5,387 research outputs found
Bayesian Updating of Nonlinear Model Predictions using Markov Chain Monte Carlo Simulation
The usual practice in system identification is to use system
data to identify one model from a set of possible models and
then to use this model for predicting system behavior. In contrast,
the present robust predictive approach rigorously combines
the predictions of all the possible models, appropriately weighted
by their updated probabilities based on the data. This Bayesian
system identification approach is applied to update the robust reliability
of a dynamical system based on its measured response
time histories. A Markov chain simulation method based on the
Metropolis-Hastings algorithm and an adaptive scheme is proposed
to evaluate the robust reliability integrals. An example for
updating the reliability of a Duffing oscillator is given to illustrate
the proposed method
Duality and Symmetry in Chiral Potts Model
We discover an Ising-type duality in the general -state chiral Potts
model, which is the Kramers-Wannier duality of planar Ising model when N=2.
This duality relates the spectrum and eigenvectors of one chiral Potts model at
a low temperature (of small ) to those of another chiral Potts model at a
high temperature (of ). The -model and chiral Potts model
on the dual lattice are established alongside the dual chiral Potts models.
With the aid of this duality relation, we exact a precise relationship between
the Onsager-algebra symmetry of a homogeneous superintegrable chiral Potts
model and the -loop-algebra symmetry of its associated
spin- XXZ chain through the identification of their eigenstates.Comment: Latex 34 pages, 2 figures; Typos and misprints in Journal version are
corrected with minor changes in expression of some formula
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
On -model in Chiral Potts Model and Cyclic Representation of Quantum Group
We identify the precise relationship between the five-parameter
-family in the -state chiral Potts model and XXZ chains with
-cyclic representation. By studying the Yang-Baxter relation of the
six-vertex model, we discover an one-parameter family of -operators in terms
of the quantum group . When is odd, the -state
-model can be regarded as the XXZ chain of
cyclic representations with . The symmetry algebra of the
-model is described by the quantum affine algebra via the canonical representation. In general for an arbitrary
, we show that the XXZ chain with a -cyclic representation for
is equivalent to two copies of the same -state
-model.Comment: Latex 11 pages; Typos corrected, Minor changes for clearer
presentation, References added and updated-Journal versio
Hydration temperature rise and thermal stresses induced in segment-on-pier of prestressed concrete box girder bridge
The heat generation from chemical reactions of hardening concrete causes temperature rise and thermal expansion. When the concrete temperature eventually cools down to the ambient, thermal contraction would result. If the tendency of volume change and associated thermal movement are restrained, thermal stresses would be induced and this would lead to early thermal cracking. The issue of thermal cracking should be duly considered in mass concrete construction. Regarding concrete bridge construction, the piles, pile caps, bridge piers, crosshead girders, and bridge diaphragms are typical examples of mass concrete elements. A bridge project in real-life is selected for study in this paper, with focus on the segment-on-pier accommodating the diaphragm of prestressed concrete girder deck. The segment was instrumented to measure its actual early age temperature rise on site. Finite element simulation and analysis was conducted to evaluate the time variations of temperature distributions and thermal stresses induced in the bridge segment. The risk of thermal cracking can be indicated by the measurement and analysis results. The techniques employed in this study are useful for planning of temperature control measures in similar projects
Logarithmic perturbation theory for quasinormal modes
Logarithmic perturbation theory (LPT) is developed and applied to quasinormal
modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is
especially convenient because summation over a complete set of unperturbed
states is not required. Attention is paid to potentials with exponential tails,
and the example of a Poschl-Teller potential is briefly discussed. A numerical
method is developed that handles the exponentially large wavefunctions which
appear in dealing with QNMs.Comment: 24 pages, 4 Postscript figures, uses ioplppt.sty and epsfig.st
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 -model, we derive
factorized formulae for general finite-size Ising model spin matrix elements,
proving a recent conjecture by Bugrij and Lisovyy
De novo variants disturbing the transactivation capacity of POU3F3 cause a characteristic neurodevelopmental disorder
POU3F3, also referred to as Brain-1, is a well-known transcription factor involved in the development of the central nervous system, but it has not previously been associated with a neurodevelopmental disorder. Here, we report the identification of 19 individuals with heterozygous POU3F3 disruptions, most of which are de novo variants. All individuals had developmental delays and/or intellectual disability and impairments in speech and language skills. Thirteen individuals had characteristic low-set, prominent, and/or cupped ears. Brain abnormalities were observed in seven of eleven MRI reports. POU3F3 is an intronless gene, insensitive to nonsense-mediated decay, and 13 individuals carried protein-truncating variants. All truncating variants that we tested in cellular models led to aberrant subcellular localization of the encoded protein. Luciferase assays demonstrated negative effects of these alleles on transcriptional activation of a reporter with a FOXP2-derived binding motif. In addition to the loss-of-function variants, five individuals had missense variants that clustered at specific positions within the functional domains, and one small in-frame deletion was identified. Two missense variants showed reduced transactivation capacity in our assays, whereas one variant displayed gain-of-function effects, suggesting a distinct pathophysiological mechanism. In bioluminescence resonance energy transfer (BRET) interaction assays, all the truncated POU3F3 versions that we tested had significantly impaired dimerization capacities, whereas all missense variants showed unaffected dimerization with wild-type POU3F3. Taken together, our identification and functional cell-based analyses of pathogenic variants in POU3F3, coupled with a clinical characterization, implicate disruptions of this gene in a characteristic neurodevelopmental disorder
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