A Mathematical Theory of Semantic Communication

The year 1948 witnessed the historic moment of the birth of classic information theory (CIT). Guided by CIT, modern communication techniques have approached the theoretic limitations, such as, entropy function $H(U)$, channel capacity $C=\max_{p(x)}I(X;Y)$ and rate-distortion function $R(D)=\min_{p(\hat{x}|x):\mathbb{E}d(x,\hat{x})\leq D} I(X;\hat{X})$. Semantic communication paves a new direction for future communication techniques whereas the guided theory is missed. In this paper, we try to establish a systematic framework of semantic information theory (SIT). We investigate the behavior of semantic communication and find that synonym is the basic feature so we define the synonymous mapping between semantic information and syntactic information. Stemming from this core concept, synonymous mapping $f$, we introduce the measures of semantic information, such as semantic entropy $H_s(\tilde{U})$, up/down semantic mutual information $I^s(\tilde{X};\tilde{Y})$ $(I_s(\tilde{X};\tilde{Y}))$, semantic capacity $C_s=\max_{f_{xy}}\max_{p(x)}I^s(\tilde{X};\tilde{Y})$, and semantic rate-distortion function $R_s(D)=\min_{\{f_x,f_{\hat{x}}\}}\min_{p(\hat{x}|x):\mathbb{E}d_s(\tilde{x},\hat{\tilde{x}})\leq D}I_s(\tilde{X};\hat{\tilde{X}})$. Furthermore, we prove three coding theorems of SIT by using random coding and (jointly) typical decoding/encoding, that is, the semantic source coding theorem, semantic channel coding theorem, and semantic rate-distortion coding theorem. We find that the limits of SIT are extended by using synonymous mapping, that is, $H_s(\tilde{U})\leq H(U)$, $C_s\geq C$ and $R_s(D)\leq R(D)$. All these works composite the basis of semantic information theory. In addition, we discuss the semantic information measures in the continuous case. For the band-limited Gaussian channel, we obtain a new channel capacity formula, $C_s=B\log\left[S^4\left(1+\frac{P}{N_0B}\right)\right]$.Comment: (version 2.0 updated) 96 pages, 18 figures. This paper is submitted to IEEE Transactions on Information Theory (TIT

On A Proper Definition of Spin Current

The conventional definition of spin current is incomplete and unphysical in describing spin transport in systems with spin-orbit coupling. A proper and measurable spin current is established in this study, which fits well into the standard framework of near-equilibrium transport theory and has the desirable property to vanish in insulators with localized orbitals. Experimental implications of our theory are discussed.Comment: Final version with updated journal-re

Theory of conserved spin current and its application to two dimensional hole gas

We present a detailed microscopic theory of the conserved spin current which is introduced by us [Phys. Rev. Lett. \textbf{96}, 196602 (2006)] and satisfies the spin continuity equation even for spin-orbit coupled systems. The spin transport coefficients $\sigma_{\mu\nu}^{s}$ as a response to the electric field are shown to consist of two parts, i.e., the conventional part $\sigma_{\mu\nu}^{s0}$ and the spin torque dipole correction $\sigma_{\mu\nu }^{s\tau}$. As one key result, an Onsager relation between $\sigma_{\mu\nu }^{s}$ and other kinds of transport coefficients are shown. The expression for $\sigma_{\mu\nu}^{s}$ in terms of single-particle Bloch states are derived, by use of which we study the conserved spin Hall conductivity in the two dimensional hole gas modeled by a combined Luttinger and SIA Rashba spin-orbit coupling. It is shown that the two components in spin Hall conductivity usually have the opposite contributions. While in the absence of Rashba spin splitting, the spin Hall transport is dominated by the conventional contribution, the presence of Rashba spin splitting stirs up a large enhancement of the spin torque dipole correction, leading to an overall sign change for the total spin Hall conductivity. Furthermore, an approximate two-band calculation and the subsequent comparison with the exact four-band results are given, which reveals that the coupling between the heavy hole and light hole bands should be taken into account for strong Rashba spin splitting.Comment: 10 pages, 4 figure

Voltammetric investigation on interaction of Hyaluronic Acid with crystal violet and its analytical application

In this paper, the interaction of hyaluronic acid (HA) with crystal violet (CV) was investigated carefully by linear sweep voltammetry on the dropping mercury working electrode (DME). In pH 5.0 Britton-Robinson (B-R) buffer solution, CV has a sensitive, well-defined second order derivative linear sweep voltammetric reductive wave at –0.85 V (vs. SCE). After adding a certain amount of HA into CV solution, the reductive peak current decreased without any shift of reductive peak potential. Based on the difference in the reductive peak current, a new voltammetric method for the detection of HA was established. The reaction conditions and the electrochemical determination were studied and optimized. Under the optimized conditions, the decrease of peak current showed a good linear relationship with the HA concentration in the range from 10.0 to 40.0 mg/L. The linear regression equation was got as ∆ip″(nA)= 84.07 C–527.86  (mg/L) (n=8, γ=0.997) and the detection limit was calculated as 2.65 mg/L (3σ). This new established method was further used to HA determination in the synthetic samples with satisfactory results and good recovery. The stoichiometry of CV-HA complex was calculated and the binding mechanism was also discussed by the electrochemical data

Protective effect of Acorus tatarinowii extract against alzheimer in 3xTg-AD mice

Purpose: To investigate the protective effect of Acorus tatarinowii extract (ATE) against Alzheimer's disease in 3xTg-AD mice. Method: The cognitive function of 3xTg-AD mice was assessed using Morris water maze test. The levels of the amyloid beta deposits and NeuN in the hippocampus were evaluated by immunohistochemical assay while brain neurotrophic derived factor (BDNF) and tyrosine kinase B (TrkB) expressions were determined by western blot analysis. Results: ATE treatment significantly ameliorated learning and memory deficits in AD mice, as shown by increased time spent in the target zone during probe tests. The escape latency in animals treated with 600 mg/kg ATE (24.8 ± 1.3 s) was significantly increased relative to ontreated 3xTg-AD mice (8.5 ± 1.0 s, p < 0.01). In addition, ATE significantly decreased Aβ deposits, increased NeuN-positive cells, and upregulated the expression of BDNF (1.9 ± 0.4, p < 0.05) and TrkB (1.9 ± 0.2, p < 0.05) in 3xTg AD mice. Conclusion: These results suggest that ATE treatment may be a useful strategy for managing memory impairment induced by several neurodegenerative diseases