An extension is proposed of the Shannon entropy-based structural complexity measure introduced by Krivovichev, taking into account the geometric coordinational degrees of freedom a crystal structure has. This allows a discrimination to be made between crystal structures which share the same number of atoms in their reduced cells, yet differ in the number of their free parameters with respect to their fractional atomic coordinates. The strong additivity property of the Shannon entropy is used to shed light on the complexity measure of Krivovichev and how it gains complexity contributions due to single Wyckoff positions. Using the same property allows for combining the proposed coordinational complexity measure with Krivovichev's combinatorial one to give a unique quantitative descriptor of a crystal structure's configurational complexity. An additional contribution of chemical degrees of freedom is discussed, yielding an even more refined scheme of complexity measures which can be obtained from a crystal structure's description: the six C's of complexity.

• Klíčová slova
• Krivovichev complexity, Shannon entropy, crystal structure classification, strong additivity, structural complexity,
• Publikační typ
• časopisecké články MeSH

Uranyl sulfates, including those occurring in Nature (∼40 known members), possess particularly interesting structures. They exhibit a great dimensional and topological diversity of structures: from those based upon clusters of polyhedra to layered structures. There is also a great variability in the type of linkages between U and S polyhedra. From the point of view of complexity of those structures (measured as the amount of Shannon information per unit cell), most of the natural uranyl sulfates are intermediate (300-500 bits per cell) to complex (500-1000 bits per cell) with some exceptions, which can be considered as very complex structures (>1000 bits per cell). These exceptions are minerals alwilkinsite-(Y) (1685.95 bits per cell), sejkoraite-(Y) (1859.72 bits per cell), and natrozippeite (2528.63 bits per cell). The complexity of these structures is due to an extensive hydrogen bonding network which is crucial for the stability of these mineral structures. The hydrogen bonds help to propagate the charge from the highly charged interlayer cations (such as Y3+) or to link a high number of interlayer sites (i.e. five independent Na sites in the monoclinic natrozippeite) occupied by monovalent cations (Na+). The concept of informational ladder diagrams was applied to the structures of uranyl sulfates in order to quantify the particular contributions to the overall informational complexity and identifying the most contributing sources (topology, real symmetry, interlayer bonding).

• Klíčová slova
• Shannon information, crystal structure, ladder diagrams, structural complexity, topological complexity, uranyl sulfates,
• Publikační typ
• časopisecké články MeSH

A new method for classifying bacteria is presented and applied to a large set of biochemical data for the Enterobacteriaceae. The method minimizes the bits needed to encode the classes and the items or, equivalently, maximizes the information content of the classification. The resulting taxonomy of Enterobacteriaceae corresponds well to the general structure of earlier classifications. Minimization of stochastic complexity can be considered as a useful tool to create bacterial classifications that are optimal from the point of view of information theory.

• Klíčová slova
• Enterobacteriaceae, classification, information theory, stochastic complexity, taxonomy,
• Publikační typ
• časopisecké články MeSH

Detection of the temporal reversibility of a given process is an interesting time series analysis scheme that enables the useful characterisation of processes and offers an insight into the underlying processes generating the time series. Reversibility detection measures have been widely employed in the study of ecological, epidemiological and physiological time series. Further, the time reversal of given data provides a promising tool for analysis of causality measures as well as studying the causal properties of processes. In this work, the recently proposed Compression-Complexity Causality (CCC) measure (by the authors) is shown to be free of the assumption that the "cause precedes the effect", making it a promising tool for causal analysis of reversible processes. CCC is a data-driven interventional measure of causality (second rung on the Ladder of Causation) that is based on Effort-to-Compress (ETC), a well-established robust method to characterize the complexity of time series for analysis and classification. For the detection of the temporal reversibility of processes, we propose a novel measure called the Compressive Potential based Asymmetry Measure. This asymmetry measure compares the probability of the occurrence of patterns at different scales between the forward-time and time-reversed process using ETC. We test the performance of the measure on a number of simulated processes and demonstrate its effectiveness in determining the asymmetry of real-world time series of sunspot numbers, digits of the transcedental number π and heart interbeat interval variability.

• Klíčová slova
• compression-complexity, compressive potential, effort-to-compress, heart period variability asymmetry, interventional causality, sunspot numbers, temporal asymmetry, time-irreversibility, time-reversibility,
• Publikační typ
• časopisecké články MeSH

The massive increase in the size of deep neural networks (DNNs) is accompanied by a significant increase in energy consumption of their hardware implementations which is critical for their widespread deployment in low-power mobile devices. In our previous work, an abstract hardware-independent model of energy complexity for convolutional neural networks (CNNs) has been proposed and experimentally validated. Based on this model, we provide a theoretical analysis of energy complexity related to the computation of a fully-connected layer when its inputs, outputs, and weights are transferred between two kinds of memories (DRAM and Buffer). First, we establish a general lower bound on this energy complexity. Then, we present two dataflows and calculate their energy costs to achieve the corresponding upper bounds. In the case of a partitioned Buffer, we prove by the weak duality theorem from linear programming that the lower and upper bounds coincide up to an additive constant, and therefore establish the optimal energy complexity. Finally, the asymptotically optimal quadratic energy complexity of fully-connected layers is experimentally validated by estimating their energy consumption on the Simba and Eyeriss hardware.

• Klíčová slova
• Convolutional neural networks, Dataflow, Deep neural networks, Energy complexity, Energy consumption, Fully-connected layer,
• MeSH
• algoritmy MeSH
• deep learning MeSH
• neuronové sítě * MeSH
• počítače MeSH
• programování lineární MeSH
• Publikační typ
• časopisecké články MeSH

Recently, Pearse et al. explored the macroecology of passerine song using a large citizen science database of bird songs and machine learning techniques. They used standard deviation of frequency (SDF) as a surrogate for song complexity, finding only weak support for correlation between SDF and life-history traits such as monogamy and sexual dimorphism. Their finding that song complexity increases toward more productive environments and warmer areas seemingly contradicts several previous multitaxonomic studies. By comparing SDF scores with traditionally used song complexity metrics (syllable repertoire size and the number of syllable types per song), we found no evidence of any correlation. This may help to explain the discrepancy between their findings and findings of previous studies. While we agree that simple metrics that can be quantified and compared between multiple, highly variable species are crucial for progress in large-scale analysis of birdsong complexity, the biological relevance of SDF remains unclear and more research is needed to clarify its relevance for further studies of birdsong complexity.

• Klíčová slova
• birdsong, song complexity, syllable repertoire size,
• MeSH
• benchmarking MeSH
• vokalizace zvířat * MeSH
• zvířata MeSH
• zvláštnosti životní historie * MeSH
• Check Tag
• zvířata MeSH
• Publikační typ
• časopisecké články MeSH
• komentáře MeSH
• práce podpořená grantem MeSH

Wyckoff sequences are a way of encoding combinatorial information about crystal structures of a given symmetry. In particular, they offer an easy access to the calculation of a crystal structure's combinatorial, coordinational and configurational complexity, taking into account the individual multiplicities (combinatorial degrees of freedom) and arities (coordinational degrees of freedom) associated with each Wyckoff position. However, distinct Wyckoff sequences can yield the same total numbers of combinatorial and coordinational degrees of freedom. In this case, they share the same value for their Shannon entropy based subdivision complexity. The enumeration of Wyckoff sequences with this property is a combinatorial problem solved in this work, first in the general case of fixed subdivision complexity but non-specified Wyckoff sequence length, and second for the restricted case of Wyckoff sequences of both fixed subdivision complexity and fixed Wyckoff sequence length. The combinatorial results are accompanied by calculations of the combinatorial, coordinational, configurational and subdivision complexities, performed on Wyckoff sequences representing actual crystal structures.

• Klíčová slova
• Shannon entropy, Wyckoff sequences, combinatorics, structural complexity,
• Publikační typ
• časopisecké články MeSH

Walking is an everyday activity in our daily life. Because walking affects heart rate variability, in this research, for the first time, we analyzed the coupling among the alterations of the complexity of walking paths and heart rate. We benefited from the fractal theory and sample entropy to evaluate the influence of the complexity of paths on the complexity of heart rate variability (HRV) during walking. We calculated the fractal exponent and sample entropy of the R-R time series for nine participants who walked on four paths with various complexities. The findings showed a strong coupling among the alterations of fractal dimension (an indicator of complexity) of HRV and the walking paths. Besides, the result of the analysis of sample entropy also verified the obtained results from the fractal analysis. In further studies, we can analyze the coupling among the alterations of the complexities of other physiological signals and walking paths.

• Klíčová slova
• complexity, fractal exponent, heart rate variability, sample entropy, walking path,
• Publikační typ
• časopisecké články MeSH

Eukaryotic cells possess considerable internal complexity, differentiating them from prokaryotes. Eukaryogenesis, an evolutionary transitional period culminating in the last eukaryotic common ancestor (LECA), marked the origin of the eukaryotic endomembrane system. LECA is reconstructed as possessing intracellular complexity akin to modern eukaryotes. Construction of endomembrane compartments involved three key gene families: coatomer, BAR-domain proteins, and ESCRT. Each has a distinct evolutionary origin, but of these coatomer and BAR proteins are eukaryote specific, while ESCRT has more ancient origins. We discuss the structural motifs defining these three membrane-coating complexes and suggest that compared with BAR and ESCRT, the coatomer architecture had a unique ability to be readily and considerably modified, unlocking functional diversity and enabling the development of the eukaryotic cell.

• MeSH
• biologická evoluce MeSH
• COP-vezikuly MeSH
• endozomální třídící komplexy pro transport metabolismus   MeSH
• Eukaryota * genetika   MeSH
• eukaryotické buňky * metabolismus   MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH
• Research Support, N.I.H., Extramural MeSH
• Názvy látek
• endozomální třídící komplexy pro transport MeSH

Check dams can modify local channel and sedimentological characteristics through sediment deposition in upstream sedimentary wedges and scour processes downstream of individual check dams. However, research focusing on the channel reaches between subsequent check dams (referred to here as intermediate reaches) is limited. We evaluated channel complexity and its selected dimensions (longitudinal and cross-section heterogeneity, sediment characteristics and the presence of instream wood) in 30-m long intermediate reaches (n = 10) between subsequent check dams in comparison with channel reaches that were not treated with check dams (n = 10) in both a stepped-bed stream in a steep confined valley and an originally pool-riffle stream in an unconfined foothill valley. Check dams altered the channel complexity of intermediate reaches when compared with reaches of undisturbed streams. However, in contrast to foothills streams, check dams did not heavily affect longitudinal or cross-sectional heterogeneity of the intermediate reaches in the steep streams. Despite an increase in sediment homogeneity in steep reaches treated with check dams, the presence of coarse bed sediments helped to preserve their stepped-bed morphology. In contrast, the longitudinal profile of the treated foothill stream completely lost its vertical oscillations because of the transformation of pool-riffles to a uniform plane bed morphology. Similarly, cross-sectional heterogeneity in the foothill stream was degraded in comparison with those of untreated reaches. We did not observe differences in instream wood abundance between treated and untreated streams.

• Klíčová slova
• Channel complexity, Check dam, Mountain stream, Stream management, Western Carpathians,
• Publikační typ
• časopisecké články MeSH