Running Shoe Pedometer

Running shoe pedometer aims to solve the issue of worn out running shoes. It can be difficult to know just how many miles you have run in your shoes and when a new pair is needed. Running in old shoes and worn out shoes is heavily linked to injury. My proposed project is a device that is powered by the compressive forces on the shoes soles that counts the number of steps the wearer takes using a microcontroller. Then, when the shoe reaches milestone that indicate it has been used 75% 90% and 100% of its expected life, it will output the information to the user. In order to output the wear life of the shoes to the user, a series of color changing chemical reactions will be used. These reactions will most likely be acid/base with some type of indicator or an electrochromic material. These color changes will allow the user to see that their shoes are worn out. The device should be extremely low cost so that it can be built into a running shoe and disposed of when the shoe is worn out

Empirical Constraints on Proton and Electron Heating in the Fast Solar Wind

We analyze measured proton and electron temperatures in the high-speed solar wind in order to calculate the separate rates of heat deposition for protons and electrons. When comparing with other regions of the heliosphere, the fast solar wind has the lowest density and the least frequent Coulomb collisions. This makes the fast wind an optimal testing ground for studies of collisionless kinetic processes associated with the dissipation of plasma turbulence. Data from the Helios and Ulysses plasma instruments were collected to determine mean radial trends in the temperatures and the electron heat conduction flux between 0.29 and 5.4 AU. The derived heating rates apply specifically for these mean plasma properties and not for the full range of measured values around the mean. We found that the protons receive about 60% of the total plasma heating in the inner heliosphere, and that this fraction increases to approximately 80% by the orbit of Jupiter. A major factor affecting the uncertainty in this fraction is the uncertainty in the measured radial gradient of the electron heat conduction flux. The empirically derived partitioning of heat between protons and electrons is in rough agreement with theoretical predictions from a model of linear Vlasov wave damping. For a modeled power spectrum consisting only of Alfvenic fluctuations, the best agreement was found for a distribution of wavenumber vectors that evolves toward isotropy as distance increases.Comment: 11 pages (emulateapj style), 5 figures, ApJ, in pres

Comment on "Performance evaluation of 3 optical particle counters with an efficient multimodal calibration method" (Heim et al.,2008) - Performance of improved counter

This comment adds performance data for a modified version of one of the optical particle counters investigated in Heim et al. (2008), namely the WELAS 2100. The new version was found to have a counting efficiency much closer to unity for larger particle sizes as well as some improvement in the lower 50% detection limit

On Using Toeplitz and Circulant Matrices for Johnson-Lindenstrauss Transforms

The Johnson-Lindenstrauss lemma is one of the corner stone results in dimensionality reduction. It says that given $N$, for any set of $N$ vectors $X \subset \mathbb{R}^n$, there exists a mapping $f : X \to \mathbb{R}^m$ such that $f(X)$ preserves all pairwise distances between vectors in $X$ to within $(1 \pm \varepsilon)$ if $m = O(\varepsilon^{-2} \lg N)$. Much effort has gone into developing fast embedding algorithms, with the Fast Johnson-Lindenstrauss transform of Ailon and Chazelle being one of the most well-known techniques. The current fastest algorithm that yields the optimal $m = O(\varepsilon^{-2}\lg N)$ dimensions has an embedding time of $O(n \lg n + \varepsilon^{-2} \lg^3 N)$. An exciting approach towards improving this, due to Hinrichs and Vyb\'iral, is to use a random $m \times n$ Toeplitz matrix for the embedding. Using Fast Fourier Transform, the embedding of a vector can then be computed in $O(n \lg m)$ time. The big question is of course whether $m = O(\varepsilon^{-2} \lg N)$ dimensions suffice for this technique. If so, this would end a decades long quest to obtain faster and faster Johnson-Lindenstrauss transforms. The current best analysis of the embedding of Hinrichs and Vyb\'iral shows that $m = O(\varepsilon^{-2}\lg^2 N)$ dimensions suffices. The main result of this paper, is a proof that this analysis unfortunately cannot be tightened any further, i.e., there exists a set of $N$ vectors requiring $m = \Omega(\varepsilon^{-2} \lg^2 N)$ for the Toeplitz approach to work

BSmooth: from whole genome bisulfite sequencing reads to differentially methylated regions

DNA methylation is an important epigenetic modification involved in gene regulation, which can now be measured using whole-genome bisulfite sequencing. However, cost, complexity of the data, and lack of comprehensive analytical tools are major challenges that keep this technology from becoming widely applied. Here we present BSmooth, an alignment, quality control and analysis pipeline that provides accurate and precise results even with low coverage data, appropriately handling biological replicates. BSmooth is open source software, and can be downloaded from http://rafalab.jhsph.edu/bsmooth

Lower Bounds for Multiplication via Network Coding

Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, very recently proved by Harvey and van der Hoeven (2019), shows that two n-bit numbers can be multiplied via a boolean circuit of size O(n lg n). In this work, we prove that if a central conjecture in the area of network coding is true, then any constant degree boolean circuit for multiplication must have size Omega(n lg n), thus almost completely settling the complexity of multiplication circuits. We additionally revisit classic conjectures in circuit complexity, due to Valiant, and show that the network coding conjecture also implies one of Valiant\u27s conjectures

The 55 Cancri Planetary System: Fully Self-Consistent N-body Constraints and a Dynamical Analysis

We present an updated study of the planets known to orbit 55 Cancri A using 1,418 high-precision radial velocity observations from four observatories (Lick, Keck, Hobby-Eberly Telescope, Harlan J. Smith Telescope) and transit time/durations for the inner-most planet, 55 Cancri "e" (Winn et al. 2011). We provide the first posterior sample for the masses and orbital parameters based on self-consistent n-body orbital solutions for the 55 Cancri planets, all of which are dynamically stable (for at least $10^8$ years). We apply a GPU version of Radial velocity Using N-body Differential evolution Markov Chain Monte Carlo (RUN DMC; B. Nelson et al. 2014) to perform a Bayesian analysis of the radial velocity and transit observations. Each of the planets in this remarkable system has unique characteristics. Our investigation of high-cadence radial velocities and priors based on space-based photometry yields an updated mass estimate for planet "e" ($8.09\pm0.26$ M$_\oplus$), which affects its density ($5.51\pm^{1.32}_{1.00}$ g cm$^{-3}$) and inferred bulk composition. Dynamical stability dictates that the orbital plane of planet "e" must be aligned to within $60^o$ of the orbital plane of the outer planets (which we assume to be coplanar). The mutual interactions between the planets "b" and "c" may develop an apsidal lock about $180^o$. We find 36-45% of all our model systems librate about the anti-aligned configuration with an amplitude of $51^o\pm^{6^o}_{10^o}$. Other cases showed short-term perturbations in the libration of $\varpi_b-\varpi_c$, circulation, and nodding, but we find the planets are not in a 3:1 mean-motion resonance. A revised orbital period and eccentricity for planet "d" pushes it further toward the closest known Jupiter analog in the exoplanet population.Comment: 12 pages, 5 figures, 4 tables, accepted to MNRAS. Figure 2 (left) is updated from published version. Posterior samples available at http://www.personal.psu.edu/ben125/Downloads.htm