A statistical perspective on algorithm unrolling models for inverse problems

We consider inverse problems where the conditional distribution of the observation ${\bf y}$ given the latent variable of interest ${\bf x}$ (also known as the forward model) is known, and we have access to a data set in which multiple instances of ${\bf x}$ and ${\bf y}$ are both observed. In this context, algorithm unrolling has become a very popular approach for designing state-of-the-art deep neural network architectures that effectively exploit the forward model. We analyze the statistical complexity of the gradient descent network (GDN), an algorithm unrolling architecture driven by proximal gradient descent. We show that the unrolling depth needed for the optimal statistical performance of GDNs is of order $\log(n)/\log(\varrho_n^{-1})$, where $n$ is the sample size, and $\varrho_n$ is the convergence rate of the corresponding gradient descent algorithm. We also show that when the negative log-density of the latent variable ${\bf x}$ has a simple proximal operator, then a GDN unrolled at depth $D'$ can solve the inverse problem at the parametric rate $O(D'/\sqrt{n})$. Our results thus also suggest that algorithm unrolling models are prone to overfitting as the unrolling depth $D'$ increases. We provide several examples to illustrate these results

Field test on the biodegradation of poly(butylene adipate-co-terephthalate) based mulch films in soil

The use of plastic much films has been fundamental to promoting food production in many regions of the world. However, concern is growing about the progressive accumulation of plastic residues in soil after crop harvest and its subsequent impact on soil health and potential to enter the food chain. Although biodegradable films have been developed to prevent these problems, it is still unclear whether they are environmentally benign. Here we evaluated the physical and chemical breakdown of four commercial poly(butylene adipate-co-terephthalate) based biodegradable mulch films (BMF1, BMF2, BMF3 and BMF4) in an agricultural soil over a 26-month period. Based on visual examination, degradation followed the series BMF4 > BMF1, BMF2 > BMF3. Importantly, microplastic residues (fragments <5 mm) still remained in the soil of all 4 plastic types after 2 years, suggesting that they are likely to accumulate over time if used on an annual basis. Viscosimetry, Fourier transform infrared (FTIR) spectroscopy and Thermogravimetric Analysis (TGA) were used to characterise the breakdown process. Our results indicated that the degradation of the mulch film after burial in agricultural soil may be linked to the nature of the polymer but also to its manufacturing formulation. Although the peak changes of polyester in the infrared spectrum were not distinct, the plastic films showed other signs of degradation including a reduction in intrinsic viscosity after burial in soil. The different degradation rates of BMF1 and BMF2 at the molecular level may be due to the different CaCO3 contents. In conclusion, under field conditions, we show that slight variations in the formulations of commercial biodegradable mulch films leads to very different persistence rates in soil. Further, we conclude that their slow rate of degradation will ultimately lead to their progressive accumulation in soil if used repeatedly

Bis(μ-4-amino-3,5-dimethyl-4H-1,2,4-triazole)bis­[diiodidozinc(II)]

In the title compound, [Zn2I4(C4H8N4)2], the ZnII atom is coordinated in a distorted tetra­hedral geometry by two N atoms from the triazole rings of two 4-amino-3,5-dimethyl-4H-1,2,4-triazole (admt) ligands and two iodide ligands. Doubly bridging admt ligands connect two ZnII atoms, forming a centrosymmetric dimer. Weak N—H⋯I and C—H⋯I hydrogen bonds play an important role in the inter­molecular packing

Characterization Study of Empty Fruit Bunch (EFB) Fibers Reinforcement in Poly(Butylene) Succinate (PBS)/Starch/Glycerol Composite Sheet

In this study, a mixture of thermoplastic polybutylene succinate (PBS), tapioca starch, glycerol and empty fruit bunch fiber was prepared by a melt compounding method using an industrial extruder. Generally, insertion of starch/glycerol has provided better strength performance, but worse thermal and water uptake to all specimens. The effect of fiber loading on mechanical, morphological, thermal and physical properties was studied in focus. Low interfacial bonding between fiber and matrix revealed a poor mechanical performance. However, higher fiber loadings have improved the strength values. This is because fibers regulate good load transfer mechanisms, as confirmed from SEM micrographs. Tensile and flexural strengths have increased 6.0% and 12.2%, respectively, for 20 wt% empty fruit bunch (EFB) fiber reinforcements. There was a slightly higher mass loss for early stage thermal decomposition, whereas regardless of EFB contents, insignificant changes on decomposition temperature were recorded. A higher lignin constituent in the composite (for high natural fiber volume) resulted in a higher mass residue, which would turn into char at high temperature. This observation indirectly proves the dimensional integrity of the composite. However, as expected, with higher EFB fiber contents in the composite, higher values in both the moisture uptake and moisture loss analyses were found. The hydroxyl groups in the EFB absorbed water moisture through formation of hydrogen bonding

Time-slot based architecture for power beam-assisted relay techniques in CR-WSNs with transceiver hardware inadequacies

Over the past two decades, numerous research projects have concentrated on cognitive radio wireless sensor networks (CR-WSNs) and their benefits. To tackle the problem of energy and spectrum shortfall in CR-WSNs, this research proposes an underpinning decode-&-forward (DF) relaying technique. Using the suggested time-slot architecture (TSA), this technique harvests energy from a multi-antenna power beam (PB) and delivers source information to the target utilizing energy-constrained secondary source and relay nodes. The study considers three proposed relay selection schemes: enhanced hybrid partial relay selection (E-HPRS), conventional opportunistic relay selection (C-ORS), and leading opportunistic relay selection (L-ORS). We present evidence for the sustainability of the suggested methods by examining the outage probability (OP) and throughput (TPT) under multiple primary users (PUs). These systems leverage time switching (TS) receiver design to increase end-to-end performance while taking into account the maximum interference constraint and transceiver hardware inadequacies. In order to assess the efficacy of the proposed methods, we derive the exact and asymptotic closed-form equations for OP and TPT & develop an understanding to learn how they affect the overall performance all across the Rayleigh fading channel. The results show that OP of the L-ORS protocol is 16% better than C-ORS and 75% better than E-HPRS in terms of transmitting SNR. The OP of L-ORS is 30% better than C-ORS and 55% better than E-HPRS in terms of hardware inadequacies at the destination. The L-ORS technique outperforms C-ORS and E-HPRS in terms of TPT by 4% and 11%, respectively