Decomposition Methods for Large Scale LP Decoding

When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be used to decode error-correcting codes at bit-error-rates comparable to state-of-the-art belief propagation (BP) decoders, but with significantly stronger theoretical guarantees. However, LP decoding when implemented with standard LP solvers does not easily scale to the block lengths of modern error correcting codes. In this paper we draw on decomposition methods from optimization theory, specifically the Alternating Directions Method of Multipliers (ADMM), to develop efficient distributed algorithms for LP decoding. The key enabling technical result is a "two-slice" characterization of the geometry of the parity polytope, which is the convex hull of all codewords of a single parity check code. This new characterization simplifies the representation of points in the polytope. Using this simplification, we develop an efficient algorithm for Euclidean norm projection onto the parity polytope. This projection is required by ADMM and allows us to use LP decoding, with all its theoretical guarantees, to decode large-scale error correcting codes efficiently. We present numerical results for LDPC codes of lengths more than 1000. The waterfall region of LP decoding is seen to initiate at a slightly higher signal-to-noise ratio than for sum-product BP, however an error floor is not observed for LP decoding, which is not the case for BP. Our implementation of LP decoding using ADMM executes as fast as our baseline sum-product BP decoder, is fully parallelizable, and can be seen to implement a type of message-passing with a particularly simple schedule.Comment: 35 pages, 11 figures. An early version of this work appeared at the 49th Annual Allerton Conference, September 2011. This version to appear in IEEE Transactions on Information Theor

Mathematical Models of Physiological Responses to Exercise

This paper develops empirical mathematical models for physiological responses to exercise. We first find single-input single-output models describing heart rate variability, ventilation, oxygen consumption and carbon dioxide production in response to workload changes and then identify a single-input multi-output model from workload to these physiological variabilities. We also investigate the possibility of the existence of a universal model for physiological variability in different individuals during treadmill running. Simulations based on real data substantiate that the obtained models accurately capture the physiological responses to workload variations. In particular, it is observed that (i) different physiological responses to exercise can be captured by low-order linear or mildly nonlinear models; and (ii) there may exist a universal model for oxygen consumption that works for different individuals

Probabilistic Bag-Of-Hyperlinks Model for Entity Linking

Many fundamental problems in natural language processing rely on determining what entities appear in a given text. Commonly referenced as entity linking, this step is a fundamental component of many NLP tasks such as text understanding, automatic summarization, semantic search or machine translation. Name ambiguity, word polysemy, context dependencies and a heavy-tailed distribution of entities contribute to the complexity of this problem. We here propose a probabilistic approach that makes use of an effective graphical model to perform collective entity disambiguation. Input mentions (i.e.,~linkable token spans) are disambiguated jointly across an entire document by combining a document-level prior of entity co-occurrences with local information captured from mentions and their surrounding context. The model is based on simple sufficient statistics extracted from data, thus relying on few parameters to be learned. Our method does not require extensive feature engineering, nor an expensive training procedure. We use loopy belief propagation to perform approximate inference. The low complexity of our model makes this step sufficiently fast for real-time usage. We demonstrate the accuracy of our approach on a wide range of benchmark datasets, showing that it matches, and in many cases outperforms, existing state-of-the-art methods

Insulator-to-Metal Transition in Selenium-Hyperdoped Silicon: Observation and Origin

Hyperdoping has emerged as a promising method for designing semiconductors with unique optical and electronic properties, although such properties currently lack a clear microscopic explanation. Combining computational and experimental evidence, we probe the origin of sub-band gap optical absorption and metallicity in Se-hyperdoped Si. We show that sub-band gap absorption arises from direct defect-to-conduction band transitions rather than free carrier absorption. Density functional theory predicts the Se-induced insulator-to-metal transition arises from merging of defect and conduction bands, at a concentration in excellent agreement with experiment. Quantum Monte Carlo calculations confirm the critical concentration, demonstrate that correlation is important to describing the transition accurately, and suggest that it is a classic impurity-driven Mott transition.Comment: 5 pages, 3 figures (PRL formatted

Mathematical Models of Physiological Responses to Exercise

This paper develops empirical mathematical models for physiological responses to exercise. We first find single-input single-output models describing heart rate variability, ventilation, oxygen consumption and carbon dioxide production in response to workload changes and then identify a single-input multi-output model from workload to these physiological variabilities. We also investigate the possibility of the existence of a universal model for physiological variability in different individuals during treadmill running. Simulations based on real data substantiate that the obtained models accurately capture the physiological responses to workload variations. In particular, it is observed that (i) different physiological responses to exercise can be captured by low-order linear or mildly nonlinear models; and (ii) there may exist a universal model for oxygen consumption that works for different individuals

The importance of early arthroscopy in athletes with painful cartilage lesions of the ankle: a prospective study of 61 consecutive cases

BACKGROUND Ankle sprains are common in sports and can sometimes result in a persistent pain condition. PURPOSE Primarily to evaluate clinical symptoms, signs, diagnostics and outcomes of surgery for symptomatic chondral injuries of the talo crural joint in athletes. Secondly, in applicable cases, to evaluate the accuracy of MRI in detecting these injuries. Type of study: Prospective consecutive series. METHODS Over around 4 years we studied 61 consecutive athletes with symptomatic chondral lesions to the talocrural joint causing persistent exertion ankle pain. RESULTS 43% were professional full time athletes and 67% were semi-professional, elite or amateur athletes, main sports being soccer (49%) and rugby (14%). The main subjective complaint was exertion ankle pain (93%). Effusion (75%) and joint line tenderness on palpation (92%) were the most common clinical findings. The duration from injury to arthroscopy for 58/61 cases was 7 months (5.7–7.9). 3/61 cases were referred within 3 weeks from injury. There were in total 75 cartilage lesions. Of these, 52 were located on the Talus dome, 17 on the medial malleolus and 6 on the Tibia plafond. Of the Talus dome injuries 18 were anteromedial, 14 anterolateral, 9 posteromedial, 3 posterolateral and 8 affecting mid talus. 50% were grade 4 lesions, 13.3% grade 3, 16.7% grade 2 and 20% grade 1. MRI had been performed pre operatively in 26/61 (39%) and 59% of these had been interpreted as normal. Detection rate of cartilage lesions was only 19%, but subchondral oedema was present in 55%. At clinical follow up average 24 months after surgery (10–48 months), 73% were playing at pre-injury level. The average return to that level of sports after surgery was 16 weeks (3–32 weeks). However 43% still suffered minor symptoms. CONCLUSION Arthroscopy should be considered early when an athlete presents with exertion ankle pain, effusion and joint line tenderness on palpation after a previous sprain. Conventional MRI is not reliable for detecting isolated cartilage lesions, but the presence of subchondral oedema should raise such suspicion

Methodology for vetting heavily doped semiconductors for intermediate band photovoltaics: A case study in sulfur-hyperdoped silicon

We present a methodology for estimating the efficiency potential for candidate impurity-band photovoltaic materials from empirical measurements. This methodology employs both Fourier transform infrared spectroscopy and low-temperature photoconductivity to calculate a “performance figure of merit” and to determine both the position and bandwidth of the impurity band. We evaluate a candidate impurity-band material, silicon hyperdoped with sulfur; we find that the figure of merit is more than one order of magnitude too low for photovoltaic devices that exceed the thermodynamic efficiency limit for single band gap materials.National Science Foundation (U.S.) (Energy, Power, and Adaptive Systems Grant Contract ECCS-1102050)National Science Foundation (U.S.) (United States. Dept. of Energy NSF CA EEC-1041895)Center for Clean Water and Clean Energy at MIT and KFUP

BlinkML: Efficient Maximum Likelihood Estimation with Probabilistic Guarantees

The rising volume of datasets has made training machine learning (ML) models a major computational cost in the enterprise. Given the iterative nature of model and parameter tuning, many analysts use a small sample of their entire data during their initial stage of analysis to make quick decisions (e.g., what features or hyperparameters to use) and use the entire dataset only in later stages (i.e., when they have converged to a specific model). This sampling, however, is performed in an ad-hoc fashion. Most practitioners cannot precisely capture the effect of sampling on the quality of their model, and eventually on their decision-making process during the tuning phase. Moreover, without systematic support for sampling operators, many optimizations and reuse opportunities are lost. In this paper, we introduce BlinkML, a system for fast, quality-guaranteed ML training. BlinkML allows users to make error-computation tradeoffs: instead of training a model on their full data (i.e., full model), BlinkML can quickly train an approximate model with quality guarantees using a sample. The quality guarantees ensure that, with high probability, the approximate model makes the same predictions as the full model. BlinkML currently supports any ML model that relies on maximum likelihood estimation (MLE), which includes Generalized Linear Models (e.g., linear regression, logistic regression, max entropy classifier, Poisson regression) as well as PPCA (Probabilistic Principal Component Analysis). Our experiments show that BlinkML can speed up the training of large-scale ML tasks by 6.26x-629x while guaranteeing the same predictions, with 95% probability, as the full model.Comment: 22 pages, SIGMOD 201

Robust efficiency and actuator saturation explain healthy heart rate control and variability

The correlation of healthy states with heart rate variability (HRV) using time series analyses is well documented. Whereas these studies note the accepted proximal role of autonomic nervous system balance in HRV patterns, the responsible deeper physiological, clinically relevant mechanisms have not been fully explained. Using mathematical tools from control theory, we combine mechanistic models of basic physiology with experimental exercise data from healthy human subjects to explain causal relationships among states of stress vs. health, HR control, and HRV, and more importantly, the physiologic requirements and constraints underlying these relationships. Nonlinear dynamics play an important explanatory role––most fundamentally in the actuator saturations arising from unavoidable tradeoffs in robust homeostasis and metabolic efficiency. These results are grounded in domain-specific mechanisms, tradeoffs, and constraints, but they also illustrate important, universal properties of complex systems. We show that the study of complex biological phenomena like HRV requires a framework which facilitates inclusion of diverse domain specifics (e.g., due to physiology, evolution, and measurement technology) in addition to general theories of efficiency, robustness, feedback, dynamics, and supporting mathematical tools