The formation and invariance of the canine nose pattern is studied. Nose images of ten beagle dogs were collected for ten months from month two to month eleven. The nose patterns in these images are examined visually and by a biometric algorithm. It is found that the canine nose pattern is fully formed at the end of the second month since birth and remains invariant until the end of the eleventh month. This study also strongly indicates that the canine nose pattern can be used as a unique biometric marker for each individual dog.

The uniqueness of the canine nose pattern was studied. A total of 180 nose images of 60 dogs of diverse age, gender, and breed were collected. The canine nose patterns in these images were examined visually and by a biometric algorithm. It was found that the canine nose pattern remains invariant regardless of when the image is taken; and that the canine nose pattern is indeed unique to each dog. The same study was also performed on an enlarged dataset of 278 nose images of 70 dogs of 19 breeds. The study of the enlarged dataset also leads to the same conclusion. The result of this paper confirms and enhances the claims of earlier works by others that the canine nose pattern is indeed unique to each animal and serves as a unique biometric marker.

It is known that a variant of Ising model, called Seeded Ising Model, can be used to recover the information content of a biometric template from a fraction of information therein. The method consists in reconstructing the whole template, which is called the intruder template in this paper, using only a small portion of the given template, a partial template. This reconstruction method may pose a security threat to the integrity of a biometric identity management system. In this paper, based on the Seeded Ising Model, we present a systematic analysis of the possible security breach and its probability of accepting the intruder templates as genuine. Detailed statistical experiments on the intruder match rate are also conducted under various scenarios. In particular, we study (1) how best a template is divided into several small pieces called partial templates, each of which is to be stored in a separate silo; (2) how to do the matching by comparing partial templates in the locked-up silos, and letting only the results of these intra-silo comparisons be sent to the central tallying server for final scoring without requiring the whole templates in one location at any time.

In this paper, we define the weak P-property and the α-ψ-proximal contraction by p in which p is a τ-distance on a metric space. Then, we prove some best proximity point theorems in a complete metric space X with generalized distance. Also we define two kinds of α-p-proximal contractions and prove some best proximity point theorems.

We prove the stability of some functional equations in the random normed spaces under arbitraryt-norms.