Graph Pricing Problem on Bounded Treewidth, Bounded Genus and k-partite graphs

Consider the following problem. A seller has infinite copies of $n$ products represented by nodes in a graph. There are $m$ consumers, each has a budget and wants to buy two products. Consumers are represented by weighted edges. Given the prices of products, each consumer will buy both products she wants, at the given price, if she can afford to. Our objective is to help the seller price the products to maximize her profit. This problem is called {\em graph vertex pricing} ({\sf GVP}) problem and has resisted several recent attempts despite its current simple solution. This motivates the study of this problem on special classes of graphs. In this paper, we study this problem on a large class of graphs such as graphs with bounded treewidth, bounded genus and $k$-partite graphs. We show that there exists an {\sf FPTAS} for {\sf GVP} on graphs with bounded treewidth. This result is also extended to an {\sf FPTAS} for the more general {\em single-minded pricing} problem. On bounded genus graphs we present a {\sf PTAS} and show that {\sf GVP} is {\sf NP}-hard even on planar graphs. We study the Sherali-Adams hierarchy applied to a natural Integer Program formulation that $(1+\epsilon)$-approximates the optimal solution of {\sf GVP}. Sherali-Adams hierarchy has gained much interest recently as a possible approach to develop new approximation algorithms. We show that, when the input graph has bounded treewidth or bounded genus, applying a constant number of rounds of Sherali-Adams hierarchy makes the integrality gap of this natural {\sf LP} arbitrarily small, thus giving a $(1+\epsilon)$-approximate solution to the original {\sf GVP} instance. On $k$-partite graphs, we present a constant-factor approximation algorithm. We further improve the approximation factors for paths, cycles and graphs with degree at most three.Comment: Preprint of the paper to appear in Chicago Journal of Theoretical Computer Scienc

Polynomials that Sign Represent Parity and Descartes' Rule of Signs

A real polynomial $P(X_1,..., X_n)$ sign represents $f: A^n \to \{0,1\}$ if for every $(a_1, ..., a_n) \in A^n$, the sign of $P(a_1,...,a_n)$ equals $(-1)^{f(a_1,...,a_n)}$. Such sign representations are well-studied in computer science and have applications to computational complexity and computational learning theory. In this work, we present a systematic study of tradeoffs between degree and sparsity of sign representations through the lens of the parity function. We attempt to prove bounds that hold for any choice of set $A$. We show that sign representing parity over $\{0,...,m-1\}^n$ with the degree in each variable at most $m-1$ requires sparsity at least $m^n$. We show that a tradeoff exists between sparsity and degree, by exhibiting a sign representation that has higher degree but lower sparsity. We show a lower bound of $n(m -2) + 1$ on the sparsity of polynomials of any degree representing parity over $\{0,..., m-1\}^n$. We prove exact bounds on the sparsity of such polynomials for any two element subset $A$. The main tool used is Descartes' Rule of Signs, a classical result in algebra, relating the sparsity of a polynomial to its number of real roots. As an application, we use bounds on sparsity to derive circuit lower bounds for depth-two AND-OR-NOT circuits with a Threshold Gate at the top. We use this to give a simple proof that such circuits need size $1.5^n$ to compute parity, which improves the previous bound of ${4/3}^{n/2}$ due to Goldmann (1997). We show a tight lower bound of $2^n$ for the inner product function over $\{0,1\}^n \times \{0, 1\}^n$.Comment: To appear in Computational Complexit

Intravenous ketamine for subacute treatment of refractory chronic migraine: a case series.

BACKGROUND: Refractory migraine is a challenging condition with great impact on health related quality of life. Intravenous (IV) ketamine has been previously used to treat various refractory pain conditions. We present a series of patients with refractory migraine treated with intravenous ketamine in the hospital setting. METHODS: Based on retrospective chart review, we identified six patients with refractory migraine admitted from 2010 through 2014 for treatment with intravenous ketamine. Ketamine was administered using a standard protocol starting with a dose of 0.1 mg/kg/hr and increased by 0.1 mg/kg/hr every 3 to 4 h as tolerated until the target pain score of 3/10 was achieved and maintained for at least 8 h. Visual Analogue Scale (VAS) scores at time of hospital admission were obtained as well as average baseline VAS scores prior to ketamine infusion. A phone interview was conducted for follow-up of migraine response in the 3 to 6 months following ketamine infusion. RESULTS: The study sample had a median age of 36.5 years (range 29-54) and 83% were women. Pre-treatment pain scores ranged from 9 to 10. All patients achieved a target pain level of 3 or less for 8 h; the average ketamine infusion rate at target was 0.34 mg/kg/hour (range 0.12-0.42 mg/kg/hr). One patient reported a transient out-of-body hallucination following an increase in the infusion rate, which resolved after decreasing the rate. There were no other significant side effects. CONCLUSION: IV ketamine was safely administered in the hospital setting to patients with refractory chronic migraine. Treatment was associated with short term improvement in pain severity in 6 of 6 patients with refractory chronic migraine. Prospective placebo-controlled trials are needed to assess short term and long-term efficacy of IV ketamine in refractory chronic migraine

Modern Varieties, International Agricultural Research, and the Poor

An examination of the affects of modern crop varieties on consumption, real income, employment, and nutrition among the poor in developing countries, and critique of the body of literature regarding the same. The authors attributed serious shortcomings to the existing literature on the affects of the modern variety adoption on the poor, which they characterize as given to wide swings between prevailing optimistic and pessimistic assessments, and prone to focus on more immediate, "first round" affects of newly adopted varieties. They also found a dearth of analysis on the impacts of modern varieties on the livelihoods of small producers operating in regions which have yet to adopt new varieties, and evidence led them to warn of serious consequences to those regions that lagged behind. The implications of the study for the work CGIAR Centers suggest the need for packages of combined technologies that take into consideration the specific characteristics of the poor (be they primarily small farmers, townspeople, or laborers) as well as the changing political contexts in which poverty reduction must take place. Written by Michael Lipton and Richard Longhurst of Institute of Development Studies, University of Sussex

DFN-02, Sumatriptan 10 mg Nasal Spray with Permeation Enhancer, for the Acute Treatment of Migraine: A Randomized, Double-Blind, Placebo-Controlled Study Assessing Functional Disability and Subject Satisfaction with Treatment.

BackgroundThe commercial formulation of sumatriptan nasal spray is an effective option for migraine patients requiring or preferring a non-oral route of drug administration, but its utility is limited by poor absorption and tolerability issues. DFN-02, a new formulation of sumatriptan 10 mg nasal spray, is co-formulated with a permeation enhancer that gives it pharmacokinetics comparable to subcutaneous sumatriptan. As reported previously, DFN-02 was significantly better than placebo on multiple efficacy endpoints at 2 h postdose, including pain freedom, absence of the most bothersome symptom, and pain relief, and its safety and tolerability profiles were excellent.ObjectiveThe objective of this study was to assess the efficacy of acute treatment of migraine with DFN-02, including its effect on migraine-related functional disability and patient satisfaction with treatment.MethodsThis was a multicenter, randomized, double-blind, placebo-controlled efficacy and safety study of DFN-02 in adults with episodic migraine. Functional disability and subject satisfaction with treatment were prespecified endpoints, assessed in real-time by subjects, using an electronic diary.ResultsIn total, 107 subjects were randomized. DFN-02 was significantly superior to placebo for the reduction in functional disability score from predose level at 2 h after treatment (- 1.2 vs. - 0.6, p < 0.001). Subjects treated with DFN-02 were also more likely to be satisfied or very satisfied than subjects treated with placebo at 2 h postdose (70.0% vs. 44.2%, p = 0.027). Using the Patient Perception of Migraine Questionnaire-Revised at 24 h postdose, DFN-02 mean scores were significantly superior to placebo for the subscales of efficacy (65.2 vs. 42.5, p = 0.016) and function (68.9 vs. 42.1, p = 0.001), and for total score (71.0 vs. 56.6, p = 0.016); global medication effectiveness (p = 0.027); and overall satisfaction (p = 0.019). Placebo was significantly better than DFN-02 on the tolerability subscale (94.8 vs. 88.5, p = 0.026). At 24 h postdose, subjects reported significantly higher satisfaction with DFN-02 compared with satisfaction reported pre-randomization regarding their usual migraine medication (p = 0.012).ConclusionDFN-02 was superior to placebo for the relief of migraine-related functional disability, and provided greater satisfaction than placebo or subjects' usual acute treatment.Trial registrationClinicalTrials.gov identifier: NCT02856802

Provably Secure Virus Detection: Using The Observer Effect Against Malware

Protecting software from malware injection is one of the biggest challenges of modern computer science. Despite intensive efforts by the scientific and engineering community, the number of successful attacks continues to increase. This work sets first footsteps towards a provably secure investigation of malware detection. We provide a formal model and cryptographic security definitions of attestation for systems with dynamic memory, and suggest novel provably secure attestation schemes. The key idea underlying our schemes is to use the very insertion of the malware itself to allow for the systems to detect it. This is, in our opinion, close in spirit to the quantum Observer Effect. The attackers, no matter how clever, no matter when they insert their malware, change the state of the system they are attacking. This fundamental idea can be a game changer. And our system does not rely on heuristics; instead, our scheme enjoys the unique property that it is proved secure in a formal and precise mathematical sense and with minimal and realistic CPU modification achieves strong provable security guarantees. We envision such systems with a formal mathematical security treatment as a venue for new directions in software protection