We consider the ǫ-regime of QCD in 3 dimensions. It is shown that the leading term of the effective partition function satisfies a set of Toda lattice equations, recursive in the number of flavors. Taking the replica limit of these Toda equations allows us to derive the microscopic spectral correlation functions for the QCD Dirac operator in 3 dimensions. For an even number of flavors we reprod...

We consider the ǫ-regime of QCD in 3 dimensions. It is shown that the leading term of the effective partition function satisfies a set of Toda lattice equations, recursive in the number of flavors. Taking the replica limit of these Toda equations allows us to derive the microscopic spectral correlation functions for the QCD Dirac operator in 3 dimensions. For an even number of flavors we reprod...

We investigate the hypothesis that colour vision in primates was selected for discriminating the spectral modulations on the skin of conspecifics, presumably for the purpose of discriminating emotional states, socio-sexual signals and threat displays. Here we show that, consistent with this hypothesis, there are two dimensions of skin spectral modulations, and trichromats but not dichromats are...

Abstract. Using the spectral dynamics, we study the critical threshold phenomena in the multidimensional restricted Euler (RE) equations. We identify sub-critical and sup-critical initial data for all space dimensions, which extends the previous result for the 3D and 4D restricted Euler equations. Our result suggests that: if the number of dimensions is odd, the finite time blowup is generic; i...

Both spectral and temporal integration of tones have been explored in detail, but integration of tones varying across both dimensions has received little attention. This study explores temporal integration of tone pulses that vary over a range of frequencies. Baseline thresholds were obtained for both spectral and temporal integration with the same signals and compared with prior research. The ...

Timbre and emotion are two of the most important aspects of musical sounds. Both are complex and multidimensional, and strongly interrelated. Previous research has identified many different timbral attributes, and shown that spectral centroid and attack time are the two most important dimensions of timbre. However, a consensus has not emerged about other dimensions. This study will attempt to i...

Spectral dimensions have been widely used to understand transport properties on regular and fractal lattices. However, they have received little attention with regard to complex networks such as scale-free and small-world networks. Here, we study the spectral dimension and the return-to-origin probability of random walks on hierarchical scale-free networks, which can be either fractal or nonfra...

The regularized partition function at finite temperature for a massless scalar field interacting with two delta-like external potentials in R is evaluated in an explicit form making use of a rigorous approach based on the introduction of relative determinants associated with the presence of non compact manifold, as defined by Müller in [14], and on results of Albeverio et al. [1], dealing with ...

We report what is to our knowledge the first volume-holographic optical imaging instrument with the capability to return three-dimensional spatial as well as spectral information about semitranslucent microscopic objects in a single measurement. The four-dimensional volume-holographic microscope is characterized theoretically and experimentally by use of fluorescent microspheres as objects.