All unitary cubic curvature gravities in D dimensions

We construct all the unitary cubic curvature gravity theories built on the contractions of the Riemann tensor in D -dimensional (anti)-de Sitter spacetimes. Our construction is based on finding the equivalent quadratic action for the general cubic curvature theory and imposing ghost and tachyon freedom, which greatly simplifies the highly complicated problem of finding the propagator of cubic curvature theories in constant curvature backgrounds. To carry out the procedure we have also classified all the unitary quadratic models. We use our general results to study the recently found cubic curvature theories using different techniques and the string generated cubic curvature gravity model. We also study the scattering in critical gravity and give its cubic curvature extensions.Comment: 24 pages, 1 figure, v2: A subsection on cubic curvature extensions of critical gravity is added, v3: The part regarding critical gravity is revised. Version to appear in Class. Quant. Gra

Finite-Dimensional Calculus

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional references include

Conservative Policy Construction Using Variational Autoencoders for Logged Data With Missing Values

In high-stakes applications of data-driven decision-making such as healthcare, it is of paramount importance to learn a policy that maximizes the reward while avoiding potentially dangerous actions when there is uncertainty. There are two main challenges usually associated with this problem. First, learning through online exploration is not possible due to the critical nature of such applications. Therefore, we need to resort to observational datasets with no counterfactuals. Second, such datasets are usually imperfect, additionally cursed with missing values in the attributes of features. In this article, we consider the problem of constructing personalized policies using logged data when there are missing values in the attributes of features in both training and test data. The goal is to recommend an action (treatment) when ~X, a degraded version of Xwith missing values, is observed. We consider three strategies for dealing with missingness. In particular, we introduce the conservative strategy where the policy is designed to safely handle the uncertainty due to missingness. In order to implement this strategy, we need to estimate posterior distribution p(X|~X) and use a variational autoencoder to achieve this. In particular, our method is based on partial variational autoencoders (PVAEs) that are designed to capture the underlying structure of features with missing values

Gravitating Instantons In 3 Dimensions

We study the Einstein-Chern-Simons gravity coupled to Yang-Mills-Higgs theory in three dimensional Euclidean space with cosmological constant. The classical equations reduce to Bogomol'nyi type first order equations in curved space. There are BPS type gauge theory instanton (monopole) solutions of finite action in a gravitational instanton which itself has a finite action. We also discuss gauge theory instantons in the vacuum (zero action) AdS space. In addition we point out to some exact solutions which are singular.Comment: 17 pages, 4 figures, title has changed, gravitational instanton actions are adde

A Comparison of the LVDP and {\Lambda}CDM Cosmological Models

We compare the cosmological kinematics obtained via our law of linearly varying deceleration parameter (LVDP) with the kinematics obtained in the {\Lambda}CDM model. We show that the LVDP model is almost indistinguishable from the {\Lambda}CDM model up to the near future of our universe as far as the current observations are concerned, though their predictions differ tremendously into the far future.Comment: 6 pages, 5 figures, 1 table, matches the version to be published in International Journal of Theoretical Physic

A Non-Stochastic Learning Approach to Energy Efficient Mobility Management

Energy efficient mobility management is an important problem in modern wireless networks with heterogeneous cell sizes and increased nodes densities. We show that optimization-based mobility protocols cannot achieve long-Term optimal energy consumption, particularly for ultra-dense networks (UDNs). To address the complex dynamics of UDN, we propose a non-stochastic online-learning approach, which does not make any assumption on the statistical behavior of the small base station (SBS) activities. In addition, we introduce handover cost to the overall energy consumption, which forces the resulting solution to explicitly minimize frequent handovers. The proposed batched randomization with exponential weighting (BREW) algorithm relies on batching to explore in bulk, and hence reduces unnecessary handovers. We prove that the regret of BREW is sublinear in time, thus guaranteeing its convergence to the optimal SBS selection. We further study the robustness of the BREW algorithm to delayed or missing feedback. Moreover, we study the setting where SBSs can be dynamically turned ON and OFF. We prove that sublinear regret is impossible with respect to arbitrary SBS ON/OFF, and then develop a novel learning strategy, called ranking expert (RE), that simultaneously takes into account the handover cost and the availability of SBS. To address the high complexity of RE, we propose a contextual ranking expert (CRE) algorithm that only assigns experts in a given context. Rigorous regret bounds are proved for both RE and CRE with respect to the best expert. Simulations show that not only do the proposed mobility algorithms greatly reduce the system energy consumption, but they are also robust to various dynamics which are common in practical ultra-dense wireless networks. © 1983-2012 IEEE

Solid-State Diffusion Welding of Wrought AISI 304 Stainless Steel to Nimonic AP-1 Superalloy Powder by Hot Isostatic Pressing Dissimilar materials like stainless steels and powder metallurgy superalloys can be joined by diffusion welding using hot isostat

ABSTRACT. The diffusion welding characteristics of wrought AISI 304 stainless steel to a superalloy powder Nimonic AP-1 were examined in this study. After encapsulation, evacuation and degassing, the welds were hot isostatically pressed (HIPed) in two different cycles, i.e., 1200°C (2192°F)/3 h/147 MPa and 1270°C (2318°F)/3 h/121 MPa. A variation in surface condition of stainless steel was also studied for its influence on properties of the joints. These diffusionwelded joints were characterized for diffusion of alloying elements, microstructural features and tensile properties. Most specimens showed good weld strength for both the hot isostatic pressing (HIP) cycles, except specimens with sand blasted surfaces, which gave negligible ductility because of the presence of sand particles embedded on the surface. In general, the tensile properties of the diffusion welded specimens were limited by the mechanical properties of stainless steel and not the joint interface. The microstructural examination of a HIP welded joint showed a thin weld zone of 30-40 ~m. While the stainless steel region of the welded specimen showed a relatively clean structure, the Nimonic AP-1 region showed precipitation of dark particles near the interface extending over 20-60 pm. Electron microprobe analysis of the diffusion welded zone revealed enrichment of titanium-rich particles along prior particle boundaries (PPBs) near the interface. Electron microprobe analysis further revealed extensive diffusion of Ni, Co and AI elements into stainless steel and that of Fe into Nimonic AP-1 superalloy indicating complex composition of the weld interlayer. M. C. SOMANI and N. C. BIRLA, Scientists, are with Defence Metallurgical Research Laboratory, Hyderabad, India, and A. TEKIN is with th

Adaptive ensemble learning with confidence bounds for personalized diagnosis

With the advances in the field of medical informatics, automated clinical decision support systems are becoming the de facto standard in personalized diagnosis. In order to establish high accuracy and confidence in personalized diagnosis, massive amounts of distributed, heterogeneous, correlated and high-dimensional patient data from different sources such as wearable sensors, mobile applications, Electronic Health Record (EHR) databases etc. need to be processed. This requires learning both locally and globally due to privacy constraints and/or distributed nature of the multimodal medical data. In the last decade, a large number of meta-learning techniques have been proposed in which local learners make online predictions based on their locally-collected data instances, and feed these predictions to an ensemble learner, which fuses them and issues a global prediction. However, most of these works do not provide performance guarantees or, when they do, these guarantees are asymptotic. None of these existing works provide confidence estimates about the issued predictions or rate of learning guarantees for the ensemble learner. In this paper, we provide a systematic ensemble learning method called Hedged Bandits, which comes with both long run (asymptotic) and short run (rate of learning) performance guarantees. Moreover, we show that our proposed method outperforms all existing ensemble learning techniques, even in the presence of concept drift

ETutor: Online learning for personalized education

Given recent advances in information technology and artificial intelligence, web-based education systems have became complementary and, in some cases, viable alternatives to traditional classroom teaching. The popularity of these systems stems from their ability to make education available to a large demographics (see MOOCs). However, existing systems do not take advantage of the personalization which becomes possible when web-based education is offered: they continue to be one-size-fits-all. In this paper, we aim to provide a first systematic method for designing a personalized web-based education system. Personalizing education is challenging: (i) students need to be provided personalized teaching and training depending on their contexts (e.g. classes already taken, methods of learning preferred, etc.), (ii) for each specific context, the best teaching and training method (e.g type and order of teaching materials to be shown) must be learned, (iii) teaching and training should be adapted online, based on the scores/feedback (e.g. tests, quizzes, final exam, likes/dislikes etc.) of the students. Our personalized online system, e-Tutor, is able to address these challenges by learning how to adapt the teaching methodology (in this case what sequence of teaching material to present to a student) to maximize her performance in the final exam, while minimizing the time spent by the students to learn the course (and possibly dropouts). We illustrate the efficiency of the proposed method on a real-world eTutor platform which is used for remedial training for a Digital Signal Processing (DSP) course. © 2015 IEEE