Zero-order Reverse Filtering

In this paper, we study an unconventional but practically meaningful reversibility problem of commonly used image filters. We broadly define filters as operations to smooth images or to produce layers via global or local algorithms. And we raise the intriguingly problem if they are reservable to the status before filtering. To answer it, we present a novel strategy to understand general filter via contraction mappings on a metric space. A very simple yet effective zero-order algorithm is proposed. It is able to practically reverse most filters with low computational cost. We present quite a few experiments in the paper and supplementary file to thoroughly verify its performance. This method can also be generalized to solve other inverse problems and enables new applications.Comment: 9 pages, submitted to conferenc

Microscopic flows of suspensions of the green non-motile Chlorella micro-alga at various volume fractions: applications to intensified photo bio reactors

An experimental study of flows of the green non-motile Chlorella micro-alga in a plane microchannel is presented. Depending on the value of the cell volume fraction, three distinct flow regimes are observed. For low values of the cell volume fraction a Newtonian flow regime characterised by a Poiseuille like flow field, absence of wall slip and hydrodynamic reversibility of the flow states is observed. For intermediate values of the cell volume fraction, the flow profiles are consistent with a Poiseuille flow of a shear thinning fluid in the presence of slip at the channel's wall. For even larger cell volume fractions, a yield stress like behaviour manifested through the presence of a central solid plug is observed. Except for the Newtonian flow regime, a strong hydrodynamic irreversibility of the flow and wall slip are found. The calculation of the wall shear rate and wall stress based on the measured flow fields allows one to identify the mechanisms of wall slip observed in the shear thinning and yield stress regimes

Reversible Architectures for Arbitrarily Deep Residual Neural Networks

Recently, deep residual networks have been successfully applied in many computer vision and natural language processing tasks, pushing the state-of-the-art performance with deeper and wider architectures. In this work, we interpret deep residual networks as ordinary differential equations (ODEs), which have long been studied in mathematics and physics with rich theoretical and empirical success. From this interpretation, we develop a theoretical framework on stability and reversibility of deep neural networks, and derive three reversible neural network architectures that can go arbitrarily deep in theory. The reversibility property allows a memory-efficient implementation, which does not need to store the activations for most hidden layers. Together with the stability of our architectures, this enables training deeper networks using only modest computational resources. We provide both theoretical analyses and empirical results. Experimental results demonstrate the efficacy of our architectures against several strong baselines on CIFAR-10, CIFAR-100 and STL-10 with superior or on-par state-of-the-art performance. Furthermore, we show our architectures yield superior results when trained using fewer training data.Comment: Accepted at AAAI 201

The role of the time-arrow in mean-square estimation of stochastic processes

The purpose of this paper is to explain a certain dichotomy between the information that the past and future values of a multivariate stochastic process carry about the present. More specifically, vector-valued, second-order stochastic processes may be deterministic in one time-direction and not the other. This phenomenon, which is absent in scalar-valued processes, is deeply rooted in the geometry of the shift-operator. The exposition and the examples we discuss are based on the work of Douglas, Shapiro and Shields on cyclic vectors of the backward shift and relate to classical ideas going back to Wiener and Kolmogorov. We focus on rank-one stochastic processes for which we present a characterization of all regular processes that are deterministic in the reverse time-direction. The paper builds on examples and the goal is to provide pertinent insights to a control engineering audience.Comment: 6 page

Reversible Disjoint Unions of Well Orders and Their Inverses

A poset ${\mathbb{P}}$ is called reversible iff every bijective homomorphism $f:{\mathbb{P}} \rightarrow {\mathbb{P}}$ is an automorphism. Let ${\mathcal{W}}$ and ${\mathcal{W}} ^*$ denote the classes of well orders and their inverses respectively. We characterize reversibility in the class of posets of the form ${\mathbb{P}} =\bigcup _{i\in I}{\mathbb{L}} _i$, where ${\mathbb{L}} _i, i\in I$, are pairwise disjoint linear orders from ${\mathcal{W}} \cup {\mathcal{W}} ^*$. First, if ${\mathbb{L}} _i \in {\mathcal{W}}$, for all $i\in I$, and ${\mathbb{L}} _i \cong \alpha _i =\gamma_i+n_i\in Ord$, where $\gamma_i\in Lim \cup \{0\}$ and $n_i\in\omega$, defining $I_\alpha := \{ i\in I : \alpha_i = \alpha \}$, for $\alpha \in Ord$, and $J_\gamma := \{ j\in I : \gamma_j = \gamma \}$, for $\gamma\in Lim _0$, we prove that $\bigcup _{i\in I} {\mathbb{L}} _i$ is a reversible poset iff $\langle \alpha _i :i\in I\rangle$ is a finite-to-one sequence, or there is $\gamma =\max \{ \gamma _i : i\in I\}$, for $\alpha \leq \gamma$ we have $|I_\alpha |<\omega$, and $\langle n_i : i\in J_\gamma \setminus I_\gamma \rangle$ is a reversible sequence of natural numbers. The same holds when ${\mathbb{L}} _i \in {\mathcal{W}} ^*$, for all $i\in I$. In the general case, the reversibility of the whole union is equivalent to the reversibility of the union of components from ${\mathcal{W}}$ and the union of components from ${\mathcal{W}} ^*$.Comment: 12 page

Two-dimensional nonseparable discrete linear canonical transform based on CM-CC-CM-CC decomposition

As a generalization of the two-dimensional Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics, signal and image processing. To reduce the digital implementation complexity of the 2D NsLCT, some previous works decomposed the 2D NsLCT into several low-complexity operations, including 2D FT, 2D chirp multiplication (2D CM) and 2D affine transformations. However, 2D affine transformations will introduce interpolation error. In this paper, we propose a new decomposition called CM-CC-CM-CC decomposition, which decomposes the 2D NsLCT into two 2D CMs and two 2D chirp convolutions (2D CCs). No 2D affine transforms are involved. Simulation results show that the proposed methods have higher accuracy, lower computational complexity and smaller error in the additivity property compared with the previous works. Plus, the proposed methods have perfect reversibility property that one can reconstruct the input signal/image losslessly from the output.Comment: Accepted by Journal of the Optical Society of America A (JOSA A

Reconstructing quantum theory

We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map between pure states and maximal effects such that we get unit probability. This maximal effect does not give probability equal to one for any other pure state. Information Locality: A maximal measurement is effected on a composite system if we perform maximal measurements on each of the components. Tomographic Locality: The state of a composite system can be determined from the statistics collected by making measurements on the components. Permutability: There exists a reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. Sturdiness: Filters are non-flattening. To single out quantum theory we need only add any requirement that is inconsistent with classical probability theory and consistent with quantum theory.Comment: 27 PAGES. Contains summary of reconstruction part of arXiv:1104.2066. To appear in "Quantum Theory: Informational Foundations and Foils" edited by Guilio Chiribella and Robert Spekken

Generating controllable Laguerre-Gaussian laser modes through intracavity spin-orbital angular momentum conversion of light

The rapid developments in orbital-angular-momentum-carrying Laguerre-Gaussian (LG0 l) modes in recent years have facilitated progresses in optical communication, micromanipulation and quantum information. However, it is still challenging to efficiently generate bright, pure and selectable LG0 l laser modes in compact devices. Here, we demonstrate a low-threshold solid-state laser that can directly output selected high-purity LG0 l modes with high efficiency and controllability. Spin-orbital angular momentum conversion of light is used to reversibly convert the transverse modes inside cavity and determine the output mode index. The generated LG0 1 and LG0 2 laser modes have purities of ~97% and ~93% and slope efficiencies of ~11% and ~5.1%, respectively. Moreover, our cavity design can be easily extended to produce higher-order Laguerre-Gaussian modes and cylindrical vector beams. Such compact laser configuration features flexible control, low threshold, and robustness, making it a practical tool for applications in super-resolution imaging, high-precision interferometer and quantum correlations.Comment: 22 pages, 13 figure

Dynamical anomalies in terrestrial proxies of North Atlantic climate variability during the last 2 ka

Recent work has provided ample evidence that nonlinear methods of time series analysis potentially allow for detecting periods of anomalous dynamics in paleoclimate proxy records that are otherwise hidden to classical statis- tical analysis. Following upon these ideas, in this study we systematically test a set of Late Holocene terrestrial paleoclimate records from Northern Europe for indications of intermittent periods of time-irreversibility during which the data are incompatible with a stationary linear-stochastic process. Our analysis reveals that the onsets of both the Medieval Climate Anomaly and the Little Ice Age, the end of the Roman Warm Period and the Late Antique Little Ice Age have been characterized by such dynamical anomalies. These findings may indicate qualitative changes in the dominant regime of inter-annual climate variability in terms of large-scale atmospheric circula- tion patterns, ocean-atmosphere interactions and external forcings affecting the climate of the North Atlantic region

Experimental metrics for detection of detailed balance violation

We report on the measurement of detailed balance violation in a coupled, noise-driven linear electronic circuit consisting of two nominally identical RC elements that are coupled via a variable capacitance. The state variables are the time-dependent voltages across each of the two primary capacitors, and the system is driven by independent noise sources in series with each of the resistances. From the recorded time histories of these two voltages, we quantify violations of detailed balance by three methods: 1) explicit construction of the probability current density, 2) by constructing the time-dependent stochastic area, and 3) by constructing statistical fluctuation loops. In comparing the three methods, we find that the stochastic area is relatively simple to implement, computationally inexpensive, and provides a highly sensitive means for detecting violations of detailed balance.Comment: 12 pages, 6 figures, this version contains additional material relative to the previous on