Unique End of Potential Line

This paper studies the complexity of problems in PPAD $\cap$ PLS that have unique solutions. Three well-known examples of such problems are the problem of finding a fixpoint of a contraction map, finding the unique sink of a Unique Sink Orientation (USO), and solving the P-matrix Linear Complementarity Problem (P-LCP). Each of these are promise-problems, and when the promise holds, they always possess unique solutions. We define the complexity class UEOPL to capture problems of this type. We first define a class that we call EOPL, which consists of all problems that can be reduced to End-of-Potential-Line. This problem merges the canonical PPAD-complete problem End-of-Line, with the canonical PLS-complete problem Sink-of-Dag, and so EOPL captures problems that can be solved by a line-following algorithm that also simultaneously decreases a potential function. Promise-UEOPL is a promise-subclass of EOPL in which the line in the End-of-Potential-Line instance is guaranteed to be unique via a promise. We turn this into a non-promise class UEOPL, by adding an extra solution type to EOPL that captures any pair of points that are provably on two different lines. We show that UEOPL $\subseteq$ EOPL $\subseteq$ CLS, and that all of our motivating problems are contained in UEOPL: specifically USO, P-LCP, and finding a fixpoint of a Piecewise-Linear Contraction under an $\ell_p$-norm all lie in UEOPL. Our results also imply that parity games, mean-payoff games, discounted games, and simple-stochastic games lie in UEOPL. All of our containment results are proved via a reduction to a problem that we call One-Permutation Discrete Contraction (OPDC). This problem is motivated by a discretized version of contraction, but it is also closely related to the USO problem. We show that OPDC lies in UEOPL, and we are also able to show that OPDC is UEOPL-complete.Comment: This paper substantially revises and extends the work described in our previous preprint "End of Potential Line'' (arXiv:1804.03450). The abstract has been shortened to meet the arXiv character limi

Unique End of Potential Line

This paper studies the complexity of problems in PPAD $\cap$ PLS that have unique solutions. Three well-known examples of such problems are the problem of finding a fixpoint of a contraction map, finding the unique sink of a Unique Sink Orientation (USO), and solving the P-matrix Linear Complementarity Problem (P-LCP). Each of these are promise-problems, and when the promise holds, they always possess unique solutions. We define the complexity class UEOPL to capture problems of this type. We first define a class that we call EOPL, which consists of all problems that can be reduced to End-of-Potential-Line. This problem merges the canonical PPAD-complete problem End-of-Line, with the canonical PLS-complete problem Sink-of-Dag, and so EOPL captures problems that can be solved by a line-following algorithm that also simultaneously decreases a potential function. Promise-UEOPL is a promise-subclass of EOPL in which the line in the End-of-Potential-Line instance is guaranteed to be unique via a promise. We turn this into a non-promise class UEOPL, by adding an extra solution type to EOPL that captures any pair of points that are provably on two different lines. We show that UEOPL $\subseteq$ EOPL $\subseteq$ CLS, and that all of our motivating problems are contained in UEOPL: specifically USO, P-LCP, and finding a fixpoint of a Piecewise-Linear Contraction under an $\ell_p$-norm all lie in UEOPL. Our results also imply that parity games, mean-payoff games, discounted games, and simple-stochastic games lie in UEOPL. All of our containment results are proved via a reduction to a problem that we call One-Permutation Discrete Contraction (OPDC). This problem is motivated by a discretized version of contraction, but it is also closely related to the USO problem. We show that OPDC lies in UEOPL, and we are also able to show that OPDC is UEOPL-complete

PACS and SPIRE range spectroscopy of cool, evolved stars

Context: At the end of their lives AGB stars are prolific producers of dust and gas. The details of this mass-loss process are still not understood very well. Herschel PACS and SPIRE spectra offer a unique way of investigating properties of AGB stars in general and the mass-loss process in particular. Methods: The HIPE software with the latest calibration is used to process the available PACS and SPIRE spectra of 40 evolved stars. The spectra are convolved with the response curves of the PACS and SPIRE bolometers and compared to the fluxes measured in imaging data of these sources. Custom software is used to identify lines in the spectra, and to determine the central wavelengths and line intensities. Standard molecular line databases are used to associate the observed lines. Because of the limited spectral resolution of the spectrometers several known lines are typically potential counterparts to any observed line. To help identifications the relative contributions in line intensity of the potential counterpart lines are listed for three characteristic temperatures based on LTE calculations and assuming optically thin emission. Result: The following data products are released: the reduced spectra, the lines that are measured in the spectra with wavelength, intensity, potential identifications, and the continuum spectra, i.e. the full spectra with all identified lines removed. As simple examples of how this data can be used in future studies we have fitted the continuum spectra with three power laws and find that the few OH/IR stars seem to have significantly steeper slopes than the other oxygen- and carbon-rich objects in the sample. As another example we constructed rotational diagrams for CO and fitted a two-component model to derive rotational temperatures.Comment: A&A accepte

A Multidimensional Approach to Product Advertisement in the Virtual Environment

Internet presents a new business environment with great potential for marketers. Virtual retailing / e-shops, in particular, own the unique property of combining advertising practices and on-line sales functionality. In that context, the consumer buying process may be completed from start to end, from the need recognition stage, initiated by advertising, to the purchase decision stage, in an easy and integrated way. Thus, the role of interactive advertisement in this environment is crucial. In this paper, we examine the characteristics and potential of interactive advertisement in virtual retailing and propose a multidimensional approach to product advertisement in the virtual store, taking into account the consumer, retailer and supplier perspective

Identification of a novel ß-adrenergic octopamine receptor-like gene (ßAOR-like) and increased ATP-binding cassette B10 (ABCB10) expression in a Rhipicephalus microplus cell line derived from acaricide-resistant ticks

Background: The cattle tick Rhipicephalus (Boophilus) microplus is an economically important parasite of livestock. Effective control of ticks using acaricides is threatened by the emergence of resistance to many existing compounds. Several continuous R. microplus cell lines have been established and provide an under-utilised resource for studies into acaricide targets and potential genetic mutations associated with resistance. As a first step to genetic studies using these resources, this study aimed to determine the presence or absence of two genes and their transcripts that have been linked with acaricide function in cattle ticks: β-adrenergic octopamine receptor (βAOR, associated with amitraz resistance) and ATP-binding cassette B10 (ABCB10, associated with macrocyclic lactone resistance) in six R. microplus cell lines, five other Rhipicephalus spp. cell lines and three cell lines representing other tick genera (Amblyomma variegatum, Ixodes ricinus and Hyalomma anatolicum). Methods: End-point polymerase chain reaction (PCR) was used for detection of the βAOR gene and transcripts in DNA and RNA extracted from the tick cell lines, followed by capillary sequencing of amplicons. Quantitative real-time PCR (qPCR) was performed to determine the levels of expression of ABCB10. Results: βAOR gene expression was detected in all Rhipicephalus spp. cell lines. We observed a second amplicon of approximately 220 bp for the βAOR gene in the R. microplus cell line BME/CTVM6, derived from acaricide-resistant ticks. Sequencing of this transcript variant identified a 36 bp insertion in the βAOR gene, leading to a 12-amino acid insertion (LLKTLALVTIIS) in the first transmembrane domain of the protein. In addition, nine synonymous SNPs were also discovered in R. appendiculatus, R. evertsi and R. sanguineus cell lines. Some of these SNPs appear to be unique to each species, providing potential tools for differentiating the tick species. The BME/CTVM6 cell line had significantly higher ABCB10 (P = 0.002) expression than the other R. micropluscell lines. Conclusions: The present study has identified a new βAOR gene and demonstrated a higher ABCB10 expression level in the BME/CTVM6 cell line, indicating that tick cell lines provide a useful experimental tool for acaricide resistance studies and further elucidation of tick genetics

Computational Complexity of the ?-Ham-Sandwich Problem

?_d from each set. Steiger and Zhao [DCG 2010] proved a discrete analogue of this theorem, which we call the ?-Ham-Sandwich theorem. They gave an algorithm to find the hyperplane in time O(n (log n)^{d-3}), where n is the total number of input points. The computational complexity of this search problem in high dimensions is open, quite unlike the complexity of the Ham-Sandwich problem, which is now known to be PPA-complete (Filos-Ratsikas and Goldberg [STOC 2019]). Recently, Fearnley, Gordon, Mehta, and Savani [ICALP 2019] introduced a new sub-class of CLS (Continuous Local Search) called Unique End-of-Potential Line (UEOPL). This class captures problems in CLS that have unique solutions. We show that for the ?-Ham-Sandwich theorem, the search problem of finding the dividing hyperplane lies in UEOPL. This gives the first non-trivial containment of the problem in a complexity class and places it in the company of classic search problems such as finding the fixed point of a contraction map, the unique sink orientation problem and the P-matrix linear complementarity problem

Deep Generative Model for Simultaneous Range Error Mitigation and Environment Identification

Received waveforms contain rich information for both range information and environment semantics. However, its full potential is hard to exploit under multipath and non-line-of-sight conditions. This paper proposes a deep generative model (DGM) for simultaneous range error mitigation and environment identification. In particular, we present a Bayesian model for the generative process of the received waveform composed by latent variables for both range-related features and environment semantics. The simultaneous range error mitigation and environment identification is interpreted as an inference problem based on the DGM, and implemented in a unique end-to-end learning scheme. Comprehensive experiments on a general Ultra-wideband dataset demonstrate the superior performance on range error mitigation, scalability to different environments, and novel capability on simultaneous environment identification.Comment: 6 pages, 5 figures, Published in: 2021 IEEE Global Communications Conference (GLOBECOM

Enabling end-to-end continuous biomanufacturing by exploring integration approaches of continuous TFF

The Downstream Processing (DSP) production/process line comprises of several chromatographic process unit operations (techniques for protein isolation and purification), several liquid filtrations process unit operations and final Ultrafiltration/Diafiltration (UF/DF) process unit operation (process for product concentration to the desired final protein concentration and for exchange into final formulation buffering condition). UF/DF step is conventionally performed with the batch tangential flow filtration (TFF). However, several pump passes and a recirculation skid are required to achieve the target concentration in conventional TFF. Thus, it is impractical to implement batch TFF as continuous UF/DF step or in-line concentration step between different DSP chromatographic steps. In this work the use of single-pass tangential flow filtration (SPTFF) will be examined as continuous TFF step and as the integrational process unit operation allowing both final UF/DF step and in-line protein concentration before chromatographic step. SPTFF integration approach will be explored as continuous TFF delivering a new robust solution with a potential to overcome manufacturing bottlenecks and thus enabling the end-to-end fully continuous biomanufacturing. In this study, the process stability, volumetric concentration factor (VCF) ranges, and process economics of operating SPTFF as continuous in-line UF/DF will be explored in detail. Additionally, the placement of the SPTFF before Protein A capture chromatography unit operation will be explored. This allows coupling of these two steps and as such the potential solution to overcome low and variable protein concentration in the harvest to intensify continuous process. Limitations and requirements for a continuous TFF will be identified. Unique challenges to use technology in a fully continuous UF/DF process step, which is at an earlier phase in development, will also be presented. Please click Additional Files below to see the full abstract

The method of verse translation: dictum-modus potential (peculiarities of content and form)

The article presents the hypothesis that the method of a verse translation is determined by its dictum-modus potential expressed both explicitly and implicitly. The rhythm-syntactic level of the poem specifically organizes implicit content of the poem that is proved by a comparative verse analysis. The method of translation chosen by the author reflects dictum-modus potential of original texts and a unique style of the author-translator. This hypothesis is checked on the material of I. Bunin’s poem «Молодость» and its translation into English by I. Zheleznova “Youth”. The verse is studied as a special form of verbal organization that is not similar either to the piece of music or to the prose. The verbal form of the verse (determined by its composition, syntax and probably unique author’s characteristics) results in the necessity of implicit pragmatic information, while prose conveys to the recipient this extra linguistic information explicitly. Due to this fact, there are some specific forms and content peculiarities of the verse. The hypothesis of this article is that some line positions in a poem are “semantically strong” and others are “semantically weak”. “Semantically strong” positions are determined, on one hand, by the poem structure: this is the end of the line, stanza or the whole poem. This rhythmical structure is the semantic representation of a poem. The rhythm is capable of emphasizing the psychological verse content. On the other hand, semantically strong position is made by the syntax. The dictummodus comparative analysis of verse lets us speak about the dictum-modus potential of the original and translated poetic texts. The research interest is focused on the extra language categories of the poetic texts, expressed through the rhythmical-syntactic poem structures (strong poetic and syntactic positions), lexical-semantic repetitions of significant words. These language structures model the original text conceptual structures and are actualized in translated poetic texts. In I. Zheleznova’s translation the central poem image of youth created by I. Bunin according to the principal of contrast seasonal description is changed. In the translation there prevail the audial images expressing, probably, the translator’s autobiographical mood. The lyrical mood of the poem is expressed in the original through the strong positions (the end of the line and neutral order changes), also through poem content connections made by the lexemes