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Introduction: Phantom limb pain (PLP) as neuropathic pain affects the life of amputees. It is believed an efficient PLP treatment should consider the underlying neurological mechanisms. Hereby, we investigated brain activity in PLP and its relationships to the psychological and cognitive dimensions of chronic pain. We investigate differences in resting brain activities between amputees with and without pain. We hypothesize significant differences in the motor cortex and parietal cortex activity that are related to pain perception. Also, we hypothesize two groups have significant differences in cognitive and psychological components. Methods: Behavioral assessment (psychological status, life satisfaction, and pain level) and EEG signals of 19 amputees (12 without pain and 7 with pain) were recorded. Data were statistically compared between the two groups. Also, the association between behavioral and neurophysiological data was computed. Results: The results showed a significant decrease in the pain group for the beta and gamma waves, as well as, for the theta and delta waves in the posterior temporal on both sides, during the eye-open condition. The eyes-closed condition showed that the delta waves were decreased on the right side of the cortex. Also, data showed a significant difference in the correlation of pain features with brain waves between the two groups. Conclusion: Significant differences were mostly observed in regions related to pain perception rather than the motor cortex. This can be due to the learned strategies to deal with pain and the degree of pain. Results showed maladaptive cognitive processes had a relationship with brain wave activities. According to the result of brain wave activities, it seems that cognitive factors have a role in the experience of PLP rather than neuroplasticity through amputation.

This paper applies a powerful scheme, namely Bernoulli sub-equation function method, to some partial differential equations with high non-linearity. Many new travelling wave solutions, such as mixed dark-bright soliton, exponential and complex domain, are reported. Under a suitable choice of the values of parameters, wave behaviours of the results obtained in the paper – in terms of 2D, 3D and contour surfaces – are observed.

This paper reviews and classifies representative types of ?Differential Power Processing, DPP? architectures, focusing on the aspect of how the processed power is reduced with DPP. Comparing to existing review works on this topic, this paper provides new viewpoints from three perspectives: (1) the differential power Pdiff at both architecture level and converter level is discussed. For the calculation of the total processed power in a power architecture, instead of summing up the output power Pout delivered by the DPP converters, we account for Pdiff inside the DPP converters, because direct power exists not only at the architecture level, but also at the converter level, so the power processed in a converter may be lower than Pout. (2) The VA area modeling is applied to the DPP architectures to illustrate and visualize the processed power in the power architectures and converters, thus analyzing and comparing them at high level. (3) The processed power of different DPP architectures is compared quantitively with statistical analysis for varied operating situations.

Introduction: Natural rewards are essential for survival. However, drug-seeking behaviors can be maladaptive and endanger survival. The present study was conducted to enhance our understanding of how animals respond to food and morphine as natural and drug rewards, respectively, in a conditioned place preference (CPP) paradigm. Methods: We designed a protocol to induce food CPP and compare it as a natural reward with morphine CPP in rats. The protocol for reward induction in both groups (foods and morphine) consisted of three phases: pre-test, conditioning, and post-test. In morphine groups, we injected morphine as a reward (5 mg/kg, SC). To induce natural reward, we used two different protocols. In the first one, the rats were deprived of food for 24 h. In the other method, the rats were restricted to food for 14 days. During the conditioning period, the animals received daily chow, biscuits, or popcorn as a reward inducer. Results: Results revealed that CPP was not induced in food-deprived rats. A combination of food restriction (as a facilitator) and a biscuit or popcorn-induced reward using CPP. In contrast, food deprivation did not facilitate food CPP in response to regular food. Interestingly the CPP score of the group which received biscuits during a 7-day conditioning period was more than that of the morphine group. Conclusion: In conclusion, food restriction could be a better protocol than food deprivation to facilitate food reward.

We extend the block filtration, defined by Brown based on the work of Charlton, to all motivic multiple zeta values, and study relations compatible with this filtration. We construct a Lie algebra describing relations among motivic multiple zeta values modulo terms of lower block degree, proving Charlton's cyclic insertion conjecture in this structure, and showing the existence of a `block shuffle' relation, and a previously unknown dihedral symmetry and differential relation., Comment: 23 pages, based on work in the author's doctoral thesis. Typo in statement of Corollary 2.9 corrected

Let $k$ be a perfect field of positive characteristic and $Z$ an effective Cartier divisor in the projective line over $k$ with complement $U$. In this note, we establish some results about the formal deformation theory of overconvergent isocrystals on $U$ with fixed "local monodromy" along $Z$. En route, we show that a Hochschild cochain complex governs deformations of a module over an arbitrary associative algebra. We also relate this Hochschild cochain complex to a de Rham complex in order to understand the deformation theory of a differential module over a differential ring., 59 pages; fixed typos, improved exposition; comments welcome!

Differential-algebraic equations (DAEs) are a widespread dynamical model that describes continuously evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. As such, DAEs arise in many fields ranging from physics, chemistry, and engineering. In this article, we focus on linear DAEs, and develop a theory for their minimization up to an equivalence relation. We present differential equivalence, which relates DAE variables that have equal solutions at all time points (thus requiring them to start with equal initial conditions) and extends the line of research on bisimulations developed for Markov chains and ordinary differential equations. We apply our results to the electrical engineering domain, showing that differential equivalence can explain invariances in certain networks as well as analyze DAEs, which could not be originally treated due to their size.

This article presents an efficient method to solve of Eikonal equation by the new differential quadrature method. The purpose of this article is to obtain the accuracy and performance method for the Eikonal equation. We introduce a novel grid points to reduce errors and compared them on different issues to accelerate convergence. The accuracy and stability of numerical results for two and three-dimensional of the Eikonal equation are presented. In these numerical examples, we investigate the stability of the proposed method by adding random noises. The new differential quadrature method is a capable method for the some numerical examples and we evaluate the accuracy and performance of our proposed method.

In this paper we develop a general computer-assisted proof method for periodic solutions to delay differential equations. The class of problems considered includes systems of delay differential equations with an arbitrary number of (forward and backward) delays. When the nonlinearities include nonpolynomial terms we introduce auxiliary variables to first rewrite the problem into an equivalent polynomial one. We then apply a flexible fixed point technique in a space of geometrically decaying Fourier coefficients. We showcase the efficacy of this method by proving periodic solutions in the well-known Mackey–Glass delay differential equation for the classical parameter values.

We study a class of linear-quadratic stochastic differential games in which each player interacts directly only with its nearest neighbors in a given graph. We find a semiexplicit Markovian equilibrium for any transitive graph, in terms of the empirical eigenvalue distribution of the graph’s normalized Laplacian matrix. This facilitates large-population asymptotics for various graph sequences, with several sparse and dense examples discussed in detail. In particular, the mean field game is the correct limit only in the dense graph case, that is, when the degrees diverge in a suitable sense. Although equilibrium strategies are nonlocal, depending on the behavior of all players, we use a correlation decay estimate to prove a propagation of chaos result in both the dense and sparse regimes, with the sparse case owing to the large distances between typical vertices. Without assuming the graphs are transitive, we show also that the mean field game solution can be used to construct decentralized approximate equilibria on any sufficiently dense graph sequence.

Rainfall components likely differ in the magnitude and direction of their long-term changes for any given location, and some rainfall components may carry a greater regional signal of change than rainfall totals. This study evaluates the magnitude of change of multiple rainfall components relative to other components, and the greatest regions of change across all rainfall components in West Africa. Hourly rainfall data from the ERA5 reanalysis dataset was used to derive twelve rainfall components, which were evaluated for long-term means, interannual variability, and long-term changes. For rainfall totals and rainfall intensity, the central Sahel is witnessing increasing trends while the western Sahel is experiencing significant decreasing trends. In general, decreasing trends predominate in the study domain, especially in the northwestern Congo Basin, where annual rainfall is decreasing by 120mm per decade. Importantly, rainfall frequency accounts for 49% of all significant grid-point trends for the whole domain. In contrast, rainfall totals account for 26% of all combined significant trends across the domain, while rainfall intensity (12.6%), rainy season length (9.5%), and seasonality (3.3%) account for the remaining signals of change. Most of the changes among the rainfall components are in the Tropical Wet and Dry regions (59% of all significant trends); the Saharan and Equatorial regions account for the least changes. This study finds evidence that rainfall frequency is changing more across the regions compared to rainfall totals and should be explored as rainfall inputs in climate models to potentially improve regional predictions of future rainfall.

We show that if the cochain complex computing Ext groups (in the category of modules over Hopf algebroids) admits a cocyclic structure, then the noncommutative Cartan calculus structure on Tor over Ext dualises in a cyclic sense to a calculus on Coext over Cotor. More precisely, the cyclic duals of the chain resp. cochain spaces computing the two classical derived functors lead to complexes that compute the more exotic ones, giving a cyclic opposite module over an operad with multiplication that induce operations such as a Lie derivative, a cap product (or contraction), and a (cyclic) differential, along with higher homotopy operators defining a noncommutative Cartan calculus up to homotopy. In particular, this allows to recover the classical Cartan calculus from differential geometry or the Chevalley-Eilenberg calculus for Lie(-Rinehart) algebras without any finiteness conditions or the use of topological tensor products., Comment: 31 pages; to appear in Ann. Sc. Norm. Super. Pisa, Cl. Sci

Wastewater treatment plants (WWTP) are required to meet increasingly stringent effluent quality standards as well as to improve process sustainability in terms of energy efficiency, in line with the call for a paradigm shift towards the more sustainable concept of wastewater resource recovery facility (WRRF). In this context, optimised Instrumentation, Control and Automation (ICA) systems as well as process and plant-wide modelling have become key tools for optimising economic and environmental costs. The present work reports on the successfull integration of an innovative on-line continuous titrimeter and plant-wide modelling as a support tool for the optimisation of the nitritification unit in a large-scale industrial WWTP. The information gathered from the on-line titrimeter allowed for real-time estimation of the Ammonia Oxidation Rate of the activated sludge and, ultimately, of the nitrification residual capacity of the plant. Results on the titrimeter long-term operation and historical data modelling supported plant managing decisions, such as lowering the dissolved oxygen (DO) set-point of the oxidation unit, straightforwardly resulting in energy saving. Graphical abstract

Lesamnta‐LW‐BC is the internal block cipher of the Lesamnta‐LW lightweight hash function, specified in ISO/IEC 29192‐5:2016. It is based on the unbalanced Feistel network and Advanced Encryption Standard round function. In this study, the security of Lesamnta‐LW‐BC against integral and impossible‐differential attacks is evaluated. Specifically, the authors searched for the integral distinguishers and impossible differentials with Mixed‐Integer Linear Programming‐based methods. As a result, the discovered impossible differential can reach up to 21 rounds, while three integral distinguishers reaching 18, 19 and 25 rounds are obtained, respectively. Moreover, it is also feasible to construct a 47‐round integral distinguisher in the known‐key setting. Finally, a 20‐round key‐recovery attack is proposed based on the discovered 18‐round integral distinguisher and a 19‐round key‐recovery attack using a 17‐round impossible differential. To the best of the authors' knowledge, this is the first third‐party cryptanalysis of Lesamnta‐LW‐BC.

This article investigates transverse cracking in embankment dams resulting from cross-valley differential settlements during and post-construction, in which concentrated leak erosion may initiate. Based on case studies and numerical analyses, it is shown that valley profiles with a step in the upper part of the abutment and subject to large post-construction settlements within the embankment, or within compressible soil in the foundation, are most likely to be subject to cracking. Estimated localised strains at the crest > 1%, and in particular >2%, are likely to be indicative of conditions conducive to transverse cracking. Smaller strains but greater than about 0.25% may also result in cracking but they are likely to be narrower and shallower. The article also gives general guidance on the likely width and depth of cracking. The information presented is only suitable for preliminary dam safety assessments. For detailed dam safety assessments and risk assessments where decisions are to be made on whether risks are tolerable, or upgrades required, site-specific cross-valley numerical analyses should be carried out. These detailed analyses should model the cross-valley profile accurately, material parameters more rigorously than has been done in the parametric studies reported in this article.

The impedance parameters of a two-port network are employed to deduce the differential and common-mode as well as single-ended input impedances of a differential antenna. The relationships between these impedances are considered. It is shown that there exist simple quantitative relations, which may be used to determine one impedance from the other whose solution is already known. In addition, an important attempt is made to extend Booker's relation for differential complementary dipoles and slots to single-ended counterparts.

The fuzzy integral equation is used to model many physical phenomena which arise in many fields like chemistry, physics, and biology, etc. In this article, we emphasize on mathematical modeling of the fuzzy fractional Fredholm–Volterra integral equation. The numerical solution of the fuzzy fractional Fredholm–Volterra equation is determined in which model contains fuzzy coefficients and fuzzy initial condition. First, an operational matrix of Chebyshev polynomial of Caputo type fractional fuzzy derivative is derived in fuzzy environment. The integral term is approximated by the Chebyshev spectral method and the differential term is approximated by the operational matrix. This method converted the given fuzzy fractional integral equation into algebraic equations which are fuzzy in nature. The desired numerical solution is to find out by solving these algebraic equations. The different particular cases of our model have been solved which depict the feasibility of our method. The error tables show the accuracy of the method. We also can see the accuracy of our method by 3D figures of exact and obtained numerical solutions. Hence, our method is suitable to deal with the fuzzy fractional Fredholm–Volterra equation.

Background: Serum uric acid (UA) is positively correlated with bone mineral density (BMD). However, the mechanism by which serum UA affects BMD remains unclear. Objective: The aim was carried out to search for the functional proteins related to serum UA and femoral neck BMD to better understand the pathophysiological mechanism of osteoporosis. Materials and Methods: In this study, patients in the UA group (hyperuricaemia combined with femoral neck fracture) and the control group (normal uricaemia combined with femoral neck fracture) were selected according to the inclusion criteria. Total protein was extracted from the femoral neck of each patient. Fluorescence differential gel electrophoresis was used to separate the total proteins, and the differentially expressed protein spots were detected by image analysis. After enzyme digestion, peptide mass fingerprinting and database searches were performed to identify the differentially expressed proteins. DAVID software and Kyoto Encyclopedia of Genes and Genomes (KEGG) data were used for enrichment analysis of the screened differential proteins. Results: After mass spectrometry and database searching, 66 differentially expressed protein spots were identified between the UA group and the control group. Most differentially expressed proteins functioned in cytoskeleton formation, energy metabolism, or signal transduction. They were mainly involved in 50 biological processes, including peroxisome proliferator-activated receptor (PPAR) signalling and fatty acid metabolism. PPARγ and PLIN1 were subject to Western blotting analysis detection; results were consistent with the Label-Free result. Conclusion: Based on an analysis of the biological information, these proteins may be associated with the incidence and progression of the femoral neck bone tissues of hyperuricaemia patients.

У статті наведено результати хірургічного лікування 287 пацієнтів (463 стопи) з поперечно-розпластаною деформацією переднього відділу стоп і hallux valgus із застосуванням диференційованого підходу до вибору методу корекції деформації. Пацієнтам за індивідуальними показаннями виконувалися відомі у світі хірургічні втручання, такі як клиноподібна остеотомія першої плеснової кістки, остеотомія Austin, остеотомія Scarf, Lapidus артродез і остеотомія Akin на проксимальній фаланзі першого пальця. У 68 (23,7 %) і 159 (55,4 %) випадках досягнуті відмінні і добрі відповідно результати лікування згідно з бальною шкалою AOFAS.

Изложены представления об этиологии, патогенезе, диагностике, дифференциальной диагностике и лечении эритроцитозов. Особенные акценты сделаны на вопросах лабораторной диагностики.

Drawing inspiration from Nyberg’s paper (Nyberg, 1991) on perfect nonlinearity and the c -differential notion we defined in Ellingsen et al. (2020), in this paper we introduce the concept of c -differential bent functions in two different ways (thus extending Kumar et al. (1985) classical definition). We further extend the notion of perfect c -nonlinear introduced in Ellingsen et al. (2020), also in two different ways, and show that, in both cases, the concepts of c -differential bent and perfect c -nonlinear are equivalent (under some natural restriction of the parameters). Some constructions of functions with these properties are also provided; one such construction provides a large class of PcN functions with respect to all c in some subfield of the field under consideration. We also show that both our classes of 0-differential bents are supersets of permutation polynomials, and that Maiorana–McFarland bent functions are not differential bent (of the first kind).

By employing the properties of centered realizations, we devise a modified version of the dual Riccati equation approach to optimal $\mathcal {H}_{2}$ control for differential-algebraic systems that is guaranteed to be more computationally efficient and numerically accurate than other methods from literature. Moreover, we show that if the optimal controller has an improper transfer function matrix, then all controllers which ensure a finite $\mathcal {H}_{2}$ norm will share this property.

The present work is to solve the nonlinear singular models using the framework of the stochastic computing approaches. The purpose of these investigations is not only focused to solve the singular models, but the solution of these models will be presented to the extended form of the delayed, prediction and pantograph differential models. The Gudermannian function is designed using the neural networks optimized through the global scheme "genetic algorithms (GA)", local method "sequential quadratic programming (SQP)" and the hybridization of GA-SQP. The comparison of the singular equations will be presented with the exact solutions along with the extended form of delayed, prediction and pantograph based on these singular models. Moreover, the neuron analysis will be provided to authenticate the efficiency and complexity of the designed approach. For the correctness and effectiveness of the proposed approach, the plots of absolute error will be drawn for the singular delayed, prediction and pantograph differential models. For the reliability and stability of the proposed method, the statistical performances "Theil inequality coefficient", "variance account for" and "mean absolute deviation'' are observed for multiple executions to solve singular delayed, prediction and pantograph differential models.

A substrate integrated differential cavity-backed dual-polarized dielectric resonator antenna (DPDRA) with a wide bandwidth, low profile, high isolation and improved gain is presented. The proposed substrate integrated technique, in which the electric and magnetic walls of the cross-shaped dielectric resonator antenna (DRA) are realized by arrays of metallic and nonmetallic vias respectively, provides the design with high level of integration and low profile. The substrate integrated DRA is differentially fed by microstrip lines through coupling slots exciting a pair of orthogonal modes for the dual polarizations. The differential feeding scheme offers a direct connection to differential systems, and greatly improve the isolation between polarizations. Benefitting from the differential coupling slots and the substrate integrated back cavity, the bandwidth is broadened and the realized gain is improved. For demonstration, a prototype is designed and fabricated. The simulated and measured results show a good agreement.

It is an important task to learn how gene regulatory networks change under different conditions. Several Gaussian graphical model-based methods have been proposed to deal with this task by inferring differential networks from gene expression data. However, most existing methods define the differential networks as the difference of precision matrices, which may include false differential edges caused by the change of conditional variances. In addition, prior information about the condition-specific networks and the differential networks can be obtained from other domains. It is useful to incorporate prior information into differential network analysis. In this study, we propose a new differential network analysis method to address the above challenges. Instead of using the precision matrices, we define the differential networks as the difference of partial correlations, which can exclude the spurious differential edges due to the variants of conditional variances. Furthermore, prior information from multiple hypothesis testing is incorporated using a weighted fused penalty. Simulation studies show that our method outperforms the competing methods. We also apply our method to identify the differential network between luminal A and basal-like subtypes of breast cancers and the differential network between acute myeloid leukemia tumors and normal samples. The hub genes in the differential networks identified by our method carry out important biological functions.

In this paper, we obtain necessary and sufficient conditions for the existence of variational principles for a given first-order differential-difference operator equation with a special form of the linear operator P(t) depending on t and the nonlinear operator Q. Under the corresponding conditions the functional is constructed. These conditions are obtained thanks to the well-known criterion of potentiality. Examples show how the inverse problem of the calculus of variations is constructed for given differentialdifference operators.

A quasi‐differential type event‐triggered model predictive control (ET‐MPC) framework for continuous‐time linear systems with additional disturbances is constructed. Different from the existing ET‐MPC, the triggering condition of the proposed method is focused on the differences of the errors between the actual states and the best prediction sequence at two consecutive sampling moments. Its advantage is that the dynamic characteristics of state changes can be better considered, which will achieve a more effective balance between communication load and system control performance. Then, to deal with persistent disturbances, a time‐varying tightening robustness state constraint is utilized in this scheme, instead of conventional state constraints. Finally, the new ET‐MPC algorithm is designed based on the dual‐mode control framework, and its feasibility, the system closed‐loop stability, as well as avoidance of Zeno behaviour are rigorously verified. Simulations and comparisons are provided to demonstrate the algorithm effectiveness.

In this manuscript, we mainly focus on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order 1 r 2 . The primary outcomes of our manuscript are proved by using the results and facts associated with fractional calculus, multivalued maps, and Bohnenblust and Karlin’s fixed point theorem. Firstly, we focus the approximate controllability and then we extend the discussion to the system with nonlocal conditions. Lastly, we provide an application for the illustration of the obtained theoretical results.

We defined in Ellingsen et al. (2020) a new multiplicative c -differential, and the corresponding c -differential uniformity and we characterized the known perfect nonlinear functions with respect to this new concept, as well as the inverse function in any characteristic. Here, we extend, via this differential, the boomerang uniformity concept, as introduced at Eurocrypt ’18 by Cid et al. (2018), as a differential distinguisher of S -boxes of block ciphers. and investigate it in the context of perfect nonlinearity and related functions. We first characterize the new concept via Walsh transforms. We further investigate it in the context of perfect nonlinearity and related functions and describe this uniformity for the inverse function in even, respectively, odd characteristic. The methods are combinatorial and number theoretical in nature.

A Robin boundary sub-diffusion equation is considered with fractional partial derivatives of the Caputo type. The model is an extension of various well-known equations from mathematical physics, biology, and chemistry. Initial–boundary data are imposed upon a closed and bounded spatial domain. We state and prove two main theorems in differential and difference settings to ensure the algebraic decay rate of the long-time behavior for that kind of problem. The dissipation of the continuous solution for such a problem is discussed in the first theorem based on energy inequalities and by the aid of Gronwall inequalities. It demonstrates that with an L 2 ( Ω ) -bounded absorbing set, the solution is dissipated with respect to time. The numerical dissipativity is proved in the second theorem by using discrete energy inequalities and the discrete Paley–Wiener inequality. Finally, an example is provided to illustrate the main outcomes.

This paper presents an on-line monitoring method of IGBT module bond wires aging based on the phase-frequency characteristics (PFCs) of differential mode (DM) interference signal. Firstly, the collector current variation during IGBT chip switching is analyzed, and the relationship between the aging degree of bond wires and the PFCs of DM interference signal is studied; Secondly, a phase angle characteristic measurement system of DM interference signal is built and used to online monitor the aging of bond wires in IGBT module; Finally, taking the buck converter composed of IGBT module as the equipment under tested, the interference signal is extracted by the RF current probe and processed by the low-pass filter and signal amplifier, then the phase angle characteristics are measured by the oscilloscope board to realize the on-line monitoring of the bond wires aging of IGBT module. The experimental results show that compared with buck converter with healthy IGBT module, the phase angle of DM interference signal in Buck Converter with aging IGBT module is reduced. The proposed method does not need expensive equipment such as spectrum analyzer, and only needs to monitor the aging state of bond wires in IGBT module online through oscilloscope board. Besides, the research method in this paper provides an approximate linear monitoring method for bonding wire lift-off.