[11]Anthrahelicene on InSb(001) c(8×2): A Low‐Temperature Scanning Probe Microscopy Study

The adsorption of individual [11]anthrahelicene molecules and their self‐assembly into monolayer islands on an InSb(001) c(8×2) reconstructed surface is studied with low‐temperature scanning probe microscopy. A racemic mixture is deposited on atomically flat terraces of InSb at room temperature. At lower coverage, the molecules tend to decorate atomic step edges of the substrate. At higher coverage, [11]anthrahelicene molecules form 2D islands. A quasi‐hexagonal ordering of molecules within the layer is identified. Furthermore, it is shown that molecules adsorb with the helical axis almost perpendicular to the substrate. Interference between tunneling through the molecular layer and directly through space is reported. Finally, experimental results are compared to those of theoretical calculations.     

Isometries of generalized <Emphasis Type="Italic">MV</Emphasis>-algebras

In this paper we investigate the relations between isometries and direct product decompositions of generalized MV-algebras.     

Weak homogeneity of lattice ordered groups

In this paper we deal with weakly homogeneous direct factors of lattice ordered groups. The main result concerns the case when the lattice ordered groups under consideration are archimedean, projectable and conditionally orthogonally complete. Supported by VEGA grant 2/4134/24. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information.     

Self-Supervised Variational Auto-Encoders

Density estimation, compression, and data generation are crucial tasks in artificial intelligence. Variational Auto-Encoders (VAEs) constitute a single framework to achieve these goals. Here, we present a novel class of generative models, called self-supervised Variational Auto-Encoder (selfVAE), which utilizes deterministic and discrete transformations of data. This class of models allows both conditional and unconditional sampling while simplifying the objective function. First, we use a single self-supervised transformation as a latent variable, where the transformation is either downscaling or edge detection. Next, we consider a hierarchical architecture, i.e., multiple transformations, and we show its benefits compared to the VAE. The flexibility of selfVAE in data reconstruction finds a particularly interesting use case in data compression tasks, where we can trade-off memory for better data quality and vice-versa. We present the performance of our approach on three benchmark image data (Cifar10, Imagenette64, and CelebA).     

Sequential convergences on cyclically ordered groups without Urysohn’s axiom

In this paper we investigate sequential convergences on a cyclically ordered group G which are compatible with the group operation and with the relation of cyclic order; we do not assume the validity of the Urysohn’s axiom. The system convG of convergences under consideration is partially ordered by means of the set-theoretical inclusion. We prove that convG is a Brouwerian lattice. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information, grant I/2/2005.     

Cardinality of retracts of monounary algebras

For an uncountable monounary algebra (A, f) with cardinality κ it is proved that (A, f) has exactly 2_κ retracts. The case when (A, f) is countable is also dealt with. This work was suported by the the Slovak VEGA Grant No. 1/3003/06. This work was supported by Science and Technology Assistance Agency under the contract No. APVT-20-004104.     

Affine completeness and wreath product decompositions of lattice ordered group

Let Δ and H be a nonzero abelian linearly ordered group or a nonzero abelian lattice ordered group, respectively. In this paper we prove that the wreath product of Δ and H fails to be affine complete. Supported by VEGA grant 2/4134/24. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information, grant I/2/2005.     

Causality in Reversed Time Series: Reversed or Conserved?

The inference of causal relations between observable phenomena is paramount across scientific disciplines; however, the means for such enterprise without experimental manipulation are limited. A commonly applied principle is that of the cause preceding and predicting the effect, taking into account other circumstances. Intuitively, when the temporal order of events is reverted, one would expect the cause and effect to apparently switch roles. This was previously demonstrated in bivariate linear systems and used in design of improved causal inference scores, while such behaviour in linear systems has been put in contrast with nonlinear chaotic systems where the inferred causal direction appears unchanged under time reversal. The presented work explores the conditions under which the causal reversal happens—either perfectly, approximately, or not at all—using theoretical analysis, low-dimensional examples, and network simulations, focusing on the simplified yet illustrative linear vector autoregressive process of order one. We start with a theoretical analysis that demonstrates that a perfect coupling reversal under time reversal occurs only under very specific conditions, followed up by constructing low-dimensional examples where indeed the dominant causal direction is even conserved rather than reversed. Finally, simulations of random as well as realistically motivated network coupling patterns from brain and climate show that level of coupling reversal and conservation can be well predicted by asymmetry and anormality indices introduced based on the theoretical analysis of the problem. The consequences for causal inference are discussed.