Super-Linear Gate and Super-Quadratic Wire Lower Bounds for Depth-Two and Depth-Three Threshold Circuits

In order to formally understand the power of neural computing, we first need to crack the frontier of threshold circuits with two and three layers, a regime that has been surprisingly intractable to analyze. We prove the first super-linear gate lower bounds and the first super-quadratic wire lower bounds for depth-two linear threshold circuits with arbitrary weights, and depth-three majority circuits computing an explicit function. $\bullet$ We prove that for all $\epsilon\gg \sqrt{\log(n)/n}$, the linear-time computable Andreev's function cannot be computed on a $(1/2+\epsilon)$-fraction of $n$-bit inputs by depth-two linear threshold circuits of $o(\epsilon^3 n^{3/2}/\log^3 n)$ gates, nor can it be computed with $o(\epsilon^{3} n^{5/2}/\log^{7/2} n)$ wires. This establishes an average-case ``size hierarchy'' for threshold circuits, as Andreev's function is computable by uniform depth-two circuits of $o(n^3)$ linear threshold gates, and by uniform depth-three circuits of $O(n)$ majority gates. $\bullet$ We present a new function in $P$ based on small-biased sets, which we prove cannot be computed by a majority vote of depth-two linear threshold circuits with $o(n^{3/2}/\log^3 n)$ gates, nor with $o(n^{5/2}/\log^{7/2}n)$ wires. $\bullet$ We give tight average-case (gate and wire) complexity results for computing PARITY with depth-two threshold circuits; the answer turns out to be the same as for depth-two majority circuits. The key is a new random restriction lemma for linear threshold functions. Our main analytical tool is the Littlewood-Offord Lemma from additive combinatorics

The Orthogonal Vectors Conjecture for Branching Programs and Formulas

In the Orthogonal Vectors (OV) problem, we wish to determine if there is an orthogonal pair of vectors among n Boolean vectors in d dimensions. The OV Conjecture (OVC) posits that OV requires n^{2-o(1)} time to solve, for all d=omega(log n). Assuming the OVC, optimal time lower bounds have been proved for many prominent problems in P, such as Edit Distance, Frechet Distance, Longest Common Subsequence, and approximating the diameter of a graph. We prove that OVC is true in several computational models of interest: - For all sufficiently large n and d, OV for n vectors in {0,1}^d has branching program complexity Theta~(n * min(n,2^d)). In particular, the lower and upper bounds match up to polylog factors. - OV has Boolean formula complexity Theta~(n * min(n,2^d)), over all complete bases of O(1) fan-in. - OV requires Theta~(n * min(n,2^d)) wires, in formulas comprised of gates computing arbitrary symmetric functions of unbounded fan-in. Our lower bounds basically match the best known (quadratic) lower bounds for any explicit function in those models. Analogous lower bounds hold for many related problems shown to be hard under OVC, such as Batch Partial Match, Batch Subset Queries, and Batch Hamming Nearest Neighbors, all of which have very succinct reductions to OV. The proofs use a certain kind of input restriction that is different from typical random restrictions where variables are assigned independently. We give a sense in which independent random restrictions cannot be used to show hardness, in that OVC is false in the "average case" even for AC^0 formulas: For all p in (0,1) there is a delta_p > 0 such that for every n and d, OV instances with input bits independently set to 1 with probability p (and 0 otherwise) can be solved with AC^0 formulas of O(n^{2-delta_p}) size, on all but a o_n(1) fraction of instances. Moreover, lim_{p - > 1}delta_p = 1

Literacy skills of Australian Indigenous school children with and without otitis media and hearing loss

This study examined the relationship between reading, spelling, and the presence of otitis media (OM) and co-occurring hearing loss (HL) in metropolitan Indigenous Australian children, and compared their reading and spelling outcomes with those of their non-Indigenous peers. OM and HL may hinder language development and phonological awareness skills, but there is little empirical evidence to link OM/HL and literacy in this population. Eighty-six Indigenous and non-Indigenous children attending pre-primary, year one and year two at primary schools in the Perth metropolitan area participated in the study. The ear health of the participants was screened by Telethon Speech and Hearing Centre EarBus in 2011/2012. Participants’ reading and spelling skills were tested with culturally modifi ed sub-tests of the Queensland University Inventory of Literacy. Of the 46 Indigenous children, 18 presented with at least one episode of OM and one episode of HL. Results indicated that Indigenous participants had significantly poorer non-word and real word reading and spelling skills than their non-Indigenous peers. There was no significant difference between the groups of Indigenous participants with OM and HL and those with normal ear health on either measure. This research provides evidence to suggest that Indigenous children have ongoing literacy development difficulties and discusses the possibility of OM as one of many impacting factors

Marine Gastrobot Final Design Report

The Marine Gastrobot sponsored by Dr. Christopher Kitts of the Cal Poly Center for Applications in Biotechnology was a research and development effort intended to explore the use of microbial fuel cell technology as a power source for underwater robots. Our team Ocean Locomotion succeeded in developing a first iteration of an underwater robotic platform suitable for microbial fuel cell integration. The primary feature of the design is its sinusoidal fin propulsion intended for benthic exploration with limited risk of entanglement. During the course of development, Ocean Locomotion explored the use of low power actuation methods and determined their limited use for underwater locomotion, tested low power boost converter compatibility with microbial fuel cells, and built hardware capable of integration with microbial fuel cells

The occupational role of the lay health trainer in England: a review of practice

Health Trainers constitute an emergent occupational group in the Public Health system in England with the key purpose to reduce health inequalities by helping or ‘nudging’ people in local communities to adopt healthier lifestyles. Whilst primarily supplying health-related information and support regarding smoking cessation, diet, alcohol, physical activity and mental wellbeing issues, the role also requires awareness of, and sensitivity toward the specific needs of local communities. This literature review charts current research on the occupational context of the Health Trainer role since its implementation in the English Public Health system. It provides a critical examination of current literature whilst highlighting the theoretical basis of Health Trainers’ roles, the potential boundary-crossing nature of their work, along with professional development issues

Validation du « Hunt Squash Accuracy Test » pour évaluer la performance des joueurs dans l'exécution de leurs coups

This study examined the validity of the Hunt Squash Accuracy Test (HSAT) for predicting within-game shot performance and tournament rank. Shots from eight male junior squash players performing the HSAT and tournament match-play were analysed. A typical-error analysis from repeated trials showed the HSAT to be very reliable (1.82%). HSAT rank had significant correlations (p < 0.05) to tournament rank (r = 0.98) and tournament shot success (r = 0.95). HSAT score showed significant correlations to the percentage of winning shots during match-play (r = 0.88). HSAT shots with significant correlations to successful match-play shots were backhand-drive (r = 0.92) and backhand-volley (r = 0.97). These results suggest the HSAT is a valid method of assessing the accuracy and performance of junior squash players. It could potentially be used to track shot improvements and predict match-play performance