Neural computation of arithmetic functions

A neuron is modeled as a linear threshold gate, and the network architecture considered is the layered feedforward network. It is shown how common arithmetic functions such as multiplication and sorting can be efficiently computed in a shallow neural network. Some known results are improved by showing that the product of two n-bit numbers and sorting of n n-bit numbers can be computed by a polynomial-size neural network using only four and five unit delays, respectively. Moreover, the weights of each threshold element in the neural networks require O(log n)-bit (instead of n -bit) accuracy. These results can be extended to more complicated functions such as multiple products, division, rational functions, and approximation of analytic functions

Fast arithmetic computing with neural networks

The authors introduce a restricted model of a neuron which is more practical as a model of computation then the classical model of a neuron. The authors define a model of neural networks as a feedforward network of such neurons. Whereas any logic circuit of polynomial size (in n) that computes the product of two n-bit numbers requires unbounded delay, such computations can be done in a neural network with constant delay. The authors improve some known results by showing that the product of two n-bit numbers and sorting of n n-bit numbers can both be computed by a polynomial size neural network using only four unit delays, independent of n . Moreover, the weights of each threshold element in the neural networks require only O(log n)-bit (instead of n-bit) accuracy

On the Power of Threshold Circuits with Small Weights

Linear threshold elements (LTEs) are the basic processing elements in artificial neural networks. An LTE computes a function that is a sign of a weighted sum of the input variables. The weights are arbitrary integers; actually they can be very big integers-exponential in the number of input variables. However, in practice, it is very difficult to implement big weights. So the natural question that one can ask is whether there is an efficient way to simulate a network of LTEs with big weights by a network of LTEs with small weights. We prove the following results: 1) every LTE with big weights can be simulated by a depth-3, polynomial size network of LTEs with small weights, 2) every depth-d polynomial size network of LTEs with big weights can be simulated by a depth-(2d+1), polynomial size network of LTEs with small weights. To prove these results, we use tools from harmonic analysis of Boolean functions. Our technique is quite general, it provides insights to some other problems. For example, we were able to improve the best known results on the depth of a network of threshold elements that computes the COMPARISON, ADDITION and PRODUCT of two n-bits numbers, and the MAXIMUM and the SORTING of n n-bit numbers

A Generalization of Self-Improving Algorithms

Ailon et al. [SICOMP'11] proposed self-improving algorithms for sorting and Delaunay triangulation (DT) when the input instances $x_1,\cdots,x_n$ follow some unknown \emph{product distribution}. That is, $x_i$ comes from a fixed unknown distribution $\mathsf{D}_i$, and the $x_i$'s are drawn independently. After spending $O(n^{1+\varepsilon})$ time in a learning phase, the subsequent expected running time is $O((n+ H)/\varepsilon)$, where $H \in \{H_\mathrm{S},H_\mathrm{DT}\}$, and $H_\mathrm{S}$ and $H_\mathrm{DT}$ are the entropies of the distributions of the sorting and DT output, respectively. In this paper, we allow dependence among the $x_i$'s under the \emph{group product distribution}. There is a hidden partition of $[1,n]$ into groups; the $x_i$'s in the $k$-th group are fixed unknown functions of the same hidden variable $u_k$; and the $u_k$'s are drawn from an unknown product distribution. We describe self-improving algorithms for sorting and DT under this model when the functions that map $u_k$ to $x_i$'s are well-behaved. After an $O(\mathrm{poly}(n))$-time training phase, we achieve $O(n + H_\mathrm{S})$ and $O(n\alpha(n) + H_\mathrm{DT})$ expected running times for sorting and DT, respectively, where $\alpha(\cdot)$ is the inverse Ackermann function

Combining a non-immersive virtual reality gaming with motor-assisted elliptical exercise increases engagement and physiologic effort in children

A grant from the One-University Open Access Fund at the University of Kansas was used to defray the author's publication fees in this Open Access journal. The Open Access Fund, administered by librarians from the KU, KU Law, and KUMC libraries, is made possible by contributions from the offices of KU Provost, KU Vice Chancellor for Research & Graduate Studies, and KUMC Vice Chancellor for Research. For more information about the Open Access Fund, please see http://library.kumc.edu/authors-fund.xml.Virtual reality (VR) gaming is promising in sustaining children’s participation during intensive physical rehabilitation. This study investigated how integration of a custom active serious gaming with a robot-motorized elliptical impacted children’s perception of engagement (Intrinsic Motivation Inventory), physiologic effort (i.e., exercise speed, heart rate, lower extremity muscle activation), and joint kinematics while overriding the motor’s assistance. Compared to Non-VR condition, during the VR-enhanced condition participants’ perceived engagement was 23% greater (p = 0.01), self-selected speed was 10% faster (p = 0.02), heart rate was 7% higher (p = 0.08) and muscle demands increased. Sagittal plane kinematics demonstrated only a small change at the knee. This study demonstrated that VR plays an essential role in promoting greater engagement and physiologic effort in children performing a cyclic locomotor rehabilitation task, without causing any adverse events or substantial disruption in lower extremity joint kinematics. The outcomes of this study provide a foundation for understanding the role of future VR-enhanced interventions and research studies that weigh/balance the need to physiologically challenge a child during training with the value of promoting task-related training to help promote recovery of walking

The use of average Pavlov ratio to predict the risk of post operative upper limb palsy after posterior cervical decompression

STUDY DESIGN: A retrospective study was conducted to study the post operative upper limb palsy after laminoplasty for cervical myelopathy. OBJECTIVE: To identify a reliable and simple preoperative radiological parameter in predicting the risk of post operative upper limb palsy. BACKGROUND: Post operative upper limb palsy is one of the causes of patient dissatisfaction after surgery. There had been no simple, standard preoperative radiological parameters reliably predict the occurrence of this problem. MATERIALS AND METHODS: Seventy-four patients received posterior cervical decompression from 1998 to 2008. Medical record and preoperative radiological information were evaluated. Clinical presentations of the palsy were described. The relationship between the occurrence of palsy and different preoperative radiological information is analyzed. RESULTS: Eighteen patients (24.3%) presented with post operative upper limb palsy. Majority of patients presented with dysesthesia (17/18) and with deficit of the C5 segment (17/18). Ten patients presented with pure dysesthesia and 8 patients presented with mixed motor-sensory deficit and dysesthesia. Multilevel involvement was exclusively presented in patients with motor weakness. A longer duration of symptom (16.7 Vs 57.2 days) was noticed in patients in the motor deficit group. Average Pavlov ratio less then 0.65 (P = 0.027, Odds Ratio = 3.68) and compression at the C3/4 in preoperative MRI image (P = 0.025, Odds Ratio = 6) were significant risk factors for development of this problem. CONCLUSION: Post operative upper limb palsy is not uncommon and thorough preoperative explanation is important. There is a spectrum of clinical presentation and patients with multi-level involvement and motor deficit are associated with poorer prognosis. Average Pavlov ratio < 0.65 and compression at C3/4 segment on preoperative MRI image are simple and reliable preoperative predictor for the development of this problem