prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is Professor Tulis's forthcoming book?

Read the following text and answer briefly.

Context 1: UT College of Liberal Arts: College of Liberal Arts University of Texas at Austin Departments Graduate Resources Undergraduate Resources Courses Online Courses Dean's Office Alumni & Giving Faculty by Department Search the College of Liberal Arts
next profile Jeffrey Tulis Associate Professor — Ph D ,
E-mail: tulis@austin utexas edu
Office: MEZ 3 152
Political Theory and American Politics
Professor Tulis's interests bridge the fields of political theory and American politics, including more specifically, American political development, constitutional theory, political philosophy and the American presidency  His publications include The Presidency in the Constitutional Order (LSU, 1981; Transaction, 2010), The Rhetorical Presidency (Princeton, 1987), The Constitutional Presidency (Johns Hopkins 2009), The Limits of Constitutional Democracy (Princeton, 2010) and recent journal articles and chapters on constitutional interpretation, the logic of political change, and the meaning of political success  Four collections of essays on The Rhetorical Presidency with responses by Tulis have been published, including a special double issue of Critical Review: An Interdisciplinary Journal of Politics and Society, (2007), where his book is described as "one of the two or three most important and perceptive works written by a political scientist in the twentieth century "
He has served as President of the Politics and History Section of the American Political Science Association  He received the President's Associates Teaching Excellence Award at the University of Texas  He has held research fellowships from NEH, ACLS, Olin Foundation, Harvard Law School, and the Mellon Preceptorship at Princeton University, where he taught before moving to Texas  He has held visiting positions at Notre Dame and Harvard  He has served as associate chair of the Department of Government from 1989-2001 and was acting chair during 1992-93  and for part of each year between 1989 and 2001  During the academic year 2008-09, he was a Laurance S  Rockefeller Visiting Fellow at the University Center for Human Values at Princeton  During Spring 2016, he was a Dahrendorf Visiting Fellow at the London School of Economics and Political Science 
His forthcoming books include: Legacies of Losing in American Politics, with Nicole Mellow (University of Chicago Press, Fall 2017), and an expanded edition of The Rhetorical Presidency in the Princeton Classics series (Princeton, Fall 2017)  For two decades he served as co-editor of the Johns Hopkins Series in Constitutional Thought, and he currently co-edits (with Sanford Levinson) Constitutional Thinking, a Series at the University Press of Kansas 
GOV 370L • Pres In Constitutional Ord 38840 • Spring 2017 Meets MW 2:30PM-4:00PM CAL 221 show description
GOV 370 Seminar: The Presidency in the Constitutional Order
Spring 2017 Unique # 38840
MW 2:30 to 4pm GDC 2 402
Jeffrey K  Tulis
In this Seminar we will discuss a series of constitutional problems including: the problem of executive energy in the American Constitution; presidential selection and the problem of political legitimacy; separation of powers; delegation of powers, the constitutional status of war and foreign affairs, administration and bureaucracy and the meaning of leadership in the constitutional order 
Seminar will meet twice a week and regular attendance and thorough preparation for discussion is expected  Unexcused absence from more than three classes will result in failure of the participation component of the course  There will also be pop quizzes on the reading that will count as part of your participation grade  In addition to class participation, course requirements include four short analytic essays, and one in-class test  The course grade will be calculated as follows:
Seminar participation: 20%
In-class test: 20%
Three analytic essays 60% (20% each)
Class participation is especially important  Preparation for seminar and for your in-class test will be enhanced by careful note taking on the readings  If students appear to be unprepared, pop quizzes will be given and the grades on them will affect the participation component of your course grade 
Texts: (tentative)
Joseph M  Bessette and Jeffrey K  Tulis, The Constitutional Presidency
Michael Nelson, The Presidency in the Political System (tenth edition)
Richard Ellis and Michael Nelson, Debating the Presidency (third edition)
The Federalist (any edition, or online) GOV 310L • American Government-Honors 38335 • Fall 2016 Meets TTH 3:30PM-5:00PM BEN 1 106 show description
GOV 310 (Honors) (38335) Fall 2016
TTH 3:30-5:00pm, BEN 1 106
This honors seminar offers an introduction to American politics that emphasizes the confluence of ideas, mores, institutions, and interests, in the constitutional system  This course covers more theory, and the readings are more demanding, than other versions of GOV 310  One of the main objectives of the course is to deepen your understanding of the practical aspects of contemporary public affairs by developing your ability to understand the theoretical foundations of American politics  Although we cover the nuts and bolts of politics there is much more theory in this version of GOV 310  If you have registered for this section mainly because 310 is a legislative requirement that you need to fulfill, this is not the right version for you  There is a substantial workload in this class 
Regular attendance, thorough and timely preparation, and active participation are all necessary to do well 
Four essays (approximately 1000 words each)  Three of these will be assigned analytic essay topics  The last will be a book review of a title chosen by the student from a long list of provided possibilities  (15% each essay, 60% of total course grade)
Two in-class tests  These will count 15% each, 30% of total course grade 
Class participation  (10% of course grade)  Both informed participation and occasional leadership of the seminar will be graded 
No make-up exams or late papers, except for documented medical or other emergencies 
Mark Landy and Sidney M  Milkis, American Government: Enduring Principles, Critical Choices, Third Edition
Mary Nichols and David Nichols, Readings in American Government, Ninth Edition
Thomas Mann and Norman Ornstein, Its Even Worse Than It Looks: How the American Constitutional System Collided With the New Politics of Extremism
Bruce Ackerman,Before the Next Attack: Preserving Civil Liberties in an Age of Terrorism GOV 381L • Constitutional Conflict 38660 • Fall 2016 Meets W 3:30PM-6:30PM BAT 5 102 show description
GOV 381L Fall 2016
Constitutional Conflict
W 3:30-6:30pm, BAT 5 102
Many of the most important debates regarding the nature and character of contemporary American politics are essentially arguments regarding the structure of separation of powers  In this seminar we will consider such questions as whether the American system is prone to deadlock of stalemate in the construction of national policy; whether conflict is a hindrance to institutional responsibility or an essential attribute of responsibility; whether there are “political questions” especially suitable to resolution between President and Congress; how one can distinguish salutary from pathological conflict, and whether it is truly possible to harness the ambition of office holders to the duties of their office 
More specifically, we will review literature and arguments regarding constitutional reform; divided government; separation of powers theory; and case studies of Supreme Court appointments; the budget process; and war powers and foreign affairs  In these contexts we will also discuss current controversies surrounding war authorization, intelligence and secrecy, sequestration, government shut downs and budget resolutions, and debt ceiling politics 
The course is designed to accommodate two different student needs: it will provide a good overview of important literature relevant to the comprehensive examination in American politics and it will provide opportunities for research  This subject area is a treasure trove of “hot” topics, publication possibilities, subjects for MA theses and Ph D  dissertations  I will tailor the written requirements to the objectives of individual students 
1  All students will prepare a short analytic essay early in the semester, and an annotated bibliography at mid-semester  These assignments will count (30%) of the grade 
2  Students interested primarily in exam preparation will complete an examination near the end of the semester based on study questions assigned in advance  OR
Students interested in research will write a 20-25 page paper  (60%)
3  A basic requirement of the course is that students prepare for each seminar by carefully reading the material assigned for that week  Class discussion is an essential component of the course  (10%)
Tentative Texts:
Jones, Separate But Equal Branches
Silverstein, Imbalance of Powers
Wilson & Schram, Separation of Powers and Good Government
Burgess, Contest for Constitutional Authority
Farrier, Passing the Buck: Congress, the Budget and Deficits
Weissman, A Culture of Deference
Zeisberg, War Powers: The Politics of Constitutional Authority
Fisher, Congressional Abdication on War and Spending
Lowi, The End of Liberalism GOV 379S • Regime Persp Amer Poltc-Honors 38105 • Spring 2016 Meets TH 3:30PM-6:30PM GAR 1 134 (also listed as CTI 335, LAH 350) show description
GOV 379S Regime Perspectives on American Politics
This is a seminar on American politics and culture  Two purposes govern the selection of texts for the course and guide our discussion of them  All of our texts attempt to look at American politics as a whole  Most books and courses on America look at only a part, such as the Presidency, or elections, or popular culture  Here we attempt to think about how the parts of America fit together  Even when these texts speak about a part, for example an institution such as the presidency or the Congress, they present the topic from a vantage point on the whole polity  To see the polity as a whole also means that we will have to revisit and rethink aspects of our political life that we take for granted – that we don’t examine because those parts have become so natural or familiar to us  Seeing the polity whole enables us to render the familiar unfamiliar, to make what we take for granted strange and new 
To see the polity as a whole requires that we get some distance from our subject, much as to see the planet earth as a whole requires one to look at it from outer space  Just as it is difficult to get visual perspective on a place living within it, it is difficult to understand the promise or pathologies of a regime from within  To get critical distance from our politics, we will closely study three sets of texts that look at American politics from a distance  The first part of the course will recover the perspective of the founding debate between Federalists and Anti-federalists  This fundamental debate reveals what is a stake in the basic architecture of the American regime  The second part of the course is a close study of Tocqueville’s Democracy in America  Regarded by many as the best book ever written on democracy and the best book written on America, Tocqueville sees our polity whole because he looks at it from the vantage point of Europe, in general, and France, in particular  In the third part of the seminar we think about American politics from the perspective of thoughtful commentators who feel only nominally included in the polity  Half in and half out, these extraordinary black American writers reveal fissures and fault lines in the American regime  We end the class with a discussion of America’s place in the world today – examining a speech by a writer who articulately raises challenges to our self-understanding that are inarticulately expressed today in rage and ranting from enemies of the United States 
Three take home analytic essays, chosen from a list of topics I provide, each weighted 25% of the course grade  Late essays will not be accepted, except with a doctor’s excuse or a Dean’s excuse for family emergency 
OR as an option: you may write the two short essays (both together weighted 25%) and do a longer 15 page paper on a topic of your choice in consultation with me (weighted 50% of your course grade)  Government honors students who are thinking of doing an honors thesis next year may prefer this option to begin to develop research and writing skills for longer work  Students who prefer this option will need to designate their preferred third short essay and have discussed with me a topic for their long paper by March 30  Texts:
Selected Anti-Federalist writings
Tocqueville, Democracy in America
Essays, speeches and articles by Frederick Douglass, W E B  Dubois, Booker T  Washington, James Baldwin and Ralph Ellison GOV 382M • Democratic Theory 38120 • Spring 2016 Meets M 3:30PM-6:30PM BAT 1 104 show description
GOV 382M (38120)
Democratic Theory Spring 2016
This is a graduate seminar on contemporary topics in democratic theory  Topics to be covered include: democratic epistemology; deliberative democracy; the meaning of the people; oracular democracy; agonistic democracy; and possibly new theories of republicanism, representation and partisanship 
Texts (tentative)
Helene Landemore, Democratic Reason
Jeffrey Edward Green, The Eyes of the People
Amy Gutmann and Dennis Thompson, Why Deliberative Democracy?
Alan Keenan, Democracy in Question
Jason Frank, Constituent Moments
Jason Frank, Publius and Political Imagination
Nadia Urbanati, Democracy Disfigured
Russell Muirhead, Partisanship in a Polarized Age
Bryan Garsten, manuscript
Active seminar participation; an annotated bibliography or review essay; a research/analytic paper  GOV 310L • American Government-Honors 37615 • Fall 2015 Meets TTH 2:00PM-3:30PM BEN 1 106 show description
TTH 2-3:30/BEN 1 106
Bruce Ackerman,Before the Next Attack: Preserving Civil Liberties in an Age of Terrorism GOV 370L • Presidency In Constitutl Order 37845 • Fall 2015 Meets TTH 5:00PM-6:30PM PAR 310 show description
GOV 370L (37845)
TTH 5-6:30 PAR 310
The Presidency in the Constitutional Order
A study of the place of the presidency in the American political order that stresses tension between power and accountability inherent in the office and the system  Topics include: separation of powers, presidential selection, impeachment, relations with Congress and bureaucracy, emergency powers, presidential character, and leadership 
This is a very demanding writing flag class  If you are enrolling in this class just in order to satisfy the writing flag, you are in the wrong class  Interest in political theory and willingness to work very hard are necessary for success in this class 
Joseph M  Bessette, The Constitutional Presidency
Andrew Rudalevige, The New Imperial Presidency
Bruce Ackerman, The Rise and Decline of the American Republic
Michael Nelson, ed , The Presidency in the Political System
Michael Nelson, ed , The Evolving Presidency
Louis Fisher, Constitutional Conflicts Between Congress and the President
Active and prepared class participation
Regular quizzes on the reading
Four analytic essays (approximately 1200 words) 
One term paper, (approximately 5000 words)  GOV 379S • Regime Persp On Amer Politics 38100 • Spring 2015 Meets T 3:30PM-6:30PM MEZ 1 104 (also listed as LAH 350) show description
Essays, speeches and articles by Frederick Douglass, W E B  Dubois, Booker T  Washington, James Baldwin and Ralph Ellison GOV 382M • Tocqueville 38135 • Spring 2015 Meets M 3:30PM-6:30PM BAT 5 102 show description
This graduate seminar will be devoted to close readings of two principal writings of Tocqueville: Democracy in America and The Ancien Regime and the Revolution  We will also assess some of the best secondary studies of Tocqueville, including work by Sheldon Wolin, Harvey Mansfield, Delba Winthrop, Jon Elster, Francois Furet, and a book by Pierre Manent 
Course requirements will include two very short analytic essays and one seminar paper (20-25 pages)  GOV 310L • American Government-Honors 38722 • Fall 2014 Meets TTH 2:00PM-3:30PM GAR 2 112 show description
Joseph M  Bessette and John J  Pitney, American Government and Politics: Deliberation, Democracy and Citizenship
Mary Nichols and David Nichols, Readings in American Government
Bruce Ackerman,Before the Next Attack: Preserving Civil Liberties in an Age of Terrorism GOV 370L • Presidency In Constitutl Order 38977 • Fall 2014 Meets TTH 9:30AM-11:00AM CBA 4 332 show description
A study of the place of the presidency in the American political order that stresses
tension between power and accountability inherent in the office and the system 
Topics include: separation of powers, presidential selection, impeachment,
relations with Congress and bureaucracy, emergency powers, presidential
character, and leadership 
This is a very demanding writing flag class  If you are enrolling in this class just in order
to satisfy the writing flag, you are in the wrong class  Interest in political theory and willingness
to work very hard are necessary for success in this class 
One term paper, (approximately 5000 words)  GOV 379S • Regime Persp On Amer Politics 39395 • Spring 2014 Meets T 3:30PM-6:30PM MEZ 1 104 (also listed as CTI 335, LAH 350) show description
Essays, speeches and articles by Frederick Douglass, W E B  Dubois, Booker T  Washington, James Baldwin and Ralph Ellison GOV 381L • Constitutional Conflict 39415 • Spring 2014 Meets M 3:30PM-6:30PM BAT 1 104 show description
Lowi, The End of Liberalism GOV 330K • The American President 39140 • Fall 2013 Meets MW 3:00PM-4:30PM MEZ B0 306 show description
This course offers an over view of the place of the presidency in the American political order  Topics covered include: constitutional design of the office; nominations and elections; legislative leadership; leadership of the bureaucracy; staffing and organizing the White House; the presidency and the judiciary; war and emergencies  We will spend extra time this fall on the presidential campaign and election of 2012 
Two in-class examinations (50% of the final grade)
One short (1000 word) take-home essay (30% of the final grade)
Class participation and quizzes (20% of the final grade)
Richard J  Ellis, The Development of the American Presidency (Routledge, 2012)
Richard J  Ellis and Michael Nelson, eds, Debating the American Presidency, (2nd edition, CQ Press, 2009)
Packet of selected primary texts (to be linked or posted on Blackboard)  GOV 330K • The American President 39145 • Fall 2013 Meets MW 5:00PM-6:30PM MEZ B0 306 show description
Packet of selected primary texts (to be linked or posted on Blackboard)  GOV 381L • American Founding 39040 • Spring 2013 Meets T 6:30PM-9:30PM BAT 1 104 show description
NOTE WELL: Course meets Tuesdays, 6:30 to 9:30pm
Batts Hall 1 104
This is a seminar on American political thought and constitutional design  It is designed for students of American politics and political theory  The principal themes include: 1) the nature of founding and its constitutive significance; 2) the relation of structure and power in American politics; 3) the meaning and significance of the Federalist/Anti-Federalist debate; 4) the philosophic background of the American founding; and 5) the relevance of the founding to debate to prospects for, and pathologies of, American politics today 
We will conduct a close reading of the Madison’s Notes, of The Federalist, and selected Anti-Federalist writings  We will also study a larger and growing body of secondary literature on the constitutional convention, ratification and early American political thought 
James Madison, Notes of the Debates: In the Federal Convention of 1787
The Federalist (Rossiter, ed )
The Anti-Federalist (Storing, ed )
David Brian Robertson, The Constitution and America’s Destiny (2005)
Pauline Maier, Ratification (2012)
Gordon Wood, The Idea of America (2011)
Jack Rakove, Original Meanings: Politics & Ideas in the Making of the Constitution
Herbert Storing, What the Anti-Federalists Were For (1981)
Numerous essays and articles (to be posted on line or gathered in packet)
Grading: Active seminar participation, including three short papers and presentations (40%) and one article-length seminar paper (60%) T C 357 • Amer Founding/Probs Const Des 43095 • Spring 2013 Meets M 3:30PM-6:30PM CRD 007B show description
The American Founding and Problems of Constitutional Design
Jeffrey Tulis, Associate Professor, Department of Government
Sanford Levinson, Professor, School of Law
This Plan II seminar will be built around a close reading of the debates that informed the drafting and ratification of the U S  Constitution  We aim to recover the perspective of these founding thinkers -- their way of thinking -- as much as their concrete ideas, in order to raise fundamental questions about the American political order today  Are some of the most important pathologies of American politics today rooted in design features of our original political architecture? Are the original answers to basic founding questions (such as "how democratic is our Constitution?) still adequate for contemporary circumstances? What features of the Constitution should we preserve and what features should we amend, if possible? Would it be good for the polity as a whole to reconsider these questions in a new constitutional convention today, or would such an event be a political nightmare? Our reading will include notes from the founding conventions, writings by Federalists and Anti-Federalists, and present-day critiques of the American political order  Our aim will be to generate a dialogue between the thought of the founders and some of the best present day critics and supporters of the Constitution 
James Madison, Notes of the Debates in the Federal Convention
The Federalist, ed  Clinton Rossiter
The Anti-Federalist, ed  Herbert Storing
Pauline Maier, Ratification: The People Debate the Constitution, 1787-1788
Sanford Levinson, Framed: America’s 51 Constitutions and the Crisis of Governance
Bruce Ackerman, The Decline and Fall of the American Republic
Robert Goldwin, ed  How Democratic is the Constitution?
a course packet of selected articles, essays, and additional primary materials 
Class participation, including at least one presentation of a short discussion paper 25%
One take-home analytic essay 25%
One term paper 50%
About the Professors:
Professor Tulis's interests bridge the fields of political theory and American politics, including more specifically, American political development, constitutional theory, political philosophy and the American presidency  He received the President's Associates Teaching Excellence Award at the University of Texas  He has held research fellowships from NEH, ACLS, Olin Foundation, Harvard Law School, and the Mellon Preceptorship at Princeton University, where he taught before moving to Texas  He has held visiting positions at Notre Dame and Harvard  During the academic year 2008-09, he was a Laurance S  Rockefeller Visiting Fellow at the University Center for Human Values at Princeton 
Proefessor Levinson holds the W  St  John Garwood and W  St  John Garwood, Jr  Centennial Chair in Law, he joined the University of Texas Law School in 1980  Previously a member of the Department of Politics at Princeton University, he is also a Professor in the Department of Government at the University of Texas  The author of over 350 articles and book reviews in professional and popular journals--and a regular contributor to the popular blog Balkinization  He received the Lifetime Achievement Award from the Law and Courts Section of the American Political Science Association in 2010  He has been a visiting faculty member of the Boston University, Georgetown, Harvard, New York University, and Yale law schools in the United States and has taught abroad in programs of law in London; Paris; Jerusalem; Auckland, New Zealand; and Melbourne, Australia 
GOV 330K • The American President 38675 • Fall 2012 Meets MW 3:00PM-4:30PM MEZ B0 306 show description
Packet of selected primary texts (to be linked or posted on Blackboard)  GOV 330K • The American President 38675 • Fall 2011 Meets MW 3:30PM-5:00PM WAG 420 show description
see syllabus GOV 330K • The American President 38680 • Fall 2011 Meets MW 5:30PM-7:00PM UTC 1 146 show description
see syllabus GOV 379S • Regime Persp On Amer Polit-Hon 39110 • Spring 2011 Meets W 3:30PM-6:30PM BAT 5 102 (also listed as CTI 326, LAH 350) show description
To see the polity as a whole requires that we get some distance from our subject, much as to see the planet earth as a whole requires one to look at it from outer space  Just as it is difficult to get visual perspective on a place living within it, it is difficult to understand the promise or pathologies of a regime from within it  To get critical distance from our politics, we will closely study three sets of texts that look at American politics from a distance  The first part of the course will recover the perspective of the founding debate between Federalists and Anti-federalists  This fundamental debate reveals what is a stake in the basic architecture of the American regime  The second part of the course is a close study of Tocqueville’s Democracy in America  Regarded by many as the best book ever written on democracy and the best book written on America, Tocqueville sees our polity whole because he looks at it from the vantage point of Europe, in general, and France, in particular  In the third part of the seminar we think about American politics from the perspective of thoughtful commentators who feel only nominally included in the polity  Half in and half out, these extraordinary black American writers reveal fissures and fault lines in the American regime  We end the class with a discussion of America’s place in the world today – examining a speech by a writer who articulately raises challenges to our self-understanding that are inarticulately expressed today in rage and ranting from enemies of the United States 
Four take home writing assignments  Analytic essays, each 1000-1500 words  (Grades weighted: 10%, 25%, 25%, and 25%) Late essays will not be accepted, except with a doctor’s excuse or a Dean’s excuse for family emergency  Regular preparation and class participation: 15% 
OR as an option: By prior arrangement with me by the due date of the second analytic essay, students may substitute one longer research paper (15 – 20 pages) for two of the last three analytic papers This paper will be on a topic of the students choosing , if I approve, and the due date will be the same as the last assigned analytic essay  This project would count 50% of the students course grade 
Selected writings by Frederick Douglass, W E B  Dubois, Ralph Ellison, James Baldwin
Solzhenitsyn, “A World Split Apart”
Tocqueville, Democracy in America GOV 382M • Tocqueville 39150 • Spring 2011 Meets T 6:30PM-9:30PM BAT 5 102 show description
See syllabus GOV 370L • President, Congress, And Court 38695 • Fall 2010 Meets TTH 8:00AM-9:30AM UTC 3 112 show description
Course Description: A Study of the political relationship of the President, Congress and Court in the American constitutional order  Has this relationship changed over the course of American history? Is American national politics prone to stalemate or deadlock between the branches regarding major issues of public policy? Do we have a new “imperial presidency?” Should the Court arbitrate disputes between the President and Congress over custody of their respective powers? Has Congress abdicated its constitutional responsibilities? We will examine questions like these in light of practical problems such as executive privilege and secrecy, the war on terror, budget politics and controversies regarding appointments to the Supreme Court  Grading:Three in class essay tests, for which study questions will be distributed in advance  The exam questions will be chosen from the list of study questions  (25% each) One short take home essay (10% each)  Class participation and attendance (15%)  Tentative Texts: The FederalistFisher, Congressional Abdication on War and SpendingRudalevige, The New Imperial PresidencyBessette and Tulis, The Constitutional PresidencySkowronek, Presidency in Political TimeGoldsmith, The Terror PresidencyA course packet of articles and essays GOV 370L • President, Congress, And Court 38700 • Fall 2010 Meets TTH 5:00PM-6:30PM UTC 3 122 show description
Course Description: A Study of the political relationship of the President, Congress and Court in the American constitutional order  Has this relationship changed over the course of American history? Is American national politics prone to stalemate or deadlock between the branches regarding major issues of public policy? Do we have a new “imperial presidency?” Should the Court arbitrate disputes between the President and Congress over custody of their respective powers? Has Congress abdicated its constitutional responsibilities? We will examine questions like these in light of practical problems such as executive privilege and secrecy, the war on terror, budget politics and controversies regarding appointments to the Supreme Court  Grading:Three in class essay tests, for which study questions will be distributed in advance  The exam questions will be chosen from the list of study questions  (25% each) One short take home essay (10% each)  Class participation and attendance (15%)  Tentative Texts: The FederalistFisher, Congressional Abdication on War and SpendingRudalevige, The New Imperial PresidencyBessette and Tulis, The Constitutional PresidencySkowronek, Presidency in Political TimeGoldsmith, The Terror PresidencyA course packet of articles and essays GOV 312L • Iss & Policies In Amer Gov-Hon 38698 • Spring 2010 Meets MW 3:30PM-5:00PM UTC 3 104 show description
Government 312L satisfies the second half of the mandated six hours of government that every UT student must take  Course covers analysis of varying topics concerned with American political institutions and policies, including the United States Constitution, and assumes basic knowledge of government from GOV 310L, which is a prerequiste  May be taken for credit only once  GOV 370L • President, Congress, And Court 38966 • Spring 2010 Meets MW 5:00PM-6:30PM MEZ B0 306 show description
Prerequisite: Six semester hours of lower-division coursework in government 
GOV 370L • President, Congress, And Court 39295 • Fall 2009 Meets TTH 2:00PM-3:30PM UTC 3 112 show description
GOV 370L • President, Congress, And Court 39435 • Spring 2008 Meets MW 3:00PM-4:30PM PAR 203 show description
GOV 312L • Iss & Policies In Am Gov-Hon-W 38615-38620 • Spring 2007 Meets MW 11:00AM-12:00PM MEZ B0 306 show description
Government 312L satisfies the second half of the mandated six hours of government that every UT student must take  Course covers analysis of varying topics concerned with American political institutions and policies, including the United States Constitution, and assumes basic knowledge of government from GOV 310L, which is a prerequiste  May be taken for credit only once  GOV 312L • Iss & Policies In Am Gov-Hon-W 37600-37605 • Spring 2006 Meets MW 11:00AM-12:00PM MEZ B0 306 show description
Government 312L satisfies the second half of the mandated six hours of government that every UT student must take  Course covers analysis of varying topics concerned with American political institutions and policies, including the United States Constitution, and assumes basic knowledge of government from GOV 310L, which is a prerequiste  May be taken for credit only once  GOV 312L • Iss & Policies In Am Gov-Hon-W 34900-34905 • Spring 2004 Meets MW 11:00AM-12:00PM BUR 134 show description
Government 312L satisfies the second half of the mandated six hours of government that every UT student must take  Course covers analysis of varying topics concerned with American political institutions and policies, including the United States Constitution, and assumes basic knowledge of government from GOV 310L, which is a prerequiste  May be taken for credit only once  GOV 312L • Iss & Policies In Am Gov-Hon-W 34495-34500 • Spring 2003 Meets MW 11:00AM-12:00PM UTC 1 130 show description
Government 312L satisfies the second half of the mandated six hours of government that every UT student must take  Course covers analysis of varying topics concerned with American political institutions and policies, including the United States Constitution, and assumes basic knowledge of government from GOV 310L, which is a prerequiste  May be taken for credit only once  Publications
Tulis, JK (2011), "Plausible Futures," in Dunn, Charles W  (ed ) The Presidency in the Twenty-First Century, University Press of Kentucky Tulis, J K  and Macedo, S  (2010) The Limits of Constitutional Democracy, Princeton University Press Tulis, J K  and Macedo, S  (2010) "Constitutional Boundaries," in The Limits of Constitutional Democracy, Princeton University Press Tulis, JK (2010), "The Possibility of Constitutional Statesmanship," in Tulis, JK and Macedo, S (eds ) The Limits of Constitutional Democracy, Princeton University Press Tulis, J  (2009) The Constitutional Presidency  Johns Hopkins University Press Tulis, J  (2009) Impeachment in the Constitutional Order  In J  Tulis & J M  Bessette (Eds ), The Constitutional Presidency  Johns Hopkins University Press Tulis, J  & Bessette, J M  (2009) On the Constitution, Politics, and the Presidency  In J  Tulis & J M  Bessette (Eds ), The Constitutional Presidency  Johns Hopkins University Press Tulis, J (and Bessette, J M) (2010) The Presidency in the Constitutional Order: Historical Perspectives, Reissued Classics Series, Transaction Publishers,Tulis, J and Bessette, J M  (2010, "Introduction to the Transaction Edition," The Presidency in the Constitutional Order: Historical Perspectives, Transaction Publishers 
Tulis, JK, (2009) "The Two Constitutional Presidencies," in Nelson, Michael (ed ) The Presidency in the Political System, Congressional Quarterly Press Tulis, J  & Mellow, N  (2007) Andrew Johnson and the Politics of Failure  In S  Skowronek & M  Glassman (Eds ), Formative Acts: Reckoning with Agency in American Politics  Philadelphia: University of Pennsylvania Press Tulis, J  (2007, September) The Rhetorical Presidency in Retrospect  Critical Review: An Interdisciplinary Journal of Politics and Society, 19(2&3)  Curriculum Vitae
Context 2: \section{Introduction}
Given a data set and a model with some unknown parameters, the inverse problem aims to find the values of the model parameters that best fit the data   
In this work, in which we focus on systems of interacting elements,
 the inverse problem concerns  the statistical inference
 of the underling interaction network and of its coupling coefficients from observed data on the dynamics  of the system  
 Versions of this problem are encountered in physics, biology (e g , \cite{Balakrishnan11,Ekeberg13,Christoph14}), social sciences and finance (e g ,\cite{Mastromatteo12,yamanaka_15}), neuroscience (e g , \cite{Schneidman06,Roudi09a,tyrcha_13}), just to cite a few, and are becoming more and more important due to the increase in the amount of data available from these fields \\
 \indent 
 A standard approach used in statistical inference is to predict the interaction couplings by maximizing the likelihood function 
 This technique, however, requires the evaluation of the  
 
   partition function that, in the most general case, concerns a number of computations scaling exponentially with the system size 
  
  
    Boltzmann machine learning uses Monte Carlo sampling to compute the gradients of the Log-likelihood looking for stationary points \cite{Murphy12} but this method is computationally manageable only for small systems  A series of faster approximations, such as naive mean-field, independent-pair approximation \cite{Roudi09a, Roudi09b}, inversion of TAP equations \cite{Kappen98,Tanaka98}, small correlations expansion \cite{Sessak09}, adaptive TAP \cite{Opper01}, adaptive  cluster expansion \cite{Cocco12} or Bethe approximations \cite{Ricci-Tersenghi12, Nguyen12}  have, then, been developed  These techniques take as input means and correlations of observed variables and most of them assume a fully connected graph as underlying connectivity network, or expand  around it by perturbative dilution   In most cases, network reconstruction turns out to  be not accurate for small data sizes and/or when couplings are  strong or, else, if the original interaction network is sparse \\
\indent
 A further method, substantially improving performances for small data, is the so-called Pseudo-Likelyhood Method (PLM) \cite{Ravikumar10}  In Ref  \cite{Aurell12} Aurell and Ekeberg performed a comparison between PLM and some of the just mentioned mean-field-based algorithms on the pairwise interacting Ising-spin  ($\sigma = \pm 1$) model, showing how PLM performs sensitively better, especially on sparse graphs and in the high-coupling limit, i e , for low temperature 
 
 In this work, we aim at performing statistical inference  on a model whose interacting variables are continuous $XY$ spins, i e , $\sigma \equiv \left(\cos \phi,\sin \phi\right)$ with $\phi \in [0, 2\pi )$  The developed tools can, actually, be also straightforward applied  to the $p$-clock model  \cite{Potts52} where the phase $\phi$ takes discretely equispaced $p$ values  in the $2 \pi$ interval, $\phi_a =  a 2 \pi/p$, with $a= 0,1,\dots,p-1$  The $p$-clock model, else called vector Potts model, gives a hierarchy of discretization of the $XY$ model as $p$ increases  For $p=2$, one recovers the Ising model, for $p=4$ the Ashkin-Teller model \cite{Ashkin43}, for $p=6$ the ice-type model \cite{Pauling35,Baxter82} and the eight-vertex model \cite{Sutherland70,Fan70,Baxter71} for $p=8$   
It turns out to be very useful also for numerical implementations of the continuous $XY$ model  
Recent analysis on the multi-body $XY$ model has shown that for a limited number of discrete phase values ($p\sim 16, 32$) the thermodynamic critical properties of the $p\to\infty$ $XY$ limit are promptly recovered \cite{Marruzzo15, Marruzzo16}   
Our main motivation to study statistical inference is that these kind of models have recently turned out to be rather useful in describing the behavior of optical systems, 
including standard mode-locking lasers \cite{Gordon02,Gat04,Angelani07,Marruzzo15} and random lasers \cite{Angelani06a,Leuzzi09a,Antenucci15a,Antenucci15b,Marruzzo16}  
In particular, the inverse problem on the pairwise XY model analyzed here might be of help in recovering images from light propagated through random media  


      This paper is organized as follows: in Sec  \ref{sec:model} we introduce the general model  and we discuss its  derivation also  as a model for light transmission through random scattering media  
    In Sec  \ref{sec:plm} we introduce the PLM with $l_2$ regularization  and with decimation, two variants of the PLM respectively introduced in Ref  \cite{Wainwright06} and \cite{Aurell12} for the inverse Ising problem  
    Here, we analyze these techniques for continuous $XY$ spins and we test them on thermalized data generated by Exchange Monte Carlo numerical simulations of the original model dynamics  In Sec  \ref{sec:res_reg} we  present the results related to the PLM-$l_2$  In Sec  \ref{sec:res_dec} the results related to the PLM with decimation are reported and its performances are compared to the PLM-$l_2$ and to a variational mean-field method analyzed in Ref  \cite{Tyagi15}  In Sec  \ref{sec:conc}, we outline conclusive remarks and perspectives 

        \section{The leading $XY$ model}
      \label{sec:model}
 The leading model we are considering is defined, for a system of $N$ angular $XY$ variables, by the Hamiltonian 
 \begin{equation}
  \mathcal{H} = - \sum_{ik}^{1,N} J_{ik} \cos{\left(\phi_i-\phi_k\right)} 
  \label{eq:HXY}
 
  \end{equation} 
  
  The $XY$ model is well known in statistical mechanics, displaying important physical
  insights, starting from the Berezinskii-Kosterlitz-Thouless
  transition in two dimensions\cite{Berezinskii70,Berezinskii71,Kosterlitz72} and moving to, e g , the
  transition of liquid helium to its superfluid state \cite{Brezin82}, the roughening transition of the interface of a crystal in equilibrium with its vapor \cite{Cardy96}  In presence of disorder and frustration \cite{Villain77,Fradkin78} the model has been adopted to describe synchronization problems as the Kuramoto model \cite{Kuramoto75} and in the theoretical modeling of Josephson junction arrays \cite{Teitel83a,Teitel83b} and arrays of coupled lasers \cite{Nixon13} 
  Besides several derivations and implementations of the model in quantum and classical physics, equilibrium or out of equilibrium, ordered or fully frustrated systems, Eq  (\ref{eq:HXY}), in its generic form,
  has found applications also in other fields  A rather fascinating example being the behavior of starlings flocks  \cite{Reynolds87,Deneubourg89,Huth90,Vicsek95, Cavagna13} 
  Our interest on the $XY$ model resides, though, in optics  Phasor and phase models with pairwise and  multi-body interaction terms can, indeed, describe the behavior of electromagnetic modes in both linear and nonlinear optical systems in the analysis of problems such as light propagation and lasing \cite{Gordon02, Antenucci15c, Antenucci15d}  As couplings are strongly frustrated, these models turn out to be especially useful to the study of optical properties in random media \cite{Antenucci15a,Antenucci15b}, as in the noticeable case of random lasers \cite{Wiersma08,Andreasen11,Antenucci15e}  and they might as well be applied to linear scattering problems, e g , propagation of waves in opaque systems or disordered fibers  
  
  
  \subsection{A propagating wave model}
  We briefly mention a derivation of the model as a proxy for the propagation of light through random linear media  
 Scattering of light is held responsible to obstruct our view and make objects opaque  Light rays, once that they enter the material, only exit  after getting scattered multiple times within the material  In such a disordered medium, both the direction and the phase of the propagating waves are random  Transmitted light 
 yields a disordered interference pattern typically  having low intensity, random phase and almost no resolution, called a speckle  Nevertheless, in recent years it has been realized that disorder is rather a blessing in disguise \cite{Vellekoop07,Vellekoop08a,Vellekoop08b}  Several experiments have made it possible to control the behavior of light and other optical processes in a given random disordered medium,  
 by exploiting, e g ,  the tools developed for wavefront shaping to control the propagation of light and to engineer the confinement of light \cite{Yilmaz13,Riboli14} 
 \\
 \indent
 In a linear dielectric medium, light propagation can be described through a part of the scattering matrix, the transmission matrix $\mathbb{T}$, linking the outgoing to the incoming fields  
 Consider the case in which there are $N_I$ incoming channels and $N_O$ outgoing ones; we can indicate with $E^{\rm in,out}_k$ the input/output electromagnetic field phasors of channel $k$  In the most general case, i e , without making any particular assumptions on the field polarizations, each light mode and its polarization polarization state can be represented by means of the $4$-dimensional Stokes vector  Each $ t_{ki}$ element of $\mathbb{T}$, thus, is a $4 \times 4$ M{\"u}ller matrix  If, on the other hand, we know that the source is polarized and the observation is made on the same polarization, one can use a scalar model and adopt Jones calculus \cite{Goodman85,Popoff10a,Akbulut11}:
   \begin{eqnarray}
 E^{\rm out}_k = \sum_{i=1}^{N_I}  t_{ki} E^{\rm in}_i \qquad \forall~ k=1,\ldots,N_O
 \label{eq:transm}
 \end{eqnarray}
  We recall that the elements of the transmission matrix are random complex coefficients\cite{Popoff10a}  For the case of completely unpolarized modes, we can also use a scalar model similar to Eq  \eqref{eq:transm}, but whose variables are  the intensities of the outgoing/incoming fields, rather than the fields themselves \\ 
In the following, for simplicity, we will consider Eq  (\ref{eq:transm}) as our starting point,
where $E^{\rm out}_k$, $E^{\rm in}_i$ and $t_{ki}$ are all complex scalars  
If Eq  \eqref{eq:transm} holds for any $k$, we can write:
  \begin{eqnarray}
  \int \prod_{k=1}^{N_O} dE^{\rm out}_k \prod_{k=1}^{N_O}\delta\left(E^{\rm out}_k - \sum_{j=1}^{N_I}  t_{kj} E^{\rm in}_j \right) = 1
  \nonumber
  \\
  \label{eq:deltas}
  \end{eqnarray}

 Observed data are a noisy representation of the true values of the fields  Therefore, in inference problems it is statistically more meaningful to take that noise into account in a probabilistic way, 
 rather than looking  at the precise solutions of the exact equations (whose parameters are unknown)  
 To this aim we can introduce Gaussian distributions whose limit for zero variance are the Dirac deltas in Eq  (\ref{eq:deltas}) 
 Moreover, we move to consider the ensemble of all possible solutions of Eq  (\ref{eq:transm}) at given $\mathbb{T}$, looking at  all configurations of input fields  We, thus, define the function:
 
   \begin{eqnarray}
  Z &\equiv &\int_{{\cal S}_{\rm in}} \prod_{j=1}^{N_I}  dE^{\rm in}_j \int_{{\cal S}_{\rm out}}\prod_{k=1}^{N_O} dE^{\rm out}_k 
  \label{def:Z}
\\
    \times
  &&\prod_{k=1}^{N_O}
   \frac{1}{\sqrt{2\pi \Delta^2}}  \exp\left\{-\frac{1}{2 \Delta^2}\left|
  E^{\rm out}_k -\sum_{j=1}^{N_I}  t_{kj} E^{\rm in}_j\right|^2
\right\} 
\nonumber
 \end{eqnarray}
   We stress that the integral of Eq  \eqref{def:Z} is not exactly a Gaussian integral  Indeed, starting from Eq  \eqref{eq:deltas}, two constraints on the electromagnetic field intensities must be taken into account  

  The space of solutions is  delimited by the total power ${\cal P}$ received by system, i e , 
  ${\cal S}_{\rm in}: \{E^{\rm in} |\sum_k I^{\rm in}_k = \mathcal{P}\}$, also implying  a constraint on the total amount of energy that is transmitted through the medium, i  e , 
  ${\cal S}_{\rm out}:\{E^{\rm out} |\sum_k I^{\rm out}_k=c\mathcal{P}\}$, where the attenuation factor  $c<1$ accounts for total losses 
  As we will see more in details in the following, being interested in inferring the transmission matrix through the PLM, we can omit to explicitly include these terms in Eq  \eqref{eq:H_J} since they do not depend on $\mathbb{T}$ not adding any information on the gradients with respect to the elements of $\mathbb{T}$ 
  
 Taking the same number of incoming and outcoming channels, $N_I=N_O=N/2$, and  ordering the input fields in the first $N/2$ mode indices and the output fields in the last $N/2$ indices, we can drop the ``in'' and ``out'' superscripts and formally write $Z$  as a partition function
    \begin{eqnarray}
        \label{eq:z}
 && Z =\int_{\mathcal S} \prod_{j=1}^{N} dE_j \left(   \frac{1}{\sqrt{2\pi \Delta^2}} \right)^{N/2} 
 \hspace*{- 4cm} \exp\left\{
  -\frac{ {\cal H} [\{E\};\mathbb{T}] }{2\Delta^2}
  \right\}
  \\
&&{\cal H} [\{E\};\mathbb{T}] =
-  \sum_{k=1}^{N/2}\sum_{j=N/2+1}^{N} \left[E^*_j t_{jk} E_k + E_j t^*_{kj} E_k^* 
\right]
 \nonumber
\\
&&\qquad\qquad \qquad + \sum_{j=N/2+1}^{N} |E_j|^2+ \sum_{k,l}^{1,N/2}E_k
U_{kl} E_l^*
 \nonumber
 \\
 \label{eq:H_J}
 &&\hspace*{1 88cm } = - \sum_{nm}^{1,N} E_n J_{nm} E_m^*
 \end{eqnarray}
 where ${\cal H}$ is a real-valued function by construction, we have introduced the effective input-input coupling matrix
\begin{equation}
U_{kl} \equiv \sum_{j=N/2+1}^{N}t^*_{lj} t_{jk} 
 \label{def:U}
 \end{equation}
 and the whole interaction matrix reads (here $\mathbb{T} \equiv \{ t_{jk} \}$)
 \begin{equation}
 \label{def:J}
 \mathbb J\equiv \left(\begin{array}{ccc|ccc}
 \phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}\\
 \phantom{()}&-\mathbb{U} \phantom{()}&\phantom{()}&\phantom{()}&{\mathbb{T}}&\phantom{()}\\
\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}\\
 \hline
\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}\\
 \phantom{()}& \mathbb   T^\dagger&\phantom{()}&\phantom{()}& - \mathbb{I} &\phantom{()}\\
\phantom{a}&\phantom{a}&\phantom{a}&\phantom{a}&\phantom{a}&\phantom{a}\\
 \end{array}\right)
 \end{equation}
 
 Determining the electromagnetic complex amplitude configurations that minimize the {\em cost function} ${\cal H}$, Eq   (\ref{eq:H_J}),  means to maximize the overall distribution peaked around the solutions of the transmission Eqs  (\ref{eq:transm})  As the variance $\Delta^2\to 0$, eventually, the initial set of Eqs  (\ref{eq:transm}) are recovered  The ${\cal H}$ function, thus, plays the role of an Hamiltonian and  $\Delta^2$ the role of a noise-inducing temperature  The exact numerical problem corresponds to the zero temperature limit of the statistical mechanical problem  Working with real data, though, which are noisy, a finite ``temperature''
  allows for a better representation of the ensemble of solutions to the sets of equations of continuous variables  
  

  
  
  Now, we can express every phasor in Eq  \eqref{eq:z}  as $E_k = A_k e^{\imath \phi_k}$  As a working hypothesis we will consider the intensities $A_k^2$ as either homogeneous or as \textit{quenched} with respect to phases 
The first condition occurs, for instance, to the input intensities $|E^{\rm in}_k|$ produced by a phase-only spatial light modulator (SLM) with homogeneous illumination \cite{Popoff11} 
With \textit{quenched} here we mean, instead, that the intensity of each mode is the same for every solution of Eq  \eqref{eq:transm} at fixed $\mathbb T$ 
We stress that, including intensities in the model does not preclude the inference analysis but it is out of the focus of the present work and will be considered elsewhere  

If all intensities are uniform in input and in output, this amount to a constant rescaling for each one of the four sectors of matrix $\mathbb J$ in Eq  (\ref{def:J}) that will not change the properties of the matrices 
For instance, if the original transmission matrix is unitary, so it will be the rescaled one and the matrix $\mathbb U$ will be  diagonal 
Otherwise, if intensities are \textit{quenched}, i e , they can be considered as constants in Eq  (\ref{eq:transm}),
they are inhomogeneous with respect to phases  The generic Hamiltonian element will, therefore, rescale as 
  \begin{eqnarray}
  E^*_n J_{nm} E_m = J_{nm} A_n A_m e^{\imath (\phi_n-\phi_m)} \to J_{nm} e^{\imath (\phi_n-\phi_m)}
  \nonumber
  \end{eqnarray}
  and the properties of the original  $J_{nm}$ components are not conserved  in the rescaled one  In particular, we have no argument, anymore, to possibly set the rescaled $U_{nm}\propto \delta_{nm}$ 
  Eventually, we end up with the complex couplings $XY$ model, whose real-valued Hamiltonian is written as
 \begin{eqnarray}
  \mathcal{H}& = &  - \frac{1}{2} \sum_{nm} J_{nm} e^{-\imath (\phi_n - \phi_m)}  + \mbox{c c } 
    \label{eq:h_im}
\\    &=&  - \frac{1}{2} \sum_{nm} \left[J^R_{nm} \cos(\phi_n - \phi_m)+
  J^I_{nm}\sin (\phi_n - \phi_m)\right] 
  \nonumber
 \end{eqnarray}
where $J_{nm}^R$ and $J_{nm}^I$ are the real and imaginary parts of $J_{nm}$  Being $\mathbb J$  Hermitian, $J^R_{nm}=J^R_{mn}$ is symmetric and $J_{nm}^I=-J_{mn}^I$ is skew-symmetric 

\begin{comment}
\textcolor{red}{
F: comment about quenched:
I think that to obtain the XY model, it is not necessary that the intensities are strictly quenched (that is also a quite unfeasible situation, I guess) 
Indeed eq (2) does not deal with the dynamics of the modes, but just connect the in and out ones 
For this, what it is necessary to have the XY model, it is that the intensities are always the same on the different samples
(so that the matrix $t_{ij}$ is the same for different phase data)  If the intensities are fixed, then they can be incorporated in $t_{ij}$ and eq (2) can be written just for phases as described  \\
}
\end{comment}


  \section{Pseudolikelihood Maximization}
  \label{sec:plm}
The inverse problem consists in the reconstruction of the parameters $J_{nm}$ of the Hamiltonian, Eq  (\ref{eq:h_im})   
Given a set of $M$ data configurations of $N$ spins
 $\bm\sigma = \{ \cos \phi_i^{(\mu)},\sin \phi_i^{(\mu)} \}$, $i = 1,\dots,N$ and $\mu=1,\dots,M$, we want to \emph{infer} the couplings:
 \begin{eqnarray}
\bm \sigma  \rightarrow  \mathbb{J} 
\nonumber
 \end{eqnarray}
 With this purpose in mind,
 in the rest of this section we implement the working equations for the techniques used  
 In order to test our methods, we generate the input data, i e , the configurations, by Monte-Carlo simulations of the model 
 The joint probability distribution of the $N$ variables $\bm{\phi}\equiv\{\phi_1,\dots,\phi_N\}$, follows the Gibbs-Boltzmann distribution:
 \begin{equation}\label{eq:p_xy}
 P(\bm{\phi}) = \frac{1}{Z} e^{-\beta \mathcal{H\left(\bm{\phi}\right)}} \quad \mbox{ where } \quad Z = \int \prod_{k=1}^N d\phi_k  e^{-\beta \mathcal{H\left(\bm{\phi}\right)}}  
 \end{equation}
 and where we denote $\beta=\left( 2\Delta^2 \right)^{-1}$ with respect to Eq  (\ref{def:Z}) formalism 
 In order to stick to usual statistical inference notation, in the following we will rescale the couplings by a factor $\beta / 2$: $\beta J_{ij}/2 \rightarrow J_{ij}$  
 The main idea of the PLM is to work with the conditional probability distribution of one variable $\phi_i$ given all other variables, 
 $\bm{\phi}_{\backslash i}$:
 
  \begin{eqnarray}
	\nonumber
   P(\phi_i | \bm{\phi}_{\backslash i}) &=& \frac{1}{Z_i} \exp \left \{ {H_i^x (\bm{\phi}_{\backslash i})
  	\cos \phi_i + H_i^y (\bm{\phi}_{\backslash i}) \sin \phi_i } \right \}
	\\
 \label{eq:marginal_xy}
	&=&\frac{e^{H_i(\bm{\phi}_{\backslash i}) \cos{\left(\phi_i-\alpha_i(\bm{\phi}_{\backslash i})\right)}}}{2 \pi I_0(H_i)}
  \end{eqnarray}
  where $H_i^x$ and $H_i^y$ are defined as
   \begin{eqnarray}
   H_i^x (\bm{\phi}_{\backslash i})  &=& \sum_{j (\neq i)} J^R_{ij} \cos \phi_j  - \sum_{j  (\neq i) } J_{ij}^{I} \sin \phi_j \phantom{+  h^R_i} \label{eq:26} \\
   H_i^y  (\bm{\phi}_{\backslash i})  &=&  \sum_{j  (\neq i)} J^R_{ij}  \sin \phi_j  + \sum_{j  (\neq i) } J_{ij}^{I}   \cos \phi_j \phantom{ + h_i^{I} }\label{eq:27}
   \end{eqnarray}
and $H_i= \sqrt{(H_i^x)^2 + (H_i^y)^2}$, $\alpha_i = \arctan H_i^y/H_i^x$   and we introduced the modified Bessel function of the first kind:
  \begin{equation}
  \nonumber
   I_k(x) = \frac{1}{2 \pi}\int_{0}^{2 \pi} d \phi e^{x \cos{ \phi}}\cos{k \phi}
  \end{equation}
  
   Given $M$ observation samples $\bm{\phi}^{(\mu)}=\{\phi^\mu_1,\ldots,\phi^\mu_N\}$, $\mu = 1,\dots, M$, the
   pseudo-loglikelihood for the variable $i$ is given by the logarithm of Eq  (\ref{eq:marginal_xy}),
   \begin{eqnarray}
   \label{eq:L_i}
   L_i &=& \frac{1}{M}  \sum_{\mu = 1}^M  \ln P(\phi_i^{(\mu)}|\bm{\phi}^{(\mu)}_{\backslash i})
   \\
   \nonumber
   & =&  \frac{1}{M}  \sum_{\mu = 1}^M  \left[ H_i^{(\mu)} \cos( \phi_i^{(\mu)} - \alpha_i^{(\mu)}) - \ln  2 \pi I_0\left(H_i^{(\mu)}\right)\right] \,  
    \end{eqnarray}
The underlying idea of PLM is that an approximation of the true parameters of the model is obtained for values that maximize the functions $L_i$ 
The specific maximization scheme differentiates the different techniques 


   
   
   \subsection{PLM with $l_2$ regularization}
   Especially for the case of sparse graphs, it is useful to add a regularizer, which prevents the maximization routine to move towards high values of 
   $J_{ij}$ and $h_i$ without converging  We will adopt an $l_2$ regularization so that the Pseudolikelihood function (PLF) at site $i$  reads:
   \begin{equation}\label{eq:plf_i}
  {\cal L}_i = L_i
  - \lambda \sum_{i \neq j} \left(J_{ij}^R\right)^2 - \lambda \sum_{i \neq j} \left(J_{ij}^I\right)^2  
   \end{equation}
   with $\lambda>0$ 
   Note that the values of $\lambda$ have to be chosen arbitrarily, but not too large, in order not to overcome $L_i$ 
   The standard implementation of the PLM consists in maximizing each ${\cal L}_i$, for $i=1\dots N$, separately  The expected values of the couplings are then:
   \begin{equation}
   \{ J_{i j}^*\}_{j\in \partial i} :=  \mbox{arg max}_{ \{ J_{ij} \}}
    \left[{\cal L}_i\right]
   \end{equation}
   In this way, we obtain two estimates for the coupling $J_{ij}$, one from maximization of ${\cal L}_i$, $J_{ij}^{(i)}$, and another one from ${\cal L}_j$, say $J_{ij}^{(j)}$ 
    Since the original Hamiltonian of the $XY$ model is Hermitian, we know that the real part of the couplings is symmetric while the imaginary part is skew-symmetric  
   
     The final estimate for $J_{ij}$ can then be obtained  averaging the two results:
  
  
  
   \begin{equation}\label{eq:symm}
   J_{ij}^{\rm inferred} = \frac{J_{ij}^{(i)} + \bar{J}_{ij}^{(j)}}{2} 
   \end{equation}
   where with $\bar{J}$ we indicate the complex conjugate 
   It is worth noting that the pseudolikelihood $L_i$, Eq  \eqref{eq:L_i}, is characterized by the
   following properties: (i) the normalization term of Eq \eqref{eq:marginal_xy} can be
   computed analytically at odd with the {\em full} likelihood case that
   in general require a computational time which scales exponentially
   with the size of the systems; (ii) the $\ell_2$-regularized pseudolikelihood
   defined in Eq \eqref{eq:plf_i} is strictly concave (i e  it has a single
   maximizer)\cite{Ravikumar10}; (iii) it is consistent, i e  if $M$ samples are
   generated by a model $P(\phi | J*)$ the maximizer tends to $J*$
   for $M\rightarrow\infty$\cite{besag1975}  Note also that (iii) guarantees that  
   $|J^{(i)}_{ij}-J^{(j)}_{ij}| \rightarrow 0$ for $M\rightarrow \infty$ 
   In Secs  \ref{sec:res_reg}, \ref{sec:res_dec} 
   we report the results obtained and we analyze the performances of the PLM having taken the configurations from Monte-Carlo simulations of models whose details are known 
   

   
   \subsection{PLM with decimation}
   Even though the PLM with $l_2$-regularization allows to dwell the inference towards the low temperature region and in the low sampling case with better performances that mean-field methods, in some situations some couplings are overestimated and not at all symmetric  Moreover, in the technique there is the bias of the $l_2$ regularizer 
   Trying to overcome these problems, Decelle and Ricci-Tersenghi introduced a new method \cite{Decelle14}, known as PLM + decimation: the algorithm maximizes the sum of the $L_i$,
   \begin{eqnarray}
    {\cal L}\equiv \frac{1}{N}\sum_{i=1}^N \mbox{L}_i
    \end{eqnarray}  
    and, then, it recursively set to zero couplings which are estimated very small  We expect that as long as we are setting to zero couplings that are unnecessary to fit the data, there should be not much changing on ${\cal L}$  Keeping on with decimation, a point is reached where ${\cal L}$ decreases abruptly indicating  that relevant couplings are being decimated and under-fitting is taking place 
   Let us define  by $x$  the fraction of non-decimated couplings  To have a quantitative measure for the halt criterion of the decimation process, a tilted ${\cal L}$ is defined as,
   \begin{eqnarray}
  \mathcal{L}_t &\equiv& \mathcal{L}  - x \mathcal{L}_{\textup{max}} - (1-x) \mathcal{L}_{\textup{min}} \label{$t$PLF} 
   \end{eqnarray}
   where 
   \begin{itemize}
   \item $\mathcal{L}_{\textup{min}}$ is the pseudolikelyhood of a model with independent variables  In the XY case: $\mathcal{L}_{\textup{min}}=-\ln{2 \pi}$ 
   \item
   $\mathcal{L}_{\textup{max}}$ is the pseudolikelyhood in the fully-connected model and it is maximized over all the $N(N-1)/2$ possible couplings  
   \end{itemize}
   At the first step, when $x=1$, $\mathcal{L}$ takes value $\mathcal{L}_{\rm max}$ and  $\mathcal{L}_t=0$  On the last step, for an empty graph, i e , $x=0$, $\mathcal{L}$ takes the value $\mathcal{L}_{\rm min}$ and, hence, again $\mathcal{L}_t =0$  
   In the intermediate steps, during the decimation procedure, as $x$ is decreasing from $1$ to $0$, one observes firstly that $\mathcal{L}_t$ increases linearly and, then, it displays an abrupt decrease indicating that from this point on relevant couplings are being decimated\cite{Decelle14}  In Fig  \ref{Jor1-$t$PLF} we give an instance of this behavior for the 2D short-range XY model with ordered couplings  We notice that the maximum point of $\mathcal{L}_t$ coincides with the minimum point of the reconstruction error, the latter defined as 
   \begin{eqnarray}\label{eq:errj}
   \mbox{err}_J \equiv \sqrt{\frac{\sum_{i<j} (J^{\rm inferred}_{ij} -J^{\rm true}_{ij})^2}{N(N-1)/2}} \label{err}
   \end{eqnarray}
  We stress that the ${\cal L}_t$ maximum is obtained ignoring the underlying graph, while the err$_J$ minimum can be evaluated once the true graph has been reconstructed  
   
     \begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_tPLF_new eps}
   	\caption{The tilted likelyhood ${\cal L}_t$ curve and the reconstruction error vs the number of decimated couplings  for an ordered, real-valued J on 2D XY model with $N=64$ spins  The peak of ${\cal L}_t$ coincides with the dip of the error }  
   	\label{Jor1-$t$PLF}
   \end{figure} 
       
   
   In the next sections we will show the results obtained on the  $XY$ model analyzing the performances of the two methods and comparing them also with a mean-field method \cite{Tyagi15} 
   
  
    
   \section{Inferred couplings with PLM-$l_2$}
    \label{sec:res_reg}
    \subsection{$XY$ model with real-valued couplings}
    
    In order to obtain the vector of couplings, $J_{ij}^{\rm inferred}$ the function $-\mathcal{L}_i$ is minimized through the vector of derivatives ${\partial \mathcal{L}_i}/\partial J_{ij}$



ground_truth: Legacies of Losing in American Politics and an expanded edition of The Rhetorical Presidency in the Princeton Classics series.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How does the performance of the PLM with decimation compare to other methods?

Read the following text and answer briefly.

Context 2:  The process is repeated for all the couplings obtaining then a fully connected adjacency matrix  The results here presented are obtained with $\lambda = 0 01$ 
   For the minimization we have used the MATLAB routine \emph{minFunc\_2012}\cite{min_func}  
      
      \begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{Jor11_2D_l2_JR_soJR_TPJR}
    	\caption{Top panels: instances of single site coupling reconstruction for the case of $N=64$ XY spins on a 2D lattice with ordered $J$ (left column) and bimodal distributed $J$ (right column)  
    	
    	Bottom panels: sorted couplings }
    	\label{PL-Jor1}
    \end{figure}

   
To produce the data by means of numerical Monte Carlo simulations a system with $N=64$  spin variables  is considered on a deterministic 2D lattice with periodic boundary conditions  
Each spin has then connectivity $4$, i e , we expect to infer an adjacency matrix with $N c = 256$ couplings different from zero  
The dynamics of the simulated model is based on the Metropolis algorithm and parallel tempering\cite{earl05} is used to speed up the thermalization of the system 
The thermalization is tested looking at the average energy over logarithmic time windows and
the acquisition of independent configurations
starts only after the system is well thermalized 

   For the values of the couplings we considered two cases: an ordered case, indicated in the figure as  $J$ ordered (e g , left column of Fig  \ref{PL-Jor1}) where the couplings can take values $J_{ij}=0,J$, with $J=1$, 
   and a quenched disordered case, indicated in the figures as  $J$ disordered (e g , right column of Fig  \ref{PL-Jor1})
   where the couplings can take also  negative values, i e , 
    $J_{ij}=0,J,-J$, with a certain probability   The results here presented were obtained with bimodal distributed $J$s: 
   
    $P(J_{ij}=J)=P(J_{ij}=-J)=1/2$   The performances of the PLM have shown not to depend on $P(J)$  
   
    We recall that in Sec  \ref{sec:plm} we used the temperature-rescaled notation, i e , $J_{ij}$ stands for $J_{ij}/T$  
   
    To analyze the performances of the PLM, in Fig  \ref{PL-Jor1} the inferred couplings, $\mathbb{J}^R_{\rm inf}$, are shown on top of the original couplings,  $\mathbb{J}^R_{\rm true}$ 
     The first figure (from top) in the left column shows  the $\mathbb{J}^R_{\rm inf}$ (black) and the $\mathbb{J}^R_{\rm tru}$ (green) for a given spin
     at temperature $T/J=0 7$ and number of samples  $M=1024$  PLM appears to reconstruct the correct couplings, though zero couplings are always given a small inferred non-zero value  
     In the left column of Fig   \ref{PL-Jor1},  both the $\mathbb{J}^R_{\rm{inf}}$ and the $\mathbb{J}^R_{\rm{tru}}$ are sorted in decreasing order and plotted on top of each other  
     We can clearly see that $\mathbb{J}^R_{\rm inf}$ reproduces the expected step function  Even though the jump is smeared, the difference between inferred couplings corresponding to the set of non-zero couplings 
     and to the set of zero couplings can be clearly appreciated 
     Similarly, the plots in the right column of Fig  \ref{PL-Jor1} show the results obtained for the case with  bimodal disordered couplings, for the same working temperature and number of samples  
     In particular, note that the algorithm infers half positive and half negative couplings, as expected 
     
     
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{Jor11_2D_l2_errJ_varT_varM}
\caption{Reconstruction error $\mbox{err}_J$, cf  Eq  (\ref{eq:errj}), plotted as a function of temperature (left) for three values of the number of samples $M$ and  as a function $M$ (right) for three values of temperature in the ordered system, i e , $J_{ij}=0,1$  
The system size is $N=64$ }
\label{PL-err-Jor1}
\end{figure}

In order to analyze the effects of the number of samples and of the temperature regimes, we plot in Fig  \ref{PL-err-Jor1} the reconstruction error, Eq  (\ref{err}), as a function of temperature for three different sample sizes $M=64,128$ and $512$  
The error is seen to sharply rise al low temperature, incidentally, in the ordered case, for  $T<T_c \sim 0 893$, which is the Kosterlitz-Thouless transition temperature of the 2XY model\cite{Olsson92}  
 However, we can see that if only $M=64$ samples are considered, $\mbox{err}_J$ remains high independently on the working temperature  
 In the right plot of Fig  \ref{PL-err-Jor1},  $\mbox{err}_J$ is plotted as a function of $M$ for three different working temperatures $T/J=0 4,0 7$ and $1 3$  As we expect, 
 $\mbox{err}_J$  decreases as $M$ increases  This effect was observed also with mean-field inference techniques on the same model\cite{Tyagi15} 

To better understand the performances of the algorithms, in Fig  \ref{PL-varTP-Jor1} we show several True Positive (TP) curves obtained for various values of $M$ at three different temperatures $T$  As $M$ is large and/or temperature is not too small,  we are able to reconstruct correctly all the couplings present in the system (see bottom plots) 
The True Positive curve displays how many times the inference method finds a true link of the original network  as a function of the index of the vector of sorted absolute value of reconstructed couplings $J_{ij}^{\rm inf}$  
The index $n_{(ij)}$ represents the related spin couples $(ij)$  The TP curve is obtained as follows: 
first  the values $|J^{\rm inf}_{ij}|$ are sorted in descending order and  the spin pairs $(ij)$ are ordered according to the sorting position of $|J^{\rm inf}_{ij}|$  Then,
     	a cycle over the ordered set of pairs $(ij)$, indexed by $n_{(ij)}$, is performed, comparing with the original network coupling $J^{\rm true}_{ij}$ and verifying whether it is zero or not  The true positive curve is computed as
\begin{equation}
\mbox{TP}[n_{(ij)}]= \frac{\mbox{TP}\left[n_{(ij)}-1\right] (n_{ij}-1)+ 1 -\delta_{J^{\rm true}_{ij},0}}{n_{(ij)}}
\end{equation}
As far as $J^{\rm true}_{ij} \neq 0$, TP$=1$  As soon as the true coupling of a given $(ij)$ couple in the sorted list is zero, the TP curve departs from one  
In our case, where the connectivity per spin of the original system is  $c=4$ and there are $N=64$ spins, we know that we will have  $256$ non-zero couplings   
     	If the inverse problem is successful, hence, we expect a steep decrease of the TP curve when  $n_{ij}=256$ is overcome 

In Fig  \ref{PL-varTP-Jor1}
it is  shown that,  almost independently of $T/J$, the TP score improves as $M$ increases  Results are plotted for three different temperatures, $T=0 4,1$ and $2 2$, with increasing number of samples $M = 64, 128,512$ and $1024$ (clockwise)  
We can clearly appreciate the improvement in temperature if the size of the data-set is not very large: for small $M$, $T=0 4$ performs better  
When $M$ is high enough (e g , $M=1024$), instead, the TP curves do not appear to be strongly influenced by the temperature 

\begin{figure}[t!]
	\centering
	\includegraphics[width=1\linewidth]{Jor11_2D_l2_TPJR_varT_varM}
	\caption{TP  curves  for 2D short-range ordered $XY$ model with $N=64$ spins at three different values of $T/J$ with increasing - clockwise from top - $M$ }
	\label{PL-varTP-Jor1} 
\end{figure} 

\subsection{$XY$ model with complex-valued couplings}
For the complex $XY$ we have to contemporary  infer $2$ apart coupling matrices,  $J^R_{i j}$ and $J^I_{i j}$   As before, a system of $N=64$ spins is considered on a 2D lattice 
For the couplings we have considered both ordered and bimodal disordered cases 
In Fig  \ref{PL-Jor3}, a single row of the matrix $J$ (top) and the whole sorted couplings (bottom) are displayed for the ordered model (same legend as in Fig  \ref{PL-Jor1}) for the real, $J^R$ (left column), and the imaginary part, $J^I$   

\begin{figure}[t!]
	\centering
\includegraphics[width=1\linewidth]{Jor3_l2_JRJI_soJRJI_TPJRJI}
	\caption{Results related to the ordered complex XY model with $N=64$ spins on a  2D lattice  Top: instances of  single site reconstruction for the real, JR (left column), and
		the imaginary, JI (right column), part of $J_{ij}$  Bottom: sorted values of JR (left) and JI (right) }
		
	\label{PL-Jor3}
\end{figure}
 
 
  \section{PLM with Decimation}
 \label{sec:res_dec}
 

\begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_tPLF_varT_varM}
    	\caption{Tilted Pseudolikelyhood, ${\cal L}_t$, plotted as a function of decimated couplings  Top: Different ${\cal L}_t$ curves obtained for different values of $M$ plotted on top of each other  Here $T=1 3$  The black line indicates the expected number of decimated couplings, $x^*=(N (N-1) - N c)/2=1888$  As we can see, as $M$ increases, the maximum point of ${\cal L}_t$ approaches $x^*$  Bottom: Different ${\cal L}_t$ curves obtained for different values of T with $M=2048$  We can see that, with this value of $M$, no differences can be appreciated on the maximum points of the different  ${\cal L}_t$ curves }
   	\label{var-$t$PLF}
   \end{figure}

\begin{figure}[t!]
    \centering
    \includegraphics[width=1\linewidth]{Jor1_dec_tPLF_peak_statistics_varM_prob eps}
    	\caption{Number of most likely decimated couplings, estimated by the maximum point of $\mathcal{L}_t$, as a function of the number of samples $M$  We can clearly see that the maximum point of $\mathcal{L}_t$ tends toward $x^*$, which is the right expected number of zero couplings in the system }  
    	\label{PLF_peak_statistics}
    \end{figure}
      
      For the ordered real-valued XY model we show in Fig  \ref{var-$t$PLF}, top panel, the outcome on the tilted pseudolikelyhood, $\mathcal{L}_t$ Eq  \eqref{$t$PLF}, of the progressive decimation: from a fully connected lattice  down to an empty lattice  The figure shows the behaviour of $\mathcal{L}_t$ for three different data sizes $M$  A clear data size dependence of the maximum point of  $\mathcal{L}_t$, signalling the most likely value for decimation, is shown  For small $M$ the most likely number of  couplings is overestimated and for increasing $M$ it tends to the true value, as displayed in Fig  \ref{PLF_peak_statistics}   In the bottom panel of Fig  \ref{var-$t$PLF} we display instead different 
 $\mathcal{L}_t$ curves obtained for three different values of $T$ 
  Even though the values of $\mathcal{L}_t$ decrease with increasing temperature, the value of the most likely number of decimated couplings appears to be quite independent on $T$ with $M=2048$ number of samples 
In Fig  \ref{fig:Lt_complex} we eventually display the tilted pseudolikelyhood for a 2D network with complex valued ordered couplings, where the decimation of the real and imaginary coupling matrices proceeds in parallel, that is, 
when a real coupling is small enough to be decimated its imaginary part is also decimated, and vice versa 
One can see that though the apart errors for the real and imaginary parts are different in absolute values, they display the same dip, to be compared with the maximum point of $\mathcal{L}_t$ 
     
       \begin{figure}[t!]
    	\centering
      	\includegraphics[width=1\linewidth]{Jor3_dec_tPLF_new}
      	\caption{Tilted Pseudolikelyhood, ${\cal L}_t$, plotted with the reconstruction errors for the XY model with $N=64$ spins on a 2D lattice  These results refer to the case of  ordered and complex valued couplings  The full (red) line indicates ${\cal L}_t$  The dashed (green) 
      		and the dotted (blue) lines show the reconstruction errors (Eq  \eqref{eq:errj}) obtained for the real and the imaginary couplings respectively  We can see that both ${\rm err_{JR}}$ and ${\rm err_{JI}}$ have a minimum at $x^*$ }
          	\label{fig:Lt_complex}
    \end{figure}

\begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_JR_soJR_TPJR}
   	\caption{XY model on a 2D lattice with $N=64$ sites and real valued couplings  The graphs show the inferred (dashed black lines) and true couplings (full green lines) plotted on top of each other  The left and right columns refer to the
   		 cases of ordered and bimodal disordered couplings, respectively  Top figures: single site reconstruction, i e , one row of the matrix $J$  Bottom figures: couplings are plotted sorted in descending order }  
   	\label{Jor1_dec}
   \end{figure}
   
\begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{Jor3_dec_JRJI_soJRJI_TPJRJI}
    	\caption{XY model on a 2D lattice with $N=64$ sites and ordered complex-valued couplings 
    		The inferred and true couplings are plotted on top of each other  The left and right columns show the real and imaginary parts, respectively, of the couplings  Top figures refer to a single site reconstruction, i e , one row of the matrix $J$  Bottom figures report the couplings sorted in descending order }
    	\label{Jor3_dec}
    \end{figure}
    
       







       \begin{figure}[t!]
     	\centering
     	\includegraphics[width=1\linewidth]{MF_PL_Jor1_2D_TPJR_varT}
     	\caption{True Positive curves obtained with the three techniques: PLM with decimation, (blue) dotted line,  PLM with $l_2$ regularization, (greed) dashed line, and mean-field, (red) full line   These results refer to real valued ordered couplings with $N=64$ spins on a 2D lattice  The temperature is here $T=0 7$ while the four graphs refer to different sample sizes: $M$ increases clockwise }
     	\label{MF_PL_TP}
     \end{figure}
    
    \begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{MF_PL_Jor1_2D_errJ_varT_varM}
    	\caption{Variation of reconstruction error, ${\rm err_J}$, with respect to temperature as obtained with the three different techniques, see Fig  \ref{MF_PL_TP}, for four different sample size:  clockwise from top   $M=512,1024, 2048$ and $4096$ } 
    	\label{MF_PL_err}
    \end{figure}
    
     Once the most likely network has been identified through the decimation procedure, we perform the same analysis displayed in Fig  \ref{Jor1_dec}  for ordered and then quenched disordered real-valued couplings
and in Fig  \ref{Jor3_dec} for  complex-valued ordered couplings   In comparison to the results shown in Sec  \ref{sec:res_reg},
  the PLM with decimation leads to rather cleaner results  In Figs  \ref{MF_PL_err} and \ref{MF_PL_TP} we compare the performances of the PLM with decimation in respect to ones of the PLM with $l_2$-regularization  These two techniques are also analysed in respect to a mean-field technique previously implemented on the same XY systems\cite{Tyagi15} 
  
    For what concerns the network of connecting links, in Fig  \ref{MF_PL_TP} we compare the TP curves obtained with the three techniques  The results refer to the case of ordered and real valued couplings, but similar behaviours were obtained for the other cases analysed  
  The four graphs are related to different sample sizes, with $M$ increasing clockwise  When $M$ is high enough, all techniques reproduce the true network  
  However, for lower values of $M$ the performances of the PLM with $l_2$ regularization and with decimation drastically overcome those ones of the previous mean field technique  
  In particular, for $M=256$ the PLM techniques still reproduce the original network while the mean-field method fails to find more than half of the couplings  
  When $M=128$, the network is clearly reconstructed only through the PLM with decimation while the PLM with $l_2$ regularization underestimates the couplings  
  Furthermore, we notice that the PLM method with decimation is able to clearly infer the network of interaction even when $M=N$ signalling that it could be considered also in the under-sampling regime $M<N$   
 
 
In Fig  \ref{MF_PL_err} we compare the temperature behaviour of the reconstruction error 
In can be observed that for all temperatures and for all sample sizes  the reconstruction error, ${\rm err_J}$, (plotted here in log-scale) obtained with the PLM+decimation is always smaller than 
that one obtained with the other techniques  The temperature behaviour of ${\rm err_J}$ agrees with the one already observed for Ising spins in \cite{Nguyen12b} and for XY spins  in \cite{Tyagi15} with a mean-field approach:  ${\rm err_J}$ displays a minimum around $T\simeq 1$ and then it increases for very lower $T$; however,
 the error obtained with the PLM with decimation is several times smaller  than the error estimated by the other methods 



 
 

     
     \section{Conclusions}
     \label{sec:conc}


Different statistical inference methods have been applied to the inverse problem of the XY model 
After a short review of techniques based on pseudo-likelihood and their formal generalization to the model we have tested their performances against data generated by means of Monte Carlo numerical simulations of known instances
with diluted, sparse, interactions 

The main outcome is that the best performances are obtained by means of the  pseudo-likelihood method combined with decimation  Putting to zero (i e , decimating) very weak bonds, this technique turns out to be very precise for  problems whose real underlying interaction network is sparse, i e , the number of couplings per variable does not scale with number of variables 
The PLM + decimation method is compared to the PLM + regularization method, with $\ell_2$ regularization and to a mean-field-based method  The behavior of the quality of the network reconstruction is analyzed by looking at the overall sorted couplings and at the single site couplings, comparing them with the real network, and at the true positive curves in all three approaches  In the PLM +decimation method, moreover, the identification of the number of decimated bonds at which the tilted pseudo-likelihood is maximum allows for a precise estimate of the total number of bonds  Concerning this technique, it is also shown that the network with the most likely number of bonds is also the one of least reconstruction error, where not only the prediction of the presence of a bond is estimated but also its value 

The behavior of the inference quality in temperature and in the size of data samples is also investigated, basically confirming the low $T$ behavior hinted by Nguyen and Berg \cite{Nguyen12b} for the Ising model  In temperature, in particular, the reconstruction error curve displays a minimum at a low temperature, close to the critical point in those cases in which a critical behavior occurs, and a sharp increase as temperature goes to zero  The decimation method, once again, appears to enhance this minimum of the reconstruction error of almost an order of magnitude with respect to other methods 
 
The techniques displayed and the results obtained in this work can be of use in any of the many systems whose theoretical representation is given by Eq  \eqref{eq:HXY} or Eq  \eqref{eq:h_im}, some of which are recalled in Sec  \ref{sec:model}  In particular, a possible application can be the field of light waves propagation through random media and the corresponding problem of the  reconstruction of an object seen through an opaque medium or a disordered optical fiber \cite{Vellekoop07,Vellekoop08a,Vellekoop08b, Popoff10a,Akbulut11,Popoff11,Yilmaz13,Riboli14} 

 	
Context 3: Publications of Kam W  Leong
Publications of Kam W  Leong :chronological alphabetical combined bibtex listing:
K W  Leong, Synthetic mast-cell granules as adjuvants to promote and polarize immunity in lymph nodes (2013) [PDF]
K W  Leong, Tuning Physical Properties of Nanocomplexes through Microfluidics-Assisted Confinement (2013) [PDF]
K W  Leong, Nucleic acid scavengers inhibit thrombosis without increasing bleeding (2013) [PDF]
K W  Leong, Nanotopography as modulator of human mesenchymal stem cell function (2013) [PDF]
K W  Leong, Efficacy of engineered FVIII-producing skeletal muscle enhanced by growth factor-releasing co-axial electrospun fibers (2013) [PDF]
Zhao, F  and Veldhuis, J  J  and Duan, Y  J  and Yang, Y  and Christoforou, N  and Ma, T  and Leong, K  W , Low Oxygen Tension and Synthetic Nanogratings Improve the Uniformity and Stemness of Human Mesenchymal Stem Cell Layer, Molecular Therapy, vol  18 no  5 (2010), pp  1010-1018 [abs]
Kadiyala, I  and Loo, Y  H  and Roy, K  and Rice, J  and Leong, K  W , Transport of chitosan-DNA nanoparticles in human intestinal M-cell model versus normal intestinal enterocytes, European Journal of Pharmaceutical Sciences, vol  39 no  1-3 (2010), pp  103-109 [abs]
Wang, Y  and Quek, C  H  and Leong, K W  and Fang, J , Synthesis and Cytotoxity of Luminescent InP Quantum Dots, MRS Symposium Proceeding, vol  1241E (2010)
Jiang, X  and Zheng, Y  and Chen, H  H  and Leong, K  W  and Wang, T  H  and Mao, H  Q , Dual-Sensitive Micellar Nanoparticles Regulate DNA Unpacking and Enhance Gene-Delivery Efficiency, Adv Mater (2010)
Ho, Y  P  and Leong, K  W , Quantum dot-based theranostics, Nanoscale, vol  2 no  1 (2010), pp  60-68 [PDF] [abs]
Phua, K  and Leong, K  W , Microscale oral delivery devices incorporating nanoparticles, Nanomedicine, vol  5 no  2 (2010), pp  161-163
Grigsby, C  L  and Leong, K  W , Balancing protection and release of DNA: tools to address a bottleneck of non-viral gene delivery, Journal of the Royal Society Interface, vol  7 (2010), pp  S67-S82 [abs]
Chalut, K  J  and Kulangara, K  and Giacomelli, M  G  and Wax, A  and Leong, K  W , Deformation of stem cell nuclei by nanotopographical cues, Soft Matter, vol  6 no  8 (2010), pp  1675-1681 [abs]
Chen, S  and Jones, J  A  and Xu, Y  and Low, H  Y  and Anderson, J  M  and Leong, K  W , Characterization of topographical effects on macrophage behavior in a foreign body response model, Biomaterials, vol  31 no  13 (2010), pp  3479-91 [PDF] [abs]
Yim, E  K  F  and Darling, E  M  and Kulangara, K  and Guilak, F  and Leong, K  W , Nanotopography-induced changes in focal adhesions, cytoskeletal organization, and mechanical properties of human mesenchymal stem cells, Biomaterials, vol  31 no  6 (2010), pp  1299-1306 [PDF] [abs]
Yow, S  Z  and Quek, C  H  and Yim, E  K  F  and Lim, C  T  and Leong, K  W , Collagen-based fibrous scaffold for spatial organization of encapsulated and seeded human mesenchymal stem cells, Biomaterials, vol  30 no  6 (2009), pp  1133-1142 [abs]
Kunder, C  A  and John, A  L  S  and Li, G  J  and Leong, K  W  and Berwin, B  and Staats, H  F  and Abraham, S  N , Mast cell-derived particles deliver peripheral signals to remote lymph nodes, Journal of Experimental Medicine, vol  206 no  11 (2009), pp  2455-2467 [abs]
Ho, Y P  and Chen, H H  and Leong, K W  and Wang, T H , Combining QD-FRET and microfluidics to monitor DNA nanocomplex self-assembly in real-time, J Vis Exp (2009), pp  1432
Kulangara, K  and Leong, K  W , Substrate topography shapes cell function, Soft Matter, vol  5 no  21 (2009), pp  4072-4076 [abs]
Chakraborty, S  and Liao, I  C  and Adler, A  and Leong, K  W , Electrohydrodynamics: A facile technique to fabricate drug delivery systems, Advanced Drug Delivery Reviews, vol  61 no  12 (2009), pp  1043-1054 [abs]
Oney, S  and Lam, R  T  S  and Bompiani, K  M  and Blake, C  M  and Quick, G  and Heidel, J  D  and Liu, J  Y  C  and Mack, B  C  and Davis, M  E  and Leong, K  W  and Sullenger, B  A , Development of universal antidotes to control aptamer activity, Nature Medicine, vol  15 no  10 (2009), pp  1224-1228 [PDF] [abs]
Chen, H  H  and Ho, Y  P  and Jiang, X  and Mao, H  Q  and Wang, T  H  and Leong, K  W , Simultaneous non-invasive analysis of DNA condensation and stability by two-step QD-FRET, Nano Today, vol  4 no  2 (2009), pp  125-134 [PDF] [abs]
Ho, Y  P  and Chen, H  H  and Leong, K  W  and Wang, T  H , The convergence of quantum-dot-mediated fluorescence resonance energy transfer and microfluidics for monitoring DNA polyplex self-assembly in real time, Nanotechnology, vol  20 no  9 (2009), pp  - [abs]
Liao, I  C  and Chen, S  L  and Liu, J  B  and Leong, K  W , Sustained viral gene delivery through core-shell fibers, Journal of Controlled Release, vol  139 no  1 (2009), pp  48-55 [abs]
Lou, Y  L  and Peng, Y  S  and Chen, B  H  and Wang, L  F  and Leong, K  W , Poly(ethylene imine)-g-chitosan using EX-810 as a spacer for nonviral gene delivery vectors, Journal of Biomedical Materials Research Part A, vol  88A no  4 (2009), pp  1058-1068 [abs]
Chew, S  Y  and Mi, R  and Hoke, A  and Leong, K  W , The effect of the alignment of electrospun fibrous scaffolds on Schwann cell maturation, Biomaterials, vol  29 no  6 (2008), pp  653-61 [abs]
Chen, H  H  and Ho, Y  P  and Jiang, X  and Mao, H  Q  and Wang, T  H  and Leong, K  W , Quantitative comparison of intracellular unpacking kinetics of polyplexes by a model constructed from quantum Dot-FRET, Molecular Therapy, vol  16 no  2 (2008), pp  324-332 [abs]
Chan, B  P  and Leong, K  W , Scaffolding in tissue engineering: general approaches and tissue-specific considerations, European Spine Journal, vol  17 (2008), pp  S467-S479 [abs]
Tsurushima, H  and Yuan, X  and Dillehay, L  E  and Leong, K  W , Radiation-inducible caspase-8 gene therapy for malignant brain tumors, International Journal of Radiation Oncology Biology Physics, vol  71 no  2 (2008), pp  517-525 [abs]
Bowman, K  and Sarkar, R  and Raut, S  and Leong, K  W , Gene transfer to hemophilia A mice via oral delivery of FVIII-chitosan nanoparticles, Journal of Controlled Release, vol  132 no  3 (2008), pp  252-259 [abs]
Choi, J  S  and Leong, K  W  and Yoo, H  S , In vivo wound healing of diabetic ulcers using electrospun nanofibers immobilized with human epidermal growth factor (EGF), Biomaterials, vol  29 no  5 (2008), pp  587-96 [abs]
Liao, I  C  and Liu, J  B  and Bursac, N  and Leong, K  W , Effect of Electromechanical Stimulation on the Maturation of Myotubes on Aligned Electrospun Fibers, Cellular and Molecular Bioengineering, vol  1 no  2-3 (2008), pp  133-145 [abs]
Prow, T  W  and Bhutto, I  and Kim, S  Y  and Grebe, R  and Merges, C  and McLeod, D  S  and Uno, K  and Mennon, M  and Rodriguez, L  and Leong, K  and Lutty, G  A , Ocular nanoparticle toxicity and transfection of the retina and retinal pigment epithelium, Nanomedicine-Nanotechnology Biology and Medicine, vol



ground_truth: It outperforms mean-field methods and the PLM with $l_2$ regularization in terms of reconstruction error and true positive rate.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What are the titles of one of Kam W. Leong's publications in Journal of Controlled Release?

Read the following text and answer briefly.

Context 3:  4 no  4 (2008), pp  340-349 [abs]
Tan, S  C  W  and Pan, W  X  and Ma, G  and Cai, N  and Leong, K  W  and Liao, K , Viscoelastic behaviour of human mesenchymal stem cells, Bmc Cell Biology, vol  9 (2008), pp  - [abs]
Chalut, K  J  and Chen, S  and Finan, J  D  and Giacomelli, M  G  and Guilak, F  and Leong, K  W  and Wax, A , Label-free, high-throughput measurements of dynamic changes in cell nuclei using angle-resolved low coherence interferometry, Biophysical Journal, vol  94 no  12 (2008), pp  4948-4956 [abs]
Haider, M  and Cappello, J  and Ghandehari, H  and Leong, K  W , In vitro chondrogenesis of mesenchymal stem cells in recombinant silk-elastinlike hydrogels, Pharmaceutical Research, vol  25 no  3 (2008), pp  692-699 [abs]
N  Bursac and Y  H  Loo and K  Leong and L  Tung, Novel anisotropic engineered cardiac tissues: Studies of electrical propagation, Biochemical And Biophysical Research Communications, vol  361 no  4 (October, 2007), pp  847 -- 853, ISSN 0006-291X [abs]
Chen, Beiyi and Dang, Jiyoung and Tan, Tuan Lin and Fang, Ning and Chen, Wei Ning and Leong, Kam W  and Chan, Vincent, Dynamics of smooth muscle cell deadhesion from thermosensitive hydroxybutyl chitosan, Biomaterials, vol  28 no  8 (2007), pp  1503 - 1514 [027] [abs]
Chen, B  and Dang, J  and Tan, T  L  and Fang, N  and Chen, W  N  and Leong, K  W  and Chan, V , Dynamics of smooth muscle cell deadhesion from thermosensitive hydroxybutyl chitosan, Biomaterials, vol  28 no  8 (2007), pp  1503-14 [abs]
Park, D  J  and Choi, J  H  and Leong, K  W  and Kwon, J  W  and Eun, H  S , Tissue-engineered bone formation with gene transfer and mesenchymal stem cells in a minimally invasive technique, Laryngoscope, vol  117 no  7 (2007), pp  1267-71 [abs]
Tsurushima, H  and Yuan, X  and Dillehay, L  E  and Leong, K  W , Radioresponsive tumor necrosis factor-related apoptosisinducing ligand (TRAIL) gene therapy for malignant brain tumors, Cancer Gene Therapy, vol  14 no  8 (2007), pp  706-716 [abs]
Chai, C  and Leong, K  W , Biomaterials approach to expand and direct differentiation of stem cells, Molecular Therapy, vol  15 no  3 (2007), pp  467-480 [abs]
Zhang, Y  and Chai, C  and Jiang, X  S  and Teoh, S  H  and Leong, K  W , Fibronectin immobilized by covalent conjugation or physical adsorption shows different bioactivity on aminated-PET, Materials Science & Engineering C-Biomimetic and Supramolecular Systems, vol  27 no  2 (2007), pp  213-219 [abs]
Song, R  J  and Liu, S  Q  and Leong, K  W , Effects of MIP-1 alpha, MIP-3 alpha, and MIP-3 beta on the induction of HIV Gag-specific immune response with DNA vaccines, Molecular Therapy, vol  15 no  5 (2007), pp  1007-1015 [abs]
Yim, E  K  F  and Liao, I  C  and Leong, K  W , Tissue compatibility of interfacial polyelectrolyte complexation fibrous scaffold: Evaluation of blood compatibility and biocompatibility, Tissue Engineering, vol  13 no  2 (2007), pp  423-433 [abs]
Sharma, B  and Williams, C  G  and Kim, T  K  and Sun, D  N  and Malik, A  and Khan, M  and Leong, K  and Elisseeff, J  H , Designing zonal organization into tissue-engineered cartilage, Tissue Engineering, vol  13 no  2 (2007), pp  405-414 [abs]
Chua, K  N  and Tang, Y  N  and Quek, C  H  and Ramakrishna, S  and Leong, K  W  and Mao, H  Q , A dual-functional fibrous scaffold enhances P450 activity of cultured primary rat hepatocytes, Acta Biomaterialia, vol  3 no  5 (2007), pp  643-650 [abs]
Chua, K  N  and Chai, C  and Lee, P  C  and Ramakrishna, S  and Leong, K  W  and Mao, H  Q , Functional nanofiber scaffolds with different spacers modulate adhesion and expansion of cryopreserved umbilical cord blood hematopoietic stem/progenitor cells, Experimental Hematology, vol  35 no  5 (2007), pp  771-781 [abs]
Yim, E  K  F  and Pang, S  W  and Leong, K  W , Synthetic nanostructures inducing differentiation of human mesenchymal stem cells into neuronal lineage, Experimental Cell Research, vol  313 no  9 (2007), pp  1820-1829 [abs]
Chew, S  Y  and Mi, R  F  and Hoke, A  and Leong, K  W , Aligned protein-polymer composite fibers enhance nerve regeneration: A potential tissue-engineering platform, Advanced Functional Materials, vol  17 no  8 (2007), pp  1288-1296 [abs]
Tsurushima, H  and Yuan, X  and Dillehay, L  E  and Leong, K  W , Radio-responsive gene therapy for malignant glioma cells without the radiosensitive promoter: Caspase-3 gene therapy combined with radiation, Cancer Letters, vol  246 no  1-2 (2007), pp  318-323 [abs]
Dang, J M  and Leong, K  W , Myogenic induction of aligned mesenchymal stem cell sheets by culture on thermally responsive electrospun nanofibers, Advanced Materials, vol  19 no  19 (2007), pp  2775-2779
Dai, H  and Jiang, X  and Tan, G  C  and Chen, Y  and Torbenson, M  and Leong, K  W  and Mao, H  Q , Chitosan-DNA nanoparticles delivered by intrabiliary infusion enhance liver-targeted gene delivery, International Journal of Nanomedicine, vol  1 no  4 (2006), pp  507-522 [abs]
Le Visage, C  and Kim, S  W  and Tateno, K  and Sieber, A  N  and Kostuik, J  P  and Leong, K  W , Interaction of human mesenchymal stem cells with disc cells - Changes in extracellular matrix biosynthesis, Spine, vol  31 no  18 (2006), pp  2036-2042
Ong, S  Y  and Dai, H  and Leong, K  W , Inducing hepatic differentiation of human mesenchymal stem cells in pellet culture, Biomaterials, vol  27 no  22 (2006), pp  4087-4097
Bright, C  and Park, Y  S  and Sieber, A  N  and Kostuik, J  P  and Leong, K  W , In vivo evaluation of plasmid DNA encoding OP-1 protein for spine fusion, Spine, vol  31 no  19 (2006), pp  2163-2172
Yim, E  K  and Wan, A  C  and Le Visage, C  and Liao, I  C  and Leong, K  W , Proliferation and differentiation of human mesenchymal stem cell encapsulated in polyelectrolyte complexation fibrous scaffold, Biomaterials, vol  27 no  36 (2006), pp  6111-22 [abs]
Luong-Van, E  and Grondahl, L  and Chua, K  N  and Leong, K  W  and Nurcombe, V  and Cool, S  M , Controlled release of heparin from poly(epsilon-caprolactone) electrospun fibers, Biomaterials, vol  27 no  9 (2006), pp  2042-2050
Dang, J  M  and Leong, K  W , Natural polymers for gene delivery and tissue engineering, Advanced Drug Delivery Reviews, vol  58 no  4 (2006), pp  487-499
Li, J  and Li, X  and Ni, X  P  and Wang, X  and Li, H  Z  and Leong, K  W , Self-assembled supramolecular hydrogels formed by biodegradable PEO-PHB-PEO triblock copolymers and alpha-cyclodextrin for controlled drug delivery, Biomaterials, vol  27 no  22 (2006), pp  4132-4140
Yim, E  K  F  and Wen, J  and Leong, K  W , Enhanced extracellular matrix production and differentiation of human embryonic germ cell derivatives in biodegradable poly(epsilon-caprolactone-co-ethyl ethylene phosphate) scaffold, Acta Biomaterialia, vol  2 no  4 (2006), pp  365-376
Chew, S  Y  and Hufnagel, T  C  and Lim, C  T  and Leong, K  W , Mechanical properties of single electrospun drug-encapsulated nanofibres, Nanotechnology, vol  17 no  15 (2006), pp  3880-3891
Zhang, Y  and Chai, C  and Jiang, X  S  and Teoh, S  H  and Leong, K  W , Co-culture of umbilical cord blood CD34(+) cells with human mesenchymal stem cells, Tissue Engineering, vol  12 no  8



ground_truth: Sustained viral gene delivery through core-shell fibers and Gene transfer to hemophilia A mice via oral delivery of FVIII-chitosan nanoparticles.