On the duality relation for correlation functions of the Potts model

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

Preliminary Observations on the Effects In Vivo and In Vitro of Low Dose Laser on the Epithelia of the Bladder, Trachea and Tongue of the Mouse

The effects of low dose CW laser were studied by in vivo and in vitro systems. The experimental tissues that were used included bladders, tracheas and tongues as experimental tissues. Buddings (round surface projections) from the transitional epithelium of bladder were frequently observed 3 days after laser treatment in both in vivo and in vitro systems. The trachea and tongue were less affected. In both the in vivo and in vitro systems, some epithelial cells of the trachea showed decreased microvilli and cilia 3 days after treatment whereas the epithelial cells of the tongue revealed no response to laser treatment in both systems. Low dose laser, however, appeared to promote the rate of healing of experimental tongue ulcer: healing was about 1 day earlier in the laser treated than non-treated animals and vessel infiltration and epithelialization were detected earlier in the treated

Stimulation of Collagen Formation in the Intestinal Anastomosis by Low Dose He-Ne Laser

The effect of low dose He-Ne laser on the healing of intestinal anastomosis was studied in the albino rat. A small piece of jejunum was removed from each rat and the ends sutured back with a simple interrupted pattern. In the experimental animal, the anastomosis was Irradiated through an optic fiber with a He-Ne laser (1 mW) for 15 minutes whereas in the control animal, the anastomosis was not irradiated. The differences between the two groups were compared by histology, transmission electron microscopy, scanning electron microscopy and autoradiography 3 and 7 days after operation. The laser treated experimental animals demonstrated thicker collagen fibers and an increased quantity of collagen at the junction of the anastomosis compared to control animals. Increased uptake of labelled proline was also evident in the laser treated animals. These observations all point to a possible enhancement of collagen synthesis triggered by laser irradiation

Enhancing heart disease prediction using a self-attention-based transformer model

Cardiovascular diseases (CVDs) continue to be the leading cause of more than 17 million mortalities worldwide. The early detection of heart failure with high accuracy is crucial for clinical trials and therapy. Patients will be categorized into various types of heart disease based on characteristics like blood pressure, cholesterol levels, heart rate, and other characteristics. With the use of an automatic system, we can provide early diagnoses for those who are prone to heart failure by analyzing their characteristics. In this work, we deploy a novel self-attention-based transformer model, that combines self-attention mechanisms and transformer networks to predict CVD risk. The self-attention layers capture contextual information and generate representations that effectively model complex patterns in the data. Self-attention mechanisms provide interpretability by giving each component of the input sequence a certain amount of attention weight. This includes adjusting the input and output layers, incorporating more layers, and modifying the attention processes to collect relevant information. This also makes it possible for physicians to comprehend which features of the data contributed to the model's predictions. The proposed model is tested on the Cleveland dataset, a benchmark dataset of the University of California Irvine (UCI) machine learning (ML) repository. Comparing the proposed model to several baseline approaches, we achieved the highest accuracy of 96.51%. Furthermore, the outcomes of our experiments demonstrate that the prediction rate of our model is higher than that of other cutting-edge approaches used for heart disease prediction

Responses of Astrocytes in Culture After Low Dose Laser Irradiation

The effect of Helium-Neon low dose laser on astrocytes was investigated in cultures of isolated astrocytes from albino neonatal rats. The laser appeared to inhibit the growth of astrocytes as exemplified by the smaller sizes of the cells and the decreased leucine uptake in each cell after treatment. Temporary decrease in the number of mitoses was also observed, but this trend was reversed soon after. Electron microscopic studies revealed an increase in buddings from cell bodies and processes (branches) after irradiation

Quasinormal Modes of Dirty Black Holes

Quasinormal mode (QNM) gravitational radiation from black holes is expected to be observed in a few years. A perturbative formula is derived for the shifts in both the real and the imaginary part of the QNM frequencies away from those of an idealized isolated black hole. The formulation provides a tool for understanding how the astrophysical environment surrounding a black hole, e.g., a massive accretion disk, affects the QNM spectrum of gravitational waves. We show, in a simple model, that the perturbed QNM spectrum can have interesting features.Comment: 4 pages. Published in PR

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

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

Perturbative Approach to the Quasinormal Modes of Dirty Black Holes

Using a recently developed perturbation theory for uasinormal modes (QNM's), we evaluate the shifts in the real and imaginary parts of the QNM frequencies due to a quasi-static perturbation of the black hole spacetime. We show the perturbed QNM spectrum of a black hole can have interesting features using a simple model based on the scalar wave equation.Comment: Published in PR