Trash: a local solution to a global problem

Gemstone Team GREEN JUSTICE

Using the Higgs to Probe Naturalness

The extreme sensitivity of the mass of the Higgs boson to quantum corrections from high mass states, makes it 'unnaturally' light in the standard model. This 'hierarchy problem' can be solved by symmetries, which predict new particles related, by the symmetry, to standard model fields. The Large Hadron Collider (LHC) can potentially discover these new particles, thereby finding the solution to the hierarchy problem. However, the dynamics of the Higgs boson is also sensitive to this new physics. We show that in many scenarios the Higgs can be a complementary and powerful probe of the hierarchy problem at the LHC and future colliders. If the top quark partners carry the color charge of the strong nuclear force, the production of Higgs pairs is affected. This effect is tightly correlated with single Higgs production, implying that only modest enhancements in di-Higgs production occur when the top partners are heavy. However, if the top partners are light, we show that di-Higgs production is a useful complementary probe to single Higgs production. We verify this result in the context of a simplified supersymmetric model. If the top partners do not carry color charge, their direct production is greatly reduced. Nevertheless, we show that such scenarios can be revealed through Higgs dynamics. We find that many color neutral frameworks leave observable traces in Higgs couplings, which, in some cases, may be the only way to probe these theories at the LHC. Some realizations of the color neutral framework also lead to exotic decays of the Higgs with displaced vertices. We show that these decays are so striking that the projected sensitivity for these searches, at hadron colliders, is comparable to that of searches for colored top partners. Taken together, these three case studies show the efficacy of the Higgs as a probe of naturalness.

Detection methods for common problems in solar home systems

Gemstone Team SHINE (Students Helping to Implement Natural Energy)

Anomaly Detection in Noisy Images

Finding rare events in multidimensional data is an important detection problem that has applications in many fields, such as risk estimation in insurance industry, finance, flood prediction, medical diagnosis, quality assurance, security, or safety in transportation. The occurrence of such anomalies is so infrequent that there is usually not enough training data to learn an accurate statistical model of the anomaly class. In some cases, such events may have never been observed, so the only information that is available is a set of normal samples and an assumed pairwise similarity function. Such metric may only be known up to a certain number of unspecified parameters, which would either need to be learned from training data, or fixed by a domain expert. Sometimes, the anomalous condition may be formulated algebraically, such as a measure exceeding a predefined threshold, but nuisance variables may complicate the estimation of such a measure. Change detection methods used in time series analysis are not easily extendable to the multidimensional case, where discontinuities are not localized to a single point. On the other hand, in higher dimensions, data exhibits more complex interdependencies, and there is redundancy that could be exploited to adaptively model the normal data. In the first part of this dissertation, we review the theoretical framework for anomaly detection in images and previous anomaly detection work done in the context of crack detection and detection of anomalous components in railway tracks. In the second part, we propose new anomaly detection algorithms. The fact that curvilinear discontinuities in images are sparse with respect to the frame of shearlets, allows us to pose this anomaly detection problem as basis pursuit optimization. Therefore, we pose the problem of detecting curvilinear anomalies in noisy textured images as a blind source separation problem under sparsity constraints, and propose an iterative shrinkage algorithm to solve it. Taking advantage of the parallel nature of this algorithm, we describe how this method can be accelerated using graphical processing units (GPU). Then, we propose a new method for finding defective components on railway tracks using cameras mounted on a train. We describe how to extract features and use a combination of classifiers to solve this problem. Then, we scale anomaly detection to bigger datasets with complex interdependencies. We show that the anomaly detection problem naturally fits in the multitask learning framework. The first task consists of learning a compact representation of the good samples, while the second task consists of learning the anomaly detector. Using deep convolutional neural networks, we show that it is possible to train a deep model with a limited number of anomalous examples. In sequential detection problems, the presence of time-variant nuisance parameters affect the detection performance. In the last part of this dissertation, we present a method for adaptively estimating the threshold of sequential detectors using Extreme Value Theory on a Bayesian framework. Finally, conclusions on the results obtained are provided, followed by a discussion of possible future work.

RICH AND EFFICIENT VISUAL DATA REPRESENTATION

Increasing the size of training data in many computer vision tasks has shown to be very effective. Using large scale image datasets (e.g. ImageNet) with simple learning techniques (e.g. linear classifiers) one can achieve state-of-the-art performance in object recognition compared to sophisticated learning techniques on smaller image sets. Semantic search on visual data has become very popular. There are billions of images on the internet and the number is increasing every day. Dealing with large scale image sets is intense per se. They take a significant amount of memory that makes it impossible to process the images with complex algorithms on single CPU machines. Finding an efficient image representation can be a key to attack this problem. A representation being efficient is not enough for image understanding. It should be comprehensive and rich in carrying semantic information. In this proposal we develop an approach to computing binary codes that provide a rich and efficient image representation. We demonstrate several tasks in which binary features can be very effective. We show how binary features can speed up large scale image classification. We present learning techniques to learn the binary features from supervised image set (With different types of semantic supervision; class labels, textual descriptions). We propose several problems that are very important in finding and using efficient image representation.

ADVERTISEMENT ALLOCATION AND TRUST MECHANISMS DESIGN IN SOCIAL NETWORKS

Social network sites (SNS), such as Facebook, Google+ and Twitter, have attracted hundreds of millions of users daily since their appearance. Within SNS, users connect to each other, express their identity, disseminate information and form cooperation by interacting with their connected peers. The increasing popularity and ubiquity of SNS usage and the invaluable user behaviors and connections give birth to many applications and business models. We look into several important problems within the social network ecosystem. The first one is the SNS advertisement allocation problem. The other two are related to trust mechanisms design in social network setting, including local trust inference and global trust evaluation. In SNS advertising, we study the problem of advertisement allocation from the ad platform's angle, and discuss its differences with the advertising model in the search engine setting. By leveraging the connection between social networks and hyperbolic geometry, we propose to solve the problem via approximation using hyperbolic embedding and convex optimization. A hyperbolic embedding method, \hcm, is designed for the SNS ad allocation problem, and several components are introduced to realize the optimization formulation. We show the advantages of our new approach in solving the problem compared to the baseline integer programming (IP) formulation. In studying the problem of trust mechanisms in social networks, we consider the existence of distrust (i.e. negative trust) relationships, and differentiate between the concept of local trust and global trust in social network setting. In the problem of local trust inference, we propose a 2-D trust model. Based on the model, we develop a semiring-based trust inference framework. In global trust evaluation, we consider a general setting with conflicting opinions, and propose a consensus-based approach to solve the complex problem in signed trust networks.

THE STOCHASTIC NAVIER STOKES EQUATIONS FOR HEAT CONDUCTING, COMPRESSIBLE FLUIDS

This dissertation is devoted to the equations of motion governing the evolution of a fluid or gas at the macroscopic scale. The classical model is a PDE description known as the Navier-Stokes equations. The behavior of solutions is notoriously complex, leading many in the scientific community to describe fluid mechanics using a statistical language. In the physics literature, this is often done in an ad-hoc manner with limited precision about the sense in which the randomness enters the evolution equation. The stochastic PDE community has begun proposing precise models, where a random perturbation appears explicitly in the evolution equation. Although this has been an active area of study in recent years, the existing literature is almost entirely devoted to incompressible fluids. The purpose of this thesis is to take a step forward in addressing this statistical perspective in the setting of compressible fluids. In particular, we study the well posedness for the corresponding system of Stochastic Navier Stokes equations, satisfied by the density, velocity, and temperature. The evolution of the momentum involves a random forcing which is Brownian in time and colored in space. We allow for multiplicative noise, meaning that spatial correlations may depend locally on the fluid variables. Our main result is a proof of global existence of weak martingale solutions to the Cauchy problem set within a bounded domain, emanating from large initial datum. The proof involves a mix of deterministic and stochastic analysis tools. Fundamentally, the approach is based on weak compactness techniques from the deterministic theory combined with martingale methods. Four layers of approximate stochastic PDE's are built and analyzed. A careful study of the probability laws of our approximating sequences is required. We prove appropriate tightness results and appeal to a recent generalization of the Skorohod theorem. This ultimately allows us to deduce analogues of the weak compactness tools of Lions and Feireisl, appropriately interpreted in the stochastic setting.

Energy Cooperation in Energy Harvesting Communication Systems

In energy harvesting communications, users transmit messages using energy harvested from nature. In such systems, transmission policies of the users need to be carefully designed according to the energy arrival profiles. When the energy management policies are optimized, the resulting performance of the system depends only on the energy arrival profiles. In this dissertation, we introduce and analyze the notion of energy cooperation in energy harvesting communications where users can share a portion of their harvested energy with the other users via wireless energy transfer. This energy cooperation enables us to control and optimize the energy arrivals at users to the extent possible. In the classical setting of cooperation, users help each other in the transmission of their data by exploiting the broadcast nature of wireless communications and the resulting overheard information. In contrast to the usual notion of cooperation, which is at the signal level, energy cooperation we introduce here is at the battery energy level. In a multi-user setting, energy may be abundant in one user in which case the loss incurred by transferring it to another user may be less than the gain it yields for the other user. It is this cooperation that we explore in this dissertation for several multi-user scenarios, where energy can be transferred from one user to another through a separate wireless energy transfer unit. We first consider the offline optimal energy management problem for several basic multi-user network structures with energy harvesting transmitters and one-way wireless energy transfer. In energy harvesting transmitters, energy arrivals in time impose energy causality constraints on the transmission policies of the users. In the presence of wireless energy transfer, energy causality constraints take a new form: energy can flow in time from the past to the future for each user, and from one user to the other at each time. This requires a careful joint management of energy flow in two separate dimensions, and different management policies are required depending on how users share the common wireless medium and interact over it. In this context, we analyze several basic multi-user energy harvesting network structures with wireless energy transfer. To capture the main trade-offs and insights that arise due to wireless energy transfer, we focus our attention on simple two- and three-user communication systems, such as the relay channel, multiple access channel and the two-way channel. Next, we focus on the delay minimization problem for networks. We consider a general network topology of energy harvesting and energy cooperating nodes. Each node harvests energy from nature and all nodes may share a portion of their harvested energies with neighboring nodes through energy cooperation. We consider the joint data routing and capacity assignment problem for this setting under fixed data and energy routing topologies. We determine the joint routing of energy and data in a general multi-user scenario with data and energy transfer. Next, we consider the cooperative energy harvesting diamond channel, where the source and two relays harvest energy from nature and the physical layer is modeled as a concatenation of a broadcast and a multiple access channel. Since the broadcast channel is degraded, one of the relays has the message of the other relay. Therefore, the multiple access channel is an extended multiple access channel with common data. We determine the optimum power and rate allocation policies of the users in order to maximize the end-to-end throughput of this system. Finally, we consider the two-user cooperative multiple access channel with energy harvesting users. The users cooperate at the physical layer (data cooperation) by establishing common messages through overheard signals and then cooperatively sending them. For this channel model, we investigate the effect of intermittent data arrivals to the users. We find the optimal offline transmit power and rate allocation policy that maximize the departure region. When the users can further cooperate at the battery level (energy cooperation), we find the jointly optimal offline transmit power and rate allocation policy together with the energy transfer policy that maximize the departure region.