Development of an Artificial Finger-Like Knee Loading Device to Promote Bone Health

This study presents the development of an innovative artificial finger-like device that provides position specific mechanical loads at the end of the long bone and induces mechanotransduction in bone. Bone cells such as osteoblasts are the mechanosensitive cells that regulate bone remodelling. When they receive gentle, periodic mechanical loads, new bone formation is promoted. The proposed device is an under-actuated multi-fingered artificial hand with 4 fingers, each having two phalanges. These fingers are connected by mechanical linkages and operated by a worm gearing mechanism. With the help of 3D printing technology, a prototype device was built mostly using plastic materials. The experimental validation results show that the device is capable of generating necessary forces at the desired frequencies, which are suitable for the stimulation of bone cells and the promotion of bone formation. It is recommended that the device be tested in a clinical study for confirming its safety and efficacy with patients

Optimal Data Placement on Networks With Constant Number of Clients

We introduce optimal algorithms for the problems of data placement (DP) and page placement (PP) in networks with a constant number of clients each of which has limited storage availability and issues requests for data objects. The objective for both problems is to efficiently utilize each client's storage (deciding where to place replicas of objects) so that the total incurred access and installation cost over all clients is minimized. In the PP problem an extra constraint on the maximum number of clients served by a single client must be satisfied. Our algorithms solve both problems optimally when all objects have uniform lengths. When objects lengths are non-uniform we also find the optimal solution, albeit a small, asymptotically tight violation of each client's storage size by $\epsilon$lmax where lmax is the maximum length of the objects and $\epsilon$ some arbitrarily small positive constant. We make no assumption on the underlying topology of the network (metric, ultrametric etc.), thus obtaining the first non-trivial results for non-metric data placement problems

Constant Approximation for kk-Median and kk-Means with Outliers via Iterative Rounding

In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an $(\alpha_1 + \epsilon \leq 7.081 + \epsilon)$-approximation algorithm for $k$-median with outliers, greatly improving upon the large implicit constant approximation ratio of Chen [Chen, SODA 2018]. For $k$-means with outliers, we give an $(\alpha_2+\epsilon \leq 53.002 + \epsilon)$-approximation, which is the first $O(1)$-approximation for this problem. The iterative algorithm framework is very versatile; we show how it can be used to give $\alpha_1$- and $(\alpha_1 + \epsilon)$-approximation algorithms for matroid and knapsack median problems respectively, improving upon the previous best approximations ratios of $8$ [Swamy, ACM Trans. Algorithms] and $17.46$ [Byrka et al, ESA 2015]. The natural LP relaxation for the $k$-median/$k$-means with outliers problem has an unbounded integrality gap. In spite of this negative result, our iterative rounding framework shows that we can round an LP solution to an almost-integral solution of small cost, in which we have at most two fractionally open facilities. Thus, the LP integrality gap arises due to the gap between almost-integral and fully-integral solutions. Then, using a pre-processing procedure, we show how to convert an almost-integral solution to a fully-integral solution losing only a constant-factor in the approximation ratio. By further using a sparsification technique, the additive factor loss incurred by the conversion can be reduced to any $\epsilon > 0$

A FAST AND SENSITIVE SPECTROPHOTOMETRIC METHOD FOR THE DETERMINATION OF HYDRAZINE IN ATAZANAVIR SULFATE DRUG SUBSTANCE

Objective: To develop a fast and sensitive UV spectrophotometric method for the quantitative estimation of Hydrazine in Atazanavir Sulfate drug substances and validate as per ICH guidelines. Methods: The method was based upon the observation, that a characteristic colour results upon addition of a solution of p-Dimethylaminobenzaldehyde in ethyl alcohol and hydrochloric acid to hydrazine and estimated at absorbance maximum  458 nm in Atazanavir drug substance. Results: The developed method resulted in Hydrazine exhibiting linearity in the range 0.2 to 2.7 µg/g. The Intraday and interday precision is exemplified by relative standard deviation of 0.959 % and 0.947%. Percentage Mean recovery was found to be in the range of 97â€101%, during accuracy studies. The limit of detection (LOD) and limit of quantitiation (LOQ) were found to be 0.2 µg/g and 0.6 µg/g respectively. Conclusion: The present work was aimed to develop a visible spectrophotometric method, which is simple, sensitive, accurate and cost effective to evaluate the quality of the bulk and pharmaceutical formulations

Capacitated Center Problems with Two-Sided Bounds and Outliers

In recent years, the capacitated center problems have attracted a lot of research interest. Given a set of vertices $V$, we want to find a subset of vertices $S$, called centers, such that the maximum cluster radius is minimized. Moreover, each center in $S$ should satisfy some capacity constraint, which could be an upper or lower bound on the number of vertices it can serve. Capacitated $k$-center problems with one-sided bounds (upper or lower) have been well studied in previous work, and a constant factor approximation was obtained. We are the first to study the capacitated center problem with both capacity lower and upper bounds (with or without outliers). We assume each vertex has a uniform lower bound and a non-uniform upper bound. For the case of opening exactly $k$ centers, we note that a generalization of a recent LP approach can achieve constant factor approximation algorithms for our problems. Our main contribution is a simple combinatorial algorithm for the case where there is no cardinality constraint on the number of open centers. Our combinatorial algorithm is simpler and achieves better constant approximation factor compared to the LP approach

Experimental demonstration of near-infrared negative-index metamaterials

Metal-based negative refractive-index materials have been extensively studied in the microwave region. However, negative-index metamaterials have not been realized at near-IR or visible frequencies due to difficulties of fabrication and to the generally poor optical properties of metals at these wavelengths. In this Letter, we report the first fabrication and experimental verification of a transversely structured metal-dielectricmetal multilayer exhibiting a negative refractive index around 2 mu m. Both the amplitude and the phase of the transmission and reflection were measured experimentally, and are in good agreement with a rigorous coupled wave analysis

Bladder Neuromodulation in Acute Spinal Cord Injury via Transcutaneous Tibial Nerve Stimulation: Cystometrogram and Autonomic Nervous System Evidence From a Randomized Control Pilot Trial

Aim: Percutaneous tibial nerve stimulation is used to decrease incontinence in chronic neurogenic bladder. We report the findings from a subset of patients in a randomized control trial of transcutaneous tibial nerve stimulation (TTNS) for bladder neuromodulation in acute spinal cord injury (SCI) in whom heart rate variability (HRV) was recorded before and after cystometrogram (CMG). The aim was to correlate autonomic nervous system (ANS) changes associated with the CMG changes after the trial using HRV analyses.Methods: The study was a double-blinded sham-controlled 2-week trial with consecutive acute SCI patients admitted for inpatient rehabilitation, randomized to TTNS vs. control sham stimulation. Pre- and Post- trial CMG were performed with concurrent 5-min HRV recordings with empty bladder and during filling. Primary outcomes were changes with CMG between/within groups and associations to the HRV findings.Results: There were 10 subjects in the TTNS group and 6 in the control group. Pre-trial baseline subject characteristics, blood pressures (BPs), and CMG were similar between groups. In both groups, the pre-trial systolic BP increased during filling CMG. After the trial, the control group had significantly increased detrusor pressure and counts of detrusor-sphincter dyssynergia on CMG, not seen in the TTNS group. Also, the control group did not maintain rising BP post-trial, which was observed pre-trial and remained in the TTNS group post-trial. HRV was able to detect a difference in the ANS response to bladder filling between groups. Post-trial HRV was significant for markers of overall increased parasympathetic nervous system activity during filling in the controls, not seen in the TTNS group.Conclusion: Preliminary evidence suggests that TTNS in acute SCI is able to achieve bladder neuromodulation via modulation of ANS functions.Clinical Trial Registration:clinicaltrials.gov, NCT02573402

Incremental Medians via Online Bidding

In the k-median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F. The goal is to find a set F of k facilities that minimizes the sum, over all customers, of their service costs. Following Mettu and Plaxton, we study the incremental medians problem, where k is not known in advance, and the algorithm produces a nested sequence of facility sets where the kth set has size k. The algorithm is c-cost-competitive if the cost of each set is at most c times the cost of the optimum set of size k. We give improved incremental algorithms for the metric version: an 8-cost-competitive deterministic algorithm, a 2e ~ 5.44-cost-competitive randomized algorithm, a (24+epsilon)-cost-competitive, poly-time deterministic algorithm, and a (6e+epsilon ~ .31)-cost-competitive, poly-time randomized algorithm. The algorithm is s-size-competitive if the cost of the kth set is at most the minimum cost of any set of size k, and has size at most s k. The optimal size-competitive ratios for this problem are 4 (deterministic) and e (randomized). We present the first poly-time O(log m)-size-approximation algorithm for the offline problem and first poly-time O(log m)-size-competitive algorithm for the incremental problem. Our proofs reduce incremental medians to the following online bidding problem: faced with an unknown threshold T, an algorithm submits "bids" until it submits a bid that is at least the threshold. It pays the sum of all its bids. We prove that folklore algorithms for online bidding are optimally competitive.Comment: conference version appeared in LATIN 2006 as "Oblivious Medians via Online Bidding

Maximum gradient embeddings and monotone clustering

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous one. To appear in "Combinatorica