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 $\epsilon > 0$

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

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

Multi-center, single-blind randomized controlled trial comparing functional electrical stimulation therapy to conventional therapy in incomplete tetraplegia

BackgroundLoss of upper extremity function after tetraplegia results in significant disability. Emerging evidence from pilot studies suggests that functional electrical stimulation (FES) therapy may enhance recovery of upper extremity function after tetraplegia. The aim of this trial was to determine the effectiveness of FES therapy delivered by the Myndmove stimulator in people with tetraplegia.MethodsA multi-center, single-blind, parallel-group, two-arm, randomized controlled trial was conducted comparing FES to conventional therapy in adults (≥18 years) with C4–C7 traumatic incomplete tetraplegia between 4 and 96 months post-injury, and with a baseline spinal cord injury independence measure III -self-care (SCIM III-SC) score of ≤10. Participants were enrolled at four SCI-specialized neurorehabilitation centers in the U.S. and Canada. Participants were stratified by center and randomized in a 1:1 ratio to receive either 40 sessions of FES or conventional therapy targeting upper extremities over a 14-week period. Blinded assessors measured SCIM III, Toronto Rehabilitation Institute Hand Function Test, and Graded Redefined Assessment of Strength, Sensibility, and Prehension at baseline, after 20th session, after 40th session or 14 weeks after 1st session, and at 24 weeks after 1st session. The primary outcome measure was change in SCIM III-SC from baseline to end of the treatment. Based on the primary outcome measure, a sample size of 60 was calculated. Seventeen participants' progress in the study was interrupted due to the COVID-19 lockdown. The protocol was modified for these participants to allow them to complete the study.ResultsBetween June 2019 to August 2021, 51 participants were randomized to FES (n = 27) and conventional therapy (n = 24). Both groups gained a mean of 2 points in SCIM-SC scores at the end of treatment, which was a clinically meaningful change. However, there was no statistically significant difference between the groups on any outcomes.ConclusionForty sessions of FES therapy delivered by the MyndMove stimulator are as effective as conventional therapy in producing meaningful functional improvements that persist after therapy is completed. Limitations of this study include the impact of COVID-19 limiting the ability to recruit the target sample size and per-protocol execution of the study in one-third of the participants.RegistrationThis trial is registered at www.ClinicalTrials.gov, NCT03439319

Magnetic Nano Cobalt Ferrite Catalyzed Synthesis of 4H-Pyrano[3,2-h]quinoline Derivatives under Microwave Irradiation

Abstract A microwave irradiated magnetically separable nano cobalt ferrite catalyzed green method for the synthesis of 4-phenyl-4H-pyrano[3,2-h]quinolin-2-amine and 2-amino-4-phenyl-4H-pyrano[3,2-h] quinoline-3-carbonitrile derivatives through cyclization of aromatic aldehyde, acetonitrile/malononitrile and 8-hydoxyquinoline is developed and presented in this paper. The cubic magnetic cobalt ferrite nano particles were synthesized by sol-gel citrate precursor method and characterized by FT-IR, XRD, SEM and TEM techniques and the structures of the synthesized pyranoquinoline derivatives were assigned by IR, MASS and 1 H NMR techniques. The reaction is carried out in a domestic microwave oven with a heat-resistant microwave safe glass container with a lid

Accelerator Magnet Development Based on COMB Technology with STAR Wires

This paper reports progress in the development of COMB magnet technology with STAR wires. A two-layer dipole magnet with 60 mm clear bore has been recently fabricated and tested in liquid nitrogen. The purpose of the test was to determine what kind of critical current degradation occurs in the process of winding the STAR wire into the COMB structure.Comment: CEC/ICMC2

A Clinical Practice Guideline for the Management of Patients With Acute Spinal Cord Injury: Recommendations on Hemodynamic Management

STUDY DESIGN Clinical practice guideline development following the GRADE process. OBJECTIVES Hemodynamic management is one of the only available treatment options that likely improves neurologic outcomes in patients with acute traumatic spinal cord injury (SCI). Augmenting mean arterial pressure (MAP) aims to improve blood perfusion and oxygen delivery to the injured spinal cord in order to minimize secondary ischemic damage to neural tissue. The objective of this guideline was to update the 2013 AANS/CNS recommendations on the hemodynamic management of patients with acute traumatic SCI, acknowledging that much has been published in this area since its publication. Specifically, we sought to make recommendations on 1. The range of mean arterial pressure (MAP) to be maintained by identifying an upper and lower MAP limit; 2. The duration of such MAP augmentation; and 3. The choice of vasopressor. Additionally, we sought to make a recommendation on spinal cord perfusion pressure (SCPP) targets. METHODS A multidisciplinary guideline development group (GDG) was formed that included health care professionals from a wide range of clinical specialities, patient advocates, and individuals living with SCI. The GDG reviewed the 2013 AANS/CNS guidelines and voted on whether each recommendation should be endorsed or updated. A systematic review of the literature, following PRISMA standards and registered in PROSPERO, was conducted to inform the guideline development process and address the following key questions: (i) what are the effects of goal-directed interventions to optimize spinal cord perfusion on extent of neurological recovery and rates of adverse events at any time point of follow-up? and (ii) what are the effects of particular monitoring techniques, perfusion ranges, pharmacological agents, and durations of treatment on extent of neurological recovery and rates of adverse events at any time point of follow-up? The GDG combined the information from this systematic review with their clinical expertise in order to develop recommendations on a MAP target range (specifically an upper and lower limit to target), the optimal duration for MAP augmentation, and the use of vasopressors or inotropes. Using methods outlined by the GRADE working group, recommendations were formulated that considered the balance of benefits and harms, financial impact, acceptability, feasibility and patient preferences. RESULTS The GDG suggested that MAP should be augmented to at least 75-80 mmHg as the "lower limit," but not actively augmented beyond an "upper limit" of 90-95 mmHg in order to optimize spinal cord perfusion in acute traumatic SCI. The quality of the evidence around the "target MAP" was very low, and thus the strength of this recommendation is weak. For duration of hemodynamic management, the GDG "suggested" that MAP be augmented for a duration of 3-7 days. Again, the quality of the evidence around the duration of MAP support was very low, and thus the strength of this recommendation is also weak. The GDG felt that a recommendation on the choice of vasopressor or the use of SCPP targets was not warranted, given the dearth of available evidence. CONCLUSION We provide new recommendations for blood pressure management after acute SCI that acknowledge the limitations of the current evidence on the relationship between MAP and neurologic recovery. It was felt that the low quality of existing evidence and uncertainty around the relationship between MAP and neurologic recovery justified a greater range of MAP to target, and for a broader range of days post-injury than recommended in previous guidelines. While important knowledge gaps still remain regarding hemodynamic management, these recommendations represent current perspectives on the role of MAP augmentation for acute SCI

Interventions to Optimize Spinal Cord Perfusion in Patients With Acute Traumatic Spinal Cord Injury: An Updated Systematic Review

STUDY DESIGN: Systematic review update. OBJECTIVES: Interventions that aim to optimize spinal cord perfusion are thought to play an important role in minimizing secondary ischemic damage and improving outcomes in patients with acute traumatic spinal cord injuries (SCIs). However, exactly how to optimize spinal cord perfusion and enhance neurologic recovery remains controversial. We performed an update of a recent systematic review (Evaniew et al, J. Neurotrauma 2020) to evaluate the effects of Mean Arterial Pressure (MAP) support or Spinal Cord Perfusion Pressure (SCPP) support on neurological recovery and rates of adverse events among patients with acute traumatic SCI. METHODS: We searched PubMed/MEDLINE, EMBASE and ClinicalTrials.gov for new published reports. Two reviewers independently screened articles, extracted data, and evaluated risk of bias. We implemented the Grades of Recommendation, Assessment, Development, and Evaluation (GRADE) approach to rate confidence in the quality of the evidence. RESULTS: From 569 potentially relevant new citations since 2019, we identified 9 new studies for inclusion, which were combined with 19 studies from a prior review to give a total of 28 studies. According to low or very low quality evidence, the effect of MAP support on neurological recovery is uncertain, and increased SCPP may be associated with improved neurological recovery. Both approaches may involve risks for specific adverse events, but the importance of these adverse events to patients remains unclear. Very low quality evidence failed to yield reliable guidance about particular monitoring techniques, perfusion ranges, pharmacological agents, or durations of treatment. CONCLUSIONS: This update provides an evidence base to support the development of a new clinical practice guideline for the hemodynamic management of patients with acute traumatic SCI. While avoidance of hypotension and maintenance of spinal cord perfusion are important principles in the management of an acute SCI, the literature does not provide high quality evidence in support of a particular protocol. Further prospective, controlled research studies with objective validated outcome assessments are required to examine interventions to optimize spinal cord perfusion in this setting

A Clinical Practice Guideline for the Management of Patients With Acute Spinal Cord Injury: Recommendations on Hemodynamic Management

STUDY DESIGN: Clinical practice guideline development following the GRADE process. OBJECTIVES: Hemodynamic management is one of the only available treatment options that likely improves neurologic outcomes in patients with acute traumatic spinal cord injury (SCI). Augmenting mean arterial pressure (MAP) aims to improve blood perfusion and oxygen delivery to the injured spinal cord in order to minimize secondary ischemic damage to neural tissue. The objective of this guideline was to update the 2013 AANS/CNS recommendations on the hemodynamic management of patients with acute traumatic SCI, acknowledging that much has been published in this area since its publication. Specifically, we sought to make recommendations on 1. The range of mean arterial pressure (MAP) to be maintained by identifying an upper and lower MAP limit; 2. The duration of such MAP augmentation; and 3. The choice of vasopressor. Additionally, we sought to make a recommendation on spinal cord perfusion pressure (SCPP) targets. METHODS: A multidisciplinary guideline development group (GDG) was formed that included health care professionals from a wide range of clinical specialities, patient advocates, and individuals living with SCI. The GDG reviewed the 2013 AANS/CNS guidelines and voted on whether each recommendation should be endorsed or updated. A systematic review of the literature, following PRISMA standards and registered in PROSPERO, was conducted to inform the guideline development process and address the following key questions: (i) what are the effects of goal-directed interventions to optimize spinal cord perfusion on extent of neurological recovery and rates of adverse events at any time point of follow-up? and (ii) what are the effects of particular monitoring techniques, perfusion ranges, pharmacological agents, and durations of treatment on extent of neurological recovery and rates of adverse events at any time point of follow-up? The GDG combined the information from this systematic review with their clinical expertise in order to develop recommendations on a MAP target range (specifically an upper and lower limit to target), the optimal duration for MAP augmentation, and the use of vasopressors or inotropes. Using methods outlined by the GRADE working group, recommendations were formulated that considered the balance of benefits and harms, financial impact, acceptability, feasibility and patient preferences. RESULTS: The GDG suggested that MAP should be augmented to at least 75-80 mmHg as the lower limit, but not actively augmented beyond an upper limit of 90-95 mmHg in order to optimize spinal cord perfusion in acute traumatic SCI. The quality of the evidence around the target MAP was very low, and thus the strength of this recommendation is weak. For duration of hemodynamic management, the GDG suggested that MAP be augmented for a duration of 3-7 days. Again, the quality of the evidence around the duration of MAP support was very low, and thus the strength of this recommendation is also weak. The GDG felt that a recommendation on the choice of vasopressor or the use of SCPP targets was not warranted, given the dearth of available evidence. CONCLUSION: We provide new recommendations for blood pressure management after acute SCI that acknowledge the limitations of the current evidence on the relationship between MAP and neurologic recovery. It was felt that the low quality of existing evidence and uncertainty around the relationship between MAP and neurologic recovery justified a greater range of MAP to target, and for a broader range of days post-injury than recommended in previous guidelines. While important knowledge gaps still remain regarding hemodynamic management, these recommendations represent current perspectives on the role of MAP augmentation for acute SCI

Dynamic temporary blood facility location-allocation during and post-disaster periods

The key objective of this study is to develop a tool (hybridization or integration of different techniques) for locating the temporary blood banks during and post-disaster conditions that could serve the hospitals with minimum response time. We have used temporary blood centers, which must be located in such a way that it is able to serve the demand of hospitals in nearby region within a shorter duration. We are locating the temporary blood centres for which we are minimizing the maximum distance with hospitals. We have used Tabu search heuristic method to calculate the optimal number of temporary blood centres considering cost components. In addition, we employ Bayesian belief network to prioritize the factors for locating the temporary blood facilities. Workability of our model and methodology is illustrated using a case study including blood centres and hospitals surrounding Jamshedpur city. Our results shows that at-least 6 temporary blood facilities are required to satisfy the demand of blood during and post-disaster periods in Jamshedpur. The results also show that that past disaster conditions, response time and convenience for access are the most important factors for locating the temporary blood facilities during and post-disaster periods