Principal Component Analysis and t-Distributed Stochastic Neighbor Embedding Analysis in the Study of Quantum Approximate Optimization Algorithm Entangled and Non-Entangled Mixing Operators.

In this paper, we employ PCA and t-SNE analyses to gain deeper insights into the behavior of entangled and non-entangled mixing operators within the Quantum Approximate Optimization Algorithm (QAOA) at various depths. We utilize a dataset containing optimized parameters generated for max-cut problems with cyclic and complete configurations. This dataset encompasses the resulting RZ, RX, and RY parameters for QAOA models at different depths (1L, 2L, and 3L) with or without an entanglement stage within the mixing operator. Our findings reveal distinct behaviors when processing the different parameters with PCA and t-SNE. Specifically, most of the entangled QAOA models demonstrate an enhanced capacity to preserve information in the mapping, along with a greater level of correlated information detectable by PCA and t-SNE. Analyzing the overall mapping results, a clear differentiation emerges between entangled and non-entangled models. This distinction is quantified numerically through explained variance in PCA and Kullback-Leibler divergence (post-optimization) in t-SNE. These disparities are also visually evident in the mapping data produced by both methods, with certain entangled QAOA models displaying clustering effects in both visualization techniques.

Quantum Information Entropy for Another Class of New Proposed Hyperbolic Potentials.

In this work, we investigate the Shannon entropy of four recently proposed hyperbolic potentials through studying position and momentum entropies. Our analysis reveals that the wave functions of the single-well potentials U0,3 exhibit greater localization compared to the double-well potentials U1,2. This difference in localization arises from the depths of the single- and double-well potentials. Specifically, we observe that the position entropy density shows higher localization for the single-well potentials, while their momentum probability density becomes more delocalized. Conversely, the double-well potentials demonstrate the opposite behavior, with position entropy density being less localized and momentum probability density showing increased localization. Notably, our study also involves examining the Bialynicki-Birula and Mycielski (BBM) inequality, where we find that the Shannon entropies still satisfy this inequality for varying depths u¯. An intriguing observation is that the sum of position and momentum entropies increases with the variable u¯ for potentials U1,2,3, while for U0, the sum decreases with u¯. Additionally, the sum of the cases U0 and U3 almost remains constant within the relative value 0.01 as u¯ increases. Our study provides valuable insights into the Shannon entropy behavior for these hyperbolic potentials, shedding light on their localization characteristics and their relation to the potential depths. Finally, we extend our analysis to the Fisher entropy F¯x and find that it increases with the depth u¯ of the potential wells but F¯p decreases with the depth.

Quantum Information Entropy for a Hyperbolic Double Well Potential in the Fractional Schrödinger Equation.

In this study, we investigate the position and momentum Shannon entropy, denoted as Sx and Sp, respectively, in the context of the fractional Schrödinger equation (FSE) for a hyperbolic double well potential (HDWP). We explore various values of the fractional derivative represented by k in our analysis. Our findings reveal intriguing behavior concerning the localization properties of the position entropy density, ρs(x), and the momentum entropy density, ρs(p), for low-lying states. Specifically, as the fractional derivative k decreases, ρs(x) becomes more localized, whereas ρs(p) becomes more delocalized. Moreover, we observe that as the derivative k decreases, the position entropy Sx decreases, while the momentum entropy Sp increases. In particular, the sum of these entropies consistently increases with decreasing fractional derivative k. It is noteworthy that, despite the increase in position Shannon entropy Sx and the decrease in momentum Shannon entropy Sp with an increase in the depth u of the HDWP, the Beckner-Bialynicki-Birula-Mycielski (BBM) inequality relation remains satisfied. Furthermore, we examine the Fisher entropy and its dependence on the depth u of the HDWP and the fractional derivative k. Our results indicate that the Fisher entropy increases as the depth u of the HDWP is increased and the fractional derivative k is decreased.

Quantum Information Entropy of Hyperbolic Potentials in Fractional Schrödinger Equation.

In this work we have studied the Shannon information entropy for two hyperbolic single-well potentials in the fractional Schrödinger equation (the fractional derivative number (0

Entanglement Property of Tripartite GHZ State in Different Accelerating Observer Frames.

According to the single-mode approximation applied to two different mo des, each associated with different uniformly accelerating reference frames, we present analytical expression of the Minkowski states for both the ground and first excited states. Applying such an approximation, we study the entanglement property of Bell and Greenberger-Horne-Zeilinger (GHZ) states formed by such states. The corresponding entanglement properties are described by studying negativity and von Neumann entropy. The degree of entanglement will be degraded when the acceleration parameters increase. We find that the greater the number of particles in the entangled system, the more stable the system that is studied by the von Neumann entropy. The present results will be reduced to those in the case of the uniformly accelerating reference frame.

Pentapartite Entanglement Measures of GHZ and W-Class State in the Noninertial Frame.

We study both pentapartite GHZ and W-class states in the noninertial frame and explore their entanglement properties by carrying out the negativities including 1-4, 2-3, and 1-1 tangles, the whole entanglement measures such as algebraic and geometric averages π5 and Π5, and von Neumann entropy. We illustrate graphically the difference between the pentapartite GHZ and W-class states. We find that all 1-4, 2-3 tangles and the whole entanglements, which are observer dependent, degrade more quickly as the number of accelerated qubits increases. The entanglements of these quantities still exist even at the infinite acceleration limit. We also notice that all 1-1 tangles of pentapartite GHZ state Nαß=NαIß=NαIßI=0 where α,ß∈(A,B,C,D,E), whereas all 1-1 tangles of the W-class state Nαß,NαIß and NαIßI are unequal to zero, e.g., Nαß=0.12111 but NαIß and NαIßI disappear at r>0.61548 and r>0.38671, respectively. We notice that the entanglement of the pentapartite GHZ and W-class quantum systems decays faster as the number of accelerated particles increases. Moreover, we also illustrate the difference of von Neumann entropy between them and find that the entropy in the pentapartite W-class state is greater than that of GHZ state. The von Neumann entropy in the pentapartite case is more unstable than those of tripartite and tetrapartite subsystems in the noninertial frame.

Quantum Information Entropies on Hyperbolic Single Potential Wells.

In this work, we study the quantum information entropies for two different types of hyperbolic single potential wells. We first study the behaviors of the moving particle subject to two different hyperbolic potential wells through focusing on their wave functions. The shapes of these hyperbolic potentials are similar, but we notice that their momentum entropy densities change along with the width of each potential and the magnitude of position entropy density decreases when the momentum entropy magnitude increases. On the other hand, we illustrate the behaviors of their position and momentum entropy densities. Finally, we show the variation of position and momentum entropies Sx and Sp with the change of the potential well depth u and verify that their sum still satisfies the BBM inequality relation.

Exact solutions of the harmonic oscillator plus non-polynomial interaction.

The exact solutions to a one-dimensional harmonic oscillator plus a non-polynomial interaction a x 2 + b x 2/(1 + c x 2) (a > 0, c > 0) are given by the confluent Heun functions H c (α, ß, γ, δ, η;z). The minimum value of the potential well is calculated as V min ( x ) = - ( a + | b | - 2 a | b | ) / c at x = ± [ ( | b | / a - 1 ) / c ] 1 / 2 (|b| > a) for the double-well case (b < 0). We illustrate the wave functions through varying the potential parameters a, b, c and show that they are pulled back to the origin when the potential parameter b increases for given values of a and c. However, we find that the wave peaks are concave to the origin as the parameter |b| is increased.

YAP activation promotes the transdifferentiation of cardiac fibroblasts to myofibroblasts in matrix remodeling of dilated cardiomyopathy

Yes-associated protein (YAP) is an important regulator of cellular proliferation and transdifferentiation. However, little is known about the mechanisms underlying myofibroblast transdifferentiation in dilated cardiomyopathy (DCM). We investigated the role of YAP in the pathological process of cardiac matrix remodeling. A classic model of DCM was established in BALB/c mice by immunization with porcine cardiac myosin. Cardiac fibroblasts were isolated from neonatal Sprague-Dawley rats by density gradient centrifugation. The expression levels of α-smooth muscle actin (α-SMA) and collagen volume fraction (CVF) were significantly increased in DCM mice. Angiotensin II (Ang II)-mediated YAP activation promoted the proliferation and transdifferentiation of neonatal rat cardiac fibroblasts, and this effect was significantly suppressed in the shRNA YAP + Ang II group compared with the shRNA Control + Ang II group in vitro (2.98±0.34 ×105 vs 5.52±0.82 ×105, P<0.01). Inhibition of endogenous Ang II-stimulated YAP improved the cardiac function by targeting myofibroblast transdifferentiation to attenuate matrix remodeling in vivo. In the valsartan group, left ventricular ejection fraction and fractional shortening were significantly increased compared with the DCM group (52.72±5.51% vs 44.46±3.01%, P<0.05; 34.84±3.85% vs 26.65±3.12%, P<0.01). Our study demonstrated that YAP was a regulator of cardiac myofibroblast differentiation, and regulation of YAP signaling pathway contributed to improve cardiac function of DCM mice, possibly in part by decreasing myofibroblast transdifferentiation to inhibit matrix remodeling.

YAP activation promotes the transdifferentiation of cardiac fibroblasts to myofibroblasts in matrix remodeling of dilated cardiomyopathy.

Yes-associated protein (YAP) is an important regulator of cellular proliferation and transdifferentiation. However, little is known about the mechanisms underlying myofibroblast transdifferentiation in dilated cardiomyopathy (DCM). We investigated the role of YAP in the pathological process of cardiac matrix remodeling. A classic model of DCM was established in BALB/c mice by immunization with porcine cardiac myosin. Cardiac fibroblasts were isolated from neonatal Sprague-Dawley rats by density gradient centrifugation. The expression levels of α-smooth muscle actin (α-SMA) and collagen volume fraction (CVF) were significantly increased in DCM mice. Angiotensin II (Ang II)-mediated YAP activation promoted the proliferation and transdifferentiation of neonatal rat cardiac fibroblasts, and this effect was significantly suppressed in the shRNA YAP + Ang II group compared with the shRNA Control + Ang II group in vitro (2.98±0.34 ×105 vs 5.52±0.82 ×105, P<0.01). Inhibition of endogenous Ang II-stimulated YAP improved the cardiac function by targeting myofibroblast transdifferentiation to attenuate matrix remodeling in vivo. In the valsartan group, left ventricular ejection fraction and fractional shortening were significantly increased compared with the DCM group (52.72±5.51% vs 44.46±3.01%, P<0.05; 34.84±3.85% vs 26.65±3.12%, P<0.01). Our study demonstrated that YAP was a regulator of cardiac myofibroblast differentiation, and regulation of YAP signaling pathway contributed to improve cardiac function of DCM mice, possibly in part by decreasing myofibroblast transdifferentiation to inhibit matrix remodeling.

Worldwide incidence and prevalence of inflammatory bowel disease in the 21st century: a systematic review of population-based studies.

BACKGROUND: Inflammatory bowel disease is a global disease in the 21st century. We aimed to assess the changing incidence and prevalence of inflammatory bowel disease around the world. METHODS: We searched MEDLINE and Embase up to and including Dec 31, 2016, to identify observational, population-based studies reporting the incidence or prevalence of Crohn's disease or ulcerative colitis from 1990 or later. A study was regarded as population-based if it involved all residents within a specific area and the patients were representative of that area. To be included in the systematic review, ulcerative colitis and Crohn's disease needed to be reported separately. Studies that did not report original data and studies that reported only the incidence or prevalence of paediatric-onset inflammatory bowel disease (diagnosis at age <16 years) were excluded. We created choropleth maps for the incidence (119 studies) and prevalence (69 studies) of Crohn's disease and ulcerative colitis. We used temporal trend analyses to report changes as an annual percentage change (APC) with 95% CI. FINDINGS: We identified 147 studies that were eligible for final inclusion in the systematic review, including 119 studies of incidence and 69 studies of prevalence. The highest reported prevalence values were in Europe (ulcerative colitis 505 per 100 000 in Norway; Crohn's disease 322 per 100 000 in Germany) and North America (ulcerative colitis 286 per 100 000 in the USA; Crohn's disease 319 per 100 000 in Canada). The prevalence of inflammatory bowel disease exceeded 0·3% in North America, Oceania, and many countries in Europe. Overall, 16 (72·7%) of 22 studies on Crohn's disease and 15 (83·3%) of 18 studies on ulcerative colitis reported stable or decreasing incidence of inflammatory bowel disease in North America and Europe. Since 1990, incidence has been rising in newly industrialised countries in Africa, Asia, and South America, including Brazil (APC for Crohn's disease +11·1% [95% CI 4·8-17·8] and APC for ulcerative colitis +14·9% [10·4-19·6]) and Taiwan (APC for Crohn's disease +4·0% [1·0-7·1] and APC for ulcerative colitis +4·8% [1·8-8·0]). INTERPRETATION: At the turn of the 21st century, inflammatory bowel disease has become a global disease with accelerating incidence in newly industrialised countries whose societies have become more westernised. Although incidence is stabilising in western countries, burden remains high as prevalence surpasses 0·3%. These data highlight the need for research into prevention of inflammatory bowel disease and innovations in health-care systems to manage this complex and costly disease. FUNDING: None.

Hydrogen atom in a quantum plasma environment under the influence of Aharonov-Bohm flux and electric and magnetic fields.

This study presents the confinement influences of Aharonov-Bohm (AB) flux and electric and magnetic fields directed along the z axis and encircled by quantum plasmas on the hydrogen atom. The all-inclusive effects result in a strongly attractive system while the localizations of quantum levels change and the eigenvalues decrease. We find that the combined effect of the fields is stronger than a solitary effect and consequently there is a substantial shift in the bound state energy of the system. We also find that to perpetuate a low-energy medium for the hydrogen atom in quantum plasmas, a strong electric field and weak magnetic field are required, whereas the AB flux field can be used as a regulator. The application of the perturbation technique utilized in this paper is not restricted to plasma physics; it can also be applied in molecular physics.

The effects of unequal ionic sizes for an electrolyte in a charged slit.

The modified Gouy-Chapman (MGC) theory has been used to study the electrical double layer near two charged plates immersed in a model electrolyte. The effects of assigning to the cations and anions different distances of closest approach to the charged surfaces are examined. The dependence of overcharging and charge reversal on the system parameters such as concentration, ion size and valence, is investigated both inside and outside the charged slit.

Periodic precursors of nonlinear dynamical transitions.

We study the resonant response of a nonlinear system to external periodic perturbations. We show by numerical simulation that the periodic resonance curve may anticipate the dynamical instability of the unperturbed nonlinear periodic system, at parameter values far away from the bifurcation points. In the presence of noise, the buried intrinsic periodic dynamics can be picked out by analyzing the system's response to periodic modulation of appropriate intensity.

Noise-induced coherence in bistable systems with multiple time delays.

We study the correlation properties of noise-driven bistable systems with multiple time-delay feedbacks. For small noisy perturbation and feedback magnitude, we derive the autocorrelation function and the power spectrum based on the two-state model with transition rates depending on the earlier states of the system. A comparison between the single and double time delays reveals that the auto correlation functions exhibit exponential decay with small undulation for the double time delays, in contrast with the remarkable oscillatory behavior at small time lags for the single time delay.