Wavelet-Based Compressive Sensing for Point Scatterers

Compressive Sensing (CS) allows for the sam-pling of signals at well below the Nyquist rate but does so, usually, at the cost of the suppression of lower amplitude sig-nal components. Recent work suggests that important infor-mation essential for recognizing targets in the radar context is contained in the side-lobes as well, which are often sup-pressed by CS. In this paper we extend existing techniques and introduce new techniques both for improving the accu-racy of CS reconstructions and for improving the separa-bility of scenes reconstructed using CS. We investigate the Discrete Wavelet Transform (DWT), and show how the use of the DWT as a representation basis may improve the accu-racy of reconstruction generally. Moreover, we introduce the concept of using multiple wavelet-based reconstructions of a scene, given only a single physical observation, to derive re-constructions that surpass even the best wavelet-based CS reconstructions. Lastly, we specifically consider the effect of the wavelet-based reconstruction on classification. This is done indirectly by comparing outputs of different algo-rithms using a variety of separability measures. We show that various wavelet-based CS reconstructions are substan-tially better than conventional CS approaches at inducing (or preserving) separability, and hence may be more useful in classification applications

Lower Bounds for Symmetric Circuits for the Determinant

Dawar and Wilsenach (ICALP 2020) introduce the model of symmetric arithmetic circuits and show an exponential separation between the sizes of symmetric circuits for computing the determinant and the permanent. The symmetry restriction is that the circuits which take a matrix input are unchanged by a permutation applied simultaneously to the rows and columns of the matrix. Under such restrictions we have polynomial-size circuits for computing the determinant but no subexponential size circuits for the permanent. Here, we consider a more stringent symmetry requirement, namely that the circuits are unchanged by arbitrary even permutations applied separately to rows and columns, and prove an exponential lower bound even for circuits computing the determinant. The result requires substantial new machinery. We develop a general framework for proving lower bounds for symmetric circuits with restricted symmetries, based on a new support theorem and new two-player restricted bijection games. These are applied to the determinant problem with a novel construction of matrices that are bi-adjacency matrices of graphs based on the CFI construction. Our general framework opens the way to exploring a variety of symmetry restrictions and studying trade-offs between symmetry and other resources used by arithmetic circuits

Symmetric Arithmetic Circuits.

We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the restriction amounts to requiring that the shape of the circuit is invariant under row and column permutations of the matrix. We establish unconditional, nearly exponential, lower bounds on the size of any symmetric circuit for computing the permanent over any field of characteristic other than 2. In contrast, we show that there are polynomial-size symmetric circuits for computing the determinant over fields of characteristic zero

A new precision measurement of the {\alpha}-decay half-life of 190Pt

A laboratory measurement of the $\alpha$-decay half-life of $^{190}$Pt has been performed using a low background Frisch grid ionisation chamber. A total amount of 216.60(17) mg of natural platinum has been measured for 75.9 days. The resulting half-life is $(4.97\pm0.16)\times 10^{11}$ years, with a total uncertainty of 3.2%. This number is in good agreement with the half-life obtained using the geological comparison method

Symmetric Circuits for Rank Logic.

Fixed-point logic with rank (FPR) is an extension of fixed-point logic with counting (FPC) with operators for computing the rank of a matrix over a finite field. The expressive power of FPR properly extends that of FPC and is contained in P, but it is not known if that containment is proper. We give a circuit characterization for FPR in terms of families of symmetric circuits with rank gates, along the lines of that for FPC given by [Anderson and Dawar 2017]. This requires the development of a broad framework of circuits in which the individual gates compute functions that are not symmetric (i.e., invariant under all permutations of their inputs). This framework also necessitates the development of novel techniques to prove the equivalence of circuits and logic. Both the framework and the techniques are of greater generality than the main result

Receptive vocabulary and early literacy skills in emergent bilingual Northern Sotho-English children

This study explored receptive vocabulary size and early literacy skills (namely: letter naming, knowledge of phoneme-grapheme correspondences and early writing) in emergent bilingual Northern Sotho-English children. Two groups of Grade 1 learners were tested in both English and in Northern Sotho. Group 1 (N = 49) received their formal schooling in English, whilst group 2 (N = 50) received their formal schooling in Northern Sotho. Receptive vocabulary was tested using the Peabody Picture Vocabulary Test. Letter knowledge was assessed by asking learners to name letter cards, whilst knowledge of phoneme-grapheme correspondences was tested by asking children to match letter cards with spoken sounds. Early writing was assessed by asking children to write their names. Statistical analyses indicated that both English and Northern Sotho receptive vocabulary knowledge had a significant effect on early literacy skills, whilst no main effect was found for the language of instruction. Group 1 performed significantly better than Group 2 in English receptive vocabulary, in knowledge of phonemegrapheme correspondences and in early writing, but no group differences were found for Northern Sotho receptive vocabulary or for letter knowledge. English receptive vocabulary significantly predicted the outcome of all of the early literacy skills, whilst Northern Sotho receptive vocabulary significantly predicted phoneme-grapheme correspondences and early writing

Phonological awareness and reading in Northern Sotho – Understanding the contribution of phonemes and syllables in Grade 3 reading attainment

Background: The role of phonological awareness (PA) in successful reading attainment in Northern Sotho has received some attention. However, the importance of developing an awareness to the different phonological grain sizes that underlie decoding (i.e. to different dimensions of PA) has not been established in this language. Aim: This study assessed different levels of PA in Northern Sotho learners in order to determine the relationship between phoneme awareness, syllable awareness and reading. Setting: The research was conducted in Atteridgeville, a suburb in Tshwane. The participants were Grade 3 learners who spoke Northern Sotho as home language, and who received their literacy instruction in Northern Sotho in the foundation phase. Methods: The research was cross-sectional, with a correlational component. Phoneme awareness was assessed via a phoneme identification and elision task, whereas syllable awareness was assessed with a syllable elision task. Results: Statistical analyses revealed that Northern Sotho learners are significantly better at identifying syllables than phonemes, but that phoneme awareness predicts reading outcomes more accurately. Conclusion: This study suggests that phoneme awareness does not necessarily develop early or automatically in languages with a simple syllable structure and a transparent orthography and evaluates this finding against the predictions of the Psycholinguistic Grain Size Theory. The importance of explicitly teaching phoneme–grapheme correspondences to Northern Sotho learners is highlighted

Symmetric Circuits and Model-Theoretic Logics

The question of whether there is a logic that characterises polynomial-time is arguably the most important open question in finite model theory. The study of extensions of fixed-point logic are of central importance to this question. It was shown by Anderson and Dawar that fixed-point logic with counting (FPC) has the same expressive power as uniform families of symmetric circuits over a basis with threshold functions. In this thesis we prove a far-reaching generalisation of their result and establish an analogous circuit characterisation for each from a broad range of extensions of fixed-point logic. In order to do so we fist develop a very general framework for defining and studying extensions of fixed-point logics, which we call generalised operators. These operators generalise Lindström quantifiers as well as the counting and rank operators used to define FPC and fixed-point logic with rank (FPR). We also show that in order to define a symmetric circuit model that goes beyond FPC we need to consider circuits with gates that are allowed to compute non-symmetric functions. In order to do so we develop a far more general framework for studying circuits. We also show that key notions, such as the notion of a symmetric circuit, can be analogously defined in this more general framework. The characterisation of FPC in terms of symmetric circuits, and the treatment of circuits generally, relies heavily on the assumption that the gates in the circuit compute symmetric functions. We develop a broad range of new techniques and approaches in order to study these more general symmetric circuit models. As a corollary of our main result we establish a circuit characterisation of FPR. We also show that the question of whether there is a logic that characterises polynomial-time can be understood as a question about the symmetry property of circuits. We lastly propose a number of new approaches that might exploit this new-found connection between circuit complexity and descriptive complexity.Gates Cambridge Scholarship