text:
using System;
using System.Net;
using System.Runtime.Serialization;

using Carbon.Data.Annotations;
using Carbon.Data.Sequences;
using Carbon.Security;

namespace Carbon.Cloud.Logging
{
    [Dataset("Clients", Schema = "Logs")]
    [DataContract]
    public class Client : IClient
    {
        public Client() { }

        public Client(Uid id, IPAddress ip, string userAgent)
        {
            Ensure.NotNull(ip, nameof(ip));
            Ensure.NotNull(userAgent, nameof(userAgent));

            Id        = id;
            Ip        = ip;
            UserAgent = userAgent;
            Hash      = ClientHash.Compute(this); // sha1(id, ip, userAgent)
        }

        [Member("id"), Key]
        [DataMember(Name = "id", Order = 1)]
        public Uid Id { get; }

        [Member("hash"), Key]
        [FixedSize(ClientHash.Length)]
        [DataMember(Name = "hash", Order = 2)]
        public byte[] Hash { get; }

        [Member("ip")]
        [DataMember(Name = "ip", Order = 3)]
        public IPAddress Ip { get; }

        [Member("userAgent")]
        [StringLength(1000)]
        [DataMember(Name = "userAgent", Order = 3)]
        public string UserAgent { get; }

        [Member("location")]
        [StringLength(255)]
        [DataMember(Name = "location", Order = 4, EmitDefaultValue = false)]
        public string Location { get; set; }

        #region IClient

        string IClient.Id => Id.ToString();

        #endregion
    }
}

redpajama_set_name: RedPajamaGithub


text:
Cotton Comes to Harlem | Village Voice
by R.C. Baker
Jacob Lawrence: "Migration Series" The Phillips Collection
As a teenager during the Harlem Renaissance, Jacob Lawrence (1917–2000) heard tales of the great African-American exodus from the Jim Crow South to the big northern cities after World War I. But the hoped-for promised land often proved unwelcoming—whites resented the influx of cheap labor, and many of the migrants suffered from their new home's harsh climate, a sentiment conveyed in Langston Hughes's "Po' Boy Blues": "When I was home de/Sunshine seemed like gold./Since I come up North de/Whole damn world's turned cold." Still, the North offered greater opportunity for education (the migration was characterized as "from medieval America to modern" by Alain Locke, the nation's first black Rhodes Scholar), and Lawrence studied art at the public library on 135th Street while trekking regularly to the Met to take in Giotto, Goya, and Matisse. In 1941, the still-maturing painter completed the 60 panels of his "Migration Series"; quickly recognized as a major achievement, it was featured in Fortune magazine and sent on a nationwide tour. Executed in tempera on board, 18 by 12 inches each, the paintings retain a powerful modernist aura. The figures are succinctly abstracted and vibrant, revealing the influence of Lawrence's Depression-era community: "Our homes were very decorative, full of pattern, like inexpensive throw rugs, all around the house. . . . I got ideas from them, the arabesques, the movement and so on." The 17 panels exhibited here come from Washington, D.C.'s Phillips Collection and include No. 9, "They left because the boll weevil had ravaged the cotton crop," which pictures snaking green stalks topped by pink and yellow puffs surmounted by cartoonish black insects. The brilliantly simplified view in No. 31—a tricolor apartment wall jazzily syncopated with red, yellow, and blue window blinds—recalls the semaphore rhythm of shades and awnings in Hopper'sEarly Sunday Morning (1930), while also looking ahead to a kinship with Mondrian's final, stripped-down primary abstraction,Broadway Boogie Woogie, which was completed two years later. One of the strongest panels, No. 1, depicts crowds moving through gates marked "Chicago," "New York," and "St. Louis"—the throng breaks into three distinct pyramids echoed by triangular travelers. These layers of repeated shapes at different scales imbue the composition with movement and narrative drama: an oppressed people in search of a better life majestically marching into the unknown. It's not hard to imagine Lawrence himself in that colorful tumult, a visionary whose masterpiece has come home to Harlem.
Kohei Yoshiyuki: "The Park"
Yossi Milo Gallery
Kohei Yoshiyuki
September 6–October 20
Yossi Milo, 525 W 25th, 212-414-0370
During the 1970s, Yoshiyuki ventured into Tokyo's public parks with camera and flash at the ready, capturing nocturnal trysters and crouching onlookers—some of whom joined the anonymous lovers—on infrared film. There is little nudity in these black- and-white shots, mostly hands reaching under uplifted skirts, spectators crawling through leafy bushes toward entwined couples, and men warily pairing up as they edge around tree trunks. Yet there's a queasy, erotic charge that photographer Martin Parr identified as "the loneliness, sadness, and desperation that so often accompany sexual or human relationships in a big, hard metropolis like Tokyo."
Robert Miller, 524 W 26th, 212-366-4774
An artist who often recycled her own drawings and canvases for collages, Krasner (1908–1984) showed grit and resilience in her work (and in her difficult marriage to Jackson Pollock). A piece such asWater
#20 (1969), with its lithe drips of lavender over thick blotches of magenta on rough-hewn paper, conveys a forcefulness that belies its seven-by-10-inch dimensions. In Heiroglyph #4, umber splatters are barely constrained within a cruiform maze of calligraphic brushstrokes. This energetic gouache painting foreshadows the violent beauty found in the hard-edged arcs and drippy arabesques of her large collage canvases.
Liset Castillo
Black and White, 636 W 28th, 212-244-3007
This Cuban-born artist photographs elaborate cityscapes that she sculpts from sand, mixing geography and architectural epochs. One image includes the massive monument to Christ the Redeemer (in reality, perched high over Rio de Janeiro) cheek by jowl with a collapsed Empire State Building and the Taj Mahal. A different incarnation of Castillo's ever-changing metropolis features a spiraling Tower of Babel contrasted against the inverted cone of the Guggenheim Museum. Her imaginary world is literally as ephemeral as a sand castle, yet the photographs proffer documentary "truth," lending historical gravitas to these fleeting civilizations.
Poe and Twain Projects
September 8–December 2
Wave Hill, 675 W 252nd, the Bronx, 718-549-3200
Three artists tackle the legacies of Edgar Allan Poe and Mark Twain in this spectacular garden setting overlooking the Hudson River. Allison Smith's period room riffs on Twain's riverboat themes and Wave Hill's flora and fauna. Simon Leung's video project is built upon intersecting scenes that explore some of Poe's most famous stories, while Amy Yoes expands on her recent delightful multimedia show at the Michael Steinberg gallery by delving into Poe's "Philosophy of Furniture" in an installation featuring sculpture and animated film.
Mark Stillwell: Super Defense Force
September 14–October 14
Front Room, 147 Roebling St., Brooklyn, 718-782-2556
Coney Island is under attack! Panicked throngs flee gargantuan insect-monsters in the shadow of the Wonder Wheel! Stillwell constructs his DIY tableaux from plastic bottles, paper-towel rolls, takeout cups, painted cardboard, plastic straws, and other homely materials that add exuberant charm to this gallery-filling panorama of carnage amid the carnival rides.
Piranesi as Designer
September 14–January 20
Cooper Hewitt, National Design Museum, 2 E 91st, 212-849-8400
You probably already know his labyrinthine views of "Imaginary Prisons," filled with shafts of Spielbergian light and zigzagging shadows, but Piranesi (1720–1778) only managed such convincing drama through solid compositional skills that resonate with architects and designers to this day. Promising a "major reassessment of Piranesi as a radical design reformer," the show will include comparisons of his work with antique pieces such as an 1802 Settee in the Egyptian Taste, made of gilded and ebonized beech and viridescent silk, and the architectural plans of such modern heavy hitters as Peter Eisenman (represented by his rendering for the Cardinals' stadium in Arizona).
Dara Friedman: Musical
September 17–October 5
Between Grand Central to Central Park South and Broadway to Park Avenue
You're walking along some leafy block just off Park Avenue (you don't live there, of course—just passing through to the Modern), and suddenly the doorman of a tony apartment building steps from under the awning and bursts into song. Later—maybe on your trip back to the No. 6 train—a young girl begins serenading passersby. What's up? Well, since Gotham is the greatest back lot ever, Friedman, a Miami-based video artist, has orchestrated nearly 100 spontaneous performances intended to "turn the volume up on the song that's going on in your head as you're walking down the street." Do we have to tip her crooning cabbies extra?
Molle Babbe at
"the age of rembrandt" at the Met
"The Age of Rembrandt"
September 18–January 6
The Metropolitan Museum of Art, 1000 Fifth Ave., 212-535-7710
The masters are all here: Rembrandt! Vermeer! Hals! Plus lesser-known artists representing the 228 Dutch paintings in the Met's collection, begun in 1871, when an American publishing magnate acquired a bumper crop of European canvases during the upheavals of the Franco-Prussian War. (Wars are always a good time to snatch up masterpieces at fire-sale prices.) In addition to the marquee names celebrating Rembrandt's 400th birthday (technically, last year), there will be paintings by their imitators—an unforgiving portrait of a stout woman done in the "style of Franz Hals" was described by Henry James as "a miracle of ugliness"—and one of only two known paintings by Margareta Haverman, a luminous and maniacally detailed still life of flowers.
November 7–December 22
up2 Apex Art, 291 Church St., 212-431-5270
Gentrification is the scourge of art. When brokers start eyeing that ratty outer-borough studio warren, can luxury lofts (and artists' migration to Peekskill) be far behind? This show promises artworks that will "explicitly concern themselves with the claiming and naming of space," while considering the ethics of squatting and how "the possession, habitation or designation of a site alters the place itself." The international roster, including Romanian Dan Perjovshci (witty cartoons) and Icelander Katrin Sigurdardottir (topographical constructions), will perhaps give us locals solace—we're not the only ones just workin' for the rent.
"Beatific Soul: Jack Kerouac on the Road"
November 9–March 16
The New York Public Library, Fifth Ave. and 42nd St., 212-930-0830
This broad exhibit features the Beat icon's "scroll" manuscript of On the Road—60 feet (or roughly half of the entire work) unrolled in specially built glass cases. Ephemera and relics include a pair of crutches Kerouac kept after he'd been injured playing football for Columbia, and a lantern from his days as a railroad brakeman, plus manuscripts and drawings by such usual suspects as William Burroughs and Lawrence Ferlinghetti. Topping it off: a selection of lurid paperbacks representing publishers' attempts to cash in on the "Beatnik" wave, and detailed fantasy-baseball materials that Kerouac created as a kid and played with throughout his life.
Ron Klein
Howard Scott, 529 W 20th, 646-486-7004
Sponges, sea shells, twisted twigs, and pine cones only hint at the organic cornucopia that Klein pins to the wall in these rhythmically cascading assemblages. The 11-foot-high Monk's Rhyme pairs the double helix of a thickly barbed vine with two large seed pods gathered from equatorial rainforests; these hard-shelled, banana-shaped scoops are filled with wax that has settled at steep angles, as if it had cooled in mid-pour. Klein leavens these natural shapes with springs, steel stars, fan belts, and other industrial bric-a-brac to create elegant deadfalls from some hybrid jungle.
More:Fall ArtsHarlemJacob LawrenceKohei YoshiyukiRon KleinVisual Arts

redpajama_set_name: RedPajamaCommonCrawl


Our rigorous strategy, environment friendly processes and practical guidelines that cover every contractual difficulty have made us the leading arbitral establishment. We design dispute resolution provisions tailored to our consumer and the particular transaction, conserving in thoughts the pliability and adaptability of arbitration and its potential to offer parties of different nationalities a impartial discussion board. The arbitrators' resolution is given after an informal continuing where each side presents evidence and witnesses.
Arbitration can solely happen if each parties have agreed to it. Within the case of future disputes arising beneath a contract, the parties insert an arbitration clause in the relevant contract. Alternatively, the Heart can counsel potential arbitrators with relevant expertise or straight appoint members of the arbitral tribunal. Binding Arbitration is a form of arbitration the place the choice by the arbitrator is legally binding and enforceable, just like a court order.
The Normal Clause, which is the inspiration for each customized clause, gives for arbitration under the Swiss Guidelines of International Arbitration with the choice to initiate mediation under the Swiss Rules of Business Mediation at any time before or during the arbitral proceedings. For cases the place the dispute is submitted to a three-member arbitral tribunal, time-limits of 30 days can be lowered to 15 days.
Worldwide arbitration can be utilized to resolve any dispute that's considered to be arbitrable," a time period whose scope varies from State-to-State, but which includes the vast majority of commercial disputes. Parties and FAI may choose arbitrators with optimal expertise, expertise and different skills to resolve a particular dispute. If a passable decision cannot be reached, the events can pursue a lawsuit.
Any dispute that can be settled by agreement between the parties could also be referred to arbitration for remaining determination. An arbitral tribunal can solely act with authorized impact if the events have agreed to refer disputes to it. This should already be executed at the contract signing, since it is troublesome to agree on an arbitration establishment or on an "ad hoc" proceeding as soon as a dispute has arisen.


We've created short instruction for Crypto Arbitrage Trading.
6. Make test trades with min possible lot sizes to make sure that API key are valid and settings are correct.
9. Try to find best matching diff to open and diff to close values for your trading pairs.
Diff to open and diff to close should be adjusted to fit your actual diffs, for example, if you see 3.6%/-3.5% current diffs it is not optimal to set 0.8% diff to to open and 0.8% diff to close. It would be much better to set 3.6% or little higher % to open and -2.0% to close (negative values allowed here). You keep estimated profit the same (0.8+0.8=3.6-2.0), but closing conditions will be met much faster.


how quickly will my house sell Fair Oaks options.
You remain in a customers market. There are a lot of residences to buy, yet inadequate customers to absorb them all. Because of this, lots of residences have been sitting on the market for months. Vendors are determined and distressed to sell. You discover a house that is provided for $275,000. You bring up a handful of comparable sales from the last month or two, as well as you find that the typical list price was $255,000.
Buying A House In Mexico Bottom line: No person should write off their imagine homeownershippurely because they can't fathom developing a deposit. There's always hope, so do not create your optionsoff till you look into them. That understands? You might end up pleasantly Fair Oaksd.
Tips On Buying A Confiscated Residence From A Bank Wells Fair Oaks is just one of the 4 biggest financial institutions within the USA as well as was started in 1852. The bank is locateded in Fair Oaks, Georgia as well as uses financial services throughout the globe. Wells Fair Oaks Residence Mortgage is in charge of one from every four mortgage within the country.
Getting A Mortgage As A Contractor Likewise not that the very same princples of discovering a house with bad credit history also apply when you need to know how you can re-finance a house with bad credit rating. Refinancing with bad credit history is type of like you are taking a look around for a mortage once again.
Realtors rarely intend to take a residential or commercial property that is overpriced, simply for the fact that the opportunities of offering it are slim, which suggests their opportunities of making a compensation are significantly lowered. Common sense is that you should consult with several realtors prior to choosing one to represent you, but if you regularly listen to a ball park rate that seems low to you, the price may be right. Real estate agents are (or must be) totally knowledgeable about the majority of realty activities in their market, and they ought to have the most effective suggestion of exactly how a home ought to be valued.
Obtaining A Mortgage With Bad Credit Rating And Also No Down Payment In addition, loan providers will certainly usually call for a flavoring period following a bankruptcy declaring or discharge. Usually, potential buyers with a bankruptcy will should wait 2 years from the date a Chapter 7 insolvency is discharged or one year from the date a Phase 13 insolvency is filed.
Brian Cox had been asking buyers whose deals had actually been approved to pay the money right into a NatWest savings account, in contravention of the Building Ombudsmans code of technique. Nonetheless, when Money called the company it claimed it was junking the deposit plan with prompt effect.
The fact is, the proprietors typically aren't selling (officially a minimum of), so to motivate them to part with their building, youll likely have to pay a little over the marketplace rate to obtain your home. Set a reasonable ceiling of exactly what you will certainly supply before you begin and budget as you usually would.
Buying Real Estate Without Cash Down Partnership: A typical path in real estate investment is through collaborations. What one financier does not have, the various other could make up for and also lots of partnerships will certainly involve one partner locating a distressed residential or commercial property at a discounted cost, while the various other one uses their credit report and functioning funding to finance it; simply see to it everyone is bringing something to the table. For far better capitalists, facets such as objectives, threat, roles, as well as return should always be gone over prior to producing any type of sort of partnership.
Due to the fact that house owners disregard their home loan payments, purchasing A House In Georgia Houses obtain confiscated after. And also some property owners will overlook your home itself. Some will become disgruntled towards the lending institution, to the point that they intentionally harm your home before leaving. This suggests you have to do two things prior to buying a repossession home. You must assess the problem of the property, and you have to think about the potential expense of fixings, if fixings are needed.
How To Get A Repossession Residence We talked about the significant possibility for financial savings when getting a foreclosure residence. This could attract a great deal of financiers as well as customers. It's a affordable as well as fast-moving market. If you want to stay on top of the marketplace, you should sign up for a foreclosure-tracking solution.
In a warm realty market, it could obtain very affordable when you're bidding versus various other celebrations. One method is to simply bid on multiple residences. In most states you can legitimately do this, however if you ever before locate on your own with synchronised acceptance offers, you have to instantly revoke the offer for your home you don't desire.
PCI - Pierce Area Investors http://www.piercecountyinvestors.com South Sound Investors Team Call: Greg Towne Telephone: (253) 380-0523 When: 1st Wednesday of each month, 7:00 pm Where: Call for info, Fair Oaks.


text:
News archive January 2019
News archive February 2019
News archive March 2019
News archive April 2019
News archive May 2019
News archive June 2019
News archive July 2019
News archive August 2019
News archive September 2019
DTAs & TIEAs
OECD & Model Conventions
CJEU Rulings
CJEU judges in Case C-329/18 Altic (VAT – Interpretation of Article 168(a) of Directive 2006/112/EC – Supply by co-contractors involved in tax fraud – Duty of care of the taxable person)
On October 3, 2019 the Court of Justice of the European Union (CJEU) judged in Case C‑329/18, Valsts ieņēmumu dienests versus 'Altic' SIA (ECLI:EU:C:2019:831).
This request for a preliminary ruling concerns the interpretation of Article 168(a) of Council Directive 2006/112/EC of 28 November 2006 on the common system of value added tax (OJ 2006 L 347, p. 1), as amended by Council Directive 2010/45/EU of 13 July 2010 (OJ 2010 L 189, p. 1) ('Directive 2006/112').
This request was made in the context of a dispute between the Valsts ieņēmumu dienests (Latvian tax administration; 'the tax administration') and 'Altic' SIA concerning a payment demand made to Altic for the amount of value added tax (VAT) on the purchase of rapeseed paid upstream and deducted by Altic, together with a fine and default interest.
The dispute in the main proceedings and the questions referred for a preliminary ruling
· Altic purchased rapeseed from 'Sakorex' SIA during the months of July and August 2011 and from 'Ulmar' SIA in October 2011. It is apparent from the order for reference that those companies contacted Altic, referring to Altic's media and internet advertisements. That rapeseed was received and stored in a warehouse owned by 'Vendo' SIA. Altic deducted the VAT paid on those purchases.
· Following an audit carried out at Altic, the tax administration took the view that the purchase transactions had not actually taken place. It ordered Altic to pay to it the VAT deducted, together with a fine and default interest.
· The Administratīvā rajona tiesa (District Administrative Court, Latvia) upheld the action brought by Altic for annulment of the tax administration's decision. The decision of that court was confirmed by the Administratīvā apgabaltiesa (Regional Administrative Court, Latvia).
· The latter court noted that it was not in dispute that the rapeseed had been received in the warehouse on the dates and in the quantity indicated in Vendo's accompanying documents. It held that, in the circumstances, Altic acted in good faith and relied fully on the ability of Sakorex and Ulmar to deliver the contracted goods, an ability which Altic was not responsible for verifying. In that regard, the tax authorities did not state which specific actions arising from the relevant rules Altic had failed to take to carry out such verification.
· The tax administration appealed in cassation to the referring court, namely the Augstākā tiesa (Supreme Court, Latvia). It argues that, in accordance with Regulation No 178/2002, food business operators must be able to identify any substance intended or likely to be incorporated into food or feed and must, to that end, have systems and procedures in place to make the information available to the competent authorities. However, Altic did not carry out any minimum checks on its contracting partners or ascertain that they were registered with the Latvian Food and Veterinary Agency. That means that Altic knew or should have known that it was involved in a misuse of the common system of VAT.
· According to the referring court, it is not in dispute that there are indications that Sakorex and Ulmar are fictitious undertakings and that the origin of the goods in question cannot be established. Consequently, the question arises as to whether Altic knew or should have known that the transactions in question in the main proceedings amounted to VAT fraud.
· In that regard, the referring court notes that there is no evidence to confirm that the rapeseed purchased was exclusively intended for use in the production of fuel, as alleged by Altic, or at least that it was in no way linked to the food chain. Consequently, there is support for the view that, as regards those operations, Altic was required to comply with the provisions of Regulation No 178/2002.
· That court states that Article 18 of that regulation lays down the general principles for the traceability of foodstuffs and the identification of their suppliers. With regard to that identification, it notes that, although that regulation does not specify to what extent an undertaking must identify its supplier, it follows from the Guidelines for the implementation of Articles 11, 12, 14, 17, 18, 19 and 20 of Regulation No 178/2002 of 26 January 2010, in the Conclusions of the European Commission's Standing Committee on the Food Chain and Animal Health, that undertakings are required to keep information on the name and address of the supplier of the product and on the product identification.
· The referring court entertains doubts, however, as to whether the objective of Regulation No 178/2002, namely to guarantee the safety of food, does not require proof of greater diligence on the part of the food business operator as regards the choice of its contracting partner, which would require it to carry out checks on that partner, in particular on its registration with the competent authorities, and whether, in the absence of such diligence, that operator may be refused the right to deduct VAT. In that regard, the referring court also queries whether, in the light of that same objective, Altic's verification of the quality of the goods delivered could be such as to reduce that obligation to carry out a more detailed investigation into the contracting partner.
· The referring court further notes that, according to the tax administration, Altic's failure to ascertain whether the contracting parties were registered with the Food and Veterinary Agency shows that that company knew or should have known that the transactions at issue in the main proceedings amounted to VAT fraud. However, that court is of the view that, although the verification of registration of a food business provided for in Regulations No 852/2004 and No 882/2004 ensures that it participates legally in the food chain, the registration of a business does not rule out its economic activity being fictitious and, conversely, the absence of registration does not automatically establish that it is fictitious, so that the lack of verification cannot decisively support the tax administration's finding.
· In those circumstances, the Augstākā tiesa (Supreme Court) decided to stay the proceedings and to refer the following questions to the Court of Justice for a preliminary ruling:
'(1) Having regard to the aim of ensuring food safety established in [Regulation No 178/2002] (which is achieved, amongst other means, by ensuring food traceability), should Article 168(a) of [Directive 2006/112] be interpreted as not precluding a refusal to allow deduction of input tax where the taxable person involved in the food chain, in choosing his co-contractor, has failed to demonstrate greater diligence (beyond normal commercial practice) entailing, in essence, a requirement to carry out checks on his co-contractor, but where he has at the same time verified the quality of the foodstuffs, thus meeting the aim of [Regulation No 178/2002]?
(2) Does the requirement in Article 6 of Regulation No 852/2004 and in Article 31 of Regulation No 882/2004 concerning regulation of a food business, as interpreted in the light of Article 168(a) of [Directive 2006/112], require a party that contracts with that business to check that the business is registered, and is that check relevant for the purposes of determining whether that party knew or should have known that it was taking part in a transaction with a fictitious undertaking, having regard to the particular characteristics of the transaction in question?'
The CJEU judged as follows:
1. Article 168(a) of Council Directive 2006/112/EC of 28 November 2006 on the common system of value added tax, as amended by Council Directive 2010/45/EU of 13 July 2010, must be interpreted as precluding a taxable person who participates in the food chain from being refused the right to deduct input value added tax (VAT) on the sole ground, assuming that it has been duly established, that that taxable person has not complied with his obligations under Article 18(2) of Regulation (EC) No 178/2002 of the European Parliament and of the Council of 28 January 2002 laying down the general principles and requirements of food law, establishing the European Food Safety Authority and laying down procedures in matters of food safety, to identify his suppliers for the purposes of traceability of foodstuffs, which it is for the referring court to ascertain. Non-compliance with those obligations may, however, constitute one element among others which, taken together and in a consistent manner, tend to show that the taxable person knew or should have known that he was involved in a transaction involving VAT fraud, which it is for the referring court to assess.
2. Article 168(a) of Directive 2006/112, as amended by Directive 2010/45, must be interpreted as meaning that the failure, by a taxable person who participates in the food chain, to ascertain that his suppliers are registered with the competent authorities, in accordance with Article 6(2) of Regulation (EC) No 852/2004 of the European Parliament and of the Council of 29 April 2004 on the hygiene of foodstuffs and Article 31(1) of Regulation (EC) No 882/2004 of the European Parliament and of the Council of 29 April 2004 on official controls performed to ensure the verification of compliance with feed and food law, animal health and animal welfare rules, is not relevant for the purpose of determining whether the taxable person knew or should have known that he was involved in a transaction involving VAT fraud.
From the consideration of the Court
The first question
· By its first question, the referring court asks, in essence, whether Article 168(a) of Directive 2006/112 must be interpreted as precluding a taxable person who participates in the food chain from being denied the right to deduct input VAT on the ground that he has failed to comply with his obligations under Article 18(2) of Regulation No 178/2002 to identify his suppliers for the purposes of the traceability of foodstuffs.
· First, it must be borne in mind that, in accordance with the settled case-law of the Court, the right of taxable persons to deduct from the VAT that they are liable to pay the VAT due or paid on goods purchased and services received by them as inputs is a fundamental principle of the common system of VAT. The deduction system is intended to relieve the trader entirely of the burden of the VAT payable or paid in the course of all his economic activities, provided that his activities are themselves subject, in principle, to VAT (see, to that effect, judgment of 19 October 2017, Paper Consult, C‑101/16, EU:C:2017:775, paragraphs 35 and 37 and the case-law cited).
· The right of deduction is an integral part of the VAT mechanism and cannot, in principle, be limited if the material and formal requirements or conditions to which this right is subject are respected by taxable persons wishing to exercise it (see, to that effect, judgment of 19 October 2017, Paper Consult, C‑101/16, EU:C:2017:775, paragraphs 36 and 38 and the case-law cited).
· In addition to those requirements or material and formal conditions, which derive from Article 168(a) and Article 178(a) of Directive 2006/112 (see, to that effect, judgment of 19 October 2017, Paper Consult, C‑101/16, EU:C:2017:775, paragraphs 39 and 40), Article 273 of that directive allows the Member States, subject to certain conditions, to impose other obligations which they deem necessary to ensure the correct collection of VAT and to prevent fraud.
· Second, it must also be borne in mind that the prevention of tax evasion, tax avoidance and potential abuse is an objective recognised and promoted by Directive 2006/112. The Court has held that EU law cannot be relied on by individuals for abusive or fraudulent ends. Accordingly, it is for the national courts and authorities to refuse the right of deduction, if it is shown, in the light of objective evidence, that that right is being relied on for fraudulent or abusive ends (judgment of 13 March 2014, FIRIN, C‑107/13, EU:C:2014:151, paragraph 40 and the case-law cited).
· If that is the case where tax evasion is committed by the taxable person himself, it is also the case where a taxable person knew or should have known that, by his acquisition, he was involved in a transaction involving VAT fraud (judgment of 22 October 2015, PPUH Stehcemp, C‑277/14, EU:C:2015:719, paragraph 48 and the case-law cited).
· It is for the tax authorities, having found fraud or irregularities committed by the issuer of the invoice in question, to establish, in the light of objective factors and without requiring the addressee of that invoice to carry out checks which are not his responsibility, that the addressee knew or should have known that the transaction relied on to establish the right of deduction was involved in VAT fraud (judgment of 22 October 2015, PPUH Stehcemp, C‑277/14, EU:C:2015:719, paragraph 50 and the case-law cited).
· As regards the level of diligence required of a taxable person wishing to exercise his right to deduct VAT, the Court has held that traders who take every precaution which could reasonably be required of them to ensure that their transactions are not connected with fraud, be it the fraudulent evasion of VAT or other fraud, must be able to rely on the legality of those transactions without the risk of losing their right to deduct the input VAT, the determination of the measures which may, in a particular case, reasonably be required of a taxable person to that end depending essentially on the circumstances of that particular case (see, to that effect, judgments of 21 June 2012, Mahagében and Dávid, C‑80/11 and C‑142/11, EU:C:2012:373, paragraphs 53 and 59, and of 22 October 2015, PPUH Stehcemp, C‑277/14, EU:C:2015:719, paragraph 51).
· In the main proceedings, the tax administration, taking the view that Altic's suppliers were fictitious companies and that there was therefore a question of fraud of the common VAT system, refused Altic the right to deduct VAT. In particular, it was of the opinion that Altic, as a food business operator, was required to carry out a thorough verification of its contracting parties in accordance with Article 18(2) of Regulation No 178/2002. Failure to comply with such an obligation shows that Altic knew or ought to have known that it was a party to transactions involved in that fraud.
· However, on the one hand, as the Advocate General noted point 46 of his Opinion, the refusal of the right to deduct VAT as a consequence of the failure to comply with the obligations arising from that provision of Regulation No 178/2002 has no legal basis in Directive 2006/112. The obligations laid down in Regulation No 178/2002 are not related to the requirements or the material and formal conditions attaching to the right of deduction laid down in that directive. Nor it is apparent from the evidence before the Court that that ground for refusal is based on the relevant national VAT legislation.
· On the other hand, and with regard to the fact that, according to the findings of the referring court, Altic was involved in the food chain and therefore had to comply with the provisions of Regulation No 178/2002, it should be noted that the obligation relating to the traceability of foodstuffs laid down in Article 18(2) of that regulation pursues a purpose different from that of detecting VAT fraud. Indeed, it follows from recitals 28 and 29 of that regulation that the obligation to identify food suppliers is intended to allow targeted and precise withdrawals of foodstuffs and to inform consumers or official inspectors, in order to avoid the possibility of more significant and unnecessary disruption to the internal market. Failure to comply with that obligation may result in penalties under national law, in accordance with the third subparagraph of Article 17(2) of that regulation.
· It follows that such an obligation cannot, as such, be regarded as a measure which the taxable person may reasonably be required to adopt in order to ensure that his transactions are not involved in fraud against the common VAT system. Accordingly, as the Advocate General pointed out in point 56 of his Opinion, any breach of that obligation cannot in itself and automatically justify the refusal to allow that taxable person to deduct VAT.
· In that context, it is also necessary to recall that the obligation referred to in Article 18(2) of Regulation No 178/2002 consists, in the very terms of that provision, in the identification of any supplier of a foodstuff and in the establishment of systems and procedures to ensure that such information is made available to the competent authorities at their request.
· As regards the data required for that identification, the view must be taken that those data must make it possible to achieve the objective of traceability, as described in paragraph 35 of this judgment, so that, in principle, it is sufficient to identify suppliers by their name and address. It follows that the argument put forward by the tax administration before the referring court and by the Latvian Government in its written observations that the regulation generally requires a thorough check of the contracting partner cannot be accepted.
· It would be otherwise only if it were duly established that, because of particular circumstances, the purchaser of the foodstuffs concerned should have had serious doubts as to the true existence or identity of the supplier of the foodstuffs whom Regulation No 178/2002 requires him to identify, in such a way that he is careful to be certain of that identity, which it will be for the referring court to ascertain, if necessary.
· Assuming that to be the case, that fact could constitute one of a number of indications which, taken together and in a consistent manner, tend to show that that taxable person knew or should have known that he was involved in a transaction involving VAT fraud.
· In the light of the foregoing considerations, the answer to the first question is that Article 168(a) of Directive 2006/112 must be interpreted as precluding a taxable person who participates in the food chain from being refused the right to deduct input VAT on the sole ground, assuming that it has been duly established, that that taxable person has not complied with his obligations under Article 18(2) of Regulation No 178/2002 to identify his suppliers for the purposes of traceability of foodstuffs, which it is for the referring court to ascertain. Non-compliance with those obligations may, however, constitute one element among others which, taken together and in a consistent manner, tends to show that the taxable person knew or should have known that he was involved in a transaction involving VAT fraud, which it is for the referring court to assess.
The second question
· By its second question, the referring court asks, in essence, whether Article 168(a) of Directive 2006/112 must be interpreted as meaning that the failure by a taxable person who participates in the food chain to ascertain that his suppliers are registered with the competent authorities, in accordance with Article 6(2) of Regulation No 852/2004 and Article 31(1) of Regulation No 882/2004, is relevant for the purpose of determining whether the taxable person knew or should have known that he was involved in a transaction involving VAT fraud.
· In that regard, Article 6(2) of Regulation No 852/2004 provides that a food business operator is to inform the appropriate competent authority of each of its establishments involved in the production, processing and distribution of foodstuffs with a view to their registration. In accordance with Article 31(1)(a) and (b) of Regulation No 882/2004, the competent authorities are required to define the procedures to be followed by those operators when applying for the registration of their establishments and to maintain an up-to-date list of registered operators.
· It must be noted that Regulations No 852/2004 and No 882/2004 do not contain any obligation for a food business operator to check whether its suppliers are registered in accordance with the requirements of those regulations. Nor does such an obligation to make checks, for the purposes of VAT deduction, arise from Directive 2006/112.
· However, as pointed out in paragraph 31 of this judgment, where tax authorities, having found fraud or irregularities committed by the issuer of the invoice in question, seek to establish that the addressee of that invoice knew or should have known that the transaction relied on to establish the right of deduction was involved in VAT fraud, they may not require that addressee to carry out checks which are not his responsibility (see, to that effect, judgment of 22 October 2015, PPUH Stehcemp, C‑277/14, EU:C:2015:719, paragraph 50).
· In that context, the Court has previously held that tax authorities cannot require the taxable person wishing to exercise the right to deduct VAT to produce documents issued by his supplier of bovine animals mentioning the eartags of the animals subject to the identification and registration system established by Regulation (EC) No 1760/2000 of the European Parliament and of the Council of 17 July 2000 establishing a system for the identification and registration of bovine animals and regarding the labelling of beef and beef products and repealing Council Regulation (EC) No 820/97 (OJ 2000 L 204, p. 1) (see, to that effect, judgment of 18 July 2013, Evita-K, C‑78/12, EU:C:2013:486, paragraph 42).
· Similarly, for the purposes of establishing that a taxable person who participates in the food chain knew or should have known that his suppliers were involved in VAT fraud, tax authorities cannot require that taxable person to verify that those suppliers have complied with their registration obligations as required by EU law on the regulation of foodstuffs.
· Consequently, the answer to the second question is that Article 168(a) of Directive 2006/112 must be interpreted as meaning that the failure, by a taxable person who participates in the food chain, to ascertain that his suppliers are registered with the competent authorities, in accordance with Article 6(2) of Regulation No 852/2004 and Article 31(1) of Regulation No 882/2004, is not relevant for the purpose of determining whether the taxable person knew or should have known that he was involved in a transaction involving VAT fraud.
For further information click here be forwarded to the text of the judgment as published on the website of the CJEU, which will open in a new window.
The opinion in this case as delivered on May 22, 2019 by Advocate General Bobek can be found here.
Did you know that in our section CJEU Rulings we have made a selection of rulings of the CJEU? We have organized these rulings based on the subject they relate to (e.g. Freedom of establishment, Free movement of capital, Indirect taxes on the raising of capital, etc).
Copyright – internationaltaxplaza.info
Stay informed: Subscribe to International Tax Plaza's Newsletter! It's completely FREE OF CHARGE!
Follow International Tax Plaza on Twitter (@IntTaxPlaza)
The MLI entered into force with respect to the Russian Federation
The MLI entered into force with respect to India
The MLI entered into force with respect to Belgium
Iceland deposits its instrument of ratification for the MLI
General Court of the European Union confirms that Luxembourg granted illegal State Aid to Fiat Chrysler Finance Europe
General Court of the European Union judges that Starbucks did not receive illegal State Aid from the Netherlands
CJEU judges in Case C-700/17 Peters (VAT — Article 132(1)(b) and (c) of Dir 2006/112/EC — Exemptions — Hospital and medical care — Provision of medical care in the exercise of the medical and paramedical professions)
The MLI entered into force with respect to United Arab Emirates
Switzerland deposits its instrument of ratification for the MLI
Canada deposits its instrument of ratification for the MLI
Saudi Arabia signed the MCAA on the Exchange of Country-by-Country Reports
Dominican Republic deposits its Instrument of Ratification for the OECD's Multilateral Convention on Mutual Administrative Assistance in Tax Matters
The OECD Multilateral Convention on Mutual Administrative Assistance in Tax Matters entered into force on August 1, 2019 with respect to Dominica
VAT Compliance Specialist (Action – Netherlands, Zwaagdijk-Oost)
Senior Tax Analyst (The Walt Disney Company (Corporate) – Hong Kong, Kwun Tong)
Tax & Statutory Reporting Specialist (Mars Polska – Poland, Warsaw or Sochaczew)
Intern, Tax (Volvo Construction Equipment – China, Shanghai)
Manager - International Tax (m/w/d) (ProSiebenSat.1 Media SE – Germany, München)
Tax Manager - M&A (m/w/d) (ProSiebenSat.1 Media SE – Germany, München)
Manager Taxes (f/m/x) (BMW Manufacturing Hungary Kft. – Hungary, Debrecen)
Tax Director - Governance (Lego – Denmark, Billund)
Senior Tax Control Manager – London or Billund (DK) (Lego – United Kingdom, London or Denmark, Billund)
© 2020 INTERNATIONAL TAX PLAZA


Saif Ali Khan, Fatima Sana Shaikh and Ali Fazal have been finalised as the cast of Pavan Kirpalani's upcoming directorial, Bhoot Police.
The makers of the film have unveiled the first look of the film announcing the cast.
In the picture, Saif and Ali Fazal can be seen standing dressed in black t-shirts, while Fatima can be seen sitting pretty in a grey boat-neck top.
Directed by Pavan Kirpalani, the film will be presented and produced by Fox Star Studios. Bhoot Police is scheduled to go on the floors from August 2019.
Previous articleइन 7 बॉलीवुड स्टार्स को नहीं है वोट डालने का अधिकार, जानिए क्या है वजह!


Fix final remaining bugs in the TIA emulation (mostly done at this point).
Add support for remaining esoteric controllers (KidVid and Lightgun), and improve CompuMate emulation (accessing standalone cassette player).
Add more debugger features, improve graphics access tracking, improve GUI, etc.
Look into adding movie recording or net play, and/or interface better with 3rd-party recorders.
Probably a thousand other things that I've forgotten. See the issues list at https://github.com/stella-emu /stella/issues for all items marked 'enhancement'.
As always, if you feel you can contribute to this list in any way (either with suggestions or actual implementation), please contact me by email or create an issue on Github.


text:
| Dublin,
Kuehne + Nagel's Pamela Quinn named as Ireland's Most Trusted Leader 2019
Kuehne + Nagel Ireland's National Manager, Pamela Quinn, was last night recognised as Ireland's Most Trusted Leader 2019, as part of the Best Workplaces Awards 2019. The Best Workplaces programme recognises the very best employers in Ireland, shining a spotlight on the companies that are fostering high-trust workplace cultures. Employees are invited to participate in a Trust Index Employee Survey, which measures sentiment across a range of business drivers.
Pamela Quinn, National Manager Kuehne + Nagel Ireland
Ireland's Most Trusted Leader 2019
"We are committed to providing an environment where every employee is able to bring their best self to work; encouraging an agile organisation which is better placed to respond to a rapidly changing world."
Kuehne + Nagel Ireland were also recognised as the 7th Best Workplace in Ireland at the awards ceremony, the 7th year in a row being recognised as a Top 10 workplace. Furthermore, Kuehne + Nagel Ireland was placed on the inaugural Best Workplaces for Women list. This new award takes the global standard Best Workplaces methodology as its basis, and recognises those organisations that go above and beyond to ensure that the women in their workforce are treated fairly when it comes to pay, recognition, training and promotion opportunities.
Pamela Quinn confirms Kuehne + Nagel Ireland's pledge to continuous improvement as a Best Workplace: "Kuehne + Nagel Ireland is committed to developing high-trust relationships throughout every level of our organisation. This is demonstrated through our active involvement with the Great Place to Work® institute for the last 9 years. The insights gained from the employee survey give Kuehne + Nagel Ireland clear direction on where we excel as an employer and areas where we can develop year on year, demonstrating our commitment to continuous improvement as a Best Workplace for our colleagues."
Through the annual survey for Great Place to Work, Kuehne + Nagel Ireland gain definitive insights showing consistent growth in their Trust scores. These scores clearly indicate that trust in their leader is at an all-time high. The Great Place to Work model defines the Employee Perspective of a Great Workplace as one where you trust the people you work for, you have pride in the work you do, and you enjoy the people you work with.
The Best Workplace accolade is a remarkable achievement, since it demonstrates to customers and competitors alike that Kuehne + Nagel have unlocked the business benefits of a high-trust, high performing culture. Pamela Quinn confirms "Kuehne + Nagel Ireland is dedicated to maintaining a culture that values entrepreneurial spirit, diversity, innovation and teamwork. We are committed to providing an environment where every employee is able to bring their best self to work; encouraging an agile organisation which is better placed to respond to a rapidly changing world."


Deaf-blindness is defined by the Individuals with Disabilities Education Act as a "concomitant hearing and visual impairments, the combination of which causes such severe communication and other developmental and educational needs that they cannot be accommodated in special education programs solely for children with deafness or children with blindness."
The term deafblindness does NOT mean a child must be completely unable to see or hear. The term refers to the combination of visual and hearing impairments that serve to impair a child's ability to communicate and to learn to the extent that specialized instruction is required to support the child's education.
The range of vision and hearing that children with the designation deafblind have is great. Some with have more vision that hearing and others more hearing than vision. Most will have sufficient vision to move about in their environment and to recognize faces. Most will have enough hearing to recognize familiar sounds and develop speech themselves.
There are a number of syndromes that are rare that have combined visual and hearing impairment as aspects of the disorder. They include: Alport Syndrome, Congenital Rubella Syndrome, Cytomegalovirus (CMV), CHARGE Association, Down Syndrome, Marshall Syndrome, Rubella Syndrome, Stickler Syndrome.


Konshens displays gratitude for his fiancee, Latoya, as he shares an intimate photo on social media.
Dancehall artiste Konshens took to social media to flaunt off his fiancée Latoya Wright.
The "Gal A Bubble" deejay has been off the market since summer 2014 when he reportedly engaged to his long-time girlfriend, but has always kept the details of his love life private.
While it was reported that the couple was planning to have a private wedding ceremony in 2014, the Jamaican artiste has yet to confirmed.
Konshens, whose real name is Garfield Spence, and his boo Latoya welcomed their son named Liam on March 1st, 2015. The artiste also has a daughter named Sajhi for a previous love partner.


Please See Below Our Junior Goalkeeper Gloves: You will NOT get a better professional junior goalkeeper glove at this price level, anywhere on the Internet As J4K prides ourselves In providing quality high specification goalkeeper gloves at very fair prices. IMPORTANT: IF You Are Opting For Finger Save Goalkeeper Gloves, Please Do Not forget To Oder The Finger Spines Separately. IF YOU NEED ANY GLOVE GUIDANCE CONTACT J4K ANYTIME.
Inspire V1 Hybrid (Roll+Neg) Goalkeeper Glove Cut : Hybrid (Roll+Neg) Pin Hole Mesh Black ..


What can you do with a degree from one of the accredited tax accounting schools in South Dakota featured on this page? An associate's degree can teach you the basics – the principles of accounting, tax forms for businesses and individuals, accounting software, financial records, and the like. Armed with this knowledge, you can get a job as a tax preparer or working with an accountant. It can also be an excellent start to a more in-depth education. A bachelor's degree is generally accepted as the baseline education for an accountant; a master's degree allows you to really specialize in tax accountancy. These are more detailed courses of study. They include classes like taxation for corporations, tax laws and regulations, finance, and auditing.


text:
Our approach to learning
Parent feedback
Outstanding experiences
Our social purpose
Creativity and culture
Our international school in Nantong
Our leading bilingual school in Nantong provides an outstanding bilingual education for bright young minds.
Our Strategic Alliance
Our day and boarding school in Nantong provides an outstanding bilingual education for children aged 6-18 years old. At our school, your child will achieve academic excellence and make lifelong friends.
We blend the very best of eastern and western education, teaching the Chinese national curriculum and the International Baccalaureate diploma programme. Our bilingual learning environment helps your child master English and Chinese while gaining the international qualifications, creativity and confidence they need for their future.
Our custom-built campus, with large playing fields, a swimming pool and an auditorium for performing arts, provides the space and facilities your child needs to learn and thrive. Our exclusive collaborations with prestigious institutions such as Massachusetts Institute of Technology (MIT) and world-leading performing arts school Juilliard mean we're at the forefront of educational thinking, creating life-changing experiences for your child.
A wide variety of exclusive extracurricular school activities means your child's learning continues stretches far beyond the classroom, building important personal and social skills for life.
Our passionate, high-quality teachers personalise your child's learning, encouraging their talents and ambitions to shine. Through Global Campus, our online learning platform, students interact online and share work and ideas with their classmates at our family of schools around the world.
We're proud that our students become confident young people with a global outlook, ready to make their mark on the world.
Our school in Nantong
Day & Boarding
China, Nantong
Nord Anglia School Nantong
Ages 6-18 from ¥125,000 pa
other cities in china
Our three private schools in Beijing provide a forward-thinking, rigorous international and bilingual education that prepares your child for an exciting future.
We offer the finest education in Chengdu, combining a globally respected curriculum with exclusive extracurricular activities to help your child succeed in whatever they choose to do or be in life.
Our two leading international and bilingual schools in Dalian provide a rich learning experience so our students excel at whatever they want to do or be in life.
Our high-quality teachers and world-class learning environment in Foshan will give your child an outstanding bilingual education.
Our three international and bilingual schools in Guangzhou combine a proven academic approach and outstanding teachers, with state-of-the-art learning environments.
At our award-winning school in Hong Kong we'll help your child discover their talents and achieve more than they ever thought possible.
Our highly qualified teachers and friendly community in Jiaxing will give your child an outstanding bilingual learning experience.
Our leading international school in Nanjing provides an outstanding bilingual education for bright young minds.
Our leading bilingual international school in Ningbo will help your child achieve more than they ever imagined.
Our three international and bilingual schools in Shanghai provide a forward-thinking, challenging education that prepares your child for a bright and exciting future.
At our bilingual school in Shenzhen your child will discover their talents and achieve more than they ever imagined.
Our bilingual school in Suzhou is a state-of-the-art, world-class learning and teaching environment providing the space and support for your child to achieve more than they ever thought possible.
See fewer
By joining our mailing list, we can keep you up to date with any future newsletters, events and announcements from our family of 76 premium schools.
Please enter a real email address
enquiries@nordanglia.com
4th Floor, Nova South
SW1E 5LB
© 2022 Nord Anglia Education Accessibility Modern slavery statement UK tax strategy Cookie policy Privacy policy Legal notice Equality, diversity and inclusion
We use cookies to improve your online experiences. To learn more and choose your cookies options, please refer to our cookie policy.


text:
Upcoming and Recent Performances
Solo music performances
Blog: Muse Moments
Music Presentations
Church Muse
Nearer My God, to Thee - The RooHorn Ensemble, 2017
As a little girl, the earliest thing I remember hearing about the hymn, "Nearer My God, to Thee" was that it was played by the musicians on the Titanic as it sank. However, the tune that most of us associate with the hymn was written several years later than the text, and not the tune those musicians played.
"Nearer My God, to Thee" was written in 1841 by Sarah Flowers Adams, a British actress who had turned to hymn and poetry writing when she had to give up her performing career due to health reasons. Her pastor was putting together a new hymnal and asked her and her sister, a talented musician and composer, to write some hymns for it. He specifically asked for one on Genesis 28:11-19, known as the story of "Jacob's Dream," or "Jacob's Ladder." The text for "Nearer My God, to Thee" is based on the dream that Jacob had in the desert when he was running away from home after Essau, his brother, had threatened to kill him. Using a rock for a pillow he laid down in the wilderness and dreamt angels ascending and descending on a heavenly ladder.
It appears that Sarah's sister's tune for the hymn is long forgotten; the tune that most of us know is called "Bethany" and was written specifically for the text by Lowell Mason in 1856. As far as the Titanic story goes, the musicians most likely played the tune, "Propior Deo," which was written by Sir Arthur Sullivan (of the famed Gilbert and Sullivan operetta team) and was most often sung in the Methodist church. Walter Hartley, the band leader on the Titanic, was a Methodist, and had shared with his family that he wanted "Nearer My God to Thee" to be sung at his funeral. All in all, there are five tunes linked to this hymn, all by different composers.
The tune used for the instrumental version here is "Bethany." It was arranged for french horn choir by our friend, J.D. Shaw. This performance by my husband Marty's horn students (he's conducting) was part of the UMKC Conservatory's 2017 "Crescendo" gala concert at the Kauffman Center for the Performing Arts in beautiful Helzberg Hall.
There are six verses to the hymn, five by the original author, and a sixth by Edward Henry Bickersteth, who was a bishop in the Church of England in the 19th century. I feel that Sarah's 3rd verse, and the bishop's added verse are most apropos for our present plight.
We can't be near each other right now, but there is no reason we can't, or shouldn't, be nearer to God. Stay home, stay safe, stay close to God!
3. There let the way appear steps unto heav'n;
All that Thou sendest me in mercy giv'n;
Angels to beckon me nearer, my God, to Thee,
Nearer, my God, to Thee, nearer to Thee!
6. There in my Father's home, safe and at rest,
There in my Saviour's love, perfectly blest;
Age after age to be, nearer my God to Thee,
https://drive.google.com/file/d/1TsvMSG2Atb76HfTdRE8HL2BOhF0niDlW/view?usp=sharing
About "Muse Moments," formerly known as "Church Muse"
"Smizing" when you don't feel like it - Charles Chaplin's "Smile" sung by Nat King Cole
Dealing with Heartbreak - "It is Well with My Soul"


text:
Solar Decathlon Gives Women Engineering Students a Chance to Shine
The women on Team Orange County, sponsored by Edison International and SCE, worked on the solar home to be featured at the annual event.
Teagan Barnes, a UCI mechanical engineering major, works on some equipment for Team Orange County's solar-powered house at their work site at Irvine Valley College.
Reem Habib (left), a UCI urban planning and civil engineering major, and Team Orange County teammate Andy Truong, work on a specially-designed diffuser that will be used with a cold water tank to help cool the solar-powered house they are building.
Members of the Team Orange County Solar Decathlon team at their Irvine Valley College work site. From left: Teagan Barnes, Will Vicent (an SCE adviser), Moritz Limpinsel, Paige Svehlak, Jack Brouwer, UCI engineering professor and decathlon adviser, and Reem Habib.
Woman engineers rock #SolarDecathlon. http://3bl.me/zzf82p
Friday, August 21, 2015 - 12:00pm
NEWSROOM: Edison International
CONTENT: Article
Edison's Online Newsroom
Steel toe work boots. How hard could it be in Southern California to find work boots? But it was for Reem Habib.
"When I tried to buy steel toe boots, I couldn't find any in my size — they had no women's sizes," she said. She settled for a smaller size in a man's boot.
It is just one of the adjustments women engineers make in a profession historically dominated by men. As of 2013, only 11.7 percent of engineers in the U.S. were women, according to the Bureau of Labor Statistics.
Habib needed the boots to work on a solar-powered house she is helping build with other members of Team Orange County for the U.S. Department of Energy's Solar Decathlon 2015. Team Orange County will vie against 16 other college teams Oct. 8-18 to see who can design, build and operate the best solar-powered house that is cost-effective, energy-efficient and attractive.
Edison International, parent of Southern California Edison (SCE), and SCE donated a combined $400,000 to the solar decathlon and to support Team Orange County. The team is a joint effort of students from Chapman University, Irvine Valley College, Saddleback College and UCI.
Read full story in Edison's Online Newsroom.
CATEGORY: Diversity & Inclusion
More From Edison International
Laptop, Hot Spot Donations Help Bridge Digital Divide
Protecting the Sierra Nevada's Yosemite Toad
Wednesday, November 11, 2020 - 10:45am
Edison Strengthens Commitment to Black Employees by Joining AABE Energy Equity Initiative
Tuesday, November 10, 2020 - 10:10am
Videos from Edison International
SCE Funds 'Critical Aerial Support' for Daytime, Nighttime Firefighting
SCE Crews Insulate Power Lines to Prepare for Active Wildfire Season
7 Leaves Brings Sustainability to Popular Vietnamese Drinks


text:
\section{Introduction}
The field of synthetic biology is concerned with designing and constructing biological modules, biological systems, and biological machines \cite{cameron2014brief} and can be traced back to the 1960s when logic in genetic regulation was discovered \cite{jacob1961genetic}. The key goal is to program living cells to exhibit desired functionality. Biomolecular processes are typically nonlinear, stochastic, and non-modular making the design and construction process difficult. This is where control theory meets synthetic biology to produce robust functionality \cite{del2016control}.

Thus far, the main focus of the field of synthetic biology has been in designing and building digital logic genetic circuits. A wide variety of digital computation using synthetic genetic circuits has been achieved including but not limited to switches \cite{gardner2000construction}, counters \cite{friedland2009synthetic}, logic gates \cite{singh2014recent}, classifiers \cite{didovyk2015distributed}, edge detectors \cite{tabor2009synthetic}, and most recently digital displays \cite{millacura2019parallel,shin2020programming}. The state-of-the-art software called CELLO \cite{nielsen2016genetic} automates the design of digital logic genetic circuits and has paved the way for larger genetic circuits to be developed. Moreover, network reconstruction algorithms which infer dynamic network architectures have been developed to debug failure modes in these digital logic devices \cite{yeung2015global,ward2009comparison,sontag2004inferring,hasnain2019data}. However, there are cellular mechanisms and limitations that make it unclear whether or not digital computation can scale up to perform complex computations in living cells.

Biological systems such as colonies of bacteria inherently implement hybrid-analog computing \cite{sarpeshkar2014analog}, which was a staple paradigm of computation in the 1950s and 1960s. Analog computers need to be custom designed for a specific task and are less reliable than their digital counterparts. However, the benefits of analog computing, combined with the non-von Neumann sense of computing, is two-fold, i) it is customizable to address desired functionality (also seen as a disadvantage as noted prior), and ii) it gives rise to a type of computation where memory and processing are collocated, making for a more efficient computing architecture. We want to exploit the analog, tunable nature to perform biological computation. Specifically, we aim to design an input-output function in bacteria that takes chemical inducers as input and outputs the maximum steady state concentration. The bacterial colony as a whole can be viewed as the central processing unit with memory \cite{ben2009learning}. In cellular computing, data may be thought of as being encoded by biomolecules such as DNA strands and molecular biology tools may act on the data to perform various operations \cite{paun2005dna}.

There exists no general theory for how cells perform computation. Likewise, there is no general theory for many of the \textit{known} biomolecular mechanisms. This provides difficulty when designing and constructing synthetic biological components. Hypothesis-driven modeling is one approach to better understand these biomolecular mechanisms and how to control them \cite{yeung2017biophysical,jayanthi2013retroactivity}. A downside of hypothesis-driven modeling is that the models can be difficult to validate, often requiring iteration upon iteration of experimentation to fit model parameters. Futhermore, when the biological process occurs in new environmental conditions, it is likely that new experimental data will need to be collected for model refinement.

The above issues and more motivate the need for purely data-driven algorithms to accelerate the advancement of design of genetic circuits. We frame the analog computing challenge - is it possible to harness the natural dynamics of the cell to generate a steady state input-output function? Specifically, how do we utilize time-series measurements of a biological system to design control inputs to achieve a target steady state output from living cells in a data-driven fashion?

For this, we turn to Koopman operator theory, which is a powerful tool for data-driven analysis of nonlinear dynamical systems. Researchers working in this space have shown that it is possible to identify and learn the fundamental modes of a nonlinear dynamical system from data \cite{rowley2009spectral,mezic2005spectral}. The Koopman operator is an infinite-dimensional linear operator that represents nonlinear dynamics as a dynamically equivalent linear system. The development of Dynamic Mode Decomposition (DMD) \cite{schmid2010dynamic} has led to rapid growth in the use of Koopman spectral analysis of nonlinear dynamical systems in areas such as system identification \cite{mauroy2019koopman,boddupalli2019koopman}, prediction and control \cite{korda2018linear,korda2019optimal,proctor2016dynamic,proctor2018generalizing}, and sensor placement \cite{sinha2016operator,hasnain2019optimal}. More recently, learning higher dimensional Koopman operators from data has become computationally tractable, largely due to advances in integrating machine learning and deep learning to generate efficient representations of observable bases \cite{yeung2019learning,lusch2018deep,otto2019linearly,takeishi2017learning}.

Previously, researchers have explored control strategies to reprogram the steady states of cooperative monotone
dynamical systems \cite{shah2018reprogramming} and in \cite{del2017blueprint}, a synthetic genetic
feedback controller that dynamically steers the concentration
of a genetic regulatory network's key transcription factors
was developed to reprogram the steady state. We propose to
alter the steady state, or generate a genetic program with output being steady state values, of nonlinear systems with hyperbolic
fixed points by designing an optimal control policy for the
Koopman model identified directly from data. Specifically,
we utilize deep Dynamic Mode Decomposition (deepDMD)
[33] to learn approximate Koopman invariant subspaces
of dynamical systems to program their steady state. The
framework can be extended to systems with other types of
attractors and can be modified to solve many optimal control
problems e.g. target state and reference tracking.

In section \ref{sec:koop}, we briefly review Koopman operator theory for discrete-time nonlinear systems the numerical approximations of the Koopman operator. Section \ref{sec:ssProgramming} describes the steady state programming framework and discusses issues
that arise when dealing with mixed terms of the state and
input. Lastly, we demonstrate our method on two nonlinear
systems that are commonly seen in biomolecular feedback
systems and synthetic biology.

\section{Koopman Operators and their finite-dimensional approximation} \label{sec:koop}
In this section we briefly review Koopman operator theory as it applies to controlled systems. See \cite{kaiser2019data} for an overview of the field. In this paper, we consider discrete-time dynamical systems to be consistent with the nature of time-series data.

\subsection{Koopman operator theory for control systems}
Consider a non-affine control discrete-time nonlinear dynamical system of the form
\begin{equation}
    x_{k+1} = f(x_k,u_k),
    \label{eq:stateDyn}
\end{equation}
where $x_k \in \mathbb{R}^n$ is the state of the system, $u_k \in \mathbb{R}^m$ is the control input, and $f: \mathbb{R}^n \oplus \mathbb{R}^m \rightarrow \mathbb{R}^n$ is the analytic and unknown transition mapping. The dynamics can be always be decomposed in the following way
\begin{equation}
    x_{k+1} = f_x(x_k) + f_{xu}(x_k,u_k) + f_u(u_k),
    \label{eq:stateDynDecomp}
\end{equation}
where $f_x$, $f_{xu}$, $f_u$ are terms only in $x$, mixed terms in $x$ and $u$, and only in $u$, respectively. The Koopman operator acts on a set of observables and we consider each observable as an element of an infinite-dimensional Hilbert space $\mathcal{F}$.

The observables $\psi: \mathbb{R}^n \oplus \mathbb{R}^m \rightarrow \mathbb{R}$ are functions of the state and the input such that they can be functions of only $x$, mixed terms of both $x$ and $u$, and only of $u$. The observables can also be thought of as vector-valued functions of the state and the input such that $\psi: \mathbb{R}^n \oplus \mathbb{R}^m \rightarrow \mathbb{R}^{o}$.

Then the Koopman operator, $\mathcal{K}: \mathcal{F} \rightarrow \mathcal{F}$ acts on the Hilbert space of observables to produce linear dynamics
\begin{equation}
    \mathcal{K}\psi(x_k,u_k) \triangleq \psi(f(x_k,u_k),u_{k+1})
    \label{eq:koopEqgeneral}
\end{equation}
so that
\begin{equation}
    \psi(x_{k+1},u_{k+1}) = \mathcal{K}\psi(x_k,u_k)
\end{equation}
which can be decomposed similarly to (\ref{eq:stateDynDecomp}) into the three components
\begin{equation}
    \begin{bmatrix}\psi_x(x_{k+1}) \\ \psi_{xu}(x_{k+1},u_{k+1}) \\ \psi_u(u_{k+1}) \end{bmatrix} = \begin{bmatrix} \mathcal{K}_x & \mathcal{K}_{xu} & \mathcal{K}_u \\\mathcal{K}_{21} & \mathcal{K}_{22} & \mathcal{K}_{23} \\ \mathcal{K}_{31} & \mathcal{K}_{32} & \mathcal{K}_{33} \end{bmatrix} \begin{bmatrix}\psi_x(x_{k}) \\ \psi_{xu}(x_{k},u_{k}) \\ \psi_u(u_{k}) \end{bmatrix}
    \label{eq:koopDecomp}
\end{equation}
where $\psi_x: \mathbb{R}^n \rightarrow \mathbb{R}^{n_L}$, $\psi_{xu}: \mathbb{R}^n \oplus \mathbb{R}^m \rightarrow \mathbb{R}^{M_L}$, and $\psi_x: \mathbb{R}^m \rightarrow \mathbb{R}^{m_L}$.
\begin{assumption}
\textit{We assume that the inputs $u_k$ are exogenous disturbances without state space dynamics. }
\label{ass:exogenousInputs}
\end{assumption}
The above Assumption \ref{ass:exogenousInputs} allows us to be concerned only with the first block equation in (\ref{eq:koopDecomp}), i.e.
\begin{equation}
    \psi_x(x_{k+1}) = \mathcal{K}_x \psi_x(x_{k}) + \mathcal{K}_{xu}\psi_{xu}(x_{k},u_{k}) + \mathcal{K}_u\psi_u(u_{k}).
    \label{eq:xkoopDecomp}
\end{equation}
We refer the readers to \cite{yeung2018koopman} for more discussion on this decomposition and a proof for the existence of Koopman operators for nonlinear systems.
\subsection{Finite dimensional approximations}
\subsubsection{Dynamic mode decomposition with control}
Dynamic mode decomposition with control (DMDc) developed in \cite{proctor2016dynamic,proctor2018generalizing} is an extension of DMD for systems with external actuation and is used to identify a finite dimensional approximation to the Koopman operator, $K$. The idea is to find the best-fit linear operators $A$ and $B$ to provide the following relationship:
\begin{equation*}
    x_{k+1} = Ax_k + Bu_k
\end{equation*}
for measurement $x_k$, present control $u_k$, and future measurement $x_{k+1}$. To do this, data snapshots are collected from the dynamical system (\ref{eq:stateDyn}) of the state and input over time and formed into the following data matrices:
\begin{equation*}
\begin{aligned}
    X_p &= \begin{bmatrix} x_0 & x_1 & \hdots & x_{N-1} \end{bmatrix},\\
    X_f &= \begin{bmatrix} x_1 & x_2 & \hdots & x_N \end{bmatrix},\\
    U_p &= \begin{bmatrix} u_0 & u_1 & \hdots & u_{N-1} \end{bmatrix},
\end{aligned}
\end{equation*}
where N is the number of snapshots collected. The above matrices are known as snapshot matrices since each column represents a snapshot at time $k$ of the state of the dynamical system. If data is collected from more than one trajectory, the additional time-series can be appended as additional columns in the snapshot matrices. To identify the best-fit linear operators, the algorithm solves the following optimization problem:
\begin{equation*}
\begin{aligned}
    \begin{bmatrix}A&B\end{bmatrix} &= \text{arg}\min_{A,B} \sum_{i=0}^{N-1} || x_{i+1} - Ax_i-Bu_i  ||_2,  \\
    &= \text{arg}\min_{A,B} || X_f - AX_p - BU_p||_F, \\
    & = X_f\begin{bmatrix}X_p \\ U_p\end{bmatrix}^{\dagger}
\end{aligned}
\end{equation*}
where $\dagger$ represents the Moore-Penrose pseudinverse. Here $A$ corresponds to $K_x$ and $B$ to $K_u$ while $K_{xu}=0$. Thus DMDc is limited in its system identification capabilites as it does not account for mixed terms of $x$ and $u$ in its formulation.
If trajectories of the dynamical system without inputs is available, the state transition matrix $A$ can first be identified and treated to be a constant in the learning of the control matrix $B$ from the trajectories with inputs \cite{hasnain2019data}. This disambiguates the impact of the control input on the state dynamics.

\subsubsection{Deep dynamic mode decomposition with control}
Another approach to learning Koopman invariant subspaces for controlled nonlinear systems is given in \cite{williams2016extending}, but a difficulty in this approach is that the user must choose the observables manually. We use the deep learning approach deep Dynamic Mode Decomposition (deepDMD) developed in \cite{yeung2019learning} to identify an efficient representation of the invariant subspace. The approach here is to represent the observable functions as many compositions of linear transformations and ReLU (Rectified Linear Units) functions and learn both the observables and the Koopman operator simultaneously. The neural network is tasked with solving the following optimization problem
\begin{equation*}
\begin{aligned}
    &\min_{K_x,K_{xu},K_u,\theta} || \Psi_x(X_f,\theta) - K_x\Psi_x(X_p,\theta) \\& \qquad \qquad \quad - K_{xu}\Psi_{xu}(X_p,U_p,\theta) - K_u\Psi_{u}(U_p,\theta)  ||_F \\& \qquad \qquad \quad
    + \lambda_1||K||_2 + \lambda_2||\theta||_1
\end{aligned}
\end{equation*}
where the parameters $\theta$ are the neural networks biases and weights and $\lambda_1$ and $\lambda_2$ are regularization parameters. The snapshot matrix $\Psi_x$, is now represented as
\begin{equation*}
    \Psi_x(X_p,\theta) = \begin{bmatrix} \psi_x(x_0,\theta) & \psi_x(x_1,\theta) & \hdots & \psi_x(x_{N-1},\theta) \end{bmatrix}
\end{equation*}
and the other snapshot matrices are similarly formed. The neural network identifies a model that relates the data in observable space as
\begin{equation*}
    \psi_x(x_{k+1}) = K_x\psi_x(x_k) + K_{xu}\psi_{xu}(x,u) + K_u\psi_u(u),
\end{equation*}
where we have dropped the dependency on $\theta$ for brevity.

\section{Steady state programming} \label{sec:ssProgramming}

In this section, when we refer to the Koopman operator, we are referring to the finite-dimensional approximation of the actual Koopman operator. The focus of this paper is to design an input $u$ to maximize a single direction of the state at equilibrium. We emphasize that we are not solving a dynamic control policy planning problem, but that the control policy is a constant input that maximizes the equilibrium value of a single direction in state space. Furthermore, we consider nonlinear systems which have hyperbolic fixed points. At steady state we have the optimization problem
\begin{equation}
\begin{aligned}
&\min_{u \in \mathcal{U}} \quad - \hat{e}^{\top}_i x_{k,e} \\
& \quad \textrm{s.t.} \quad  x_{k,e} = f(x_{k,e},u_k),
  \label{eq:ssOpt}
\end{aligned}
\end{equation}
where $\mathcal{U}$ is a bounded set of inputs, $\hat{e}_i$ is the unit column vector in the $i^{th}$ direction of the state (the state we aim to maximize), and the subscript $e$ denotes equilibrium values. Since the form of $f$ is unknown, it is difficult to design an input which solves this program. Therefore, we propose to identify a Koopman invariant subspace by extending the states and the inputs into a space of observables. The identified Koopman model then allows us to formulate the optimization problem in the lifted space where the problem has some tractability.

\subsection{Steady state programming using DMD with linear control}

For a linear time-invariant system with $(I - A)$ invertible, if $u$ does not come from a bounded set $\mathcal{U}$ but from an unbounded set $\hat{\mathcal{U}}$ and the observable mapping is the identity, there is no bounded $u$ that solves optimization problem (\ref{eq:ssOpt}). To see this, under the conditions above, the optimization problem (\ref{eq:ssOpt}) becomes
\begin{equation*}
  \min_{u \in \hat{\mathcal{U}}} \quad -\hat{e}^{\top}_i(I - A)^{-1}Bu_k
\end{equation*}
and note that the objective is linear in $u$. Differentiating with respect to $u$ we have
\begin{equation*}
    \frac{\partial}{\partial u_k} -\hat{e}^{\top}_i(I - A)^{-1}B u_k = -\hat{e}^{\top}_i(I - A)^{-1}B
\end{equation*}
and so for any $(A,B)$, there is no bounded $u^*$ that solves the optimization problem. If $u$ comes from the bounded set $\mathcal{U}$, then the minimum value of the objective on $\mathcal{U}$ occurs on the boundary $\partial \mathcal{U}$ due to the maximum modulus principle. This results from the fact that the objective function to be optimized is linear in $u$ and therefore it is an uninteresting case. This case corresponds to identifying a linear model using DMD with control, where the observable mapping is simply the identity and the measurement snapshots are all that is used to compute the state-transition matrix and the control matrix. For nonlinear systems that can be represented linearly by considering a linear basis, the above approach will work effectively. However, we aim to develop a method which can handle nonlinear systems that \textit{require} a basis that is a nonlinear function of the original states.

\subsection{Steady state programming using deepDMD with nonlinear control }
Consider the case where the observable mapping is not the identity.
\begin{assumption}
\textit{We assume that the state transition Koopman operator $K_x$ has $n_L$ linearly independent eigenvectors and that none of the corresponding $n_L$ eigenvalues are equal to 1. }
\label{ass:invertibleIminusKx}
\end{assumption}
At equilibrium, (\ref{eq:xkoopDecomp}) becomes
\begin{equation}
    \psi_x(x_{e}) = K_x\psi_x(x_{e}) + K_{xu}\psi_{xu}(x_{e},u_{k}) + K_u\psi_u(u_{k})
    \label{eq:ssKoopEq}
\end{equation}
and under Assumption \ref{ass:invertibleIminusKx}, $(I - K_x)$ is invertible, so we have
\begin{equation*}
    \psi_x(x_{e}) = (I - K_x)^{-1} \left[K_{xu}\psi_{xu}(x_{e},u_{k}) + K_u\psi_u(u_{k})\right].
\end{equation*}
For the optimization problem (\ref{eq:ssOpt}) we now have
\begin{equation}
\begin{aligned}
&\min_{\psi_u(u_k) \in \mathcal{U}_{\Psi}} \quad - \hat{e}^{\top}_i \psi_x(x_{e}) \\
& \quad \textrm{s.t.} \quad \psi_x(x_{e}) = (I - K_x)^{-1} \\ & \qquad \qquad \left[K_{xu}\psi_{xu}(x_{e},u_{k}) + K_u\psi_u(u_{k})\right]
\end{aligned}
\label{eq:ssOptKoop}
\end{equation}
stating that we want to find the input $\psi_u(u)$ that maximizes the equilibrium value of a single direction in observable space. Here $\mathcal{U}_{\Psi}$ is a bounded set of lifted inputs. If we assume away the mixed terms of $x$ and $u$ then the problem becomes immediately tractable as we have $\psi_x(x_e)$ as a function of just terms in $\psi_u(u)$. However, assuming away the mixed terms seemingly requires a strong assumption about the nonlinearities present in original dynamics. Specifically it assumes that the input affects the state dynamics through additive means \textit{only}. This is typically not the case in biological systems. Another important point to make is that this is an implicit optimization of $\psi_x(x_e)$, another layer of difficulty when dealing with the mixed terms.

Since we transform the state space coordinates to an abstract observable-space, we want to keep the interpretability of the original system intact. Therefore we make the following assumption:
\begin{assumption}
\textit{We assume state-inclusive and input-inclusive observables $\psi_{x}(x)$ and $\psi_u(u)$, respectively, i.e.}
\begin{equation}
\begin{aligned}
    \psi_x(x) &= \begin{bmatrix} x \\ \varphi_x(x) \end{bmatrix}, \\
    \psi_u(u) & = \begin{bmatrix} u \\ \varphi_u(u) \end{bmatrix}
\end{aligned}
\end{equation}
\textit{with $\varphi_x(x) \in \mathbb{R}^{n_L-n}$ and $\varphi_u(u) \in \mathbb{R}^{m_L -m}$.}
\end{assumption}
Again, since the mixed terms of $x$ and $u$ cause issues in solving program (\ref{eq:ssOptKoop}), we want to examine the structure of these terms when an EDMD \cite{williams2016extending} with control approach  is used. A typical EDMD dictionary may consist of functions such as monomials, polynomials (Legendre and Hermite), radial basis functions, trigonometric functions, and logistic functions. It can be shown that for most of these common dictionary elements, the mixed terms are separable in $x$ and $u$. To illustrate what we want to achieve, consider an example system with state-inclusive ($n=2$ and $m=2$) observables with up to second order monomials in the state and input. Then for $\psi_x: \mathbb{R}^n \rightarrow \mathbb{R}^{n_L = 5}$ and $\psi_u: \mathbb{R}^m \rightarrow \mathbb{R}^{m_L = 5}$ we have that
\begin{equation*}
    \psi_x(x) = \begin{bmatrix} x_1 \\ x_2 \\ x_1x_2 \\ x_1^2 \\ x_2^2 \end{bmatrix}, \quad
    \psi_u(u) = \begin{bmatrix} u_1 \\ u_2 \\ u_1u_2 \\ u_1^2 \\ u_2^2 \end{bmatrix}
\end{equation*}
where we have left out the zeroth order terms for brevity. For this example, the subscripts on the states and inputs represent different components of the state and input, not timepoints. As we have no knowledge of the form of the dynamics $f$, we may consider forming all possible combinations of $\psi_x(x)$ and $\psi_u(u)$ and using those elements to form $\psi_{xu}(x,u)$,
\begin{equation*}
    \psi_{xu}(x,u) = \begin{bmatrix} x_1\psi_u(u) \\ x_2\psi_u(u) \\ x_1x_2\psi_u(u) \\ x_1^2\psi_u(u) \\ x_2^2\psi_u(u) \end{bmatrix} \text{or} \quad \psi_{xu}(x,u) = \begin{bmatrix} u_1\psi_x(x) \\ u_2\psi_x(x) \\ u_1u_2\psi_x(x) \\ u_1^2\psi_x(x) \\ u_2^2\psi_x(x) \end{bmatrix}
\end{equation*}
with $\psi_{xu}: \mathbb{R}^n \oplus \mathbb{R}^m \rightarrow \mathbb{R}^{M_L = 25}$, such that $M_L = n_L \times m_L$. Note that $\psi_{xu}(x,u)$ can now be written as a matrix times $\psi_u(u)$ or a matrix times $\psi_x(x)$ as
\begin{equation}
    \psi_{xu}(x,u) = \begin{bmatrix} D_x(x_1) \\ D_x(x_2) \\ D_x(x_1x_2) \\ D_x(x_1^2) \\ D_x(x_2^2) \end{bmatrix} \psi_u(u) = M_x \psi_u(u)
    \label{eq:sepxu}
\end{equation}
or
\begin{equation}
    \psi_{xu}(x,u) = \begin{bmatrix} D_u(u_1) \\ D_u(u_2) \\ D_u(u_1u_2) \\ D_u(u_1^2) \\ D_u(u_2^2) \end{bmatrix} \psi_x(x) = M_u \psi_x(x)
    \label{eq:sepux}
\end{equation}
where $D_x(\cdot) \in \mathbb{R}^{n_L\times m_L}$ and $D_u(\cdot) \in \mathbb{R}^{m_L\times n_L}$ are diagonal matrices with their argument as the diagonal elements. The matrices $M_x \in \mathbb{R}^{M_L \times m_L}$ and $M_u \in \mathbb{R}^{M_L \times n_L}$ consist of terms only in $x$ and only in $u$, respectively.

A more general statement is that if $f(x,u)$ in (\ref{eq:stateDynDecomp}) is separable into some $G(u)h(x)$, then the mixed observable $\psi_{xu}(x,u)$ are also similarly separable. To see this, consider continuous-time dynamics $\dot{x} = f(x,u)$ for ease of presentation. If $f(x,u)$ is multiplicatively separable in $x$ and $u$, it can be written as
\begin{equation}
    f(x,u) = WG(u)h(x),
\end{equation}
with the weight matrix $W \in \mathbb{R}^{n\times M_L}$, the matrix $G(u) \in \mathbb{R}^{M_L \times n_L}$ is a function of $u$, and the vector $h(x) \in \mathbb{R}^{n_L}$. From the Koopman generator \cite{budivsic2012applied}, we have that
\begin{equation}
    \dot{\psi}_x(x) = \frac{\partial \psi_x(x)}{\partial x }f(x,u) = \frac{\partial \psi_x(x)}{\partial x } WG(u)h(x).
\end{equation}
and therefore, any mixed terms are entirely separable in the observable space as well. This may mean that the deep learning approach can take care of the necessity of having mixed terms without explicitly learning the $K_{xu}$ parameters.

Using the idea that we can separate the mixed terms as in (\ref{eq:sepxu}) and (\ref{eq:sepux}), (\ref{eq:ssKoopEq}) can be written as
\begin{equation}
    \psi_x(x_{e}) = K_x\psi_x(x_{e}) + K_{xu}M_u \psi_x(x_e) + K_u\psi_u(u_{k})
    \label{eq:ssKoopEqsepux}
\end{equation}
or as
\begin{equation}
    \psi_x(x_{e}) = K_x\psi_x(x_{e}) + K_{xu}M_x \psi_u(u_k) + K_u\psi_u(u_{k}).
    \label{eq:ssKoopEqsepxu}
\end{equation}
From (\ref{eq:ssKoopEqsepux}) we have that at equilibrium,
\begin{equation*}
    \psi_x(x_{e}) = (I-K_x-K_{xu}M_u)^{-1}K_u\psi_u(u_{k})
\end{equation*}
if $(I-K_x-K_{xu}M_u)$ is invertible. From (\ref{eq:ssKoopEqsepxu}) we have that at equilibrium,
\begin{equation*}
    \psi_x(x_{e}) = (I-K_x)^{-1}\left[K_{xu}M_x+K_u\psi_u(u_{k})\right]
\end{equation*}
and from Assumption \ref{ass:invertibleIminusKx} $(I-K_x)$ is invertible.

Of these two options, if we use (\ref{eq:ssKoopEqsepxu}) to program the steady state of nonlinear systems, it only requires that $(I-K_x)$ to be invertible, which has already been assumed. Equation (\ref{eq:ssKoopEqsepux}) on the other hand requires that $(I-K_x-K_{xu}M_u)$ be invertible. An advantage is that the right hand side is entirely a function of $u$ whereas (\ref{eq:ssKoopEqsepxu}) has a right hand side which is a function of both $u$ and $x$, requiring implicit optimization. From this analysis, we can again rewrite the steady state programming problem (\ref{eq:ssOptKoop}) as
\begin{equation}
\begin{aligned}
&\min_{\psi_u(u_k) \in \mathcal{U}_{\Psi}} \quad - \hat{e}^{\top}_i \psi_x(x_{e}) \\
& \quad \textrm{s.t.} \quad \psi_x(x_{e}) = (I-K_x-K_{xu}M_u)^{-1}K_u\psi_u(u_{k})  \\
& \quad \textrm{or s.t.} \quad  \psi_x(x_{e}) = (I-K_x)^{-1}\left[K_{xu}M_x+K_u\psi_u(u_{k})\right]  \\
& \quad \textrm{or s.t.} \quad \psi_x(x_{e}) = (I-K_x)^{-1}K_u\psi_u(u_{k})
\label{eq:ssOptFinal}
\end{aligned}
\end{equation}
where the last constraint comes from setting $K_{xu}=0$ i.e. stating that $\psi_{xu}$ terms are unimportant. We consider this last case since deepDMD offers the flexibility to learn accurate Koopman invariant subspaces even without considering the mixed terms, as will be demonstrated.

This program is in its most general form nonlinear and will yield local optima. EDMD or any neural network approach do not provide a structure to guarantee a global optimum for this problem and is thus NP-hard. We use the Sequential Least Squares Quadratic Programming (SLSQP) solver from the scipy.optimize python package to solve program (\ref{eq:ssOptFinal}). If DMD is used for steady state programming, any convex optimization solver will suffice.

\section{Numerical Results}
\subsection{Example: Feedforward Loop}
We consider the following nonlinear dynamical system describing a feedforward loop of five proteins (states) under the influence of two inducers (inputs):

\begin{equation} \label{eq:iffl}
\begin{aligned}
    \dot{x}_0  &= \frac{k_0u_0}{1+\frac{u_1}{K_{d_4}}} - \delta_0x_0 \\
    \dot{x}_1  &= \frac{k_1u_1}{1+\frac{x_0}{K_{d_1}}} - \delta_1x_1 \\
    \dot{x}_2  &= k_2x_1+k_3u_0 - \delta_2x_2 \\
    \dot{x}_3  &= \frac{k_4u_1}{1+\frac{x_2}{K_{d_2}}} - \delta_3x_3 \\
    \dot{x}_4 &= \frac{k_5u_0}{1+\frac{x_3}{K_{d_3}}} - \delta_4x_4 .
\end{aligned}
\end{equation}

\normalsize
The states, $x$, describe the concentration of proteins, the inputs $u$ are inducers which activate or repress the protein production and $K_d, \delta, k$ are constant parameters. For simulation, a fourth-order Runge-Kutta scheme is used. 100 timesteps from 100 different initial conditions each with a different input are used for training and testing. The inputs are always step inputs in these simulations. The neural network is a dense feedforward network with the output being the observable basis which spans the approximate Koopman invariant subspace. We take the case where the mixed terms are assumed to be zero. To evaluate accuracy of our Koopman model, we perform a multi-step prediction test. Predictions on a single test trajectory (a trajectory that the neural network has not seen) is given in Figure \ref{fig:ifflPred}. This prediction is done starting from an initial condition and predicting 99 steps into the future and compared with the actual trajectory. The error for this trajectory is $\approx 5\%$ and similar errors are computed for 49 other test trajectories. We then solve program (\ref{eq:ssOptFinal}) and obtain the optimal step input ($0 < u^* < 10$) to achieve a maximum steady state for both state $x_0$ and state $x_3$ as can be seen in Figure \ref{fig:iffl_optInput}. Each trajectory starts from the same initial condition, but only the trajectory corresponding to the black dashed line sees the optimal input and all the other trajectories see a random input between ($0 < u < 10$). It can be seen that the optimal input computed from our framework does give the maximum steady state when applied to the system. Note that the optimal input was applied to the original nonlinear system, \textit{not} to the identified Koopman model.

\begin{figure}
\centering
\includegraphics[scale=0.3]{figures/incoherent_ff_loop_final_nstep_prediction.pdf}
\caption{99 step prediction from a new initial condition using the neural network identified Koopman model of the feedforward loop (\ref{eq:iffl}). Predictions are given by dashed lines while the true trajectory is given by dotted lines.}
\label{fig:ifflPred}
\end{figure}

\begin{figure}
\centering
\hspace*{-0.3cm}
\includegraphics[scale=0.25]{figures/iffl_optimal_input_x0x3.pdf}
\caption{Results of the optimal input computed from the steady state programming problem applied to states $x_0$ (left) and $x_3$ (right) of the feedforward loop (\ref{eq:iffl}). The trajectory corresponding to the optimal input is given in black dashed lines and the other trajectories correspond to other inputs that are suboptimal.}
\label{fig:iffl_optInput}
\end{figure}

\subsection{Example: Combinatorial promoter}
For a second example, we consider a combinatorial promoter which takes both a repressor and an activator as input, allowing genes to be switched on and off based on the concentration of the activator and repressor \cite{del2015biomolecular}. The dynamics are given by the following set of differential equations

\begin{equation} \label{eq:combPromoter}
\begin{aligned}
    \dot{x}_0  &= -k_{1f}x_0u_0 + k_{1r}x_2 \\
    \dot{x}_1  &= -k_{2f}x_1u_1 + k_{2r}x_3 -k_{4f}x_1x_4 + k_{4r}x_6 - k_{5f}x_1x_5 \\ &+ k_{5r}x_7 + 0.2x_{10} \\
    \dot{x}_2  &= k_{1f}x_0u_0 - k_{1r}x_2 - k_{3f}x_2x_4 + k_{3r}x_5 - k_{6f}x_2x_6 \\ &+ k_{6r}x_7\\
    \dot{x}_3  &= k_{2f}x_1u_1 - k_{2r}x_3 - 0.2x_3 \\
    \dot{x}_4  &= -k_{3f}x_2x_4 + k_{3r}x_5 - k_{4f}x_1x_4 + k_{4r}x_6\\
    \dot{x}_5  &= k_{3f}x_2x_4 - k_{3r}x_5 - k_{5f}x_1x_5 + k_{5r}x_7 - k_{7f}x_5x_8 \\ &+ k_{7r}x_9 + k_{8f}x_9\\
    \dot{x}_6  &=  -k_{6f}x_2x_6 + k_{6r}x_7 - k_{4r}x_6 + k_{4f}x_1x_4\\
    \dot{x}_7  &=  k_{5f}x_1x_5 - k_{5r}x_7 + k_{6f}x_2x_6 - k_{6r}x_7\\
    \dot{x}_8  &=  -k_{7f}x_5x_8 + (k_{7r}+ k_{8f})x_9\\
    \dot{x}_9  &=  k_{7f}x_5x_8 - (k_{7r}+ k_{8f})x_9\\
    \dot{x}_{10}  &=  k_{8f}x_9 - \delta x_9^2\\
\end{aligned}
\end{equation}

\normalsize
where the inputs $u$ are the repressor or activator and are continuous, monotonically increasing functions of time. For simulation, a fourth-order Runge-Kutta scheme is used. 1000 timesteps from 80 different initial conditions each with a different input are used for training and testing. The neural network is the same as in Example 1. We again take the case where the mixed terms are assumed to be zero since the deep learning approach is flexible enough to provide a model that predicts well many steps into the future. We again solve program (\ref{eq:ssOptFinal}) and obtain the optimal step input ($0.01 < u^* < 1$) to achieve a maximum steady state for both state $x_6$ and state $x_{10}$ as can be seen in Figure \ref{fig:combPromoter_optInput}. Each trajectory starts from the same initial condition, but only the trajectory corresponding to the black dashed line sees the optimal input and all the other trajectories see a random input between ($0.01 < u < 1$). For this example of a combinatorial promoter, the learned optimal input gives the maximum steady state value for each direction in state space. Again, we want to emphasize that the optimal input was identified using the Koopman model, but it was applied to the original nonlinear system.
\begin{figure}
\centering
\hspace*{-0.4cm}
\includegraphics[scale=0.26]{figures/combinatorial_promoters_optimal_input_x6x10.pdf}
\caption{Results of the optimal input computed from the steady state programming problem applied to states $x_6$ (left) and $x_{10}$ (right) of the combinatorial promoter system (\ref{eq:combPromoter}). The trajectory corresponding to the optimal input is given in black dashed lines and the other trajectories correspond to other inputs that are suboptimal.}
\label{fig:combPromoter_optInput}
\end{figure}

These numerical results demonstrate that it is possible, by harnessing the natural analog computational power of cells and through a data-driven operator theoretic framework, to generate steady state input-output functions.

\section{Conclusions}
In this paper we presented a formulation for programming the steady state of controlled nonlinear systems with hyperbolic fixed points. We used deep dynamic mode decomposition (deepDMD) with control to compute approximate Koopman invariant subspaces and Koopman operators which represent the original nonlinear system as an approximate linear system. This allowed us to pose and solve an optimization problem wherein we maximize the steady state value of a single direction in state space. The formulation can be extended to handle various cases e.g. maximize the ratio of two directions in state space at steady state. The formulation can be slightly revised to solve common optimal control tasks e.g. reaching a target state and dynamic reference tracking. The method can also be extended to nonlinear systems with other types of attractors. It was shown that mixed terms of the state and the input can provide difficulties and we discuss a way of dealing with these terms. Finally, we demonstrated our method on two example nonlinear systems that are commonly dealt with in biological processes and briefly discuss broader biological computation implications.

\section*{Acknowledgements}
The authors thank Igor Mezic, Robert Egbert, Bassam Bamieh, Sai Pushpak, Sean Warnick, and Umesh Vaidya for stimulating conversations. This work was supported by a Defense Advanced Research Projects Agency (DARPA) Grant No. DEAC0576RL01830 and an Institute of Collaborative Biotechnologies Grant. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Defense Advanced Research Projects Agency (DARPA), the Department of Defense, or the United States Government.

\bibliographystyle{abbrv}

redpajama_set_name: RedPajamaArXiv