**Author details**

Meenakshi Pardasani\* and Nixon M. Abraham\* Laboratory of Neural Circuits and Behaviour (LNCB), Department of Biology, Indian Institute of Science Education and Research (IISER), Pune, Maharashtra, India

\*Address all correspondence to<EMAIL_ADDRESS>and<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


*3.3. Risk of Bias Assessment*

Thirteen studies [22–29,34,37,40,42,43] that used an appropriate random sequence generation method such as random number tables were evaluated as having a low risk of selection bias, and three studies [21,32,37] that properly concealed allocation using an opaque sealed envelope were also evaluated as having a low risk of selection bias. Three studies [34,36,37] that reported that the practitioners who were not blinded were at high risk of performance bias, and one study [42] that reported that both participants and personnel were blinded was evaluated as having a low risk of performance bias. Five studies [20,21,36,37,42] reporting blindness of outcome assessors were evaluated as having a low risk of detection bias. Three studies [32,39,43] that performed per-protocol analysis without specifying the reason for dropout were evaluated as having a high risk of attrition bias. Three studies [18,39,43] did not report raw data, and four studies [23,24,41,46] that did not report pulmonary function-related outcomes were evaluated as having a high risk of reporting bias. One study [28] without baseline characteristic data and one study [34] with cross-over design was evaluated as having a high risk of other potential biases (Figure 2). *Healthcare* **2021**, *9*, x 11 of 18

**Figure 2.** Risk of bias for all included studies. Low, unclear, and high risk, respectively, are represented with the following symbols: "+", "?", and "−". difference in FEV1 (MD 0.05 L, 95% CI from −0.24 to 0.34) and FEV1/FVC (MD 0.84%, 95% **Figure 2.** Risk of bias for all included studies. Low, unclear, and high risk, respectively, are represented with the following symbols: "+", "?", and "−".

Manipulation showed no differences compared with sham in lung functions (FEV1: MD 0.23 L, 95% CI from −0.12 to 0.58; FVC: MD −0.02 L, 95% CI from −0.57 to 0.53; FEV1/FVC: MD 3.01%, 95% CI from −6.90 to 12.92), exercise capacity (6MWD: MD 64.80 m, 95% CI from −12.94 to 142.54), and incidence of AE (RR 0.50, 95% CI: from 0.11 to 2.38). Additional massage significantly improved FEV1/FVC (MD 20.00%, 95% CI from 15.46 to 24.54) and total effective rate (TER) calculated using the severity of respiratory symptoms (RR 1.17, 95% CI from 1.00 to 1.38), compared with ROC alone. However, there were no differences between them in the FEV1 (MD 0.68 L, 95% CI from −0.62 to 1.99), 6MWD (MD 56.20 m, 95% CI from −8.18 to 120.58), and incidence of AE (RR 8.89, 95% CI from 0.48 to 165.55). When comparing additional acupressure with ROC alone, although there was no

**Table 1.**Characteristics of included studies using Western manual

 therapy.

**Table 1.** *Cont.*

**Table 2.**

Characteristics

 of included

 studies using Eastern manual

 therapy.

**Table 2.** *Cont.*

**Table 2.** *Cont.*

medical research council dyspnea scale; NR—not recorded; pv—predicted value; SGRQ—St. George respiratory questionnaire; TER—total effective rate; 6MWD—6 min walking

distance.


*Article* **Many-Body Localization and the Emergence of Quantum Darwinism**

**Nicolás Mirkin \*,† and Diego A. Wisniacki †**

> Departamento de Física "J. J. Giambiagi" and IFIBA, FCEyN, Universidad de Buenos Aires, Buenos Aires 1428, Argentina<EMAIL_ADDRESS>
**\*** Correspondence<EMAIL_ADDRESS>
† These authors contributed equally to this work.

**Abstract:** Quantum Darwinism (QD) is the process responsible for the proliferation of redundant information in the environment of a quantum system that is being decohered. This enables independent observers to access separate environmental fragments and reach consensus about the system's state. In this work, we study the effect of disorder in the emergence of QD and find that a highly disordered environment is greatly beneficial for it. By introducing the notion of lack of redundancy to quantify objectivity, we show that it behaves analogously to the entanglement entropy (EE) of the environmental eigenstate taken as an initial state. This allows us to estimate the many-body mobility edge by means of our Darwinistic measure, implicating the existence of a critical degree of disorder beyond which the degree of objectivity rises the larger the environment is. The latter hints the key role that disorder may play when the environment is of a thermodynamic size. At last, we show that a highly disordered evolution may reduce the spoiling of redundancy in the presence of intra-environment interactions.

**Keywords:** decoherence; Quantum Darwinism; many-body localization; disorder


**Chapter 2**

swarm optimization. International Journal of Machine Learning and Cybernetics, 8(5), 1595–1605. https:// doi.org/10.1007/s13042-016-0530-2

discrete-time PD controller in the IISv1.3 robot arm control. Open Physics (Central European Journal of Physics), 11(6), 750–759. https://doi.org/10.2478/

[38] Ostalczyk, P. (2019). Analysis of a closed loop system with DC micromotor electrical drive with propeller and variable-fractional order PID controller. In 2019 20th International Carpathian Control Conference (ICCC). pp. 1–6. IEEE. ISBN 978–1–7281-0703-5

[39] Oziablo, P., Mozyrska, D., Wyrwas, M. (2020). Discrete-Time Fractional, Variable-Order PID Controller for a Plant With Delay. Entropy, Vol.22. No.7, 771. DOI:10.3390/e22070771

[40] Sierociuk, D., & Macias, M. (2013). Comparison of variable fractional order PID controller for different types of variable order derivatives. Proceedings

Carpathian Control Conference, ICCC 2013. https://doi.org/10.1109/Carpathia

[41] Sierociuk D., Wiraszka M.S. (2018) A new Variable Fractional-Order PI Algorithm. IFAC PapersOnLine, 2018, vol.51. No.4. pp.745–750. DOI:https:// doi.org/10.1016/j.ifacol.2018.06.207

of the 2013 14th International

nCC.2013.6560565

s11534-013-0254-9

*Control Based on PID Framework - The Mutual Promotion of Control and Identification…*

[31] Merrikh-Bayat, F. (2012). General rules for optimal tuning the PI*λ*D*μ* controllers with application to firstorder plus time delay processes. Canadian Journal of Chemical

Engineering. https://doi.org/10.1002/

[32] Liu, L., Pan, F., & Xue, D. (2015). Variable-order fuzzy fractional PID controller. ISA Transactions. https://doi.

[33] Aydogdu, O., Korkmaz, M. (2019).

Optimization Algorithms. International Journal of Advanced Computer Science and Applications, 10(3). https://doi.org/

[34] Chen, L., Chen, G., Wu, R., Lopes, A. M., Machado, J. A. T., Niu, H. (2020). Variable coefficient fractional-order PID controller and its application to a SEPIC device. IET Control Theory & Applications, 14(6), pp.900–908.

[35] Dabiri, A., Moghaddam, B. P., Machado, J. T. (2018). Optimal variableorder fractional PID controllers for dynamical systems. Journal of

339, pp.40–48.DOI:10.1016/j.

MMAR.2012.6347829

**16**

Computational and Applied Mathematics,

cam.2018.02.029Corpus ID: 19098724

[36] Ostalczyk, P. (2012). Variable-, fractional-order discrete PID controllers. 2012 17th International Conference on Methods and Models in Automation and Robotics, MMAR 2012, 534–539. https://doi.org/10.1109/

[37] Ostalczyk, P., Brzeziński, D. W., Duch, P., Łaski, M., & Sankowski, D. (2013). The variable, fractional-order

org/10.1016/j.isatra.2014.09.012

Optimal Design of a Variable Coefficient Fractional Order PID Controller by using Heuristic

10.14569/IJACSA.2019.

cjce.21643


**5. Conclusions**

Composites consisting of silver nanoparticles and polyphenol inclusion compounds were synthesized using two preparation media, one based on chitosan oligomers in an hydroalcoholic solution and the other based on a deep eutectic solvent. Both types of composites showed an increase in the water solubility of the polyphenols and in the in vitro antifungal activity against *Phytophthora cinnamomi* (MYC43 isolate). Nonetheless, the DES-based samples efficacy was remarkably higher than that of their counterparts with a chitosan oligomers-based matrix: Complete inhibition of mycelial growth was attained at concentrations of 250 and 500 μg·mL−1, and even at the lowest dose of 125 μg·mL−1, they resulted in a 90% growth inhibition. As regards the impact of the choice of the different polyphenols, for the DES-based treatments, the highest sensitivity of *P. cinnamomi* corresponded to the composite with gallic acid (EC50 = 0.1 μg·mL−1), followed by those with silymarin and ferulic acid, and finally by the one with curcumin, with EC50 values of 0.6, 0.6 and 8.9 μg·mL−1, respectively. This may be ascribed to the fact that gallic acid is extremely well absorbed, and very soluble in water as compared with other polyphenols. The reported activities for the composites were remarkably higher than those reported for *Phytophthora* spp. using AgNPs, chitosan or polyphenols separately. This points to the possibility of a successful application of these nanocomposites in agriculture, with the aim of reducing the use of toxic and expensive conventional systemic fungicides. Further research on the ability of the prepared nanocomposites to inhibit growth of *P. cinnamomi* in the context of a plant infection model and on the basic mechanism involved, fungistatic or fungicidal, is underway.


**Chapter 16**

*Genetic Variation*

2009;36(9):1873-1875.

2014;33(6):791-797.

2015;74(9):1659-1666.

[47] Youssef W, Yan A, Russell AS. Palindromic rheumatism: a response to chloroquine. The Journal of rheumatology. 1991;18(1):35-37.

[48] Gonzalez-Lopez L, Gamez-Nava JI, Jhangri G, Russell AS, Suarez-Almazor ME. Decreased progression to rheumatoid arthritis or other connective

tissue diseases in patients with palindromic rheumatism treated with antimalarials. Journal of rheumatology.

[49] Edwards JC, Szczepański L, Szechiński J, Filipowicz-Sosnowska A, Emery P, Close DR, et al. Efficacy of B-cell–targeted therapy with rituximab in patients with rheumatoid arthritis. New England Journal of Medicine.

2004;350(25):2572-2581.

2000;27(1):41-46.

outcomes of 60 patients diagnosed in 1967-84. The Journal of rheumatology. [50] Van Vollenhoven RF,

2012;367(6):508-519.

traditional herbs. 2017.

Research. 2017;9(5):547.

[51] Nighojkar PA, Momin M, Phadatare SP. Rheumatoid arthritis– Pharmacology and its management with

[52] Zarei L, Naji-Haddadi S, Pourjabali M, Naghdi N, Tasbih-Forosh M, Shahsavari S. Systematic review of anti-rheumatic medicinal plants: An overview of the effectiveness of articular tissues and joint pain associated with rheumatoid arthritis. Journal of Pharmaceutical Sciences and

Fleischmann R, Cohen S, Lee EB, García Meijide JA, Wagner S, et al. Tofacitinib or adalimumab versus placebo in rheumatoid arthritis. New England Journal of Medicine.

[44] Emad Y, Anbar A, Abo-Elyoun I,

[45] Sanmartí R, Cabrera-Villalba S, Gómez-Puerta JA, Ruiz-Esquide V, Hernández MV, Salvador G, et al. Palindromic rheumatism with positive anticitrullinated peptide/protein antibodies is not synonymous with rheumatoid arthritis. A longterm followup study. The Journal of

rheumatology. 2012;39(10):1929-1933.

[46] Rakieh C, Nam J, Hunt L, Hensor E, Das S, Bissell L, et al. Predicting the development of clinical arthritis in anti-CCP positive individuals with nonspecific musculoskeletal symptoms: a prospective observational cohort study. Annals of the rheumatic diseases.

El-Shaarawy N, Al-Hanafi H, Darwish H, et al. In palindromic rheumatism, hand joint involvement and positive anti-CCP antibodies predict RA development after 1 year of follow-up. Clinical rheumatology.

**272**


[25] Pozdzik AA, Berton A, Schmeiser HH, Missoum W, Decaestecker C, Salmon IJ, Vanherweghem JL, Nortier JL .2010; Aristolochic acid nephropathy revisited: A Place for innate and adaptive immunity? Histopathol., 56(4): 449-463.

[26] Mengs U.1987. Acute toxicity of aristolochic acid in redents. Aech Toxicol59 (5): 328-333(Support not

**107**

*Analysis of* Aristolochia longa *L. Medicinal Plant from Algeria*

and cytotoxicity of essential oils From Aristolochia mollissima. Environmental Toxicology and Pharmacology 23.2007;

[35] Benchaabane A, Abbad A .1997. Medicinal Plants marked in Marrakech. Trace of the Present. Marrakech, p. 74

[36] FDA.1995. Dietary Supplement Health and Education Act of 1994. U.S.Food and Drug Administration. http://www.cfsan.fda.gov/dms/ dietsupp.html Last accessed: 7/1/06

p. 162- 167

*DOI: http://dx.doi.org/10.5772/intechopen.95298*

reported. Authors affiliated with Dr. Madaus Gmbh & Co., Germany)

[27] U.S.National library of Medicine –

[28] Mengs U, Stotzem CD .1993. Renal toxicity of aristolochic acid in rats as an example of nephrotoxicity testing in routine toxicology. Arch. Toxicol., 67:

[29] Chung-Hsin Chen et al . Aristolochic acid – associated urotherial cancer in Taiwan PNAS /may 221,2012 /vol 109 /

[30] U.S. Department of Health and Human Services Public Health Services National Toxicology Program Research Triangle Park, NC 27709: final Report on Carcinogens Background Document for Aristolochic Acids September 2,

[31] Flurer RA,Jones MB, Vela N, Ciolino LA, Wolnick KA.2001. Determination of Aristolochic Acid in Traditional Chines Medicines and Dietary Supplements , DFS/ORO/ ORA NO.4212. U.S. Food and Drug

Administration 13 pp.

University, Japan.)

[32] Tanaka A,Nishida R,

Yoshida T, Koshikawa M, Goto M, Kuwahara T.2001. Outbreak of Chinese Herb nephropathy in Japan: are thre any differences from Belgium ? Intern Med 40(4): 296- 300.(Support not reported . Authors affiliated With Osaka Saiseikai Nakatsu Hospital, Japan; Kyoto

[33] Kupchan SM, Doskotch RW.1962. Tumor inhibitors. I. Aristolochic acid, the active principle of Aristolochia indica. JMed Pharm Chem91: 657-659. (Supported by the National Cancer Institute. Authors affiliated with University of Wisconsin.)

[34] Jian Qing Yu, Zhi Xiong Liao et al. Composition, Antimicrobial activity

Bethesda MD August7, 2013

307- 311.

2008

n° 21 /8241- 8246

*Analysis of* Aristolochia longa *L. Medicinal Plant from Algeria DOI: http://dx.doi.org/10.5772/intechopen.95298*

reported. Authors affiliated with Dr. Madaus Gmbh & Co., Germany)

*Trace Elements and Their Effects on Human Health and Diseases*

[21] Hashimoto K, Higuchi M, Makino B, Sakakibara I, Kubo M, Komatsu Y, Maruno M, Okada M.1999. Quantitative analysis of aristolochic acids, toxic compounds, contained in some medicinal plants. J E thnopharm 64: 185-189. (Support not reported. Authors affiliated with Tsumara and C company, Japan; Toyama Medical and Pharmaceutical University, Japan.)

[22] Kite GC, Yule MA, Leon C, Simmonds MS.2002. Detecting aristolochic acids in herbal remedies by lquid chromatography/serial mass spectrometry. Rapid Commun Mass Spectrom 16(6): 585-590 (support not reported. Authors affiliated with Royal Botanic Gardens, UK and University of

[23] IARC, 2002. Some Traditional Herbs Medicines , Some Mycotoxins, Naphtalene and Styrene, IARC Monographs on the Evaluation of Carcinogenic Risk of Chemicals to Humans .vol.82,Lyon, France International Agency for Research on

[24] Grollman AP, Jelacovie B.2007. Role of environnemental toxins in endemic (Balkan) nephropathy. October .2006, Zagreb, Crotia. J Am Soc Nephrol 18(11): 2817-23.(Supported by NIEHS, Fogarty International Center and the Croation Ministries of Science and Health Authors affiliated with stony Brook University , NY; Zagreb University School of Medicine and University Hospital Center, Croatia)

[25] Pozdzik AA, Berton A, Schmeiser HH, Missoum W, Decaestecker C, Salmon IJ, Vanherweghem JL, Nortier JL .2010; Aristolochic acid nephropathy revisited:

A Place for innate and adaptive immunity? Histopathol., 56(4):

[26] Mengs U.1987. Acute toxicity of aristolochic acid in redents. Aech Toxicol59 (5): 328-333(Support not

449-463.

Greenwich, UK.)

Cancer .p.69 -128

Vanhaelen-Fastre R, Vanhaelen M.1993. Rapidly progressive interstitial renal fibrosis in young women : association with slimming regimen including Chinese herbs . Lancet 341(8842): 387- 391.(support not reported, Authors affiliated with Université Libre de Bruxelles , Belgium, Vrje Universiteit Brussel, Belgium, Catholique de

[16] Kupchan SM, Doskotch RW.1962. Tumor inhibitors. I. Aristolochic acid, the active principle of Aristolochic India. Jmed Pharm Chem 91 : 657-659. (Supported by the National Cancer Institute. Authors affiliated with

Louvain , Belgium)

University of Wisconsin)

Hospital, USA)

[17] Jackson I., Kofman S, Weiss A, Brodovsky H.1964, Aristolochic acid ( NSC- 50413): Phase I clinical study. Cancer Chemother Rep 42:35-37. (Support not reported. Authors

affiliated with Jefferson Medical College Hospital and Presbyterian. St. Luke's

[18] Mix DB, Guinaudeau H,Shamma M.

1982. The aristolochic acids and aristolactams. JNat Prod 45(6): 657- 666.( Support not reported Authors affiliated with Pennsylvania state University , PA; Universite de Limoges, France; Centre d'Etudes

Pharmaceutiques, France)

[19] Kumar V , Poonam, Prasad AK , Parmar VS.2003. Naturally occuring aristolactams ,aristolochic acids and dioxoporphines and their biological activities. Nat P rod Rep 20(6): 565-583. (Supported by the Council of Scientific and Industrial Research. Authors affiliated with University of Delhi,

[20] Arlt VM, Stiborova M, Schmeiser HH .2002. Aristolochic acid as a probable human cancer hazard in Herbal remedies : A review. Mutagenesis, 17(4): 265-277

**106**

India)

[27] U.S.National library of Medicine – Bethesda MD August7, 2013

[28] Mengs U, Stotzem CD .1993. Renal toxicity of aristolochic acid in rats as an example of nephrotoxicity testing in routine toxicology. Arch. Toxicol., 67: 307- 311.

[29] Chung-Hsin Chen et al . Aristolochic acid – associated urotherial cancer in Taiwan PNAS /may 221,2012 /vol 109 / n° 21 /8241- 8246

[30] U.S. Department of Health and Human Services Public Health Services National Toxicology Program Research Triangle Park, NC 27709: final Report on Carcinogens Background Document for Aristolochic Acids September 2, 2008

[31] Flurer RA,Jones MB, Vela N, Ciolino LA, Wolnick KA.2001. Determination of Aristolochic Acid in Traditional Chines Medicines and Dietary Supplements , DFS/ORO/ ORA NO.4212. U.S. Food and Drug Administration 13 pp.

[32] Tanaka A,Nishida R, Yoshida T, Koshikawa M, Goto M, Kuwahara T.2001. Outbreak of Chinese Herb nephropathy in Japan: are thre any differences from Belgium ? Intern Med 40(4): 296- 300.(Support not reported . Authors affiliated With Osaka Saiseikai Nakatsu Hospital, Japan; Kyoto University, Japan.)

[33] Kupchan SM, Doskotch RW.1962. Tumor inhibitors. I. Aristolochic acid, the active principle of Aristolochia indica. JMed Pharm Chem91: 657-659. (Supported by the National Cancer Institute. Authors affiliated with University of Wisconsin.)

[34] Jian Qing Yu, Zhi Xiong Liao et al. Composition, Antimicrobial activity

and cytotoxicity of essential oils From Aristolochia mollissima. Environmental Toxicology and Pharmacology 23.2007; p. 162- 167

[35] Benchaabane A, Abbad A .1997. Medicinal Plants marked in Marrakech. Trace of the Present. Marrakech, p. 74

[36] FDA.1995. Dietary Supplement Health and Education Act of 1994. U.S.Food and Drug Administration. http://www.cfsan.fda.gov/dms/ dietsupp.html Last accessed: 7/1/06

## *Edited by Daisy Joseph*

This book is an excellent compilation of trace elements and their positive and negative effects on human health and the environment. Over two sections, the book examines the adverse effects of trace elements in the human body and the atmosphere and how to overcome them.

Published in London, UK © 2021 IntechOpen © Navapon\_Plodprong / iStock

Trace Elements and Their Effects on Human Health and Diseases

Trace Elements and Their

Effects on Human Health and

Diseases

*Edited by Daisy Joseph*


**Abstract**

This study evaluated the effect that tree species traits and wet/dry periods display on soil microbial communities in a tropical dry forest in Puerto Rico. Understanding the ecological role of soil microorganisms in tropical dry forests and how they relate to different tree species is necessary to protect these fragile forest ecosystems. Thus, by using 454 pyrosequencing, we explored how microbial diversity was affected by dominant tree species during the wettest and driest periods at the Guánica Dry Forest. We found that 9 out of 17 phyla were more abundant during the dry period demonstrating that soil communities have adapted to historically low rainfall patterns. The most abundant phyla during both periods were Proteobacteria, Actinobacteria, and Bacteroidetes. During the dry period, Actinobacteria increased significantly (p < 0.0001), whereas Proteobacteria and Bacteroidetes decreased significantly (p < 0.0001; p < 0.001). Canonical correspondence analysis (CCA) also demonstrated that soil microbes are shaped by wet and dry periods, thus axis 1 of CCA explained 80% of the variation. This study offers baseline information in order to help elucidate how microbial diversity is affected by climate change in tropical areas and extrapolate this information to agricultural areas in order to develop better management practices.

**Keywords:** historical rainfall patterns, bacterial resilience, soil microbiome, soil microbial ecology, soil enzyme activity, Guánica Dry Forest, Puerto Rico, bacterial diversity, DNA sequencing


**2. Epidemiology of colorectal cancer**

Colorectal cancer is among the leading malignant tumours both by incidence and by death rate [1]. Globally, in the year 2012, it was the 3rd most frequent cancer in men and the 2nd in women [2]. The incidence and mortality is higher in males (Table 1). The highest incidence rates are found in Australia and New Zealand, Europe and North America contrasting with low incidence in Africa and South Central Asia. As shown in Table 2, the incidence is generally higher in more developed countries [2]. The decrease in colorectal cancer incidence in USA reflects successful screening and removal of colorectal adenomas. The incidence growth, recently observed in Western Asia (Kuwait and Israel) and Eastern Europe (Czech Republic and Slovakia), reflects increased prevalence of risk factors as diet, obesity and smoking.

1 Among all cancers.

**1. Introduction**

170 Recent Advances in Liver Diseases and Surgery

formed [9].

Colorectal cancer (CRC) represents one of the leading malignant tumours both by incidence and death rate [1, 2]. Metastatic spread to liver occurs in 70–75% of patients, and 20–35% of CRC patients present with synchronous liver metastases [1, 3, 4]. Although the presence of metastatic disease significantly adversely affects the survival, a wide scope of treatment options exists. To ensure that each colorectal cancer patient receives the best care, the medical society should be well informed about the possibilities in the treatment of liver metastases of

Surgery is the preferred option for long term survival. The operation extent ranges from major hepatic resection (trisegmentectomy, hepatectomy, extended hepatectomy, and hemihepatec‐ tomy) to parenchyma-sparing minor resection such as segmentectomy or wedge resection [4]. Laparoscopic approach and robotic surgery can be considered, especially in advanced centres [5, 6]. In patients with questionable adequacy of the liver remnant and wide intrahepatic tumour spread, portal vein occlusion, forced liver hypertrophy and staged resection can be helpful [7, 8]. Recently, liver transplantation for metastatic colorectal cancer has been per‐

Surgery at present assumes significant role in treatment of metastatic liver lesions. However, it demands not only appropriate surgical technique but also correct preoperative diagnosis

Adequately timed and exact imaging is necessary prior to the surgical or nonsurgical treatment to reveal the metastases and assess the feasibility of resection. Magnetic resonance imaging (MRI), computed tomography (CT), ultrasonography (US) and 18F-2fluoro-D-glucose posi‐ tron emission tomography in association with computed tomography (PET-CT) are used for imaging metastatic lesions in the liver [1]. The radiologic evaluation can be combined with traditional and novel cancer markers [10–12] and biopsy examination. Among serological markers, carcinoembryonic antigen (CEA) has been used traditionally despite the limitations [4] and lack of unified guidelines. MicroRNAs represent a rapidly advancing research field hopefully yielding diagnostic blood tests to diagnose the cancer by location and to identify the

If the surgical treatment is not possible, other options must be considered, including systemic or transarterial chemotherapy; embolisation; ablation by cryotreatment, radiofrequency or

Due to the wide scope of treatment options, the median survival of patients affected by metastatic colorectal cancer has increased significantly [13, 14]. The 5-year and 10-year survival

In conclusion, liver metastases of colorectal cancer represent a frequent and serious condition. The remarkable medical advances request dynamic systematisation of up-to-dated evidence. The present chapter on the surgical treatment of colorectal cancer metastases is intended to summarise the present knowledge in regard to the approach to patient with liver metastases

of colorectal cancer, discussing the diagnostics, treatment and evaluation of response.

microwaves; or radiotherapy and targeted external beam radio therapy [1].

colorectal cancer regarding the methods, indications and limits.

and reliable plan for postoperative treatment.

presence of residual tumour or early recurrence.

reaches 58% and 36%, correspondingly [15].

ASR, age-standardised ratio per 100,000.

**Table 1.** Global incidence and mortality attributable to colorectal cancer (2012) by Globocan data [16]

1 Includes Europe, North America, Australia, New Zealand and Japan.

2 Includes Africa, Asia (except Japan), Latin America, Melanesia, Micronesia and Polynesia.

ASR, age-standardised ratio per 100,000.

**Table 2.** Incidence and mortality caused by colorectal cancer by regional welfare [2]

Colorectal cancer could be prevented avoiding obesity, alcohol, smoking and excessive consumption of red and processed meat, as well as maintaining physical activity. There are also several screening methods, including guaiac-based or immunochemical test for occult blood in stools, faecal DNA test, virtual colonoscopy by computed tomography imaging, double-contrast barium enema, flexible sigmoidoscopy and colonoscopy [2]. MicroRNA stool test could appear in the nearest future. Despite the possibilities of prevention and screening, metastatic disease is common. Metastatic spread to liver occurs in 70–75% of patients, and 20– 35% of CRC patients are diagnosed with synchronous liver metastases [1, 3, 4]. Although the presence of metastatic disease significantly adversely affects the survival, a wide scope of treatment options exist.


2.2.1. Social Sciences in the Cold War and Beyond

The migration of German social scientists added divisiveness and fragmented international exchange during and after WWII. During the Cold War, in 1963, mainstream US social scientists conferred to frame a middle course between the far right and the socialist frame marginalized by McCarthyism [24]. The next year, Marcuse [25] severely criticized this approach. A Jewish scholar who had been part of the Frankfurt School, Marcuse became one of the few left-leaning US social scientists during the Cold War. On the other extreme, Leo Strauss, a noted German philosopher, became the thought leader of the new conservative right [26]. Strauss criticized liberal democracy because the German democratic system made it possible for Hitler to seize power, giving rise to the Nazi regime [27].

Almost as echoes of this anti-democratic social thinking, right-leaning scholars advocated for a return to Western civilizations as foundations for collegiate undergraduate education in the US, e.g., [28,29]. They advocated restructuring the high school curriculum to emphasize a college preparatory curriculum for all students [30]. The political left in the

US also promoted this strategy for preparing all students with advanced courses in math and science previously necessary for entry to collegiate Engineering programs. Liberal scholars advocated for preparing all students for Science, Technology, Engineering, and Math (STEM) fields because of the history of tracking minorities into vocational education into vocational high school programs [31–33]. Rather than updating and modernizing vocational education, the path chosen by the EU, the US marginalized technical for working class families.

These contrasting arguments in academic discourse come into question as nationalism reemerges as a fragmenting force. For example, Brexit ushered in a reconstruction of trade agreements in the EU. European nations have benefited from trade and economic exchange within the EU—the flow of labor and products—but the UK's financial future is now uncertain [34]. Given China's ascent in world trade and strong relationships with the EU, Trump's agenda on global and Pacific trade agreements has left the US more isolated in international trade, at least before Biden's election. Biden's alliance-building with Europe during Russia's invasion of Ukraine may reshape these trade alliances, depending on China's support for Russia. Claims thrown back and forth about Nazi nationalism underlie this contemporary rhetorical battle, further accelerated by the Ukraine war.

The global appeal of the US university model further complicates the post-neoliberal political shifts [35]. Trump's criticisms of China created reluctance among Chinese students to study in the US even before COVID-19 [36]. Israeli universities have benefited from the shift in students' interests [37], illustrating that international economic and political alliances impact educational exchange.


**8.1 Studies**

110 Cancer of the Uterine Endometrium – Advances and Controversies

additional risks posed by a systematic LND and the benefits of performing the surgery by

In a large retrospective study, Cragun et al. (2005) summarized the morbidities of LND by laparotomy. Two to three percent of patients had small bowel obstruction or ileus, deep vein thrombosis and lymphocysts requiring drainage. Patients undergoing PLND and PaLND required longer anesthesia time and hospital stay and had greater blood loss compared to those who had PLND alone. Up to 8% of patients had a wound infection. Chronic

Querleu et al. (2006) audited 1,000 patients who had a *laparoscopic LND*. Only 1.3% were converted to laparotomy. Intra- and early post-operative complication and lymphocyst formation rates were 2.0%(bowel complication 0.7%; urinary tract complications 0.5%; nerve

**7.1 RCTs comparing laparotomy to minimally invasive surgery for endometrial cancer**  In the LAP-2 study, an RCT carried out by the Gynecologic Oncology Group (GOG), 2,616 patients with endometrial carcinoma confined to the uterus were randomly assigned to laparoscopy or laparotomy (Walker, 2009). All patients had complete surgical staging including PLND and PaLND. Laparoscopic-assisted vaginal hysterectomy, total laparoscopic hysterectomy or robotic-assisted total laparoscopic hysterectomy was allowed. They found that laparoscopy resulted in similar intra-operative complications, fewer post-operative moderate or severe adverse events (14% versus 21% by laparotomy, p<0.0001), shorter hospital stay, less use of pain medication and quicker resumption of daily activities but required longer operating time. Twenty five percent of patients randomized to laparoscopy were converted to laparotomy. Patients at higher risk for a conversion to laparotomy were elderly (>63 years) and those with metastatic disease and a high BMI (17% in patients with a BMI of 25kg/m2, 26% with a BMI of 35kg/m2, 57%

In an Australian RCT (n=361), which also compared total laparoscopic hysterectomy with abdominal hysterectomy in early endometrial carcinoma, 52% of the patients had a pelvic or para-aortic lymphadenectomy. Only 2.4% of patients assigned to laparoscopy were converted to laparotomy. Patients who had laparoscopic surgery reported significantly greater improvement in QoL from baseline compared with those who had laparotomy, this difference persisted for up to 6 months after surgery. Operating time was significantly longer in the laparoscopy group (138 minutes [SD 43]) versus 109 minutes [SD 34]; p=0.001). Intra-operative adverse events were similar between groups (laparotomy 5.6% versus laparoscopy 7.4%]; p=0.53), but postoperatively, twice as many patients in the laparotomy group experienced adverse events of Grade 3 or higher (23.2% versus 11.6%; p=0.004). The authors concluded that QoL improvements from baseline during early and later phases of recovery, and the adverse event profile, favor laparoscopy over laparotomy for the

Other studies that investigated the feasibility of minimally invasive surgery (laparoscopy and robot-assisted surgery) in elderly and obese patients concluded that neither age nor BMI is a contraindication to minimally invasive procedures, as it is these patients who benefit the most (Boggess et al., 2008; Gehrig et al., 2008; Janda et al., 2010; Obermair et al.,

lymphedema of the lower limbs was observed in 2.5% (Abu-Rustum et al., 2006).

laparoscopy or robotic surgery.

injuries 0.5%), 2.9% and 7.1%, respectively.

with a BMI >40kg/m2).

treatment of Stage I endometrial cancer.

2005; Scribner et al., 2001).

The Postoperative Radiation Therapy in Endometrial Cancer (PORTEC) Trial randomized 715 patients with Stage IB (Grades 2 and 3) and with IC (Grades 1 and 2) endometrial cancer after standard surgery without PLND to observation or pelvic RT with 46 Gy. Although the five-year actuarial locoregional recurrence rates were 4% in the radiotherapy group and 14% in the control group (p=0.001, the overall survival rates were similar in the two groups: 81% (radiotherapy) and 85% (controls), p=0.31. Endometrial-cancer-related death rates were 9% in the radiotherapy group and 6% in the control group (p=0.37). Treatment-related complications occurred in 25% of radiotherapy patients and in 6% of the controls (p=0.0001). One third of the complications were Grade 2 or higher. Seven out of eight Grade 3 to 4 complications were in the radiotherapy group (2%). The observation that the higher incidence of locoregional recurrences in the control group is not reflected in the overall survival was explained by the post-relapse survival. Twenty-three out of 51 patients with a locoregional relapse died, of whom only seven died due to their locoregional recurrence. By contrast, 21 of 30 patients with distant metastases as first failure died, of whom 19 died from the metastases. Salvage treatment of vaginal relapse was often successful. After vaginal recurrence, the two-year survival rate was 79% in contrast to 21% after pelvic or distant relapse. At three years, the survival was 69% and 13%, respectively (p=0.001). As for the survival after first relapse by treatment arm, the survival rate was better for patients in the control group than for patients in the radiotherapy group (p=0.02). The authors concluded that post-operative radiotherapy in Stage 1 endometrial carcinoma reduces locoregional recurrence but has no impact on overall survival and that radiotherapy increases treatmentrelated morbidity. Therefore, a trade-off between the risk of locoregional recurrence and the survival rate after salvage treatment on the one hand, and the morbidity and cost of adjuvant pelvic radiotherapy on the other, has to be made for each subgroup of Stage 1 endometrial carcinoma. These findings further support the need for a systematic LND whenever possible for patients with intermediate or high risk of endometrial cancer.

#### **8.2 Conclusion**

Adjuvant radiotherapy cannot be substituted for a systematic LND in intermediate- and high-risk endometrial cancer patients.


**4. JAK Inhibitors and Rheumatoid Arthritis**

RA is a chronic inflammatory polyarthropathy characterized by the symmetrical involvement of peripheral joints, internal organ involvements, and systemic symptoms [1]. The etiology of the disease is not precisely understood but at the current level of knowledge and our understanding based on the disease mechanism, the pathogenesis is believed to be the mosaics of environmental, genetic, and lifestyle-related factors. All these factors when working together contribute to the aberrant immunological response and create the autoimmune reactions. Targeting many pro-inflammatory cytokines with a single small molecule created a unique opportunity to block several signaling pathways involved in the development of autoimmune diseases including RA. The obvious background to target JAK was to reduce the level of IL-6, one of the pivotal cytokines in RA. The other cytokines, although not directly involved into the pathogenesis of RA, create permissive background for inflammatory response contributing to the development of cellular response [45], including the Th1, Th2, and Th17 cells, which are directly involved in the development of autoimmune and inflammatory disorders [46]. Understanding the role of JAK in the pathogenesis of various autoimmune disorders led to the synthesis of several JAK inhibitors. Followed the approval of the first JAK inhibitor, tofacitinib, in the treatment of RA in 2012 and in 2017 in the USA and Europe, respectively, baricitinib and upadacitinib were subsequently approved for RA in DMARD failure patients.

Based on the selectivity of a given JAK molecule, JAK inhibitors are commonly subcategorized as first and next generation. First generation of JAK inhibitors (i.e., tofacitinib, baricitinib, and peficitinib, all approved for RA in Japan) block two or more JAK molecules resulting in inhibition of several cytokines. Consequently, inhibiting a JAK molecule may block more than one pathway, which may in part explain both the drug efficacy and some of the adverse effects observed with JAK inhibitor treatment [47]. In contrast, next generation of JAK inhibitors (i.e., upadacitinib and filgotinib, which are not approved for RA yet) is characterized by high selectivity, and thus administration of inhibitors blocks only one specific JAK molecule and selectively inhibits signal from one or limited number of cytokines. This provide the precise mechanism enabling to target one cytokine with one drug.

The current strategy for the treatment of RA is based on early starting classic synthetic DMARDs (csDMARDs), mainly methotrexate (which is still recognized as an anchor drug in the treatment regimen), administered alone or in combination with glucocorticosteroids. In case of MTX failure or intolerance, other csDMARDs (i.e., sulfasalazine or leflunomide) are available. The other group of therapeutic agents including bDMARDs or targeted synthetic DMARDs (tsDMARDs) with JAK inhibitors being the most important representative.

Blocking several cytokines with a single small molecule was a successful approach. In many clinical trials, JAK inhibitors were proven to be equal to bDMARDs [10,48,49]. Two studies designed as non-inferiority trials have shown statistical superiority of baricitinib or upadacitinib compared with adalimumab (all in combination with MTX) [50,51]. However, a third study using tofacitinib+MTX did not show such efficacy [52]. Therefore, the European League Against Rheumatism (EULAR) task force decided that clinical significance is too low to prefer tsDMARDs over bDMARDs. In line with this conclusion, current EULAR recommendation indicates adding bDMARD or a tsDMARD to the treatment regimen when the treatment target is not achieved with the first csDMARD strategy and poor prognostic factors are observed. Moreover, EULAR task force revised the preference of bDMARDs over tsDMARDs (proposed in earlier recommendation) because of new evidence regarding the successful long-term efficacy and safety of JAK inhibitors [53–55]. Currently, four JAK inhibitors are approved for

the treatment of RA, namely tofacitinib, baricitinib, upadacitinib, and peficitinib (approved for RA in Japan), but many other compounds are currently tested in RA and other autoimmune diseases [56].

### **5. Safety Issues of JAK Inhibitors**

Blocking several cytokines with one small molecule may potentially bring many pathophysiological consequences. It is especially true when we consider how blocking the different pathways translates to change the activity of various, sometime critical body systems. Firstly, targeting JAK3 attached to γ-cytokines leads to impairment of signaling via IL-2, IL-4, IL-7, IL-9, IL-15, and IL-21 (Figure 1). This is of the special importance as those cytokines are responsible for proper T-cell development and immunoglobulin synthesis. JAK3 blockade resembles severe immunodeficiency syndrome, with a switch off mutation in γ-chain resulting in X-linked SCID [57]. Therefore, infection, especially viral infections attracted the main attention of researches. Targeting JAK and blocking transmission of several cytokines may also lead to some safety issues in the cardiovascular system.


*Article* **Evolutionary Multiobjective Optimization with Endmember Priori Strategy for Large-Scale Hyperspectral Sparse Unmixing**

**Zhao Wang 1,\*, Jinxin Wei 1, Jianzhao Li 1, Peng Li 1 and Fei Xie 2**

**Abstract:** Mixed pixels inevitably appear in the hyperspectral image due to the low resolution of the sensor and the mixing of ground objects. Sparse unmixing, as an emerging method to solve the problem of mixed pixels, has received extensive attention in recent years due to its robustness and high efficiency. In theory, sparse unmixing is essentially a multiobjective optimization problem. The sparse endmember term and the reconstruction error term can be regarded as two objectives to optimize simultaneously, and a series of nondominated solutions can be obtained as the final solution. However, the large-scale spectral library poses a challenge due to the high-dimensional number of spectra, it is difficult to accurately extract a few active endmembers and estimate their corresponding abundance from hundreds of spectral features. In order to solve this problem, we propose an evolutionary multiobjective hyperspectral sparse unmixing algorithm with endmember priori strategy (EMSU-EP) to solve the large-scale sparse unmixing problem. The single endmember in the spectral library is used to reconstruct the hyperspectral image, respectively, and the corresponding score of each endmember can be obtained. Then the endmember scores are used as a prior knowledge to guide the generation of the initial population and the new offspring. Finally, a series of nondominated solutions are obtained by the nondominated sorting and the crowding distances calculation. Experiments on two benchmark large-scale simulated data to demonstrate the effectiveness of the proposed algorithm.

**Keywords:** large-scale multiobjective optimization; sparse unmixing; hyperspectral image; evolutionary algorithm

#### **1. Introduction**

Hyperspectral imagery, which contains a wealth of spectral information for the surface features in each pixel, has been widely used in various remote sensing applications, such as geological analysis, environmental monitoring and military reconnaissance. However, due to the low spatial resolution and the ground substances intimate mixtures, the mixed pixels inevitably appear in the hyperspectral images. To solve this problem, the spectral unmixing technique aims to extract the pure spectral signatures (also called endmembers) from hyperspectral images and estimate their corresponding proportions (also called abundances).

The spectral unmixing assumes that there is no multiple scattering between endmembers in the spectrum, each pixel is a linear combination of elements from the endmember set in the linear mixed model (LMM) [1]. Under this model, various methods such as geometry-based [2], nonnegative matrix factorization-based (NMF) [3–5] and statisticalbased [6] have been conducted research in the hyperspectral spectral unmixing, which also obtained a very ideal unmixing effect. However, these methods suffer from poor performance when the assumption of pure pixels or the generation of virtual endmembers do not satisfy.

**Citation:** Wang, Z.; Wei, J.; Li, J.; Li, P.; Xie, F. Evolutionary Multiobjective Optimization with Endmember Priori Strategy for Large-Scale Hyperspectral Sparse Unmixing. *Electronics* **2021**, *10*, 2079. https://doi.org/10.3390/ electronics10172079

Academic Editor: George A. Papakostas

Received: 17 July 2021 Accepted: 24 August 2021 Published: 27 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

As an emerging spectral unmixing technology, Hyperspectral sparse unmixing aims to find the optimal subset of the true endmembers for reconstructing the mixed pixels based on the known spectral library in advance. Compared to the number of endmembers in the spectral library, the number of endmembers use for reconstructing is is relatively sparse. Mathematically speaking, it is a *l*0 norm problem, which is highly non-convex and NP-hard [7]. The relaxation methods, such as the *l*1 norm or the *lp* norm (0 < *p* <1), are some of the relatively effective solutions to deal with the *l*0 norm problem. Bioucas-Dias et al. [8] solves the sparse unmixing problem by the alternating direction method of multipliers, but the SUnSAL [8] only focuses on the spectral information without taking the spatial structure information between different pixels into account. To take advantage of the relationship between pixels in the hyperspectral image, many strategies such as collaborative sparse regression framework [9] or spectral regularization terms [10,11] are applied in the sparse unmixing model to promote the spatial correlation.

However, these algorithms are very sensitive to parameter settings, which greatly affect the stability of unmixing algorithms. Recently, the intelligent optimization algorithms have been greatly developed. Połap et al. [12] proposed a red fox optimization algorithm by simulating the hunting behavior of fox. In [13], a polar bear optimization algorithm was proposed to simulate the hunting behavior of a polar bear into the stage of global search and the stage of local search. Khishe et al. [14] proposed a chimp optimization algorithm to further alleviate the two problems of slow convergence speed and trapping in local optima in solving high-dimensional problems. Nevertheless, in solving the NP hard problems, the multiobjective evolutionary algorithms (MOEAs) have attracted extensive attention because of the global search ability. Therefore, some excellent algorithms proposed in [15–18] have applied the multiobjective optimization to sparse unmixing. However, most of MOEA-based algorithms in sparse unmixing only focus on solving pixel by pixel efficiently without considering the spatial structure information because of the curse of dimensions. In addition, MOEA-based algorithms suffer from the problem of being timeconsuming, resulting in inefficiency and impracticality. Compared with the large-scale spectral library, the number of endmembers used to reconstruct the hyperspectral image is actually sparse. Therefore, many existing MOEAs suffer from a large number of decision variables when dealing with the sparse multiobjective optimization problems, which consumes the expensive computing resources to search in a large decision space with an arbitrary initialization.

To alleviate the above problems, an evolutionary multiobjective hyperspectral sparse unmixing algorithm with endmember priori strategy (EMSU-EP) is proposed in this paper. In the proposed EMSU-EP, each decision variable is taken out separately for evaluation in the initialization, and their corresponding scores are recorded for the subsequent crossover and mutation. In the subsequent genetic operation, a new genetic operator is designed to ensure the sparsity of the offspring in a uniform interval. With the prior knowledge of the quality of each decision variable and the new genetic operators for binary variables, the proposed EMSU-EP can achieve the better convergence performance and diversity, and the result of unmixing has been greatly improved. The main contributions of the proposed EMSU-EP are summarized as follows.

(1) We propose a novel multiobjective optimization framework for sparse unmixing, which can guide the subsequent evolution of the algorithm according to the prior knowledge obtained from the spectrum library.

(2) A special initialization mechanism is designed, it is demonstrated that the proposed EMSU-EP can obtain the diverse and targeted population compare with the state-of-the-art MOEA-based sparse unmixing methods.

(3) The particular crossover and mutation operators are proposed to maintain the sparsity of the population, which can not only promote the convergence of the algorithm, but also improve the performance of sparse unmixing.

The rest of this paper is organized as follows. In Section 2, the related works are summarized. In Section 3, the framework of our proposed EMSU-EP algorithm is introduced

in detail. The experimental results are presented and analyzed in Section 4. Finally, the work in this paper is concluded in Section 5.

#### **2. Related Works**

In this section, the related works on sparse unmixing and the multiobjective optimization are introduced.

#### *2.1. Sparse Unmixing*

As shown in Figure 1, sparse unmixing aims to find the optimal set of endmembers for modeling the mixed pixels from a large-scale and pre-known spectral library. Therefore, a mixed pixel (*y* ∈ R*L*×1) with *L* spectral bands can be formulated as

$$y = A\mathbf{x} + \mathbf{n} \tag{1}$$

where *A* ∈ R*L*×*D* is the spectral library, *x* ∈ R*D*×1 represents the corresponding fractional abundance vector and *n* ∈ R*L*×1 is the noise term. In the absence of noise, the sparse unmixing method of the Formula (1) is mathematically expressed as

$$\begin{array}{ll}\min\_{\mathbf{x}} \|\mathbf{x}\|\_{0} \\ \text{s.t.} \quad \|\mathbf{y} - \mathbf{A}\mathbf{x}\|\_{2}^{2} \leq \delta \end{array} \tag{2}$$

where *δ* ≥ 0 denotes the error tolerance, *x*-0 is the *l*0 norms of *x*, which is highly nonconvex and NP-hard. It was not well solved until Candes et al. [7] proved that *l*1 norm can induce sparsity instead of *l*0 norm under a certain restricted isometry property condition. In [8], the SUnSAL was proposed to solve the sparse unmixing problem of mixed pixels by establishing constrained sparse regression as

$$\min\_{\mathbf{x}} (1/2) \|\mathbf{y} - \mathbf{A}\mathbf{x}\|\_2^2 + \lambda \|\mathbf{x}\|\_1 + \iota\_{\mathbf{R}+}(\mathbf{x}) + \iota\_{\{1\}}(\mathbf{1}^\mathbf{T}\mathbf{x}) \tag{3}$$

where *x*-1 denotes the *l*1 norm of *x*, *λ* is a regularization parameter that controls the relative weight of the error term and the sparse term, **1** denotes a column vector of 1's, the *ιR*+(*x*) and *ι*{1}(**1T***x*) represent the abundance non-negativity constraint (ANC) and the abundance sum-to-one constraint (ASC) [19], respectively.

**Figure 1.** Illustration of the hyperspectral sparse unmixing problem, *Y* is the image to be unmixed, *A* is the large-scale spectral library, and *X* is the obtained abundance matrix. Only colored active endmembers participate in the reconstruction of endmembers.

However, the SUnSAL [8] only focuses on the spectral information without taking the spatial structure information between different pixels into account. In general, a hyperspectral image (*Y* ∈ R*L*×*n*) with *n* pixels structured in the matrix can be formulated as

$$\mathbf{Y} = A\mathbf{X} + \mathbf{N} \tag{4}$$

where *Y* = [*y*1, *y*2, ... , *yn*], *yi* is the *i*-th mixed pixel, *X* ∈ R*D*×*n* is the abundance matrix, and *N* ∈ R*L*×*n* is the corresponding error term. The formula (4) can be transformed into an optimization problem expressed as

$$\begin{array}{ll}\min\_{\mathbf{X}} \|\mathbf{X}\|\_{0} \\ \text{s.t.} \quad \|\mathbf{Y} - \mathbf{A}\mathbf{X}\|\_{F}^{2} \leq \delta \end{array} \tag{5}$$

where -*X*-0 = |supp(*X*)|, supp(*X*) = {1 ≤ *i* ≤ *D*, **x***i* = **0**}, *xi* is *i*th row of *X*. To take advantage of the relationship between pixels in the hyperspectral image, CLSUnSAL [9] assumes that all pixels share the same active endmembers to reduce the influence of the spectral coherence between endmembers on the unmixing effect. The model is shown as follows

$$\min\_{\mathbf{X}} \|\mathbf{Y} - \mathbf{A}\mathbf{X}\|\_F^2 + \lambda \|\mathbf{X}\|\_{2,1} + \iota\_{\mathbb{R}+}(\mathbf{X}) \tag{6}$$

where -**X**-2,1 = ∑*m k*=1 1 1**x***k* 1 1 2 represents the *l*2,1 norm, *ιR*+(*X*) = ∑*n i*=1 *ιR*+(**x***i*) denotes the indicator function. Moreover, many spectral regularization terms, such as the total variation regularization term [10] and the non-local regularization terms [11], are integrated into the sparse unmixing model to promote the spatial correlation.

#### *2.2. Multiobjective Optimization*

The multiobjective evolutionary algorithms (MOEAs) have attracted extensive attention because of the global search ability in solving the sparse unmixing problems. In [15], Gong et al. proposed the multiobjective sparse unmixing model with a cooperative coevolutionary strategy. Jiang et al. [16] formulated the sparse unmixing problem into a two-phase multiobjective problem to estimate the endmembers and determine the abundances, respectively. In [17,18], the multiobjective evolutionary algorithm based on decomposition (MOEA/D) [20] has also been explored and applied in the sparse unmixing problem. For the multiobjective optimization problem, the mathematical form with *a* objectives and *b* decision variables can be described as

$$\begin{array}{l}\min F(\mathbf{x}) = (f\_1(\mathbf{x}), f\_2(\mathbf{x}), \dots, f\_d(\mathbf{x}))^T\\\text{s.t.} \ x = (\mathbf{x}\_1, \mathbf{x}\_2, \dots, \mathbf{x}\_b)^T \in \Omega \end{array} \tag{7}$$

where *x* is the decision vector, *F*: **Ω** → R*a*, **Ω** is the decision space and R*a* is the objective space.

In the majority of cases, there is no single solution capable of minimizing all the objectives at the same time. Instead, the best trade-off between the objectives can be defined as Pareto optimality. Therefore, in order to evaluate the pros and cons of multiple solutions, the nondominated fronts and crowding distances of the individual can be applied. If the individuals are dominated by the same number of individuals, these individuals belong to the same nondominated front. In addition, the crowding distance of an individual can be obtained by calculating the side length of the rectangle formed between two adjacent individuals that belong to the same nondominated front with the individual. Assuming that *p*1 and *p*2 are two individuals in the population, individual *p*2 is preferred over *p*1 (i.e., *p*2 *p*1) if any one of the following conditions holds [21], (1) NF2 < NF1, (2) NF2 = NF1 and CD2 > CD1, where NF1 and NF2 represent the nondominated fronts of individuals *p*1 and *p*2, respectively. CD1 and CD2 represent the crowding distances of individuals *p*1 and *p*2, respectively.

#### **3. Proposed Method**

For the sparse unmixing problem, there are two conflicting objectives to be optimized, namely the sparse endmember term and the reconstruction error term. Therefore, the multiobjective optimization problem for sparse unmixing is

$$\min\_{\mathbf{X}} \left( \left\| \mathbf{X} \right\| \left\| \mathbf{0}\_{\prime} \left\| \mathbf{Y} - \mathbf{A} \mathbf{X} \right\| \right\|\_{F}^{2} \right) \tag{8}$$

where the -*X*-0 is the sparse term and the -*Y* − *AX*-2 *F* represents the reconstruction error. The Formula (8) can be solved with the multiobjective optimization to obtain the Pareto Front (PF) of a compromise between these two objectives. Then the knee point is selected as the final solution, which is the preferred solution on PF with the maximum marginal utility and can be obtained from the individual with the maximum angle with the two adjacent individuals. In addition, two constrains for the abundance are required by

$$\begin{cases} \text{ANC}: \text{X} = [\mathbf{x}\_1, \dots, \mathbf{x}\_n] \ge \mathbf{0} \\ \text{ASC}: \forall \mathbf{x}\_i \in \mathbf{X}, \mathbf{1}^T \mathbf{x}\_i = 1, i = 1, \dots, n \end{cases} \tag{9}$$

The pseudocode of the proposed EMSU-EP is shown in Algorithm 1. First of all, in the initialization, the *k*-th endmember is extracted from the spectral library at a time to reconstruct the hyperspectral image *Y*ˆ *k* for obtaining the corresponding reconstruction error with the original image. This operation needs to run through all the endmembers in the spectral library. The reconstruction errors of all endmembers are sorted in ascending order, and the corresponding *Scorek* represents the position order. Then the spectral library is encoded into a binary vector with dimension *D*, where "1" and "0" represent the selected and unselected endmembers, respectively. Then EMSU-EP randomly selects two elements from the D-dimensional decision variables each time, and uses the endmember score as the evaluation criterion to set one of to "1" with the binary tournament selection method, which is shown in Figure 2. In order to ensure the diversity of the initial population, the *rand()* operator is employed to uniformly distribute *N* individuals in the sparse interval [0, *D*], respectively. Unlike the inefficiency of random initialization, the more likely real endmembers can be selected to form the initial population with the prior knowledge.

#### **Algorithm 1** Pseudocode of EMSU-EP

**Input:** *A* (the spectral library), *Y* (the hyperspectral image), *N* (population size), *tmax* (maximum number of iterations).

**Output:** *X*∗ (the estimated abundance map).

With the prior knowledge of decision variables, those decision variables with higher scores should be given more attention in the subsequent genetic operations. Therefore, the genetic operators of crossover and mutation proposed in [22] are employed to generate the offspring, which are represented by Crossover() and Mutation(), respectively, in Algorithm 1. The left gray box and the the right gray box represent the Crossover() operator and the Mutation() operator, respectively, in Figure 3. Before evolution, two individuals *p*1 and *p*2 are randomly selected from population as the parents. There are two situations in the Crossover(). On the one hand, the original offspring *c* inherits *p*1, then two non-zero elements are randomly selected from the differential gene positions of *p*1 and *p*2, and one of the gene positions of *c* is set to "0" based on endmember scores (the larger the better). On the other hand, two zero elements are randomly selected from the differential gene positions of *p*1 and *p*2, and one of the gene positions of *c* is set to "1" based on endmember scores (the smaller the better). In the Mutation(), two non-zero elements are randomly selected from the offspring *c*, and one of the gene positions is set to "0" determined by the larger score. To the opposite, two zero elements are randomly selected from *c*, and set one of the gene positions is set to "1" determined by the smaller score. A zero or non-zero element in the binary vector is flipped with the same probability as shown in Figure 3. Compared with the single-point crossover (SPC) and bitwise mutation (BitM), the operators designed by the EMSU-EP select the element to be flipped according to the score of the decision variable to ensure the sparsity of the offspring.

During the evolution of the population, if too many endmembers are selected, some solutions are no longer sparse. To prevent this problem from happening, the sparsity limit *d* is applied to the population evolution. When the number of selected endmembers in an individual exceeds the sparsity limit *d*, EMSU-EP will only retain the endmember whose endmember score sorting in the first *d*-th, and the rest will not be selected (i.e., set to 0).

**Figure 2.** Obtaining the score of every endmember and generate the initial population.

**Figure 3.** Illustration of the flow of crossover and mutation operators. The middle procedure represents the generation process of a offspring, the left procedure represents the crossover operation, and the right procedure represents the mutation operation.

Finally, all individuals of the parent and offspring are evaluated for nondominated sorting and crowding distance calculation [23], and the best *N* individuals are selected to form the next generation population. After satisfying the end of the iteration, the knee point in the last generation population is returned [24]. The set of non-zero elements are extracted from this optimal binary vector, which also represents the corresponding endmember subset *As*∗ from the spectral library *A*. Therefore, the abundance map *Xs*∗ can be calculated according to the least square method, which is shown as follows

$$X\_{\mathbb{S}^\*} = \arg\min\_{X\_{\mathbb{S}^\*}} ||Y - A\_{\mathbb{S}^\*} X\_{\mathbb{S}^\*}||\_F. \tag{10}$$

According to the Formula (10), we can not only achieve dimensionality reduction of hyperspectral data, but also ensure the sparseness of unmixing solutions. After the calculation of Formula (10), the zero element is inserted into the non-zero real solution according to the original position to realize the restoration of the data dimension.

#### **4. Experimental Results and Discussion**

In this section, the effectiveness of EMSU-EP in solving large-scale sparse unmixing problems will be demonstrated. Two large-scale sparse unmixing benchmark datasets are used to validate the performance of the EMSU-EP. In order to reflect the efficiency of EMSU-EP, some advanced algorithms such as SUnSAL [8], CLSUnSAL [9], MOSU [15] and MTSR [21] will be compared with EMSU-EP.

In the experiment, the population size is set to 100, and the maximum generation Maxgen is set to 300, the population sparse limit interval *d* is 50. Part of the experiment code refers to the PlatEMO platform (PlatEMO 2.8: https://github.com/BIMK/PlatEMO (accessed on 22 August 2021)) [25]. All experiments will be added with different degrees of Gaussian white noise (SNR = 20, 30 and 40 dB). All experimental results are obtained from the average of 100 independent repeated runs.

#### *4.1. Dataset and Evaluation Indicators*

#### 4.1.1. Dataset

Data 1 is a 64 × 64 synthetic image containing 224 bands provided by Tang [26], its digital spectral library A1 is a sub-library of 498 spectral features selected from the USGS spectral library (http://speclab.cr.usgs.gov/spectral.lib06 (accessed on 22 August 2021)). These spectral signals are evenly distributed at 0.25–0.4 μm. The true abundance map of all five endmembers of data 1 is shown in Figure 4. Data 2 is an image of 100 × 100 pixels and 224 bands per pixel, provided by Iordache et al. [10], its digital spectral library A2 is a sublibrary with 230 spectral signatures of the USGS spectral library. The true abundance map of all nine endmembers of data 2 is shown in Figure 5.

To summarize, data 1 needs to accurately select five endmembers from 498 spectral signals and estimate the corresponding abundance, and data 2 needs to select nine endmembers from 230 spectral signals and estimate the corresponding abundance. Two

 (**a**)  (**b**)  (**c**)  (**d**)  (**e**)

datasets are sparse enough and difficult. Therefore, both data 1 and data 2 are large-scale sparse unmixing problems.

**Figure 4.** True abundance maps of five endmembers in data 1. (**a**) True abundance map of endmember 1. (**b**) True abundance map of endmember 2. (**c**) True abundance map of endmember 3. (**d**) True abundance map of endmember 4. (**e**) True abundance map of endmember 5.

**Figure 5.** True abundance maps of five endmembers in data 2. (**a**) True abundance map of endmember 1. (**b**) True abundance map of endmember 2. (**c**) True abundance map of endmember 3. (**d**) True abundance map of endmember 4. (**e**) True abundance map of endmember 5. (**f**) True abundance map of endmember 6. (**g**) True abundance map of endmember 7. (**h**) True abundance map of endmember 8. (**i**) True abundance map of endmember 9.

#### 4.1.2. Evaluation Indicators

In order to compare the accuracy and the robustness of different sparse unmixing algorithms on large-scale hyperspectral sparse unmixing problem, two evaluation indicators are considered in the experiments.

(1) Signal-to-Reconstruction Error (SRE) can be expressed as:

$$\text{SRE} \,\text{(dB)} \equiv 10 \log\_{10} \left( \frac{E\left[ \left\| \mathbf{X} \right\|\_{F}^{2} \right]}{E\left[ \left\| \mathbf{X} - \mathbf{X} \right\|\_{F}^{2} \right]} \right) \tag{11}$$

where **x** is the true fractional abundance matrix and **xˆ** is the estimated fractional abundance matrix. Without loss of generality, the larger the SRE value is, the better the unmixing accuracy will be.

(2) Success Ratio (SR): If the relative error is smaller than a given threshold *τ*, the corresponding run of this method is denoted as a successful run [27]. SR under the threshold *τ* is defined as:

$$\text{SRR}\_{\mathbf{r}} \equiv \mathbf{P}\left(\frac{\left\|\mathbf{X} - \hat{\mathbf{X}}\right\|\_{F}^{2}}{\left\|\mathbf{X}\right\|\_{F}^{2}} \le \mathbf{r}\right) \tag{12}$$

The probability is the ratio of the successful runs on 100 random instances. If we set *τ* = 5 and arrive at SR*τ* = 1, this implies that the relative error of the reconstruction result is less than 5 with probability one.

The Hypervolume (HV) [28] indicator can be used to evaluate the quality of PF, which can reflect the convergence and diversity of the solutions. HV is calculated by utilizing a reference point who is 1% larger in every component than the corresponding nadir point. In this paper, we use it to evaluate the performance on large-scale sparse unmixing problem by crossover and mutation operations of EMSU-EP, traditional SPC and BitM.

#### *4.2. Experiments on Synthetic Data*

Figure 6 shows the PF of the 50-th generation population obtained by different methods on data 1 and data 2. Whether compared to the PF obtained by SPC and BitM with the initial population of EMSU-EP or the PF obtained by SPC and BitM with the random initial population, EMSU-EP obviously has better convergence and a clearer knee point area, which will be very helpful to choose the final solution later.

**Figure 6.** Illustration of the Pareto Front of the 50th generation on data 1 and data 2.

In order to reflect the advantages of EMSU-EP in each generation, Figure 7 uses the HV indicator to evaluate the PF of the first 100 generations. As shown by the red and purple curves in Figure 7, since the SPC and BitM operation has the same initial population of EMSU-EP, a higher HV value can be obtained from the first generation compared to the SPC and BitM with the random initial population, which corresponds to a better initial population quality and shows the guiding effect of endmember scores on the production of

initial population. However, as shown by the blue and red curves in Figure 7, after the *2*0-th generation on data 1 and the *5*0-th generation on data 2, there are large static difference between the HV value of EMSU-EP and the HV value of the SPC and BitM operation, which shows the guiding effect of endmember scores on the evolution of the population.

**Figure 7.** Illustration of the HV value of each evolution step on data 1 and data 2.

The estimated abundance maps of some endmembers obtained by different algorithms on data 1 and data 2 are shown in Figures 8 and 9, respectively. These experimental results are all on the 30dB SNR. In Figure 8, the abundance maps obtained by SUnSAL, CLSUnSAL, MOSU, MTSR and EMSU-EP are exhibited from left to right, endmember 1, endmember 2 and endmember 5 of data 1 are arranged from top to bottom. In Figure 9, the abundance maps obtained by SUnSAL, CLSUnSAL, MOSU, MTSR, and EMSU-EP are exhibited from left to right, endmember 1, endmember 5 and endmember 8 of data 2 are arranged from top to bottom. As shown in Figures 8 and 9, it is obvious to see that EMSU-EP always has the best performance compared to other algorithms, the unmixing maps color of EMSU-EP is the closest to the real image. Nevertheless, the performance of EMSU-EP in reducing noise is not stable enough, only the abundance map of endmember 1 has the least noise points in Figure 8, and only the abundance map of endmember 8 has the least noise points in Figure 9. Tables 1 and 2 show the SRE (dB) and SR*τ* of the unmixing results obtained by different algorithms on data1 and data 2, respectively. The two data sets are corrupted by different levels of correlated noise (SNR = 20, 30 and 40 dB). According to Tables 1 and 2, EMSU-EP has the highest SRE (dB) and SR*τ* compared to other algorithms at three SNR levels, which indicates that EMSU-EP has the best unmixing accuracy and robustness. The experimental results of two hyperspectral datasets demonstrate that the proposed EMSU-EP method can improve the performance of the sparse unmixing model by utilizing the endmember prior information.

**Table 1.** Comparison of EMSU-EP with other algorithms on data 1. The value of *τ* is set to 0.15.

**Table 2.** Comparison of EMSU-EP with other algorithms on data 2. The value of *τ* is set to 0.15.

**Figure 8.** The estimated abundance maps of endmember 1, endmember 2 and endmember 5 for data 1 on 30 dB SNR obtained by different algorithms.

**Figure 9.** The estimated abundance maps of endmember 1, endmember 5 and endmember 8 for data 2 on 30 dB SNR obtained by different algorithms.

#### **5. Conclusions**

In this paper, we proposed an evolutionary multiobjective hyperspectral sparse unmixing algorithm with an endmember a priori strategy (EMSU-EP) to solve the large-scale hyperspectral sparse unmixing problem. EMSU-EP reconstructs the hyperspectral image by a single endmember to generate every endmember score first. Then the obtained endmember scores are used as prior knowledge to guide the generation of initial populations and new individuals. Experiments have demonstrated that the proposed EMSU-EP algorithm is effective in solving large-scale sparse unmixing problems, and EMSU-EP can maintain the superiority compared with the state-of-the-art sparse unmixing algorithms.

In the future, we will focus on reducing the noise on hyperspectral sparse unmixing problems and exploring the further improvement of EMSU-EP performance.

**Author Contributions:** Conceptualization, Z.W. and J.W.; methodology, Z.W.; validation, Z.W., J.W. and F.X.; investigation, J.L.; writing—original draft preparation, Z.W., J.W. and J.L.; writing review and editing, F.X., J.L. and P.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of Shaanxi Province (grant no. 2021JQ-210), the Fundamental Research Funds for the Central Universities (Grant no. XJS200216), Key R & D programs of Shaanxi Province (Grant no. 2021ZDLGY02-06) and the National Natural Science Foundation of China (Grant no. 61973249).

**Data Availability Statement:** The data 1 and data 2 can be downloaded from http://levir.buaa.edu. cn/Code.htm (accessed on 22 August 2021).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**