Derivation of tight bounds on f -divergences and related distances is of interest in information theory and statistics. This paper improves some existing bounds on f -divergences. In some cases, an alternative approach leads to a simplified proof of an existing bound. Following bounds on the chi-squared divergence, an improved version of a reversed Pinsker’s inequality is derived for an arbitra...

In the 1960s, several groups of scientists, including Emile Zuckerkandl and Linus Pauling, had noted that proteins experience amino acid replacements at a surprisingly consistent rate across very different species. This presumed single, uniform rate of genetic evolution was subsequently described using the term 'molecular clock'. Biologists quickly realised that such a universal pacemaker could...

For dimensions close to D = 4, the Feynman integrals in momentum space derived in Chapter 4 do not converge since their integrands fall off too slowly at large momenta. Divergences arising from this short-wavelength region of the integrals are called ultraviolet (UV)-divergences. For massive fields, these are the only divergences of the integrals. In the zero-mass limit relevant for critical ph...

Cartusia hunanesis sp. nov. was isolated from a stream in China, and two strains (ZJJ02 ZJJ03) of which were inquired using morphological features, ecological evidence, molecular data consisting the 16S rRNA gene 16S–23S intergenic transcribed spacer (ITS) region. varies type species fontana by having only single trichome sheath large granules near cross wall. The investigated C. revealed to be...

Mitochondrial 16s rDNAwas sequenced fromninedifferentpopulationsofAphelinidae and 10 of aphidiinae. Sequence divergences between populations within a species are low, ranging from 0 to 0.38%. Divergences among species within the same genus range from 0 to 8.71%. Aphelinus asychisWalker has a sequence divergence from the otherAphelinus spp. of 8.71%,which is evenhigher than the divergences among...

An analysis of the one-loop vacuum fluctuations associated with a massless scalar field, confined in the interior of a rectangular infinitely long waveguide is presented. To identify the infinities of the vacuum fluctuations we are using different analytic regularization procedures, instead of the usual point-splitting Green's function method. The infinities which occur in ϕ 2 (x) fall into two...

We review recent results concerning the all-order structure of infrared and collinear divergences in massless gauge theory amplitudes. While the exponentiation of these divergences for nonabelian gauge theories has been understood for a long time, in the past couple of years we have begun to unravel the all-order structure of the anomalous dimensions that build up the perturbative exponent. In ...

A wide variety of distortion functions, such as squared Euclidean distance, Mahalanobis distance, Itakura-Saito distance and relative entropy, have been used for clustering. In this paper, we propose and analyze parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergences. The proposed algorithms unify centroid-based parametric clust...

Estimating branch lengths in proportion to time is confounded by the fact that the rate of evolution and time are intrinsically linked when inferring genetic differences between species. A model of lineage-specific substitution rate variation must be applied to tease apart rate and time. When applied in methods for divergence time estimation, the resulting trees have branch lengths that are pro...

The family of density power divergences is an useful class which generates robust parameter estimates with high efficiency. None of these divergences require any non-parametric density estimate to carry out the inference procedure. However, these divergences have so far not been used effectively in robust testing of hypotheses. In this paper, we develop tests of hypotheses based on this family ...