For a zero-mean, unit-variance stationary univariate Gaussian process we derive the probability that a record at the time n, say $X_n$ , takes place, and derive its distribution function. We study the joint distribution of the arrival time process of records and the distribution of the increments between records. We compute the expected number of records. We also consider two consecutive and non-consecutive records, one at time j and one at time n, and we derive the probability that the joint records $(X_j,X_n)$ occur, as well as their distribution function. The probability that the records $X_n$ and $(X_j,X_n)$ take place and the arrival time of the nth record are independent of the marginal distribution function, provided that it is continuous. These results actually hold for a strictly stationary process with Gaussian copulas.

The paucity of the extant written record left by the Third Franklin Expedition (1845−1848) has presented challenges to the efforts of generations of searchers and scholars. Additionally, it has underscored the reliance of Western culture on written records when establishing narratives and understanding events. This paper explores the sparse written records of the expedition in the context of their contextualisation over the years within an ersatz Franklin archive which includes a variety of discourses and documentary intents. By situating the Franklin records within an archival context, it is possible to reconsider these materials as part of a collection while also examining the ways in which they stand on their own by virtue of the (sometimes unknowable) circumstances of their creation, circulation, and preservation. Combining this archival approach with Derrida’s notion of hauntology, this paper analyses the written records of the Third Franklin Expedition as an ephemeral, and ultimately inscrutable, representation of a vanished expedition.

Do archaeologists recover the material record of past processes or the residues of the material conditions that made the presence of a kind of humanness possible? This paper attempts to emphasize the importance of distinguishing between these two options and argues the case for, and briefly contemplates the practical implications of, an archaeology of the human presence.

We prove strong convergence and asymptotic normality for the record and the weak record rate of observations of the form Yn = Xn + Tn, n ≥ 1, where (Xn)n ∈ Z is a stationary ergodic sequence of random variables and (Tn)n ≥ 1 is a stochastic trend process with stationary ergodic increments. The strong convergence result follows from the Dubins-Freedman law of large numbers and Birkhoff's ergodic theorem. For the asymptotic normality we rely on the approach of Ballerini and Resnick (1987), coupled with a moment bound for stationary sequences, which is used to deal with the random trend process. Examples of applications are provided. In particular, we obtain strong convergence and asymptotic normality for the number of ladder epochs in a random walk with stationary ergodic increments.

Two specimens of Chromis notata (Pomacentridae) and one specimen of Sagamia geneionema (Gobiidae) were captured in Suttsu Bay, the Sea of Japan. These constitute the first records of the species from Hokkaido Island, northern Japan.

A recent stranding of a basking shark Cetorhinus maximus in north-western Bali represents the first confirmed record of this large, filter-feeding shark species in Indonesian waters. Based on measurements of the fins and claspers, the adult male specimen was estimated to be between 5.6 and 8.1 m LT, with an average estimate of 6.7 m LT. It is possible that the Indonesian Throughflow is an important route for this species during transequatorial migrations.

A six metre adult male of the white shark Carcharodon carcharias was caught by demersal longliners operating off Dompu, Indonesia. The specimen was landed and sold at Tanjung Luar landing site in eastern Lombok. Photographic evidence for this specimen is provided and an upper lateral tooth was retained. This is the first confirmed record of the species in Indonesian waters.

The long-finned mullet, Osteomugil perusii was caught along the eastern and western coasts of India. The finding of 12 specimens extends the current knowledge about the distribution of this mullet in the western Indo-Pacific to the Indian coast.

Rafting is proposed as the mechanism of dispersal influencing the speciation and population structure of Hippocampus. Recently, rafting was confirmed in Hippocampus patagonicus by the direct observation of juveniles attached to floating debris. This study discusses the implications of the record of an individual in deep waters, suggesting that the species can disperse away from their coastal populations.

Numerous specimens of Ophistognathus panamaensis were observed along the coast of Oaxaca in western Mexico and one specimen was collected by Hawaiian sling in the coral reef zones of Huatulco, Mexico in November 2012. Therefore, this paper reports for the first time the occurrence of O. panamaensis in Mexico and extends its previous distribution by 1245 km north of the Eastern Pacific equatorial zone.

In this paper we study the number of random records in an arbitrary split tree (or, equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for the convergence of sums of triangular arrays to infinitely divisible distributions can be used to determine the distribution of this number. After normalization the distributions are shown to be asymptotically weakly 1-stable. This work is a generalization of our earlier results for the random binary search tree in Holmgren (2010), which is one specific case of split trees. Other important examples of split trees include m-ary search trees, quad trees, medians of (2k + 1)-trees, simplex trees, tries, and digital search trees.

A sequence of independent Bernoulli random variables with success probabilities a / (a + b + k − 1), k = 1, 2, 3, …, is embedded in a marked Poisson process with intensity 1. Using this, conditional Poisson limits follow for counts of failure strings.

The record in the northern Adriatic Sea in 1874 of a specimen of the Salaria basilisca is discussed. This northernmostrecord for the Mediterranean area is confirmed by analysing the specimen fromthe Natural History Museum of Vienna.

In a sequence of independent Bernoulli trials the probability for success in the kth trial is pk, k = 1, 2, …. The number of strings with a given number of failures between two subsequent successes is studied. Explicit expressions for distributions and moments are obtained for the case in which pk = a/(a + b + k − 1), a > 0, b ≥ 0. Also, the limit behaviour of the longest failure string in the first n trials is considered. For b = 0, the strings correspond to cycles in random permutations.

Let X1,X2,… be a sequence of independent and identically distributed random variables with some continuous distribution function F. Let L(n) and X(n) denote the nth record time and the nth record value, respectively. We refer to the variables Xi as near-nth-record observations if Xi∈(X(n)-a,X(n)], with a>0, and L(n)<i<L(n+1). In this work we study asymptotic properties of the number of near-record observations. We also discuss sums of near-record observations.

Consider a sequence (Xn) of independent and identically distributed random variables taking nonnegative integer values, and call Xn a record if Xn> max{X1,…,Xn−1}. By means of martingale arguments it is shown that the counting process of records among the first n observations, suitably centered and scaled, is asymptotically normally distributed.