Counting Value Sets: Algorithm and Complexity

Let $p$ be a prime. Given a polynomial in \F_{p^m}[x] of degree $d$ over the finite field \F_{p^m}, one can view it as a map from \F_{p^m} to \F_{p^m}, and examine the image of this map, also known as the value set. In this paper, we present the first non-trivial algorithm and the first complexity result on computing the cardinality of this value set. We show an elementary connection between this cardinality and the number of points on a family of varieties in affine space. We then apply Lauder and Wan's $p$-adic point-counting algorithm to count these points, resulting in a non-trivial algorithm for calculating the cardinality of the value set. The running time of our algorithm is $(pmd)^{O(d)}$. In particular, this is a polynomial time algorithm for fixed $d$ if $p$ is reasonably small. We also show that the problem is #P-hard when the polynomial is given in a sparse representation, $p=2$, and $m$ is allowed to vary, or when the polynomial is given as a straight-line program, $m=1$ and $p$ is allowed to vary. Additionally, we prove that it is NP-hard to decide whether a polynomial represented by a straight-line program has a root in a prime-order finite field, thus resolving an open problem proposed by Kaltofen and Koiran in \cite{Kaltofen03,KaltofenKo05}

Diagnosis of the Coenosia pedella-group (Diptera: Muscidae), with descriptions of three new species from China

The Coenosia pedella-group is established and defined by the combination of the following characters: most species have one presutural dorsocentral seta, costa reaching the tip of media vein, abdomen with distinct spots, hind tibia with dorsal setae, lower calypter at least subequal in length to upper calypter, basis of cerci and surstyli of male short, length of cerci at most four times as long as its width, most of cerci enlarged in distal 1/3 and surstyli subtriangular with width of basal part longer than 1/3 of length. Three new species are described: C. disclambosa Xue & Wang sp. n., C. maoershanensis Xue & Wang sp. n. and C. sublacteipennis Xue&Wang sp. n. A key to the males of Palaearctic Region species of the Coenosia pedella-group is given

Three new species of the Phaonia acerba group (Diptera: Muscidae) from Palaearctic and Oriental Regions

Three new species of the Phaonia acerba group fromthe Palaearctic and Oriental Regions are described: P. gaoligongshanensis Xue & Yu, sp. n., P. zhangxianggi Xue & Yu, sp. n. and P. hongkuii Xue & Yu, sp. n. An identification key to the males of 8 species of the Phaonia acerba group from the Palaearctic and Oriental Regions is provided

Internal Model Controller Design Method in Discrete Non-square Multivariable System

the discrete controller has begun to play an important role in the process industry, thus leading internal model controller, which has good tracking performance, become the focus of the researchers ’ study [1]. Meanwhile, industrial field exists a large number of non-square multivariable systems, therefore it is significantly practical to study on non-square system. So this paper puts forward the design scheme of internal model controller, based on the discrete control system. At first, the paper presents the concept of discrete channel gain, and through discrete channels relative gain, square subsystem can be chose from non-square system. Then by using the square subsystem, the controller is designed. However, if the system is designed in this way, the control effect and the robustness of system will not be perfect. To solve this problem, we add a low pass filter based on the original control system. Through this way, the robustness and stability of the system will be increase. Copyright © 2013 IFSA

One-step implementation of multi-qubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity

The diamond nitrogen-vacancy (NV) center is an excellent candidate for quantum information processing, whereas entangling separate NV centers is still of great experimental challenge. We propose an one-step conditional phase flip with three NV centers coupled to a whispering-gallery mode cavity by virtue of the Raman transition and smart qubit encoding. As decoherence is much suppressed, our scheme could work for more qubits. The experimental feasibility is justified.Comment: 3 pages, 2 figures, Accepted by Appl. Phys. Let

STEEL: Singularity-aware Reinforcement Learning

Batch reinforcement learning (RL) aims at leveraging pre-collected data to find an optimal policy that maximizes the expected total rewards in a dynamic environment. Nearly all existing algorithms rely on the absolutely continuous assumption on the distribution induced by target policies with respect to the data distribution, so that the batch data can be used to calibrate target policies via the change of measure. However, the absolute continuity assumption could be violated in practice (e.g., no-overlap support), especially when the state-action space is large or continuous. In this paper, we propose a new batch RL algorithm without requiring absolute continuity in the setting of an infinite-horizon Markov decision process with continuous states and actions. We call our algorithm STEEL: SingulariTy-awarE rEinforcement Learning. Our algorithm is motivated by a new error analysis on off-policy evaluation, where we use maximum mean discrepancy, together with distributionally robust optimization, to characterize the error of off-policy evaluation caused by the possible singularity and to enable model extrapolation. By leveraging the idea of pessimism and under some mild conditions, we derive a finite-sample regret guarantee for our proposed algorithm without imposing absolute continuity. Compared with existing algorithms, by requiring only minimal data-coverage assumption, STEEL significantly improves the applicability and robustness of batch RL. Extensive simulation studies and one real experiment on personalized pricing demonstrate the superior performance of our method in dealing with possible singularity in batch RL

Function annotation of hepatic retinoid x receptor α based on genome-wide DNA binding and transcriptome profiling.

BackgroundRetinoid x receptor α (RXRα) is abundantly expressed in the liver and is essential for the function of other nuclear receptors. Using chromatin immunoprecipitation sequencing and mRNA profiling data generated from wild type and RXRα-null mouse livers, the current study identifies the bona-fide hepatic RXRα targets and biological pathways. In addition, based on binding and motif analysis, the molecular mechanism by which RXRα regulates hepatic genes is elucidated in a high-throughput manner.Principal findingsClose to 80% of hepatic expressed genes were bound by RXRα, while 16% were expressed in an RXRα-dependent manner. Motif analysis predicted direct repeat with a spacer of one nucleotide as the most prevalent RXRα binding site. Many of the 500 strongest binding motifs overlapped with the binding motif of specific protein 1. Biological functional analysis of RXRα-dependent genes revealed that hepatic RXRα deficiency mainly resulted in up-regulation of steroid and cholesterol biosynthesis-related genes and down-regulation of translation- as well as anti-apoptosis-related genes. Furthermore, RXRα bound to many genes that encode nuclear receptors and their cofactors suggesting the central role of RXRα in regulating nuclear receptor-mediated pathways.ConclusionsThis study establishes the relationship between RXRα DNA binding and hepatic gene expression. RXRα binds extensively to the mouse genome. However, DNA binding does not necessarily affect the basal mRNA level. In addition to metabolism, RXRα dictates the expression of genes that regulate RNA processing, translation, and protein folding illustrating the novel roles of hepatic RXRα in post-transcriptional regulation