Necessary and Probably Sufficient Test for Finding Valid Instrumental Variables

Can instrumental variables be found from data? While instrumental variable (IV) methods are widely used to identify causal effect, testing their validity from observed data remains a challenge. This is because validity of an IV depends on two assumptions, exclusion and as-if-random, that are largely believed to be untestable from data. In this paper, we show that under certain conditions, testing for instrumental variables is possible. We build upon prior work on necessary tests to derive a test that characterizes the odds of being a valid instrument, thus yielding the name "necessary and probably sufficient". The test works by defining the class of invalid-IV and valid-IV causal models as Bayesian generative models and comparing their marginal likelihood based on observed data. When all variables are discrete, we also provide a method to efficiently compute these marginal likelihoods. We evaluate the test on an extensive set of simulations for binary data, inspired by an open problem for IV testing proposed in past work. We find that the test is most powerful when an instrument follows monotonicity---effect on treatment is either non-decreasing or non-increasing---and has moderate-to-weak strength; incidentally, such instruments are commonly used in observational studies. Among as-if-random and exclusion, it detects exclusion violations with higher power. Applying the test to IVs from two seminal studies on instrumental variables and five recent studies from the American Economic Review shows that many of the instruments may be flawed, at least when all variables are discretized. The proposed test opens the possibility of data-driven validation and search for instrumental variables

On the homotopy theory of G\mathbf{G} - spaces

The aim of this paper is to show that the most elementary homotopy theory of $\mathbf{G}$-spaces is equivalent to a homotopy theory of simplicial sets over $\mathbf{BG}$, where $\mathbf{G}$ is a fixed group. Both homotopy theories are presented as Relative categories. We establish the equivalence by constructing a strict homotopy equivalence between the two relative categories. No Model category structure is assumed on either Relative Category

One and two-dimensional quantum models: quenches and the scaling of irreversible entropy

Using the scaling relation of the ground state quantum fidelity, we propose the most generic scaling relations of the irreversible work (the residual energy) of a closed quantum system at absolute zero temperature when one of the parameters of its Hamiltonian is suddenly changed; we consider two extreme limits namely, the heat susceptibility limit and the thermodynamic limit. It is then argued that the irreversible entropy generated for a thermal quench at low enough temperature when the system is initially in a Gibbs state, is likely to show a similar scaling behavior. To illustrate this proposition, we consider zero-temperature and thermal quenches in one and two-dimensional Dirac Hamiltonians where the exact estimation of the irreversible work and the irreversible entropy is indeed possible. Exploiting these exact results, we then establish: (i) the irreversible work at zero temperature indeed shows an appropriate scaling in the thermodynamic limit; (ii) the scaling of the irreversible work in the 1D Dirac model at zero-temperature shows logarithmic corrections to the scaling which is a signature of a marginal situation. (iii) Furthermore, remarkably the logarithmic corrections do indeed appear in the scaling of the entropy generated if temperature is low enough while disappears for high temperatures. For the 2D model, no such logarithmic correction is found to appear.Comment: 7 pages, 6 figure

Experimental realization of mixed-synchronization in counter-rotating coupled oscillators

Recently, a novel mixed-synchronization phenomenon is observed in counter-rotating nonlinear coupled oscillators. In mixed-synchronization state: some variables are synchronized in-phase, while others are out-of-phase. We have experimentally verified the occurrence of mixed-synchronization states in coupled counter-rotating chaotic piecewise Rossler oscillator. Analytical discussion on approximate stability analysis and numerical confirmation on the experimentally observed behavior is also given

Categorification of Dijkgraaf-Witten Theory

The goal of the paper is to categorify Dijkgraaf-Witten theory, aiming at providing foundation for a direct construction of Dijkgraaf-Witten theory as an Extended Topological Quantum Field Theory. The main tool is cohomology with coefficients in a Picard groupoid, namely the Picard groupoid of hermitian lines.Comment: 28 pages; submitted version containing minor modification

New Silicon Carbide (SiC) Hetero-Junction Darlington Transistor

Basic SiC bipolar transistors have been studied in the past for their applications where high power or high temperature operation is required. However since the current gain in SiC bipolar transistors is very low and therefore, a large base drive is required in high current applications. Therefore, it is important to enhance the current gain of SiC bipolar transistors. Using two dimensional mixed mode device and circuit simulation, for the first time, we report a new Darlington transistor formed using two polytypes 3C-SiC and 4H-SiC having a very high current gain as a result of the heterojunction formation between the emitter and the base of transistor. The reasons for the improved performance are analyzed.Comment: http://web.iitd.ac.in/~mamidala

Tuning the presence of dynamical phase transitions in a generalized XYXY spin chain

We study an integrable spin chain with three spin interactions and the staggered field ($\lambda$) while the latter is quenched either slowly (in a linear fashion in time ($t$) as $t/\tau$ where $t$ goes from a large negative value to a large positive value and $\tau$ is the inverse rate of quenching) or suddenly. In the process, the system crosses quantum critical points and gapless phases. We address the question whether there exist non-analyticities (known as dynamical phase transitions (DPTs)) in the subsequent real time evolution of the state (reached following the quench) governed by the final time-independent Hamiltonian. In the case of sufficiently slow quenching (when $\tau$ exceeds a critical value $\tau_1$), we show that DPTs, of the form similar to those occurring for quenching across an isolated critical point, can occur even when the system is slowly driven across more than one critical point and gapless phases. More interestingly, in the anisotropic situation we show that DPTs can completely disappear for some values of the anisotropy term ($\gamma$) and $\tau$, thereby establishing the existence of boundaries in the $(\gamma-\tau)$ plane between the DPT and no-DPT regions in both isotropic and anisotropic cases. Our study therefore leads to a unique situation when DPTs may not occur even when an integrable model is slowly ramped across a QCP. On the other hand, considering sudden quenches from an initial value $\lambda_i$ to a final value $\lambda_f$, we show that the condition for the presence of DPTs is governed by relations involving $\lambda_i$, $\lambda_f$ and $\gamma$ and the spin chain must be swept across $\lambda=0$ for DPTs to occur.Comment: 8 pages, 5 figure

Predictability of Popularity: Gaps between Prediction and Understanding

Can we predict the future popularity of a song, movie or tweet? Recent work suggests that although it may be hard to predict an item's popularity when it is first introduced, peeking into its early adopters and properties of their social network makes the problem easier. We test the robustness of such claims by using data from social networks spanning music, books, photos, and URLs. We find a stronger result: not only do predictive models with peeking achieve high accuracy on all datasets, they also generalize well, so much so that models trained on any one dataset perform with comparable accuracy on items from other datasets. Though practically useful, our models (and those in other work) are intellectually unsatisfying because common formulations of the problem, which involve peeking at the first small-k adopters and predicting whether items end up in the top half of popular items, are both too sensitive to the speed of early adoption and too easy. Most of the predictive power comes from looking at how quickly items reach their first few adopters, while for other features of early adopters and their networks, even the direction of correlation with popularity is not consistent across domains. Problem formulations that examine items that reach k adopters in about the same amount of time reduce the importance of temporal features, but also overall accuracy, highlighting that we understand little about why items become popular while providing a context in which we might build that understanding.Comment: 10 pages, ICWSM 201

A Framework for Prefetching Relevant Web Pages using Predictive Prefetching Engine (PPE)

This paper presents a framework for increasing the relevancy of the web pages retrieved by the search engine. The approach introduces a Predictive Prefetching Engine (PPE) which makes use of various data mining algorithms on the log maintained by the search engine. The underlying premise of the approach is that in the case of cluster accesses, the next pages requested by users of the Web server are typically based on the current and previous pages requested. Based on same, rules are drawn which then lead the path for prefetching the desired pages. To carry out the desired task of prefetching the more relevant pages, agents have been introduced.Comment: 9 page

Symmetric monoidal categories and Γ\Gamma-categories

In this paper we construct a symmetric monoidal closed model category of coherently commutative monoidal categories. The main aim of this paper is to establish a Quillen equivalence between a model category of coherently commutative monoidal categories and a natural model category of Permutative (or strict symmetric monoidal) categories, $\mathbf{Perm}$, which is not a symmetric monoidal closed model category. The right adjoint of this Quillen equivalence is the classical Segal's Nerve functor