Beyond Convexity: Stochastic Quasi-Convex Optimization

Stochastic convex optimization is a basic and well studied primitive in machine learning. It is well known that convex and Lipschitz functions can be minimized efficiently using Stochastic Gradient Descent (SGD). The Normalized Gradient Descent (NGD) algorithm, is an adaptation of Gradient Descent, which updates according to the direction of the gradients, rather than the gradients themselves. In this paper we analyze a stochastic version of NGD and prove its convergence to a global minimum for a wider class of functions: we require the functions to be quasi-convex and locally-Lipschitz. Quasi-convexity broadens the con- cept of unimodality to multidimensions and allows for certain types of saddle points, which are a known hurdle for first-order optimization methods such as gradient descent. Locally-Lipschitz functions are only required to be Lipschitz in a small region around the optimum. This assumption circumvents gradient explosion, which is another known hurdle for gradient descent variants. Interestingly, unlike the vanilla SGD algorithm, the stochastic normalized gradient descent algorithm provably requires a minimal minibatch size

On Graduated Optimization for Stochastic Non-Convex Problems

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms of theoretical convergence analysis. In this paper we describe a new first-order algorithm based on graduated optimiza- tion and analyze its performance. We characterize a parameterized family of non- convex functions for which this algorithm provably converges to a global optimum. In particular, we prove that the algorithm converges to an {\epsilon}-approximate solution within O(1/\epsilon^2) gradient-based steps. We extend our algorithm and analysis to the setting of stochastic non-convex optimization with noisy gradient feedback, attaining the same convergence rate. Additionally, we discuss the setting of zero-order optimization, and devise a a variant of our algorithm which converges at rate of O(d^2/\epsilon^4).Comment: 17 page

RadArnomaly: Protecting Radar Systems from Data Manipulation Attacks

Radar systems are mainly used for tracking aircraft, missiles, satellites, and watercraft. In many cases, information regarding the objects detected by the radar system is sent to, and used by, a peripheral consuming system, such as a missile system or a graphical user interface used by an operator. Those systems process the data stream and make real-time, operational decisions based on the data received. Given this, the reliability and availability of information provided by radar systems has grown in importance. Although the field of cyber security has been continuously evolving, no prior research has focused on anomaly detection in radar systems. In this paper, we present a deep learning-based method for detecting anomalies in radar system data streams. We propose a novel technique which learns the correlation between numerical features and an embedding representation of categorical features in an unsupervised manner. The proposed technique, which allows the detection of malicious manipulation of critical fields in the data stream, is complemented by a timing-interval anomaly detection mechanism proposed for the detection of message dropping attempts. Real radar system data is used to evaluate the proposed method. Our experiments demonstrate the method's high detection accuracy on a variety of data stream manipulation attacks (average detection rate of 88% with 1.59% false alarms) and message dropping attacks (average detection rate of 92% with 2.2% false alarms)

Birthweight and risk markers for type 2 diabetes and cardiovascular disease in childhood: the Child Heart and Health Study in England (CHASE).

AIMS/HYPOTHESIS: Lower birthweight (a marker of fetal undernutrition) is associated with higher risks of type 2 diabetes and cardiovascular disease (CVD) and could explain ethnic differences in these diseases. We examined associations between birthweight and risk markers for diabetes and CVD in UK-resident white European, South Asian and black African-Caribbean children. METHODS: In a cross-sectional study of risk markers for diabetes and CVD in 9- to 10-year-old children of different ethnic origins, birthweight was obtained from health records and/or parental recall. Associations between birthweight and risk markers were estimated using multilevel linear regression to account for clustering in children from the same school. RESULTS: Key data were available for 3,744 (66%) singleton study participants. In analyses adjusted for age, sex and ethnicity, birthweight was inversely associated with serum urate and positively associated with systolic BP. After additional height adjustment, lower birthweight (per 100 g) was associated with higher serum urate (0.52%; 95% CI 0.38, 0.66), fasting serum insulin (0.41%; 95% CI 0.08, 0.74), HbA1c (0.04%; 95% CI 0.00, 0.08), plasma glucose (0.06%; 95% CI 0.02, 0.10) and serum triacylglycerol (0.30%; 95% CI 0.09, 0.51) but not with BP or blood cholesterol. Birthweight was lower among children of South Asian (231 g lower; 95% CI 183, 280) and black African-Caribbean origin (81 g lower; 95% CI 30, 132). However, adjustment for birthweight had no effect on ethnic differences in risk markers. CONCLUSIONS/INTERPRETATION: Birthweight was inversely associated with urate and with insulin and glycaemia after adjustment for current height. Lower birthweight does not appear to explain emerging ethnic difference in risk markers for diabetes

Antimicrobial polymers as synthetic mimics of host‐defense peptides

Antibiotic‐resistant bacteria ‘superbugs’ are an emerging threat to public health due to the decrease in effective antibiotics as well as the slowed pace of development of new antibiotics to replace those that become ineffective. The need for new antimicrobial agents is a well‐documented issue relating to world health. Tremendous efforts have been given to developing compounds that not only show high efficacy, but also those that are less susceptible to resistance development in the bacteria. However, the development of newer, stronger antibiotics which can overcome these acquired resistances is still a scientific challenge because a new mode of antimicrobial action is likely required. To that end, amphiphilic, cationic polymers have emerged as a promising candidate for further development as an antimicrobial agent with decreased potential for resistance development. These polymers are designed to mimic naturally occurring host‐defense antimicrobial peptides which act on bacterial cell walls or membranes. Antimicrobial‐peptide mimetic polymers display antibacterial activity against a broad spectrum of bacteria including drug‐resistant strains and are less susceptible to resistance development in bacteria. These polymers also showed selective activity to bacteria over mammalian cells. Antimicrobial polymers provide a new molecular framework for chemical modification and adaptation to tune their biological functions. The peptide‐mimetic design of antimicrobial polymers will be versatile, generating a new generation of antibiotics toward implementation of polymers in biomedical applications. WIREs Nanomed Nanobiotechnol 2013, 5:49–66. doi: 10.1002/wnan.1199 Conflict of interest: K. K. is a coinventor on a patent application filed by the University of Pennsylvania covering ‘Antimicrobial Copolymers and Uses Thereof’. The patent application has been licensed to PolyMedix Inc. (Radnor, PA). PolyMedix did not play a role in the design and conduct of this study; in the collection, analysis, or interpretation of the data; or in the preparation, review, or approval of the article. For further resources related to this article, please visit the WIREs website .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94848/1/1199_ftp.pd

Lasers and ancillary treatments for scar management Part 2: Keloid, hypertrophic, pigmented and acne scars

The formation of a wide range of excessive scars following various skin injuries is a natural consequence of healing. Scars resulting from surgery or trauma affect approximately 100 million people per annum in the developed world and can have profound physical, aesthetic, psychological and social consequences. Thus, scar treatment is a priority for patient and physician alike. Laser treatment plays an important role in scar management with additional support from ancillary modalities. Subsequent to part 1: Burns scars, part 2 focuses on our strategies and literature review of treatment of keloid, hypertrophic, pigmented and acne scars where lasers are used in conjunction with other measures, and illustrated with case studies

Medical-grade honey enriched with antimicrobial peptides has enhanced activity against antibiotic-resistant pathogens

Honey has potent activity against both antibiotic-sensitive and -resistant bacteria, and is an interesting agent for topical antimicrobial application to wounds. As honey is diluted by wound exudate, rapid bactericidal activity up to high dilution is a prerequisite for its successful application. We investigated the kinetics of the killing of antibiotic-resistant bacteria by RS honey, the source for the production of Revamil® medical-grade honey, and we aimed to enhance the rapid bactericidal activity of RS honey by enrichment with its endogenous compounds or the addition of antimicrobial peptides (AMPs). RS honey killed antibiotic-resistant isolates of Pseudomonas aeruginosa, Staphylococcus epidermidis, Enterococcus faecium, and Burkholderia cepacia within 2 h, but lacked such rapid activity against methicillin-resistant S. aureus (MRSA) and extended-spectrum beta-lactamase (ESBL)-producing Escherichia coli. It was not feasible to enhance the rapid activity of RS honey by enrichment with endogenous compounds, but RS honey enriched with 75 μM of the synthetic peptide Bactericidal Peptide 2 (BP2) showed rapid bactericidal activity against all species tested, including MRSA and ESBL E. coli, at up to 10–20-fold dilution. RS honey enriched with BP2 rapidly killed all bacteria tested and had a broader spectrum of bactericidal activity than either BP2 or honey alone