Efficiently Mapping Linear Algebra to High-Performance Code

Aware of the role that linear algebra plays in scientific applications, we investigate if/how matrix expressions can be efficiently evaluated with current high-level languages. On the one hand, the numerical linear algebra community has put a lot of effort in developing and optimizing a relatively small set of “universally” useful operations. These are packaged in libraries such as BLAS and LAPACK, and serve as building blocks for more complex computa- tions. On the other hand, the linear algebra expressions that arise in many domains are significantly more complex than those building blocks. We refer to the problem of expressing a linear algebra expression in terms of a set of available building blocks as the ”Linear Algebra Mapping Problem” (LAMP). In practice, users have two alternatives to solve a given LAMP: 1) either “manually”, by using C/C++ or FORTRAN in combination with explicit calls to BLAS & LAPACK 2) or “automatically” by using one of the high-level languages (or libraries) with an API that directly captures the expressions. In this presentation, we focus only on the latter. Specifically, we consider 6 languages (or libraries): Matlab, Julia, R, NumPy (Python), Eigen (C++), and Armadillo (C++), and carefully assess how effectively they translate linear algebra expressions to code, i.e., how well they solve LAMPs. We investigate a number of aspects that are critical for the efficient solution of a LAMP. These range from the most basic mapping problem “Given the expression A*B, does the language map it to a call to GEMM?”, to the optimal parenthesization, to the exploitation of properties, to the identification & elimination -if advantageous- of common sub-expressions, and more. Ultimately, the purpose of this study is to exhibit the core challenges related to the effective computation of linear algebra expressions, and to help the development of languages and libraries.Texas Advanced Computing Center (TACC

MatchPy: A Pattern Matching Library

Pattern matching is a powerful tool for symbolic computations, based on the well-defined theory of term rewriting systems. Application domains include algebraic expressions, abstract syntax trees, and XML and JSON data. Unfortunately, no lightweight implementation of pattern matching as general and flexible as Mathematica exists for Python Mathics,MacroPy,patterns,PyPatt. Therefore, we created the open source module MatchPy which offers similar pattern matching functionality in Python using a novel algorithm which finds matches for large pattern sets more efficiently by exploiting similarities between patterns.Comment: arXiv admin note: substantial text overlap with arXiv:1710.0007

Neural cell adhesion molecules in rat endocrine tissues and tumor cells: distribution and molecular analysis

The adhesive properties of neural cell adhesion molecules (NCAMs) can be modified by alternative splicing of the primary transcript or posttranslational modifications. In the present study, we describe distinct forms of alternative splicing and posttranslational modification of the extracellular domain of NCAM of various endocrine tissues and derived tumor cells of the rat. Using an antiserum detecting the immunoglobulin-like domains of NCAM as well as a monoclonal antibody recognizing the NCAM-specific polysialic acid (PSA), we observed a similar staining pattern in adrenals, pituitary, and neoplastic endocrine cells. In endocrine tumor cells [pheochromocytoma (PC12), insulinoma (RINA2), and pituitary tumor cells (GH3)], NCAM immunoreactivity was most intense at contact sites between the cells. The immunocytochemical data were substantiated by results of in situ hybridization histochemistry. Specifically, higher levels of NCAM mRNA were detected in the adrenal cortex than in the medulla. In the pituitary, NCAM mRNA was more abundant in the anterior and intermediate lobes than in the neural lobe. The sequence of NCAM mRNAs in endocrine cells was analyzed by polymerase chain reaction and S1 nuclease protection assays. We found that major exons 4-13 of the NCAM mRNA in endocrine tissues and related tumor cell lines were homologous to those in the brain. However, PC12, RINA2, and GH3 tumor cells; normal rat pituitaries; and adrenals contained different amounts of NCAM mRNA with an alternative extra exon, termed VASE (also called pi in mouse) between constitutive exons 7 and 8. In addition, in pituitaries, we detected an alternative exon in splice site a between the constitutive exons 12 and 13, termed a15, with or without an AAG triplett. These sites are thought to be important for the adhesive properties of NCAM. Therefore, these results suggest that modifications of NCAM may be important for adhesive interactions in normal and neoplastic endocrine cells

A TWO-DIMENSIONAL KINEMATIC ANALYSIS OF A "BUNNY HOP" PERFORMED BY A SKILLED MOUNTAIN BIKER

The motions taken by a skilled mountain biker during the temporal stages of a bunny hop over an obstacle were determined in this study. A "bunny hop" is defined as a hop (usually over an obstacle) performed by a cyclist in which there is no ramp or other means of launching the cyclist and bicycle. This study is of value because it provides qualitative and quantitative information about a skill in which there is little or no research available. One male subject (age 21, height 185 cm, weight 75 Kg) performing a bunny hop over an obstacle (height 33 cm) was analyzed. A Panasonic WV-D5 100HS camera was placed in line with the subject's plane of motion and was used strictly for qualitative analysis to assure that the subject went over (not around) the obstacle and did not twist. The quantitative analysis was done using a tape from a Panasonic WV-D5 100HS camera placed perpendicular to the subject's plane of motion (15 meters from the obstacle) and Peak 5 Performance Motion Analysis Software. Both cameras were genlocked and recorded the trial with a shutter speed of 111000 sec., a filming speed of 60 fields (30 frames) per sec. with a SMPTE time code generated on both tapes. The 31 points on the subject and bicycle were digitized for 82 fields of videotape (1.394 sec.) then conditioned using a Butterworth filter with a cutoff frequency set at the optimum Hertz for each point on the subject and bicycle. The time between each field was 0.017 sec. The bunny hop was divided into a prejump, airborne and post-jump phase. The phases lasted 0.547,0.476 and 0.340 sec., respectively. The kinematic variables analyzed were linear velocity and acceleration and joint angular velocity and acceleration. The subject and bicycle traveled at an average horizontal velocity of 4.6032 + 0.1052 meters per sec. All points on the subject above the knee achieved maximum upward vertical velocity immediately prior to the airborne phase with the exception of the wrist (0.017 sec. into the airborne phase). All points on the subject and bicycle achieved maximum downward vertical velocity during the last 0.068 sec. of the airborne phase. Maximum upward vertical acceleration was achieved prior to the final 0.102 sec. of the pre-jump phase for the points at or above the shoulder. Analysis of joint angular velocities showed that just prior to the airborne phase, the elbow and knee achieved maximum extension velocity and the ankle achieved maximum plantar flexion velocity. Around the point of landing, the shoulder achieved maximum extension velocity while the ankle achieved maximum dorsi flexion velocity. The results of this study can be compared to that of King (1991). King compared vertical standing jump height with and without arm swing and concluded that arm swing can contribute up to a 25% gain in jump height. The gain in jump height was caused by the transfer of momentum from the arms to the total body. Similarly, a cyclist performing a bunny hop must have an upward acceleration of a portion of his or her body mass prior to a deceleration, or reversal, of that portion of body mass just before the hop. This study concludes with a description of how to perform a bunny hop based on the qualitative and quantitative findings