Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices

It has been shown in earlier works that for Q=0 and L a multiple of N, the ground state sector eigenspace of the superintegrable tau_2(t_q) model is highly degenerate and is generated by a quantum loop algebra L(sl_2). Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2 algebras. For Q not equal 0, we shall show here that the corresponding eigenspace of tau_2(t_q) is still highly degenerate, but splits into two spaces, each containing 2^{r-1} independent eigenvectors. The generators for the sl_2 subalgebras, and also for the quantum loop subalgebra, are given generalizing those in the Q=0 case. However, the Serre relations for the generators of the loop subalgebra are only proven for some states, tested on small systems and conjectured otherwise. Assuming their validity we construct the eigenvectors of the Q not equal 0 ground state sectors for the transfer matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages, uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added, improvements and minor corrections made, erratum to paper 2 included. Version 3: Small paragraph added in introductio

Eigenvectors in the Superintegrable Model I: sl_2 Generators

In order to calculate correlation functions of the chiral Potts model, one only needs to study the eigenvectors of the superintegrable model. Here we start this study by looking for eigenvectors of the transfer matrix of the periodic tau_2(t)model which commutes with the chiral Potts transfer matrix. We show that the degeneracy of the eigenspace of tau_2(t) in the Q=0 sector is 2^r, with r=(N-1)L/N when the size of the transfer matrix L is a multiple of N. We introduce chiral Potts model operators, different from the more commonly used generators of quantum group U-tilde_q(sl-hat(2)). From these we can form the generators of a loop algebra L(sl(2)). For this algebra, we then use the roots of the Drinfeld polynomial to give new explicit expressions for the generators representing the loop algebra as the direct sum of r copies of the simple algebra sl(2).Comment: LaTeX 2E document, 11 pages, 1 eps figure, using iopart.cls with graphicx and iopams packages. v2: Appended text to title, added acknowledgments and made several minor corrections v3: Added reference, eliminated ambiguity, corrected a few misprint

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-dependent correlation function of the quantum chain, a.k.a. the q-dependent diagonal susceptibility in the 2d Ising model, in great detail with very little computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references added and minor changes of style. vs3: Corrections made and reference adde

On τ(2)\tau^{(2)}-model in Chiral Potts Model and Cyclic Representation of Quantum Group Uq(sl2)U_q(sl_2)

We identify the precise relationship between the five-parameter $\tau^{(2)}$-family in the $N$-state chiral Potts model and XXZ chains with $U_q (sl_2)$-cyclic representation. By studying the Yang-Baxter relation of the six-vertex model, we discover an one-parameter family of $L$-operators in terms of the quantum group $U_q (sl_2)$. When $N$ is odd, the $N$-state $\tau^{(2)}$-model can be regarded as the XXZ chain of $U_{\sf q} (sl_2)$ cyclic representations with ${\sf q}^N=1$. The symmetry algebra of the $\tau^{(2)}$-model is described by the quantum affine algebra $U_{\sf q} (\hat{sl}_2)$ via the canonical representation. In general for an arbitrary $N$, we show that the XXZ chain with a $U_q (sl_2)$-cyclic representation for $q^{2N}=1$ is equivalent to two copies of the same $N$-state $\tau^{(2)}$-model.Comment: Latex 11 pages; Typos corrected, Minor changes for clearer presentation, References added and updated-Journal versio

A Three-dimensional Printed Low-cost Anterior Shoulder Dislocation Model for Ultrasound-guided Injection Training.

Anterior shoulder dislocations are the most common, large joint dislocations that present to the emergency department (ED). Numerous studies support the use of intraarticular local anesthetic injections for the safe, effective, and time-saving reduction of these dislocations. Simulation training is an alternative and effective method for training compared to bedside learning. There are no commercially available ultrasound-compatible shoulder dislocation models. We utilized a three-dimensional (3D) printer to print a model that allows the visualization of the ultrasound anatomy (sonoanatomy) of an anterior shoulder dislocation. We utilized an open-source file of a shoulder, available from embodi3D® (Bellevue, WA, US). After approximating the relative orientation of the humerus to the glenoid fossa in an anterior dislocation, the humerus and scapula model was printed with an Ultimaker-2 Extended+ 3D® (Ultimaker, Cambridge, MA, US) printer using polylactic acid filaments. A 3D model of the external shoulder anatomy of a live human model was then created using Structure Sensor®(Occipital, San Francisco, CA, US), a 3D scanner. We aligned the printed dislocation model of the humerus and scapula within the resultant external shoulder mold. A pourable ballistics gel solution was used to create the final shoulder phantom. The use of simulation in medicine is widespread and growing, given the restrictions on work hours and a renewed focus on patient safety. The adage of see one, do one, teach one is being replaced by deliberate practice. Simulation allows such training to occur in a safe teaching environment. The ballistic gel and polylactic acid structure effectively reproduced the sonoanatomy of an anterior shoulder dislocation. The 3D printed model was effective for practicing an in-plane ultrasound-guided intraarticular joint injection. 3D printing is effective in producing a low-cost, ultrasound-capable model simulating an anterior shoulder dislocation. Future research will determine whether provider confidence and the use of intraarticular anesthesia for the management of shoulder dislocations will improve after utilizing this model

Impact of Seismic Risk on Lifetime Property Values

This report presents a methodology for establishing the uncertain net asset value, NAV, of a real-estate investment opportunity considering both market risk and seismic risk for the property. It also presents a decision-making procedure to assist in making real-estate investment choices under conditions of uncertainty and risk-aversion. It is shown that that market risk, as measured by the coefficient of variation of NAV, is at least 0.2 and may exceed 1.0. In a situation of such high uncertainty, where potential gains and losses are large relative to a decision-maker's risk tolerance, it is appropriate to adopt a decision-analysis approach to real-estate investment decision-making. A simple equation for doing so is presented. The decision-analysis approach uses the certainty equivalent, CE, as opposed to NAV as the basis for investment decision-making. That is, when faced with multiple investment alternatives, one should choose the alternative that maximizes CE. It is shown that CE is less than the expected value of NAV by an amount proportional to the variance of NAV and the inverse of the decision-maker's risk tolerance, [rho]. The procedure for establishing NAV and CE is illustrated in parallel demonstrations by CUREE and Kajima research teams. The CUREE demonstration is performed using a real 1960s-era hotel building in Van Nuys, California. The building, a 7-story non-ductile reinforced-concrete moment-frame building, is analyzed using the assembly-based vulnerability (ABV) method, developed in Phase III of the CUREE-Kajima Joint Research Program. The building is analyzed three ways: in its condition prior to the 1994 Northridge Earthquake, with a hypothetical shearwall upgrade, and with earthquake insurance. This is the first application of ABV to a real building, and the first time ABV has incorporated stochastic structural analyses that consider uncertainties in the mass, damping, and force-deformation behavior of the structure, along with uncertainties in ground motion, component damageability, and repair costs. New fragility functions are developed for the reinforced concrete flexural members using published laboratory test data, and new unit repair costs for these components are developed by a professional construction cost estimator. Four investment alternatives are considered: do not buy; buy; buy and retrofit; and buy and insure. It is found that the best alternative for most reasonable values of discount rate, risk tolerance, and market risk is to buy and leave the building as-is. However, risk tolerance and market risk (variability of income) both materially affect the decision. That is, for certain ranges of each parameter, the best investment alternative changes. This indicates that expected-value decision-making is inappropriate for some decision-makers and investment opportunities. It is also found that the majority of the economic seismic risk results from shaking of S[subscript a] < 0.3g, i.e., shaking with return periods on the order of 50 to 100 yr that cause primarily architectural damage, rather than from the strong, rare events of which common probable maximum loss (PML) measurements are indicative. The Kajima demonstration is performed using three Tokyo buildings. A nine-story, steel-reinforced-concrete building built in 1961 is analyzed as two designs: as-is, and with a steel-braced-frame structural upgrade. The third building is 29-story, 1999 steel-frame structure. The three buildings are intended to meet collapse-prevention, life-safety, and operational performance levels, respectively, in shaking with 10%exceedance probability in 50 years. The buildings are assessed using levels 2 and 3 of Kajima's three-level analysis methodology. These are semi-assembly based approaches, which subdivide a building into categories of components, estimate the loss of these component categories for given ground motions, and combine the losses for the entire building. The two methods are used to estimate annualized losses and to create curves that relate loss to exceedance probability. The results are incorporated in the input to a sophisticated program developed by the Kajima Corporation, called Kajima D, which forecasts cash flows for office, retail, and residential projects for purposes of property screening, due diligence, negotiation, financial structuring, and strategic planning. The result is an estimate of NAV for each building. A parametric study of CE for each building is presented, along with a simplified model for calculating CE as a function of mean NAV and coefficient of variation of NAV. The equation agrees with that developed in parallel by the CUREE team. Both the CUREE and Kajima teams collaborated with a number of real-estate investors to understand their seismic risk-management practices, and to formulate and to assess the viability of the proposed decision-making methodologies. Investors were interviewed to elicit their risk-tolerance, r, using scripts developed and presented here in English and Japanese. Results of 10 such interviews are presented, which show that a strong relationship exists between a decision-maker's annual revenue, R, and his or her risk tolerance, [rho is approximately equal to] 0.0075R[superscript 1.34]. The interviews show that earthquake risk is a marginal consideration in current investment practice. Probable maximum loss (PML) is the only earthquake risk parameter these investors consider, and they typically do not use seismic risk at all in their financial analysis of an investment opportunity. For competitive reasons, a public investor interviewed here would not wish to account for seismic risk in his financial analysis unless rating agencies required him to do so or such consideration otherwise became standard practice. However, in cases where seismic risk is high enough to significantly reduce return, a private investor expressed the desire to account for seismic risk via expected annualized loss (EAL) if it were inexpensive to do so, i.e., if the cost of calculating the EAL were not substantially greater than that of PML alone. The study results point to a number of interesting opportunities for future research, namely: improve the market-risk stochastic model, including comparison of actual long-term income with initial income projections; improve the risk-attitude interview; account for uncertainties in repair method and in the relationship between repair cost and loss; relate the damage state of structural elements with points on the force-deformation relationship; examine simpler dynamic analysis as a means to estimate vulnerability; examine the relationship between simplified engineering demand parameters and performance; enhance category-based vulnerability functions by compiling a library of building-specific ones; and work with lenders and real-estate industry analysts to determine the conditions under which seismic risk should be reflected in investors' financial analyses

Factorized finite-size Ising model spin matrix elements from Separation of Variables

Using the Sklyanin-Kharchev-Lebedev method of Separation of Variables adapted to the cyclic Baxter--Bazhanov--Stroganov or $\tau^{(2)}$-model, we derive factorized formulae for general finite-size Ising model spin matrix elements, proving a recent conjecture by Bugrij and Lisovyy

Structural studies of glucose-6-phosphate and NADP+ binding to human glucose-6-phosphate dehydrogenase

Human glucose-6-phosphate dehydrogenase (G6PD) is NADP(+)-dependent and catalyses the first and rate-limiting step of the pentose phosphate shunt. Binary complexes of the human deletion mutant, DeltaG6PD, with glucose-6-phosphate and NADP(+) have been crystallized and their structures solved to 2.9 and 2.5 A, respectively. The structures are compared with the previously determined structure of the Canton variant of human G6PD (G6PD(Canton)) in which NADP(+) is bound at the structural site. Substrate binding in DeltaG6PD is shown to be very similar to that described previously in Leuconostoc mesenteroides G6PD. NADP(+) binding at the coenzyme site is seen to be comparable to NADP(+) binding in L. mesenteroides G6PD, although some differences arise as a result of sequence changes. The tetramer interface varies slightly among the human G6PD complexes, suggesting flexibility in the predominantly hydrophilic dimer-dimer interactions. In both complexes, Pro172 of the conserved peptide EKPxG is in the cis conformation; it is seen to be crucial for close approach of the substrate and coenzyme during the enzymatic reaction. Structural NADP(+) binds in a very similar way in the DeltaG6PD-NADP(+) complex and in G6PD(Canton), while in the substrate complex the structural NADP(+) has low occupancy and the C-terminal tail at the structural NADP(+) site is disordered. The implications of possible interaction between the structural NADP(+) and G6P are considered.published_or_final_versio