The classic game of Battleship involves two players taking turns attempting to guess the positions of a fleet of vertically or horizontally positioned enemy ships hidden on a $10\times 10$ grid. One variant of this game, also referred to as Battleship Solitaire, Bimaru or Yubotu, considers the game with the inclusion of X-ray data, represented by knowledge of how many spots are occupied in each row and column in the enemy board. This paper considers the Battleship puzzle problem: the problem of reconstructing an enemy fleet from its X-ray data. We generate non-unique solutions to Battleship puzzles via certain reflection transformations akin to Ryser interchanges. Furthermore, we demonstrate that solutions of Battleship puzzles may be reliably obtained by searching for solutions of the associated classical binary discrete tomography problem which minimise the discrete Laplacian. We reformulate this optimisation problem as a quadratic unconstrained binary optimisation problem and approximate solutions via a simulated annealer, emphasising the future practical applicability of quantum annealers to solving discrete tomography problems with predefined structure.

A quantum annealer exploits quantum effects to solve a particular type of optimization problem. The advantage of this specialized hardware is that it effectively considers all possible solutions in parallel, thereby potentially outperforming classical computing systems. However, despite quantum annealers having recently become commercially available, there are relatively few high-level programming models that target these devices. In this article, we show how to compile a subset of Prolog enhanced with support for constraint logic programming into a two-local Ising-model Hamiltonian suitable for execution on a quantum annealer. In particular, we describe the series of transformations one can apply to convert constraint logic programs expressed in Prolog into an executable form that bears virtually no resemblance to a classical machine model yet that evaluates the specified constraints in a fully parallel manner. We evaluate our efforts on a 1,095-qubit D-Wave 2X quantum annealer and describe the approach's associated capabilities and shortcomings.

The second-order visual mechanisms perform the operation of integrating the spatially distributed local visual information. Their organization is traditionally considered within the framework of the filter-rectify-filter model. These are the second-order filters that provide the ability to detect texture gradients. However, the question of the mechanisms' selectivity to the modulation dimension remains open. The aim of this investigation is to answer the above question by using visual evoked potentials (VEPs). Stimuli were textures consisting of staggered Gabor patches. The base texture was nonmodulated (NM). Three other textures represented the base texture which was sinusoidally modulated in different dimensions: contrast, orientation, or spatial frequency. EEG was recorded with 20 electrodes. VEPs of 500 ms duration were obtained for each of the four textures. After that, VEP to the NM texture was subtracted from VEP to each modulated texture. As a result, three different waves (d-waves) were obtained for each electrode site. Each d-wave was then averaged across all the 48 observers. The revealed d-waves have a latency of about 200 ms and, in our opinion, reflect the second-order filters reactivation through the feedback connection. The d-waves for different modulation dimensions were compared with each other in time, amplitude, topography, and localization of the sources of activity that causes the d-wave (with sLORETA). We proceeded from the assumption that the d-wave (its first component) represents functioning of the second-order visual mechanisms and activity changes at the following processing stages. It was found that the d-waves for different modulation dimensions significantly differ in all parameters. The obtained results indicate that the spatial modulations of different texture parameters caused specific changes in the brain activity, which could be evidence supporting the specificity of the second-order visual mechanisms to modulation dimension.

The neuronal generators of the b- and d-waves of the electroretinogram (ERG) were investigated in the tiger salamander retina to determine if amacrine and ganglion cells contribute to this field potential. Several agents were used that affect third-order neurons, such as tetrodotoxin, baclofen, and NMDA agonists and antagonists. Baclofen, an agent that enhances light responses in third-order neurons, increased the d-wave and reduced the b-wave. In contrast, agents that decrease light responses in third-order neurons had the opposite effect of enhancing the b-wave and depressing the d-wave. The effect on the d-wave was particularly pronounced. The results indicate that third-order neuronal activity influences b- and d-waves of the ERG. The opposing actions suggest that the b-wave to d-wave ratio might serve as an measure of ganglion cell function.

We studied the off-response of the rat ERG evoked with long duration, mesopic stimuli during light and dark adaptation, and after intravitreal injection of aspartate and (±)-cis-piperidine-2,3-dicarboxilic acid (PDA). At stimulus offset, the dark-adapted ERG always showed a rapid negative deflection followed by a positive deflection after which the potential returned to baseline. When the stimulus was turned off in the presence of a background of scotopic intensity, the positive deflection consisted of two components. One component was relatively small, fast, and insensitive to rod light adaptation. It resembled the d-wave of the rod ERG. The other component was slow and its amplitude grew with rod light adaptation. In the presence of aspartate, the fast-positive component was absent from the ERG while the remaining positive-going decay of the receptor potential had a time course similar to that of the slow-positive component in the untreated eye. Scotopically matched red and blue stimuli of mesopic intensity elicited equal ERG responses from the dark-adapted eye, including the two positive components in the off-response. These stimuli were also used to assess changes in the ERG off-response during recovery from a strong bleach. Even though the cone contribution to the rat ERG is very small, the presence of a small positive-going component in the off-response following an intense bleach suggested that this response originated from the cone pathway. PDA which suppresses the light response of hyperpolarizing bipolar cells and horizontal cells selectively eliminated the fast-positive component from the ERG. The findings of this study are inconsistent with the idea that the d-wave reflects the decay of the rod receptor potential. They support the possibility that signals from rods cross rod–cone gap junctions at mesopic light intensities, and drive second-order neurons in the cone pathway.