Olivera Kotevska

Ahmed Lbath
email: ahmed.lbath@imag.fr

J Gelernter

Event model to facilitate data sharing among services Closing the Gap between Research and Implementation

Keywords: Complex Event Processing, CEP, event metadata model, event model, smart city service

Event model to facilitate data sharing among services

I. INTRODUCTION

Problem. Half of the world population lived in cities by 2013. Historically, people live in and work for their cities; we want to make the cities work for them. Or rather, to make their devices work for them by creating city service applications. Complex event processing applications correlate data streams in real time as events occur, using pre-defined rules to identify events of interest. A common data structure will allow different data streams to be used by multiple services more easily.

Others' approaches. Event metadata models for Complex Event Processing provide the time and data backbone to allow those data streams to work together. Event models tend to be rich in metadata fields which may or may not be relevant to the service at hand. The impracticality of the metadata-rich models is not recognized because use cases are rare. Also, when data is provided, it is often simulated to match a modelwhich does not demonstrate whether or not a model is robust for a particular data stream.

Our approach. Our event model defines only necessary fields, and gives parameter wildcards for potential metadata expansion in three categories (EventProfile for the data stream, EventSource for the device that provides the data stream, and Event). These parameters are added based on the service by the developer at the time of model implementation. Our model is validated in a smart cities case study.

Significance. Developers' adoption of a standard event model -that is, a package that any data could fit into for delivery into applications in the upper layer of the Internetcould advance smart city services. Different services might access the same data concurrently, so the model would facilitate data sharing as well as integration.

Case study in city safety. We created an algorithm for pedestrian safety using real-world data, and then supplied the algorithm with data from our event model to test our model's usefulness.

We devised the case study in answer to an on-going need by local government to improve safety in Montgomery County, Maryland, U.S.A. In 2007, a Pedestrian Safety Initiative was introduced in Montgomery County that used education, streetscape and road signs, as well as traffic calming and road rule enforcement to lower the number of accidents. 1 Our application is intended for county representatives, and adds to Pedestrian Safety Initiative by showing where the most accidents are predicted to occur. The county can then better deploy resources to change street signs or deploy traffic police, for example, to heighten safety at the times and locations predicted to be unsafe.

This Introduction is followed with Section 2 on Background and Related work. Section 3 presents our event model; in Section 4 we demonstrate evaluation scenario; in Section 5 we discuss about our results and Section 6 summarizes the conclusions and future work.

Our contributions are (1) a generic, highly-scalable semantic model as a core component of complex event processing architecture, (2) validation of the proposed event model in an algorithm for a smart cities problem of pedestrian safety, and (3) bringing to the attention of the research community an Internet of Things testbed that includes both sensor and human data. 2

II. BACKGROUND AND RELATED WORK

A. Complex Event Processing (CEP)

Complex event processing is a strategy to create applications, or services in which data streams containing events produced by resources such as people, devices or sensors are filtered for particular event changes of interest, called instances. These changes then automatically trigger some response. Events are given names so that they can be shared among services. To enable sharing, common metadata and sometimes also vocabulary for the names comes from ontologies.

The diagram below shows event data in basic Complex Event Processing. Data is received from multiple streams, events are detected, and an appropriate response is triggered. This sequence diagram the Figure resembles the standard event driven architecture proposed by Fujitsu [START_REF]Fujitsu Develops Distributed and Parallel Complex Event Processing Technology that Rapidly Adjusts Big Data Load Fluctuations Online[END_REF], Microsoft [START_REF] Chiu | Announcing Azure Stream Analytics for realtime event processing[END_REF], IBM [START_REF] Selman | Event Driven Architecture and Decision Management[END_REF] and Oracle [START_REF] Kress | Event-Driven SOA[END_REF]. Note that the vertical box in Fig. 1, "Event instances in model," where the data is organized to be stored in database server or event cloud, is central to the process.

Queries to the event processing system might be in SPARQL for RDF, TESLA-a formally defined Event Specification Language [START_REF] Cugola | TESLA: a formally defined event specification language[END_REF], or EP-SPARQL [START_REF] Anicic | EP-SPARQL: a unified language for event processing and stream reasoning[END_REF], or in Event Processing Language, 3 or Big Data Processing Language (BDPL) [START_REF] Stühmer | PLAY: Semantics-based event marketplace[END_REF].

These rules have the ability not only to indicate events relevant to the application, but also when data is faulty or noisy or missing information, or includes non-events [START_REF] Alevizos | Complex event recognition under uncertainty: a short survey[END_REF]. Response to data uncertainty can make the system more robust. For example, events missing values can be marked incomplete, and system maintenance would analyze marked records to determine what had gone wrong.

B. Alternatives to this architecture

The event model is one part of the CEP architecture. Other proposed middleware solutions ensure that low level signals can work together without use of an event model. For example, the IoT Semantic Smart Gateway Framework [START_REF] Kostis | Semantic interoperability on the Internet of Things: The Semantic Smart Gateway Framework[END_REF], and the Smart M3 open source software platform that provides infrastructure between resources [START_REF] Smirnov | Development of the on-the-fly ontology matching model for smart spaces[END_REF]. Even these solutions require common terms so that different devices can communicate -in what makes the solutions "smart".

C. Event model in Complex Event Processing

An event model is core to Complex Event Processing architecture, so it is understandable that more than a dozen event models have appeared in the academic literature since 2000. Some are specific to data type or domain type, or must be paired with certain controlled vocabularies in ontologies, or with particular query languages.

Event models specify metadata fields for the data streams that carry or pertain to events. The most basic metadata fields for event models are data type, and time. The idea of the model primitives is that the basic data message is independent of any application. What metadata fields go beyond the primitive? Authors from [START_REF] Pongpaichet | EventShop: Recognizing situations in web data streams[END_REF] explain that data fields such be considered during the "thought process" of setting up a system. This is the logic we follow when specifying "Parameters" for our model. Other researchers [START_REF] Scherp | F-A Model of Events based on the foundational ontology DOLCE+DnS Ultralite[END_REF] assume that more primitive are better. See the comparison chart with evaluation metrics in the Appendix.

D. Role of the ontologies in event models

Ontologies are required in event models such as Event F [19][19], OntoEvent [START_REF] Ma | OntoEvent: An ontology-based event description language for semantic complex event processing[END_REF], REseT [START_REF] Uma | Event order generation using Reference Event based qualitative Temporal (REseT) relations in Time Event Ontology[END_REF], and LODE [START_REF] Shaw | LODE: Linking Open Descriptions of Events in 'The Semantic Web[END_REF]. In some cases, as in OntoEvent and REseT, the ontology was created specifically for the event model.

The metadata fields in our model, for the most part, align with those in the DOLCE ontology (See Fig. 1) That will make it easier for data in different streams to fit into the same event model, and it will help insure interoperability. These event models are called semantic because the meaning of the data field titles is essential to the model.

Requiring an ontology on a particular topic for an event model can restrict data types that can be used, as well as the domain. Authors in [START_REF] Jiang | The construction of ontology in the area of traffic violations[END_REF] have a method to develop an ontology for traffic violations. In our particular application, the World Wide Web Consortium is developing a Traffic Event Ontology, which we could use for at least one data stream, but this ontology is not available as of the writing of this paper. 4 A domain-specific ontology might be useful to extract events from a natural language data stream, but it is probable that Named Entity Recognition tools such as the Stanford NER toolkit would do well in extracting proper nouns and locations required. 5

E. How event models have been validated

Many event models in the academic literature have not been validated; the models are either entirely theoretical, or use data that has been created to fit the model. EventShop is an event processing platform that can be used to validate components of the architecture. It accepts data streams and includes modules to query the data that will isolate event instances relevant to the application. Their events are put into a grid structure called Emage, that can integrate events from heterogeneous data streams [START_REF] Pongpaichet | EventShop: Recognizing situations in web data streams[END_REF].

By contrast, to validate our event model, we have devised a service that incorporates multiple data streams. We have vetted our event model when real-world data streams fit the model and then are accepted into the service.

III. OUR EVENT MODEL

Our model shown in Fig. 2 below in Unified Modeling Language (UML) has three classes: EventProfile, EventSource, and Event. Location metadata is required but is not in the diagram because location metadata changes classes depending upon the service. For stationary devices, "Location" is stored with the device information, whereas for mobile devices, location will be needed continually to correspond to events. Metadata fields within the three classes of our event model are defined below. Our model is extensible. Some services will require only its specified metadata fields, whereas other services will require consideration of which parameters are relevant. EventProfile and EventSource send their data at system start or re-start, whereas the Event class sends data continually. Data from the 5 http://nlp.stanford.edu/ner/ Event class is filtered using rules or machine learning into instances relevant to the service.

The EventProfile class holds metadata about the data stream. "Description" explains what data is being stored for services. "Data frequency" presents the rate data streams are expected to be received, while "type of data" provides information about the data that has been collected. "Parameters" represent any additional information related to the data stream that are important, like measurement type, expected states, or frequency.

The EventSource class holds the data related to devices or sensors. It has the following attributes:" Agent" provides information for the event source, like county police or weather channel. "Address" is the address from where data was collected or original source of observed data. "Device type" is the type of device, such as temperature sensor, mobile device etc. "Parameters" represents additional information related to the device, such as serial number, model, and battery expiration date.

The Event class holds the data related to events in the data stream, like temperature, heart rate, pedestrian movement, or car accident. It has the following attributes: "Description" is auto-filtered from an event text stream or is set up beforehand to describe the events. "StartTime" is the date and time when the event started, "EndTime" is the date and time when event stopped. The frequency of "StartTime" and "EndTime" can be set by adding a parameter to the EventProfile. Parameters for the event represent additional information related to the event that are useful for a particular service. The events could be sent in as received, or they could be aggregated and then sent at some pre-determined frequency.

Ontology. The system designer should choose an ontology used by the other applications for wide data sharing among applications. Rather than share or link ontologies [START_REF] Gyrard | Semantic web methodologies, best practices, and ontology engineering applied to Internet of Things[END_REF], an upper level ontology such as DOLCE could be used to bridge domain ontologies. 6 DOLCE includes reasoning without controlled vocabulary, and it was used in the F event model [START_REF] Scherp | F-A Model of Events based on the foundational ontology DOLCE+DnS Ultralite[END_REF]. In aligning our model with DOLCE, Feature is the category for our Description, and Physical Quality is the category for Type.

Uniqueness and benefits. We conducted an extensive survey of event models and found that our event model differs from others in two main aspects: (1) fewer required metadata fields, and (2) some of the metadata is sent once only. Fewer metadata fields allows the model to be maximally re-usable for different data and domain types, although it means that some thought will be needed each time the model is implemented. Sending some metadata once only lessens the data load on the network somewhat to speed processing.

Instances in the event stream. Recall that instances or occurrences are the events being monitored for. A script apart from the model filters the event data stream to recognize instances relevant to the application, and to set bounds on what belongs in the event model. For example, an expected range of values for some metadata field could be specified, and data that went beyond that range would be dismissed. Filtering for the model also could be handled on a data stream-by-stream basis so that a data stream that did not flow at an expected frequency, might indicate sensor or device malfunction.

IV. CASE STUDY

This experiment shows how different forms of event data and metadata in the model are suitable for a smart cities application.

A. Objective

We want to use our event model to supply data for an actual application. Our research question is: Is it possible to show the influence of time, weather, and community happenings on pedestrian safety incidents in a given location by postal zip code?

B. Use case and data for the experiment

Events for 2015 traffic incidents, weather, and community happenings for Montgomery County, Maryland are posted on the open web. 7 The county updates the data regularly. We intend to supplement the Pedestrian Safety Initiative in Montgomery County, Maryland, by offering an algorithm to predict unsafe event areas according to zip code. To show differences in time-of-day, the service could output predicted locations every few hours.

C. Method

Event processing methods work well for passive data collection because they allow large quantities of data to be processed if necessary in different locations (also called distributed systems). Event processing also is scalable, and using corrective rules can help make the system fault tolerant. For example, only accept into the model if the time is between 1pm and 6pm Eastern Time.

Getting data into the model. Our data included road violations, weather, and community happenings. Of these, the road violations and community happenings include a lot of text. But event recognition in text data can be difficult due to human language ambiguity. To recognize which events were relevant instances, we experimented by comparing a nondomain specific ontology, the Freebase knowledge-base, and a classifier we trained on a portion of the data. We found that the classifier was the most accurate filter to find relevant instances.

Handling data uncertainty. Uncertainty in the general case could be minimized with the combination of rules (for instance, only accept into the model if it includes a beginning time). Specifically, in our application, we lacked zip codes for some of the community happenings that were city-wide (such as elections), so for these, we entered zip codes for the entire city. Also for the case of missing data in the location fields, we used alternative data entry, like longitude and latitude and get the zip code and city information. Our metadata fields correspond to categories in the DOLCE ontology. DOLCE allows natural language descriptions, so we leave our text data streams as sent.

D. Data analytics and findings

The proposed method predicts which county region by zip code will be safest based on the past number of pedestrian incidents per zone. Analysis is performed using the R software environment for statistical computing and graphics. We experimented with both Poisson Regression and Probabilistic Graphical models (PGM) to determine which was more suitable for prediction with our data. Poisson regression is used for point data, such as we have, and it is commonly used for predicting the probability that an event will occur based on several predictor variables that may either be numerical or categorical. PGM has the ability to represent dependencies among events on a graph. The table shows that the statistical method selected, whether a PGM or the Poisson Regression, is not a significant factor in predictive accuracy.

TABLE I. ACCURACY OF TWO METHODS TO PREDICT UNSAFE LOCATIONS

Probability of a (negative) pedestrian event in a location

Probabilistic Graphical Model Poisson Regression

Average accuracy 0.864 0.869

E. Evaluation and visualization

To show the relative effectiveness of the pedestrian safety algorithm on data from the event model, two means of evaluation are used: comparative maps (Fig. 6 and7), and the confusion matrix as performance measures for accuracy calculated in Table 1. Figure 6 show maps for 2015 actual pedestrian incidents for the period from January to March and incidents predicted for the same period using Probabilistic Graphical Models. Comparing output colors in the actual (top map) and predicted (bottom map) shows that our algorithm achieved excellent results. We split the 2015 data into four 3-month segments and show the map pair only for the first 3-month segment due to space limitations, even though mapped results throughout the year were equally good.

The high quality mapping results were confirmed by the .86 predictive accuracy shown in Table 1 of both the Probabilistic Graphical Model and the Poisson Regression. Based on the fact that the different data streams fed easily from the event model to the pedestrian safety algorithm shows that the event model is robust to at least three data types.

In creating an algorithm, we tried several statistical models for prediction. We evaluated results by creating a mapped output comparing actual pedestrian events to predicted events (Fig. 6 and7), and by using the accuracy statistic averaged over a year of predictions (Table 1). The accuracy match between our prediction model and the real world data shows our service using data from our event model is accurate to .86 using either Probabilistic Graphical Models or a Poisson Regression. We can extend the algorithm to predict time as well as location.

Our pedestrian safety algorithm is limited by the fact that we do not have a record of pedestrian safety incidents in the county for 2015 that is entirely complete since we are limited to data that is available publically.

However, it is strengthened by the fact that we found event instances to a high degree of accuracy. In a real-time application, there will likely be additional errors identifying event instances.

F. How government officials could use the system

Data from the Montgomery County, Maryland open government stream in JSON/xml first would be set to flow into the application. We would create a web-based interface for the application that would be active around the clock.

Users could examine the county map by zip code in the interface to see which areas in the county are having pedestrian incidents at that time (as in Fig. 7), and can then make informed decisions where county resources should be deployed to heighten safety. Our experiments have shown that the prediction algorithm is up to 86% accurate, and so the officials should feel confident that the resources would be deployed effectively. It would straightforward for us to add analytics to the interface as well, so that the officials could see trends over time.

V. DISCUSSION

A. Semantic model for event processing architecture: toward a standard Numerous event models in the literature vary with respect to required data fields and the role of ontologies. It is rare to find research that discusses deploying an event model: how to get data in and out, and how to handle missing data, for example. That makes it impossible to "plug in" other event models into our architecture for comparison. This paper has covered both the data modeling and some flexibles rules to guide deployment of our event model in a city service.

Our model requires a minimum of metadata fields, and it is efficient, minimizing the amount of network traffic by linking a continuous time dependent data stream to non-time dependent meta-information stored on an event server or cloud.

Overlap among different types of data sources should be handled by an upper level ontology such as DOLCE. We made the data field types in our model align with DOLCE categories in order to facilitate getting data from different streams into the same model.

A one-set-of-metadata-fits-all model would be more convenient than ours, but it would not necessarily capture what each particular service requires. That is why some thought will still be required to add parameters to suit the service being implemented.

Relying on a standard event model will make it easier for developers to build Complex Event Processing systems. In that our event model is generic in suiting a variety of data streams and a variety of domains, we propose it as basis for an event model standard.

B. Event model in Complex Event Processing architecture

Event models in complex event processing diagrams are ubiquitous. Actual systems that perform event processing are less common, and in fact, input of heterogeneous data fields into a single system is still coming into focus. The event model fits different data types into the same framework, thus making data integration easier.

Getting data into the model for highly structured can be as simple as matching metadata field names. But when the data flow does not include metadata, or when it is a natural language stream --as in the police reports used here --Natural Language Processing tools will employ data extraction. The most recent Named Entity Recognition (NER) tools to extract person, organization, location, and other objects that are proper nouns, are well advanced, achieving accuracies in the 90% range.

C. Publically-available, updated Internet of Things testbed

We applied Internet of Things data to help solve an actual problem: determine which areas of Montgomery County, Maryland require more monitoring and local resources to improve pedestrian safety. We used that algorithm to test our event model.

Few Internet of Things data sets at the time of writing are publically available for experimentation. It is not surprising, therefore, that we found that few of the research papers on event models use real-world data. Many papers are entirely theoretical, and some use synthetic data sets which were created or assembled from the web for the purposes of demonstrating a point.

Internet of Things data sets are obscured from a general web search because they are not referred to as Internet of Things, or sensor data -the keywords we use in computer science literature. The scientific community should look for human and sensor data relevant for Internet of Things research in open city projects. Our data come from Maryland, and New York has an even broader data set, 8 and the Open Data Portal has data from around the world. 9VI. CONCLUSION An event model with an ontology to control word descriptions will bridge smart cities services by reusing data streams across applications. This approach will make applications more financially viable and expand the potential number and scope of smart city services. Our event model should be tested with more data stream types. Even better to test the event model would be to create services complementary to this in pedestrian safety to ensure that the same data can be used in multiple ways.

ACKNOWLEDGMENT

We are grateful for Maxence Lefort's advice on the design of our event model.

Fig. 1 .

 1 Fig. 1. Complex event processing architecture, with arrows showing event data sequence direction. An event model is a component.

  3 https://docs.oracle.com/cd/E13157_01/wlevs/docs30/epl_guide/overv iew.html

Fig. 2 .

 2 Fig. 2. Our model for event data shown in Universal Modeling Language (UML). EventProfile and EventSource parameters could include data rate for system failure checking, and parameters could include location for devices that are mobile; otherwise, location would be a parameter for Event.

  7 https://data.montgomerycountymd.gov/ Example of data in the model. The following Figures3,4,5show how community happenings, weather and traffic violation metadata fit into our event model. We took this data from the Montgomery County open data website for this case study, but in a real time application, the EventSource would provide the actual source of the data flow with its parameters.

Fig. 3 .Fig. 5 .

 35 Fig. 3. Community happening metadata in our event model

Fig. 6 .Fig. 7 .

 67 Fig. 6. Actual traffic violations in Montgomery County, Maryland related to pedestrian safety events January -March 2015 by zip code

  The work was done in conjunction with the Information Technology Laboratory of the National Institute of Standards and Technology. The identification of any commercial product or trade name does not imply endorsement or recommendation by the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.

						Appendix: Comparison chart for event models *
					Processing					Required fields				Other requirements
	Event Model	Raw data into	model	Handle missing	data	Handle uncertainty	Data types	Static/dynamic	Action/verb/event	Participant/actor/s	ubject/Agent	Object	Time	Location	Device associated	Device affected	Ontology	Processing	language
	Event Modeling
	in UML (Baekgaard,	ns	ns	ns	ns	ns	Y	Y		Y	ns ns	ns	ns	no	no
	2002) [3]
	Eventory (Wang et al, 2007) [26]	Y		ns	ns	ns	ns	Y	Y		ns	Y	Y	ns	ns	no	no
	Event ML
	(IPTC, release	ns	ns	ns	ns	ns	Y	Y		ns	Y	Y	ns	ns	no	XML
	2014)
	SsVM (Ekin et al, 2004) [8]	ns	ns	ns	video	ns	Y	Y		Y	Y	Y	ns	ns	no	SQL
	Event E (Westermann et al, 2007 ) [27]	ns	ns	Y	Multi-media	ns	Y	Y		ns	Y	Y	ns	ns	no	no
	Event F (Scherp et al, 2009) [19]	ns	Y		ns	Any	ns	Y	Y		ns	Y	Y	ns	ns	DOLCE+D nS	RDF/XML
	OntoEvent (Ma et al, 2015)	ns	ns	ns	Location, Common data types	ns	Y	Y		ns	Y		ns	ns	Created by them	OntoEvent lang.
	REseT (Uma et al, 2014) [25]	Y		ns	ns	Common data types	ns	Y	Y		ns	Y	Y	ns	ns	Created by them	DL
	Common Event Model (Fowler et al, 2009) [9]	ns	ns	ns	Location, common data types	ns	Y	Y		Y	Y	Y	Y	ns	Created by them	RDF/XML
	Event ontology (Zhong et al, 2012) [28]	ns	ns	ns	Common data types	ns	Y	Y		ns	Y	Y	ns	ns	Created by them	RDF/XML
	VERL (Francois et al, 2005) [10]	ns	ns	ns	Multi-media	ns	Y	Y		Y	Y	Y	ns	ns	VEML 2.0/OWL	VEML/OW L-DL
	CIDOC CRM
	(Doerr et al,	ns		ns	ns	ns	ns	ns	Y		ns	Y	Y	ns	ns	ISO 21127	XML
	2007) [7]
	SOUPA (Chen et al, 2005) [4]	ns	ns	ns	Common data types	ns	Y	Y		ns	Y	Y	Y	ns	COBRA-ONT/OWL	RDF/XML
	LODE (Shaw et al, 2009) [21]	Y		ns	Y	ns	ns	ns	Y		ns	Y	Y	ns	ns	Created by them	RDF/XML
	EventOntology (Raimond et al, 2007) [18]	Y		ns	ns	Multi-media	ns	Y	Y		Y	Y	Y	ns	ns	Created by them	RDF/XML
	Event Calculus (Shanahan, 2001) [22]	ns	ns	ns	ns	ns	Y	ns	ns	Y	Y	ns	ns	no	Some logic language
	Ours (Kotevska et al, 2016)	Y		Set by coder	Y	any	Y	Y	no	no	Y	Y	Y	no	any	any
	*ns = not specified, Y = yes

http://www.montgomerycountymd.gov/DOT-PedSafety/overview.html; https://volunteer.truist.com/mcvc/org/opp/10610402110.html

2 https://data.montgomerycountymd.gov/, with data updated regularly

https://www.w3.org/community/traffic/

http://www.loa.istc.cnr.it/old/q.html

https://data.ny.gov/

dataportals.org/search


V K Vlasko-Vlasov

F Colauto

A I Buzdin

D Rosenmann

T Benseman

W.-K Kwok

Magnetic gates and guides for superconducting vortices

I. INTRODUCTION

It is clearly recognized that power dissipation is a major issue in contemporary high density semiconductor microcircuits for computers and communication technologies. In this regard, superconducting (SC) single flux quantum devices [START_REF] Toepfer | Design infrastructure for rapid single flux quantum circuits[END_REF][START_REF] Anders | European roadmap on superconductive electronicsstatus and perspectives[END_REF][START_REF] Mukhanov | Energy-efficient single flux quantum technology[END_REF][START_REF] Likharev | Superconductor digital electronics[END_REF][START_REF] Kunert | Recent developments in superconductor digital electronics technology at FLUXONICS Foundry[END_REF][START_REF] Holmes | Energyefficient superconducting computing-power budgets and requirements[END_REF][START_REF] Golod | Single Abrikosov vortices as quantized information bits[END_REF] provide a route towards novel digital microelectronics. Such cryodevices, based on SC elements with minute losses, offer superior performance in speed and exceptionally low power consumption. They operate with magnetic vortices, each carrying a single magnetic flux quantum [START_REF] Abrikosov | On the magnetic properties of superconductors of the second group[END_REF] that can perform as natural bits for digital operations. The notion of utilizing SC vortices in digital microprocessors and memories has been discussed for a while (see references in Refs. [START_REF] Toepfer | Design infrastructure for rapid single flux quantum circuits[END_REF][START_REF] Anders | European roadmap on superconductive electronicsstatus and perspectives[END_REF][START_REF] Mukhanov | Energy-efficient single flux quantum technology[END_REF][START_REF] Likharev | Superconductor digital electronics[END_REF][START_REF] Kunert | Recent developments in superconductor digital electronics technology at FLUXONICS Foundry[END_REF][START_REF] Holmes | Energyefficient superconducting computing-power budgets and requirements[END_REF][START_REF] Golod | Single Abrikosov vortices as quantized information bits[END_REF]). However, presently their technical realization is still in the research and development stage. Most of the efforts in vortex technology, termed fluxtronics, are devoted to the design and study of Josephson vortex circuits, where single flux quantum functionality is achieved by fine tuning assemblies of Josephson junctions (see, e.g., Ref. [START_REF] Kunert | Recent developments in superconductor digital electronics technology at FLUXONICS Foundry[END_REF]). Meanwhile, the alternative of constructing circuits based on single Abrikosov vortices remains largely unexplored. The idea of such devices was first suggested in the 1980s [START_REF] Hebard | A memory device utilizing the storage of Abrikosov vortices at an array of pinning sites in a superconducting film[END_REF][START_REF] Bachtold | The vortex file: A proposal for a new application of type-II superconductivity[END_REF][START_REF] Uehara | Trapped vortex memory cells[END_REF][START_REF] Parisi | Experimental study of a superconducting vortex-memory device[END_REF][START_REF] Parisi | A superconducting vortex-memory system[END_REF][START_REF] Miyahara | Abrikosov vortex memory with improved sensitivity and reduced write current levels[END_REF] and was revisited recently by the Stockholm group [START_REF] Golod | Single Abrikosov vortices as quantized information bits[END_REF]. A number of proposed fluxonic devices relied on tunable trapping and translation of vortices in SC films with arrays of nanoholes of different shapes and symmetries [START_REF] Wambaugh | Superconducting Fluxon Pumps and Lenses[END_REF][START_REF] Hastings | Ratchet Cellular Automata[END_REF][START_REF] Zhu | Controllable step motors and rectifiers of magnetic flux quanta using periodic arrays of asymmetric pinning defects[END_REF][START_REF] Villegas | A superconducting reversible rectifier that controls the motion of magnetic flux quanta[END_REF][START_REF] Berciu | Manipulating spin and charge in magnetic semiconductors using superconducting vortices[END_REF][START_REF] Ooi | Nonlinear Nanodevices Using Magnetic Flux Quanta[END_REF][START_REF] Milosevic | Fluxonic cellular automata[END_REF][START_REF] Yu | Asymmetric weak-pinning superconducting channels: Vortex ratchets[END_REF][START_REF] Gillijns | Origin of Reversed Vortex Ratchet Motion[END_REF][START_REF] Verellen | Switchable magnetic dipole induced guided vortex motion[END_REF][START_REF] Yu | Tunable anisotropic nonlinearity in superconductors with asymmetric antidot array[END_REF][START_REF] Woerdenweber | Pattern induced phase transition of vortex motion in high-T-c films[END_REF][START_REF] He | Magneto-optical observation of anisotropic critical current density in Nb films with artificial asymmetric pinning potential[END_REF][START_REF] Jin | High-frequency vortex ratchet effect in a superconducting film with a nanoengineered array of asymmetric pinning sites[END_REF][START_REF] Kapra | The guidance of vortex-antivortex pairs by in-plane magnetic dipoles in a superconducting finite-size film[END_REF][START_REF] Kapra | Controlling magnetic flux motion by arrays of zigzag-arranged magnetic bars[END_REF][START_REF] Trastoy | Tunable Flux-Matching Effects in High-Tc Superconductors with Nonuniform Pinning Arrays[END_REF][START_REF] Del Valle | Superconducting/magnetic threestate nanodevice for memory and reading applications[END_REF][START_REF] Dobrovolskiy | Alternating current-driven microwave loss modulation in a fluxonic metamaterial[END_REF]. Extensive citations on the subject can be found in Ref. [START_REF] Moshchalkov | Nanostructured Superconductors[END_REF]. These studies showed that it is possible to strongly enhance vortex pinning at integer and fractional matching fields, to induce guided motion of vortices, to realize vortex ratcheting or diode effects, and to synchronize vortex dynamics in ac fields.

Some of these works used small magnetic dots or ferromagnetic (FM) layers with domains in close proximity to a SC film to manipulate the SC transition temperature, T c , and vortex dynamics. The micro-and nanopatterning of the FM layer allowed various designs where SC channels can exist between normal regions, in which T c was suppressed by the stray fields of the FM structures. For example, it was possible to create SC channels along domain walls between normal state regions formed under FM domains (so-called domain wall superconductivity [START_REF] Yu | Domain-wall superconductivity in hybrid superconductor-ferromagnet structures[END_REF][START_REF] Yang | Domain-wall superconductivity in superconductor-ferromagnet hybrids[END_REF]) and subsequently to expand these channels by countering the stray fields' effect in the FM domains with an external field. Furthermore, guided vortex motion can be generated [START_REF] Kapra | Controlling magnetic flux motion by arrays of zigzag-arranged magnetic bars[END_REF][START_REF] Silhanek | Local probing of the vortex-antivortex dynamics in superconductor/ferromagnet hybrid structures[END_REF] with arrays of in-plane polarized magnetic nanobars, where the stray fields emanating from their ends produce weak channels of suppressed order parameter in the SC layer. Alternatively, magnetic arrays can provide strong, temperature independent magnetic pinning of vortices. For example, FM dots with perpendicular magnetic moments, M, can act as dipoles, attracting vortices polarized along the same direction towards their center while positioning oppositely polarized vortices at the dot's periphery, where the stray fields are aligned against M. For in-plane magnetized FM dots, there will be a dipolar potential with attraction and repulsion maxima for vortices located on opposite sides of the dot in the direction of M. Arrays of asymmetric magnetic dots (e.g., triangular) will form asymmetric potentials and thus assist unidirectional vortex motion along the asymmetry axis [START_REF] Villegas | A superconducting reversible rectifier that controls the motion of magnetic flux quanta[END_REF].

Early investigations of periodically patterned superconducting films and hybrid FM/SC structures were pioneered by the groups of Pannetier [START_REF] Geoffroi | Magnetic and transport properties of ferromagnetic particulate arrays fabricated on superconducting thin-films[END_REF][START_REF] Otani | Magnetostatic interactions between magnetic arrays and superconducting thin-films[END_REF], Bruynseraede and Moshchalkov [START_REF] Metlushko | Matching effects in Pb/Ge multilayers with the lattice of submicron holes[END_REF][START_REF] Baert | Composite Flux-Line Lattices Stabilized in Superconducting Films by a Regular Array of Artificial Defects[END_REF], Schuller and Vicent [START_REF] Martin | Flux Pinning in a Superconductor by an Array of Submicrometer Magnetic Dots[END_REF][START_REF] Jaccard | Magnetic pinning of the vertex lattice by arrays of submicrometric dots[END_REF][START_REF] Martin | Artificially Induced Reconfiguration of the Vortex Lattice by Arrays of Magnetic Dots[END_REF], and theoretically supported by works of Lyuksyutov and Pokrovky [START_REF] Lyuksyutov | Magnetization Controlled Superconductivity in a Film with Magnetic Dots[END_REF][START_REF] Lyuksyutov | Frozen flux superconductors[END_REF][START_REF] Erdin | Interaction of mesoscopic magnetic textures with superconductors[END_REF], Peeters and Milosevic [START_REF] Marmorkos | Vortex structure around a magnetic dot in planar superconductors[END_REF][START_REF] Milosevic | Magnetic pinning of vortices in a superconducting film: The (anti)vortexmagnetic dipole interaction energy in the London approximation[END_REF][START_REF] Milosevic | Interaction between a superconducting vortex and an out-of-plane magnetized ferromagnetic disk: Influence of the magnet geometry[END_REF][START_REF] Milosevic | Vortex pinning in a superconducting film due to in-plane magnetized ferromagnets of different shapes: The London approximation[END_REF][START_REF] Milosevic | Vortex-antivortex nucleation in superconducting films with arrays of in-plane dipoles[END_REF], Nori, Reichhardt and Olson [START_REF] Wambaugh | Superconducting Fluxon Pumps and Lenses[END_REF][START_REF] Hastings | Ratchet Cellular Automata[END_REF][START_REF] Zhu | Controllable step motors and rectifiers of magnetic flux quanta using periodic arrays of asymmetric pinning defects[END_REF][START_REF] Ooi | Nonlinear Nanodevices Using Magnetic Flux Quanta[END_REF][START_REF] Olson | Collective Interaction-Driven Ratchet for Transporting Flux Quanta[END_REF][START_REF] Misko | Enhancing the critical current in quasiperiodic pinning arrays below and above the matching magnetic flux[END_REF][START_REF] Misko | Magnetic flux pinning in superconductors with hyperbolic-tesselation arrays of pinning sites[END_REF], and Carneiro [START_REF] De Souza Silva | Simple model for dynamical melting of moving vortex lattices interacting with periodic pinning[END_REF][START_REF] De Souza Silva | Transverse pinning and vortex displacement fluctuations of moving vortex lattices interacting with periodic pinning[END_REF][START_REF] Carneiro | Pinning and creation of vortices in superconducting films by a magnetic dipole[END_REF][START_REF] Carneiro | Interaction between vortices in superconducting films and magnetic dipole arrays[END_REF][START_REF] Carneiro | Tunable interactions between vortices and a magnetic dipole[END_REF][START_REF] Carneiro | Tunable ratchet effects for vortices pinned by periodic magnetic dipole arrays[END_REF] with collaborators. Together with more recent works, these studies demonstrated the high potential for vortex manipulation with magnetic structures. A broad analysis of the vortex dynamics in FM/SC hybrids is presented in a number of comprehensive reviews [START_REF] Lyuksyutov | Ferromagnet/ superconductor hybrids[END_REF][START_REF] Velez | Superconducting vortex pinning with artificial magnetic nanostructures[END_REF][START_REF] Yu | Nucleation of superconductivity and vortex matter in superconductor/ferromagnet hybrids[END_REF], describing the basic effects and the underlying physics. References to the latest works on the subject can be found in Refs. [START_REF] Brisbois | Imprinting superconducting vortex footsteps in a magnetic layer[END_REF][START_REF] Reichhardt | Transverse ac-driven and geometric ratchet effects for vortices in conformal crystal pinning arrays[END_REF][START_REF] Trezza | Change of the topology of a superconducting thin film electromagnetically coupled with an array of ferromagnetic nanowires[END_REF][START_REF] Dobrovolskiy | Abrikosov fluxonics in washboard nanolandscapes[END_REF][START_REF] Adamus | Influence of magnetic domain landscape on the flux dynamics in superconductor/ferromagnet bilayers[END_REF].

Our group also contributed to the studies of different hybrid structures, including bilayers of SC/FM films containing magnetic strip domains [START_REF] Vlasko-Vlasov | Guiding superconducting vortices with magnetic domain walls[END_REF][START_REF] Vlasko-Vlasov | Soft magnetic lithography and giant magnetoresistance in superconducting/ferromagnetic hybrids[END_REF][START_REF] Vlasko-Vlasov | Coupled domain structures in superconductor/ferromagnet Nb-Fe/garnet bilayers[END_REF][START_REF] Vlasko-Vlasov | Domain structure and magnetic pinning in ferromagnetic/superconducting hybrids[END_REF] and lithographically patterned FM strips with in-plane magnetization on top of a SC film [START_REF] Vlasko-Vlasov | Self-healing patterns in ferromagnetic-superconducting hybrids[END_REF]. We showed that FM stripe domains and the edges of FM strips could be used to guide vortices along them and serve as barriers for vortex motion across them. In our recent paper [START_REF] Vlasko-Vlasov | Triode for magnetic flux quanta[END_REF], we demonstrated that an array of closely spaced soft magnetic strips could allow triodelike control of Abrikosov vortices. By rotating the magnetization M of the strips using relatively small in-plane fields, the magnetic charge responsible for the stray fields at the strip edges can be easily tailored from zero (at M||edge) to a maximum (at Medge). Consequently, the strip edges can become easy channels or barriers for vortex motion. The strength of the barrier and flux channeling effects are both defined by the orientation of M with respect to the strip edges and by the magnitude of |M|. In this paper, we extend our work to samples with larger interstrip gaps, which allows us to reveal flux distributions at oppositely polarized strip edges and to image and analyze fine details of the vortex dynamics. We show that the main guidance and pinning effects occur at strip edges with the same magnetic charge polarity as that of entering vortices generated by an applied normal field, while the effect of oppositely charged edges is very weak.

II. EXPERIMENT AND DISCUSSION

A. Sample preparation

The sample is a 2 × 2 mm 2 square of 100 nm SC Nb film (T c = 8.7 K) with parallel FM permalloy (Py) strips deposited on top. Both Nb and Py films were sputtered using a highvacuum dc magnetron system. The Nb square was defined on oxidized Si substrate by laser lithography and, after sputtering and lift-off, covered with 15 nm SiO 2 layer to avoid proximity effects. Subsequently, an array of 35 μm wide and 40 nm thick Py strips with 5 µm gaps was fabricated on top of the Nb square, 200 μm away from the square edges using e-beam lithography and a lift-off process. An optical image of the sample is shown in Fig. 1(a).

The sample was covered with a garnet indicator film and placed on the cold finger of a closed cycle optical cryostat (Montana Instruments). Observations of the normal flux patterns at temperatures, T, ranging from 3.5 to 8.5 K were performed with a polarized light microscope using a magneto-optical (MO) imaging technique [START_REF] Vlasko-Vlasov | Magneto-optical studies of magnetization processes in high-Tc superconductors[END_REF]. The sample was cooled to a fixed T < T c in the presence of a relatively small (20-150 Oe) in-plane field H || , oriented at different angles with respect to the strips in order to polarize the Py strips. In the described experiments H || remained unchanged after cooling, securing the strip polarization. We checked that in-plane fields up to 1 kOe do not modify the normal flux dynamics in the reference 100 nm Nb film [START_REF] Vlasko-Vlasov | Crossing fields in thin films of isotropic superconductors[END_REF]. Background images revealing the stray fields at the edges of the Py strips, which depend on the strip polarization, were taken before application of the normal (perpendicular to the Nb film surface) field H z . These images were then subtracted from the images taken with the applied normal field such that only new vortices generated by H z would be displayed. Below, we illustrate the main features of the dynamics of the entering H z vortices in the presence

B. Transverse polarization of Py strips

Our thin Py strips have the preferred magnetization direction in the film plane, negligible in-plane anisotropy, and a small coercivity. When an in-plane magnetic field of a few tens of Oersted is applied across the strips, their magnetic moments M orient parallel with the field and form strongly localized magnetic charges along the long edges of the strips [Fig. 1(b)]. The magnetic charge density is defined by the divergence of the magnetization near the strip edge, ρ M = -divM. For strips with a rectangular cross section, ρ M is proportional to the magnetization component M n perpendicular to the edge face yielding surface charge density σ M = M n . Since the Py strip thickness, d f = 40 nm, is much smaller than the strip and gap width (W = 35 μm and G = 5 μm, respectively), we can consider each strip edge as a magnetically charged filament with a linear charge density M n d f . The interaction of this linear charged edge with Abrikosov vortices, which can be described as point monopoles carrying magnetic charges of two flux quanta [78] 2 0 [START_REF] Carneiro | Vortex lines in films: Fields and interactions[END_REF], is analogous to the interaction between an electrically charged line and electric point charges. This analogy allows a straightforward intuitive analysis of the vortex behavior in our hybrid structure, as described below.

The magnetic charges produce alternating magnetic stray fields, H s , at the Py strip edges, as revealed in Fig. 1(c) by the bright and dark contrast in the MO image. The dark and bright contrasts depict down and up directions of H s , respectively, and correspond to the sign of the magnetic charge at each strip edge. In the following illustrations, these H s generated MO patterns will be subtracted from images obtained with an additional applied normal-to-surface field, H z , to reveal only vortex evolution generated by this field.

Small normal fields applied to thin SC films and plates are screened by a Meissner current, which induces concentrated H z fields at the perimeter of our square Nb film visualized as bright contrast along the rim of the sample. With increasing H z , Abrikosov vortices enter the film from all four sides of the sample in the shape of light flux lobes caused by defects and fractal flux dynamics (see Ref. [START_REF] Vlasko-Vlasov | Experimental test of the self-organized criticality of vortices in superconductors[END_REF] and references therein) in conditions of strongly nonlinear supercurrent flow [START_REF] Friesen | Nonlinear current flow in superconductors with restricted geometries[END_REF].

They overlap and form a pillow-shaped flux front, as shown in Fig. 2 reduced critical currents across the strips, J ⊥ c . An estimate of the anisotropy ratio from Fig. 2(d) yields J c /J ⊥ c ∼ 2.6. When H z is increased further, the MO picture remains qualitatively the same, although the anisotropy decreases, as demonstrated by the shortening of the dark central horizontal line in the critical state envelope in Fig. 2(e) (J c /J ⊥ c ∼ 1.9). At an even larger normal field, the anisotropy reduces only slightly from this value.

Ramping the field down from a maximum (in this case, H max z = 276 Oe) inverts the critical currents and the dark MO lines, corresponding to maximum screening transform into bright lines of maximum trapped B z [Fig. 2(f)]. The envelopelike shape of the critical state pattern remains the same, as in the case for increasing H z . With further decreasing field, the horizontal center line of the envelope lengthens, indicating the increased anisotropy of the critical currents at smaller B z [Fig. 2(g)]. The decrease and increase of the anisotropy upon ramping the field up and down, respectively, demonstrate the competition of intervortex interactions with the effect of the magnetic strips.

Reducing H z further causes negative flux (dark contrast) induced by the reversed currents to enter near the sample edges, and the critical state envelope shows a pronounced asymmetry with respect to the left and right sides of the strip array [Fig. 2(h)]. The horizontal center line shifts to the left, and the bright SCT lines on the left side of the Py pattern become shorter. Also, a qualitative difference in the negative vortex entry is observed at the left and right sides of the sample. The asymmetry is better seen in the expanded view of the two sides upon both increasing and decreasing H z in Fig. 3. With increasing H z [Fig. 3(a)], the positive vortices are delayed at the first positively charged edge on the right but pass easier across the furthest most left negatively charged edge and accumulate at the next positive edge (the left and right edges of the Py pattern are marked by double arrows in Fig. 3). Hence, positively charged strip edges provide stronger pinning for positive H z vortices than negatively charged edges. Such a behavior is unusual because the maximum pinning force, F p , for the oppositely charged edges should be practically the same. We associate the asymmetry with the dynamic nature of the vortex crossing over the strip edges. When the positive vortex approaches the negatively charged line, it is attracted and accelerates towards the line. In contrast, a similar vortex approaching the positively charged line will decelerate and stop at the line.

With reducing H z [Fig. 3(b)], the normal induction drops and changes sign around the most left edge of the Py pattern (contrast changes to dark), resulting in the increased local current along this edge. This yields a zigzag shift of the SCT line in the patterned area, as marked by the blue arrows in Fig. 3(b) and schematically shown in Fig. 3(c). The average direction of the SCT lines under the strips remains the same, but the triangular region bound by these lines on the left becomes smaller than that on the right. As a result, the centerline of the critical state envelope pattern extends to the left. At larger H z , the left-right asymmetry disappears due to the increased vortex-vortex interactions overcoming the magnetic pinning. For opposite polarity of the transverse in-plane field, the asymmetric patterns mirror-flip horizontally.

Reducing the positive H z field to zero and applying a negative H z lead to advanced penetration of negative vortices along the Py strips [Fig. 2(k)], which eventually results in an anisotropic critical state similar to that in positive H z (not shown). A new feature that emerges with increasing negative field is the unexpected appearance of extended negative vortex regions near the middle of the sample [dark streaks around the center line in Fig. 2(k)] prior to their formation near the top and bottom strip ends. These regions aligned with the strips appear irregularly across the horizontal SCT line. We associate them with dynamic instabilities caused by the strip-induced anisotropy of the vortex motion, which breaks the continuous loops of current flowing around the horizontal center line of the sample. As a result, a chain of current loops appear, supporting locally enhanced negative fields between them. The situation is similar to the inversion of field between current rings of the same chirality. At larger negative fields, these negative vortex regions merge, with streaks of negative B z extending along the interstrip gaps from the top and bottom sides of the Py pattern, and form a structure similar to that observed with positive H z . After ramping down the negative H z , the positive vortices induced near the sample edges by the inverted critical currents are delayed stronger on the right side of the Py pattern but easily cross the leftmost strip. Also, the SCT center line shifts to the right. The asymmetry is opposite to that observed for negative vortex entry when reducing positive H z .

Fine details of vortex entry dynamics induced by transversely polarized Py strips can be better seen in the MO images taken at larger magnification. Before the flux front induced by H z reaches the tips of the Py strips, brighter lines of positive B z appear along the longitudinal strip edges [marked by red vertical arrows and ellipse in Fig. 4(b)]. At the same time, dark spots of negative B z emerge near the strip ends [marked by tilted arrows and circle in Fig. 4(b)]. This unusual behavior is associated with vortices formed upon cooling the sample through T c in the presence of stray fields (H s ) at the long Py strip edges. As shown in the cross-section schematic of the sample in Fig. 4, near the longitudinal Py edges with positive magnetic charge and diverging stray field H s , the H s -created vortices carry negative B z . At the opposing longitudinal edge of the adjacent Py strip with negative magnetic charge, the H s vortices carry positive B z . When an external H z is ramped up at T < T c , the Meissner current induced Lorentz force F L acts on the H s vortices in opposite directions. For positive H s vortices, F L is pointing inside the sample while for negative H s vortices, F L is directed towards the sample edges. When the B z front approaches the ends of the strips, the Meissner current, J M , ahead of the flux front becomes comparable with the critical current J c flowing behind the front, and F L overcomes the pinning force. As a consequence, the positive H s vortices advance inside, while negative H s vortices move to the ends of the strips where they assemble into dark droplets of negative B z , as illustrated in Fig. 4(b). With further increasing field, incoming positive H z -induced vortices annihilate these droplets and move into the interstrip gaps forming bright lines of enhanced positive B z along them [Fig. 4(c)]. Also, the sharp B z front enters in the shape of fingers across the uncharged ends of the Py strips [indicated by arrows in Fig. 4(c)]. At higher fields, the modulated B z front advances inside the sample and forms an inhomogeneous distribution of B z , where the density of vortices is maximum near the left sides of the gaps and smoothly decreases to the right [strips of bright contrast in Fig. 4(d)]. Thin lines in Fig. 4(d) mark the middle of the interstrip gaps. Clearly, new positive H z vortices pile up on the left of the interstrip gaps at the positively charged strip edges, but they pass more easily to the right across neighboring negatively charged strip edges. This forms a flux gradient with B z decaying rightward from the gap into the strips. The above flux pattern corresponds to the wiggling current trajectories sharply bending near the positively charged edge of the Py strips, as sketched in Fig. 5 [82]. Here the increasing B z corresponds to the downward arching and decreasing B z to the upward arching of the current lines, and sharper bends in the current trajectory yield enhanced concentration of positive vortices at the positive edges. In Fig. 5(a), the increasing distance between the current lines towards the top of the picture reflects the decay of the Meissner current towards the center of the sample. The meandering current trajectories yield spatially oscillating anisotropic supercurrent density. The longitudinal current density (J parallel to strips) is maximum, and the transverse current density (J ⊥ perpendicular to strips) is minimum at the positively charged strip edges. Towards the middle of the strips, J drops, and J ⊥ increases. The resulting SCT lines in the global critical state also meander but straighten with increasing H z .

The described flux evolution, in the presence of the transversely polarized Py strips, is a consequence of the interactions between entering H z vortices induced by the applied normal field and the magnetic potential formed at the edges of the strips. In the beginning these interactions are modified by the presence of field cooled H s vortices. As already mentioned, we can consider edges of the thin Py strips polarized across their length as magnetically charged filaments. Positive and negative charge signs on opposite sides of the strip should form a potential barrier ridge and a potential valley groove for the positive H z vortices, as shown in Fig. 6. For a long line with a linear charge density ρ l = ±Md f , the magnetic field is directed radially from the line and decays as H s = ρ l /2πR, with radius R about the line. This approximation is valid when the length of the line is much larger than all other dimensions in the problem. Then for a normal vortex evaluated as a point magnetic charge of 2 0 [START_REF] Carneiro | Vortex lines in films: Fields and interactions[END_REF], the charged strip edge will form a linear potential U = ± 2 0 H s dx for vortex motion across the edge, logarithmically decaying with R. The spatial variations of the potential U ∼ lnR and appropriate pinning forces F p ∼ 1/R (in arbitrary units) in the gap area between the Py strips are shown in Fig. 6. Here the divergence of U and F p at small distances is eliminated by a cutoff radius of the order of the FM film thickness. The large distance divergence of the logarithm cancels due to the opposite charges on either side of the interstrip gaps.

Accurate calculations of the strip edge-vortex coupling force with exact analytical formulas that account for the SC screening effects are discussed in the Appendix. They yield a magnetic pinning curve very close to that shown in Fig. 6 interpretation. Qualitatively similar description of magnetic pinning by FM microstructures was obtained within the London approximation for individual in-plane magnetized FM bars above a SC film in Ref. [START_REF] Milosevic | Vortex pinning in a superconducting film due to in-plane magnetized ferromagnets of different shapes: The London approximation[END_REF]. However, the integral formulas in Ref. [START_REF] Milosevic | Vortex pinning in a superconducting film due to in-plane magnetized ferromagnets of different shapes: The London approximation[END_REF] are dependent on the magnet bar shape, which is different from our geometry. In our case, long edges of the transversely polarized Py strips introduce strong anisotropy to the critical currents with preferred current flow along the strip edges. Such anisotropy, responsible for the oscillating current patterns shown in Fig. 5, is clearly revealed in our experiments (Figs. 234).

C. Temperature variations of the vortex motion anisotropy induced by transversely polarized strips

In Fig. 7, we present the global critical state pictures observed in the sample at different temperatures. As noted above, in the areas without magnetic strips at the sample periphery, the SCT lines follow the square diagonals due to the isotropic currents in pure Nb film. In the area under the magnetic strips, the SCT lines change their direction and form an envelopelike pattern, corresponding to the critical current anisotropy. The ratio of the average currents along and across the strips, k = J c /J c⊥ , depends on the applied normal field and changes with temperature. Estimates of k(T) obtained from the MO patterns at smaller (squares) and larger H z (circles) are presented in Fig. 8. At T > 7 K, the positions of the SCT lines in the Py pattern area are not well defined, and the values of k can be estimated only approximately. Figures 7 and8 clearly show that the anisotropy increases with temperature. Such a behavior could be expected since at high temperatures the conventional vortex pinning by inherent defects decreases and the magnetic pinning by Py strip edges becomes the dominant factor dictating vortex motion. At T < 7 K, the error in the k values is small, and the plot shows that at least in this temperature range the anisotropy decreases at larger fields. This corresponds to the decreased efficiency of Py strip induced magnetic pinning upon enhancement of intervortex interactions.

D. Longitudinal polarization of Py strips

For in-plane magnetic fields applied parallel to the strip length, the magnetic charges are localized at the narrow strip ends, as shown in Fig. 9. Small gaps between strips are neutral, although there are decaying stray fields from the neighboring strip ends. As before, we can consider the ends of the thin Py strips, which are much longer than the film thickness, as filaments of positively and negatively charged magnetic monopoles. Therefore, they should form potential barrier ridges and potential valley grooves for H z -vortex motion. However, unlike the transverse strip polarization, which induces periodic potential lines all over the magnetic pattern, the longitudinal polarization of the strips yields only two dashed potential lines (interrupted by the interstrip gaps) at the top and bottom edges of the patterned area. The sign of the charge at the strip ends will define the vortex entry across them. Indeed, we observe accumulation of positive H z vortices at the positively charged strip ends [dashed bright contrast near the bottom line of the strip ends in Figs. 9(a)-9(d) and in the expanded view Fig. 9(h)], and unobstructed vortex entry across the negatively charged strip ends at the top of the sample. At the bottom, the flux penetrates in the patterned area through the gaps between the positively charged ends. Here vortices enter in the shape of extended B z balloons, and vortex-free (dark) triangular regions remain behind the strip ends [Figs. 9(b) and 9(h)]. Although the depth of B z penetration at the top and bottom of the sample appear to be practically identical, the total amount of vortices entering across the positively charged strip ends is smaller than that passing through the negatively charged ends. This difference is more noticeable for narrower gaps between the strips [START_REF] Vlasko-Vlasov | Triode for magnetic flux quanta[END_REF]. On the left and right neutral sides of the Py pattern, the effect of the strips is not visible.

With further increasing H z , the normal flux penetrates deeper from all sides [Fig. 9(c)]. However, new vortices enter without a delay across the top (negative) and left and right (uncharged) edges of the Py pattern, where they form a smooth pillow-shaped front. The only barrier remains at the positively charged bottom strip ends, where the flux enters through the interstrip gaps and then spreads under neighboring strips. Deeper into the sample, the extended vortex balloons coalesce into a smooth B z front. New vortices accumulate near the external side of the positive strip ends, leaving the small vortex density at their inner side, as revealed by characteristic bright/dark diamonds in Figs. 8(b), 8(c), and 8(k). At larger normal fields, when B z occupies the entire sample and forms the global critical state, the SCT lines follow the square diagonals of the sample, indicating the absence of the average current anisotropy [Fig. 9(d)]. However, the darker/brighter diamonds (although with weaker contrast) still remain along the bottom Py strip ends.

The contrast in the MO images inverts with subsequent ramp down of H z . The exiting positive H z vortices now accumulate at the inner side of the positively charged strip ends, leaving a smaller B z on the outer side, hence forming the inverted diamond patterns [Figs. 9(e) and 9(k)]. Finally, at H z = 0, balloons of negative vortices (dark) enter from the sample edges across the positive (bottom) ends of the Py strips without obstruction [see green arrows in Fig. 9(f)].

At T > 6 K, the flux patterns in both increasing and decreasing normal fields reveal an apparent interaction between the longitudinally polarized Py strips and the incoming and outgoing H z induced vortices. Figures 10(a)-10(c) show that with increasing H z , the flux streaks extend along the strips and follow the strip period. Minimum B z position, separating the streaks, is settled along the middle lines of the strips. Maximum B z forms along the interstrip gaps, indicating the preferable propagation of the positive vortices along the gaps. This occurs at both top and bottom ends of the strips, even though the dark-bright diamonds appear only at the positive (bottom) strip ends. Vortex motion across the strips at the left and right sides of the strip pattern remains basically unperturbed with a smooth B z distribution absent of strip periodicity. With decreasing H z , the vortices preferentially exit the sample along the interstrip gaps, leaving behind bands of reduced B z [Figs. 10(d)-10(f)]. The observed flux periodicity indicates that at larger temperature, the coupling between the vortices and the Py strips (probably due to weak polarization of Py by the vortex field) overcomes vortex pinning by inherent defects even when the long strip edges are not magnetically charged. This coupling is also revealed by the appearance of the anisotropic envelope pattern in the global critical state. It is better seen in Figs. 10(e) and 10(f), where a short vertical SCT line appears at the center. It points to slightly smaller average currents along Py strips, corresponding to easier vortex exit across the strips towards their gaps along which they then exit to the sample edges. This anisotropy, though, is much smaller than that for the transversely polarized strips.

E. Diagonally polarized Py strips

When the in-plane magnetic field is applied along the diagonal of the Py pattern, the magnetic charges, although smaller, appear along both the long sides and short ends of the strips. Here, we observe both vortex guiding along the interstrip gaps and magnetic pinning at the positively charged strip ends (Fig. 11). However, both effects are weaker than for purely transverse and longitudinal strip polarizations, as described below.

In Fig. 12, the H z -vortex distributions are compared for transverse, diagonal, and longitudinal polarizations of the Py pattern at the same fixed normal field and temperature of H z = 15.4 Oe and T = 4 K, respectively. Qualitatively, the diagonally magnetized strips act very similar to the transversely polarized strips, although the penetration of B z along the interstrip gaps [bright lines in Figs. 12(a) and 12(b)] is shallower. Also, at the bottom strip ends, there are dark/bright diamond structures, as in the case for longitudinal polarization but with weaker contrast (i.e., with smaller B z gradient).

In Figs. 12(d)-12(f), we compare the global critical state images at 4 K for all three directions of H || at H z = 66.2 Oe. As expected, the envelope pattern shows smaller anisotropy for diagonal Py strip polarization than for the perpendicular polarization.

The above observations show that vortex guided motion resulting from magnetic charges along the long strip edges is the major effect of the Py strip array. It produces the largest dynamic anisotropy, which can be easily tuned by changing the angle of the in-plane field with respect to the magnetic strips. In addition, at the ends of the Py strips, it is possible to create a grid of strong pinning barriers regulating the entry of normal vortices through the interstrip gaps. The barrier effect is maximum for longitudinal strip polarization and also can be tuned by rotating the in-plane field from the long strip axis. Therefore, it is possible to manipulate the normal vortex entry in the Py patterned area in a controllable way.

III. CONCLUSIONS

A parallel array of soft FM strips with in-plane magnetization on top of a SC film allows tunable manipulation of Abrikosov vortices. Extending our earlier finding [START_REF] Vlasko-Vlasov | Triode for magnetic flux quanta[END_REF], in this paper we conducted a comprehensive study of the interactions between thin Py strips and vortices in a Nb film and discussed the nature of the observed vortex guiding and magnetic pinning effects.

The main action of Py strips on the underlying vortex dynamics is the control of vortex entry and exit in the sample. It arises from the magnetic charges emerging at the polarized strip edges and is defined by their magnetization component perpendicular to the edge. Abrikosov vortices interact with these linear charges as positive or negative pointlike magnetic monopoles, depending on the vortex polarity. When the strips are transversely magnetized by the in-plane field, positive and negative magnetic charges formed at opposite long edges create repulsive barrier ridge and attractive valley groove for the Abrikosov vortices. The strongly increasing magnetic potential at small distances from the lines of charged strip edges (in the first approximation as lnR) causes a substantial supercurrent anisotropy. The anisotropy is enhanced locally near the strip edges and results in meandering current trajectories with sharp bends at the edges. It supports advanced penetration of vortices along the strip edges of the same magnetic polarity and increased pinning for vortices moving across the edges. For vortices of the opposite magnetic polarity, the strip edges do not show a noticeable delay due to acceleration of vortices attracted towards such edges.

When the Py strips are polarized longitudinally, their ends can work as a grid, where the gaps between the strips act as gates, while the ends themselves form an efficient barrier for Abrikosov vortices. Reducing the gap width provides stronger gating effect [START_REF] Vlasko-Vlasov | Triode for magnetic flux quanta[END_REF]. By rotating the magnetization of the Py strips with a relatively small in-plane field, the magnetic charges at their edges can be changed, which allows tuning the effects of the strip pattern on the flux dynamics from vortex acceleration to inhibition.

We envision that by choosing appropriate material parameters (such as low pinning SC and soft FM components) and dimensions of the hybrid structure (thickness of SC and FM films, length and width of the strips, and the size of the interstrip gap), it will be possible to fabricate components for controlling individual vortex motion for flux quantum electronics.

APPENDIX

Here we calculate the current in the SC film (in the XY plane) induced by the edge of a long FM strip (||Y), where magnetization is directed perpendicular to the edge face (M||X). This current multiplied by the flux quantum gives the Lorentz force acting on the Abrikosov vortex from the strip edge. The force is repulsive (positive) for the same sign of the magnetic charge of the vortex and the edge and attractive (negative) for opposite magnetic charges. When the FM film thickness is much smaller than all other dimensions in the problem, the magnetic field can be presented as a field of a linear monopole (long thin charged filament ||Y). It is directed radially perpendicular to the filament and decays with radius r as B = b/r. The magnetic charge per unit length in this case is b = 2Md f , where M is the saturation magnetization and d f is the FM film thickness. The vector potential of the filament is A y = bϕ, where ϕ is azimuthal angle around the filament axis. One can check that The total vector potential and the magnetic field can be divided into components due to the magnetic monopole of the vortex ( A V , B V ) and due to currents induced by the magnetic filament ( A s , B s ): -(q 2 + k 2 )A s (q,k) = [A M (q,z = 0) + A s (q,z = 0)] 1 λ eff with λ eff = λ 2 d , q = (q x ,q y ), and k = k z .

A = A V + A s and B = B V + B s.
Then skipping the index z = 0, we write the relation for A M (q) and A s (q) as A s (q) = A s (q,k) dk 2π = -A M + A s 2πλ eff dk q 2 + k 2

= -

A M + A s 2λ eff q , so that A s (q) = -A M (q) 1+2λ eff q . Then current in the SC film is

j (q) = - c 4πλ eff ( A M + A s ) = - c 4πλ eff 2λ eff q 1 + 2λ eff q A M = - c 2π q 1 + 2λ eff q A M .
Now we consider the gap between two magnetic strips, where the fields are produced by two oppositely charged filaments at a distance w and at some height h above the superconductor (h ∼ d f /2). Using the azimuthal angle ϕ = arctg(x/ h), the total vector potential A M is

A y (x) = b arctg x h -arctg x + w h .
Accounting for the fact that h is small, we replace arctg with a step function of height π so that the Fourier transform of A y (x) becomes

A y q = πb W 0 e iqx dx = - πb iq (1 -e iqw ).
Then the current distribution can be calculated as inverse Fourier Transform by substituting A y q in the above formula for J q, J (x) = 1 2π

∞ -∞

J q e -iqx dq = 1 2π ∞ 0 (J q e -iqx + J -q e iqx )dq Ci(x → 0) → γ + ln x(γ = 0.5772 is the Euler constant), while Ci(x → ∞) → 0.

The sine integral at small x tends to zero Si(x → 0) → 0, and Si(x → ±∞) → ±π/2.

However, one has to carefully choose the branches of Ci(x) and Si(x) for the intermediate x, which otherwise can result in a strongly oscillating function.

FIG. 1 .

 1 FIG. 1. (a) Optical picture of 2 × 2 mm Nb square with Py strips in the middle. (b) Schematic of magnetic charges along the long edges of transversely polarized Py strips. Each edge forms a magnetic monopole line with radially diverging magnetic stray fields H s . (c) MO image of the stray fields induced by the array of transversely polarized Py strips. Bright and dark contrast indicate the up and down directions of H s . The overlayed rectangle in (c) shows the positions of the strip ends and gaps.

FIG. 2 .

 2 FIG. 2. MO images of the normal flux distribution in the sample with transversely polarized strips; T = 4 K. Direction of H || is shown by the arrow in (a). Dashed square in (a) outlines the area of the Py pattern. The applied normal field H z increases in (a)-(e), decreases in (f)-(h), and changes sign in (k). Values of H z are shown on the panels. Intensity of bright contrast corresponds to the density of positive H z vortices. Dark contrast at the sample edges in (h)-(k) and along the strips in (k) reveals negative B z . Current schemes at the bottom correspond to isotropic (l) and anisotropic (m) homogeneous samples and the sample with anisotropic middle part (n). In the presented geometrical model of the critical state (l)-(n) distances between the supercurrent lines are inversely proportional to the current density. The angle of the SCT lines, where maximum screening occurs in the increasing H z [dark lines in (d) and (e)] or maximum trapped flux remains in the decreasing H z [bright lines in (f)-(h)], is defined by the ratio of J x /J y .

  FIG. 3. Left-right asymmetry of the vortex patterns for transversely polarized Py strips. The left and right sides of the sample at 4 K in increasing [(a): H z = 23.8 Oe)] and decreasing field [(b): H z = 0 after H max z = 276 Oe]. The furthest most left and right edges of the Py magnetic strips are marked by red double arrows. The shift of the bright SCT lines on the left side in (b) is shown by blue arrows. Positive vortices (bright) are not pinned at the most left strip edge in (a) (see left ellipse), but negative vortices (dark) are impeded at this edge in (b). Vice versa, positive vortices are delayed and accumulated at the most right edge in (a) (right ellipse), but negative vortices move across it smoothly in (b). (c) Schematic explaining the zigzag shift of the SCT line in (b) due to enhanced J c along the left side of the magnetic pattern. Similar but smaller zigzag shifts appear at each interstrip gap [not shown on the schematic but revealed on zigzagging SCT lines in (b)].

FIG. 5 .

 5 FIG. 5. Current trajectories (red lines) for the flux patterns in Figs. 4(b) and 4(d). Inset top left shows position of the strip gaps.

FIG. 6 .

 6 FIG. 6. The magnetic potential U ∼ lnR (top) and magnetic pinning force F p ∼ 1/R (bottom) for Abrikosov vortices moving across the gap between thin long transversely polarized FM strips. U and F p are in arbitrary units, and the distance R is in units of half the gap (D/2) between the strips. Potential barrier ridge and potential valley groove are formed along positively and negatively charged edges respectively (||Y).

FIG. 7 .

 7 FIG. 7. Temperature variations of anisotropic critical states for transversely polarized strips at smaller field H fill , when vortices first fill the entire sample (top set: H fill decreases from 55 Oe to 5 Oe with increasing T from 3.1 K to 8 K) and at larger field (bottom set: H z = 110 Oe). The anisotropy increases with T and drops with H z .

  FIG. 8. Ratio of the critical currents along and across transversely polarized Py strips estimated from positions of SCT lines in MO patterns. At T > 7 K, estimates are approximate and presented by double dots.

FIG. 9 .

 9 FIG. 9. Normal flux in the sample with longitudinally polarized Py strips in increasing (a)-(d) and decreasing (e) and (f) magnetic field H z at T = 4 K. The direction of the in-plane field is shown in (a) by the arrow. (g) Schematic of magnetic charges emerging at short ends of the strips. (h) Expanded view of the vortex distribution near the bottom line of strip ends at smaller H z . (k) Inversion of the flux "rhombs" near the positive strip ends with increasing (top) and decreasing H z (bottom).

FIG. 10 .

 10 FIG. 10. Normal flux entry (a)-(c) and exit (d)-(f) in the sample with longitudinally polarized strips at 7 K. The flux streaks from the top and bottom Py pattern sides follow the strip periodicity with maximum B z at the interstrip gaps. The flux entry across the strips (from the left and right sides of the Py pattern) lacks periodicity. The anisotropy of the exiting vortex dynamics yields short vertical SCT line in the sample center as shown in (e) and (f).

FIG. 12 .

 12 FIG. 12. Comparison of the flux distributions at the initial stage of magnetization (top row: H z = 15.4 Oe) and in the total critical state (bottom row: H z = 66.2 Oe) for three different polarization directions of the Py strip obtained at T = 4 K. Directions of the in-plane field are shown in the top pictures by white arrows.

  Below we use the Pearl's approximation for thin SC films (d < λ), admitting a two-dimensional distribution of sheet currents, j s , in the SC film. Then rot B = 4π c j s = -A λ 2 dδ(z).

2 λ 2 [

 22 dδ(z),rot B V = 0 → rot B s A V (z = 0) + A s (z = 0)]rot B s = -∇ 2 A s , and after Fourier transformation:

  2qλ eff {(1e -iqW )e -iqx -(1e +iqW ) × e +iqx }dq = cb 2π ∞ 0 sinq(x + w)sinqx 1 + 2qλ eff dq which after substitution, 2qλ eff = q, x 2λ eff = x, W 2λ eff = W , becomes J (x) = Ci(x)sinx -Si(x)cosx + π 2 cosx, where Ci(x) = -∞ x cost t dt is the cosine integral and Si(x) = x 0 sint t dt is the sine integral. Then, J (x) = cb 4πλ eff [f (x + w)f (x)]. Asymptotically, the cosine integral shows the logarithmic behavior for small arguments and saturates at large x:

  Division. The work of F. Colauto at Argonne National Laboratory was supported by the São Paulo Research Foundation (FAPESP) under Grant No. 2015/06.085-3. We used sample manufacturing facilities of the Center for Nanoscale Materials, supported by the U. S. DOE, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. A. I. Buzdin acknowledges support from the French National Research Agency (ANR) project "SUPERTRONICS."

ACKNOWLEDGMENTS

This paper was supported by the U.S. Department of Energy (DOE), Office of Science, Materials Sciences and Engineering