Loss characteristics of commercial real estate loan portfolios

Basel capital accord ; Bank capital ; Risk management ; Real property

Time-Frequency Analysis of Systems with Changing Dynamic Properties

Time-frequency analysis methods transform a time series into a two-dimensional representation of frequency content with respect to time. The Fourier Transform identifies the frequency content of a signal (as a sum of weighted sinusoidal functions) but does not give useful information regarding changes in the character of the signal, as all temporal information is encoded in the phase of the transform. A time-frequency representation, by expressing frequency content at different sections of a record, allows for analysis of evolving signals. The time-frequency transformation most commonly encountered in seismology and civil engineering is a windowed Fourier Transform, or spectrogram; by comparing the frequency content of the first portion of a record with the last portion of the record, it is straightforward to identify the changes between the two segments. Extending this concept to a sliding window gives the spectrogram, where the Fourier transforms of successive portions of the record are assembled into a time-frequency representation of the signal. The spectrogram is subject to an inherent resolution limitation, in accordance with the uncertainty principle, that precludes a perfect representation of instantaneous frequency content. The wavelet transform was introduced to overcome some of the shortcomings of Fourier analysis, though wavelet methods are themselves unsuitable for many commonly encountered signals. The Wigner-Ville Distribution, and related refinements, represent a class of advanced time-frequency analysis tools that are distinguished from Fourier and wavelet methods by an increase in resolution in the time-frequency plane. I introduce several time-frequency representations and apply them to various synthetic signals as well as signals from instrumented buildings. vi For systems of interest to engineers, investigating the changing properties of a system is typically performed by analyzing vibration data from the system, rather than direct inspection of each component. Nonlinear elastic behavior in the forcedisplacement relationship can decrease the apparent natural frequencies of the system - these changes typically occur over fractions of a second in moderate to strong excitation and the system gradually recovers to pre-event levels. Structures can also suffer permanent damage (e.g., plastic deformation or fracture), permanently decreasing the observed natural frequencies as the system loses stiffness. Advanced time-frequency representations provide a set of exploratory tools for analyzing changing frequency content in a signal, which can then be correlated with damage patterns in a structure. Modern building instrumentation allows for an unprecedented investigation into the changing dynamic properties of structures: a framework for using time-frequency analysis methods for instantaneous system identification is discussed

Global Real Estate Markets - Cycles and Fundamentals

The correlations among international real estate markets are surprisingly high, given the degree to which they are segmented. While industrial, office and retail properties exist all around the world, they are not economic substitutes because of locational specificity. In addition, the broad securitization of real estate property companies has, until recently, lagged that of other types of companies. Never-the-less, international property returns move together in dramatic fashion. In this paper, we use eleven years of global property returns to explore the factors influencing this co-movement. We attribute a substantial amount of the correlation across world property markets to the effects of changes in GNP, suggesting that real estate is a bet on fundamental economic variables which are correlated across countries. A decomposition shows that a local production factor is more important in some countries than in others.

Results of Millikan Library Forced Vibration Testing

This report documents an investigation into the dynamic properties of Millikan Library under forced excitation. On July 10, 2002, we performed frequency sweeps from 1 Hz to 9.7 Hz in both the East-West (E-W) and North-South (N-S) directions using a roof level vibration generator. Natural frequencies were identified at 1.14 Hz (E-W fundamental mode), 1.67 Hz (N-S fundamental mode), 2.38 Hz (Torsional fundamental mode), 4.93 Hz (1st E-Wovertone), 6.57 Hz (1st Torsional overtone), 7.22 Hz (1st N-S overtone), and at 7.83 Hz (2nd E-Wovertone). The damping was estimated at 2.28% for the fundamental E-W mode and 2.39% for the N-S fundamental mode. On August 28, 2002, a modal analysis of each natural frequency was performed using the dense instrumentation network located in the building. For both the E-W and N-S fundamental modes, we observe a nearly linear increase in displacement with height, except at the ground floor which appears to act as a hinge. We observed little basement movement for the E-W mode, while in the N-S mode 30% of the roof displacement was due to basement rocking and translation. Both the E-W and N-S fundamental modes are best modeled by the first mode of a theoretical bending beam. The higher modes are more complex and not well represented by a simple structural system

Enhancing the trap of lady\u27s slippers: a new technique for discovering pollinators yields new data from Cypripedium parviflorum (Orchidaceae)

Approximately one-third of orchid species offer no reward to their floral visitors and instead trick them into pollination. Typically, these deceptive systems have low visitation and fruiting rates because pollinators can learn to avoid non-rewarding species. Consequently, pollination ecology studies in these species often require long hours in the field to witness relatively few floral visitations relative to rewarding plants. Cypripedium parviflorum is a food-deceptive orchid with a pouch-like trap that temporarily imprisons pollinators. To escape, pollinators exert pressure on the stigma which facilitates pollination and widens the escape holes located near each anther. This study reports the use of a ribbon and clip to block the escape passageway of this species in order to retain and observe visiting insects. The device was tested in a large population and was shown to increase significantly the probability of observing floral visitors by nearly three-fold. Ten species of hymenopteran visitors in the families Andrenidae, Apidae, Halictidae and Megachilidae were observed, with two female Adrena tridens and one male Adrena perplexa successfully removing pollen. Insect visitation to the orchids occurred during the first half of the flowering period and was significantly associated with warm, clear days. (C) 2009 The Linnean Society of London, Botanical Journal of the Linnean Society, 2009, 160, 1-10

Variations in the dynamic properties of structures: the Wigner-Ville distribution

The Wigner-Ville Distribution (WVD) is a promising method for analyzing frequency variations in seismic signals, including those of interest for structural monitoring. Nonlinearities in the force displacement relationship will temporarily decrease the apparent natural frequencies of structures during strong to moderate excitation, and earthquake damage can permanently change building stiffnesses. A Fourier Transform of a building record contains information regarding frequency content, but it can not resolve the exact onset of changes in natural frequency – all temporal resolution is contained in the phase of the transform. The spectrogram is better able to resolve temporal evolution of frequency content, but has a trade-off in time resolution versus frequency resolution in accordance with the uncertainty principle. Time-frequency transformations such as the WVD allow for instantaneous frequency estimation at each data point, for a typical temporal resolution of fractions of a second. We develop a mathematical foundation for analyzing the evolution of frequency content in a signal, and apply these techniques to synthetic records from linear and nonlinear FEM analysis (including plastic rotation and weld fractures). Our analysis techniques are then applied to earthquake records from damaged buildings

The Observed Wander of the Natural Frequencies in a Structure

The Southern California Seismic Network (scsn) has recently installed seismic stations in two buildings on the Caltech campus (Millikan Library and the Broad Center). Continuous real-time accelerometer data from these structures are now freely available to the community. This dataset provides a new opportunity to observe, and better understand, the variances in the primary dynamic property of a building system, its natural frequencies. Historical data (triggered strong-motion records, ambient and forced vibration tests) from the well-studied Millikan Library show dramatic decreases in natural frequencies, attributed mainly to moderately large local earthquakes. The current forced vibration east–west fundamental frequency is 22% lower than that originally measured in 1968. Analysis of the new continuous data stream allows the examination of other previously unrecognized sources of measurable change in the fundamental frequencies, such as weather (wind, rain, and temperature), as well as nonlinear building vibrations from small local and moderate regional earthquakes. Understanding these nonlinear shifts is one of the long-term goals of real-time building instrumentation and is critical if these systems are to be used as a postearthquake damage assessment tool