text:
UNIVERSITY MASTER'S DEGREE IN TEACHINGOF SPANISH AS A FOREIGN LANGUAGE (MELE) LANGUAGE
Why study MELE
Master's Degree in Teaching Spanish as a Foreign Language language
carousel_teachers
teachers_text1
The Master's Degree participates in the globalapproach which also characterises the activity of the ILCE which, as an international research institute in second language acquisition, recruits visiting professors and visiting lecturers from other institutions around the world to enrich research in the teaching and learning of Spanish language and culture at the University of Navarra. The Master's team professor is composed of experienced teachers, researchers and instructors of Spanish as a foreign language.
teachers-deployables
Professors University of Navarra
Dr. Yvonne Gavela-Ramos | Evaluation in the teaching of Spanish as a foreign language language ; The digital story and the teaching of Spanish as a foreign language language ; Teaching Spanish for specific purposes
Lectora, Institute of language and Spanish Culture - ILCE
University of Navarra (Spain)
Ph.D. Pennsylvania State University (USA)
Dr. Mark Gibson Action research and innovation in Spanish language teaching
Professor teaching assistant Linguistics, department de Filología
D. from the Complutense University in Madrid (Spain).
Dr. Ramón González Ruiz Teaching and learning of skill grammar and skill pragmatics
Senior Associate Professor Spanish Linguistics and language , department de Philology
D. from the University of Navarra (Spain)
Dr. Carmen Llamas Sáiz Teaching and learning of the skill grammar and the skill pragmatic
Profesora Titular Lingüística y language Española, department de Filología
PhD from the University of Navarra (Spain).
Dr. Oihane Muxika Practicum I and II
Ph.D. Ohio State University (USA)
Dr. Eduardo Neguerela Azarola | Sociocultural theory and language learning; Classroom planning and dynamics for collaborative and autonomous learning; Theories of second language learning; Action research and innovation in Spanish language teaching.
Visiting Professor Linguistics and language Spanish, department de Filología
Ph.D. The Pennsylvania State University (USA)
Dr. Cristina Tabernero conference room | Spanish as a global language language
Dr. Susana Madinabeitia | Assessment and certification in ELE; New technologies in Spanish language teaching.
Ph.D. at the University of Navarra (Spain)
Dr. Silvia Aguinaga Service learning and the teaching of Spanish
Ph.D. University of California Davis (USA)
Iranzu Peña Pascual | Assessment and certification in ELE
PhD Candidate at the University of Navarra (Spain)
Dr. Francisco Meizoso | Practicum I, II and III
Lector, Institute of language and Spanish Culture - ILCE
Ph.D. University of Massachusetts Amherst (USA)
Dr. Alberto Bruzos Coordination and supervision of programmes and teachers
Senior Lecturer. Director of the Spanish Language Program
Princeton University (USA)
Ph.D. from the University of León (Spain)
Dr. Andrew Lynch | Global Seminars: Teaching Spanish around the World (USA)
Associate Professor. Director of Spanish Heritage Language Program University of Miami (USA)
Ph.D. University of Minnesota (U.S.A.)
Dr. Elisa Gironzetti Action research and innovation in Spanish language teaching
Assistant Professor of Spanish Applied Linguistics
University of Maryland (USA)
Ph.D. Texas A&M University-Commerce (USA)
Dr. Javier Muñoz-Basols Global Seminars: Teaching Spanish in the World (Europe)
Senior trainer in Spanish
Oxford University (United Kingdom)
PhD from the Universitat Pompeu Fabra (Spain)
Dr. Montserrat Sanz Global Seminars: Teaching Spanish in the World (Asia)
Full professor and the head of the Spanish Department at Kobe City University of Foreign Studies in Kobe (Japan)
Kobe City University of Foreign Studies (Japan)
Ph.D. University of Rochester (USA)
Dr. Carlos Schmidt Foó development professional and teaching competences; Teaching Spanish for specific purposes
Director of the Business Spanish for Communication Unit
IESE Business School (Spain)
PhD from the Universitat de Barcelona (Spain)
Iolanda Nieves de la Vega :: Iolanda Nieves de la Vega development professional and teaching competences
Professor of the Business Spanish for Communication Unit
Dr. Elena Verdía | Practicum II
Head of department for Teacher Training Instituto Cervantes, Alcalá de Henares (Madrid)
Ph.D., Universidad Nacional de Educación a Distancia (Spain)
Mentoring practices
Iranzu Peña Pascual | Practicum I and II
Dr. Silvia Aguinaga Practicum I, II and III
Dr. Susana Madinabeitia | Practicum I and II
Ph.D. University of Navarra (Spain)
Dr. Yvonne Gavela-Ramos Practicum I and II
Francisco Meizoso | Practicum I, II and III
Guest mentors (summer intensives)
Dr. Yamile Silva Practicum III
Associate Professor of World Languages & Cultures
University of Scranton (USA)
Ph.D. University of Massachusetts (USA)
Dr. Andrew Lynch Practicum III
Associate Professor Modern Languages and Literatures
University of Miami (USA)
Ph.D. University of Minnesota (USA)
Dr. Antoni Fernández Parera Practicum III
Modern Languages and Literatures, Graduate Student
Barnard College (USA)
Ph.D. University of Miami (U.S.A.)
Dr. Francisca Aguiló Mora Practicum III
Lecturer Department of Latin American and Iberian Cultures
Columbia University (USA)
Ph.D. University of Miami (USA)
Dr. Sergio Adrada Rafael Practicum III
Fairfield University (USA)
Ph.D. Georgetown University (USA)
Guest lecturers - Previous editions
Dr. Lourdes Ortega, Georgetown University (USA)
Dr. Rafael Salaberry, Rice University (USA)
Dr. Lucía Osa Melero, Duquesne University (USA)
Dr. Carmen Carracelas, The University of Southern Mississippi (USA)
Dr. Nausica MarcosDenison University (USA)
Dr. Olga Esteve, Pompeu Fabra University (Spain)
Dr. James P. Lantolf, The Pennsylvania State University (USA)
Dr. Próspero García, Rutgers University (USA)
Dr. Manel Lacorte, University of Maryland (USA)
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Tel. +34 948 42 56 00 | masterele@unav.es


This entry was posted on Thursday, February 6th, 2014 at 4:53 am	and is filed under Technology News And Updates. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.


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redpajama_set_name: RedPajamaGithub


Blazecaller is a 7 Mana Cost Epic Neutral Minion Elemental card from the Journey to Un'Goro set!
His flavour text should be, " I eat Ancient of Wars for breakfast".
Besides the obvious massive value of this card, Elemental Shaman now has 28 face damage rolled into 6 massive drops (2x Fire Ele 2x Blaze, Kalinos & Al-Akir) that are all on curve of each other. I think this will slaughter Jade Druid in the midgame.
It's only OP in elemental decks, and it won't mess up arena being epic, moreover, I don't think it's going to be that easy to pull off, since you basically have to save cards to play on a curve. You lose a lot of tempo if your hand is not "just right". Still , elementals is the new dragon.
Well at least it's epic so it won't destroy arena like firelands portal. Seriously Blizzard devs are In a downward spiral at this point.
Indeed. It's not just a 6/6, but also an Elemental, so you get the "If you played an Elemental last turn" synergy.
Still, it's only worse than Firelands in Arena, where you would need a fairly decent amount of Elementals to pull this off.


So you will see some color and type, but the main focus of this round is still the logo itself.
This slide show starts with the original 4E goes through some of the tweaking. It is always nice to have a solid single color version of your logo, but the places the Zollikon logo is going to be used I think it could easily exist in two or more. So you will see a two tone version below as well.
Since you mentioned being drawn to 4E for it's roundness I wanted to revisit 1E but as round. It has some intresting characteristics as see in the animation below.
Version of an abstract half.


text:
Енего, Енеґо (, ) — муніципалітет в Італії, у регіоні Венето, провінція Віченца.

Енего розташоване на відстані близько 460 км на північ від Рима, 75 км на північний захід від Венеції, 45 км на північ від Віченци.

Населення —   (2014).
Щорічний фестиваль відбувається 7 жовтня. Покровитель — Santa Giustina.

Демографія

Сусідні муніципалітети

 Азіаго
 Фоца
 Галліо
 Арсьє
 Чизмон-дель-Граппа
 Вальстанья
 Гриньо

Див. також
 Список муніципалітетів провінції Віченца

Примітки

Муніципалітети провінції Віченца

redpajama_set_name: RedPajamaWikipedia


text:
Tourism Futures International
Strategy development and forecasting in aviation, travel and tourism
The Future of Travel
Impact Assessments
Home > The Future of Travel > Insights > Technological
One of the major influences on airline costs, route selection and profitability over the next decade will be the new aircraft types being delivered.
New aircraft types including the A350 and the new variants of the A330 and of the narrow body aircraft, A320s and B737s, will join the A380s and B787s in airline fleets over the next few years. The new aircraft designs save on fuel, increase range and improve cost efficiency. See table below for aircraft characteristics. The stimulus to replace current aircraft with the new more fuel-efficient models is highest during periods of high fuel prices.
For the A380 there were 27 deliveries during 2015, with an additional 14 delivered during the first half of 2016, taking the total in operation to 193 worldwide. The A380 first entered service in October 2007 and is now operated by 13 airlines on over 100 routes. As at the end-June 2016 Airbus had 126 of the aircraft still on order. The A380 currently seats from 379 passengers (a Singapore Airlines four class layout) to 615 passengers (an Emirates two class layout) over a range of up to 8,200 nautical miles. Emirates has the largest A380 fleet with 81 in service and 61 still on order.
Boeing has delivered 306 B787-8s to 33 customers and 125 B787-9s to 19 customers as at end-June 2016; 724 of the B787 family aircraft are still on firm order. The B787-8 first entered service in October 2011 and the B787-9 in June 2014. The B787s are reported to use 20-25% less fuel with 20-25% fewer emissions than the airplanes they replace. With three variants the B787 seats between 242 and 330 passengers with a range of up to 7,635 nautical miles.
Airbus delivered its first A350 XWB (extra wide body) to launch customer Qatar Airways in December 2014. As at end-June 2016, 27 of the -900 variant were in service, operated by seven airlines; 578 were still on order from 41 customers. Airbus also has 181 orders, from ten customers, for the -1000 variant. Only 16 orders remain on the books for the -800 variant as airlines have moved towards the larger -900 variant, and development of the -800 has reportedly been suspended. The A350 family provides a long-range capability from 7,950 to 8,200 nautical miles, with typical seating capacities of 280 to 366 passengers.
Airbus has also launched an upgrade of its medium range wide-body A330 passenger jet, with two versions of the A330neo (new engine option). As at the end-June 2016 Airbus had 176 orders for the -900neo variant from eight customers and 10 orders for the
-800neo variant. First deliveries are scheduled to start in the fourth quarter of 2017. The A330neo is reported to reduce fuel consumption by 14% per seat compared with the A330, and increase the range by up to 400 nautical miles while offering up to ten extra seats.
Boeing's newest family of single-aisle airplanes is the B737 MAX. First deliveries to customers are expected to commence in 2017. The B737 Max 8 is the first in the family to be developed and is expected to reduce fuel use and CO2 emissions by 20% compared with the original Next-Generation 737s when they first entered service, and to have an additional 405-580 nautical mile range. The 737 MAX 200, a new variant based on the B737 MAX 8 has recently been launched, capable of accommodating up to 200 seats. As at end-June 2016 Boeing had over 3,200 orders for the B737 MAX aircraft, with first delivery now expected to take place during the first half of 2017.
Similarly, the newest member of the A320 family, the A320neo (new engine option), reports to offer up to 20% fuel savings per seat in comparison with the current engine option aircraft and up to 500 nautical miles additional range. An A321neo variant has also been launched to deliver the longest range of any single-aisle aircraft (4,000 nautical miles), with particular suitability for transatlantic routes. Airbus reports that as at end-June 2016 firm orders for the A320neo family stood at over 4,500 aircraft, with eight of the A320neos so far delivered. Large orders have been placed by some of the Asia Pacific LCCs.
The following table summarises the specifications and orders for these aircraft. The information has been obtained from various sources and will be updated as new information becomes available.
Max Take-off Weight (tonnes)
Delivered at Jun-16
On Order at Jun-16
A380 15,200 544-853 575 Oct-07 193 126
B787-8 13,620 242 228 Sep-11 306 125
B787-9 14,140 290 254 Jun-14 125 446
B787-10 11,910 330 254 2018 153
A350-800 15,200 280-440 259 (a) 16
A350-900 15,000 325-440 280 Dec-14 27 578
A350-1000 14,750 366-440 308 Mid-2017 181
A330-800neo 13,900 257-406 242 Early-2018 10
A330-900neo 12,130 287-440 242 End-2017 176
A319neo 6,950 140-160 75 2017 58
A320neo 6,500 165-189 79 Jan-16 8 3,388
A321neo 7,400 206-240 97 End-2016 1,129
B737MAX 3,218
B737MAX 7 6,200 126-149 72
B737MAX 8 6,500 162-189 82 2017
B737MAX 200 200 2019
Note: (a) A350-800 may not be further developed. Source: Airbus, Boeing, airline news releases.
© Tourism Futures International 2009
Home - Company Overview - The Future of Travel - Services - Contact Us

redpajama_set_name: RedPajamaCommonCrawl


[00:12.85]Good evening Ms Wang .
[00:19.98]and calls from students about English learning.
[00:38.31]is a real headache for me.
[00:44.57]but I still forget them.
[00:46.42]What else can I do?
[00:53.59]in your house where you see it often?
[01:10.59]but also try to use them.
[01:15.10]or write English,you will remember them.
[01:20.14]but the grammar is very difficult for me .
[01:28.65]I still make mistakes .
[01:30.85]What else should I do?
[01:36.07]writing sentences with that grammar point.
[01:46.64]to practice using it a lot.
[01:52.01]It's common to make mistakes.
[01:54.43]So don't be afraid of making mistakes.
[01:59.83]I'm always nervous when I listen to English.
[02:08.24]while you are listening to English.
[02:15.00]the material for the first time.
[02:29.01]My third advice is:keep practicing .
[02:33.42]The more you listen,the more you'll understand.
[02:51.76]but it will help you learn faster.
[02:59.61]several times to explain youself in English.
[03:07.60]or join English book clubs.
[03:14.05]if you're not sure about something in English.
[03:17.94]that you don't know the answer.
[03:20.05]Be honest with yourself and your teacher.
[03:23.04]Finally.do your English homework carefully.


The Asia Pacific Centre for Animal Health (APCAH) is an internationally focused research and research training centre that aims to optimise animal production and product quality through improved control of infectious agents.
The Centre conducts multidisciplinary research to develop fundamental understanding of the epidemiology and pathogenesis of infectious diseases of animals and applies this to enhancing control of disease through improved strategies for vaccination, diagnosis and management. Our expertise extends across the full range of production animal species (cattle, sheep, poultry and pigs), as well as companion animal species (dogs, cats and horses) and wildlife.
Among the achievements of the Centre are the development of novel diagnostic antigens for serological diagnosis of mycoplasmosis in poultry and pigs, and the development of novel vaccines to control disease caused by Mycoplasma gallisepticum, Mycoplasma synoviae, Mycoplasma hyopneumoniae, Mycoplasma bovis, chicken anaemia virus and infectious laryngotracheitis virus. The mycoplasma vaccines developed by the Centre are marketed under the trade names Vaxsafe MG, Vaxsafe MS and Vaxsafe MHP. Our vaccines against M. bovis, chicken anaemia virus and infectious laryngotracheitis virus are currently being evaluated by commercial collaborators.
We are part of the NHMRC National Centre of Excellence in Antimicrobial Stewardship (NCAS), with the aim of optimising the use of antimicrobial therapy in production and companion animals.
In addition to discovery-based research, APCAH also conducts contract research for the development and registration of novel animal health products to international standards and provides microbiological diagnostic services.
Discovered the role played by recombination between attenuated vaccines in the genesis of novel virulent strains of infectious laryngotracheitis virus vaccines, and demonstrated the role of recombination in the evolution of other major animal herpesviruses.
Discovered the basis for high frequency antigenic variation in pathogenic mycoplasmas, work that has explained the persistence of these important infectious agents and that has explained problems encountered in serological diagnosis.
Defined the immunomodulatory effect of glycoprotein G of infectious laryngotracheitis virus and shown that deletion of the gene encoding it reduces the virulence of this important viral pathogen. This work has led to the development of a novel attenuated vaccine to control infectious laryngotracheitis.
Demonstrated that high concentrations of Rhodococcus equi are exhaled by young foals and thus that they may represent a contagious risk to each other. This work has led to suggestions for changes in management aimed at reducing the prevalence and severity of this disease on horse studs.
Defined the major bacterial pathogens responsible for peracute mastitis in sheep in Australia, indicating the targets for future vaccination strategies.
Identified virulence factors required by E. coli to cause disease in the respiratory tract in chickens and in the reproductive tract in dogs.
Identified key indicators of susceptibility to endometritis in mares.
Our recent studies have been applying high throughput sequencing and bioinformatics analysis to discovery of novel pathogens and to conducting detailed genetic mapping studies for epidemiological investigations. We have also been integrating genomics and metabolomics to explore the roles of specific genes in virulence.
Mycoplasma gallisepticum ts-11, an attenuated live vaccine strain that is licensed through the world for control of mycoplasmosis in chickens.
Mycoplasma synoviae MS-H, an attenuated live vaccine strain that is licensed through the world for control of mycoplasmosis in chickens.
Mycoplasma hyopneumoniae ts-19, an attenuated live vaccine strain that is licensed for control of enzootic pneumonia in pigs.
An attenuated vaccine against infectious laryngotracheitis virus that is currently being assessed for development by commercial partners.
We have also developed candidate vaccines for the control of colibacillosis in poultry and mycoplasmosis in cattle.
APCAH staff and students have developed novel recombinant antigens for improved serological diagnosis of Mycoplasma bovis, Mycoplasma gallisepticum, Mycoplasma synoviae, Mycoplasma hyopneumoniae, Mycoplasma pneumoniae and laryngotracheitis virus infections. The ELISAs based in these antigens have offered infectious improved sensitivity and specificity over previously available assays and a number of these antigens are now the basis of commercially available kits produced by our commercial collaborators.
Real-time polymerase chain reaction assays have been developed for most major bacterial and viral pathogens of poultry and applied to diagnosis and strain differentiation. These assays are offered to the industry and the public through our diagnostic laboratory and offer improved sensitivity and specificity over previously available assays, as well as strain differentiation for some pathogens.
Polymerase chain reaction assays have been developed to detect feline and equine respiratory pathogens and are provided as a diagnostic service to the veterinary profession.
The primary goal of antimicrobial stewardship is to optimise clinical outcomes while minimising unintended consequences of antimicrobial use, including the emergence of resistance. Given the association between antimicrobial use and the selection of resistant pathogens, the frequency of inappropriate antimicrobial use is often used as a surrogate marker for the avoidable impact on antimicrobial resistance. The combination of effective antimicrobial stewardship with a comprehensive infection control program has been shown to limit the emergence and transmission of antimicrobial-resistant bacteria.
APCAH conducts safety and efficacy testing of animal health products to international Good Laboratory Practice standards for commercial partners. We also routinely perform potency, innocuity and freedom from adventitious agents testing on poultry vaccines for a range of clients.
We are able to house poultry in HEPA-filtered isolators under specific pathogen free conditions.
Our animal house and supporting laboratory facilities are accredited by the National Association of Testing Authorities to perform biological testing.
Our facilities have been used to prepare dossiers for successful national and international applications for registration of veterinary vaccines.
APCAH's diagnostic laboratories, based on our Werribee campus, provide serological and virological diagnostic services to the poultry industry. We also provide a routine veterinary bacteriology service.
More specialised services include a comprehensive suite of diagnostic polymerase chain reaction assays for rapid diagnosis of poultry diseases and, for some pathogens, strain identification.
We also provide polymerase chain reaction diagnostic assays for identification and discrimination of viral and bacterial pathogens causing upper respiratory tract disease in cats and viral respiratory and abortigenic pathogens of horses.
Our staff and students work on projects that bridge from fundamental studies of molecular biology, pathogenesis and epidemiology, through to applied studies in vaccine and diagnostic test development. They have been the recipients of multiple awards from national and international veterinary and scientific organizations, including the Derrick Edward Award of the International Organisation for Mycoplasmology (P. Markham), Houghton Trust Lecture Award by the World Veterinary Poultry Association (A. H. Noormohammadi), the Science and Innovation Award for Young People in Agriculture, Fisheries and Forestry (Bureau of Rural Science) (J. M. Devlin, N. Wawegama), Australian Research Council Future Fellowship (J. M. Devlin) the Gilruth Prize of the Australian Veterinary Association, the Ian Clunies Ross Memorial Award of the Australian College of Veterinary Scientists (G. F. Browning) and the Clunies Ross Medal of the Australian Academy of Technological Sciences and Engineering (K. G. Whithear).
Project: Development of an Attenuated Vaccine for Oedema Disease.
Project : Diseases of zoonotic and biosecurity importance in Australian common brushtail (Trichosurus vulpecula) and common ringtail (Pseudocheirus peregrinus) possums.
Project: Investigations into bacterial causes of disease in swine with emphasis on airborne pathogens.
Project: Genetic diversity of Infectious laryngotracheitis virus after recombination events in the natural host as model of infection.
Project: Infectious Laryngotracheitis virus vaccines and latency in natural host.
Project: Investigation of recombination among isolates of equine herpesvirus 2 and 5.
Project: Neutrophil Extracellular Traps (NETs) in Mycoplasma bovis.
Project: The role of major surface proteins of infectious laryngotracheitis virus (ILTV) in protection against ILT in chicken.
Project: Q fever in intensively managed dairy goat farms. The disease dynamics, its impact on herd performance and applicable control measures.
Project: Avian coronaviruses in Australia.
Project: Environmental Resistome and Antimicrobial Resistance Patterns in an Australian Veterinary Referral Hospital.
Project: Antimicrobial stewardship in Australian Veterinary Practices.
Project: Investigation of the role of NAD synthesis in the replication of Coxiella burnetii.
Project: Enhancing control of virulent recombinant strains of infectious laryngotracheitis virus.
Project: Calf health and welfare in dairy systems.
Project: Investigation of viral recombination between ILTV vaccine strains using in vitro, in ovo, and in vivo systems.
Project: Genetic manipulation of mycoplasmas in domestic animals.
Project: Characterising the epidemiology of Coxiella burnetii infection in Australian wildlife and livestock species using existing and novel diagnostic tools.
Project: Molecular analysis of pathogenicity of Mycoplasma synoviae.
Project: Diversity and association of antibiotic and metal resistance genes in faecal bacteria from Australian livestock.
Agnew-Crumpton R, Vaz PK, Devlin JM, O'Rourke D, Blacker-Smith HP, Konsak-Ilievski B, Hartley CA, Noormohammadi AH. 2016. Spread of the newly emerging infectious laryngotracheitis viruses in Australia. Infect Genet Evol 43:67-73.
Amery-Gale J, Marenda MS, Owens J, Eden PA, Browning GF, Devlin JM. 2017. A high prevalence of beak and feather disease virus in non-psittacine Australian birds. J Med Microbiol 66:1005-1013.
Auplish A, Clarke AS, Van Zanten T, Abel K, Tham C, Bhutia TN, Wilks CR, Stevenson MA, Firestone SM. 2017. Estimating the intra-cluster correlation coefficient for evaluating an educational intervention program to improve rabies awareness and dog bite prevention among children in Sikkim, India: A pilot study. Acta Trop 169:62-68.
Bond KA, Vincent G, Wilks CR, Franklin L, Sutton B, Stenos J, Cowan R, Lim K, Athan E, Harris O, Macfarlane-Berry L, Segal Y, Firestone SM. 2016. One Health approach to controlling a Q fever outbreak on an Australian goat farm. Epidemiol Infect 144:1129-41.
Chu DH, Stevenson MA, Nguyen LV, Isoda N, Firestone SM, Nguyen TN, Nguyen LT, Matsuno K, Okamatsu M, Kida H, Sakoda Y. 2017. A cross-sectional study to quantify the prevalence of avian influenza viruses in poultry at intervention and non-intervention live bird markets in central Vietnam, 2014. Transbound Emerg Dis doi:10.1111/tbed.12605.
Cowled BD, Stevenson MA, Madin B. 2016. An assessment of the association between soil pH and ovine Johne's disease using Australian abattoir surveillance data. Prev Vet Med 126:208-19.
Cutcher Z, Williamson E, Lynch SE, Rowe S, Clothier HJ, Firestone SM. 2017. Predictive modelling of Ross River virus notifications in southeastern Australia. Epidemiol Infect 145:440-450.
Cuttance EL, Laven RA, Stevenson MA. 2017. Variability in measurement of Pithomyces chartarum spore counts. N Z Vet J 65:192-197.
Cuttance EL, Stevenson MA, Laven RA, Mason WA. 2016. Facial eczema management protocols used on dairy farms in the North Island of New Zealand and associated concentrations of zinc in serum. N Z Vet J 64:343-50.
Death C, Coulson G, Kierdorf U, Kierdorf H, Ploeg R, Firestone SM, Dohoo I, Hufschmid J. 2017. Skeletal fluorosis in marsupials: A comparison of bone lesions in six species from an Australian industrial site. Sci Total Environ 584-585:1198-1211.
Devlin JM, Vaz PK, Coppo MJ, Browning GF. 2016. Impacts of poultry vaccination on viruses of wild bird. Curr Opin Virol 19:23-9.
Garner MG, East IJ, Stevenson MA, Sanson RL, Rawdon TG, Bradhurst RA, Roche SE, Van Ha P, Kompas T. 2016. Early Decision Indicators for Foot-and-Mouth Disease Outbreaks in Non-Endemic Countries. Front Vet Sci 3:109.
Gebrekidan H, Gasser RB, Stevenson MA, McGrath S, Jabbar A. 2017. Assessing the performance of multiplexed tandem PCR for the diagnosis of pathogenic genotypes of Theileria orientalis using pooled blood samples from cattle. Mol Cell Probes 31:70-75.
Hancock AS, Younis PJ, Beggs DS, Mansell PD, Stevenson MA, Pyman MF. 2016. An assessment of dairy herd bulls in southern Australia: 1. Management practices and bull breeding soundness evaluations. J Dairy Sci 99:9983-9997.
Hancock AS, Younis PJ, Beggs DS, Mansell PD, Stevenson MA, Pyman MF. 2016. An assessment of dairy herd bulls in southern Australia: 2. Analysis of bull- and herd-level risk factors and their associations with pre- and postmating breeding soundness results. J Dairy Sci 99:9998-10008.
Hardefeldt LY, Browning GF, Thursky K, Gilkerson JR, Billman-Jacobe H, Stevenson MA, Bailey KE. 2017. Erratum to "Antimicrobials used for surgical prophylaxis by companion animal veterinarians in Australia" [Vet. Microbiol. 203C (2017) 301-307]. Vet Microbiol 208:74-76.
Hardefeldt LY, Browning GF, Thursky K, Gilkerson JR, Billman-Jacobe H, Stevenson MA, Bailey KE. 2017. Antimicrobials used for surgical prophylaxis by companion animal veterinarians in Australia. Vet Microbiol 203:301-307.
Hardefeldt LY, Browning GF, Thursky K, Gilkerson JR, Billman-Jacobe H, Stevenson MA, Bailey KE. 2017. Antimicrobials used for surgical prophylaxis by equine veterinary practitioners in Australia. Equine Vet J doi:10.1111/evj.12709.
Hardefeldt LY, Browning GF, Thursky KA, Gilkerson JR, Billman-Jacobe H, Stevenson MA, Bailey KE. 2017. Cross-sectional study of antimicrobials used for surgical prophylaxis by bovine veterinary practitioners in Australia. Vet Rec doi:10.1136/vr.104375.
Hardefeldt LY, Holloway S, Trott DJ, Shipstone M, Barrs VR, Malik R, Burrows M, Armstrong S, Browning GF, Stevenson M. 2017. Antimicrobial Prescribing in Dogs and Cats in Australia: Results of the Australasian Infectious Disease Advisory Panel Survey. J Vet Intern Med 31:1100-1107.
Haydock LAJ, Pomroy WE, Stevenson MA, Lawrence KE. 2016. A growing degree-day model for determination of Fasciola hepatica infection risk in New Zealand with future predictions using climate change models. Vet Parasitol 228:52-59.
Hidano A, Carpenter TE, Stevenson MA, Gates MC. 2016. Evaluating the efficacy of regionalisation in limiting high-risk livestock trade movements. Prev Vet Med 133:31-41.
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text:
\section{Introduction}
\label{sec:intro}
Environmental issues such as the level of emissions and global warming have become increasingly important during the past decades.
On the one hand, there is a growing commitment among the countries' governments to global agreements such as the Kyoto Protocol
and the Paris Agreement. On the other hand, companies display significant efforts to address socially responsible issues raised by stakeholders such as consumers and employees. The latter is reflected in the accounting practices of the large companies, in which environmental and social accounting are frequently reported within the companies annual reports. Other important corporate strategies include the award of international certification stating compliance with social and environmental issues such as ISO 14001.

The impact of social reputation and environmental compliance on profits is nowadays taken very seriously, particularly by large companies. Once a firm is inspected and declared non-compliant, there might be impact on revenues, market-share and costs: fines might be imposed by auditors and consumers can enforce product boycotts such as the one Royal Dutch Shell suffered due to the intention of the latter to dispose its Brent Spar offshore storage buoy in the sea (The Economist, 1995; Klein, Smith and John, 2002). Despite such a risk, social or environmental commitment and profits cannot be simultaneously maximized unless compliance investment contributes to profit maximization (Husted and Salazar, 2006). Consequently, environmental compliance has to be enforced by policy makers through auditing processes. But enforcement is also a costly process due to inspection costs, noisy monitoring due to the presence of multiple firms discharging pollutants in the same neighbourhood or even due to uninspectability (Heyes, 1998). The latter is particularly true in the US where the 4$^{th}$ Amendment obligates auditors to run the first inspections from outside the firms' fence. Corruption, privately funded political campaigns, bribery or the lack of auditors commitment, among other factors, may aggravate the situation.

Moreover, sanctions might depend on several factors such as the degree of non-compliance, i.e., the difference between the observed and the accepted pollution level, as well as on the effort demonstrated by the firm to minimize the social negative externality due to pollution. Firms showing an investment plan in clean production are rarely punished if found to be non-compliant with regulations (Arguedas and Hamoudi, 2004). As a result, firms tend to comply with environmental regulation only if the investment to do so is offset by the expected cost of being inspected and caught. The latter can be increased through different mechanisms such as higher fines imposed on non-compliant firms or decreasing the inspection costs, which might lead to a higher probability of inspection.

There is a wide literature on environmental compliance, particularly focusing on the conflict of interests between policy makers and corporations. One branch of the literature addressing such problem is based on the principal-agent framework. Arguedas and Hamoudi (2004) develop a principal-agent model in which sanctions depend on both the environmental technology employed by the firm as well as on the degree of non-compliance. The regulator chooses the pollution standard and the probability of inspection while the firm decides on the emission level and the environmental technology to be adopted. A cleaner technology leads to smaller fines when those are applied. Generally, principal-agent models are better suited when the aim is to optimize the structure of regulation and enforcement in a single-firm setting, as pointed out in Malik (2007).

When dealing with more competitive markets, a game theoretical model should be used. The latter can be based either on classic or evolutionary game theory. Zhao et al. (2012) propose a game model to study the behaviour of manufacturers in response to drivers to reduce environmental risk and carbon emissions in the context of green supply chain management. In the same vein, Zhu and Dou (2007) propose an evolutionary game model to study the interplay between enterprises and the government during enforcement of regulation. While the companies face a cost of compliance, there are also benefits due to savings in energy consumption and lower discharge costs. Monitoring is costly to the government and the latter also faces pollution treatment costs when companies fail to implement green supply chain measures. Public revenues come from fines paid by non-compliant firms.

In a different context, that of auditing processes dealing with financial reports, Anastasopoulos and Anastasopoulos (2012), propose an evolutionary game in which auditors might conduct either a basic or an extended (and more costly) set of audit procedures. Only the latter are able to distinguish between companies that commit or not intentional fraud in their reports. The authors point out that evolutionary game models have advantages when compared to their classic game theory counterparts. Evolutionary games are capable of explaining how players achieve the equilibrium, i.e., the game is dynamic and agents might review their actions over time, and if the stationary points of the game are stable or not. Moreover, evolutionary games allow for bounded rationality, which is closer to real world corporate decisions. As Arthur (1994) points out, the type of rationality assumed in economics demands much of human behaviour and breaks down under complicated problems. In such situations, psychologists tend to agree that humans think inductively with bounded rationality. Over time, feedback from the competitive environment comes in and individuals replace their strategies whenever better adapted actions display more successful results.

In light of all these facts, we present an evolutionary game to study a competitive market in which auditors might or not inspect firms. The latter might be environmentally compliant or not. We closely follow Arguedas and Hamoudi (2004) with regard to the profit functions of the firms depending positively on the emission level and on dirtier (i.e., cheaper) technologies. All firms discharge some level of pollution, thus generating a negative social externality. Fines increase the dirtier the technology a company chooses to use and on the level of emission. We assume an initial condition equivalent to a social context of pollution trap, i.e., where almost none of the firms are compliant and almost the totality of the auditors display a lenient culture of not inspecting the firms.

We start with a base model where there is no spatial structure as in Zhu and Dou (2007) and Anastasopoulos and Anastasopoulos (2012), i.e., each auditor might inspect any firm in the population. Then we introduce one of the main contributions of our model, which is to assume that firms and auditors are spatially allocated at different geographical locations. The latter seems more realistic given that a firm tends to adopt similar practices as those of its local neighbours. Thus, a firm located in a region with several polluters would have incentives to do the same. On the side of auditors, it would be less likely that a particular auditor was selected to inspect a firm located far away due to cost constraints. While the framework adopting two well-mixed populations in which any firm can interact with any auditor recovers the same oscillatory pattern as in Anastasopoulos and Anastasopoulos (2012), without an evolutionary equilibrium in the long run, the extension assuming structured populations allows for a quite rich dynamics depending on the monitoring cost, with the possibility of different robust equilibria as well as the possibility of the oscillatory pattern observed in the well-mixed population case.

Our structured population approach is closely related to cellular automata (CA) models. The latter have been used in a wide scope of problems, ranging from the seminal theoretical Game of Life by John Conway (see Gardner, 1970) to more applied problems such as the model in Duff et al. (2015) used to determine optimal travel routes for vehicles travelling from bases to forest fires. In CA models, an array of identically programmed cells (automata) interact with one another in a local neighbourhood. Each automaton has an initial state which might change or not over time according to some transition function. The latter specifies some rule(s) which generally depend on the state or some other entity of a particular cell and its closest neighbours. Local patters of behaviour then influence the entire population. Transition rules from the current to the next discrete time step might be completely deterministic as in Pereira et al. (2008) where the updating rule consists in every automaton copying the state of the best performing automata in the local neighbourhood or as in Conway's game of life where the state of each automaton could be alive or dead conditional on how many local neighbours were in the alive state in the previous time step.

We here follow a probabilistic transition rule in which each cell contains one auditor and one firm. Individuals compare their performance within their own population although their profits come from the game played with individuals in the other population. Updating is synchronous such that, in each Montecarlo step (MSC), after all individuals have computed the payoffs obtained from the game, each individual selects a local neighbour to compare payoffs. If the neighbour's payoff is larger, there is an increasing probability of copying the neighbour's strategy the larger the difference in payoffs is. Games where players compare their performance and update their strategies probabilistically can be found in the literature as in Chen et al. (2015), although generally such class of models only deals with one-population games.

The remainder of the paper is organized as follows. In Section 2, we setup and solve the evolutionary game model assuming well-mixed populations. In Section 3, the game is extended to the case of structured populations. Results are compared and discussed. Section 4 concludes.

\section{Model}
\label{sec:model}
We follow Arguedas and Hamoudi (2004) with regard to firm profit and social welfare function. A firm's private profit $\pi(k,e,\beta)=ke-e^2\beta^{-1}$ is strictly concave on the emission level $e>0$ and is monotonically increasing on a profitability parameter $k>0$ and on the type of production technology employed $\beta\in[1,\bar{\beta}]$, where a higher $\beta$ is associated with a cheaper and dirtier technology. Pollution generates a negative externality $d(e,\beta)=\beta e^2$ which is convex increasing on the emission level and linearly increasing the dirtier the technology adopted. On the policy maker side, auditors might inspect firms or not. If a firm is inspected and declared non-compliant, it faces a fine $f(e,\beta,s)=\beta(e-s)^2$, where $s$ is the maximum emission level acceptable.

Differently from the principal-agent monopoly framework in Arguedas and Hamoudi (2004), we assume a very large number of firms in a competitive market, thus making inspectability through emission level more difficult (see Heyes, 1998). We thus normalize the emission standard to $s=0$, making fines harsher, i.e., due to a higher required effort to correctly measure the emission level, the policy maker adopts a stricter environmental policy. The decision to punish is solely based on visual inspection of the type of technology employed in corporate plants and punishment is enforced whenever $\beta$ is high. The penalty consists in charging a fine equal to $d(e,\beta)$, i.e., a fine equivalent to the complete internalization of the negative environmental externality that a firm generates while producing.

We also assume bounded rational agents such that the decision to select the optimal technology is carried out through maximizing profits but the profit maximizing function that is chosen by managers is purely based on their corporate culture. In other words, when firms decide which technology to use, environmentally compliant firms internalize the negative externality in their private profit function while non-compliant firms do not, i.e., the choice of environmental policy is naive and agents do not know in the long run which corporate policy is the best performing strategy. Such an approach is similar to that used in Xiao and Yu (2006) supply chain model, where agents rationally maximize their utilities (either revenue or profit functions) but they are naive regarding which preference function is the best over time.

Regarding inspection, there is a very large number of auditors, which are randomly allocated to visit firms. Each auditor either inspects or not. While in Arguedas and Hamoudi (2004) the inspection probability faced by the only firm in the model was a continuous variable $p\in[0,1]$, here it can only assume one of two values for one particular firm at the microscopic local level, i.e., $p=0\vee p=1$, depending on the strategy chosen by the auditor visiting the firm. But at the macroscopic level, every firm on average faces $p\in[0,1]$ depending on the strategy distribution (state) in the auditors population at a given time step. With regard to welfare, the policy maker has a social welfare function according to which he takes into account the firm's private profit, the negative externality it generates and the expected cost of inspection. Fines are not taken into account once the fine paid by a firm cancels out with the public revenue it generates:
\begin{equation}
W(k,e,\beta,p,c)=ke-e^2\beta^{-1}-\beta e^2-pc
\label{welfare}
\end{equation}
Whenever an auditor visits a firm, the game played is given by:
\begin{equation}
\bordermatrix {&\text{Non-compliant (P)}&\text{Compliant (C)}\cr
	\text{Inspects (I)} &\pi_A^{IP},\pi_F^{IP}& \pi_A^{IC},\pi_F^{IC} \cr
	\text{No Inspection (N)} &\pi_A^{NP},\pi_F^{NP}& \pi_A^{NC},\pi_F^{NC}\cr}
\label{Matrix-I}
\end{equation}
where the auditor, denoted by subscript $A$ (resp. the firm, denoted by subscript $F$), stands as the row (resp. column) player in the payoff matrix above. When a firm is called to play the stage-game in (\ref{Matrix-I}), all the managers can do is to adjust the emission level selecting the optimal emission that maximizes the profit function depending if the auditor the firm faces will inspect it or not and depending on which environmental policy the firm follows. In other words, we further assume that the optimal decisions regarding $\beta$ and $e$ are taken rationally but independently at each firm. This assumption, which is also in line with bounded rationality, takes into account the lack of synergy between corporate divisions where the long-run investment decision regarding the technology to be used is made by a planning team while the more short-run decision on the emission level is carried out by the operating team.

If the firm is compliant with the environmental regulation, technology choice is based on the following maximization problem:
\begin{equation*}
\max_{\beta}\pi(k,e,\beta)=ke-e^2\beta^{-1}- \beta e^2
\end{equation*}
which internalizes the negative externality into the firm's private profit for the sake of selecting $\beta^*$. First order condition (FOC) leads to:
\begin{equation*}
\frac{\partial\pi}{\partial\beta}=-e^2\left( 1-\beta^{-2}\right)=0\Rightarrow\beta^*=1
\end{equation*}
Instead, a non-compliant firm only takes into account its private profit function, leading to the following FOC and technology optimal choice:
\begin{equation*}
\frac{\partial\pi}{\partial\beta}=e^2\beta^{-2}>0\Rightarrow\beta^*=\bar{\beta}
\end{equation*}
Given that we are left with only two choices of technology $\beta\in\left\lbrace1,\bar{\beta} \right\rbrace$, whenever an auditor visits a firm and decides to inspect it, the firm is fined if it employs a technology $\beta=\bar{\beta}$. The optimal emission level for a compliant firm is independent on being audited or not:
\begin{equation*}
\max_{e}\pi(k,e,1)=ke-e^2-e^2\Rightarrow\frac{\partial\pi}{\partial e}=k-4e=0\Rightarrow e^*=k/4
\end{equation*}
leading to a private profit $\pi_F^{IC}=\pi_F^{NC}=3k^2/16$ and social welfare $\pi_A^{NC}=k^2/8$ if the firm is not inspected and $\pi_A^{IC}=k^2/8-c$ otherwise. We emphasize that, although compliant firms always internalize the pollution cost into their private profit function for the sake of selecting their optimal decisions $\beta^*$ and $e^*$, they never get fined, thus never facing the social cost $d(e,\beta)$ due to pollution.
Regarding non-compliant firms, if a firm is not inspected, it is not declared non-compliant and does not have to internalize the environmental damage into its private profit function. The FOC for profit maximization leads to:
\begin{equation*}
\max_{e}\pi(k,e,\bar{\beta})=ke-e^2\bar{\beta}^{-1}\Rightarrow\frac{\partial\pi}{\partial e}=k-2e\bar{\beta}^{-1}=0\Rightarrow e^*=k\bar{\beta}/2
\end{equation*}
Thus, the firm optimal private profit is $\pi_F^{NP}=k^2\bar{\beta}/4$, leading to a corresponding social welfare of $\pi_A^{NP}=k^2\bar{\beta}(1-\bar{\beta}^2)/4$. On the other hand, a non-compliant firm facing inspection is fined and has to internalize the pollution cost, not only when making the optimal emission decision but also decreasing its private profit that is left to be reinvested. The optimization problem becomes:
\begin{equation*}
\max_{e}\pi(k,e,\bar{\beta})=ke-e^2\bar{\beta}^{-1}-\bar{\beta} e^2
\end{equation*}
leading to $e^*=k\bar{\beta}(1+\bar{\beta}^2)^{-1}/2$, $\pi_F^{IP}=k^2\bar{\beta}(1+\bar{\beta}^2)^{-1}/4$ and $\pi_A^{IP}=k^2\bar{\beta}(1+\bar{\beta}^2)^{-1}/4-c$.
From the analysis above, while a compliant firm always voluntarily internalizes the pollution damage into its profit function whenever managers make optimal decisions about technology and emission level, non-compliant firms only do so when an auditor inspects its non-switchable production technology and imposes environmental compliance through the fine. The latter has the effect of adjusting the firm's pollution discharge to a lower emission level. While a non-compliant uninspected firm is better-off than any other firm with regard to private profit, i.e., $k^2\bar{\beta}/4>3k^2/16>k^2\bar{\beta}(1+\bar{\beta}^2)^{-1}/4$, a non-compliant inspected firm faces the lowest possible payoff. Despite employing the cheapest technology, getting punished and having to adjust the emission level using the worst technology leads to a too low optimal emission level, i.e.,  $k\bar{\beta}(1+\bar{\beta}^2)^{-1}/2<k/4<k\bar{\beta}/2;\ \forall\bar{\beta}>1$. On top of this, the firm's private profit is also decreased due to the additional cost to pay the fine.

The payoff matrix in (\ref{Matrix-I}) with possible private profits $\pi_F$ and social welfares $\pi_A$ then becomes:
\begin{equation}
\bordermatrix {&\text{Non-compliant (P)}&\text{Compliant (C)}\cr
	\text{Inspects (I)} &k^2\bar{\beta}(1+\bar{\beta}^2)^{-1}/4-c,\ k^2\bar{\beta}(1+\bar{\beta}^2)^{-1}/4& k^2/8-c,\ 3k^2/16 \cr
	\text{No Inspection (N)} &k^2\bar{\beta}(1-\bar{\beta}^2)/4,\ k^2\bar{\beta}/4& k^2/8,\ 3k^2/16\cr}
\label{Matrix-II}
\end{equation}
From (\ref{Matrix-II}), enforcement of environmental compliance is only feasible if $k^2\bar{\beta}(1+\bar{\beta}^2)^{-1}/4-c>k^2\bar{\beta}(1-\bar{\beta}^2)/4$, leading to a maximum inspection cost $c<\bar{c}=k^2\bar{\beta}^5(1+\bar{\beta}^2)^{-1}/4$. Above $\bar{c}$, not inspecting is a strictly dominant strategy for auditors, independently of the corporate culture the visited firm follows, and society falls into a pollution trap scenario in the long run where polluters always perform better than any compliant firm, thus driving the latter to extinction. Moreover, the largest social welfare $k^2/8$ is achieved whenever a compliant firm does not require any inspection effort. In contrast, the largest private profit that can be achieved $k^2\bar{\beta}/4$ is obtained when auditors fail to inspect a non-compliant firm. Hence, the game payoff matrix points out the conflict of interest between the policy maker and firms in the competitive market.

\subsection{Mean field approximation: solving the well-mixed population game}
\label{sec:game}
In this section, we start analysing the evolution of the states of both populations playing the game in (\ref{Matrix-II}) using replicator dynamics (RD). The latter is suitable when populations are well-mixed, i.e., any firm can be visited by any auditor. Moreover, RD assumes replication, i.e., any profit obtained by a compliant (resp. non-compliant) firm is completely reinvested in another compliant (resp. non-compliant) firm. Under RD only natural selection of strategies is taken into account and there is no mutation, i.e., a firm does not reinvest in another firm experimenting a different corporate culture. Assuming that at a given time step $p$ is the proportion of auditors that inspect firms and $q$ is the proportion of non-compliant firms, one can derive a system of nonlinear ordinary differential equations governing the evolution of both populations over time. Each equation of the RD system governs the change in the state of one population over time. For the case of our game, we have:
\begin{equation}
\frac{\partial p}{\partial t}=\dot{p}=p(1-p)(\pi_A^{I}-\pi_A^{N})\Rightarrow \dot{p}=p(1-p)\left(\frac{k^2\bar{\beta}^5}{4(1+\bar{\beta}^2)}q-c \right)
\label{RDp}
\end{equation}
\begin{equation}
\frac{\partial q}{\partial t}=\dot{q}=q(1-q)(\pi_F^{P}-\pi_F^{C})\Rightarrow \dot{q}=q(1-q)\left(\frac{k^2(4\bar{\beta}-3)}{16}-\frac{k^2\bar{\beta}^3}{4(1+\bar{\beta}^2)}p \right)
\label{RDq}
\end{equation}
where $\pi_A^{I}$ and $\pi_A^{N}$ (resp. $\pi_F^{P}$ and $\pi_F^{C}$) are respectively the expected social welfares when an auditor inspects and does not inspect a firm (resp. the expected private profits for a non-compliant and a compliant firm). The RD system in (\ref{RDp}-\ref{RDq}) does not have an evolutionary equilibrium (Hofbauer and Sigmund, 1998). It has a neutrally stable state $p^*=\bar{\beta}^{-3}(4\bar{\beta}-3)(1+\bar{\beta}^2)/4;\ q^*=4c(1+\bar{\beta}^2)k^{-2}\bar{\beta}^{-5}=c/\bar{c}$, corresponding to the only (mixed strategy) Nash equilibrium of the stage-game in (\ref{Matrix-II}), about which the states of both populations oscillate over time indefinitely. Such evolutionary pattern is similar to that found in Anastasopoulos and Anastasopoulos (2012).

In Figure \ref{fig:1} we present a numerical simulation for $k=1$, $\bar{\beta}=2$, $c=0.30\bar{c}=0.48$ and initial conditions in which only 35\% of the firms are compliant and only 35\% of the auditors are committed to inspect firms, $p_0=0.35\wedge q_0=0.65$. It can be seen that compliance and inspection keep oscillating in both populations without achieving an equilibrium. The initial proportion of two-thirds of the firms being non-compliant induces a sharp rise in the proportion of inspecting auditors over time. The increase in the likelihood of being inspected favours the increase of compliance among firms. When the proportion of non-compliant firms has decreased sharply, close to 5\% of the population of firms, auditors become more lenient and the likelihood of inspecting falls down to 10\%. The cycle then restarts.
\begin{figure}[htp]
	\centering
	\begin{tabular}{cc}
		\epsfig{file=Fig01,height=5cm,width=5cm,angle=0}&
		\epsfig{file=Fig01b,height=5cm,width=8cm,angle=0}
	\end{tabular}
	\vspace{.5cm}
	\caption{(color online) Phase diagram and time evolution for parameters: $k=1$, $\bar{\beta}=2$, $c=0.30\bar{c}$ and initial conditions $(p_0=0.35,q_0=0.65)$.}
	\label{fig:1}
\end{figure}

Regarding the neutrally stable state $(p^*,q^*)$, it represents the average behaviour of the populations over a long interval of time (Cressman et al., 1998). Given that $\lim_{\bar{\beta}\rightarrow 1} p^*=0.5$, one can see that there is a bias towards inspection, i.e., on average the majority of the auditors inspects the firms they visit. Moreover, from (\ref{Matrix-II}), the expected profit of a non-compliant firm is given by $\pi_F^{P}=\frac{k^2\bar{\beta}}{4(1+\bar{\beta}^2)}\left[ 1+(1-p)\bar{\beta}^2\right] $, thus $\frac{\partial\pi_F^{P}}{\partial p}=-\frac{k^2\bar{\beta}^3}{4(1+\bar{\beta}^2)}<0$, i.e., given $\bar{\beta}\wedge k$, whenever the probability of inspection increases, the expected profit of non-compliant firms decreases. Consequently, given the expected profit of compliant firms $\pi_F^{C}=\frac{3k^2}{16}$ is unaffected by changes in $p$, the incentive to comply with the environmental regulation increases. On the side of the policy maker, the difference between the expected social welfare with and without inspection is given by $\pi_A^{I}-\pi_A^{N}=\frac{k^2\bar{\beta}^5}{4(1+\bar{\beta}^2)}q-c$. Thus, $\frac{\partial\left(\pi_A^{I}-\pi_A^{N} \right) }{\partial q}>0$ and $\frac{\partial\left(\pi_A^{I}-\pi_A^{N} \right) }{\partial c}<0$. Hence, given $\bar{\beta}\wedge k$, whenever non-compliance spreads in the population of firms, the incentive for inspection increases as well. On the other hand, larger costs of inspection induce a lower incentive to inspect firms. This analysis is valid $\forall\bar{\beta};\ \forall k$.

One drawback of employing RD to model the evolution of both populations over time is that, by assuming well-mixed populations, RD does not take into account the geographical location of firms and auditors. It is equivalent to a network where all agents are neighbours of each other. In the next section, we overcome this issue by assuming that both populations are spatially located in an $L\times L$ square grid with periodic boundary conditions. In such setup, firms and auditors only interact with their local geographic neighbours.

\section{Spatial Game}
\label{sec:spatial}
In order to increase realism, we extend the game in Section \ref{sec:model} assuming individuals in both populations keep playing the same stage-game in (\ref{Matrix-II}) but now each player has a specific geographical location. While it seems obvious to account for firms' spatial location, it is also reasonable to make the same assumption with regard to auditors. Generally, public servants are allocated to work in a particular region of the country or state and they are in charge of inspections in the neighbourhood of the area where they work.

The extended game model considers a regular square grid of size $L\times L$, with periodic boundary conditions, thus a planar representation of a torus. We assumed each population with $L^2=10,000$ individuals such that there is no noise due to small population effects. Each location of the grid is occupied by two players, one auditor and one firm, and each player has a von-Neumann (vNM) neighbourhood with four neighbours. At the beginning of each simulation, each firm in the grid is randomly allocated either strategy $C$ or $P$ according to some pre-defined initial condition $q_0$. Regarding the population of auditors, we assumed the government selects a particular region of the country to start a pilot task force to try to promote inspection within the entire population of auditors. We focused on countries starting from a pollution trap scenario in which $p_0=0.05\wedge q_0=0.95$. Thus, at the initial conditions, all auditors are allocated strategy $N$, except in a strip representing a compact spatial cluster composed of $p_0 L$ auditors playing $I$.

Once the allocation is carried out, every individual $i$ in both populations plays the game against all individuals in the opponent population allocated in his vNM neighbourhood plus the opponent allocated at the same location he occupies. The sum of the payoffs obtained in each contest is computed, $\Pi_i=\sum_{i=1}^{n=5}\pi_i$, and a random neighbour $j$ from the same population is chosen to compare payoffs. If $\Pi_i>\Pi_j$, player $i$ keeps his strategy, otherwise his strategy is updated with probability $(\Pi_j-\Pi_i)/\left[ 5(\max\pi_i-\min\pi_i)\right] $, where $\max\pi_i$ (resp. $\min\pi_i$) is the maximum (resp. minimum) attainable payoff player $i$ can get in the stage-game payoff matrix. After all individuals have had the chance to update their strategies, the MCS ends and both populations are updated synchronously.

We carried out numerical simulations keeping $k=1$ and $\bar{\beta}=2$ as in Section \ref{sec:model} and varied parameter $\xi=c/\bar{c}\in[0.05;0.99]$ given that, as seen in subsection \ref{sec:game}, the inspection cost plays an important role by decreasing the incentive to inspect and, consequently, decreasing the firms' long run average compliance behaviour. For all values of $\xi$, the stage-game still has one unique mixed-strategy Nash equilibrium, leading to the same cyclical evolutionary pattern found in subsection \ref{sec:game} when both populations are well-mixed. We found that, despite this fact, the numerical results displayed a quite rich dynamics in the spatial game. Moreover, in more than one case, a robust long-run equilibrium is attainable in both populations.

We used $\xi=\left\lbrace 0.05;0.25;0.40;0.50;0.55;0.60;0.65;0.75;0.90;0.99\right\rbrace$. We ran a set of 50 simulations for each value of $\xi$, with each realization using a different seed. Each realization ran for 5,000 MCS, which was more than enough to ensure either convergence towards the long run equilibrium or to display a clear cyclical long run behaviour. The only exception was for $\xi=0.99$, which never displayed a cyclical behaviour but long run equilibrium required always a larger number of MCS to be achieved. Particular interest was given to the evolution of $p$ and $q$ over time, the snapshots of strategy distribution in the grid for both populations and the long run average state of each population when cyclical behaviour was displayed. Based on the numerical results, we formulate three propositions.\\

\textbf{Proposition 1:} For low to intermediate inspection cost, there is a long run robust evolutionary equilibrium in which the pollution trap scenario disappears. All auditors inspect firms and the latter comply with environmental regulations.

\textbf{Discussion:}
Using the case when $\xi=0.25$, a low cost of inspection, the corresponding payoff matrix in (\ref{Matrix-II}) becomes:
\begin{equation}
\bordermatrix {&\text{Non-compliant (P)}&\text{Compliant (C)}\cr
	\text{Inspects (I)} &-0.300,0.100& -0.275,0.1875 \cr
	\text{No Inspection (N)} &-1.500,0.500 & 0.125,0.1875\cr}
\end{equation}

with just one mixed-strategy Nash equilibrium. In the well-mixed population model, as shown in subsection \ref{sec:game}, this corresponds to a dynamics in which the state of each population would oscillate over time without achieving a long run equilibrium. In contrast to the well-mixed population game, for all simulations performed with $\xi\in\left[  0.05;0.55\right] $, non-compliant firms and no-inspecting auditors were led to extinction in the long run. In Figure \ref{fig:2} we present the $L\times L$ square lattice for a particular realization using $k=1$, $\bar{\beta}=2$, $\xi=0.25$ and initial conditions $p_0=0.05\wedge q_0=0.95$ (pollution trap). The figure displays the evolution of the strategy distribution in each population from Montecarlo step $T=1$ to $T=800$. In Figure \ref{fig:3} the evolution of both populations over time is displayed.
\begin{figure}[htp]
	\centering
	\begin{tabular}{cc}
		\epsfig{file=c025MCS1,height=3.95cm,width=8cm,angle=0}&
		\epsfig{file=c025MCS17,height=3.95cm,width=8cm,angle=0}\\
		\epsfig{file=c025MCS100,height=3.95cm,width=8cm,angle=0}&
		\epsfig{file=c025MCS150,height=3.95cm,width=8cm,angle=0}\\
		\epsfig{file=c025MCS500,height=3.95cm,width=8cm,angle=0}&
		\epsfig{file=c025MCS800,height=3.95cm,width=8cm,angle=0}
	\end{tabular}
	\caption{(color online) evolution of the state of each population for parameters: $k=1$, $\bar{\beta}=2$, $\xi=0.25$ and initial conditions $(p_0=0.05,q_0=0.95)$. In both populations, blue (resp. red) corresponds to strategy 1 (resp. 2). From top left to bottom right, square lattice at $T=1;17;100;150;500;800$.}
	\label{fig:2}
\end{figure}

At $T=1$, one can see the thin blue strip with $\approx p_0L=500$ inspecting auditors in population 1 and the red dots corresponding to the $\approx(1-q_0)L=500$ compliant firms geographically spread in population 2. Due to a state in which 95\% of firms are non-compliant in population 2, the best response for auditors is to inspect ($\pi_A^{IP}=-0.300>\pi_A^{NP}=-1.500$). But the vast majority of the non-inspecting auditors are neighbours to each other, hence, even if they perform worse than inspecting auditors in terms of payoff, they do not switch strategy. The exception to the latter occurs at the boundaries between both clusters of inspecting and non-inspecting auditors. At the boundaries, inspecting auditors perform better and non-inspecting auditors start to switch strategy. The cluster with inspecting auditors remains compact and starts to get larger ($T=17$), covering already more than half of the grid area by $T=100$, until non-inspecting auditors are driven out from population 1.

In contrast, in population 2, compliant firms have already disappeared by $T=17$, except in the region corresponding to the cluster of inspecting auditors in population 1 (Figure \ref{fig:3} shows that during the initial MCS non-compliance actually increases in population 2). In that region, compliant firms perform better ($\pi_F^{IP}=0.100<\pi_F^{IC}=0.1875$) and very small compact clusters of compliant firms start to form. As the cluster of inspecting auditors becomes larger in population 1, the clusters of compliant firms start to merge ($T=100$), becoming a single cluster that keeps growing ($T=150$) until driving all non-compliant firms out from population 2.

Although the evolutionary process seems straightforward, there is one key element for the success of this long run equilibrium ($p^*=1,q^*=0$): the speed at which the cluster of inspecting auditors spreads in population 1 is much faster than the spreading speed of the cluster of compliant firms in population 2. And this fact remains true until only inspecting auditors survive in population 1. By $T=150$, in the region of the square lattice corresponding to the cluster of compliant firms, the best response for auditors now is not to inspect. But in that region all auditors' neighbours do inspect so they are not able to revert their strategy back to no inspection. Given the cluster of inspecting auditors moves faster than the cluster of compliant firms, at the boundaries between clusters in population 1 the best response of inspecting remains true. And the same happens with the best response to comply in population 2 until the evolutionary equilibrium is achieved $\bullet$
\begin{figure}[htp]
	\centering
	\begin{tabular}{c}
		\epsfig{file=c025b,height=5cm,width=10cm,angle=0}
	\end{tabular}
	\caption{(color online) time evolution of the state of each population for $k=1$, $\bar{\beta}=2$, $\xi=0.25$ and $T=\left[ 0,800\right] $ MCS.}
	\label{fig:3}
\end{figure}

\textbf{Proposition 2:} For intermediate to high inspection cost, there is either a long run robust evolutionary equilibrium in which the pollution trap scenario disappears or an oscillatory long run behaviour after a transient period in which the shares of inspecting auditors and of compliant firms keep changing over time without reaching an equilibrium. Moreover, the likelihood of reaching an evolutionary equilibrium decreases with increasing cost of inspection. The long run average behaviour of each population does not match with that found in the well-mixed population evolutionary game, although the long run average values of $p$ and $q$ do follow the sensitivity analysis discussed in subsection \ref{sec:game}, i.e., $\frac{\partial\left(\pi_A^{I}-\pi_A^{N} \right) }{\partial c}<0\wedge\frac{\partial\pi_F^{P}}{\partial p}<0$: as the inspection cost increases, the likelihood of inspecting decreases, leading also to an increase in the share of non-compliant firms.

\textbf{Discussion:} The numerical simulations displayed possible oscillatory behaviour for $0.60\leq\xi\leq 0.90$. Out of 50 realizations performed with different seeds for each value of $\xi$, oscillatory long run behaviour was registered 4 ($\xi=0.60$), 3 ($\xi=0.65$), 31 ($\xi=0.75$) and 50 ($\xi=0.90$) times. Thus, as the cost of inspection increases, it reaches a boundary above which a long run equilibrium is not possible. In Figure \ref{fig:5} the evolution of both populations over time is displayed for the case $\xi=0.75$ showing the first 20,000 MCS and just the first 5,000 MCS as well. From the latter, it can be seen that after 500 MCS the non-oscillatory transient period is already over. Similar evolutionary patterns were found for $\xi=0.60$, $\xi=0.65$ and $\xi=0.90$.

In Figure \ref{fig:6} we present the evolution of the $L\times L$ square lattice for a particular realization when oscillation occurs, using $k=1$, $\bar{\beta}=2$, $\xi=0.75$ and initial conditions $p_0=0.05\wedge q_0=0.95$ (pollution trap), from Montecarlo step $T=1$ to $T=20,000$. When compared to a realization without oscillation, the main important difference is that, when the cluster of inspecting auditors starts to spread in population 1, the spreading speed is not as fast as the speed in realizations with lower costs of inspection (e.g.: compare the size of the blue strip in population 1 for $T=22$ in Figure \ref{fig:6} with that for $T=17$ in Figure \ref{fig:2}). This happens because, although the best response for auditors is still to inspect, the difference in profits now is smaller. Then, when inspecting auditors compare their payoffs with non-inspecting auditors in their neighbourhood, although the former tend to perform better, the strategy switching process is probabilistically increasing in the payoff difference. Hence, the switching process now becomes slower than when the inspection cost was lower. With the clusters of compliant firms starting to grow in population 2, non-inspecting auditors at the boundary between clusters are now able to re-invade that region and create a small compact cluster (see $T=100$). Once this happens, convergence to an evolutionary equilibrium with one strategy being driven to extinction is each population is doomed. Clusters of different strategies keep moving around the square lattice in both populations due to invasion and re-invasion with the state of both populations oscillating over time.

In order to understand the long run average behaviour of each population, simulations with 50,000 MCS were carried out for each value of $\xi$ and we computed the average state of each population after 3,000 MCS, updating the computation step after step until 50,000 MCS, in order to guarantee the transient period was over and had no effect on the computed average states. In Figure \ref{fig:4} the long run average shares of inspecting auditors in population 1 and of non-compliant firms in population 2 are displayed. Clearly, as the cost of inspection increases, the long run proportion of inspecting auditors decreases and the proportion of non-compliant firms increases. In order to ensure that 50,000 MCS were more than enough to capture the long run average behaviour of each population, we repeated the same procedure but with 500,000 MCS for the case with $\xi=0.60$. Results are displayed in Figure \ref{fig:8} and one can see a very good level of agreement between averaged values of both $p$ and $q$ when compared to those in Figure \ref{fig:4} using only 50,000 MCS $\bullet$\\

\textbf{Proposition 3:} When the inspection cost approaches $\bar{c}$, the oscillatory evolutionary pattern ceases to occur and is replaced by a different long run evolutionary equilibrium in which $p^*=1$ and $q^*=1$, i.e., a country where all auditors carry out a very costly and ineffective inspection process that does not lead to corporate environmental compliance. Moreover, the few compliant firms that were located in the country are driven to extinction.

\textbf{Discussion:} As in Propositions 1 and 2, the inspecting cluster in the population of auditors starts to grow but now the growth speed is so slow that in population 2 the cluster of compliant firms in the same region grows at a similar speed. Consequently, non-inspecting auditors are able to re-invade the small strip to an extent that the growth of compliant firms slows down and becomes negative until all compliant firms disappear from the population. Once this happens, the cluster with inspecting auditors starts to increase again at a very slow speed until taking over population 1, but without any impact on compliance given all compliant firms were driven out of the country. The evolution of the state of both populations is displayed in the left panel of Figure \ref{fig:7} $\bullet$\\

Increasing $c$ further, $c>\bar{c}$ and the stage game in (\ref{Matrix-II}) has one unique Nash equilibrium in pure strategies $p^*=0$ and $q^*=1$, i.e., a pollution trap. Within this range of values in which $\xi>1$, the numerical simulations showed that the only evolutionary equilibrium in both the well-mixed population and the spatial game do match the classic game Nash equilibrium. The right panel in Figure \ref{fig:7} shows the evolution of both populations for the case $\xi=1.02$.
\begin{figure}[htp]
	\centering
	\begin{tabular}{cc}
		\epsfig{file=c75plot01II,height=4.25cm,width=7.75cm,angle=0}&
		\epsfig{file=c75plot02II,height=4.25cm,width=7.75cm,angle=0}
	\end{tabular}
	\caption{(color online) time evolution of the state of each population for $k=1$, $\bar{\beta}=2$, $\xi=0.75$ and $(p_0=0.05,q_0=0.95)$.}
	\label{fig:5}
\end{figure}
\begin{figure}[htp]
	\centering
	\begin{tabular}{cc}
		\epsfig{file=c075MCS1II,height=3.6cm,width=8cm,angle=0}&
		\epsfig{file=c075MCS8II,height=3.6cm,width=8cm,angle=0}\\
		\epsfig{file=c075MCS22II,height=3.6cm,width=8cm,angle=0}&
		\epsfig{file=c075MCS100II,height=3.6cm,width=8cm,angle=0}\\
		\epsfig{file=c075MCS200II,height=3.6cm,width=8cm,angle=0}&
		\epsfig{file=c075MCS500II,height=3.6cm,width=8cm,angle=0}\\
		\epsfig{file=c075MCS8000II,height=3.6cm,width=8cm,angle=0}&
		\epsfig{file=c075MCS20000II,height=3.6cm,width=8cm,angle=0}
	\end{tabular}
	\caption{(color online) evolution of the state of each population for parameters: $k=1$, $\bar{\beta}=2$, $\xi=0.75$ and initial conditions $(p_0=0.05,q_0=0.95)$. In both populations, blue (resp. red) corresponds to strategy 1 (resp. 2). From top left to bottom right, square lattice at $T=1;8;22;100;200;500;8,000;20,000$.}
	\label{fig:6}
\end{figure}
\begin{figure}[H]
	\centering
	\begin{tabular}{cccc}
		\epsfig{file=c60plot03N50000,height=3.7cm,width=7.75cm,angle=0}&
		\epsfig{file=c60plot04N50000,height=3.7cm,width=7.75cm,angle=0}\\
		\epsfig{file=c65plot03N50000,height=3.7cm,width=7.75cm,angle=0}&
		\epsfig{file=c65plot04N50000,height=3.7cm,width=7.75cm,angle=0}\\
		\epsfig{file=c75plot03N50000,height=3.7cm,width=7.75cm,angle=0}&
		\epsfig{file=c75plot04n50000,height=3.7cm,width=7.75cm,angle=0}\\
		\epsfig{file=c90plot03N50000,height=3.7cm,width=7.75cm,angle=0}&
		\epsfig{file=c90plot04N50000,height=3.7cm,width=7.75cm,angle=0}
	\end{tabular}
	\caption{(color online) long run average state of each population for $k=1$, $\bar{\beta}=2$ and $(p_0=0.05,q_0=0.95)$ for MCS from $T=3,000$ to $T=50,000$. From top to bottom, $\xi=0.60$; $\xi=0.65$; $\xi=0.75$; $\xi=0.90$.}
	\label{fig:4}
\end{figure}
\begin{figure}[H]
	\centering
	\begin{tabular}{cccc}
		\epsfig{file=c60plot03N500000,height=3.5cm,width=7.75cm,angle=0}&
		\epsfig{file=c60plot04N500000,height=3.5cm,width=7.75cm,angle=0}\\
	\end{tabular}
	\caption{(color online) long run average state of each population for $k=1$, $\bar{\beta}=2$, $\xi=0.60$ and $(p_0=0.05,q_0=0.95)$ for MCS from $T=3,000$ to $T=500,000$.}
	\label{fig:8}
\end{figure}
\begin{figure}[H]
	\centering
	\begin{tabular}{cc}
		\epsfig{file=c99plot02,height=3.5cm,width=7.75cm,angle=0}&
		\epsfig{file=c102plot02,height=3.5cm,width=7.75cm,angle=0}
	\end{tabular}
	\caption{(color online) time evolution of the state of each population for $k=1$, $\bar{\beta}=2$, $(p_0=0.05,q_0=0.95)$, $\xi=0.99$ (left panel) and $\xi=1.02$ (right panel).}
	\label{fig:7}
\end{figure}

Based on the long run behaviour of population 2 displayed in Figures \ref{fig:4}-\ref{fig:7}, except for the case when $\xi\rightarrow 1$, the spatial grid favoured environmental compliance given that results showed a long run average value of $q$ below the one found in the mean-field approximation, i.e., for $\xi\in\left[0.05;0.90 \right]$, $\bar{q}_{\text{SPATIAL}}<\bar{q}_{\text{MEAN-FIELD}}\equiv\xi$.

\section{Conclusion}
\label{sec:conclusion}
We studied the interplay between corporate environmental compliance and policy regulation in a context of a competitive market where enforcement requires costly inspections and there is a trade-off between maximizing social welfare and maximizing private profits. Firms are better off whenever they are non-compliant with environmental regulations and they do not suffer any form of inspection. On the other hand, social welfare is maximized whenever the policy maker does not need to enforce inspection and firms have a corporate culture of internalizing the negative externality due to pollution when making their production decisions. Such decisions take into account both the type of production technology they use as well as the level of emission. We assumed a society in a pollution trap scenario, i.e., a scenario in which the vast majority of firms are not environmental friendly and auditors have a culture of not inspecting firms.

An evolutionary game was used to model such trade-off involving the conflict of interests between firms and the policy maker. All players were bounded rational such that, despite being able to compute, maximize and compare profits given their decision variables, they were not sure which strategy was the best in the long run. We started with a benchmark model assuming that populations were well-mixed, i.e., firms were neighbours to each other and could also be inspected by any randomly designated auditor. This approach was in line with previous evolutionary game models found in the literature such as in Anastasopoulos and Anastasopoulos (2012), Cressman et al. (1998) and Xiao and Yu (2006), among others. Using replicator dynamics to model the game, results did not find a long run evolutionary equilibrium. Instead, there was an oscillatory evolutionary pattern in which the state of each population kept changing over time, similar to the pattern found in the Lotka-Volterra model.

We then extended the benchmark model by assuming the two populations were allocated in a square grid, with each location being shared by a firm and an auditor. This is more in line with the real world where firms are geographically spread and auditors tend to work close to where they live. The extended model displayed a quite rich dynamics in which not only cyclical evolution was still possible but robust evolutionary equilibria could exist, depending on the cost of inspection. When the latter was very close to the maximum cost of inspection, the extended model showed that there is no advantage in the auditing process. The latter not only is not able to remove society from the pollution trap scenario, but it also leads the very few compliant firms located in the country to extinction.

Further research could take into account the impact of different degrees of environmental compliance across countries as well as the impact of internationalization on the corporate culture of firms. This could be modelled using a multilayer network as described in da Silva Rocha (2017). An initial idea could consider a two-layer network in which each layer would be an $L\times L$ square lattice with periodic boundary conditions. Each layer would correspond to a different country and each corresponding site of both layers would have an international subsidiary of each firm. Layers would be physically disconnected and interdependence would be only via the payoffs earned by firms from playing the evolutionary game against auditors in each layer. Auditors would be part of two independent populations, one in each layer, whose states would differ depending on the degree of inspection commitment. As in our model, a country in a pollution trap scenario would correspond to a layer with a residual proportion of auditors playing the strategy Inspect. Strategies used by players in each layer would be updated independently by comparing each player's payoff with that of a randomly chosen neighbour located in the corresponding layer. The main difference when compared to our model would be the fact that in each layer firms would compute their payoffs as a weighted average of the payoffs earned by each subsidiary (see Wang et al. 2012). A firm $X$ would compute the overall private profit of its subsidiary located in layer $x$ as $\Pi_x =\alpha\pi_x +(1-\alpha)\pi_x^{'}$, where $\pi_x$ (resp. $\pi_x^{'}$) would be the local profit earned by its subsidiary playing the game in layer $x$ (resp. $x^{'}$). Similarly, for its subsidiary located in layer $x^{'}$, the overall private profit would be $\Pi_x^{'} =(1-\alpha)\pi_x^{'}+\alpha\pi_x$. Parameter $\alpha\in[0,1]$ would measure the bias in the consideration of payoffs collected in the two layers, where the bias could favour, for example, the country with the most important consumer market.

\section*{Acknowledgements}
This work is supported by ``Programa de Incentivo \`a Produtividade em Ensino
e Pesquisa'' from PUC-Rio.

redpajama_set_name: RedPajamaArXiv


text:
Q: Wrap text around pseudocode I use algorithm/algorithmic packages to write some pseudocode. The width of the box spans across the entire page and I was wondering if there is any way to constrain it (since the actual code doesn't exceed the mid of the page). Practically, I want to wrap text around my pseudocode.
ps: I tried wrapfig package, but I had some problems. Would be also helpful if anyone could verify whether this approach works.
Any ideas ?

A: You can achieve the same result using algorithm2e package and without minipage.
\documentclass{article}
\usepackage{wrapfig}
\usepackage{lipsum}
\usepackage[ruled]{algorithm2e}
\begin{document}
  \lipsum[1]
  \begin{wrapfigure}[6]{L}{0.5\textwidth} %<-- Wrapfigure covers 6 lines
      \begin{algorithm}[H]                %<-- Remove float environment
        \SetCustomAlgoRuledWidth{0.45\textwidth}  %<-- For aesthetics
        \caption{assignment algorithm}
           i $\leftarrow$ j
      \end{algorithm}
  \end{wrapfigure}
  \lipsum
\end{document}

A: You can put the algorithm inside of a minipage, put that inside of the wrapfigure, and it should work like a charm.
\documentclass{article}
\usepackage{algorithmic}
\usepackage{algorithm}
\usepackage{wrapfig}
\usepackage{lipsum}
\begin{document}
  \lipsum[1]
  \begin{wrapfigure}{L}{0.5\textwidth}
    \begin{minipage}{0.5\textwidth}
      \begin{algorithm}[H]
        \caption{assignment algorithm}
        \begin{algorithmic}
          \STATE i $\leftarrow$ j
        \end{algorithmic}
      \end{algorithm}
    \end{minipage}
  \end{wrapfigure}
  \lipsum
\end{document}

And the result:

You might want to tweak the alignment modifier on the minipage to get vertical alignment to work out a little better. Alternatively, you can play with the optionial lineheight of wrapfigure.

redpajama_set_name: RedPajamaStackExchange


text:
New York Style vs. Chicago Style – What's the difference?
April 3, 2013	In	Blog
The debate over which pizza style reigns supreme – Chicago or New York – has waged for years, with each city passionately supporting their signature slice. The classic thick crust of a Chicago pie and the traditional thin crust on a New York pizza have divided lovers of gourmet pizza for decades, but their regional characteristics go beyond mere crust thickness. Here's a closer look at some of the elements that make each style unique:
Crust Depth: Chicago style crust is not just thicker, but also deeper. Since the dough is pressed into a pie dish before being filled, the average Chicago slice ranges from one to three inches. New York style dough is pulled and baked very thin and flat.
Toppings: Chicago pies are layered heavily, and in the opposite direction of a New Yorker: cheese on the bottom, then toppings, then sauce. NY slices allow for a thin scattering of ingredients that rest on top of the sauce and cheese.
Handling: Whether enjoyed on the street or as gourmet pizza delivery, New York style pizza is convenient: the large, triangular slices can be folded over and eaten with your hands just about anywhere. Chicago style pizza is more like a casserole and requires a plate, fork, and knife.
Oiliness: Chicago pies are often drier than their New York counterparts, which are known for their oil-dripping greasiness.
Because they are so distinct and unique, lovers of gourmet pizza delivery say it is impossible to even compare Chicago and New York pies: their distinct constructions and endless variations make it so they rarely even taste similar. Personal preference also comes into play: some people just don't like eating their pie with a fork and knife. But the argument continues and the 'winner' tends to unsurprisingly go to the city in which a person lives. On a national scale, thin crust is definitely more popular- including some of the best pizza in Phoenix- but it's possible that's just because it's more familiar.
At Sardella's Pizza and Wings, we have crust options for every possible preference: choose from our original hand-tossed, thin crust New York style, Sicilian thick crust, even wheat crust. And if you're looking for gluten-free options, we have some of the best pizza in Phoenix for people on gluten free diets. Whether you're looking for pizza specials in Peoria or the fastest pizza delivery in Phoenix, Sardella's has it- whatever your style. To experience our true gourmet pizza delivery order online today.


Major chunk of the revenue attributes to the excellent sales-figure of the latest Galaxy S9 flagships.
Kudos to its stellar flagship devices of the past year and the latest Galaxy S9's, Samsung has registered a record earnings in Q1 2018. The South-Korean giant has just recently published the earning details for the first quarter of this year. On which, Samsung's mobile division registered 28.45 trillion won or $26.3 billion in revenue this past quarter compared to 23.5 trillion won or $21.8 billion in Q1 2017.
In terms of operating profit, the firm bagged 3.77 trillion won or $3.5 billion compared to 2.07 trillion won or $1.9 billion in the same time period last year. Samsung acknowledges that the increased sales of its flagship devices especially the Galaxy S9 had paved the way for registering such a record first-quarter revenue. Also, the not-so-quickly diminishing demand for the yesteryear's Galaxy S8 and S8+ too helped in achieving good number.
However, coming to the full Samsung Q1 2018 earnings that had been posted yesterday. Samsung's operating profit hiked 58.03 percent to 15.64 trillion won or $14.49 billion in the first quarter of this year. It has posted 11.7 trillion won or $10.8 billion in net profit which is a 52 percent increase from Q1 2017. Sales elevated nearly 20 percent year-over-year to hit 60.5 trillion won or just over $56 billion. And, as usual the Semi-Conductor industry have been the real cash-cow for the South-Korean conglomerate.
In a nutshell, the Q1 2018 earnings of Samsung have really beaten the market expectations. However, it's to be seen how the firm can keep up the same momentum for the second quarter as well.