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Abstract Out-of-distribution data points diverge from the general profile of the data, typically defined by the specific task for which the machine learning model is being constructed. Machine learning models are more reliable when out-of-distribution detection is part of the pipeline. Out-of-domain detection models are employed not just to sieve input into a model, but also to scrutinise output from a generative model, a process known as selective generation [1]. In literature, Mahalanobis distance is widely used in anomaly detection. In this work, we leverage the relation of Mahalanobis distance to Hotelling’s T-squared and Chi-squared distribution, which is further adapted for the inference on out-of-domain detection task. Data is usually categorised into three types: a) in-domain, b) out-of-domain, and c) background data. We explore approaches: a) constructed solely with in-domain data, and b) constructed using both in-domain and background data. Our proposed approaches are background free and efficient, and shows promising results compared to existing work in the literature which employ background data. We show that Hotelling’s T-square approach improves upon the Chi-square approach.

The usual Minimum Covariance Determinant (MCD) estimator of a covariance matrix is robust against casewise outliers. These are cases (that is, rows of the data matrix) that behave differently from the majority of cases, raising suspicion that they might belong to a different population. On the other hand, cellwise outliers are individual cells in the data matrix. When a row contains one or more outlying cells, the other cells in the same row still contain useful information that we wish to preserve. We propose a cellwise robust version of the MCD method, called cellMCD. Its main building blocks are observed likelihood and a penalty term on the number of flagged cellwise outliers. It possesses good breakdown properties. We construct a fast algorithm for cellMCD based on concentration steps (C-steps) that always lower the objective. The method performs well in simulations with cellwise outliers, and has high finite-sample efficiency on clean data. It is illustrated on real data with visualizations of the results.

We design a novel calibration procedure that is designed to handle the specific characteristics of options on cryptocurrency markets, namely large bid-ask spreads and the possibility of missing or incoherent prices in the considered data sets. We show that this calibration procedure is significantly more robust and accurate than the ordinary one based on trade and mid-prices.

R LAZARSFELD M MUSTAT , A. -In his work on log-concavity of multiplicities, Okounkov showed in passing that one could associate a convex body to a linear series on a projective variety, and then use convex geometry to study such linear systems. Although Okounkov was essentially working in the classical setting of ample line bundles, it turns out that the construction goes through for an arbitrary big divisor. Moreover, this viewpoint renders transparent many basic facts about asymptotic invariants of linear series, and opens the door to a number of extensions. The purpose of this paper is to initiate a systematic development of the theory, and to give some applications and examples. R. -Dans son travail sur la log-concavit des multiplicits, Okounkov montre au passage que l'on peut associer un corps convexe un systme linaire sur une varit projective, puis utiliser la gomtrie convexe pour tudier ces systmes linaires. Bien qu'Okounkov travaille essentiellement dans le cadre classique des fibrs en droites amples, il se trouve que sa construction s'tend au cas d'un grand diviseur arbitraire. De plus, ce point de vue permet de rendre transparentes de nombreuses proprits de base des invariants asymptotiques des systmes linaires, et ouvre la porte de nombreuses extensions. Le but de cet article est d'initier un dveloppement systmatique de la thorie et de donner quelques applications et exemples.

We consider a two‐degree‐of‐freedom block‐spring model, in which two blocks (Block 1 and Block 2) are connected by a spring and driven by a slowly moving driver. Assuming a rate‐ and state‐dependent friction law, we set the friction parameters such that dynamic instability occurs at Block 1. Episodic aseismic slip occurs at Block 2 when its frictional parameters are near the stability transition. When the stress has accumulated to approximately a steady state level during an interseismic period, Block 2 starts a slow slip. Quasi‐static oscillation in the stress and slip velocity occurs with decaying fluctuation amplitudes leading to the steady state values. The decaying oscillation could be a plausible generation mechanism of the episodic aseismic slip observed in the Tokai district, Japan, since 2001. We also consider various slip modes on a plate boundary based on this two‐block model associated with the interaction between different frictional properties.

A suite of algorithms and associated procedures, originally developed for mineral exploration applications, are adapted for application to terahertz hyperspectral images measured in reflection mode. Such data are often quite noisy due to the low reflectivity of many materials at terahertz frequencies. The algorithms and procedures are based on an extended linear mixture model consisting of two parts. The first part, called the “foreground”, models the distinguishing parts of the spectra of materials (including mixtures) of interest (especially their diagnostic absorption features). The second part, called the “background”, models parts of the spectra that are typically of lesser interest, such as variation in low frequencies and water vapor. The model and procedures are exemplified with a spectral library of six materials and are applied to three hyperspectral images, one consisting only of pure pellets, some of which are not in the library, and two of which contain both pure and mixed pellets of three of the materials in the library. The associated procedures include the following: estimating the number of materials in the mixture at each pixel; identifying pixels with materials that are well modeled by the background terms only; identifying pixels with materials not in the library; and identifying pixels containing metal. Finally, this article concludes with a discussion of some outstanding issues.

Let $(X/Z,B)$ be a lc pair with $K_X+B$ pseudo-effective$/Z$ and $Z$ affine. We show that $(X/Z,B)$ has a good log minimal model if and only if its log canonical algebra and modules are finitely generated.

Schumacher F, Ademmer T, Bülter S, Kneiphoff A. Hochschulen im Lockdown - Lehren aus dem Sommersemester 2020. <em>Arbeitspapier Hochschulforum Digitalisierung</em>. 2021;4(58):1-76.

The aim of the present work was to design and fabricate all purpose, positioning-tolerant and efficient interconnects between single-mode fibers and integrated waveguides out of polymers. The developed structures are part of the optical packaging of integrated optical chips. Integrated optics have gathered tremendous interest throughout recent years from research as well as from the industry, and most likely the demand will further grow in the future. Today’s trend is to establish optical data communication not only in far-distance transmission but also in end-user or so called fiber-to-home configurations, or, in the near future, also on board or even chip level. In addition, integrated optical sensors are gaining more and more importance. In the future, lab-on-a-chip systems may be able to simplify and accelerate analysis methods within health care or allow for a continuous monitoring of almost any environmental variable. All these applications call for robust optical packaging solutions. Many integrated optical chips are using a silicon-on-insulator design. Technologies which were originally intended for the manufacturing of integrated circuits can be utilized for the fabrication of such silicon-on-insulator chips. Point-of-care testing, which is a considerable part of bio-sensing, in some cases only allows the use of disposable transducer elements. The fabrication of these transducers, also including almost all other system parts, may be possible using polymers. Alternative fabrication methods like nanoimprint lithography can be applied for the patterning of polymers. With these, the extension of already known working principles or even entirely new device architectures become feasible for mass production. The direct patterning of polymers by means of nanoimprint was used to fabricate interconnects for integrated waveguides. In contrast to conventional lithography approaches, where a patterned resist layer is used as a masking layer for subsequent process steps, direct patterning allows the immediate use of the structures as functional elements. Firstly, nanoimprint allows diffraction-unlimited patterning with nanometer resolutions as well as the replication of complex three-dimensional patterns. These unique properties were used within this work to pattern shallow gratings atop an integrated waveguide within only one single manufacturing step. The gratings are used as coupling elements and can be utilized either to couple light from external elements to the chip or vice versa. Considerations regarding the optical effects on single-mode polymer waveguides as well as grating couplers were obtained from simulation. They are specific to the chosen design and the used polymer and cannot be found elsewhere so far. Compared to similar designs and fabrication strategies proposed in literature, the ones followed here allow for a higher efficiency. The dimensions and process windows obtained from simulation did serve as a basis for the subsequent fabrication of the grating couplers. All steps which are necessary to turn the calculated design into reality, ranging from master fabrication, to working mold cast and imprint, are shown in detail. The use of a working mold strategy is of crucial importance for the fabrication process and is discussed in detail. The use of a working mold preserves a costly master and further allows for a cost-efficient production. Parameters which are relevant for the production as well as for the final polymer patterns were analyzed and discussed. On the basis of the obtained data, a process optimization was performed. The optical characterization was also part of the presented work. A comparison with the results obtained from simulation is included and additional effects were revealed. Most of them may be subject to further improvement in future designs. In summary, the present work contributes to the field of optical packaging. It shows a viable route for the design and fabrication of interconnects of single-mode polymer waveguides. The presented design can be used as a building block which can be placed at almost any positions within an integrated optical chip. The fabrication method includes a minimum number of process steps and is still able to increase performance compared to similar approaches. Moreover, all process steps allow for scaling and are potential candidates for mass production.

Based on the model describing the regulation of the P RM operator region of λ phage proposed by Jeff Hasty et al., we study the noise effects on the oscillator network. We find that the additive noise cannot change the period and the amplitude of the relaxation oscillator, but in the multiplicative case, the period of the relaxation oscillator increases to a constant value with the increase of the strength of noise, and the amplitude of the relaxation oscillator also shows increases with the increase of the strength of noise. This novel results suggest that an external multiplicative noise source could be used to control gene expression.

Because of the continuing advances in developing lasers in the far-ultraviolet and x-ray ranges, studies of the behavior of atoms under a high-frequency laser field are of theoretical and practical interest. In the present paper, we review various analytical results obtained by the method of separating rapid and slow subsystems for various polarizations of the laser field. Specifically, we review the corresponding analytical results both in terms of the quantum description of the phenomena involved and in terms of the classical description of the phenomena involved. We point out that, for the classical description of hydrogen atoms in a high-frequency laser field, there are interesting celestial analogies. We discuss hidden symmetries of these physical systems, the advantages of this analytical method, and the connection between these results and the transition to chaos.

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