Tranberglarkin6084

We supply corrected proofs of the invariance of completion and the chain rule for the Shannon information measures of arbitrary fields, as stated by Dębowski in 2009. check details Our corrected proofs rest on a number of auxiliary approximation results for Shannon information measures, which may be of an independent interest. As also discussed briefly in this article, the generalized calculus of Shannon information measures for fields, including the invariance of completion and the chain rule, is useful in particular for studying the ergodic decomposition of stationary processes and its links with statistical modeling of natural language.Non-Hermitian quantum-Hamiltonian-candidate combination H λ of a non-Hermitian unperturbed operator H = H 0 with an arbitrary "small" non-Hermitian perturbation λ W is given a mathematically consistent unitary-evolution interpretation. The formalism generalizes the conventional constructive Rayleigh-Schrödinger perturbation expansion technique. It is sufficiently general to take into account the well known formal ambiguity of reconstruction of the correct physical Hilbert space of states. The possibility of removal of the ambiguity via a complete, irreducible set of observables is also discussed.High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the "blessing of dimensionality", has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.Previous literature has demonstrated that hypoglycemic events in patients with type 1 diabetes (T1D) are associated with measurable scalp electroencephalography (EEG) changes in power spectral density. In the present study, we used a dataset of 19-channel scalp EEG recordings in 34 patients with T1D who underwent a hyperinsulinemic-hypoglycemic clamp study. We found that hypoglycemic events are also characterized by EEG complexity changes that are quantifiable at the single-channel level through empirical conditional and permutation entropy and fractal dimension indices, i.e., the Higuchi index, residuals, and tortuosity. Moreover, we demonstrated that the EEG complexity indices computed in parallel in more than one channel can be used as the input for a neural network aimed at identifying hypoglycemia and euglycemia. The accuracy was about 90%, suggesting that nonlinear indices applied to EEG signals might be useful in revealing hypoglycemic events from EEG recordings in patients with T1D.In this paper, we obtain upper bounds on the minimum distance for turbo codes using fourth degree permutation polynomial (4-PP) interleavers of a specific interleaver length and classical turbo codes of nominal 1/3 coding rate, with two recursive systematic convolutional component codes with generator matrix G = [ 1 , 15 / 13 ] . The interleaver lengths are of the form 16 Ψ or 48 Ψ , where Ψ is a product of different prime numbers greater than three. Some coefficient restrictions are applied when for a prime p i ∣ Ψ , condition 3 ∤ ( p i - 1 ) is fulfilled. Two upper bounds are obtained for different classes of 4-PP coefficients. link2 For a 4-PP f 4 x 4 + f 3 x 3 + f 2 x 2 + f 1 x ( mod 16 k L Ψ ) , k L ∈ 1 , 3 , the upper bound of 28 is obtained when the coefficient f 3 of the equivalent 4-permutation polynomials (PPs) fulfills f 3 ∈ 0 , 4 Ψ or when f 3 ∈ 2 Ψ , 6 Ψ and f 2 ∈ ( 4 k L - 1 ) · Ψ , ( 8 k L - 1 ) · Ψ , k L ∈ 1 , 3 , for any values of the other coefficients. The upper bound of 36 is obtained when the coefficient f 3 of the equivalent 4-PPs fulfills f 3 ∈ 2 Ψ , 6 Ψ and f 2 ∈ ( 2 k L - 1 ) · Ψ , ( 6 k L - 1 ) · Ψ , k L ∈ 1 , 3 , for any values of the other coefficients. Thus, the task of finding out good 4-PP interleavers of the previous mentioned lengths is highly facilitated by this result because of the small range required for coefficients f 4 , f 3 and f 2 . It was also proven, by means of nonlinearity degree, that for the considered inteleaver lengths, cubic PPs and quadratic PPs with optimum minimum distances lead to better error rate performances compared to 4-PPs with optimum minimum distances.We present a history of thermodynamics. Part 1 discusses definitions, a pre-history of heat and temperature, and steam engine efficiency, which motivated thermodynamics. Part 2 considers in detail three heat conservation-based foundational papers by Carnot, Clapeyron, and Thomson. For a reversible Carnot cycle operating between thermal reservoirs with Celsius temperatures t and t + d t , heat Q from the hot reservoir, and net work W, Clapeyron derived W / Q = d t / C ( t ) , with C ( t ) material-independent. Thomson used μ = 1 / C ( t ) to define an absolute temperature but, unaware that an additional criterion was needed, he first proposed a logarithmic function of the ideal gas temperature T g . Part 3, following a discussion of conservation of energy, considers in detail a number of energy conservation-based papers by Clausius and Thomson. As noted by Gibbs, in 1850, Clausius established the first modern form of thermodynamics, followed by Thomson's 1851 rephrasing of what he called the Second Law. In 1854, Clausius theoretically established for a simple Carnot cycle the condition Q 1 / T 1 + Q 2 / T 2 = 0 . He generalized it to ∑ i Q i / T g , i = 0 , and then ∮ d Q / T g = 0 . This both implied a new thermodynamic state function and, with appropriate integration factor 1 / T , the thermodynamic temperature. In 1865, Clausius named this new state function the entropy S.How different are the emerging and the well-developed stock markets in terms of efficiency? To gain insights into this question, we compared an important emerging market, the Chinese stock market, and the largest and the most developed market, the US stock market. Specifically, we computed the Lempel-Ziv complexity (LZ) and the permutation entropy (PE) from two composite stock indices, the Shanghai stock exchange composite index (SSE) and the Dow Jones industrial average (DJIA), for both low-frequency (daily) and high-frequency (minute-to-minute)stock index data. We found that the US market is basically fully random and consistent with efficient market hypothesis (EMH), irrespective of whether low- or high-frequency stock index data are used. The Chinese market is also largely consistent with the EMH when low-frequency data are used. link3 However, a completely different picture emerges when the high-frequency stock index data are used, irrespective of whether the LZ or PE is computed. In particular, the PE decreases substantially in two significant time windows, each encompassing a rapid market rise and then a few gigantic stock crashes. To gain further insights into the causes of the difference in the complexity changes in the two markets, we computed the Hurst parameter H from the high-frequency stock index data of the two markets and examined their temporal variations. We found that in stark contrast with the US market, whose H is always close to 1/2, which indicates fully random behavior, for the Chinese market, H deviates from 1/2 significantly for time scales up to about 10 min within a day, and varies systemically similar to the PE for time scales from about 10 min to a day. This opens the door for large-scale collective behavior to occur in the Chinese market, including herding behavior and large-scale manipulation as a result of inside information.In this paper, a new image encryption transmission algorithm based on the parallel mode is proposed. This algorithm aims to improve information transmission efficiency and security based on existing hardware conditions. To improve efficiency, this paper adopts the method of parallel compressed sensing to realize image transmission. Compressed sensing can perform data sampling and compression at a rate much lower than the Nyquist sampling rate. To enhance security, this algorithm combines a sequence signal generator with chaotic cryptography. The initial sensitivity of chaos, used in a measurement matrix, makes it possible to improve the security of an encryption algorithm. The cryptographic characteristics of chaotic signals can be fully utilized by the flexible digital logic circuit. Simulation experiments and analyses show that the algorithm achieves the goal of improving transmission efficiency and has the capacity to resist illegal attacks.A novel lightweight Al-Ti-Cr-Mn-V medium-entropy alloy (MEA) system was developed using a nonequiatiomic approach and alloys were produced through arc melting and drop casting. These alloys comprised a body-centered cubic (BCC) and face-centered cubic (FCC) dual phase with a density of approximately 4.5 g/cm3. However, the fraction of the BCC phase and morphology of the FCC phase can be controlled by incorporating other elements. The results of compression tests indicated that these Al-Ti-Cr-Mn-V alloys exhibited a prominent compression strength (~1940 MPa) and ductility (~30%). Moreover, homogenized samples maintained a high compression strength of 1900 MPa and similar ductility (30%). Due to the high specific compressive strength (0.433 GPa·g/cm3) and excellent combination of strength and ductility, the cast lightweight Al-Ti-Cr-Mn-V MEAs are a promising alloy system for application in transportation and energy industries.In graph theory, Hamiltonian path refers to the path that visits each vertex exactly once. In this paper, we designed a method to generate random Hamiltonian path within digital images, which is equivalent to permutation in image encryption. By these means, building a Hamiltonian path across bit planes can shuffle the distribution of the pixel's bits. Furthermore, a similar thought can be applied for the substitution of pixel's grey levels. To ensure the randomness of the generated Hamiltonian path, an adjusted Bernoulli map is proposed. By adopting these novel techniques, a bit-level image encryption scheme was devised. Evaluation of simulation results proves that the proposed scheme reached fair performance. In addition, a common flaw in calculating correlation coefficients of adjacent pixels was pinpointed by us. After enhancement, correlation coefficient becomes a stricter criterion for image encryption algorithms.In this article an energy disaggregation architecture using elastic matching algorithms is presented. The architecture uses a database of reference energy consumption signatures and compares them with incoming energy consumption frames using template matching. In contrast to machine learning-based approaches which require significant amount of data to train a model, elastic matching-based approaches do not have a model training process but perform recognition using template matching. Five different elastic matching algorithms were evaluated across different datasets and the experimental results showed that the minimum variance matching algorithm outperforms all other evaluated matching algorithms. The best performing minimum variance matching algorithm improved the energy disaggregation accuracy by 2.7% when compared to the baseline dynamic time warping algorithm.