TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: As food becomes an important part of modern life, recipes shared on the web are a great indicator of civilizations and culinary attitudes in different countries. Similarly, ingredients, flavors, and nutrition information are strong signals of the taste preferences of individuals from various parts of the world. Yet, we do not have a thorough understanding of these palate varieties. In this paper, we present a large-scale study of recipes published on the Web and their content, aiming to understand cuisines and culinary habits around the world. Using a database of more than 157K recipes from over 200 different cuisines, we analyze ingredients, flavors, and nutritional values which distinguish dishes from different regions, and use this knowledge to assess the predictability of recipes from different cuisines. We then use country health statistics to understand the relation between these factors and health indicators of different nations, such as obesity, diabetes, migration, and health expenditure. Our results confirm the strong effects of geographical and cultural similarities on recipes, health indicators, and culinary preferences between countries around the world.

SOLUTION: Kissing Cuisines: Exploring Worldwide Culinary Habits on the Web

PROBLEM: Polynomial approximations to boolean functions have led to many positive results in computer science. In particular, polynomial approximations to the sign function underly algorithms for agnostically learning halfspaces, as well as pseudorandom generators for halfspaces. In this work, we investigate the limits of these techniques by proving inapproximability results for the sign function. Firstly, the "polynomial regression" algorithm of Kalai et al. (SIAM J. Comput. 2008) shows that halfspaces can be learned with respect to log-concave distributions on Rn in the challenging agnostic learning model. The power of this algorithm relies on the fact that under log-concave distributions, halfspaces can be approximated arbitrarily well by low-degree polynomials. We ask whether this technique can be extended beyond log-concave distributions, and establish a negative result. We show that polynomials of any degree cannot approximate the sign function to within arbitrarily low error for a large class of non-log-concave distributions on the real line, including those with densities proportional to exp(|x|0.99). This impossibility result extends to multivariate distributions, and thus gives a strong limitation on the power of the polynomial regression algorithm for halfspaces. Secondly, we investigate the derandomization of Chernoff-type concentration inequalities. Chernoff-type tail bounds on sums of independent random variables have pervasive applications in theoretical computer science. Schmidt et al. (SIAM J. Discrete Math. 1995) showed that these inequalities can be established for sums of random variables with only O(log(1/))-wise independence, for a tail probability of . We show that their results are tight up to constant factors. These results rely on techniques from weighted approximation theory, which studies how well functions on the real line can be approximated by polynomials under various distributions. We believe that these techniques will have further applications in other areas of theoretical computer science. Harvard University, School of Engineering and Applied Sciences. Supported by an NDSEG Fellowship and NSF grant CNS-1237235. Harvard University, School of Engineering and Applied Sciences. Supported by NSF grant CCF-1116616 and the Lord Rutherford Memorial Research Fellowship.

SOLUTION: Weighted Polynomial Approximations: Limits for Learning and Pseudorandomness

PROBLEM: Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answer-set programming where fully declarative and nonmonotonic languages are applied. In this context, obtaining a modular structure for programs is by no means straightforward since the output of an entire program cannot in general be composed from the output of its components. To better understand the effects of disjunctive information on modularity we restrict the scope of analysis to the case of disjunctive logic programs (DLPs) subject to stable-model semantics. We define the notion of a DLP-function, where a well-defined input/output interface is provided, and establish a novel module theorem which indicates the compositionality of stable-model semantics for DLP-functions. The module theorem extends the well-known splitting-set theorem and enables the decomposition of DLP-functions given their strongly connected components based on positive dependencies induced by rules. In this setting, it is also possible to split shared disjunctive rules among components using a generalized shifting technique. The concept of modular equivalence is introduced for the mutual comparison of DLP-functions using a generalization of a translation-based verification method.

SOLUTION:
Modularity Aspects of Disjunctive Stable Models