On complete representations and minimal completions in algebraic logic, both positive and negative results

Fix a finite ordinal \(n\geq 3\) and let \(\alpha\) be an arbitrary ordinal. Let \(\mathsf{CA}_n\) denote the class of cylindric algebras of dimension \(n\) and \(\sf RA\) denote the class of relation algebras. Let \(\mathbf{PA}_{\alpha}(\mathsf{PEA}_{\alpha})\) stand for the class of polyadic (equality) algebras of dimension \(\alpha\). We reprove that the class \(\mathsf{CRCA}_n\) of completely representable \(\mathsf{CA}_n$s, and the class \(\sf CRRA\) of completely representable \(\mathsf{RA}\)s are not elementary, a result of Hirsch and Hodkinson. We extend this result to any variety \(\sf V\) between polyadic algebras of dimension \(n\) and diagonal free \(\mathsf{CA}_n\)s. We show that that the class of completely and strongly representable algebras in \(\sf V\) is not elementary either, reproving a result of Bulian and Hodkinson. For relation algebras, we can and will, go further. We show the class \(\sf CRRA\) is not closed under \(\equiv_{\infty,\omega}\). In contrast, we show that given \(\alpha\geq \omega\), and an atomic \(\mathfrak{A}\in \mathsf{PEA}_{\alpha}\), then for any \(n<\omega\), \(\mathfrak{Nr}_n\A\) is a completely representable \(\mathsf{PEA}_n\). We show that for any \(\alpha\geq \omega\), the class of completely representable algebras in certain reducts of \(\mathsf{PA}_{\alpha}\)s, that happen to be varieties, is elementary. We show that for \(\alpha\geq \omega\), the the class of polyadic-cylindric algebras dimension \(\alpha\), introduced by Ferenczi, the completely representable algebras (slightly altering representing algebras) coincide with the atomic ones. In the last algebras cylindrifications commute only one way, in a sense weaker than full fledged commutativity of cylindrifications enjoyed by classical cylindric and polyadic algebras. Finally, we address closure under Dedekind-MacNeille completions for cylindric-like algebras of dimension \(n\) and \(\mathsf{PA}_{\alpha}\)s for \(\alpha\) an infinite ordinal, proving negative results for the first and positive ones for the second.

The crisis “Archetypogram” – of prisoners, soldiers, sages and jesters

Introduction: Archetypes in psychology are complete models of behaviours, thoughts and feelings, representative of universal experiences. From Plato’s description of Forms to Jung’s analytical introduction to archetypes in psychology, to common use of Moore’s masculine archetypes in popular culture, we use such “complete representations” to enable change. Methods: In examining psychologically driven responses to the recent and ongoing pandemic crisis, the use of a graphic representation of interacting archetypes is proposed—the ‘archetypogram’. Results: Drawing on concepts from psychodynamic therapy practise, including Transactional Analysis and Jungian theory, four main archetypes are proposed for their interdependence—the prisoner, the soldier, the sage and the jester/trickster, and a model describing their interactions is presented with the intention of enabling helpful behaviours in response to crisis. The model further proposes positive and negative positions within each archetype, labelled as ‘creating’ and ‘consuming’ behaviours respectively. The ‘archetypogram’ thus is a visual representation of three main components - the four archetypes, creating vs consuming behaviours, and movement between the various positions. Use of the ‘archetypogram’ is aimed at enabling individuals in crisis to move from consuming to creating behaviours. Conclusion: The ‘archetypogram’ is a model of change which may be applied to persons distressed in crisis, and is able to move behaviours towards positive and creating self-states.

Free and forced components of shoaling long waves in the absence of short wave breaking

Long waves are generated and transform when short-wave groups propagate into shallow water, but the generation and transformation processes are not fully understood. In this study we develop an analytical solution to the linearized shallow-water equations at the wave-group scale, which decomposes the long waves into a forced solution (a bound long wave) and free solutions (free long waves). The solution relies on the hypothesis that free long waves are continuously generated as short-wave groups propagate over a varying depth. We show that the superposition of free long waves and a bound long wave results in a shift of the phase between the short-wave group and the total long wave, as the depth decreases prior to short-wave breaking. While it is known that short-wave breaking leads to free long generation, through breakpoint forcing and bound wave release mechanisms, we highlight the importance of an additional free long wave generation mechanism due to depth variations, in the absence of breaking. This mechanism is important because as free long waves of different origins combine, the total free long wave amplitude is dependent on their phase relationship. Our free and forced solutions are verified against a linear numerical model, and we show how our solution is consistent with prior theory that does not explicitly decouple free and forced motions. We also validate the results with data from a nonlinear phase-resolving numerical wave model and experimental measurements, demonstrating that our analytical model can explain trends observed in more complete representations of the hydrodynamics.

Performance evaluation of compressive sensing matching pursuit backtracking iterative hard thresholding algorithm for improving reconstruction

Now-a-days due to advancements in technologies most of the applications in signal processing were using the models based on the sparse signal. Sub optimal strategies were used in these models to estimate the sparsest coefficients. In this work various algorithms were analyzed to address its optimal solutions. The sparsest solution can be found for the linear equations which are under determined. In this work, a complete study is carried out based on Compressive Sensing Matching Pursuit Back Tracking Iterative Hard Threshold (CMPBIHT) algorithm in the real-world scenario. As the BIHT algorithm may often fail to converge and its performance seems to be degraded if the conditions fail. To address these challenges, we have modified the BIHT algorithm to guarantee the convergence using the proposed method, even in this regime. Further the proposed CMPBIHT algorithm is evaluated and compared with the state of art techniques and it is observed that the proposed algorithm retains the similarities of the original algorithm. In this proposed model we have adopted the Compressive Sensing (CS) schemes along with Orthogonal Matching Pursuit (OMP). With this proposal we are able to solve the least squares problem for the new residual. We also investigated the reliability in sparse solutions along with compressive sensing techniques while decoding and over complete representations. An extensive research is carried out at the reconstruction side with the fundamental theme of CS, IHT and OMP techniques. The simulation results perform better efficiency at the reconstruction of the Gaussians signals by guaranteeing the productions in the residual error and noise. Further the proposed algorithm performs better at the reconstruction with nominal complexity in each of the iteration computationally.

Spatial co-fragmentation pattern of cell-free DNA recapitulatesin vivochromatin organization and identifies tissues-of-origin

ABSTRACTThree-dimensional chromatin organization varies across cell types and is essential for gene regulation. However, current technologies are unable to assessin vivogenome-wide chromatin organization non-invasively. Here we show that distant correlations in the fragment length of cell-free DNA (cfDNA) recapitulate three-dimensional chromatin organization. The inferred organization is highly concordant with that measured by Hi-C in white blood cells from healthy donors, and is not explained by technical bias or sequence composition. Furthermore, the inferred organization reflects different genomic organization in the various cell types contributing to cfDNA, allowing identification and quantification of tissues of origin. This approach is concordant with previous methods, but with more complete representations of cfDNA. Our results, demonstrated in cfDNA from healthy individuals and cancer patients, may enable noninvasive monitoring ofin vivogenome organization and accurate quantification of cell death in different clinical conditions.

Data-driven models reveal the organization of diverse cognitive functions in the brain

Our daily life is realized by the complex orchestrations of diverse brain functions including perception, decision, and action. One of the central issues in cognitive neuroscience is to reveal the complete representations underlying such diverse functions. Recent studies have revealed representations of natural perceptual experiences using encoding models1–5. However, there has been little attempt to build a quantitative model describing the cortical organization of multiple active, cognitive processes. Here, we measured brain activity using functional MRI while subjects performed over 100 cognitive tasks, and examined cortical representations with two voxel-wise encoding models6. A sparse task-type encoding model revealed a hierarchical organization of cognitive tasks, their representation in cognitive space, and their mapping onto the cortex. A cognitive factor encoding model utilizing continuous intermediate features by using metadata-based inferences7 predicted brain activation patterns for more than 80 % of the cerebral cortex and decoded more than 95 % of tasks, even under novel task conditions. This study demonstrates the usability of quantitative models of natural cognitive processes and provides a framework for the comprehensive cortical organization of human cognition.

Numerical Methods in Atmospheric Models

The astonishing development of computer technology since the mid-20th century has been accompanied by a corresponding proliferation in the numerical methods that have been developed to improve the simulation of atmospheric flows. This article reviews some of the numerical developments concern the ongoing improvements of weather forecasting and climate simulation models. Early computers were single-processor machines with severely limited memory capacity and computational speed, requiring simplified representations of the atmospheric equations and low resolution. As the hardware evolved and memory and speed increased, it became feasible to accommodate more complete representations of the dynamic and physical atmospheric processes. These more faithful representations of the so-called primitive equations included dynamic modes that are not necessarily of meteorological significance, which in turn led to additional computational challenges. Understanding which problems required attention and how they should be addressed was not a straightforward and unique process, and it resulted in the variety of approaches that are summarized in this article. At about the turn of the century, the most dramatic developments in hardware were the inauguration of the era of massively parallel computers, together with the vast increase in the amount of rapidly accessible memory that the new architectures provided. These advances and opportunities have demanded a thorough reassessment of the numerical methods that are most successfully adapted to this new computational environment. This article combines a survey of the important historical landmarks together with a somewhat speculative review of methods that, at the time of writing, seem to hold out the promise of further advancing the art and science of atmospheric numerical modeling.

CR-GAN: Learning Complete Representations for Multi-view Generation

Generating multi-view images from a single-view input is an important yet challenging problem. It has broad applications in vision, graphics, and robotics. Our study indicates that the widely-used generative adversarial network (GAN) may learn ?incomplete? representations due to the single-pathway framework: an encoder-decoder network followed by a discriminator network.We propose CR-GAN to address this problem. In addition to the single reconstruction path, we introduce a generation sideway to maintain the completeness of the learned embedding space. The two learning paths collaborate and compete in a parameter-sharing manner, yielding largely improved generality to ?unseen? dataset. More importantly, the two-pathway framework makes it possible to combine both labeled and unlabeled data for self-supervised learning, which further enriches the embedding space for realistic generations. We evaluate our approach on a wide range of datasets. The results prove that CR-GAN significantly outperforms state-of-the-art methods, especially when generating from ?unseen? inputs in wild conditions.