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A well-known result in dynamical systems asserts that any Cantor minimal system $(X,T)$ has a maximal rational equicontinuous factor $(Y,S)$ which is in fact an odometer, and realizes the rational subgroup of the $K_0$-group of $(X,T)$, that is, $\mathbb{Q}(K_0(X,T), 1) \cong K^0(Y,S)$. We introduce the notion of a maximal UHF subalgebra and use it to obtain the C*-algebraic alonog of this result. We say a UHF subalgebra $B$ of a unital C*-algebra $A$ is a maximal UHF subalgebra if it contains the unit of $A$ any other such C*-subalgebra embeds unitaly into $B$. We prove that if $K_0(A)$ is unperforated and has a certain $K_0$-lifting property, then $B$ exists and is unique up to isomorphism, in particular, all simple separable unital C*-algebras with tracial rank zero and all unital Kirchberg algebras whose $K_0$-groups are unperforated, have a maximal UHF subalgebra. Not every unital C*-algebra has a maximal UHF subalgebra, for instance, the unital universal free product $\mathrm{M}_2 \ast_{r} \mathrm{M}_3$. As an application, we give a C*-algebraic realization of the rational subgroup $\mathbb{Q}(G,u)$ of any dimension group $G$ with order unit $u$, that is, there is a simple unital AF algebra (and a unital Kirchberg algebra) $A$ with a maximal UHF subalgebra $B$ such that $(G,u)\cong (K_0(A), [1]_0)$ and and $\mathbb{Q}(G,u)\cong K_0(B)$., Comment: 27 pages

Due to the concerns of the society about the increase of antibiotic resistant infections, many studies and research have been done on nanoparticles and applications of nano-biotechnology. Zirconium Oxide ($\text{ZrO}_{2}$) in which called zirconia, is a white oxide of zirconium metal that its diameter is 20 nm. The colloidal size of these particles is often smaller than bacterial and eukaryotic cells. The main intention of this paper is to investigate the effect of different doses of $\text{ZrO}_{2}$ NPs on the sequences changes for the $\textit{Escherichia coli}$ ($\textit{E. coli}$) genome. At the first step, $\textit{E. coli}$ was cultured in eosin methylene blue agar and brain heart broth (BHB) mediums, respectively. Then, bacteria were treated with $\text{ZrO}_{2}$ NPs at concentrations of 100, 250, and 350 $\mu$g/ml. After treatment, the growth of bacteria was evaluated by utilizing spectrophotometry at 600 nm after incubation times including 2, 4, 6, 8, and 24 hours at 37 $^{\circ}$C. At the second step, the extraction of DNA was performed by using control and treated samples. Then, the changes in the sequence of bacterial genome were investigated using RAPD markers. Finally, NTSYS-PC platform was employed in order to analyze of the results extracted by electrophoresis of products on agarose gel. In this paper, it was observed that $\text{ZrO}_{2}$ NPs can inhibit the growth of bacteria at concentrations of 250 and 350 $\mu$g/ml after 8 hours of treatment. It was also found that the $\text{ZrO}_{2}$ NPs at different concentrations have not changed the genome sequence of $\textit{E. coli}$. Furthermore, it was concluded that the $\text{ZrO}_{2}$ NPs with the concentration of 350 $\mu$g/ml had the highest inhibitory properties without significant changing in the genomic sequence of $\textit{E. coli}$., Comment: 18 Pages, 6 Figures, 6 Tables

A long-standing open question in the theory of group actions on C*-algebras is the stable rank of the crossed product. Specifically, N. C. Phillips asked that if a finite group $G$ acts on a simple unital C*-algebra $A$ with stable rank one, does the crossed product have stable rank one? A similar question can be asked about the real rank. Most of the existing partial answers contain a reasonable restriction (mainly, a Rokhlin-type property) on the action and assumptions on $A$. We remove all extra assumptions on $A$ (for instance, stable finiteness and that the order on projections over $A$ is determined by traces) and we prove that if the action has the tracial Rokhlin property and $A$ is simple and $\sigma$-unital with stable rank one or real rank zero, then so do the crossed product and the fixed point algebra. Moreover, we show that if the Kirchberg's central sequence algebra $\mathrm{F}(A)$ has real rank zero, then the weak tracial Rokhlin property is equivalent to the tracial Rokhlin property for actions on simple unital separable C*-algebras $A$., Comment: 17 pages. arXiv admin note: text overlap with arXiv:1711.10818

In many fMRI studies, respiratory signals are unavailable or do not have acceptable quality. Consequently, the direct removal of low-frequency respiratory variations from BOLD signals is not possible. This study proposes a one-dimensional CNN model for reconstruction of two respiratory measures, RV and RVT. Results show that a CNN can capture informative features from resting BOLD signals and reconstruct realistic RV and RVT timeseries. It is expected that application of the proposed method will lower the cost of fMRI studies, reduce complexity, and decrease the burden on participants as they will not be required to wear a respiratory bellows., Comment: 6 pages, 5 figures

We show that every topological factoring between two zero dimensional dynamical systems can be represented by a sequence of morphisms between the levels of the associated ordered Bratteli diagrams. Conversely, we will prove that given an ordered Bratteli diagram $B$ with a continuous Vershik map on it, every sequence of morphisms between levels of $B$ and $C$, where $C$ is another ordered Bratteli diagram with continuous Vershik map, induces a topological factoring if and only if $B$ has a unique infinite min path. We present a method to construct various examples of ordered premorphisms between two decisive Bratteli diagrams such that the induced maps between the two Vershik systems are not topological factorings. We provide sufficient conditions for the existence of a topological factoring from an ordered premorphism. Expanding on the modelling of factoring, we generalize the Curtis-Hedlund-Lyndon theorem to represent factor maps between two zero dimensional dynamical systems through sequences of sliding block codes., Comment: 43 pages

Light is a key information carrier, enabling worldwide high-speed data transmission through a telecommunication fibre network. This information-carrying capacity can be extended to transmitting quantum information (QI) by encoding it in single photons -- flying qubits. However, various QI-processing platforms operate at vastly different timescales. QI-processing units in atomic media, operating within nanosecond to microsecond timescales, and high-speed quantum communication, at picosecond timescales, cannot be efficiently linked due to orders of magnitude mismatch in the timescales or, correspondingly, spectral linewidths. In this work, we develop a large-aperture time lens using complex high-bandwidth electro-optic phase modulation to bridge this gap. We demonstrate coherent, deterministic spectral bandwidth compression of quantum light pulses by more than two orders of magnitude with high efficiency. It will facilitate large-scale hybrid QI-processing by linking the ultrafast and quasi-continuous-wave experimental platforms, which until now, to a large extent, have been developing independently., Comment: 8 pages + 3 supplement, 5 + 2 figures, version accepted for publication

The power spectrum of an optical field can be acquired without a spectrally resolving detector by means of Fourier-transform spectrometry, based on measuring the temporal autocorrelation of the optical field. Analogously, we here perform temporal envelope measurements of ultrashort optical pulses without time resolved detection. We introduce the technique of Fourier transform chronometry, where the temporal envelope is acquired by measuring the frequency autocorrelation of the optical field in a linear interferometer. We apply our technique, which is the time-frequency conjugate measurement to Fourier-transform spectrometry, to experimentally measure the pulse envelope of classical and single photon light pulses., Comment: 4 figures

We show that if $A$ is a simple (not necessarily unital) tracially $\mathcal{Z}$-absorbing C*-algebra and $\alpha \colon G \to \mathrm{Aut} (A)$ is an action of a finite group $G$ on $A$ with the weak tracial Rokhlin property, then the crossed product $C^*(G, A,\alpha)$ and the fixed point algebra $A^\alpha$ are simple and tracially $\mathcal{Z}$-absorbing, and they are $\mathcal{Z}$-stable if, in addition, $A$ is separable and nuclear. The same conclusion holds for all intermediate C*-algebras of the inclusions $A^\alpha \subseteq A$ and $A \subseteq C^*(G, A,\alpha)$. We prove that if $A$ is a simple tracially $\mathcal{Z}$-absorbing C*-algebra, then, under a finiteness condition, the permutation action of the symmetric group $S_m$ on the minimal $m$-fold tensor product of $A$ has the weak tracial Rokhlin property. We define the weak tracial Rokhlin property for automorphisms of simple C*-algebras and we show that -- under a mild assumption -- (tracial) $\mathcal{Z}$-absorption is preserved under crossed products by such automorphisms., Comment: 42 pages, a new main result is added (Corollary C)

Text coherence is a fundamental problem in natural language generation and understanding. Organizing sentences into an order that maximizes coherence is known as sentence ordering. This paper is proposing a new approach based on the graph neural network approach to encode a set of sentences and learn orderings of short stories. We propose a new method for constructing sentence-entity graphs of short stories to create the edges between sentences and reduce noise in our graph by replacing the pronouns with their referring entities. We improve the sentence ordering by introducing an aggregation method based on majority voting of state-of-the-art methods and our proposed one. Our approach employs a BERT-based model to learn semantic representations of the sentences. The results demonstrate that the proposed method significantly outperforms existing baselines on a corpus of short stories with a new state-of-the-art performance in terms of Perfect Match Ratio (PMR) and Kendall's Tau (Tau) metrics. More precisely, our method increases PMR and Tau criteria by more than 5% and 4.3%, respectively. These outcomes highlight the benefit of forming the edges between sentences based on their cosine similarity. We also observe that replacing pronouns with their referring entities effectively encodes sentences in sentence-entity graphs.

Computer architecture design space is vast and complex. Tools are needed to explore new ideas and gain insights quickly, with low efforts and at a desired accuracy. We propose Calipers, a criticality-based framework to model key abstractions of complex architectures and a program's execution using dynamic event-dependence graphs. By applying graph algorithms, Calipers can track instruction and event dependencies, compute critical paths, and analyze architecture bottlenecks. By manipulating the graph, Calipers enables architects to investigate a wide range of Instruction Set Architecture (ISA) and microarchitecture design choices/"what-if" scenarios during both early- and late-stage design space exploration without recompiling and rerunning the program. Calipers can model in-order and out-of-order microarchitectures, structural hazards, and different types of ISAs, and can evaluate multiple ideas in a single run. Modeling algorithms are described in detail. We apply Calipers to explore and gain insights in complex microarchitectural and ISA ideas for RISC and EDGE processors, at lower effort than cycle-accurate simulators and with comparable accuracy. For example, among a variety of investigations presented in the paper, experiments show that targeting only a fraction of critical loads can help realize most benefits of value prediction.

We define a notion of tracial $\mathcal{Z}$-absorption for simple not necessarily unital C*-algebras, study it systematically, and prove its permanence properties. This extends the notion defined by Hirshberg and Orovitz for unital C*-algebras. The Razak-Jacelon algebra, simple C*-algebras with tracial rank zero, and simple purely infinite C*-algebras are tracially $\mathcal{Z}$-absorbing. We obtain the first purely infinite examples of tracially $\mathcal{Z}$-absorbing C*-algebras which are not $\mathcal{Z}$-absorbing. We use techniques from reduced free products of von~Neumann algebras to construct these examples. A stably finite example was given by Z. Niu and Q. Wang in 2021. We study the Cuntz semigroup of a simple tracially $\mathcal{Z}$-absorbing C*-algebra and prove that it is almost unperforated and the algebra is weakly almost divisible., Comment: 46 pages. Some misprints are fixed. Some references to 2108.08970v2 and 2101.07900v1 are added