On Index Coding and Graph Homomorphism

In this work, we study the problem of index coding from graph homomorphism perspective. We show that the minimum broadcast rate of an index coding problem for different variations of the problem such as non-linear, scalar, and vector index code, can be upper bounded by the minimum broadcast rate of another index coding problem when there exists a homomorphism from the complement of the side information graph of the first problem to that of the second problem. As a result, we show that several upper bounds on scalar and vector index code problem are special cases of one of our main theorems. For the linear scalar index coding problem, it has been shown in [1] that the binary linear index of a graph is equal to a graph theoretical parameter called minrank of the graph. For undirected graphs, in [2] it is shown that $\mathrm{minrank}(G) = k$ if and only if there exists a homomorphism from $\bar{G}$ to a predefined graph $\bar{G}_k$. Combining these two results, it follows that for undirected graphs, all the digraphs with linear index of at most k coincide with the graphs $G$ for which there exists a homomorphism from $\bar{G}$ to $\bar{G}_k$. In this paper, we give a direct proof to this result that works for digraphs as well. We show how to use this classification result to generate lower bounds on scalar and vector index. In particular, we provide a lower bound for the scalar index of a digraph in terms of the chromatic number of its complement. Using our framework, we show that by changing the field size, linear index of a digraph can be at most increased by a factor that is independent from the number of the nodes.Comment: 5 pages, to appear in "IEEE Information Theory Workshop", 201

Subdeterminant Maximization via Nonconvex Relaxations and Anti-concentration

Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that maximizes the squared volume of the simplex spanned by the vectors in $S$. A motivating example is the data-summarization problem in machine learning where one is given a collection of vectors that represent data such as documents or images. The volume of a set of vectors is used as a measure of their diversity, and partition or matroid constraints over $[m]$ are imposed in order to ensure resource or fairness constraints. Recently, Nikolov and Singh presented a convex program and showed how it can be used to estimate the value of the most diverse set when ${\cal B}$ corresponds to a partition matroid. This result was recently extended to regular matroids in works of Straszak and Vishnoi, and Anari and Oveis Gharan. The question of whether these estimation algorithms can be converted into the more useful approximation algorithms -- that also output a set -- remained open. The main contribution of this paper is to give the first approximation algorithms for both partition and regular matroids. We present novel formulations for the subdeterminant maximization problem for these matroids; this reduces them to the problem of finding a point that maximizes the absolute value of a nonconvex function over a Cartesian product of probability simplices. The technical core of our results is a new anti-concentration inequality for dependent random variables that allows us to relate the optimal value of these nonconvex functions to their value at a random point. Unlike prior work on the constrained subdeterminant maximization problem, our proofs do not rely on real-stability or convexity and could be of independent interest both in algorithms and complexity.Comment: in FOCS 201

Opinion dynamics with varying susceptibility to persuasion

A long line of work in social psychology has studied variations in people's susceptibility to persuasion -- the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people's intrinsic opinions, it is also natural to consider interventions that modify people's susceptibility to persuasion. In this work, we adopt a popular model for social opinion dynamics, and we formalize the opinion maximization and minimization problems where interventions happen at the level of susceptibility. We show that modeling interventions at the level of susceptibility lead to an interesting family of new questions in network opinion dynamics. We find that the questions are quite different depending on whether there is an overall budget constraining the number of agents we can target or not. We give a polynomial-time algorithm for finding the optimal target-set to optimize the sum of opinions when there are no budget constraints on the size of the target-set. We show that this problem is NP-hard when there is a budget, and that the objective function is neither submodular nor supermodular. Finally, we propose a heuristic for the budgeted opinion optimization and show its efficacy at finding target-sets that optimize the sum of opinions compared on real world networks, including a Twitter network with real opinion estimates

Determinant criteria for designing Health benefit package in selected countries

Health benefit package described as primary health interventions that provided with government using general funds for all regardless their financial ability. This study was aimed at determine appropriate pattern for Iran using comparative survey of Health benefit package in various countries. A review exploration was done, scholars was selected population of both developed and developing countries, required information was also extracted by articles, searches and reports of reliable sources and date were analyzed by SPSS, in brief. The vast majority frequencies was respectively allocated to accessibility (40.7%), cost- effectiveness (29.6%), prioritize, efficacy and cost (22.2%). most countries located in WHO African region were selected cost-effectiveness and accessibility, WHO southeast Asia region were selected, coverage, prioritize, efficacy and quality and finally most WHO Europeans region were elected effectiveness and services costs for including services in Health benefit package. According to most Health benefit package designer emphasis on criteria including accessibility and costeffectiveness, to design Health benefit package for Iran, these criteria must be noticed

Aquacel Surgical Dressing Reduces the Rate of Acute PJI Following Total Joint Arthroplasty: A Case-Control Study.

An effort to prevent PJI has led to the development of antimicrobial dressings that support wound healing. We sought to determine whether Aquacel Surgical dressing independently reduces the rate of acute PJI following TJA. A single institution retrospective chart review of 903 consecutive cases who received the Aquacel Surgical dressing and 875 consecutive cases who received standard gauze dressing was conducted to determine the incidence of acute PJI (within 3months). The incidence of acute PJI is 0.44% in the Aquacel dressing group compared to 1.7% in the standard gauze dressing group (P=0.005). Multivariate analysis revealed that use of Aquacel dressing was an independent risk factor for reduction of PJI (odds ratio of 0.165, 95% confidence interval: 0.051-0.533). Aquacel Surgical dressing significantly reduces the incidence of acute PJI

ADAPT: a price-stabilizing compliance policy for renewable energy certificates: the case of SREC markets

Currently most Renewable Energy Certificate (REC) markets are defined based on targets which create an artificial step demand function resembling a cliff. This target policy produces volatile prices which can make investing in renewables a risky proposition. In this paper, we propose an alternative policy called Adjustable Dynamic Assignment of Penalties and Targets (ADAPT) which uses a sloped compliance penalty and a self-regulating requirement schedule, both designed to stabilize REC prices, helping to alleviate a common weakness of environmental markets. To capture market behavior, we model the market as a stochastic dynamic programming problem to understand how the market might balance the decision to use a REC now versus holding it for future periods (in the face of uncertain new supply). Then, we present and prove some of the properties of this market, and finally we show that this mechanism reduces the volatility of REC prices which should stabilize the market and encourage long-term investment in renewables

Periprosthetic joint infection increases the risk of one-year mortality.

BACKGROUND: Periprosthetic joint infection continues to potentially complicate an otherwise successful joint replacement. The treatment of this infection often requires multiple surgical procedures associated with increased complications and morbidity. This study examined the relationship between periprosthetic joint infection and mortality and aimed to determine the effect of periprosthetic joint infection on mortality and any predictors of mortality in patients with periprosthetic joint infection. METHODS: Four hundred and thirty-six patients with at least one surgical intervention secondary to confirmed periprosthetic joint infection were compared with 2342 patients undergoing revision arthroplasty for aseptic failure. The incidence of mortality at thirty days, ninety days, one year, two years, and five years after surgery was assessed. Multivariate analysis was used to assess periprosthetic joint infection as an independent predictor of mortality. In the periprosthetic joint infection population, variables investigated as potential risk factors for mortality were evaluated. RESULTS: Mortality was significantly greater (p \u3c 0.001) in patients with periprosthetic joint infection compared with those undergoing aseptic revision arthroplasty at ninety days (3.7% versus 0.8%), one year (10.6% versus 2.0%), two years (13.6% versus 3.9%), and five years (25.9% versus 12.9%). After controlling for age, sex, ethnicity, number of procedures, involved joint, body mass index, and Charlson Comorbidity Index, revision arthroplasty for periprosthetic joint infection was associated with a fivefold increase in mortality compared with revision arthroplasty for aseptic failures. In the periprosthetic joint infection population, independent predictors of mortality included increasing age, higher Charlson Comorbidity Index, history of stroke, polymicrobial infections, and cardiac disease. CONCLUSIONS: Although it is well known that periprosthetic joint infection is a devastating complication that severely limits joint function and is consistently difficult to eradicate, surgeons must also be cognizant of the systemic impact of periprosthetic joint infection and its major influence on fatal outcome in patients

Aspirin May Be Adequate for Venous Thromboembolic Event Prophylaxis after Revision Hip and Knee Arthroplasty

Introduction: The optimal prophylaxis for prevention of venous thromboembolic events (VTE) after total hip arthroplasty (THA) and total knee arthroplasty (TKA) remains unknown.(1) Current studies focus on primary arthroplasty and there are little to no data on the ideal prophylaxis for VTE following revision arthroplasty.(2) Revision surgery, due to its complexity, longer operative time, higher risk of bleeding and infection diff­ers from primary arthroplasty.(3) The objective of this study was to evaluate whether aspirin, known to be e­ffective for prevention of VTE after primary arthroplasty, is also e­ffective against such events following revision THA and TKA

New population-based exome data question the pathogenicity of some genetic variants previously associated with Marfan syndrome

BACKGROUND: Marfan syndrome (MFS) is a rare autosomal dominantly inherited connective tissue disorder with an estimated prevalence of 1:5,000. More than 1000 variants have been previously reported to be associated with MFS. However, the disease-causing effect of these variants may be questionable as many of the original studies used low number of controls. To study whether there are possible false-positive variants associated with MFS, four in silico prediction tools (SIFT, Polyphen-2, Grantham score, and conservation across species) were used to predict the pathogenicity of these variant. RESULTS: Twenty-three out of 891 previously MFS-associated variants were identified in the ESP. These variants were distributed on 100 heterozygote carriers in 6494 screened individuals. This corresponds to a genotype prevalence of 1:65 for MFS. Using a more conservative approach (cutoff value of >2 carriers in the EPS), 10 variants affected a total of 82 individuals. This gives a genotype prevalence of 1:79 (82:6494) in the ESP. A significantly higher frequency of MFS-associated variants not present in the ESP were predicted to be pathogenic with the agreement of ≥3 prediction tools, compared to the variants present in the ESP (p = 3.5 × 10(−15)). CONCLUSIONS: This study showed a higher genotype prevalence of MFS than expected from the phenotype prevalence in the general population. The high genotype prevalence suggests that these variants are not the monogenic cause of MFS. Therefore, caution should be taken with regard to disease stratification based on these previously reported MFS-associated variants

Do ceramic femoral heads reduce taper fretting corrosion in hip arthroplasty? A retrieval study.

BACKGROUND: Previous studies regarding modular head-neck taper corrosion were largely based on cobalt chrome (CoCr) alloy femoral heads. Less is known about head-neck taper corrosion with ceramic femoral heads. QUESTIONS/PURPOSES: We asked (1) whether ceramic heads resulted in less taper corrosion than CoCr heads; (2) what device and patient factors influence taper fretting corrosion; and (3) whether the mechanism of taper fretting corrosion in ceramic heads differs from that in CoCr heads. METHODS: One hundred femoral head-stem pairs were analyzed for evidence of fretting and corrosion using a visual scoring technique based on the severity and extent of fretting and corrosion damage observed at the taper. A matched cohort design was used in which 50 ceramic head-stem pairs were matched with 50 CoCr head-stem pairs based on implantation time, lateral offset, stem design, and flexural rigidity. RESULTS: Fretting and corrosion scores were lower for the stems in the ceramic head cohort (p=0.03). Stem alloy (p=0.004) and lower stem flexural rigidity (Spearman\u27s rho=-0.32, p=0.02) predicted stem fretting and corrosion damage in the ceramic head cohort but not in the metal head cohort. The mechanism of mechanically assisted crevice corrosion was similar in both cohorts although in the case of ceramic femoral heads, only one of the two surfaces (the male metal taper) engaged in the oxide abrasion and repassivation process. CONCLUSIONS: The results suggest that by using a ceramic femoral head, CoCr fretting and corrosion from the modular head-neck taper may be mitigated but not eliminated. CLINICAL RELEVANCE: The findings of this study support further study of the role of ceramic heads in potentially reducing femoral taper corrosion