using two interspecific backcrosses. The locus defined by B6-38 is designated DXYRp1. Preliminary analyses of recombination between the distal X chromosome gene amelogenin (Amg) and the PAR loci for either TelXY or sex chromosome association (Sxa) suggest that the locus DXYRp1 maps to the distal portion of the PAR.

Identification by representational difference analysis of a homozygous deletion in pancreatic carcinoma that lies within the BRCA2 region.

Homozygous deletions have been central to the discovery of several tumor-suppressor genes, but their finding has often been either serendipitous or the result of a directed search. A recently described technique [Lisitsyn, N., Lisitsyn, N. & Wigler, M. (1993) Science 259, 946-951] held out the potential to efficiently discover such events in an unbiased manner. Here we present the application of the representational difference analysis (RDA) to the study of cancer. We cloned two DNA fragments that identified a homozygous deletion in a human pancreatic adenocarcinoma, mapping to a 1-centimorgan region at chromosome 13q12.3 flanked by the markers D13S171 and D13S260. Interestingly, this lies within the 6-centimorgan region recently identified as the BRCA2 locus of heritable breast cancer susceptibility. This suggests that the same gene may be involved in multiple tumor types and that its function is that of a tumor suppressor rather than that of a dominant oncogene.

April 4, 1968: Death, Difference, and Dialogue

Robert Kennedy's announcement of the assassination of Martin Luther King, Jr., in an Indianapolis urban community that did not revolt in riots on April 4, 1968, provides one significant example in which feelings, energy, and bodily risk resonate alongside the articulated message. The relentless focus on Kennedy's spoken words, in historical biographies and other critical research, presents a problem of isolated effect because the power really comes from elements outside the speech act. Thus, this project embraces the complexities of rhetorical effectivity, which involves such things as the unique situational context, all participants (both Kennedy and his audience) of the speech act, aesthetic argument, and the ethical implications. This version of the story embraces the many voices of the participants through first hand interviews and new oral history reports. Using evidence provided from actual participants in the 1968 Indianapolis event, this project reflects critically upon the world disclosure of the event as it emerges from those remembrances. Phenomenology provides one answer to the constitutive dilemma of rhetorical effectivity that stems from a lack of a framework that gets at questions of ethics, aesthetics, feelings, energy, etc. Thus, this work takes a pedagogical shift away from discourse (verbal/written) as the primary place to render judgments about the effects of communication interaction. With a turn to explore extra-sensory reasoning, by way of the physical, emotional, and numinous, a multi-dimensional look at public address is delivered. The rhetorician will be interested in new ways of assessing effects. The communication ethicist will appreciate the work as concepts like answerability, emotional-volitional tone, and care for the other, come to life via application and consideration of Kennedy's appearance. For argumentation scholars, the interest comes forth in a re-thinking of how we do argumentation. And the critical cultural scholar will find this story ripe with opportunities to uncover the politics of representation, racialized discourse, privilege, power, ideological hegemony, and reconciliation. Through an approach of multiple layers this real-life tale will expose the power of the presence among audience and speaker, emotive argument, as well as the magical turn of fate which all contributes the possibility of a dialogic rhetoric.

Difference Blindness vs. Bias Awareness: Why Law Firms with the Best of Intentions Have Failed to Create Diverse Partnerships

This Article uses the example of BigLaw firms to explore the challenges that many elite organizations face in providing equal opportunity to their workers. Despite good intentions and the investment of significant resources, large law firms have been consistently unable to deliver diverse partnership structures - especially in more senior positions of power. Building on implicit and institutional bias scholarship and on successful approaches described in the organizational behavior literature, we argue that a significant barrier to systemic diversity at the law firm partnership level has been, paradoxically, the insistence on difference blindness standards that seek to evaluate each person on their individual merit. While powerful in dismantling intentional discrimination, these standards rely on an assumption that lawyers are, and have the power to act as, atomistic individuals - a dangerous assumption that has been disproven consistently by the literature establishing the continuing and powerful influence of implicit and institutional bias. Accordingly, difference blindness, which holds all lawyers accountable to seemingly neutral standards, disproportionately disadvantages diverse populations and normalizes the dominance of certain actors - here, white men - by creating the illusion that success or failure depends upon individual rather than structural constraints. In contrast, we argue that a bias awareness approach that encourages identity awareness and a relational framework is a more promising way to promote equality, equity, and inclusion.

Measuring color differences in automotive samples with lightness flop: a test of the AUDI2000 color-difference formula

From a set of gonioapparent automotive samples from different manufacturers we selected 28 low-chroma color pairs with relatively small color differences predominantly in lightness. These color pairs were visually assessed with a gray scale at six different viewing angles by a panel of 10 observers. Using the Standardized Residual Sum of Squares (STRESS) index, the results of our visual experiment were tested against predictions made by 12 modern color-difference formulas. From a weighted STRESS index accounting for the uncertainty in visual assessments, the best prediction of our whole experiment was achieved using AUDI2000, CAM02-SCD, CAM02-UCS and OSA-GP-Euclidean color-difference formulas, which were no statistically significant different among them. A two-step optimization of the original AUDI2000 color-difference formula resulted in a modified AUDI2000 formula which performed both, significantly better than the original formula and below the experimental inter-observer variability. Nevertheless the proposal of a new revised AUDI2000 color-difference formula requires additional experimental data.

Difference schemes for numerical solutions of lagging models of heat conduction

Non-Fourier models of heat conduction are increasingly being considered in the modeling of microscale heat transfer in engineering and biomedical heat transfer problems. The dual-phase-lagging model, incorporating time lags in the heat flux and the temperature gradient, and some of its particular cases and approximations, result in heat conduction modeling equations in the form of delayed or hyperbolic partial differential equations. In this work, the application of difference schemes for the numerical solution of lagging models of heat conduction is considered. Numerical schemes for some DPL approximations are developed, characterizing their properties of convergence and stability. Examples of numerical computations are included.

Difference schemes for time-dependent heat conduction models with delay

Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.

Influence of the Difference Between Corneal and Refractive Astigmatism on LASIK Outcomes Using Solid-State Technology

Purpose: To evaluate the influence of the difference between preoperative corneal and refractive astigmatism [ocular residual astigmatism (ORA)] on outcomes obtained after laser in situ keratomileusis (LASIK) surgery for correction of myopic astigmatism using the solid-state laser technology. Methods: One hundred one consecutive eyes with myopia or myopic astigmatism of 55 patients undergoing LASIK surgery using the Pulzar Z1 solid-state laser (CustomVis Laser Pty Ltd, currently CV Laser) were included. Visual and refractive changes at 6 months postoperatively and changes in ORA and anterior corneal astigmatism and posterior corneal astigmatism (PCA) were analyzed. Results: Postoperatively, uncorrected distance visual acuity improved significantly (P < 0.01). Likewise, refractive cylinder magnitude and spherical equivalent were reduced significantly (P < 0.01). In contrast, no significant changes were observed in ORA magnitude (P = 0.81) and anterior corneal astigmatism (P = 0.12). The mean overall efficacy and safety indices were 0.96 and 1.01, respectively. These indices were not correlated with preoperative ORA (r = −0.15, P = 0.15). Furthermore, a significant correlation was found between ORA (r = 0.81, P < 0.01) and PCA postoperatively, but not preoperatively (r = 0.12, P = 0.25). Likewise, a significant correlation of ORA with manifest refraction was only found postoperatively (r = −0.38, P < 0.01). Conclusions: The magnitude of ORA does not seem to be a predictive factor of efficacy and safety of myopic LASIK using a solid-state laser platform. The higher relevance of PCA after surgery in some cases may explain the presence of unexpected astigmatic residual refractive errors.

A compact difference scheme for numerical solutions of second order dual-phase-lagging models of microscale heat transfer

Dual-phase-lagging (DPL) models constitute a family of non-Fourier models of heat conduction that allow for the presence of time lags in the heat flux and the temperature gradient. These lags may need to be considered when modeling microscale heat transfer, and thus DPL models have found application in the last years in a wide range of theoretical and technical heat transfer problems. Consequently, analytical solutions and methods for computing numerical approximations have been proposed for particular DPL models in different settings. In this work, a compact difference scheme for second order DPL models is developed, providing higher order precision than a previously proposed method. The scheme is shown to be unconditionally stable and convergent, and its accuracy is illustrated with numerical examples.

Minutes explaining difference between first act. rendered Judge and charges to that date entered on Estate Book, 1820 February

Two pages with calculations and notes relating to the differences between the Estate Book and the account rendered by the Judge of Probate.