Matter-antimatter coexistence method for finite density QCD toward a solution of the sign problem

Toward the lattice QCD calculation at finite density, we propose "matter-antimatter coexistence method", where matter and anti-matter systems are prepared on two parallel ${\bf R}^4$-sheets in five-dimensional Euclidean space-time. We put a matter system $M$ with a chemical potential $\mu \in {\bf C}$ on a ${\bf R}^4$-sheet, and also put an anti-matter system $\bar M$ with $-\mu^*$ on the other ${\bf R}^4$-sheet shifted in the fifth direction. Between the gauge variables $U_\nu \equiv e^{iagA_\nu}$ in $M$ and $\tilde U_\nu \equiv e^{iag \tilde A_\nu}$ in $\bar M$, we introduce a correlation term with a real parameter $\lambda$. In one limit of $\lambda \rightarrow \infty$, a strong constraint $\tilde U_\nu(x)=U_\nu(x)$ is realized, and therefore the total fermionic determinant becomes real and non-negative, due to the cancellation of the phase factors in $M$ and $\bar M$, although this system resembles QCD with an isospin chemical potential. In another limit of $\lambda \rightarrow 0$, this system goes to two separated ordinary QCD systems with the chemical potential of $\mu$ and $-\mu^*$. For a given finite-volume lattice, if one takes an enough large value of $\lambda$, $\tilde U_\nu(x) \simeq U_\nu(x)$ is realized and phase cancellation approximately occurs between two fermionic determinants in $M$ and $\bar M$, which suppresses the sign problem and is expected to make the lattice calculation possible. For the obtained gauge configurations of the coexistence system, matter-side quantities are evaluated through their measurement only for the matter part $M$. The physical quantities in finite density QCD are expected to be estimated by the calculations with gradually decreasing $\lambda$ and the extrapolation to $\lambda=0$. We also consider more sophisticated improvement of this method using an irrelevant-type correlation.Comment: 4 page

A Max-Plus Model of Asynchronous Cellular Automata

This paper presents a new framework for asynchrony. This has its origins in our attempts to better harness the internal decision making process of cellular automata (CA). Thus, we show that a max-plus algebraic model of asynchrony arises naturally from the CA requirement that a cell receives the state of each neighbour before updating. The significant result is the existence of a bijective mapping between the asynchronous system and the synchronous system classically used to update cellular automata. Consequently, although the CA outputs look qualitatively different, when surveyed on "contours" of real time, the asynchronous CA replicates the synchronous CA. Moreover, this type of asynchrony is simple - it is characterised by the underlying network structure of the cells, and long-term behaviour is deterministic and periodic due to the linearity of max-plus algebra. The findings lead us to proffer max-plus algebra as: (i) a more accurate and efficient underlying timing mechanism for models of patterns seen in nature, and (ii) a foundation for promising extensions and applications.Comment: in Complex Systems (Complex Systems Publications Inc), Volume 23, Issue 4, 201

Real-time bladder volume monitoring by the application of a new implantable bladder volume sensor for a small animal model

AbstractAlthough real-time monitoring of bladder volume together with intravesical pressure can provide more information for understanding the functional changes of the urinary bladder, it still entails difficulties in the accurate prediction of real-time bladder volume in urodynamic studies with small animal models. We studied a new implantable bladder volume monitoring device with eight rats. During cystometry, microelectrodes prepared by the microelectromechanical systems process were placed symmetrically on both lateral walls of the bladder, and the expanded bladder volume was calculated. Immunohistological study was done after 1 week and after 4 weeks to evaluate the biocompatibility of the microelectrode. From the point that infused saline volume into the bladder was higher than 0.6mL, estimated bladder volume was statistically correlated with the volume of saline injected (p<0.01). Additionally, the microelectromechanical system microelectrodes used in this study showed reliable biocompatibility. Therefore, the device can be used to evaluate changes in bladder volume in studies with small animals, and it may help to provide more information about functional changes in the bladder in laboratory studies. Furthermore, owing to its biocompatibility, the device could be chronically implanted in conscious ambulating animals, thus allowing a novel longitudinal study to be performed for a specific purpose

A probabilistic approach for modeling and real-time filtering of freeway detector data

Traffic surveillance systems are a key component for providing information on traffic conditions and supporting traffic management functions. A large amount of data is currently collected from inductive loop detector systems in the form of three macroscopic traffic parameters (speed, volume and occupancy). Such information is vital to the successful implementation of transportation data warehouses and decision support systems. The quality of data is, however, affected by erroneous observations that result from malfunctioning or mis-calibration of detectors. The open literature shows that little effort has been made to establish procedures for screening traffic observations in real-time. This study presents a probabilistic approach for modeling and real-time screening of freeway traffic data. The study proposes a simple methodology to capture the probabilistic and dynamic relationships between the three traffic parameters using historical data collected from the I-4 corridor in Orlando, Florida. The developed models are then used to identify the probability that each traffic observation is partially or fully invalid

Matter-Antimatter Coexistence Method for Finite Density QCD

We propose a "matter-antimatter coexistence method" for finite-density lattice QCD, aiming at a possible solution of the sign problem. In this method, we consider matter and anti-matter systems on two parallel ${\bf R}^4$-sheets in five-dimensional Euclidean space-time. For the matter system $M$ with a chemical potential $\mu \in {\bf C}$ on a ${\bf R}^4$-sheet, we also prepare the anti-matter system $\bar M$ with $-\mu^*$ on the other ${\bf R}^4$-sheet shifted in the fifth direction. In the lattice QCD formalism, we introduce a correlation term between the gauge variables $U_\nu \equiv e^{iagA_\nu}$ in $M$ and $\tilde U_\nu \equiv e^{iag \tilde A_\nu}$ in $\bar M$, such as $S_\lambda \equiv \sum_{x,\nu} 2\lambda \{N_c-{\rm Re~tr} [U_\nu(x) \tilde U_\nu^\dagger(x)]\} \simeq \sum_x \frac{1}{2}\lambda a^2 \{A_\nu^a(x)-\tilde A_\nu^a(x)\}^2$ with a real parameter $\lambda$. In the limit of $\lambda \rightarrow \infty$, a strong constraint $\tilde U_\nu(x)=U_\nu(x)$ is realized, and the total fermionic determinant is real and non-negative. In the limit of $\lambda \rightarrow 0$, this system goes to two separated ordinary QCD systems with the chemical potential of $\mu$ and $-\mu^*$. On a finite-volume lattice, if one takes an enough large value of $\lambda$, $\tilde U_\nu(x) \simeq U_\nu(x)$ is realized and there occurs a phase cancellation approximately between two fermionic determinants in $M$ and $\bar M$, which is expected to suppress the sign problem and to make the lattice calculation possible. For the obtained gauge configurations of the coexistence system, matter-side quantities are evaluated through their measurement only for the matter part $M$. By the calculations with gradually decreasing $\lambda$ and their extrapolation to $\lambda=0$, physical quantities in finite density QCD are expected to be estimated.Comment: 6 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1705.0751

Finite-Size Effects on Return Interval Distributions for Weakest-Link-Scaling Systems

The Weibull distribution is a commonly used model for the strength of brittle materials and earthquake return intervals. Deviations from Weibull scaling, however, have been observed in earthquake return intervals and in the fracture strength of quasi-brittle materials. We investigate weakest-link scaling in finite-size systems and deviations of empirical return interval distributions from the Weibull distribution function. We use the ansatz that the survival probability function of a system with complex interactions among its units can be expressed as the product of the survival probability functions for an ensemble of representative volume elements (RVEs). We show that if the system comprises a finite number of RVEs, it obeys the $\kappa$-Weibull distribution. We conduct statistical analysis of experimental data and simulations that show good agreement with the $\kappa$-Weibull distribution. We show the following: (1) The weakest-link theory for finite-size systems involves the $\kappa$-Weibull distribution. (2) The power-law decline of the $\kappa$-Weibull upper tail can explain deviations from the Weibull scaling observed in return interval data. (3) The hazard rate function of the $\kappa$-Weibull distribution decreases linearly after a waiting time $\tau_c \propto n^{1/m}$, where $m$ is the Weibull modulus and $n$ is the system size in terms of representative volume elements. (4) The $\kappa$-Weibull provides competitive fits to the return interval distributions of seismic data and of avalanches in a fiber bundle model. In conclusion, using theoretical and statistical analysis of real and simulated data, we show that the $\kappa$-Weibull distribution is a useful model for extreme-event return intervals in finite-size systems.Comment: 33 pages, 11 figure