A splitting of the virtual class for genus one stable maps

Moduli spaces of stable maps to a smooth projective variety typically have several components. We express the virtual class of the moduli space of genus one stable maps to a smooth projective variety as a sum of virtual classes of the components. The key ingredient is a generalised functoriality result for virtual classes. We show that the natural maps from 'ghost' components of the genus one moduli space to moduli spaces of genus zero stable maps satisfy the strong push forward property. As a consequence, we give a cycle-level formula which relates standard and reduced genus one Gromov--Witten invariants of a smooth projective Calabi--Yau theefold

Reduced invariants from cuspidal maps

We consider genus one enumerative invariants arising from the Smyth-Viscardi moduli space of stable maps from curves with nodes and cusps. We prove that these invariants are equal to the reduced genus one invariants of the quintic threefold, providing a modular interpretation of the latter

Virtual classes for the working mathematician

This note is intended to be a friendly introduction to virtual classes. We review virtual classes and we give a number of properties and applications. We also include a new virtual push-forward theorem and many computations of virtual classes in simple examples

Scheduling access to shared space in multi-robot systems

Through this study, we introduce the idea of applying scheduling techniques to allocate spatial resources that are shared among multiple robots moving in a static environment and having temporal constraints on the arrival time to destinations. To illustrate this idea, we present an exemplified algorithm that plans and assigns a motion path to each robot. The considered problem is particularly challenging because: (i) the robots share the same environment and thus the planner must take into account overlapping paths which cannot happen at the same time; (ii) there are time deadlines thus the planner must deal with temporal constraints; (iii) new requests arrive without a priori knowledge thus the planner must be able to add new paths online and adjust old plans; (iv) the robot motion is subject to noise thus the planner must be reactive to adapt to online changes. We showcase the functioning of the proposed algorithm through a set of agent-based simulations

Three embeddings of the Klein simple group into the Cremona group of rank three

We study the action of the Klein simple group G consisting of 168 elements on two rational threefolds: the three-dimensional projective space and a smooth Fano threefold X of anticanonical degree 22 and index 1. We show that the Cremona group of rank three has at least three non-conjugate subgroups isomorphic to G. As a by-product, we prove that X admits a Kahler-Einstein metric, and we construct a smooth polarized K3 surface of degree 22 with an action of the group G.Comment: 43 page

Electronic property analysis of O-doped Cu3SbS3

The ternary Cu-Sb-S semiconductors are considered to be sustainable and potential alternative absorber materials in thin film photovoltaic applications. In these compounds, several phases may coexist, albeit in different proportions depending on experimental growth conditions. Additionally, the photovoltaic efficiency could be increased with isoelectronic doping. In this work we analyze the electronic properties of O-doped Cu3SbS3 in two structures: the wittichenite and the skinnerite. We use first-principles within the density functional formalism with two different exchange-correlation potentials. In addition, we estimate the potential of these compounds for photovoltaic applications

Quality of life measurement in alopecia areata. Position statement of the European Academy of Dermatology and Venereology Task Force on Quality of Life and Patient Oriented Outcomes

New treatment options may lead to an increased interest in using reliable and sensitive instruments to assess health-related quality of life in people with alopecia areata (AA). The purpose of this paper is to present current knowledge about quality of life assessment in AA. The dermatology-specific Dermatology Life Quality Index (DLQI) was the most widely reported health-related quality of life instrument used in AA. Three AA-specific (Alopecia Areata Symptom Impact Scale, Alopecia Areata Quality of Life Index and Alopecia Areata Patients'' Quality of Life) and three hair disease-specific instruments (Hairdex, Scalpdex and ‘hair-specific Skindex-29’) were identified with a range of content and validation characteristics: there is little evidence yet of the actual use of these measures in AA. Scalpdex is the best-validated hair disease-specific instrument. Further extensive validation is needed for all of the AA-specific instruments. The European Academy of Dermatology and Venereology Task Force on Quality of Life and Patient Oriented Outcomes recommends the use of the dermatology-specific DLQI questionnaire, hair disease-specific Scalpdex and the alopecia areata-specific instruments the Alopecia Areata Symptom Impact Scale or Alopecia Areata Quality of Life Index, despite the limited experience of their use. We hope that new treatment methods will be able to improve both clinical signs and health-related quality of life in patients with AA. In order to assess the outcomes of trials on these new treatment methods, it would be helpful when further development and validation of AA-specific instruments is being encouraged and also conducted. © 2021 European Academy of Dermatology and Venereology

Empirical analysis and modeling of Argos Doppler location errors in Romania

Background Advances in wildlife tracking technology have allowed researchers to understand the spatial ecology of many terrestrial and aquatic animal species. Argos Doppler is a technology that is widely used for wildlife tracking owing to the small size and low weight of the Argos transmitters. This allows them to be fitted to small-bodied species. The longer lifespan of the Argos units in comparison to units outfitted with miniaturized global positioning system (GPS) technology has also recommended their use. In practice, large Argos location errors often occur due to communication conditions such as transmitter settings, local environment, and the behavior of the tracked individual. Methods Considering the geographic specificity of errors and the lack of benchmark studies in Eastern Europe, the research objectives were: (1) to evaluate the accuracy of Argos Doppler technology under various environmental conditions in Romania, (2) to investigate the effectiveness of straightforward destructive filters for improving Argos Doppler data quality, and (3) to provide guidelines for processing Argos Doppler wildlife monitoring data. The errors associated with Argos locations in four geographic locations in Romania were assessed during static, low-speed and high-speed tests. The effectiveness of the Douglas Argos distance angle filter algorithm was then evaluated to ascertain its effect on the minimization of localization errors. Results Argos locations received in the tests had larger associated horizontal errors than those indicated by the operator of the Argos system, including under ideal reception conditions. Positional errors were similar to those obtained in other studies outside of Europe. The errors were anisotropic, with larger longitudinal errors for the vast majority of the data. Errors were mostly related to speed of the Argos transmitter at the time of reception, but other factors such as topographical conditions and orientation of antenna at the time of the transmission also contributed to receiving low-quality data. The Douglas Argos filter successfully excluded the largest errors while retaining a large amount of data when the threshold was set to the local scale (two km). Discussion Filter selection requires knowledge about the movement patterns and behavior of the species of interest, and the parametrization of the selected filter typically requires a trial and error approach. Selecting the proper filter reduces the errors while retaining a large amount of data. However, the post-processed data typically includes large positional errors; thus, we recommend incorporating Argos error metrics (e.g., error ellipse) or use complex modeling approaches when working with filtered data

Quality of life measurement in alopecia areata. Position statement of the European Academy of Dermatology and Venereology Task Force on Quality of Life and Patient Oriented Outcomes

New treatment options may lead to an increased interest in using reliable and sensitive instruments to assess health-related quality of life in people with alopecia areata (AA). The purpose of this paper is to present current knowledge about quality of life assessment in AA. The dermatology-specific Dermatology Life Quality Index (DLQI) was the most widely reported health-related quality of life instrument used in AA. Three AA-specific (Alopecia Areata Symptom Impact Scale, Alopecia Areata Quality of Life Index and Alopecia Areata Patients' Quality of Life) and three hair disease-specific instruments (Hairdex, Scalpdex and ‘hair-specific Skindex-29’) were identified with a range of content and validation characteristics: there is little evidence yet of the actual use of these measures in AA. Scalpdex is the best-validated hair disease-specific instrument. Further extensive validation is needed for all of the AA-specific instruments. The European Academy of Dermatology and Venereology Task Force on Quality of Life and Patient Oriented Outcomes recommends the use of the dermatology-specific DLQI questionnaire, hair disease-specific Scalpdex and the alopecia areata-specific instruments the Alopecia Areata Symptom Impact Scale or Alopecia Areata Quality of Life Index, despite the limited experience of their use. We hope that new treatment methods will be able to improve both clinical signs and health-related quality of life in patients with AA. In order to assess the outcomes of trials on these new treatment methods, it would be helpful when further development and validation of AA-specific instruments is being encouraged and also conducted