Comparison of Lagrangian and Multivariate Interpolation

Vol 1, Issue 6, pages 1 - 12 High School Research Journal

  Vinny Pagano

Long Beach Senior High School, New York


This project compared the "efficiency" between Lagrangian Polynomial Interpolation and Multivariate Polynomial Interpolation. The results determined what one should use to attain an equation that most resembles a set of points. Additionally, an autonomous process of interpolation was constructed for both methods using Python. The modules Numpy, Sympy, and Scipy were integrated into some of the mathematical processes that had to be implemented into the code. These included the following: Rectification, the Vandermonde Matrix, intricate integration, substitution of variables for both univariate and bivariate instances, and the determination of the roots of a polynomial. For every equation that received the Lagrangian Interpolation treatment, the same initial equation was used and received the Multivariate Interpolation treatment. The variable "t," which denotes the amount of times the function had to be further partitioned and interpolated, was compared amongst both procedures. There were many interpolated equations that did not equate to the original function. To represent these equations, the y-values of the functions at an arbitrarily high x-value were acquired because continuity and expectedness of each equation at this value can be assumed. Additionally, the percent error of the most accurate y-values for each equation type for both methods and the y-values of every original equation were analyzed through a matched pairs t-test. For the purpose of this investigation, the research question should be constructed as follows: Which Method of Polynomial Interpolation is More Efficient/Accurate: Lagrangian Interpolation or Multivariate Interpolation?

Keywords: Polynomial, Lagrangian, Multivariate

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By | December 6th, 2017|Categories: Featured, Journal Entries, Latest News|

The Influence of Genetic Variance on Attention Deficit Hyper Activity Disorder

Vol 1, Issue 5, pages 1 - 16        High School Research Journal

  Naman Bharara

High School


Genetics databases were reviewed to determine if there is a correlation between specific genes and the severity of attention deficit hyperactivity disorder (ADHD) because the condition affects the emotional, social, and academic performance of 2 to 18 % of children worldwide. Datasets from Gene Expression Omnibus Database were analyzed using Gene Spring software to compare gene variations and expressions between ADHD and non-affected individuals. Results showed an increase in the expression of CXCL8 and DDX6, while there was a decreased expression of RHOT1, RPS24, and TMEM59 in the ADHD patients. The differences in gene expressions of the genes suggests that the disorder may have genetic disorders.

Keywords: ADD, ADHD, CNVS, hyperactivity, disorder, hyperactive, attention deficit

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By | November 10th, 2017|Categories: Featured, Journal Entries, Latest News|

Controlling Coherence in The Product Channel from a Direct, Uni-Molercular Dissociation Reaction

Vol 1, Issue 4, pages 1 - 20        High School Research Journal

  Jason Getzler and Dr. Gail Richmond

Kennedy High School, New York


The critical transition from reactants to products occurs in less than a picosecond (10-12 s). Using an ultrafast femtosecond laser (10-15s), it is possible to further understand particle motion before, during, and after the chemical reaction transition. In this study, triiodide (𝐼3−), a simply-structured ion often used because of its stability and efficiency, was subjected to femtosecond laser pulses (NIR and UV wavelengths) to analyze the molecular photodissociation dynamics on an ultrashort time scale (10-12 seconds or shorter). First, vibrational oscillations from diidoide previously reported were replicated via pump-probe spectroscopy to confirm validity of experimentation model. This was followed by innovative pulse shaping techniques to maximize peak oscillations produced by molecules. Oscillation periods were statistically analyzed to understand the dynamics (the movement and vibrations of molecules) undergone by the 𝐼3−, over increased time delay. It was demonstrated that vibrational oscillations in triiodide solution, when subjected to UV pulse shaping using the MIIPS system, show a ±1.0E2 variance in optimal parameters for maximized oscillatory amplitudes and undergo cooling effects as the reaction ensues. Taken together, these observations shed new light on the application of the theoretical laws of quantum mechanics in describing the experimental dynamics of diiodide and that excited-state diiodide oscillations can be controlled by UV light to potentially undergo wavepacket focusing in the product channel of chemical reactions.

Keywords: Femtosecond chemistry, Pump-probe spectroscopy, pulse shaping, triiodide, diiodide, photodissocation, product channel

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By | October 2nd, 2017|Categories: Featured, Journal Entries, Latest News|

“Acknowledging Creativity
A Project is a Terrible Thing to Waste

Needless to say, there are many talented high school students that participate in scientific endeavors that include intra- and extra-institutional activities, including numerous competitions. They all serve to highlight our students’ momentary achievements, which can become lost with time. With the aim of providing both an immediate and sustainable long term method of validating and documenting these achievements, we, at the Long Island Conservatory (Albertson, NY) have created a scientific journal “High School Research Journal”, which will provide a highly visible method to document a student’s scientific contribution as well as archiving them via the Library of Congress journal registration program. This will provide an instantaneous method of demonstrating a person’s high school academic performance for all to see, including evaluating processes.”