Describing groups using first-order language

We investigate two notions about descriptions of groups using first-order language: quasi-finite axiomatizability, concerning infinite groups, and polylogarithmic compressibility, concerning classes of finite groups

Inner horns for 2-quasi-categories

Dimitri Ara's 2-quasi-categories, which are certain presheaves over Andr\'{e} Joyal's 2-cell category $\Theta_2$, are an example of a concrete model that realises the abstract notion of $(\infty,2)$-category. In this paper, we prove that the 2-quasi-categories and the fibrations into them can be characterised using the inner horn inclusions and the equivalence extensions introduced by David Oury. These maps are more tractable than the maps that Ara originally used and therefore our result can serve as a combinatorial foundation for the study of 2-quasi-categories.Comment: v3. 45 pages. Minor revision. Published version. [v2: Corrected an error in the proof of Lemma 3.4. Expanded/rewrote the proofs and added many pictures. Added a section on the Gray tensor product.

Submodular Stochastic Probing with Prices

We introduce Stochastic Probing with Prices (SPP), a variant of the Stochastic Probing (SP) model in which we must pay a price to probe an element. A SPP problem involves two set systems $(N,\mathcal{I}_{in})$ and $(N,\mathcal{I}_{out})$ where each $e\in N$ is active with probability $p_e$. To discover whether $e$ is active, it must be probed by paying the price $\Delta_e$. If it is probed and active, then it is irrevocably added to the solution. Moreover, at all times, the set of probed elements must lie in $\mathcal{I}_{out}$, and the solution (the set of probed and active elements) must lie in $\mathcal{I}_{in}$. The goal is to maximize a set function $f$ minus the cost of the probes. We give a bi-criteria approximation algorithm to the online version of this problem, in which the elements are shown to the algorithm in a possibly adversarial order. Our results translate to state-of-the-art approximations for the traditional (online) stochastic probing problem

Stochastic Packing Integer Programs with Few Queries

We consider a stochastic variant of the packing-type integer linear programming problem, which contains random variables in the objective vector. We are allowed to reveal each entry of the objective vector by conducting a query, and the task is to find a good solution by conducting a small number of queries. We propose a general framework of adaptive and non-adaptive algorithms for this problem, and provide a unified methodology for analyzing the performance of those algorithms. We also demonstrate our framework by applying it to a variety of stochastic combinatorial optimization problems such as matching, matroid, and stable set problems.Comment: The final draft of a paper published in Mathematical Programming (Series A

A Simple Way to Deal with Cherry-picking

Statistical hypothesis testing serves as statistical evidence for scientific innovation. However, if the reported results are intentionally biased, hypothesis testing no longer controls the rate of false discovery. In particular, we study such selection bias in machine learning models where the reporter is motivated to promote an algorithmic innovation. When the number of possible configurations (e.g., datasets) is large, we show that the reporter can falsely report an innovation even if there is no improvement at all. We propose a `post-reporting' solution to this issue where the bias of the reported results is verified by another set of results. The theoretical findings are supported by experimental results with synthetic and real-world datasets

Convex Hull Approximation of Nearly Optimal Lasso Solutions

In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study, instead of the single optimal solution, we consider finding a set of diverse yet nearly optimal solutions. To this end, we formulate the problem as finding a small number of solutions such that the convex hull of these solutions approximates the set of nearly optimal solutions. The proposed algorithm consists of two steps: First, we randomly sample the extreme points of the set of nearly optimal solutions. Then, we select a small number of points using a greedy algorithm. The experimental results indicate that the proposed algorithm can approximate the solution set well. The results also indicate that we can obtain Lasso solutions with a large diversity.Comment: 14page

Neural Inverse Rendering for General Reflectance Photometric Stereo

We present a novel convolutional neural network architecture for photometric stereo (Woodham, 1980), a problem of recovering 3D object surface normals from multiple images observed under varying illuminations. Despite its long history in computer vision, the problem still shows fundamental challenges for surfaces with unknown general reflectance properties (BRDFs). Leveraging deep neural networks to learn complicated reflectance models is promising, but studies in this direction are very limited due to difficulties in acquiring accurate ground truth for training and also in designing networks invariant to permutation of input images. In order to address these challenges, we propose a physics based unsupervised learning framework where surface normals and BRDFs are predicted by the network and fed into the rendering equation to synthesize observed images. The network weights are optimized during testing by minimizing reconstruction loss between observed and synthesized images. Thus, our learning process does not require ground truth normals or even pre-training on external images. Our method is shown to achieve the state-of-the-art performance on a challenging real-world scene benchmark.Comment: To appear in International Conference on Machine Learning 2018 (ICML 2018). 10 pages + 20 pages (appendices

Analysis of a Kepler Light Curve of the Novalike Cataclysmic Variable KIC 8751494

We analyzed a Kepler light curve of KIC 8751494, a recently recognized novalike cataclysmic variable in the Kepler field. We detected a stable periodicity of 0.114379(1) d, which we identified as being the binary's orbital period. The stronger photometric period around 0.12245 d, which had been detected from the ground-based observation, was found to be variable, and we identified this period as being the positive superhump period. This superhump period showed short-term (10-20 d) and strong variations in period most unexpectedly when the object entered a slightly faint state. The fractional superhump excess varied as large as ~30%. The variation of the period very well traced the variation of the brightness of the system. The time-scales of this variation of the superhump period was too slow to be interpreted as the variation caused by the change in the disk radius due to the thermal disk instability. We interpreted that the period variation was caused by the varying pressure effect on the period of positive superhumps. This finding suggests that the pressure effect, in at least novalike systems, plays a very important (up to ~30% in the precession rate) role in producing the period of the positive superhumps. We also described a possible detection of the negative superhumps with a varying period of 0.1071-0.1081 d in the Q14 run of the Kepler data. We also found that the phase of the velocity variation of the emission lines reported in the earlier study is compatible with the SW Sex-type classification. Further, we introduced a new two-dimentional period analysis using least absolute shrinkage and selection operator (Lasso) and showed superior advantage of this method.Comment: 10 pages, 8 figures, accepted for publication in PASJ, minor correcrtion

Mutual transformation among bound, virtual and resonance states in one-dimensional rectangular potentials

A detailed analysis has been made by R.Zavin and N.Moiseyev(2004 J. Phys. A: Math, Gen, \textbf{37} 4619) for the change of bound states into resonance states via coalescence of virtual states in a one-dimensional symmetric rectangular attractive potential as it becomes shallow, with convergent wave functions of virtual and resonance states by the complex scaling method. As a complement to such an analysis, we discuss some global features of the pole spectrum of the S-matrix by using a complex extension of the real potential $V^{(\mathrm{real})}$ to $e^{i\alpha}V^{(\mathrm{real})}$ with a real phase $\alpha$. We show the structures of trajectories of poles developed for the change of $\alpha$ in the complex momentum plane, which is useful to understand the mutual transformation among the bound, virtual and resonance states.Comment: 12 pages, 2 Fig's (each has 6 figures

Typical Approximation Performance for Maximum Coverage Problem

This study investigated typical performance of approximation algorithms known as belief propagation, greedy algorithm, and linear-programming relaxation for maximum coverage problems on sparse biregular random graphs. After using the cavity method for a corresponding hard-core lattice--gas model, results show that two distinct thresholds of replica-symmetry and its breaking exist in the typical performance threshold of belief propagation. In the low-density region, the superiority of three algorithms in terms of a typical performance threshold is obtained by some theoretical analyses. Although the greedy algorithm and linear-programming relaxation have the same approximation ratio in worst-case performance, their typical performance thresholds are mutually different, indicating the importance of typical performance. Results of numerical simulations validate the theoretical analyses and imply further mutual relations of approximation algorithms.Comment: 10 pages, 6 figure