Perinatal depression (PND) affects up to 15% of women within the United Kingdom and has a lasting impact on a woman's quality of life, birth outcomes and her child's development. Suicide is the leading cause of maternal mortality. However, it is estimated that at least 50% of PND cases go undiagnosed. This paper presents the results of the first feasibility study to examine the potential of mobile devices to engage women in antenatal mental health screening. Using a mobile application, 254 women attending 14 National Health Service midwifery clinics provided 2,280 momentary and retrospective reports of their wellbeing over a 9-month period. Women spoke positively of the experience, installing and engaging with this technology regardless of age, education, wellbeing, number of children, marital or employment status, or past diagnosis of depression. 39 women reported a risk of depression, self-harm or suicide; two-thirds of whom were not identified by screening in-clinic.

We show how to construct an optimal context tree for a given plaintext and context order. Our algorithm runs in time linear in the size of the plaintext and the size of the context, and consumes space linear in the size of the plaintext. We evaluate the algorithm's performance on the CCITT test set for bilevel images with the Euclidean-norm context order.

Given a sequence, we consider the maximum number of distinct phrases in any parsing; this definition of complexity is invariant under string reversal. We show that the Lempel-Ziv (1976, 1978) parsings can vary under reversal by a factor on the order of the log of the sequence length. We give two interpretations of maximal parsing, show that they are not equivalent and that one lacks a plausible monotonicity property.

We show that greedy left-to-right (right-to-left) parsing is optimal w.r.t. a suffix (prefix) dictionary. To exploit this observation, we show how to construct a static suffix dictionary that supports on-line, linear-time optimal parsing. From this we derive an adaptive on-line method that yields compression comparing favorably to LZW.

Tree-structured vector quantization is a technique to represent a codebook that simplifies encoding as well as quantizer design. The authors define the notion of an optimal pruned tree subject to a cost constraint, and study the computational complexity of finding such a tree. Under the assumption that all trees are equally probable, it is shown that on average the number of pruned trees in a given tree is exponential in the number of leaves. Finding an optimal pruned tree subject to constraints such as entropy or the expected depth is NP-hard. However, when the constraint is the number of leaves, the problem can be solved in O(nk) time, where n is the size of the initial tree and k the constraint size. Experimental results for image compression show the performance of the optimal pruned tree to be comparable with that of full-search vector quantizers.>

The 2nn-bit vectors can be ordered so that any vector in the sequence has some minimum Hamming distance from any vector near it in the sequence.

A test sequence is called(s,t)-universal if it exercises every function depending on t or fewer inputs on a very large scale integration (VLSI) chip withsinputs. Randomized and deterministic procedures are deseribed for the design of(s,t)-universal sequences and for the signature analysis of the test outputs.

In a recent paper Olsen, Scholtz, and Welch (OSW) describe the use of bent functions to construct families of sequences with asymptotically optimal correlation properties. We show that the sequences produced by the OSW construction possess the claimed correlation properties if and only if the underlying bent functions are pairwise orthogonal. Consequently, the cardinality of a family of OSW sequences of length2^{n}-1cannot exceed2^{n/2}. We also describe methods of selecting a maximal set of orthogonal bent functions.

A(k/n)code is a uniquely decipherable scheme mapping source words of lengthkinto channel words of lengthn. In a look-ahead code the encoding and/or decoding of a current word may depend on upcoming, as well as past, symbols. Given an\theta-ary source, a channel of

A Gray sequence is a counter sequence where the Hamming distance between successive states is one. A construction for any fixed odd distance between successive states is given based on error-correcting codes. Such sequences could be used in testing and fault diagnosis when sequencing through all possible input combinations. Sequences with the maximum possible difference between successive states, alternatelynandn-1, are given. A characterization of such maximal change sequences is given. The most nearly uniform even difference sequences are described. The distribution of bit changes or transition counts for individual variables for a counting sequence is considered.

The equivalence ofM-sequence matrices to Walsh-Hadamard matrices can be exploited to take advantage of the latter's fast transform algorithm. The nature of the obvious equivalence, its relation to theM-sequence and its implementation as address modifications realized by linear feedback shift-registers are discussed.

The construction of a class of balanced binary sequences with optimal autocorrelation properties is described. Given any odd primepand any positive integerm, a balanced( \pm 1)binary sequence of lengthp^{m} - 1whose cyclic autocorrelation functionc (\tau)satisfiesc (0) = p^{m} - 1, and, for\tau \neq 0, c (\tau) = +2or-2when(p^{m} - 1)/2is odd, andc(\tau) = 0or-4when(p^{m} - 1)/2is even is constructed. Optimality is proved by showing that every balanced binary sequence has at least two distinct out-of-phase correlation values which are at least as large as those obtained here.

We consider the spectral properties of the first difference of two-level codes. These considerations arise where signal recovery involves differencing or differentiation. We develop a general model and propose specific codes whose differences guarantee such properties as null dc, null midband, positive, and strictly positive midband content.

We discuss the prefix encoding of aQ-ary source(Q \geq 2)into anL-symbol channel alphabet withL \geq Q. We present an optimal encoding scheme that minimizes the expected cost per symbol in the case of equally probable source symbols and arbitrary channel symbol costs.

We investigate the spectral component at a desired frequency (f= p/2q) of two-level waveforms constrained to change level only at integer values of time. We conclude that the component at the frequency is maximized if and only if the level changes coincide with the pulses of a smooth sequence of rate p/q.

To seek the origins of Gray codes is to peer farther into the past than 1947. As mentioned in our note, the structure of our counter was suggested by the "Chinese rings" puzzle; the codes themselves can describe solutions to the "Tower of Hanoi" puzzle (see our [4]). More recent uses of the unitdistance principle may also be found.4

The construction of a shortest feedback shift register which generates a given finite sequence is described for the cases of linear and nonlinear feedback logic. It is shown that the ratio of the number of delay elements required in the linear case to that of the nonlinear case grows without bound for proper choice of sequences.

A Gray code counter which has an iterative and relatively simple structure is described. The code is shown to be the reflected binary Gray code, implying simple conversion of the count into binary code.

This paper is a study of linear machines and their submachines. Methods are presented for finding the reduced form of a given linear machine with or without fixed initial state. A technique is suggested for detecting whether a machine is linear or can be embedded as a submachine in a linear machine. In the latter case a state assignment is produced for the minimum linear realization. Encoded inputs and outputs are assumed, but given machines are not assumed reduced, nor are there any restrictions on the number of states in the given machine or in the linear realization. The method also detects machines that are linearly realizable when constants are available. The main results are that the reduced form of a linear machine is linear and that a linearly realizable machine with r-independent states has an r-dimensional realization.

Certain properties are proved for machines whose state and output behavior