PLUTO plus : Near-Complete Modeling of Affine Transformations for Parallelism and Locality

Affine transformations have proven to be very powerful for loop restructuring due to their ability to model a very wide range of transformations. A single multi-dimensional affine function can represent a long and complex sequence of simpler transformations. Existing affine transformation frameworks like the Pluto algorithm, that include a cost function for modern multicore architectures where coarse-grained parallelism and locality are crucial, consider only a sub-space of transformations to avoid a combinatorial explosion in finding the transformations. The ensuing practical tradeoffs lead to the exclusion of certain useful transformations, in particular, transformation compositions involving loop reversals and loop skewing by negative factors. In this paper, we propose an approach to address this limitation by modeling a much larger space of affine transformations in conjunction with the Pluto algorithm's cost function. We perform an experimental evaluation of both, the effect on compilation time, and performance of generated codes. The evaluation shows that our new framework, Pluto+, provides no degradation in performance in any of the Polybench benchmarks. For Lattice Boltzmann Method (LBM) codes with periodic boundary conditions, it provides a mean speedup of 1.33x over Pluto. We also show that Pluto+ does not increase compile times significantly. Experimental results on Polybench show that Pluto+ increases overall polyhedral source-to-source optimization time only by 15%. In cases where it improves execution time significantly, it increased polyhedral optimization time only by 2.04x.

Simple crystallizations of 4-manifolds

Minimal crystallizations of simply connected PL 4-manifolds are very natural objects. Many of their topological features are reflected in their combinatorial structure which, in addition, is preserved under the connected sum operation. We present a minimal crystallization of the standard PL K3 surface. In combination with known results this yields minimal crystallizations of all simply connected PL 4-manifolds of ``standard'' type, that is, all connected sums of CP2, S-2 x S-2, and the K3 surface. In particular, we obtain minimal crystallizations of a pair of homeomorphic but non-PL-homeomorphic 4-manifolds. In addition, we give an elementary proof that the minimal 8-vertex crystallization of CP2 is unique and its associated pseudotriangulation is related to the 9-vertex combinatorial triangulation of CP2 by the minimum of four edge contractions.

The cross-entropy method for blind multiuser detection

We consider the problem of blind multiuser detection. We adopt a Bayesian approach where unknown parameters are considered random and integrated out. Computing the maximum a posteriori estimate of the input data sequence requires solving a combinatorial optimization problem. We propose here to apply the Cross-Entropy method recently introduced by Rubinstein. The performance of cross-entropy is compared to Markov chain Monte Carlo. For similar Bit Error Rate performance, we demonstrate that Cross-Entropy outperforms a generic Markov chain Monte Carlo method in terms of operation time.

Dictadura, consenso o laissez faire en la transmisión eléctrica

Resumen: La dificultad con las redes radica en que, al ser de uso colectivo, generan conflictos sobre sus derechos de propiedad y obligaciones de pago. Por eso, existe una controversia sobre el más eficiente modo para su provisión, que se extiende desde el laissez faire hasta la dictadura. En el camino, se puede detener en algún tipo de consenso, basado en el diseño de mecanismos, adecuado para hacer revelar sus preferencias a los participantes. El proceso implica un intercambio de derechos entre los agentes para arribar a la asignación definitiva. Si, mediante una subasta, se obliga a los participantes a realizar ofertas de intercambio de derechos, los costos de transacción se reducen y la fluidez no puede sino ser mayor. Y ante una mayor fluidez en el intercambio, siempre será posible alcanzar una asignación más eficiente de esos derechos de propiedad. Para mostrar la conveniencia de esta alternativa, en este trabajo se presenta un modelo simplificado de diseño de mecanismos en donde se analiza la eficiencia asignativa de la regla propuesta.

Rigorous finite-time guarantees for optimization on continuous domains by simulated annealing

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

Los determinantes de la confianza del comprador online. Comparación con el caso de subasta

[ES] Los trabajos de investigación sobre comercio electrónico en Internet ocupan gran parte de la investigación de marketing, pero son pocos aún los que se han ocupado de estudiar el sistema de subasta. Ante las peculiares características de una compra online, transmitir confianza al consumidor en este contexto es uno de los retos más importantes y difíciles en comparación con la compra offline. No obstante, es de esperar que las señales generadoras de confianza sean diferentes en la compra online por subasta que en la compra online en otros sitios web.

Resale in Auctions with Financial Constraints

This paper analyzes auctions where bidders face nancial constraints that may force them to resell part of the property of the good (or subcontract part of a project) at a resale market. First we show that the ine¢ cient speculative equilibria of second- price auctions (Garratt and Tröger, 2006) generalizes to situations with partial resale where only the high value bidder is nancially constrained. However, when all players face nancial constraints the ine¢ cient speculative equilibria disappear. Therefore, for auctioning big facilities or contracts where all bidders are nancially constrained and there is a resale market, the second price auction remains a simple and appropriate mechanism to achieve an e¢ cient allocation.

Proceedings of the Eighteenth International Sea Turtle Symposium, 3-7 March 1998, Mazatlán, Sinaloa, Mexico

For the first time in its history, the International Symposium on Sea Turtle Biology and Conservation migrated to a site outside of the United States. Thus the Eighteenth edition was hosted by the Mazatlán Research Unit of the Instituto de Ciencias del Mar y Limnología of the Mexican National Autonomous University (UNAM) in Mazatlán, Sinaloa (Mexico) where it was held from 3-7, March, 1998. Above all, our symposium is prominent for its dynamism and enthusiasm in bringing together specialists from the world´s sea turtle populations. In an effort to extend this philosophy, and fully aware of how fast the interest in sea turtles has grown, the organizers paid special attention to bring together as many people as possible. With the tremendous efforts of the Travel Committee and coupled with a special interest by the Latin American region´s devotees, we managed to get 653 participants from 43 countries. The number of presentations increased significantly too, reaching a total of 265 papers, ranging from cutting-edge scientific reports based on highly sophisticated methods, to the experiences and successes of community-based and environmental education programs. A priority given by this symposium was the support and encouragement for the construction of "bridges" across cultural and discipline barriers. We found success in achieving a multinational dialogue among interest groups- scientists, resource managers, decision makers, ngo's, private industry. There was a broad representation of the broad interests that stretch across these sectors, yet everyone was able to listen and offer their own best contribution towards the central theme of the Symposium: the conservation of sea turtles and the diversity of marine and coastal environments in which they develop through their complicated and protracted life cycle. Our multidisciplinary approach is highly important at the present, finding ourselves at a cross roads of significant initiatives in the international arena of environmental law, where the conservation of sea turtles has a key role to play. Many, many people worked hard over the previous 12 months, to make the symposium a success. Our sincerest thanks to all of them: Program committee: Laura Sarti (chair), Ana Barragán, Rod Mast, Heather Kalb, Jim Spotilla, Richard Reina, Sheryan Epperly, Anna Bass, Steve Morreale, Milani Chaloupka, Robert Van Dam, Lew Ehrhart, J. Nichols, David Godfrey, Larry Herbst, René Márquez, Jack Musick, Peter Dutton, Patricia Huerta, Arturo Juárez, Debora Garcia, Carlos Suárez, German Ramírez, Raquel Briseño, Alberto Abreu; Registration and Secretary: Jane Provancha (chair), Lupita Polanco; Informatics: Germán Ramírez, Carlos Suárez; Cover art: Blas Nayar; Designs: Germán Ramírez, Raquel Briseño, Alberto Abreu. Auction: Rod Mast; Workshops and special meetings: Selina Heppell; Student prizes: Anders Rhodin; Resolutions committee: Juan Carlos Cantú; Local organizing committee: Raquel Briseño, Jane Abreu; Posters: Daniel Ríos and Jeffrey Semminoff; Travel committee: Karen Eckert (chair), Marydele Donnelly, Brendan Godley, Annette Broderick, Jack Frazier; Student travel: Francisco Silva and J. Nichols; Vendors: Tom McFarland and J. Nichols; Volunteer coordination: Richard Byles; Latin American Reunión: Angeles Cruz Morelos; Nominations committee: Randall Arauz, Colleen Coogan, Laura Sarti, Donna Shaver, Frank Paladino. Once again, Ed Drane worked his usual magic with the Treasury of the Symposium Significant financial contributions were generously provided by government agencies. SEMARNAP (Mexico´s Ministry of Environment, Natural Resources and Fisheries) through its central office, the Mazatlán Regional Fisheries Research Center (CRIP-Mazatlán) and the National Center for Education and Capacity Building for Sustainable Development (CECADESU) contributed to the logistics and covered the costs of auditoria and audiovisual equipment for the Symposium, teachers and their hotels for the Community Development and Environmental Education workshop in the 5th Latin American Sea Turtle Specialists; DIF (Dept of Family Affairs) provided free accomodation and food for the more than 100 participants in the Latin American Reunion. In this Reunion, the British Council-Mexico sponsored the workshop on the Project Cycle. The National Chamber of the Fisheries Industry (CANAINPES) kindly sponsored the Symposium´s coffee breaks. Personnel from the local Navy (Octave Zona Naval) provided invaluable aid in transport and logistics. The Scientific Coordination Office from UNAM (CICUNAM) and the Latin American Biology Network (RELAB) also provided funding. Our most sincere recognition to all of them. In the name of this Symposium´s compilers, I would like to also express our gratitude to Wayne Witzell, Technical Editor for his guidance and insights and to Jack Frazier for his help in translating and correcting the English of contributions from some non-native English speakers. Many thanks to Angel Fiscal and Tere Martin who helped with the typing in the last, last corrections and editions for these Proceedings. To all, from around the world, who generously helped make the 18th Symposium a huge success, shared their experiences and listened to ours, our deepest gratitude! (PDF contains 316 pages)

Proceedings fo the Seventeenth Annual Sea Turtle Symposium, 4-8 March 1997, Orlando, Florida, U.S.A.

The 17th Annual Sea Turtle Symposium was held at the Delta Orlando Resort in Orlando, Florida U.S.A. from March 4-8, 1997. The symposium was hosted by Florida Atlantic University, Mote Marine Laboratory, University of Central Florida, University of Florida, Florida Atlantic University and the Comité Nacional para la Conservación y Protección de las Totugas Marinas. The 17th was the largest symposium to date. A total of 720 participants registered, including sea turtle biologists, students, regulatory personnel, managers, and volunteers representing 38 countries. In addition to the United States, participants represented Australia, Austria, the Bahamas, Bonaire, Bermuda, Brazil, Canada, Colombia, Costa Rica, Croatia, Cuba, Cyprus, Dominican Republic, Ecuador, England, Guatemala, Greece, Honduras, India, Italy, Japan, Madagascar, Malaysia, Mexico, The Netherlands, Nicaragua, Peru, Philippines, Republic of Seychelles, Scotland, Spain, Sri Lanka, Switzerland, Taiwan, Turkey, Uruguay, and Venezuela. In addition to the 79 oral, 2 video, and 120 poster presentations, 3 workshops were offered: Selina Heppell (Duke University Marine Laboratory) provided “Population Modeling,” Mike Walsh and Sam Dover (Sea World-Orlando) conducted “Marine Turtle Veterinary Medicine” and “Conservation on Nesting Beaches” was offered by Blair Witherington and David Arnold (Florida Department of Environmental Protection). On the first evening, P.C.H. Pritchard delivered a thoughtful retrospect on Archie Carr that showed many sides of a complex man who studied and wrote about sea turtles. It was a presentation that none of us will forget. The members considered a number of resolutions at the Thursday business meeting and passed six. Five of these resolutions are presented in the Commentaries and Reviews section of Chelonian Conservation and Biology 2(3):442-444 (1997). The symposium was fortunate to have many fine presentations competing for the Archie Carr Best Student Presentations awards. The best oral presentation award went to Amanda Southwood (University of British Columbia) for “Heart rates and dive behavior of the leatherback sea turtle during the internesting interval.” The two runners-up were Richard Reina (Australian National University) for “Regulation of salt gland activity in Chelonia mydas” and Singo Minamikawa (Kyoto University) for “The influence that artificial specific gravity change gives to diving behavior of loggerhead turtles”. The winner of this year’s best poster competition was Mark Roberts (University of South Florida) for his poster entitled “Global population structure of green sea Turtles (Chelonia mydas) using microsatellite analysis of male mediated gene flow.” The two runners-up were Larisa Avens (University of North Carolina-Chapel Hill) for “Equilibrium responses to rotational displacements by hatchling sea turtles: maintaining a migratory heading in a turbulent ocean” and Annette Broderick (University of Glasgow) for “Female size, not length, is a correlate of reproductive output.” The symposium was very fortunate to receive a matching monetary and subscription gift from Anders J. G. Rhodin of the Chelonian Research Foundation. These enabled us to more adequately reward the fine work of students. The winners of the best paper and best poster awards received $400 plus a subscription to Chelonian Conservation and Biology. Each runner up received $100. The symposium owes a great debt to countless volunteers who helped make the meeting a success. Those volunteers include: Jamie Serino, Alan Bolton, and Karen Bjorndal, along with the UF students provided audio visual help, John Keinath chaired the student awards committee, Mike Salmon chaired the Program Commiteee, Sheryan Epperly and Joanne Braun compiled the Proceedings, Edwin Drane served as treasurer and provided much logistical help, Jane Provancha coordinated volunteers, Thelma Richardson conducted registration, Vicki Wiese coordinated food and beverage services, Jamie Serino and Erik Marin coordinated entertainment, Kenneth Dodd oversaw student travel awards, Traci Guynup, Tina Brown, Jerris Foote, Dan Hamilton, Richie Moretti, and Vicki Wiese served on the time and place committee, Blair Witherington created the trivia quiz, Tom McFarland donated the symposium logo, Deborah Crouse chaired the resolutions committee, Pamela Plotkin chaired the nominations committee, Sally Krebs, Susan Schenk, and Larry Wood conducted the silent auction, and Beverly and Tom McFarland coordinated all 26 vendors. Many individuals from outside the United States were able to attend the 17th Annual Sea Turtle Symposium thanks to the tireless work of Karen Eckert, Marydele Donnelly, and Jack Frazier in soliciting travel assistance for a number of international participants. We are indebted to those donating money to the internationals’ housing fund (Flo Vetter Memorial Fund, Marinelife Center of Juno Beach, Roger Mellgren, and Jane Provancha). We raise much of our money for international travel from the auction; thanks go to auctioneer Bob Shoop, who kept our auction fastpaced and entertaining, and made sure the bidding was high. The Annual Sea Turtle Symposium is unequaled in its emphasis on international participation. Through international participation we all learn a great deal more about the biology of sea turtles and the conservation issues that sea turtles face in distant waters. Additionally, those attending the symposium come away with a tremendous wealth of knowledge, professional contacts, and new friendships. The Annual Sea Turtle Symposium is a meeting in which pretenses are dropped, good science is presented, and friendly, open communication is the rule. The camaraderie that typifies these meetings ultimately translates into understanding and cooperation. These aspects, combined, have gone and will go a long way toward helping to protect marine turtles and toward aiding their recovery on a global scale. (PDF contains 342 pages)

The Linear Ordering Problem Revisited

The Linear Ordering Problem is a popular combinatorial optimisation problem which has been extensively addressed in the literature. However, in spite of its popularity, little is known about the characteristics of this problem. This paper studies a procedure to extract static information from an instance of the problem, and proposes a method to incorporate the obtained knowledge in order to improve the performance of local search-based algorithms. The procedure introduced identifies the positions where the indexes cannot generate local optima for the insert neighbourhood, and thus global optima solutions. This information is then used to propose a restricted insert neighbourhood that discards the insert operations which move indexes to positions where optimal solutions are not generated. In order to measure the efficiency of the proposed restricted insert neighbourhood system, two state-of-the-art algorithms for the LOP that include local search procedures have been modified. Conducted experiments confirm that the restricted versions of the algorithms outperform the classical designs systematically. The statistical test included in the experimentation reports significant differences in all the cases, which validates the efficiency of our proposal.

Extending Distance-based Ranking Models In Estimation of Distribution Algorithms

Recently, probability models on rankings have been proposed in the field of estimation of distribution algorithms in order to solve permutation-based combinatorial optimisation problems. Particularly, distance-based ranking models, such as Mallows and Generalized Mallows under the Kendall’s-t distance, have demonstrated their validity when solving this type of problems. Nevertheless, there are still many trends that deserve further study. In this paper, we extend the use of distance-based ranking models in the framework of EDAs by introducing new distance metrics such as Cayley and Ulam. In order to analyse the performance of the Mallows and Generalized Mallows EDAs under the Kendall, Cayley and Ulam distances, we run them on a benchmark of 120 instances from four well known permutation problems. The conducted experiments showed that there is not just one metric that performs the best in all the problems. However, the statistical test pointed out that Mallows-Ulam EDA is the most stable algorithm among the studied proposals.

The strategic behavior of rational novices

There is a growing amount of experimental evidence that suggests people often deviate from the predictions of game theory. Some scholars attempt to explain the observations by introducing errors into behavioral models. However, most of these modifications are situation dependent and do not generalize. A new theory, called the rational novice model, is introduced as an attempt to provide a general theory that takes account of erroneous behavior. The rational novice model is based on two central principals. The first is that people systematically make inaccurate guesses when they are evaluating their options in a game-like situation. The second is that people treat their decisions similar to a portfolio problem. As a result, non optimal actions in a game theoretic sense may be included in the rational novice strategy profile with positive weights.

The rational novice model can be divided into two parts: the behavioral model and the equilibrium concept. In a theoretical chapter, the mathematics of the behavioral model and the equilibrium concept are introduced. The existence of the equilibrium is established. In addition, the Nash equilibrium is shown to be a special case of the rational novice equilibrium. In another chapter, the rational novice model is applied to a voluntary contribution game. Numerical methods were used to obtain the solution. The model is estimated with data obtained from the Palfrey and Prisbrey experimental study of the voluntary contribution game. It is found that the rational novice model explains the data better than the Nash model. Although a formal statistical test was not used, pseudo R^2 analysis indicates that the rational novice model is better than a Probit model similar to the one used in the Palfrey and Prisbrey study.

The rational novice model is also applied to a first price sealed bid auction. Again, computing techniques were used to obtain a numerical solution. The data obtained from the Chen and Plott study were used to estimate the model. The rational novice model outperforms the CRRAM, the primary Nash model studied in the Chen and Plott study. However, the rational novice model is not the best amongst all models. A sophisticated rule-of-thumb, called the SOPAM, offers the best explanation of the data.

Analysis of a transcriptional network involving PU.1, Notch, and Gata3 in the lymphomyeloid lineage decision during early T-cell development

Hematopoiesis is a well-established system used to study developmental choices amongst cells with multiple lineage potentials, as well as the transcription factor network interactions that drive these developmental paths. Multipotent progenitors travel from the bone marrow to the thymus where T-cell development is initiated and these early T-cell precursors retain lineage plasticity even after initiating a T-cell program. The development of these early cells is driven by Notch signaling and the combinatorial expression of many transcription factors, several of which are also involved in the development of other cell lineages. The ETS family transcription factor PU.1 is involved in the development of progenitor, myeloid, and lymphoid cells, and can divert progenitor T-cells from the T-lineage to a myeloid lineage. This diversion of early T-cells by PU.1 can be blocked by Notch signaling. The PU.1 and Notch interaction creates a switch wherein PU.1 in the presence of Notch promotes T-cell identity and PU.1 in the absence of Notch signaling promotes a myeloid identity. Here we characterized an early T-cell cell line, Scid.adh.2c2, as a good model system for studying the myeloid vs. lymphoid developmental choice dependent on PU.1 and Notch signaling. We then used the Scid.adh.2c2 system to identify mechanisms mediating PU.1 and Notch signaling interactions during early T-cell development. We show that the mechanism by which Notch signaling is protecting pro-T cells is neither degradation nor modification of the PU.1 protein. Instead we give evidence that Notch signaling is blocking the PU.1-driven inhibition of a key set of T-regulatory genes including Myb, Tcf7, and Gata3. We show that the protection of Gata3 from PU.1-mediated inhibition, by Notch signaling and Myb, is important for retaining a T-lineage identity. We also discuss a PU.1-driven mechanism involving E-protein inhibition that leads to the inhibition of Notch target genes. This is mechanism may be used as a lockdown mechanism in pro-T-cells that have made the decision to divert to the myeloid pathway.

Descriptive set theory and the ergodic theory of countable groups

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C^*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.

Structural requirements for catalysis: studies on RTEM-1 β-lactamase

β-lactamases are a group of enzymes that confer resistance to penam and cephem antibiotics by hydrolysis of the β-lactam ring, thereby inactivating the antibiotic. Crystallographic and computer modeling studies of RTEM-1 β-lactamase have indicated that Asp 132, a strictly conserved residue among the class A β-lactamases, appears to be involved in substrate binding, catalysis, or both. To study the contribution of residue 132 to β-lactamase function, site saturation mutagenesis was used to generate mutants coding for all 20 amino acids at position 132. Phenotypic screening of all mutants indicated that position 132 is very sensitive to amino acid changes, with only N132C, N132D, N132E, and N132Q showing any appreciable activity. Kinetic analysis of three of these mutants showed increases in K_M, along with substantial decreases in k_(cat). Efforts to trap a stable acyl-enzyme intermediate were unsuccessfuL These results indicate that residue 132 is involved in substrate binding, as well as catalysis, and supports the involvement of this residue in acylation as suggested by Strynadka et al.

Crystallographic and computer modeling studies of RTEM-1 β-lactamase have indicated that Lys 73 and Glu 166, two strictly conserved residues among the class A β-lactamases, appear to be involved in substrate binding, catalysis, or both. To study the contribution of these residues to β-lactamase function, site saturation mutagenesis was used to generate mutants coding for all 20 amino acids at positions 73 and 166. Then all 400 possible combinations of mutants were created by combinatorial mutagenesis. The colonies harboring the mutants were screened for growth in the presence of ampicillin. The competent colonys' DNA were sequenced, and kinetic parameters investigated. It was found that lysine is essential at position 73, and that position 166 only tolerated fairly conservative changes (Aspartic acid, Histidine, and Tyrosine). These functional mutants exhibited decreased kcat's, but K_M was close to wild-type levels. The results of the combinatorial mutagenesis experiments indicate that Lysis absolutely required for activity at position 73; no mutation at residue 166 can compensate for loss of the long side chain amine. The active mutants found--K73K/E166D, K73KIE166H, and K73KIE166Y were studied by kinetic analysis. These results reaffirmed the function of residue 166 as important in catalysis, specifically deacylation.

The identity of the residue responsible for enhancing the active site serine (Ser 70) in RTEM-1 β-lactamase has been disputed for some time. Recently, analysis of a crystal structure of RTEM-1 β-lactamase with covalently bound intermediate was published, and it was suggested that Lys 73, a strictly conserved residue among the class A β-lactamases, was acting as a general base, activating Ser 70. For this to be possible, the pK_a of Lys 73 would have to be depressed significantly. In an attempt to assay the pK_a of Lys 73, the mutation K73C was made. This mutant protein can be reacted with 2-bromoethylamine, and activity is restored to near wild type levels. ^(15)N-2-bromoethylamine hydrobromide and ^(13)C-2-bromoethylamine hydrobromide were synthesized. Reacting these compounds with the K73C mutant gives stable isotopic enrichment at residue 73 in the form of aminoethylcysteine, a lysine homologue. The pK_a of an amine can be determined by NMR titration, following the change in chemical shift of either the ^(15)N-amine nuclei or adjacent Be nuclei as pH is changed. Unfortunately, low protein solubility, along with probable label scrambling in the Be experiment, did not permit direct observation of either the ^(15)N or ^(13)C signals. Indirect detection experiments were used to observe the protons bonded directly to the ^(13)C atoms. Two NMR signals were seen, and their chemical shift change with pH variation was noted. The peak which was determined to correspond to the aminoethylcysteine residue shifted from 3.2 ppm down to 2.8 ppm over a pH range of 6.6 to 12.5. The pK_a of the amine at position 73 was determined to be ~10. This indicates that residue 73 does not function as a general base in the acylation step of the reaction. However the experimental measurement takes place in the absence of substrate. Since the enzyme undergoes conformational changes upon substrate binding, the measured pK_a of the free enzyme may not correspond to the pK_a of the enzyme substrate complex.