Testing theories of financial decision making.

We describe the observable content of some of the most widely used models of decision under uncertainty: models of translation invariant preferences. In particular, we characterize the models of variational, maxmin, constant absolute risk aversion, and constant relative risk aversion utilities. In each case we present a revealed preference axiom that is satisfied by a dataset if and only if the dataset is consistent with the corresponding utility representation. We test our axioms using data from an experiment on financial decisions.

Intelligent Extraction of Salient Feature From Electroencephalogram Using Redundant Discrete Wavelet Transform.

At present, electroencephalogram (EEG) signals play an irreplaceable role in the diagnosis and treatment of human diseases and medical research. EEG signals need to be processed in order to reduce the adverse effects of irrelevant physiological process interference and measurement noise. Wavelet transform (WT) can provide a time-frequency representation of a dynamic process, and it has been widely utilized in salient feature analysis of EEG. In this paper, we investigate the problem of translation variability (TV) in discrete wavelet transform (DWT), which causes degradation of time-frequency localization. It will be verified through numerical simulations that TV is caused by downsampling operations in decomposition process of DWT. The presence of TV may cause severe distortions of features in wavelet subspaces. However, this phenomenon has not attracted much attention in the scientific community. Redundant discrete wavelet transform (RDWT) is derived by eliminating the downsampling operation. RDWT enjoys the attractive merit of translation invariance. RDWT shares the same time-frequency pattern with that of DWT. The discrete delta impulse function is used to test the time-frequency response of DWT and RDWT in wavelet subspaces. The results show that DWT is very sensitive to the translation of delta impulse function, while RDWT keeps the decomposition results unchanged. This conclusion has also been verified again in decomposition of actual EEG signals. In conclusion, to avoid possible distortions of features caused by translation sensitivity in DWT, we recommend the use of RDWT with more stable performance in BCI research and clinical applications.

Weak fault detection with a two-stage key frequency focusing model.

The fault diagnosis of early failure bearing can discover the potential danger in the mechanical equipment in time. It remains a great challenge due to the noise interference. Although many diagnosis methods have been proposed, the characteristics of signal have not yet been fully investigated, which leads to unsatisfactory diagnosis results. To solve this problem, a weak fault detection method with a two-stage key frequency focusing model is designed. Translation invariance in time domain and translation variance in frequency domain are systematically considered. The effectiveness is verified on four constructed datasets. The results show that the designed network has the best comprehensive performance comparing to the state-of-the-art methods.

Two-dimensional translation-invariant probability distributions: approximations, characterizations and no-go theorems.

We study the properties of the set of marginal distributions of infinite translation-invariant systems in the two-dimensional square lattice. In cases where the local variables can only take a small number d of possible values, we completely solve the marginal or membership problem for nearest-neighbours distributions (d = 2, 3) and nearest and next-to-nearest neighbours distributions (d = 2). Remarkably, all these sets form convex polytopes in probability space. This allows us to devise an algorithm to compute the minimum energy per site of any TI Hamiltonian in these scenarios exactly. We also devise a simple algorithm to approximate the minimum energy per site up to arbitrary accuracy for the cases not covered above. For variables of a higher (but finite) dimensionality, we prove two no-go results. To begin, the exact computation of the energy per site of arbitrary TI Hamiltonians with only nearest-neighbour interactions is an undecidable problem. In addition, in scenarios with d≥2947, the boundary of the set of nearest-neighbour marginal distributions contains both flat and smoothly curved surfaces and the set itself is not semi-algebraic. This implies, in particular, that it cannot be characterized via semidefinite programming, even if we allow the input of the programme to include polynomials of nearest-neighbour probabilities.

Dual tree complex wavelet transform-based signal denoising method exploiting neighbourhood dependencies and goodness-of-fit test.

A novel signal denoising method is proposed whereby goodness-of-fit (GOF) test in combination with a majority classifications-based neighbourhood filtering is employed on complex wavelet coefficients obtained by applying dual tree complex wavelet transform (DT-CWT) on a noisy signal. The DT-CWT has proven to be a better tool for signal denoising as compared to the conventional discrete wavelet transform (DWT) owing to its approximate translation invariance. The proposed framework exploits statistical neighbourhood dependencies by performing the GOF test locally on the DT-CWT coefficients for their preliminary classification/detection as signal or noise. Next, a deterministic neighbourhood filtering approach based on majority noise classifications is employed to detect false classification of signal coefficients as noise (via the GOF test) which are subsequently restored. The proposed method shows competitive performance against the state of the art in signal denoising.

Adaptation to Skew Distortions of Natural Scenes and Retinal Specificity of Its Aftereffects.

Image skew is one of the prominent distortions that exist in optical elements, such as in spectacle lenses. The present study evaluates adaptation to image skew in dynamic natural images. Moreover, the cortical levels involved in skew coding were probed using retinal specificity of skew adaptation aftereffects. Left and right skewed natural image sequences were shown to observers as adapting stimuli. The point of subjective equality (PSE), i.e., the skew amplitude in simple geometrical patterns that is perceived to be unskewed, was used to quantify the aftereffect of each adapting skew direction. The PSE, in a two-alternative forced choice paradigm, shifted toward the adapting skew direction. Moreover, significant adaptation aftereffects were obtained not only at adapted, but also at non-adapted retinal locations during fixation. Skew adaptation information was transferred partially to non-adapted retinal locations. Thus, adaptation to skewed natural scenes induces coordinated plasticity in lower and higher cortical areas of the visual pathway.

The visual system supports online translation invariance for object identification.

The ability to recognize the same image projected to different retinal locations is critical for visual object recognition in natural contexts. According to many theories, the translation invariance for objects extends only to trained retinal locations, so that a familiar object projected to a nontrained location should not be identified. In another approach, invariance is achieved "online," such that learning to identify an object in one location immediately affords generalization to other locations. We trained participants to name novel objects at one retinal location using eyetracking technology and then tested their ability to name the same images presented at novel retinal locations. Across three experiments, we found robust generalization. These findings provide a strong constraint for theories of vision.

Translation symmetry breakdown in low-dimensional lattices of pentagonal rings.

The mechanism of translation symmetry breakdown in newly proposed low-dimensional carbon pentagon-constituted nanostructures (e.g., pentagraphene) with multiple sp(2)/sp(3) sublattices was studied by GGA DFT, DFTB, and model potential approaches. It was found that finite nanoclusters suffer strong uniform unit cell bending followed by breaking of crystalline lattice linear translation invariance caused by structural mechanical stress. It was shown that 2D sp(2)/sp(3) nanostructures are correlated transition states between two symmetrically equivalent bent structures. At DFT level of theory the distortion energy of the flakes (7.5 × 10(-2) eV/atom) is much higher the energy of dynamical stabilization of graphene. Strong mechanical stress prevents stabilization of the nanoclusters on any type of supports by either van der Waals or covalent bonding and should lead to formation of pentatubes, nanorings, or nanofoams rather than infinite nanoribbons or nanosheets. Formation of two-layered pentagraphene structures leads to compensation of the stress and stabilization of flat finite pentaflakes.