The epic conclusion to my beer-bottle-into-cup saga. Here I show how I did some simple etching to give some character to my drinking vessels.
In my previous post I went through the basic steps of chemical etching and attached a couple high-res stills from my Triforce cup test. But this post will primarily be tailored to the video you should have watched above, with some updated tips based on my experiences.
The first place to start is your design. Well, the stencil really. If you look online, people suggest contact paper or vinyl sheets to make a stencil. I didn't feel like buying any of that, but I did have packing tape, which has a smooth, glossy surface. A quick test confirmed that the etching paste had no chemical effect on it.
What changed between my Triforce cup test and now was that I started using foil/parchment paper as a backing for my stencils. This lets you peel off whatever packing-tape design you cut very easily, minimizing handling. If you get fingerprints/oils onto the sticky side of the tape, it's possible for some of the etching paste to seep under it, that's what happened to the left (center) corner of my triforce mask (not the bottom left corner, halfway up). The un-etched triangle isn't perfect, it doesn't connect with the outer edge of the Triforce at a sharp point (that's where I struggled to peel off the stencil/mask).
Protip: Use a cutting mat and exacto knife instead of some newspaper/magazines. If your cutting surface isn't rigid enough, it's harder to make a clean slice through your stencil. Clean cuts = unmarred edges = crisp etch lines. Don't cheap out like I did.
When applying the stencil, again, minimize handling. Use tweezers if you must. Don't get fingerprints on the glass. Press it down firmly to ensure good adhesion, especially along the edges.
I found that dabbing on the paste was the most effective method of application. You don't need a brush (which costs a few more cents >.> ), the surface tension of the paste (more of a creamy goop) and the slickness of the stencil naturally drew it into a uniform layer.
The depth of the etch isn't significantly affected by time. I left the paste on for double the recommended time, and the etching (more of a frosting) was barely perceptible by touch. If you want a deeper etching that doesn't vanish when wet, you'll have to spring for a fine grit sandblaster.
The results of my etching attempts are pretty far from perfect. The Triforce isn't composed of perfect triangles, the power icon is a little ragged around it's circumference, and the batman symbol has slightly tattered wings (from when I accidentally tore the tape instead of cutting it completely at a corner). But I still think they look pretty darn cool, and a more ambitious design could probably pass for a quick gift with the right level of finish.
For $10 though (the price of the etching paste), this is a project you have no excuse not to try if you're at all interested. You can also buy a pack of letter stencils from a craft store to enhance your etching abilities. Give it a shot, let me know how it works out for you (either here or on my instructables post).


1) Liao, M. L., Somero, G.N., Dong, Y.W.*, 2018. Comparing mutagenesis and simulations as tools for identifying functionally important sequence changes for protein thermal adaptation. Proceedings of the National Academy of Sciences of the United States of America DOI: 10.1073/pnas.1817455116.
2) Dong, Y. W.*, Liao, M. L., Meng, X. L. Somero, G. N.*, 2018. Structural flexibility and protein adaptation to temperature: Molecular dynamics analysis of malate dehydrogenases of marine molluscs. Proceedings of the National Academy of Sciences of the United States of America 115, 1274-1279.
3) Liao, M. L., Zhang, S., Zhang, G. Y., Chu, Y. M., Somero, G. N., Dong, Y. W.* (2017). Heat-resistant cytosolic malate dehydrogenases (cMDHs) of thermophilic intertidal snails (genus Echinolittorina): protein underpinnings of tolerance to body temperatures reaching 55 °C. Journal of Experimental Biology 220, 2066-2075.
4) Dong, Y. W.*, Li, X. X., Choi, F. M. P., Williams, G. A., Somero, G. N., Helmuth, B. (2017). Untangling the roles of microclimate, behaviour and physiological polymorphism in governing vulnerability of intertidal snails to heat stress. Proceedings of the Royal Society B: Biological Sciences, 284, 1854.
5) Dong, Y. W.*, Zhang, S. (2016). Ecological relevance of energy metabolism: transcriptional responses in energy sensing and expenditure to thermal and osmotic stresses in an intertidal limpet. Functional Ecology 30, 1539-1548.
6) Dong, Y. W.*, Huang, X. W., Wang, W., Li, Y., Wang, J. (2016). The marine 'great wall' of China: local- and broad-scale ecological impacts of coastal infrastructure on intertidal macrobenthic communities. Diversity and Distributions 22, 731-744.
8) Dong, Y. W.*, Han, G. D., Huang, X. W. (2014). Stress modulation of cellular metabolic sensors: interaction of stress from temperature and rainfall on the intertidal limpet Cellana toreuma. Molecular Ecology 23, 4541-4554.
9) Bates, A. E.*, Helmuth, B., Burrows, M. T., Duncan, M. I., Garrabou, J., Guy-Haim, T., Lima, F., Queiros, A. M., Seabra, R., Marsh, R., Belmaker, J., Bensoussan, N., Dong, Y. W., Mazaris, A. D., Smale, D., Gilov, G. (2018). Biologists ignore ocean weather at their peril. Nature 560, 299-301.


text:
杨国斌:The Power of the Internet in China
By: 爱德布克. 2009-4-8. 5,714
The Power of the Internet in China: Citizen Activism Online by Guobin Yang, Columbia University Press, June 2009
Since the mid-1990s, the Internet has revolutionized popular expression in China, enabling users to organize, protest, and influence public opinion in unprecedented ways. Despite efforts to control these activities, online activism has been an agent of immense social change, allowing common citizens to disseminate content and openly challenge the authority of political and economic elites.
Guobin Yang's pioneering study follows the rise of this dynamic protest and the forces that keep it relevant and unique. Online activism encompasses an innovative range of rituals, genres, and styles, and state efforts to constrain it have only led to more creative acts of subversion. Internet businesses have encouraged these contentious activities, generating an unusual synergy between capitalism and civil organizations that sponsor critique. Based on ten years of meticulous research and grounded in theories of social movements and the public sphere, Yang's study emphasizes the mutual shaping of technology and society and highlights the important role of a transnational diaspora in the making of a Chinese Internet culture. In conclusion, Yang argues that online activism reflects important structural changes in contemporary China and points to a new era of informational politics.
Guobin Yang is an associate professor in the Department of Asian and Middle Eastern Cultures at Barnard College, Columbia University. He is coeditor, with Ching Kwan Lee, of Re-envisioning the Chinese Revolution: The Politics and Poetics of Collective Memories in Reform China.
"A boundary-breaking book. . . . A snap review of some of the hottest issues in front of the Chinese public today." — Daniel Little, Understanding Society
"Mr. Yang's work is essential reading." — Rebecca MacKinnon, Far Eastern Economic Review
"This work represents a major advancement in scholarly research. . . unquestionably, it should be on reading lists for courses related to social and political development in China. . . it is highly recommended to all. " — Jonathan Sullivan, The China Quarterly
"Of interest to sociologists and students of mass communications . . . Recommended." — Choice
"Essential reading for all those seeking a more nuanced account of the power of the internet in China than that provided by international media and human rights organizations." — Colin Hawes, The China Journal
"Yang develops a lens that centers on concrete issues and situations that are both empirical-practical and conceptual-theoretical." — Peter Marolt, International Journal of Communication
"The Power of the Internet in China by Yang Guobin is destined to be classic and obligatory reading for anyone interested in understanding the role of the internet in people's struggle for freedom, justice, and democracy in China." — Lokman Tsui, China Information
"The Power of the Internet in China offers us not only a rich study of Chinese
online activism but also raises significant questions about China's civil society." — Ming-Cheng Miriam Lo, Contemporary Sociology
"An attentive and richly detailed study of the Chinese Internet—certainly the best book I've read on the subject. Guobin Yang does a very fine job of summarizing new developments and vividly describing a variety of online communities." — Patricia M. Thornton, University of Oxford
"In today's China, who benefits more from the power of the Internet: citizen activists or state authorities? Guobin Yang comes down decisively on the side of the citizenry, seeing online activism as the revival of a Chinese revolutionary spirit that is setting the stage for the long-awaited democratic breakthrough. Although the conclusion of this richly documented study is certainly controversial, the careful research and clear reasoning are incontrovertible. Whether or not Yang's optimistic prognosis proves correct, his excellent scholarship and engaging style make for an impressive contribution to a timely debate." — Elizabeth J. Perry, Henry Rosovsky Professor of Government, Harvard University
"Much has been written about the role the Internet has played in political campaigns and grassroots politics in America, but the real transformative power of the Internet can be seen in places like China and Iran, where authoritarian governments are faced with the irreversible power of individuals coming together online. This book gives an in-depth look at the explosion of Internet use in China and the dramatic political and cultural changes it has enabled. The ultimate instrument of individual empowerment is remaking one of the most controlling societies on earth. What Chinese leadership will be forced to recognize is that this democratic surge must be accommodated. Failure to do so will either stop economic development or result in the current regime's loss of power." — Governor Howard Dean
"Transformations in China and transformations of communication are two of the great stories of the contemporary era. They come together in Guobin Yang's outstanding study of online activism in the People's Republic. The Internet expands activists' sense of themselves as participants in global movements, and it is used in distinctively Chinese ways. It circulates repertoires of collective action and occasions new forms of action. In this well-researched and well-written book, Yang gives the best account available of this experimentation, innovation, and social change." — Craig Calhoun, president, Social Science Research Council, and University Professor of the Social Sciences, New York University
Categorized: 读书生活 · READING
Tagged: China - Internet - 杨国斌
侯猛:数据如此分组能否真实反映法学现状——评《中国人文社会科学学术影响力报告》法学部分
刘皓明:《荷尔德林后期诗歌》评注卷后记

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text:
Giving to HKU
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HKU partners with TCL to establish a Joint Research Laboratory for
New Printable OLED Materials and Technology
The University of Hong Kong (HKU) and TCL Corporation Ltd (TCL) have established a strategic partnership and held an opening ceremony of the "HKU-TCL Joint Laboratory for New Printable OLED Materials and Technology" today. President and Vice-Chancellor Professor Peter Mathieson of HKU and Chief Executive Officer Mr Dongsheng Li of TCL officiated at the ceremony.
The HKU-TCL Joint Laboratory for New Printable OLED Materials and Technology is to combine HKU's strength in applying technological innovation and TCL's leadership in the industry with an objective to foster the collaborative effort in developing the high performance solution-processable gold(III) complexes that are capable of serving as phosphorescent dopants in the fabrication of OLEDs and to explore their possibilities for preparing printable inks for commercialization.
Professor Vivian W W Yam, Director and Chief Scientist of the HKU-TCL Joint Laboratory as well as Philip Wong Wilson Wong Professor in Chemistry and Energy, is delighted to partner with TCL in advancing translational research. She said: "The establishment of this HKU-TCL Joint Laboratory is timely. It will not only provide a technology platform for facilitating the collaboration with industries in the Mainland and the Guangdong Province region, for motivating midstream to downstream R&D and commercialization activities, but also in pushing basic research excellence towards translational research activities in an area of high global topical interests that leverage the unique and outstanding strengths in HKU.".
"The synergistic partnership is complementary and mutually enhancing, creating a win-win formula for HKU and TCL and the industry in the Greater China. I have each and every confidence that the Joint Laboratory will be a successful one with promising achievements to become a world-leading center in the area of new OLED materials and technology." Professor Peter Mathieson, President and Vice-Chancellor of HKU remarked.
About TCL Corporation Ltd.
TCL Corporation Ltd has developed a partnership with Hong Kong Science and Technology Parks Corporation (HKSTPC) to set up an international R&D base in Phase 3 of the Hong Kong Science Park, where TCL Corporation Ltd becomes one of the three largest partners of the Hong Kong Science Park to date. TCL Corporation Ltd aims to attract global R&D experts and further its reach into the major markets across the Asia Pacific region, and plans to collaborate with local universities and research institutes that the Hong Kong Science Park has long-standing collaboration with on design, process and product innovations.
Media enquiry:
Ms Cindy Chan, Faculty of Science (tel: 3917 5286/ 6703 0212; email: cindycst@hku.hk);
Ms Rhea Leung, Communication and Public Affairs Office (tel: 2857 8555; email: rhea.leung@hku.hk).
Professor Peter MATHIESON, President and Vice-Chancellor of The University of Hong Kong and Mr Dongsheng LI, Chairman and CEO of TCL Corporation unveiling the plaque for the opening of HKU-TCL Joint Laboratory for New Printable OLED Materials and Technology.
(From the left ) Professor Vivian YAM, Philip Wong Wilson Wong Professor in Chemistry and Energy, HKU, Professor Peter MATHIESON, President and Vice-Chancellor, HKU, Mr Dongsheng LI, Chairman and CEO of TCL Corporation, Mr Hai ZHONG, Deputy Director of Shenzhen Science, Technology and Innovation Commission, Mr Owen CHAN, President and CEO (Greater China Theatre) of Cisco Systems (Hong Kong) Ltd.
Group photo of the Opening Ceremony of the "HKU-TCL Joint Laboratory for New Printable OLED Materials and Technology"
Professor Peter MATHIESON indicating the establishment of new laboratory realizes the "3+1Is" vision of HKU – Internationalisation, Innovation and Interdisciplinarity, all converging on Impact.
Professor Vivian YAM showing her gratitude to the generous support of TCL and the University.
Chief Executive Officer of TCL Mr Dongsheng LI stating his expectation on the establishment of the new laboratory.
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This is a great remake if you've fallen in a rut ordering pizza all the time. At least if you make it yourself you can be sure all the ingredients are fresh, wholesome, and healthy. If you've ever had homemade pizza made from scratch, you may never order in again. I strongly suggest making extra dough because it saves lots of time when you make it ahead. Once you have the dough, you can make a pizza in less time than pizza delivery. Go ahead and double this recipe to make extra dough because it stores very well frozen for up to 3 months or refrigerated for a week.
Easy pizza dough for quick home pizzas anytime!
In a large measuring cup, combine the water, yeast, honey, and 1 tablespoon of the olive oil, stirring to combine.
Let sit until the mixture is foamy, about 5 minutes.
In a standing mixer or a large bowl, add 2 cups of the flour and the salt, stirring with a wooden spoon or a dough hook, until it is all incorporated.
Continue adding the flour, ¼ cup at a time, working the dough with your hands, (or the dough hook) to incorporate the flour after each addition, until the dough is smooth but still slightly sticky.
You might not need all of the flour. Turn the dough out onto a lightly floured surface and knead until the dough is smooth but still slightly tacky, 3 to 5 minutes, (or about 1 minute in the mixer).
Oil a large mixing bowl with remaining olive oil. Place the dough in the bowl, turning to coat the top with the oil.
Cover with a moist towel and set in a warm place, free from drafts until doubled in size, about 1½ hours.
Spray a baking pan or pizza stone with cooking spray and sprinkle with cornmeal to keep dough from sticking.
Take a quarter portion of the risen dough for individual pizzas, or the whole ball of dough for one and form it in your hands, letting gravity stretch it into a flat disc.
Spread sauce of your choice to within an inch of the edges, then add desired toppings on top of sauce.
Bake in middle rack of oven for about 15 minutes or until cheese is melted and well browned and crust is lightly browned.
Remove from oven and slide onto a wire rack for five minutes to cool.
Top with fresh herbs, if desired.
Place on cutting board to slice.
To reheat, place in 350 degree F oven for five minutes or as needed to warm through and crisp crust.


For the first time ever, I am disputing a charge on my credit card. I've been really lucky I guess because I've never had a problem before. It's actually a very minor charge for a pizza we bought from a local place a month or so ago. Turns out I got double charged even though the first transaction was canceled due to a "communication error" with the card reader. I even got the receipt stating it was canceled.
Unfortunately I didn't keep that receipt.
I contacted the credit card company after I noticed the transaction when I was looking at my stuff online a couple weeks later. I called them up only to find out that yes, I can dispute the transaction but it would be much quicker if I had the receipts. Well, unfortunately I didn't keep them so now it looks like I'm going to be out. Apparently there is a reasonable chance that I'll get my money back but without the receipts it's going to take a fair bit longer.
This entry was posted in General, Kemptville and tagged credit card, dispute, receipt on 2008/05/22 by Jeff Ivany.


We have a simple ordering process. If you are short of time, you will be especially happy to know that the entire process is going to take you only several minutes. Select your assignment type and explain what exactly we need to do for you.
Please note that our recommendations above are primarily intended for when to mark a question in The PM Exam Simulator.The deadline is set as soon as you have paid.Critic reviews appear in Search results with a snippet from the critic, the critic's name and the publisher icon.
Follow these tips when writing the body of your critique:Keen states that Spotify pays 0.6 cents for each play.So if you get a range from the institution like 400-500 words, you need to write at least 400 words. If you write less, it will come across like you have nothing to say, which is obviously not an impression you want to give.And he in fact ordered me breakfast due to the fact that I found it for him.
This sentence is structured in the highly specific style of a math problem, which makes it funny.Hero is a revered person in heroic epic poetry.It's human nature to defend essay revise yourself.


text:
Q: Galera Mysql wsrep_cluster_status stays Disconnected My cluster was previously running, I have made these config changes and now Galera cluster bootstrap is not working.
I tried bootstraping with /usr/bin/mysqld_bootstrap as well as service mysql start --wsrep-new-cluster . but no luck.
mysql> SHOW GLOBAL STATUS WHERE Variable_name IN ('wsrep_ready', 'wsrep_cluster_size', 'wsrep_cluster_status', 'wsrep_connected');
+----------------------+--------------+
| Variable_name        | Value        |
+----------------------+--------------+
| wsrep_cluster_size   | 0            |
| wsrep_cluster_status | Disconnected |
| wsrep_connected      | OFF          |
| wsrep_ready          | ON           |
+----------------------+--------------+
4 rows in set (0.00 sec)

root@hostname:/var/lib/mysql# cat /etc/my.cnf
[mysqld]

# character set
character_set_server = utf8
collation_server = utf8_general_ci
datadir=/var/lib/mysql
socket=/var/lib/mysql/mysql.sock
binlog_format=ROW

# Galera Cluster Configuration
wsrep_node_address="ip"
wsrep_node_name="hostname"
wsrep_cluster_name="mysql_cluster"
wsrep_cluster_address="gcomm://"
wsrep_provider_options = "gcache.size = 16G; gcache.recover = yes; gmcast.segment=0; gmcast.time_wait=PT5S; cert.log_conflicts=ON;"
wsrep_retry_autocommit=5
wsrep_slave_threads=64
wsrep_log_conflicts=ON
wsrep_provider=/usr/lib/libgalera_smm.so
wsrep_sst_method=rsync # Galera Synchronization Configuration
# wsrep_certify_nonPK=1 # make sure primary key is present in a DB

# Mysql configurations
default_storage_engine=innodb
innodb_autoinc_lock_mode=2
innodb_flush_log_at_trx_commit=2
innodb_buffer_pool_size=20G  # 80% of total memory
table_open_cache=8192
max_connections=500
innodb_buffer_pool_instances=40
thread_cache_size=128
max_allowed_packet=16M
thread_stack=192K

[mysql_safe]
log-error=/var/log/mysql/error.log
pid-file=/var/run/mysqld/mysqld.pid
#include mysql config
!includedir /etc/mysql/conf.d/

error.log
2020-05-10T14:52:11.510387Z 0 [Warning] TIMESTAMP with implicit DEFAULT value is deprecated. Please use --explicit_defaults_for_timestamp server option (see documentation for more details).
2020-05-10T14:52:11.512408Z 0 [Note] /usr/sbin/mysqld (mysqld 5.7.29-log) starting as process 38762 ...
2020-05-10T14:52:11.516208Z 0 [Note] InnoDB: PUNCH HOLE support available
2020-05-10T14:52:11.516233Z 0 [Note] InnoDB: Mutexes and rw_locks use GCC atomic builtins
2020-05-10T14:52:11.516240Z 0 [Note] InnoDB: Uses event mutexes
2020-05-10T14:52:11.516246Z 0 [Note] InnoDB: GCC builtin __atomic_thread_fence() is used for memory barrier
2020-05-10T14:52:11.516251Z 0 [Note] InnoDB: Compressed tables use zlib 1.2.11
2020-05-10T14:52:11.516259Z 0 [Note] InnoDB: Using Linux native AIO
2020-05-10T14:52:11.516566Z 0 [Note] InnoDB: Number of pools: 1
2020-05-10T14:52:11.516689Z 0 [Note] InnoDB: Using CPU crc32 instructions
2020-05-10T14:52:11.518701Z 0 [Note] InnoDB: Initializing buffer pool, total size = 128M, instances = 1, chunk size = 128M
2020-05-10T14:52:11.528085Z 0 [Note] InnoDB: Completed initialization of buffer pool
2020-05-10T14:52:11.530536Z 0 [Note] InnoDB: If the mysqld execution user is authorized, page cleaner thread priority can be changed. See the man page of setpriority().
2020-05-10T14:52:11.542537Z 0 [Note] InnoDB: Highest supported file format is Barracuda.
2020-05-10T14:52:11.559072Z 0 [Note] InnoDB: Creating shared tablespace for temporary tables
2020-05-10T14:52:11.559138Z 0 [Note] InnoDB: Setting file './ibtmp1' size to 12 MB. Physically writing the file full; Please wait ...
2020-05-10T14:52:11.601120Z 0 [Note] InnoDB: File './ibtmp1' size is now 12 MB.
2020-05-10T14:52:11.602357Z 0 [Note] InnoDB: 96 redo rollback segment(s) found. 96 redo rollback segment(s) are active.
2020-05-10T14:52:11.602377Z 0 [Note] InnoDB: 32 non-redo rollback segment(s) are active.
2020-05-10T14:52:11.602854Z 0 [Note] InnoDB: Waiting for purge to start
2020-05-10T14:52:11.653077Z 0 [Note] InnoDB: 5.7.29 started; log sequence number 3779657135
2020-05-10T14:52:11.653388Z 0 [Note] InnoDB: Loading buffer pool(s) from /var/lib/mysql/ib_buffer_pool
2020-05-10T14:52:11.653670Z 0 [Note] Plugin 'FEDERATED' is disabled.
2020-05-10T14:52:11.656614Z 0 [Note] InnoDB: Buffer pool(s) load completed at 200510  7:52:11
2020-05-10T14:52:11.665175Z 0 [Note] Found ca.pem, server-cert.pem and server-key.pem in data directory. Trying to enable SSL support using them.
2020-05-10T14:52:11.665203Z 0 [Note] Skipping generation of SSL certificates as certificate files are present in data directory.
2020-05-10T14:52:11.666274Z 0 [Warning] CA certificate ca.pem is self signed.
2020-05-10T14:52:11.666344Z 0 [Note] Skipping generation of RSA key pair as key files are present in data directory.
2020-05-10T14:52:11.667341Z 0 [Note] Server hostname (bind-address): '*'; port: 3306
2020-05-10T14:52:11.667427Z 0 [Note] IPv6 is available.
2020-05-10T14:52:11.667444Z 0 [Note]   - '::' resolves to '::';
2020-05-10T14:52:11.667487Z 0 [Note] Server socket created on IP: '::'.
2020-05-10T14:52:11.686718Z 0 [Note] Event Scheduler: Loaded 0 events
2020-05-10T14:52:11.686771Z 0 [Note] WSREP: Initial position: 00000000-0000-0000-b0f1-bf0300000000:62901600
2020-05-10T14:52:11.686784Z 0 [Warning] WSREP: Initial position was provided by configuration or SST, avoiding override
2020-05-10T14:52:11.686792Z 0 [Note] WSREP: wsrep_load(): loading provider library 'none'
2020-05-10T14:52:11.687082Z 0 [Note] /usr/sbin/mysqld: ready for connections.
Version: '5.7.29-log'  socket: '/var/run/mysqld/mysqld.sock'  port: 3306  MySQL Wsrep Server (GPL), wsrep_25.21
2020-05-10T14:52:12.732431Z 2 [Note] Access denied for user 'root'@'localhost' (using password: NO)
2020-05-10T14:57:11.957879Z 4 [Note] WSREP: Stop replication
2020-05-10T14:57:11.957918Z 4 [Note] Giving 1 client threads a chance to die gracefully

A: Make sure it belongs to mysql user and mysql group
chown mysql:mysql /etc/my.cnf
Also, and very important, make sure the library is in /etc/my.cnf
symbolic-links=0
wsrep_provider=/usr/lib64/galera3/libgalera_smm.so

A: The file /etc/my.cnf was missing read permissions. This file requires read permission for mysql user. I have set the permission to 755 and Galera configuration was loaded properly.
chmod 775 /etc/my.cnf

redpajama_set_name: RedPajamaStackExchange


Fire star / Chris D'Lacey.
Flyte / Angie Sage ; illustrations by Mark Zug.
Framed / Frank Cottrell Boyce.
On the wings of heroes / Richard Peck.
Penny from heaven / by Jennifer L. Holm.
The braid / Helen Frost.
The house where nobody lived / by Brad Strickland.
The road to Paris / Nikki Grimes.
Wabi : a hero's tale / Joseph Bruchac.
Wolf! Wolf! / John Rocco.


Defence minister says measure includes ban on dissemination of publications that 'could incite and sow discord'.
A state of emergency declared in Ethiopia after the resignation of the country's prime minister will last for six months, the minister of defence has said, as the government seeks to stem political unrest amid long-standing demands for greater freedoms.
The measure, which was first announced by state media after a cabinet meeting on Friday, includes a ban on protests and the dissemination of publications "that could incite and sow discord", Siraj Fegessa told reporters on Saturday.
"The government has previously made several efforts to curtail violence, but lives have continued to be lost, many have been displaced and economic infrastructure has been damaged," Fegessa said, as quoted by Reuters news agency.
The state of emergency order will be sent to Ethiopia's parliament within 15 days for ratification, the minister also said.
It will give law enforcement officers the power to detain anyone suspected of violating "the constitutional order" and the ability to search houses, cars and individuals, all without a court warrant, state broadcaster FANA reported.
Displaying signs "which could stir up violence" is also prohibited, FANA said.
On Thursday, Hailemariam Desalegn abruptly announced he would step down as prime minister and head of the ruling Ethiopian People's Revolutionary Democratic Front (EPRDF) coalition.
Hailemariam, who has sat at the helm of the Ethiopian government since 2012, said he will stay on as prime minister in a caretaker capacity until the EPRDF and the parliament accept his resignation and appoint his successor.
This is the second state of emergency to be declared in Ethiopia in the last two years.
The country's Oromo and Amhara people - who make up about 61 percent of the population - have staged mass demonstrations since 2015 demanding greater political inclusion and an end to human rights abuses.
The protests have continued this month, with many people expressing frustration over a perceived slow government release of political prisoners.
In January, Ethiopia promised to free all political detainees in an effort to "foster national reconciliation". More than 6,000 prisoners have been released so far, news agencies have reported.
On Saturday, the US embassy in Ethiopia said the state of emergency "undermines recent positive steps toward creating a more inclusive political space, including the release of thousands of prisoners".
"Restrictions on the ability of the Ethiopian people to express themselves peacefully sends a message that they are not being heard," the embassy said in a statement.


The renowned horn-driven funk outfit Tower of Power has been issuing albums and touring the world steadily since the early '70s, in addition to backing up countless other musicians. The group's leader since the beginning has always been tenor saxophonist Emilio Castillo, who was born in Detroit, but opted to pursue his musical dreams in Oakland, CA. It was in Oakland that Castillo put together a group called the Motowns, which as its name suggested, specialized in '60s-era soul. Castillo teamed up with a baritone sax player (and Motowns fan) Stephen "Doc" Kupka, and soon the Motowns had transformed into Tower of Power (one of the first tunes the duo penned together was "You're Still a Young Man," which would eventually go on to be one of the TOP's signature compositions). Tower of Power played regularly in the Bay Area throughout the late '60s, as its lineup often swelled up to ten members, including such other mainstays as Greg Adams on trumpet and vocals and Rocco Prestia on bass. By 1970, the funk outfit had inked a recording contract with Bill Graham's San Francisco Records, resulting in the group's debut the same year, East Bay Grease, which failed to make an impression on the charts as TOP was still trying to find their own sound.
But it all came together quickly for the group, as 1972's Bump City would touch off a string of classic hit releases, including 1973's self-titled release (which included another one of the group's most enduring tunes, "What Is Hip?"), 1974's Back to Oakland, plus 1975's Urban Renewal and In the Slot. While Tower of Power remained a must-see live act, the quality of their subsequent records became erratic, resulting in some admirable releases (Ain't Nothin' Stoppin' Us Now, Live and in Living Color) and several uninspired albums that are best skipped over (We Came to Play, Back on the Streets).
Despite the dip in the quality of their albums, Tower of Power remained a much in-demand backing group for some of pop/rock's biggest names, including Elton John, Santana, Bonnie Raitt, Huey Lewis, Little Feat, David Sanborn, Michelle Shocked, Paula Abdul, Aaron Neville, Aerosmith, Michael Bolton, Billy Preston, PiL, Rod Stewart, Toto, Merl Saunders, and others. Tower of Power remains very active to this day, keeping up a brisk touring schedule and issuing such new albums as 1999's Soul Vaccination: Live; while several compilations were issued around the same time: Rhino's double disc What Is Hip?: The Tower of Power Anthology (1999) and Very Best of Tower of Power: The Warner Years (2001), plus Epic/Legacy's Soul With a Capital "S": The Best of Tower of Power (2001).


The 2nd edition of The Care of Prints and Drawings provides practical, straightforward advice to those responsible for the preservation of works on paper, ranging from curators, facility managers, conservators, registrars, collection care specialists, private collectors, artists, or students of museum studies, visual arts, art history, or conservation. A greater emphasis is placed on preventive conservation, a trend among collecting institutions, which reflects the growing recognition that scarce resources are best expended on preventing deterioration, rather than on less effective measures of reversing it. Expanded and richly illustrated chapters include: ·Supports for Prints and Drawings discusses the properties of parchment and paper and introduces the general preservation needs and conservation problems of all works on paper, regardless of their media. ·Conservation Problems Related to the Paper Support of Prints and Drawings presents a guide to recognizing the symptoms and diagnosing the causes of damage specific to paper. ·Conservation Problems Related to the Materials and Techniques of Prints describes the conservation problems that affect certain printmaking materials and arise from specific processes. ·Conservation Problems Related to the Materials and Techniques of Drawings focuses on the various materials used to create marks on paper. ·Item-Level Collection Protection: Envelopes, Sleeves, Folders, Enclosures, Mats, Boxes, Frames, and Furniture, discusses measures taken for prints and drawings so that they can better withstand the rigors of handling, examination, exhibition, travel, and adverse environmental conditions. ·Preventive Conservation for Prints and Drawings describes how the integration of a comprehensive Collections Care Program into a Collections Management Policy can reduce the need for item-level conservation treatments. ·Basic Paper Conservation Procedures provides instructions on how to stabilize damaged works. ·How to Make Starch Paste and Methyl Cellulose Adhesive and Suppliers of Paper Conservation Materials and Equipment are appended as well as a Glossary.


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Up and Down We Go in Support of Cancer Research
On September 3rd, the Always Be Content team took to the seven hills of Edinburgh along with the Edinburgh Business Beats Cancer Board. We walked 21 kilometres in solidarity with those fighting the uphill struggle against cancer – and smashed through our fundraising goals.
Our Lou Kiddier, Co-Founder and Head of Content Production at Always Be Content, is on the board of Edinburgh Business Beats Cancer (EBBC). EBBC is a collaboration of business leaders working together to raise funds for Cancer Research UK.
Following Lou's leadership, the entire Always Be Content team have been volunteering as creative partners for EBBC.
As we pondered potential fundraising ideas for 2021, we thought about all the highs and lows we've experienced over the past few years.
This summer in particular, we saw a global pandemic keep the world in its grips against the backdrop of record heatwaves brought on by climate change. Making a bad pandemic worse, funding for cancer and other medical research had taken a hit too.
Yet, at the same time, we received life-saving vaccines, enjoyed easing lockdown restrictions and revelled in the thrills of the Summer Olympics.
No doubt, it's been a strange mix of ups and downs.
It was precisely this thought journey that brought us, and the EBBC Board, to the idea of our next fundraiser.
After all, what better way to illustrate the highs and lows of battling cancer during these strange times than to climb up and down the seven hills of Edinburgh?
We crunched the numbers and found that climbing 7 hills would mean we'd have to walk 21 kilometres across 600 metres of elevation. Ambitious and daunting as it may be (unless you're a Munro Bagger), we knew this would be possible to do in a single day.
This is how the Take On 21 challenge came to be.
The only thing left was to roll up our sleeves and get to work:
We crafted and designed a series of branded emails Board members could send out to colleagues, friends and family to invite and inform them about the event.
We created static and animated social posts for both Always Be Content and EBBC to keep everyone up to date on our fundraising progress.
We published EBBC story filters on Facebook and Instagram, so participants could share their experiences on the day of the hike.
We designed branded snoods for participants, plaques to use for photo ops at the top of each hill, and digital medals to send out as keepsakes.
We even designed and published a slick and interactive DigiMag containing the route and some helpful hiking tips to help participants prepare for our all-day hike.
It was an all-out effort for a great cause – and the results show it.
We hit our fundraising target even before we set a foot on a single hill. By the end of the day, we achieved 130% of our original target.
In total, we raised over £18,000 for cancer research!
We know that 'cancer research' and 'fundraising' seem like abstract concepts – and people tend not to engage with abstract things.
More than that, it is difficult to face cancer. It is difficult to learn that someone in the UK is diagnosed with cancer every two minutes – or that tens of thousands of people put off their cancer treatment because of the pandemic.
So, to make our success and our message of hope truly resonate, we made sure to highlight that the funds we raised would go to scientists at the Cancer Research UK Edinburgh Centre who work on life-saving developments in cancer research.
Specifically, our funds will help Professor David Cameron run clinical trials on breast cancer treatments. They help Professor Malcolm Dunlop study bowel cancer, and Dr Steve Pollard and Dr Sara Erridge study new treatments for brain tumour.
Indeed, it's fair to say that all the trekking up hills in solidarity with those fighting the uphill struggle against cancer was real, tangible work for a great cause.
When you think about it, it's remarkable what a bit of creative group effort can accomplish to make the world a better place.
Although our Take On 21 challenge has ended, our fundraising efforts continue. If you'd like to support Cancer Research UK, our fundraising site is still accepting donations.
In addition, the EBBC Board are hoping to host a fundraising event in March 2022.
Follow us on Twitter, LinkedIn and Instagram to make sure you don't miss our big announcement.
UCL: Olympic Inspiration for London's Global University
How to be content
Content Marketing Simplified
Do Androids Dream of Electric Ads?
A New Wave of Collaboration: The Key to Creative Success
SEO for the CEO


Made from a blend of the best of Italian olive varieties, including Leccino, Frantoio, Ogliarola and Coratina, our extra virgin olive oil is enhanced with 2% Ginger aroma, creating a lingering fresh and slightly tangy taste. To appreciate its finesse, we recommend enjoying this Italian kitchen staple raw – drizzled over salads, fish or meat. Looking for food gifts or food gifts ideas? This extra virgin olive oil with lemon is perfect for the foodie in your life that deserves something special. Suitable for vegetarians and vegans!


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John W Harrison
Lic. Assoc. RE Broker
jharrison@corenyc.com
Recently Rented
Additional Sales
Choose section: About John Active Listings In Contract Recently Sold Recently Rented Additional Sales Press Blog Listings Testimonials Films
About John:
John Harrison hails from a family of real estate professionals who have been involved in real estate development, investment and sales in his native Texas for many years. He loves getting to know his clients, doing his research and lining up the best possible choices for them. John works extensively downtown and in Brooklyn. He was also a member of the sales team for One Museum Mile, one of CORE's new development projects located on West 110th Street. Prior to working at CORE, John came from IBM, where he worked for a number of years as an IT Architect. Prior to that he established the Eastern European branch of a U.S. architectural/civil engineering design firm. In that role he was charged with setting up and staffing offices in Bulgaria as well as conducting seminars in Bulgaria, Hungary and Finland. Before that he lived in Italy, where he worked on international ad campaigns...
John Harrison hails from a family of real estate professionals who have been involved in real estate development, investment and sales in his native Texas for many years. He loves getting to know his clients, doing his research and lining up the best possible choices for them. John works extensively downtown and in Brooklyn. He was also a member of the sales team for One Museum Mile, one of CORE's new development projects located on West 110th Street. Prior to working at CORE, John came from IBM, where he worked for a number of years as an IT Architect. Prior to that he established the Eastern European branch of a U.S. architectural/civil engineering design firm. In that role he was charged with setting up and staffing offices in Bulgaria as well as conducting seminars in Bulgaria, Hungary and Finland. Before that he lived in Italy, where he worked on international ad campaigns for the fashion industry. The common thread in John's multifaceted career is his exceptional ability to problem-solve. He has extensive experience in generating creative solutions - whether technical, procedural or financial - for various types of projects. John views this skill as key to succeeding in real estate and he dedicates himself passionately to the investigative work involved in finding just the right home for his clients. His passion is in helping people tell their stories through the Real Estate buying and selling process. John studied computer systems management at St. Edwards University, in Austin, Texas. In addition to his passion for travel, he is involved in film, television, and theater and co-founded two New York City theater companies. John is also fluent in Italian and Spanish and speaks some French and Bulgarian. He has lived in the Financial District/ Tribeca area, The Upper West Side, Brooklyn Heights and Downtown Brooklyn.
35 Monroe Street
725 Riverside Drive
30 East 9th Street
65 Morton Street
51 Fifth Avenue
71 Horatio Street
117 East 102nd Street
68 Bradhurst Avenue
182 Conselyea
Represented Buyer
30 Park Place
1117 Jefferson
289 Cumberland Street
50 Laight Street
41 West 82nd St
139-141 West 126th Street
60 Gramercy Park North
423 Hicks Street
160 East 27thh Street
42-22 Ketcham Street
Represented Buyer - In Contract
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Model Number: PFT104
Age Range: 13 years +
Muscle Group: Full Body
Product Type: Fitness Course
Unit Size: 27' x 27'
Feel the Burn is an exercise set which includes four distinct pieces of exercise equipment which each focus on different areas of the body. The set includes a Royal Triple Station Rower which simulates the experience of paddling an actual canoe. The three rowers can even try to row the oars in unison like competitive rowers do. There is a Royal Triple Station Leg Press, where three users can stretch and strengthen their legs. The Royal Triple Station Chest Press provides great pectoral exercise with its overhead bars. Finally the Royal Triple Station Sit Up Bench will spot users as they lay on the bench to do sit ups. The 'Royal' models each include detailed instructions complete with pictures next to each station, making it easy for beginners and experts alike to use these structures with ease. The triple stations allow each of the four stations to accommodate up to three users at once. This is perfect for small groups who want to get fit together, or for crowded areas where multiple people will want to use each station at the same time. These structures can be arranged and installed in any arrangement to create your ideal workout area.


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Giacomo Manzu (1908-1991), Italian
HEAD OF POPE JOHN XXIII, NO. 3 (VARIANT), 1963
Unique cast bronze with brown patina; stamped with signature and the foundry mark "Manzu NFMM" in an impressed oval cartouche at the back of the head. Raised on an ebonzied base. Accompanied by a Photo-Certificate and document of Authenticity signed in pen and ink by the artist Manzu and dated July 11, 1978.
Bronze/Mounted height 11.5" — 29.2 cm.; 18.5" — 47 cm.
Estimate $15,000-$20,000
Realised: $14,400
About artist/note:
According to a letter from Jose M. Tasende, Galeria Tasende, Acapulco, Guerrero, dated July 27, 1978, this lot
is one of 5 variants which Manzu executed when Pope John was alive. It states further that this unique bronze was one of three heads of Pope John acquired by the Galeria Tasende from an exhibition held at the Phoenix Museum.
International Eucharistic Congress catalogue, "Exhibition of Liturgical Arts", 1976, p.67;
M. de Micheli, "Manzu", Fratelli Fabbri Editori, p. 60, inscribed to the Galerie Tasende Photo Certificate, Acapulco accompanying the lot
The artist's atelier, Ardea, Rome, accompanied by Giacomo Manzu's Photo Certificate, signed by him and dated July 11, 1978;
Sold to Jose M. Tasende, Tasende Arte Contemporaneo, Acapulco, Gro., Mexico;
Tasende Gallery, La Jola, California;
From whom purchased by a gentleman of Toronto, for a friend, Toronto, accompanied by the original Tasende receipt, No. 093, dated August 26, 1978;
Private Collection, Toronto, accompanied by the Galeria Tasende, Acapulco, Gro., original receipt, No. 1330, dated September 20, 1978;
Their Estate, Toronto
41st International Eucharistic Congress, Philadelphia Civic Center, "Exhibition of Liturgical Arts", July 29 - August 8, 1976


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Live Auction 7435 British Works on Paper
No VAT will be charged on the hammer price, but VA… Read more THE PROPERTY OF CAROLINE JOHN
Augustus John, O.M., R.A. (1878-1961)
Ida with baby
signed 'John' (centre right)
9 7/8 x 14 1/8 in. (25.2 x 36 cm.)
Executed circa 1902-1905
Purchased from the artist by Hugo Pitman Esq.
Mrs Hugo (Reine) Pitman.
Sir Caspar John;
Lady John and by descent in the family to the present owner.
The Connoisseur, October 1970, p. 89.
M. Holroyd, Augustus John, I, 'The Years of Innocence', London, 1974, p. 208.
London, National Gallery, Exhibition of 20th Century British Paintings, 1940, no. 30, lent by Hugo Pitman.
Derby, Museum and Art Gallery, after 1942, catalogue untraced.
Leeds, Temple Newsam, 1946.
London, Royal Academy, 1954, no. 29, illustrated.
Sheffield, Graves Art Gallery, 1956, no. 52, lent by Hugo Pitman.
London, Upper Grosvenor Gallery, 1965, no. 15.
Hull, University of Hull and Cardiff, National Museum of Wales, 1970, no. 38, illustrated.
London, Olympia, Augustus John, 1999, no. 90.
London, Hazlitt Holland-Hibbert, Augustus John: Masterworks from Private Collections, 2004, p. 10, illustrated.
No VAT will be charged on the hammer price, but VAT at 15% will be added to the buyer's premium which is invoiced on a VAT inclusive basis.
Ida Nettleship and Augustus John were fellow students at the Slade School of Fine Art in the 1890s. They married in 1901 and had five sons in as many years before Ida died in Paris, one hundred years ago, in 1907. She was only thirty years old and, according to contemporary reports, beautiful, original and talented ; her letters held in the National Library of Wales reveal her warmth and sense of humour and are full of comic descriptions of her young sons.
In the present work John has perfectly captured the beauty of his young wife as she cradles her newborn son. The baby was never positively identified, but within the family it was always felt that the freshness of her expression and tenderness of the scene suggested that the baby was most probably her first child, David, born in 1902 in Liverpool who became an oboist in the Sadler's Wells orchestra; or possibly her second son, Caspar, born in 1903 in Fitzrovia and destined to become a pioneer of the Fleet Air Arm and First Sea Lord in 1960. Many years later, after the drawing came into Caspar's possession, he would often look at it and reflect that he had never known his mother; he was barely four years old when she died and it may have been himself whom she was holding in her arms.
John has used the whole sheet of paper to describe the details of the scene; the cup at the bedside, Ida's wedding ring, the bedhead and the bedclothes gathered around - all of which add to the intimacy and warmth so beautifully expressed in this drawing.
We are grateful to Rebecca John for her help in preparing this catalogue entry.
More from British Works on Paper


Former works minister Dr Suruj Rambachan is lashing out at the government for failing to make funds available to pay pilots.
In a statement issued, Dr Rambachan says the refusal of pilots attached to the strategic services agency to report for duty citing the non-payment of salaries is a cause for concern.
The Tabaquite mp says the government must be held accountable.
CNC3 news understands the pilots, who are being seconded from the national helicopter services, fly the helicopters in border patrols, surveillance, natural disasters and search and rescue efforts. Sources say the division has been crippled as a result of the ongoing action by the pilots.


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\section{Introduction}
There exist variety of theoretical frameworks/specific models \cite{rev} which try to account for the large atmospheric mixing angle observed more than a decade ago.  One class of theories attribute the maximal  atmospheric mixing to the presence of some underlying flavour symmetry. This would be a preferred alternative  if the deviation of the atmospheric mixing angle from maximality is constrained to be very small.  The simplest of such flavour symmetries is the $\mu$-$\tau$  symmetry \cite{mt,hs,23,23as} which exchanges the mu and tau fields. This symmetry comes with an additional prediction that one of the three leptonic mixing angles namely, $\theta_{13}^{l}$ \cite{fnt} must be zero.

 $\mu$-$\tau$  symmetry is predictive and simple but it appears to have two shortcomings.  Successful predictions follow only if it is an effective symmetry of the neutrino mass matrix in specific basis corresponding to a diagonal charged lepton mass matrix. The underlying flavour symmetry in general may not pick up this basis. Secondly, $\mu$-$\tau$  symmetry  has been  proposed with a view of explaining the mixing angles in the leptonic sector alone. It would be  more desirable to have a symmetry providing  overall understanding of complete fermionic mass spectrum.  This can be done  using the grand unified theory as the underlying framework.
Various alternatives within such theories to simultaneously obtain small  mixing in the quark sector and large mixing among leptons have already been proposed \cite{rev,btau,asal}.

The renormalizable theories based on the $SO(10)$ group are quite powerful in constraining the fermionic mass structures. The standard fermions are assigned to the $16$ dimensional representation of the $SO(10)$ group and they can obtain masses through symmetric couplings with $10$ and $\overline{126}$ and antisymmetric couplings with the 120 dimensional representation of the Higgs fields. The minimal $SO(10)$ model containing $10,126, \overline{126}$ and $210$ representations has been extensively studied \cite{btau,early,detailed1,detailed2,detailed3,bertolini,vissani2,splitsusy}.
In this model, the  largeness of the atmospheric mixing angle gets related to the $b-\tau$ Yukawa unification if neutrinos obtain their masses through the type II \cite{typeII} seesaw mechanism \cite{seesaw}. This interesting observation in \cite{btau} led to many detailed investigations \cite{detailed3,vissani2,bertolini,splitsusy} which revealed the inadequacy of this simple picture. The supersymmetric version of the minimal model with type-II seesaw mechanism is constrained by two conflicting requirements. The overall neutrino mass scale is correctly reproduced in the model if the seesaw scale is about two to three orders of magnitude below the GUT scale. But the spectrum of the model in this case  does not allow gauge coupling unification.  Moreover, the type-II contribution to neutrino masses  does not always dominate over  the type-I contribution in the minimal model as would be required for the mechanism in \cite{btau} to go through. The conflict with the proton decay appears  in the minimal model even if the neutrinos obtain their masses through the type-I seesaw \cite{detailed3,vissani2,bertolini}. These problems have led to studies of the non-minimal models containing an additional 120-plet of Higgs \cite{charan120,grimus1,grimus2}. Theoretical understanding of the largeness of the atmospheric mixing angle gets lost in all these approaches although one can choose the parameters to obtain the observed value.

It would be welcome to integrate $\mu$-$\tau$  symmetry into the grand unified framework. This has been done for the $SU(5)$ model in \cite{su5moh}. We do so here in the more predictive $SO(10)$ framework.  There are several motivations for unifying  $SO(10)$ and $\mu$-$\tau$  symmetry.  Rather than remaining a leptonic symmetry, such symmetry would provide constraining picture of both quark and lepton spectrum. Role of this symmetry in the description of the quark mixing is already discussed in \cite{23,23as}.  In addition, it can provide additional constraints and reduces the number of the Yukawa couplings which describe fermion masses. Some examples of models unifying $SO(10)$ with other discrete symmetries can be found in \cite{discrete}.

We investigate the consequences of imposing a generalized $\mu$-$\tau$  symmetry exchanging the second and the third generation fields on a renormalizable $SO(10)$ model. We deviate from the minimal model and add a 120 plet. This plays a crucial role in generating CP violation and the $\mu$-$\tau$  symmetry breaking.  Fermion masses with 120 plet have been discussed  in several earlier works \cite{charan120, grimus1,grimus2,charan2,1202,1203,mohparity,yangwang}. Following \cite{mohparity,grimus1,grimus2,yangwang} we impose also the  parity symmetry which leads to Hermitian mass matrices for all fermions thereby reducing  the number of parameters compared  to more general models. All the fermion masses and mixing are described
in our approach in terms of  14 (15)  real parameters in case of type-II (type-I) seesaw mechanism.  They provide an excellent description of fermion masses and mixing in contrast to a general model employing $10+120+\overline{126}$ Higgs fields which needs \cite{mohparity}  31  parameters in the fermionic sector. Moreover, the (near) maximality of the atmospheric mixing and smallness of the angle $\theta_{13}^{l}$ get related here to the approximately broken $\mu$-$\tau$  symmetry.

We define our model implementing $\mu$-$\tau$  symmetry and discuss its consequences in the next section. Section(III) presents numerical fits both in case of the type-II and type-I seesaw mechanism and discusses various predictions. Last section contains a summary.
\section{$\mu$-$\tau$  symmetric $SO(10)$}
 If  $\mu$-$\tau$  symmetry is to be integrated with grand unification then a more general
symmetry which exchanges the second and  third generations of fermions should be imposed.
Consequences of this generalization were  first considered in \cite{23}. It was subsequently noted \cite{23as} that this generalization automatically leads to understanding of why Cabibbo angle is larger than other two angles and a mild breaking of this symmetry was shown to lead to a correct description of the quark mixing angles and masses.  Most of these works did not use the grand unified framework.
Here, we consider a model based on the $SO(10)\otimes Z_2^{\mu-\tau}\otimes Z_2^P$. The first $Z_2$ corresponds to the generalized $\mu$-$\tau$  symmetry. The second $Z_2$ symmetry called \cite{mohparity}  ``parity''  interchanges two  components of the $16$ field transforming as $(4,2,1)$ and $(\overline{4},1,2)$ under the Pati-Salam group decomposition of $SO(10)$.

Our basic formalism is similar to \cite{mohparity,grimus1,grimus2,yangwang}. 16 dimensional fermions obtain their masses from coupling to three Higgs multiplets transforming as $10,\overline{126}$ and $120$ representations under $SO(10)$. The $SO(10)$ breaking can be achieved with a $210$-plet.  An additional $126$-plet of Higgs is needed in the supersymmetric context to preserve the supersymmetry at the GUT breaking scale. These Higgs  multiplets contain altogether six doublets with quantum numbers of the minimal supersymmetric standard model (MSSM) field $H_d$ and six with that of  $H_u$.
It is assumed that only two appropriate linear combinations of these  Higgs doublets remain light and play the role of the $H_d$ and $H_u$ fields.
This is achieved by the fine tuning conditions \cite{vissani2}.  After this fine tuning, the resulting fermion masses can be written as
\begin{eqnarray} \label{mass term}
-\mathcal{L}_{mass}= \overline{f}_{L} M_{f} f_{R} + \overline{\nu}_{L} M_{D} \nu_{R} + \frac{1}{2} \overline{\nu}_{L} M_{L} \nu_{L}^c + \frac{1}{2} \overline{\nu^{c}_{R}} M_{R} \nu_{R} + h.c. ~,
\end{eqnarray}
where $f=u,d,l$ denote the up and down quarks and the charged leptons respectively.  The mass matrices appearing in the above equation can be suitably written  (see \cite{grimus1,grimus2} for details) as
\begin{eqnarray} \label{matrices}
M_d&=& H+F+i~ G~,\nonumber \\
M_u&=&r H+s F+i~ t~ G~, \nonumber\\
M_l&=& H-3 F+i ~p~ G~,\nonumber\\
M_D&=&r H-3s F+i ~q~ G~,\nonumber\\
M_L&=& r_L F~,\nonumber\\
M_R&=& r_R^{-1} F.\end{eqnarray}
Here $M_D$ denotes the neutrino Dirac mass matrix. $M_L(M_R)$ is the Majorana mass matrix for the left(right) handed neutrinos which receives contribution only from the vacuum expectation value (vev) of the $\overline{126}$ field. Gauge coupling unification in the minimal model requires that the vev contributing to $M_R$  be close to the GUT scale. The dimensionless parameters $r,s,t,p,q,r_L$ and $r_R$ are determined by the CG coefficients, ratios of vevs and  mixing among the Higgs fields \cite{grimus1}.

The matrices $H,F,G$ originate from the fermion couplings to the $10,\overline{126}$ and $120$ fields respectively. ($G$) $H,F$  are complex (anti) symmetric matrices in general. However, generalized parity makes them real. In addition, if
all vevs and (hence $r,s,t,p,q,r_L,r_R$) are real then all the Dirac masses in eq.(\ref{matrices}) are Hermitian and $M_L,M_R$ are real.

We assume that the Higgs field in the $10$ and $\overline{126}$ representations are invariant under the generalized $\mu$-$\tau$  symmetry while the $120$ dimensional representation changes sign. This assumption allows spontaneous breaking of the $\mu$-$\tau$  symmetry. The resulting structures for $H,F,G$ are given by
\begin{equation} \label{hfg} \begin{array}{ccc}
H=\left( \begin{array}{ccc} h_{11}&h_{12}&h_{12}\\h_{12}&h_{22}&h_{23}\\
h_{12}&h_{23}&h_{22}\\ \end{array} \right);
&
F=\left( \begin{array}{ccc} f_{11}&f_{12}&f_{12}\\f_{12}&f_{22}&f_{23}\\f_{12}&f_{23}&f_{22}\\ \end{array} \right);
&
G=\left( \begin{array}{ccc}0&g_{12}&-g_{12}\\-g_{12}&0&g_{23}\\g_{12}&-g_{23}&0\\ \end{array} \right) \end{array} \end{equation}
All the coefficients in these matrices  are real. They satisfy
\begin{equation}
\label{yukawasymmetry}
S^T(H,F,G)S=(H,F,-G)~, \end{equation}
where
\begin{equation} \label{s} S=\left( \begin{array}{ccc} 1&0&0\\
                                                0&0&1\\
                                                0&1&0 \\ \end{array} \right) \end{equation}
exchanges the second and the third generations.
The effective neutrino mass matrix ${\cal M}_\nu$ for the three light neutrinos  follows from eq.(\ref{mass term}) and eq.(\ref{matrices}):
\begin{equation} \label{mnu}
{\cal M}_\nu=r_L F-r_R M_D F^{-1} M_D^T \equiv {\cal M}_\nu^{II}+{\cal M}_{\nu}^{I}~. \end{equation}
Here $r_{L,R}$ are inversely related to the vev of the RH triplet component in $\overline{126}$.  This vev may be identified with the GUT scale in the absence of any intermediate scale. In addition, they depend upon the details of the superpotential. Specific expressions for $r_{L,R}$ in the minimal case can be found in  \cite{vissani2, bertolini}. The first term corresponds to the type-II seesaw while the second is the conventional type-I seesaw. In general, both contributions are present but one may dominate over the other. We shall be considering two separate cases corresponding to the type-II and type-I dominance respectively.

The relations $\theta_{23}^{l}=\frac{\pi}{4}$ and $\theta_{13}^{l}=0$ are major predictions and motivation for imposing the $\mu$-$\tau$  symmetry. These can arise if the effective neutrino mass matrix ${\cal M}_{\nu f}$ in flavour basis possesses a $\mu$-$\tau$  symmetry. Let us see how this can come about in our approach. It is easy to see that the fermionic mass matrices in our model satisfy:
\begin{equation} \label{sq}
S^{-1} M_fS=M_f^* ~, \end{equation}
\begin{equation} \label{st2} S^{-1}{\cal M}_\nu^{II} S={\cal M}_\nu^{II} ~,\end{equation}
\begin{equation} \label{st1}S^{-1}{\cal M}_\nu^I S={\cal M}_\nu^{I*}~.\end{equation}
$f=u,d,l,D$ label the (Dirac) fermionic mass matrices. The ${\cal M}_\nu^{I,II}$ correspond to the type-I and II contributions to the light neutrino mass matrix, eq.(\ref{mnu}).
Let us note that
\begin{itemize}
\item Eq.(\ref{st2}) implies an exact $\mu$-$\tau$  symmetry for ${\cal M}_\nu^{II}$.
\item  Eqs.(\ref{sq},\ref{st1}) correspond to an invariance under the generalized CP transformation defined \cite{hs,maximal} as
\begin{equation} f_{\alpha}\rightarrow i S_{\alpha \beta} \gamma^{0} C \overline{f_{\beta}}^{T} \end{equation}
\item If eq.(\ref{st2}) represents the neutrino masses in flavour basis then
one obtains the predictions $\theta_{23}^{l}=\frac{\pi}{4}$ and $\theta_{13}^{l}=0$.
\item If eq.(\ref{st1}) holds in the flavour basis then only the $\theta_{23}^{l}$ is maximal with definite correlations of $\theta_{13}^{l}$ with the CP violating phase $\delta_{PMNS}$ \cite{maximal}.
\item  $M_l$ is not diagonal here and hence these predictions do not follow immediately. It is still possible to recover these predictions even with a non-diagonal $M_l$.
\end{itemize}
Define
\begin{equation} \label{ul}  U_l^{\dagger} M_l U_l=D_l  ~,\end{equation}
where $D_l$ is the  diagonal mass matrix for the charged leptons. By factoring out a diagonal phase matrix
$P_{l}$, the $U_l$ can be written as:
\begin{equation} \label{ul1} U_l\equiv \tilde{U}_l P_l ~\end{equation}
The neutrino mass matrix in the flavour basis is then given by
\begin{equation} \label{mnuf} {\cal M}_{\nu f}=P_l^\dagger\tilde{U}_l^\dagger{\cal M}_\nu \tilde{U}_l^\ast P_l^\ast\equiv P_l^\dagger{\cal \tilde{M}}_{\nu f} P_l^\ast ~ \end{equation}
The predictions of the $\mu$-$\tau$  symmetry are recovered if ${\cal \tilde{M}}_{\nu f} $ is $\mu$-$\tau$  invariant. This does not require a diagonal $M_l$. A general  $\mu$-$\tau$  symmetric $\tilde{U}_l$ satisfying $S^{-1}\tilde{U_l}S=\tilde{U}_l$ will do the job in case of the type-II dominance.
In case of the type-I dominance, one
obtains
$$S^{-1}{\cal \tilde{M}}_{\nu f}S={\cal \tilde{M}}_{\nu f}^*$$
provided $\tilde{U}_l$ also satisfies the same equation. This makes it possible to recover the predictions of the $\mu$-$\tau$  symmetry for a non-diagonal $M_l$ and obtain reasonably good fits to other fermion masses and mixing.

It is known \cite{hs,maximal}  that  with appropriate choice of  $P_{l}$, $\tilde{U}_l$ can be cast into the following form  if $M_l$ satisfies eq.(\ref{sq}):
\begin{equation} \label{utildel} \tilde{U}_l=\left( \begin{array}{ccc}
u_{1l}&u_{2l}&u_{3l}\\
w_{1l}&w_{2l}&w_{3l}\\
w_{1l}^*&w_{2l}^*&w_{3l}^* \\ \end{array} \right) ~,\end{equation}
with real $u_{il}$.
A unitary matrix with this form  can be  parametrized in terms of two angles and a phase.
\begin{equation} \label{utildelpara} \tilde{U}_l=P_\eta\left( \begin{array}{ccc}
c_1&s_1c_2&s_1 s_2\\
\frac{s_1}{\sqrt{2}} &-\frac{1}{\sqrt{2}}(c_1 c_2-i\epsilon s_2)&-\frac{1}{\sqrt{2}}(c_1 s_2+i \epsilon c_2)\\
\frac{s_1}{\sqrt{2}} &-\frac{1}{\sqrt{2}}(c_1 c_2+i\epsilon s_2)&-\frac{1}{\sqrt{2}}(c_1 s_2-i \epsilon c_2)\\ \end{array} \right) ~,\end{equation}
where $\epsilon=\pm 1,s_{1,2}\equiv \sin\theta_{1,2}~,c_{1,2}=\cos\theta_{1,2}$. $c_2$ and $s_2$ can be chosen positive with appropriate choice of $P_l$ in eq.(\ref{ul1}).
$$ P_\eta={\rm diag.} (1,e^{-i\eta},e^{i\eta})$$ is a diagonal phase matrix. The above $\tilde{U_l}$ becomes $\mu$-$\tau$  symmetric if $s_2=c_2$ and $\eta=0$. This defines a one parameter family of the leptonic mass matrices which lead to the prediction
of the $\mu$-$\tau$  symmetry in case of the type-II dominance. We will use this form subsequently in our numerical analysis.

There is an important but unwelcome feature associated with the generalized CP invariance of the mass matrices in eq.(\ref{sq}).
The CKM matrix in this case turns out to be real. To see this explicitly, we note that just as in case of $U_l$, the matrices $U_{u,d}$ diagonalizing the up and down quark masses can be written as $\tilde{U}_{u,d}P_{u,d}$. $\tilde{U}_{u,d}$ have the same form as the RHS of eq.(\ref{utildel}) with the replacement of
$u_{il}$ with $u_{iu,id}$ and $w_{il}$ with $w_{iu,id}$. The phase matrices $P_{u,d}$ can be absorbed in redefining the quark fields and the
remaining part of the CKM matrix  is given by
$$V_{ij}\equiv (\tilde{U}_{u}^\dagger \tilde{U}_{d})_{ij}=u_{iu}u_{jd}+2 Re(w_{iu}w_{jd}^*)$$
which is real since $u_{iu,id}$ are real.

One can generate CP violation in the model by breaking the generalized CP invariance of the mass matrices. This can be done in two ways.  Either one allows complex vev for some of the Higgs doublets as in \cite{grimus1}  or one retains the real vev but allows breaking of the $\mu$-$\tau$  symmetry in the Yukawa couplings. In the following, we will discuss the second alternative.

\section{Fitting fermion spectrum with and without the $\mu$-$\tau$  symmetry}

We now discuss the numerical implications of our model in detail. We assume that either the type-I or the type-II term in the neutrino mass matrix dominates  and carry out analysis separately in each of these two cases. Our input parameters are
$r,s,t,p,q$, eq.(\ref{matrices}) , the real elements of the matrices $G,H,F$, eq.(\ref{hfg})
and the overall scales $r_{R,L}$, eq.(\ref{mnu}). Parameter $q$ is absent in the type-II case. An overall rotation $R$ on $G,H,F$: $(G,H,F)\rightarrow R^T(G,H,F)R$  amounts to a choice of initial basis for the 16-plet of fermions. We can use this freedom to set say, $h_{12}=0$. This is done with a specific choice $R=R_{23}^T(\frac{\pi}{4})R_{12}(\theta_{12}^h)R_{23}(\frac{\pi}{4})$. Here $R_{ij}(\theta)$ denotes rotation in the $ij^{th}$ plane by an angle $\theta$ and
$$\tan2 \theta_{12}^h=\frac{2 \sqrt{2} h_{12}}{h_{11}-h_{22}-h_{23}}~.$$ This rotation amounts to redefinition of elements
of $F$ and $G$ which still retain the same form as in eq.(\ref{hfg}).  We continue to use the same notation  for the parameters of the redefined $F,G$. With the choice $h_{12}=0$, we have 14 (15) input parameters in case of type-II (type-I) seesaw dominance. These input parameters together generate 12 fermion masses and six mixing angles. As already remarked, the exact $\mu$-$\tau$  symmetric $H,F,G$ are not able to generate CP violation. We introduce this CP violation by adding a small $\mu$-$\tau$  breaking difference between the 22 and 33 elements in $H$. This one additional parameter now leads to four CP violating phases, one in  the CKM matrix and three in the PMNS matrix.

Our choice of the values of the physical observables  is based on numbers given in \cite{bertolini,grimus2}. We reproduce them here in Table~({\ref{tab:input})  for convenience.
\begin{small}
\begin{table} [h]
\begin{math}
\begin{array}{|c|c||c|c|}
\hline
 m_d &  1.03\pm 0.41&\Delta m^2_{sol}&(7.9\pm 0.3)\times10^{-5} \\
m_s&19.6\pm 5.2&\Delta m^2_{atm}&\left(2.2_{-0.27}^{+0.37}\right)\times 10^{-3}\\
m_b & 1063.6_{-86.5}^{+141.4} & \sin  \theta _{12}^q & 0.2243\pm 0.0016 \\
 m_u & 0.45\pm 0.15 & \sin  \theta _{23}^q & 0.0351\pm 0.0013 \\
 m_c&210.3273_{-21.2264}^{+19.0036} & \sin  \theta _{13}^q & 0.0032\pm 0.0005 \\
 m_t&82433.3_{-14768.6}^{+30267.6}& \sin ^2 \theta _{12}^l & 0.31\pm 0.025 \\
 m_e &0.3585\pm 0.0003 &\sin ^2 \theta _{23}^l&0.5\pm 0.065 \\
 m_{\mu }&75.6715_{-0.0501}^{+0.0578} & \sin ^2\theta _{13}^l & < 0.0155 \\
m_{\tau }&1292.2_{-1.2}^{+1.3}&\delta_{CKM}&60^{\circ }\pm 14^{\circ }\\
\hline
\end{array}
\end{math}
\vspace{0.5cm}
\caption{Input values for quark and leptonic masses and mixing angles at $M_{GUT}=2\times 10^{16}$ GeV and $\tan\beta=10$ which we use in our numerical analysis.}
\label{tab:input}
\end{table}
\end{small}

The given numbers for quark masses and mixing correspond to the respective values at the GUT scale obtained from low energy values using MSSM and $\tan \beta=10$. The neutrino masses and mixing that we use are  the low scale values but the effects of
the evolution to $M_{GUT}$ on the ratio of the solar to atmospheric mass scale and on the mixing angles are known to be small for the normal hierarchical spectrum that we obtain here .  While fitting, we omit the parameters $r_R,r_L$ which define the overall scales of neutrino masses in case of the type-I and type-II seesaw respectively. The ratio of the solar and atmospheric mass scales and neutrino mixing parameters are independent of these overall scales and are used in our definition of $\chi^2$ function instead of the individual neutrino masses. In addition, we assume $\Delta m^2_{atm}$ to be positive corresponding to the normal neutrino mass hierarchy. Parameters $r_R,r_L$ are fixed subsequent to minimization using the atmospheric scale.

\subsection{Numerical analysis: type-II seesaw}
We perform the minimization  in three physically different cases.\\

(A) In this case, we impose the conditions $\theta_{23}^{l}=\frac{\pi}{4}$ and $\theta_{13}^{l}=0$ using a $\mu$-$\tau$  symmetric $\tilde{U}_l$. As discussed in the earlier section,  this is done using parametrization in eq.(\ref{utildelpara}) with $s_2=c_2=\frac{1}{\sqrt{2}}$. The charged lepton mass matrix is then determined completely in terms of three masses and the angle  $\theta_1$.  Using the third of eq.(\ref{matrices}), the real and imaginary parts of $M_l$ can be used to determine respectively elements of   $H$ in terms of that of $F$ and elements of $G$ in terms of p, the charged lepton masses and  $\theta_1$. $f_{12}$ also gets determined in terms of these parameters because of the choice $h_{12}=0$. Thus $f_{22},f_{23},f_{11}, r,s,t,p,\theta_{1}$ are the only free parameters which determine the 11 remaining observables- six quark masses, three angles of the CKM matrix, the solar angle and the solar to atmospheric mass ratio. The $\chi^2$ we minimize is defined in terms of these observables using the values and errors given in Table~(\ref{tab:input}). The result of the minimization are shown in Tables(\ref{tab:2a},\ref{tab:2b}). One obtains a reasonably good fit to all observables except the down and bottom
quark  masses which are respectively $\sim 1.5$ and $\sim 2.5$ sigma away from their  respective mean values.  All other observables are reproduced correctly with very small pulls as seen in the table.\\

(B) In this case, we do not impose the maximality of $\theta_{23}^{l}$ but include $\sin^2\theta_{23}^{l}$  in the  $\chi^2$ to be minimized. $\sin^{2}\theta_{13}^{l}$ is not included in the definition of $\chi^2$ but we require it to be  $\leq 0.0155$ during the minimization. $r,s,t,p$ and elements of $H,F,G$  are now treated as free and the $\chi^2$ definition now includes the charged lepton masses as well. This results in significant improvement in the fit and one is able to fit 15 observables in terms of 13 parameters with $\chi^2=3.01$. The fit to the bottom and the down quark masses also improves. $\delta_{CKM}$ remains zero in this case.\\

(C) For this case, we depart from the exact $23$ symmetry and take $h_{22}$ different from $h_{33}$.  As already discussed, this breaks the generalized CP and results in a non-trivial CKM phase. Remarkably, a very small ($\sim 8\%$) breaking of the $23$ symmetry is able to generate a non-trivial CKM phase and $\chi^2_{min}=3.02$ with 2 degrees of freedom. Bottom quark mass is the only variable which deviates from its central value considerably. \\

\begin{table} [ht]
\begin{small}
\begin{math}
\begin{array}{|c|c|c|c|}
\hline
&A   &B   &C  \\
\text{\textbf{Quantity}}&\text{\textbf{Pull}} & \text{\textbf{Pull}} &  \text{\textbf{Pull}} \\
\hline
 m_d & -1.47532 	& 0.167255 	& 0.0620115 \\
 m_s & -0.8225		& 0.271662 	& -0.0545523 \\
 m_b & -2.52388		& 1.68787 	& 1.72811 \\
 m_u & 0.274609 	&-0.00446626  	& -0.00184452 \\
 m_c & -0.0125887 	& 0.000159604 	& 0.00744292 \\
 m_t & 0.00190476 	& 0.00901941 	& -0.0199522 \\
 m_e & 0 	& -0.000951761 	& 0.000179815 \\
 m_{\mu } & 0 	& 0.0176266 	& -0.000749102 \\
 m_{\tau } & 0 & -0.0192274 	& -0.017642 \\
 \frac{\Delta m^2_{sol}}{\Delta m^2_{atm}} & 0.679035 & -0.169337
& -0.0544521 \\
 \sin  \theta _{12}^q & -0.0116059 	& 0.00250491 	& -0.00412383 \\
 \sin  \theta _{23}^q &  0.155231 	& -0.00717926 	& 0.0402861 \\
 \sin  \theta _{13}^q & -0.0705362 	& 0.0000163982 	& 0.0163964 \\
 \sin ^2 \theta _{12}^l & 0.112082 	& -0.111783 	& -0.00578002 \\
 \sin ^2 \theta _{23}^l & 0 & 0.129873 	& -0.141465 \\
 \delta _{\text{CKM}} & - 		& - 		& -0.0364271 \\
\hline
 \chi ^2 & 9.80473 & 3.00957 & 3.02019\\
\hline
\hline
\text{\textbf{ }}&\text{\textbf{Predictions}} & \text{\textbf{Predictions}} &  \text{\textbf{Predictions}} \\
\hline
\sin ^2 \theta _{23}^l & 0.5 &- & - \\
\sin ^2 \theta _{13}^l & 0 &  0.000471537 &  0.000226908 \\
\delta _{\text{CKM}} & 0^{\circ} &  0^{\circ} & - \\
\delta _{\text{PMNS}} & 0^{\circ}  & 0^{\circ} & -12.759^{\circ}  \\
\alpha _1 & 180^{\circ} &  180^{\circ} & 169.80^{\circ}  \\
\alpha _2 & 0^{\circ} &  0^{\circ} & -9.445^{\circ}  \\
r_L & 2.8714\times10^{-10}  & 1.8183\times10^{-9} & 1.8645\times10^{-9}\\
\hline
\end{array}
\end{math}
\end{small}
\vspace{0.5cm}
\caption{Best fit solutions for fermion masses and  mixing obtained assuming the type-II seesaw dominance. Various observables
and their pulls obtained at the minimum are shown in three cases (A)-(C) defined in the text.}
\label{tab:2a}
\end{table}

Some of the observables are not part of the $\chi^2$ and their values get fixed at the minimum. These are shown as predictions in Table~(\ref{tab:2a}). These include the CP violating Dirac phase $\delta_{PMNS}$ and the Majorana phases $\alpha_{1,2}$ as defined in \cite{fnt}. These are trivial for the cases (A) and (B) due to the generalized CP invariance but one obtains non-zero values displayed in the Table in case (C).\\

\begin{table}[h]
\begin{small}
\begin{math}
\begin{array}{|c|c|c|c|}
\hline
 \text{\textbf{Parameters}} & A & B & C \\
\hline
 h_{11} & 1.95914 & -0.357916 & -0.818923 \\
 h_{22} & 466.637 & -649.2 &-701.354 \\
 h_{23} & 283.929 & -54.7552 & -32.0485 \\
 h_{33} & 466.637 & -649.2 & -598.783 \\
 f_{11} & -1.25174 & -0.176133 & -0.343138 \\
 f_{12} & 14.2058 & -2.16375 & -2.07269 \\
 f_{22} & -71.54 & 11.5434 & 11.2606 \\
 f_{23} & 95.5358 & -14.754 & -14.3836 \\
 g_{12} & -1.66646 & 3.54811 & 4.19817 \\
 g_{23} & -26.5205 & 614.356 & 617.845 \\
 r & 106.129 & 61.8507 & 61.1056 \\
 s & 114.802 & -109.87 & -121.664 \\
 t & -1.9006 & 67.0199 & 65.9824 \\
 p & 22.8456 & -0.989943 & -0.980791 \\
\hline
\end{array}
\end{math}\end{small}
\vspace{0.5cm}
\caption{Values of parameters of the fermionic mass matrices in eq.(\ref{matrices}) corresponding to the best fit solutions displayed in table(\ref{tab:2a}). The cases(A)-(C) are defined in the text}
\label{tab:2b}
\end{table}
Before going into the more detailed predictions, let us underline some important points connected with the above fits.
\begin{itemize}
\item Detailed fits to fermion masses have been considered in a number of papers with \cite{grimus1, grimus2} or without
\cite{bertolini,splitsusy} the addition of the 120-plet to the minimal $10+\overline{126}$ Higgs fields. The minimal model without the 120-plet  but not imposing reality of the coupling has more parameters than the present case but the fit is not better compared to here, {\it e.g.} the fit in pure type-II
case \cite{bertolini}  with 18 parameters and 15 data points gives a minimum $\chi^2$ around 14.5 \\
\item The  best fit solutions
in  cases (B) and (C) give $\theta_{23}^{l}$ close to maximal and $\theta_{13}^{l}$ close to zero as seen from Table~(\ref{tab:2a}). \\
\item We have fixed the overall scale  of neutrino mass $r_L$ in eq.(\ref{mnu} ) by using the atmospheric scale as normalization. The resulting values are
displayed in Table~(\ref{tab:2a}). In all three cases, $r_L$ comes close to $10^{-10}$.  $r_L$ is related to the mass of the left handed triplet residing in the $\overline{126}$ representation  and to other parameters in the superpotential. Detailed analysis \cite{detailed3,vissani2,bertolini,splitsusy}  has shown that one needs this triplet mass to be at an intermediate scale $\sim 10^{12}$ GeV if the overall neutrino mass scale is to be correctly reproduced.  The presence of such light  triplet conflicts with the gauge coupling unification. An additional $120$-plet does not qualitatively alter the situation. One possible solution suggested \cite{moh54} in the literature is to add a 54-plet of Higgs and allow $SO(10)$ to break first to $SU(5)$ leaving
a complete 15-plet of Higgs light at around $10^{12}$ GeV.  Other solution corresponds to having split supersymmetry breaking \cite{splitsusy}. Third possibility is to allow type-I seesaw dominance \cite{charan120,charan2}. We shall look at this in the next subsection in the present context.
\end{itemize}

We now turn to predictions in the neutrino sector. The firm predictions of the scheme can be obtained by checking the variation of $\chi^2$ with the values of various observables. As in \cite{bertolini,grimus2} we pin down a specific value  $p_0$ of an observable $P$ by adding a term $$\chi_p^2=\left(\frac{P-p_0}{0.01 p_0}\right)^2$$ to $\chi^2$
and then minimizing
$$\hat{\chi}^2\equiv \chi^2+\chi_P^2~.$$ If $P$ happens to be one of the observables used in defining $\chi^2$ then its contribution is removed from there.
 Artificially introduced small error  fixes the value $p_0$  for $P$ at the minimum of the  $\hat{\chi}^2$.  We then look at the variation of
\begin{equation} \label{chibar}
\bar{\chi}^2_{min}\equiv (\hat{\chi}^2 - \chi_p^2) |_{min}
\end{equation}
 with $p_0$.  The results are displayed in Figs.(1-3). \\

\begin{figure}[h]
 \centering
 \includegraphics[bb=0 0 317 203]{fig1.eps}

 \caption{Variation of $\bar{\chi}^2_{min}$ with $\sin^2\theta_{23}^{l}$ in Type-II seesaw.}
 \label{fig:1}
\end{figure}

\begin{figure}[ht]
 \centering
 \includegraphics[bb=0 0 320 208]{fig2.eps}

 \caption{Variation of $\bar{\chi}^2_{min}$ with $\sin^2\theta_{13}^{l}$ in Type-II seesaw.}
 \label{fig:2}
\end{figure}

\begin{figure}[ht]
 \centering
 \includegraphics[bb=0 0 315 208]{fig3.eps}

 \caption{Variation of $\bar{\chi}^2_{min}$ with $\sin\delta_{PMNS}$ in Type-II seesaw.}
 \label{fig:3}
\end{figure}

Fig.(\ref{fig:1}) shows the variation of $\bar{\chi}_{min}^2$ for various pinned downed values of $\sin^2\theta_{23}^{l}$. It is seen that the minimum occurs when $\sin^2\theta_{23}^{l}$ is fixed to around $~0.46$ rather than the value $~0.5$ obtained in the fits shown in Table~({\ref{tab:2a}). The variation of $\bar{\chi}_{min}^2$ is not drastic and all values in the range $0.3-0.7$ are allowed at 90$\% $CL. In comparison, variation of $\bar{\chi}_{min}^2$ with $\sin^2\theta_{13}^{l}$ shown in Fig.(\ref{fig:2}) is little more significant. There is a preference for values close to zero but values up to 0.008 cannot be ruled out at 90$\%$ confidence level. Fig.(\ref{fig:3}) shows the prediction for the PMNS phase in the leptonic mixing matrix.  Clear prediction is the negative values for the $\sin\delta_{PMNS}$. However, all negative values are allowed within the 90$\%$ confidence limit. \\

\subsection{Numerical analysis: type-I seesaw}
The structure of the neutrino mass matrix in the type-I case is qualitatively different compared to the type-II case. Unlike ${\cal M}_\nu^{II}$, ${\cal M}_\nu^I$ is not $\mu$-$\tau$  invariant in general. But it can be made approximately $\mu$-$\tau$  symmetric if either $120$ contribution or the $10+\overline{126}$
dominates in $M_D$, see eq.(\ref{matrices}). We discuss below fits in three qualitatively different cases as done for the type-II dominance.\\

(A) Here we impose the exact $\mu$-$\tau$  symmetry for ${\cal M}_\nu^{I}$ by hand, i.e. by choosing $q=0$ in $M_D$. As before, $U_l$ is also chosen $\mu$-$\tau$  symmetric. The input parameters and observables are the same as in the case (A) of type-II seesaw. The results of the fits are displayed in the first column of the Table~(\ref{tab:3a}). The total $\chi^2$ involves 11  observables and is determined by 8 parameters . The minimum value is $\sim 13$.  While most observables can be fitted nicely, the top quark mass  deviate by $3.6\sigma$ from the central value. Enforcing the exact $\mu$-$\tau$  symmetry does not appear to be a very good choice.\\

(B) In this case, we do not take $q=0$. ${\cal M}_\nu^I$ now satisfies  eq.(\ref{st1})   and is  not symmetric under $\mu$-$\tau$  symmetry.
    $\theta_{23}^{l}$ is not fixed to be maximal but is included in the definition of $\chi^2$. As in the earlier case (B), $\chi^2$ is defined by 15 observables and is determined in terms of 14 parameters. The CP violating phases are zero in this case and the CKM phase is therefore not included in $\chi^2$.  Experimental bound on $\theta_{13}^{l}$ shown in Table~(\ref{tab:input}) is imposed during  the minimization. One now gets excellent fit to all the included variables with $\chi^2_{min}=0.017$.\\

(C) In this  case  we introduce a small explicit $\mu$-$\tau$  symmetry breaking by assuming $h_{22}\not =h_{33}$ in eq.(\ref{matrices}). This allows CP violation. $\chi^2$ definition now includes all 16 observables and depends on 15 parameters. Bound on $\theta_{13}^{l}$ is imposed during minimization. Once again we get an excellent fit to all the observables with $\chi^2_{min}=0.18$. CP violating phases in the PMNS matrix come as predictions.\\
\begin{small}
\begin{table}[ht]
\noindent\(
\begin{array}{|c|c|c|c|}
\hline
 &A   &B   &C  \\
   \text{\textbf{Quantity}} & \text{\textbf{Pull}} & \text{\textbf{Pull}} &  \text{\textbf{Pull}} \\
\hline
 m_d  & -0.31569  & 0.0346007  & -0.379829 \\
 m_s  & 0.473034 & -0.0483779 & -0.0717277 \\
 m_b  & -0.108264 & -0.113763 & -0.114314 \\
 m_u & 0.50263 & 0.00026323 & 0.00344698 \\
 m_c & -0.151225 & -0.000606809 & -0.00938266 \\
 m_t & -3.60744 & -0.0193107 & 0.0122663 \\
 m_e & 0 & -4.874\times10^{-6} & 0.0000348858 \\
 m_{\mu } & 0 & 0.000480511 & 0.00078371 \\
 m_{\tau } & 0 & 0.00254153 & -0.0106065 \\
 \frac{\Delta m^2_{sol}}{\Delta m^2_{atm}}  & -0.00977627 &
-0.00192856 & 0.0125218 \\
 \sin  \theta _{12}^q &0.0218205 &  -0.00061312 & 0.00761817 \\
 \sin  \theta _{23}^q & 0.00289271 & 0.00129946 & 0.0284214 \\
 \sin  \theta _{13}^q & -0.238953 & -0.00823361 & 0.0366413 \\
 \sin ^2 \theta _{12}^l & -0.0129712 & 0.000590904 & -0.00265193 \\
 \sin ^2 \theta _{23}^l & 0 & -0.00544523 & 0.0289959 \\
 \delta _{\text{CKM}} & - & - & -0.120278 \\
\hline
 \chi ^2 & 13.6821 & 0.0169632 &0.180526\\
\hline
\hline
\text{\textbf{ }}&\text{\textbf{Predictions}} & \text{\textbf{Predictions}} &  \text{\textbf{Predictions}} \\
\hline
\sin ^2 \theta _{23}^l & 0.5 &- & - \\
 \sin ^2 \theta _{13}^l & 0  & 0.0135605 & 0.013505\\
 \delta _{\text{CKM}} & 0^{\circ} & 0^{\circ}  & -\\
 \delta _{\text{PMNS}} & 0^{\circ} & 0^{\circ} & -0.287748^{\circ} \\
 \alpha _1 & 180^{\circ} & 0^{\circ} & 2.156^{\circ}  \\
\alpha _2 & 0^{\circ} &  0^{\circ} & 2.616^{\circ}  \\
r_R & 4.1143\times10^{-11}  & 5.2329\times10^{-18} & 5.0093\times10^{-18}\\
\hline
\end{array}
\)
\vspace{0.5cm}
\caption{Best fit solutions for fermion masses and  mixing obtained assuming the type-I seesaw dominance. Various observables
and their pull obtained at the minimum are shown in three cases (A)-(C) defined in the text.}
\label{tab:3a}
\end{table}
\end{small}

Noteworthy features of the fits in (B) and (C) cases above are the following:
\begin{itemize}
\item The overall neutrino mass scale is determined to be around $r_R\sim 5\times 10^{-18}$.  $r_R$ is related to the ratio of the vev of the doublet and the RH triplet components in $\overline{126}$. The values of $r_R$ obtained here are similar to the values obtained in \cite{grimus2} which assume $\overline{126}$ RH triplet vev to be at the GUT scale. Thus one does not need an intermediate scale in order to fit the neutrino masses and one can obtain the gauge  coupling unification. This is consistent with observations in \cite{charan2,grimus1, grimus2}.\\
\item Maximality of $\theta_{23}^{l}$ is not imposed. But it is fixed to be very close to $\frac{\pi}{4}$ at the minimum in both the cases. The departure from the $\mu$-$\tau$  symmetry results in $\theta_{13}^{l}$ being non-zero and is fixed around the upper bound at the minimum as seen from the Table~(\ref{tab:2a}).\\
\item Although an explicit breaking of the $\mu$-$\tau$  symmetry is introduced in case (C), the amount of the breaking required in order to obtain the large CP violating phase is extremely  tiny,
\begin{equation}
\label{23breaking}
 \frac{h_{22}-h_{33}}{h_{22}+h_{33}}\sim 0.0045 ~.\end{equation}
\item The exact $\mu$-$\tau$  symmetry is known \cite{23as} to lead to the unwanted predictions $V_{ub}=V_{cb}=\sin^2\theta_{23}^{l}=0$.
Here we have two sources of breaking this symmetry, spontaneous through the vev of the 120-plet and explicit through
eq.(\ref{23breaking}) which allows one to reproduce the mixing angles correctly. In spite of the $\mu$-$\tau$  breaking, the final fermion
mass matrices display a remarkably good $\mu$-$\tau$  symmetry. We make this explicit by giving the quark and lepton mass matrices
in the case (C) above in Appendix (A). $M_{u,d,l}$ and ${\cal M}_\nu^I$ are seen to be nearly $\mu$-$\tau$  symmetric. There is an order of magnitude difference in the imaginary parts of the 12 and 13 elements of ${\cal M}_\nu^{I}$.  But these imaginary parts are much smaller than the corresponding $\mu$-$\tau$  symmetric real parts. The only source of the large $\mu$-$\tau$  breaking occurs as a difference between the 12 and 13 elements of the  Dirac neutrino mass matrix $M_D$. This  results from the spontaneous breakdown and rather large value of the parameter $q$.
\item As in \cite{grimus1,grimus2} we have concentrated here in obtaining generic fits to fermion masses rather than considering the entire parameter space of the theory given by the Yukawa couplings and basic parameters in the superpotential.  Parameters in fermion mass matrices are related to the strengths of the light Higgs components in various $SO(10)$ Higgs representations. These are determined by the fine tuning conditions and the full superpotential. Grimus and K\"{u}hb\"{o}ck \cite{grimus1} have laid down consistency constraints on these parameters following from  these
fine tuning relations  and from the requirement that the Yukawa couplings stay in the perturbative regime. We have checked that these conditions are satisfied by the parameters given in the Table~(\ref{tab:2b},\ref{tab:3b}).
\end{itemize}
\begin{small}
\begin{table}[ht]
\begin{math}
\begin{array}{|c|c|c|c|}
\hline
 \text{\textbf{Parameters}} & A & B & C \\
\hline
 h_{11} & 907.294 & 34.9749 & 35.0178 \\
 h_{22} & 119.541 & 554.305 & 556.777 \\
 h_{23} & -119.052 & 554.457 & 554.429 \\
 h_{33} & 119.541 & 554.305 & 551.775 \\
 f_{11} & 74.5214 & -15.7284 & -15.716 \\
 f_{12} & -2.82327 & 20.8852 & 20.8951 \\
 f_{22} & -74.237 & -29.4577 & -29.4636 \\
 f_{23} & 74.2104 & -29.5265 & -29.5305 \\
 g_{12} & 182.676 & 3.10944 & 2.79728 \\
 g_{23} & -4.5309 & -3.5854 & -3.21385 \\
 r & 1.24579 & 83.0642 & 83.7973 \\
 s & 0.266298 & 176.883 & 178.571 \\
 t & 0.844656 & 0.450978 & 1.0715 \\
 p & 2.35413 & 0.0117737 & 0.011244 \\
 q & 0 & 4042.93 & 4537.34\\
\hline
\end{array}\end{math}
\vspace{0.5cm}
\caption{Values of parameters of the fermionic mass matrices in eq.(\ref{matrices}) corresponding to the best fit solutions displayed in table(\ref{tab:3a}). The cases (A)-(C) are defined in the text}
\label{tab:3b}
\end{table}
\end{small}

We follow a similar procedure as in the type-II case to obtain possible predictions on the neutrino mixing variables. We pin down an observable P to a specific value $p_0$ by adding a contribution $\chi_P^2$  to $\chi^2$. We then determine the variation of $\bar{\chi}_{min}^2$ defined earlier with $p_0$. Variations of $\bar{\chi}_{min}^2$ obtained at different local
minima are shown as scattered plots in Fig.(4-6). \\

\begin{figure} [h]
 \centering
 \includegraphics[width=7cm,height=11cm,angle=270,bb=0 0 504 720]{fig4.ps}

\vspace{1cm}
\caption{Variation of $\bar{\chi}^2_{min}$ with $\sin^2\theta_{23}^{l}$ in Type-I seesaw.}
 \label{fig:4}
\end{figure}

\begin{figure}[h]
 \centering
 \includegraphics[width=7cm,height=11cm,angle=270,bb=0 0 504 720]{fig5.ps}

\vspace{1cm}
 \caption{Variation of $\bar{\chi}^2_{min}$ with $\sin^2\theta_{13}^{l}$ in Type-I seesaw.}
 \label{fig:5}
\end{figure}

\begin{figure}[h]
 \centering
 \includegraphics[width=7cm,height=11cm,angle=270,bb=0 0 504 720]{fig6.ps}

\vspace{1cm}
 \caption{Variation of $\bar{\chi}^2_{min}$ with $\sin\delta_{PMNS}$ in Type-I seesaw.}
 \label{fig:6}
\end{figure}

Clear predictions emerge unlike in the type-II case. As Fig.(\ref{fig:4}) shows, the $\sin^2\theta_{23}^{l}$ is preferentially restricted near $0.5$ and one obtains the limit $\sim 0.42-0.63$ at the 90$\%$ CL. Fig.(\ref{fig:5}) shows similar variation with respect to  $\sin^2\theta_{13}^{l}$. Here, the preferred values occur near the present limit and one obtains $\sin^2\theta_{13}^{l}>0.005$ at 90$\%$ CL. The predicted values for $\sin\delta_{PMNS}$  are displayed in Fig.(\ref{fig:6}). These are negative but very small.

All the above solutions are obtained through an extensive  search using  the random search algorithm in  Mathematica and
the MINUIT sub-routine in FORTRAN and we have shown in tables the solutions corresponding to the minimum $\chi^2$ that we obtained. Considering the non-linearity and complexity of the problem here, it is difficult to rule out the existence of still lower minima and predictions  may improve if they exist.

We end this section with a comment on the specific $\mu$-$\tau$  symmetry defined by $S$ used in eq.(\ref{s}). Definition of $S$ is basis-dependent.  One could change the original basis of the 16-plet through an arbitrary rotation $R$.  The structure of the Yukawa couplings and the resulting  fermionic mass matrices would look different in the new basis. The new Yukawa couplings would  still  satisfy the same equation as (\ref{yukawasymmetry}) but now with a rotated $S$: $S_R\equiv R^TSR$. Thus the $\mu$-$\tau$  symmetry may appear to look different with different choices of $R$. Specifically, if $R$ corresponds to a rotation by $\frac{\pi}{4}$ in the 23 plane then the $S_R$ assumes the form
\begin{equation} \label{sr} S_R=\left( \begin{array}{ccc} 1&0&0\\
                                                0&-1&0\\
                                                0&0&1 \\ \end{array} \right) ~.\end{equation}
This is nothing but the $Z_2$ symmetry imposed in \cite{grimus1} which is  thus equivalent to  the  generalized $\mu$-$\tau$  symmetry considered here if both remain unbroken. Difference arises after these symmetries are broken.
Ref. \cite{grimus1} uses complex vev to achieve $Z_2$ breaking as a result of which analogue of eqs.(\ref{sq}-\ref{st2}) do not hold in their case.
In our approach, we introduce small explicit breaking of   $\mu$-$\tau$   symmetry in $H$.   The model in \cite{grimus1} has 20 free parameters compared to 15  used here.

Note that the  explicit breaking of the $\mu$-$\tau$  symmetry is technically natural in the supersymmetric context.  Alternatively, one can achieve such breaking by introducing an additional 10-plet of the Higgs field which changes sign under the $\mu$-$\tau$  symmetry. Combined contributions of these two 10-plets would then give an explicitly $\mu$-$\tau$  non-invariant  $H$.
 \section{Summary}  Aim of this paper was to integrate the successful $\mu$-$\tau$ symmetry within the $SO(10)$ framework in order to obtain a constrained  picture of fermion masses and theoretical understanding of the largeness of the atmospheric mixing angle. The explicit model discussed here provides this integration rather well as shown by the  detailed fits to fermion masses presented in  Tables~({\ref {tab:2a},\ref{tab:3a}).
Interestingly, mass matrices obtained in the model under consideration display a generalized CP invariance if Yukawa couplings are taken to be $\mu$-$\tau$  symmetric. Small explicit breaking of this symmetry is sufficient to generate the required CP violating phase.
The best scenario is obtained in the type-I seesaw model with very tiny explicit $\mu$-$\tau$  symmetry breaking. This scenario is characterized by the predictions $\sin^2\theta_{23}^{l}\sim 0.42-0.63$, $\sin^2\theta_{13}^{l}>0.005$ and negligible CP violation in neutrino oscillations.
Final quark, the charged lepton and the light neutrino  mass matrices (collected in the Appendix)  respect  $\mu$-$\tau$  symmetry to a very good approximation indicating that this symmetry provides a good description of the entire fermion spectrum rather than being restricted to the neutrino sector alone.
\section{Acknowledgments}
We thank C. S. Aulakh for useful discussions.
\section{Appendix (A)}
We list here the fermion mass matrices following from eq.(\ref{matrices}) using the best fit values of the parameters given in Table~(\ref{tab:3b}) corresponding to the type-I seesaw mechanism. The neutrino mass matrix is expressed in eV units while all other  mass matrices are expressed in MeV units.
\begin{small}
\begin{equation}
M_d=\left(
\begin{array}{ccc}
 19.3018 & 20.8951+2.79728 i & 20.8951-2.79728 i \\
 20.8951-2.79728 i & 527.314 & 524.898-3.21385 i \\
 20.8951+2.79728 i & 524.898+3.21385 i & 522.311
\end{array}
\right) \end{equation}
\begin{equation}
M_u= \left(
\begin{array}{ccc}
 127.971 & 3731.25+2.99727 i & 3731.25-2.99727 i \\
 3731.25-2.99727 i & 41395.1 & 41186.3-3.44363 i \\
 3731.25+2.99727 i & 41186.3+3.44363 i & 40975.9
\end{array}
\right)\end{equation}
\begin{equation}
M_l=\left(
\begin{array}{ccc}
 82.1659 & -62.6852+0.0314526 i & -62.6852-0.0314526 i \\
 -62.6852-0.0314526 i & 645.168 & 643.02-0.0361365 i \\
 -62.6852+0.0314526 i & 643.02+0.0361365 i & 640.166
\end{array}
\right) \end{equation}
\begin{equation}
M_D=\left(
\begin{array}{ccc}
 11353.7 & -11193.7+12692.2 i & -11193.7-12692.2 i \\
 -11193.7-12692.2 i & 62440.4 & 62279.4-14582.3 i \\
 -11193.7+12692.2 i & 62279.4+14582.3 i & 62021.3
\end{array}
\right) \end{equation}
\begin{equation}
{\cal M}_\nu^{I}=\left(
\begin{array}{ccc}
 -0.0242264 & -0.0143681+0.0004742 i & -0.0143657-0.0000755678 i \\
 -0.0143681+0.0004742 i & -0.0128288+0.00678282 i & -0.0163109+0.000214216 i \\
 -0.0143657-0.0000755678 i & -0.0163109+0.000214216 i & -0.0127693-0.00629525 i
\end{array}
\right)
 \end{equation}
\end{small}

redpajama_set_name: RedPajamaArXiv


text:
Metropolitan Community College training city of Independence police recruits
By: Andres Gutierrez
INDEPENDENCE, Mo. — Like so many police departments in the metro area, the city of Independence is looking to hire more officers.
There's a new partnership that will help them train more recruits so they can get them on the streets sooner.
Shawn Kavadas, 22, has a track record of protecting and serving — first as a member of the U.S. Marine Corps, and soon as a police officer.
"That's what it's about, being able to help those people that need that help and being able to pull them out those tight spots that they're in," Kavadas said.
He saw it first-hand four years ago when an EF-3 tornado tore through his hometown of Oak Grove.
"The relationship they had and the way that they helped the public and the citizens in Oak Grove at that time, was really what got me super, super, interested into it," Kavadas said.
While in the Marines, Kavadas heard of Metropolitan Community College Blue River Public Safety Institute's Police Academy.
In a week, he'll be graduating with a job waiting for him at the Independence Police Department, who recently announced a new partnership with MCC.
"So, it automatically gets them in the field quicker based upon when an academy starts, with our starting in January," Craig McMein, MCC-Blue River Public Safety Institute Director said.
McMein said it speeds up the process of when new officers can start working in the field.
"That gets them graduated by May, and then in the field [and] into their three to four month process of becoming out of the FTO (field training officer) process and being on their own," he said.
According to Independence Police, there are currently 183 sworn officers and 230 would have the department fully staffed.
The department has the money to fill the vacancies, now they just need to the hire officers.
So, instead of just relying on the Regional Police Academy to train recruits, sending them to MCC gives IPD more flexibility.
At MCC's police academy, future officers receive basic training required by the state of Missouri along with some additional training.
"We have added a mental awareness course," McMein said. "It's very similar to the C.I.T. (crisis intervention training) which is what officers get traditionally in their first to two years of experience."
All of it, Kavadas says is a worthy experience.
"You understand that people are going through a tough time and stuff like that," Kavadas said. "That's what it's all about. It's not just, you know, going in arresting everyone you see. I think that's kind of the problem right now between some of the public and some of law enforcement — is that's what some people think that law enforcement is."
Independence police will have two more recruits starting at the MCC police academy in January.